A45349	----	A plain declaration of the vulgar new heavens flatform serving not onely fore this age, but also fore the future age of 100 years. Halley, Edmond, 1656-1742. 1679 Approx. 18 KB of XML-encoded text transcribed from 3 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2009-03 (EEBO-TCP Phase 1). A45349 Wing H452 ESTC R39228 18283100 ocm 18283100 107300 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A45349) Transcribed from: (Early English Books Online ; image set 107300) Images scanned from microfilm: (Early English books, 1641-1700 ; 1635:8) A plain declaration of the vulgar new heavens flatform serving not onely fore this age, but also fore the future age of 100 years. Halley, Edmond, 1656-1742. 4 p. s.n., [London? : 1679] Attributed by Wing to Halley. Date of publication suggested by Wing. Reproduction of original in the British Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. EEBO-TCP is a partnership between the Universities of Michigan and Oxford and the publisher ProQuest to create accurately transcribed and encoded texts based on the image sets published by ProQuest via their Early English Books Online (EEBO) database (http://eebo.chadwyck.com). The general aim of EEBO-TCP is to encode one copy (usually the first edition) of every monographic English-language title published between 1473 and 1700 available in EEBO. EEBO-TCP aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the Text Encoding Initiative (http://www.tei-c.org). The EEBO-TCP project was divided into two phases. The 25,363 texts created during Phase 1 of the project have been released into the public domain as of 1 January 2015. Anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. Users should be aware of the process of creating the TCP texts, and therefore of any assumptions that can be made about the data. Text selection was based on the New Cambridge Bibliography of English Literature (NCBEL). If an author (or for an anonymous work, the title) appears in NCBEL, then their works are eligible for inclusion. Selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. In general, first editions of a works in English were prioritized, although there are a number of works in other languages, notably Latin and Welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. Image sets were sent to external keying companies for transcription and basic encoding. Quality assurance was then carried out by editorial teams in Oxford and Michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet QA standards were returned to the keyers to be redone. After proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. Any remaining illegibles were encoded as <gap>s. Understanding these processes should make clear that, while the overall quality of TCP data is very good, some errors will remain and some readable characters will be marked as illegible. Users should bear in mind that in all likelihood such instances will never have been looked at by a TCP editor. The texts were encoded and linked to page images in accordance with level 4 of the TEI in Libraries guidelines. Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Astronomy -- Observations -- Early works to 1800. Sun -- Observations -- Early works to 1800. Dialing -- Early works to 1800. 2008-04 TCP Assigned for keying and markup 2008-06 SPi Global Keyed and coded from ProQuest page images 2008-07 Paul Schaffner Sampled and proofread 2008-07 Paul Schaffner Text and markup reviewed and edited 2008-09 pfs Batch review (QC) and XML conversion A plain DECLARATION of the vulgar new HEAVENS FLATFORM . Serving not onely fore this Age , but also fore the future Age of 100 years . HEre you are at first to knowe , that the motion of the Sun and the time do alwayes concur , and therefore is the one the measure of the other . Fore by the Time is to be knowne the place of the Sun , and again by the Suns place you may knowe the Time : therefore you must either knowe the Time or the place of the Sun , both of them you may easily find in the Heavens-Flatform , do but lay the dial A or B on the desired day of the yeare and see then what degree the dial doth touch upon the Sodiack , and you wil find the thing desired . I. EXEMPLE . How to knowe at anny time of the yeare in what Degree of the Sodiack the Sun is . ●y Exemple on the first day of May , lay the dial A upon the suid day , and see what degree the dial doth cut upon the Sodiack , you wil finde it to be the 12th of Taurus being the place of the Sun. II. EXEMPLE . How at anny time to knowe the rising and going under of the Sun. Suppose it be the 24th . of May , then you must lay the dial on the said day , and see where it cuts the Sodiac , there you must make upon the dial a signe of chalck or anny thing else that may easily be rubbed out , which signe demonstrates the Sun , turn then the dial first so long to the East-side of Heaven , til the said signe comes to touch the crombe Horizon , see then without upon what houre and minute the dial doth lye on the houre cirkle , you wil find the Suns rising at 4 a clock in the morning , and if you turn the said point to the West-side of Heaven upon the Horizon , then you wil see the dial to lye upon 8 a clock in the evening , being the going under of the Sun , then you wil also see that the Sun riseth then 36 degr . 30 minut . from the East to the Northward , and by consequence so manny Degrees and min. lesse from the West to the Northward . III. EXEMPLE . Hou you may see in the Night by the Starrs what time it is , Suppose you doe but see anny acquainted Starre to rise or stand in the S. N. E. or Westward , let it be the three Kings arising the first day of October , in the night , and that by it you would knove how late it is ; then you must lay the dial A on the said day , and the dial B over the 3 Kings , and give then a signe upon the dial B over the 3 Kings , then you must firmly turn both dials alike to the Eastward , til the said signe upon the dial B doth cut or touch the Horizon , and see then upon what houre and minute the dial A lieth , you 'l find it to be 11 a clock in the evening , beingh the right time of the night . I. PROBLEME . How you may upon every Poles higth find the riseing and going under of the Heavens lights after you have taken the Poles higth , and the declination or anny aquainted Starres . You must place one foot of the Compassis in the Centrum of the Heavens-Mirrour , upon the Dial A , and the other downewards , as far as the Degree of the Declination of the Sun or Starres ; with this opening of the Compassis you must place the one foot upon the edge-side of the dial A upon the complement of the Poles higth which you have taken ; and slide the dial A towards 6 a clock , ( or to the dial B which may be laid along by 6 a clock ( or the edge-side of the dial B. ) See then how in anny degrees the dial A lieth upon the houre-circkle from 6 a clock , which wil be the true breadth of the rising and going under of the Sun or Starres . I. EXEMPLE . Desiring to knowe on the 21th . of June , where the Sun riseth and goeth under , being beginning of Cancer , on the Poles heigth of 52 degrees . Then you must place one foot of the Compassis in the Centrum of the dial A , and the other downewards as far as on 23 degr . 30 min. being then the Declination of the Sun ; with this opening of the Compassis you must place one foot on the edge-side of the dial A upon the Complement of the Poles heigth , being 38 degr . then you must turn the dial A towards 6 a clock , til the other foot of the Compassis comes triangularly to touch the lin . of 6 a clock . See then how manny degrees the dial A lieth off from 6 a clock . You 'l find it to be very neare 40 degr . 20 min. And so far doth the Sun then rise from the E. to the N. upon each Northern breadth of 52 degr . and goeth likewise 40 degr . 20 min. under from the W. to the Northward . And if the Sun be in the first degr . of Capricornus , then it is just the same . II. EXEMPLE . Desiring to know on the Northern breadth of 50 degr . how manny degrees the Southern Ey of the Bul called ●●debaran riseth from the E. to the N. Fore the doing of it , you must place one foot of the Compassis in the Centrum , 〈◊〉 the dial A , and the other as far as the Declination of Aldebaran being 16 degrees , with this opening of the Compassis you must place one foot upon the complement of the Poles heigth of 40 degrees , on the dial A , then you mus● turn the said dial til the other foot of the Compassis comes triangularly to touch te line of 6 a clock . See then how manny degrees the dial A lieth off from 6 a clock , you 'l find verry neare 25 deg . 20. min. And so manny d●g . doth Aldebaran then rise from the E. to the N. it doth also go under 25 deg . 20 min. lesse from the W. to the N. III. EXEMPLE . Desiring to knowe on the Southern breadth of 20 degr . how many degrees the Spica Virginis riseth from the E. 〈◊〉 the S. and that , because the declination of Spica Virginis is Sourhly . You must place one foot of the Compassis in the Center of the Dial A , and the other downewards as far as on 9 degr . being the declination of Spica Virginis , with this opening you must place one foot of the Dial A upon the complement of the Poles higth of 70 degrees , then you must turn the Dial A from the E. to the S. till the other foot of the compassis comes triangularly to touch the East line or the line of 6 a clock . See then how manny degr . the Dial A lieth off from 6 a clock , you find verry neare 10 degr . and so far doth S. Virginis from the E. to the S. and goeth like wise so far unter from the W. to the S. II. PROBLEME . How to find the rising and going under of the Sun , or of anny acquainted Starrs , and that upon every Poles higth . Place one foot of the Compassis in the center of the dial B , and the other downeward , along by the Edge-side as far as on the degree of the Declination of the Sun or Starrs , with this opening of the Compassis you must place one foot on the edge-side of the dial B upon the Complement of the Poles heigth , add slide the Dial B from the E. to the N. or S. til the other foot comes triangularly to touch the line of 6 a clock . Then you must see o● what houre and min. the dial B lieth , which is the true time of the Suns rising , which you may also being to the going under . I. EXEMPLE . Desiring to knowe the rising of the Sun , on the N. breadth of 25 degr . being the 21th . of June , when the Suns Declination is Northly 23 degr . 32 min. you must place one foot of the Compassis in the Centrum of the dial B , and open the other foot douwnewards as far as on 23 degr . 32 min. with this opening of the Compassis you must place one foot on the edge-side of the dial B upon the Complement of the Poles hitgh of 38 degrees , sliding the dial B from the E. to the N. til the other foot of the Compassis comes triangulary to touch the line of 6 a clock . See then upon what houre and min. the dial B lieth on the houre circkle , you 'l find it to be in the morning at 5 a clock 15 min. being the right ti●● of the Suns rising , the same is in the evening at 8 a clock 15 min. the Suns going under . II. EXEMPLE . Desiring to knowe on the Southern breadth of 40 degr . being on the 21 of June , at what time the Sun doth there rise . Then you must place one foot of the Compassis in the Centrum of the dial B , and the other foot downewards , as far as on 23 deg . 30 min. being at the said time the Declination of the Sun , with this opening you must place one foot of the Compassis on the dial B upon the complement of the Poles higth of 50 degr . and turn the dial B from the E. to the N. til the other foot of the Compassis comes triangularly to touch the East line of 6 a clock , see then upon what houre and min. the dial B lieth , you 'l find neare enough in the morning 17 houres 30 min. being there the rising of the Sun , the same is its going under in the evening at 4 a clock 35 min. Nota. You must knowe that if you wil , use the Heavens Flatform over the South-side of the Equinoctial Line , then you must take the house contrary to that as they are signed upon the Heavens Mirrour , fore that which is over the North-line 4 a clock in the morning , the same is Southly from the line 8 a clock in the morning , and so is the rest accordingly . III. EXEMPLE . Desiring to knowe on the Northern breadth of 40 degrees , being the first of August , what time the great Dog Syrius shal rise . Lay the Dial B over Syrius and the Dial A upon the first of August , then you must place one foot of the compassis upon the Center of the Dial B , and open the other as far as on 16 degr . 15 min. being the declination of Syrius , with this opening you must place one foot the compassis on the Dial B , upon the complement of the Poles higth of degrees . Then you must firmly turn both Dials alike from the E. to the S. , till the other foot of the compassis comes triangularly to touch the East line of 6 a clock . See then upon what houre and minutes the Dial lieth , you 'l find neare enough 4 a clock 42 minutes . Fore to find its going under , you must firmly turn both dials alike from the West to the Southward til the other foot of the compassis comes triangularly to touch the West line of 6 a clock , see then upon what houre and min. the Dial A lieth , you 'l find 2 a clock 48 minutes . III PROBLEME . How to find at al set times the Declination of the Sun upon the Heavens mirrorr . Which is indeed verry proffitable for al Sea men , fore it serves not onely fore this present Age , but also fore the future Age of 100 years ; when al Books that are made fore that purposse shal be of no worth . Fore to find the Declination of the Sun upon the Heavens-Mirrour , you must knowe that the Suns place is there set according to the two Jears , before and after the Leape-yeare , and that especially upon the future Age , which doth almost differ a whole degree in the Sodiack with this present Age to the yeare 1700 , and in the Suns Declination in March and September about 24 minutes . So that al Tables of the Suns Declination which are reckened out with such a difficult calculation , shal after the yeare of 1700 be of no use or worth to a●ny Seaman ; because the yeare of 1700 must be a common yeare . Desiring then to knowe the Declination of the ●un upon some certain or set day in this present Age , then you must alwayes lay the dial A one daye farther then the set day , and in the second yeare after the Leap-yeare you must lay the dial upon the midst of the day , but being the third yeare after the Leape-yeare , then you must lay the dial A on the first fourth part , being in the Sodiack about 15 min. backward . But being the first yeare after the Leap-yeare , then you must lay the dial upon the third fourth part of the day , being verry neare 20 min. farther in the Sodiack , then in the third yeare . And when it is a Leap-yeare , then you must lay the dial A upon the beginning of the day , til to the 28 of February ; but being after the 28 of February , then you must al the yeare along lay the dial A upon the end of the day . And if you do truely understand and perform this , then you wil at al times knowe the Declination of the Sun so perfect and exactly , as the Navigation requires . This is the Head thing I have to say of my Heavens-Mirrour . I. EXEMPLE . Desiring to knowe the Suns Declination on the 30th . day of April 1691 or 95 being the third yeare after the Leap-yeare , then you must lay the dial A upon the first of May , to wit upon the fourth part of the parck of that day . See then where the Dial dath cut or touch the Sodiack , you find it to be verry neare the 10th . degr . 15 min. ( being at the ●ame time the true place of the Sun ) that is 40 degr . 15 min. of ♈ . Farther you must lay the Dial A over the 40 degr . 15 min. off from ♈ . , in the degrees of the Equinoctial or houre cirkle , then you must place one foot of the Compassis on the dial A upon the greatest Declination of the Sun , being 23 degrees 32 min. then you must open the other foot of the Compassis towards the Line of 6 a clock , to come triangularly with this opening of the compassis . Then you must place one foot of it in the Center of the Dial A , and turn the other downewards , and see where it falls , you find it to be verry neare 14 degrees 55 minutes , being at the said time the Suns Declination . II. EXEMPLE . Desiring to knowe the Suns Declination on the 30th . of April 1688 or 92. being the first yeare after the Leap-yeare . Then you must lay the dial A on the first of May , upon the utmost of the days parck , see then where the dial A doth cut the Sodiack , you find it to be verry neare the eleventh degree of Taurus , being the true place of the set time , that is 41 degrees of ♈ . Then you must further lay the dial A on 41 degrees of ♈ . as before , and place one foot of the Compassis on the dial A upon the greatest Declination of the Sun , being 23 degr . 32 min. then you must open the other foot of the Compassis , til it comes rect-angularly to touch the Line of 6 a clock , with this opening of the Compassis , you must place one foot of it in the Center of the dial A , and the other you must turn downewards , seeing upon what degree and minute it falls , you 'l find it to be verry neare 15 degr . and 10 min. being at the set time the true Declination of the Sun , differing litle or nothing with the wise and artificial calculation , do so at al other times , til to the yeare of 1700 , but after that time you must lay the dial upon the set day , considering that this use is principally ( as I told you ) practised and formed upon the future Age , where upon we shal also give some exemples , which also wil serve fore the better understanding of the former . III. EXEMPLE . Desiring to knowe the Suns declination on the 30th day of April 1706. being the second yeare after the Leape-yeare . Then you must at the same time lay the Dial upon the midle of the parck of the said day , and see where the Dial A doth toutch the Sodiack , you 'l find it to be verry neare the 9th degree and 30th minute of Taurus , being at the said time the true-place of the Sun , differing almost a whole degree with the Yeare of 1686 , fore the Sun is 39 degr . 30 minut . of ♈ Then you must further place the Dial A on 39 degrees 30 minutes of ♈ . upon the Dial , in the same manner as I told you before , and then you must place one foot of the Compassis on the Dial A upon the greatest declination of the Sun , being 23 degrees 32 min. , then you must open the other foot of the Compassis , till it comes triangularly to toutch the Line of 6 a clock : with this opening you must place one foot of Compassis in the Centrum of the Dial A , and the other downewards , see then on what degre and minute the foot stands , you 'l find it to be verry neare 14 degrees 42 minutes , which is on the said 30 day of April about noon , the declination of the Sun , differing also in the Suns declination with the Yeare of 1686 almost 18 min. So that by this exemple you may see that al Boocks and Tables ●●●●●ning this matter which are formerly made , wil altogether be in vain , and of no vallue , as soon as ever the Yeare of 1700 begins . IV. EXEMPLE . Desiring to knowe the Suns Declination in the yeare of 1710. whe the Sun is in the 18th . degr . of ♌ . Then you must lay the dial A upon the 18 degr . you 'l also see that the dial doth then lie on the eleventh day of August , about on the third fourth part of the parck of that day , being in the evening about 6 a clock . Then you must further lay the dial A upon the 42th . degree , from ♎ . to Cancer upon the houre circkle , being on the 18th . degree of ♌ , then you must place one foot of the Compassis on the dial A upon 23 degr . 32 min. as before , en then you must open the other foot , rectangularly unto the Line of 6 a clock , with this opening you must place one foot of the Compassis in the Centrum of the dial A , and then you must turn the other foot downewards , and see on what degree and minute it falls , you 'l find it to be verry neare 15 degr . 30 min. being at the said time the Declination of the Sun. FINIS . 
A16631	----	Learned: Tico Brahæ his astronomicall coniectur of the new and much admired [star] which appered in the year 1572 Astronomiae instauratae progymnasmata. Conclusio. English Brahe, Tycho, 1546-1601. 1632 Approx. 55 KB of XML-encoded text transcribed from 21 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2007-10 (EEBO-TCP Phase 1). A16631 STC 3538.5 ESTC S106182 22142171 ocm 22142171 25151 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A16631) Transcribed from: (Early English Books Online ; image set 25151) Images scanned from microfilm: (Early English books, 1475-1640 ; 734:15 or 1747:3) Learned: Tico Brahæ his astronomicall coniectur of the new and much admired [star] which appered in the year 1572 Astronomiae instauratae progymnasmata. Conclusio. English Brahe, Tycho, 1546-1601. V. V. S. [12], 26, [2] p., 1 leaf of plates : ill., port. By B.A. and T.F. for Michaell [Sparke] and Samuell Nealand, Printed at London : 1632. "Translated according to his originall astronomicall prediction"--P. 1. Engraved and illustrated t.p. on double leaf (with rebuses for the words "star" and "spark"). Translator's dedication signed: V.V.S. Translation of the conclusion of: Astronomiae instauratae progymnasmata. Signatures: [pi]³ A-D⁴ E². Colophon imprint: London : Printed by B.A. and T.F. for Michael Sparke, at the Blue Bible in Greene-Arbor, 1632. Reproductions of originals in the British Library (reel 734) and Peterborough Cathedral (reel 1747). Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. EEBO-TCP is a partnership between the Universities of Michigan and Oxford and the publisher ProQuest to create accurately transcribed and encoded texts based on the image sets published by ProQuest via their Early English Books Online (EEBO) database (http://eebo.chadwyck.com). The general aim of EEBO-TCP is to encode one copy (usually the first edition) of every monographic English-language title published between 1473 and 1700 available in EEBO. EEBO-TCP aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the Text Encoding Initiative (http://www.tei-c.org). The EEBO-TCP project was divided into two phases. The 25,363 texts created during Phase 1 of the project have been released into the public domain as of 1 January 2015. Anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. Users should be aware of the process of creating the TCP texts, and therefore of any assumptions that can be made about the data. Text selection was based on the New Cambridge Bibliography of English Literature (NCBEL). If an author (or for an anonymous work, the title) appears in NCBEL, then their works are eligible for inclusion. Selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. In general, first editions of a works in English were prioritized, although there are a number of works in other languages, notably Latin and Welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. Image sets were sent to external keying companies for transcription and basic encoding. Quality assurance was then carried out by editorial teams in Oxford and Michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet QA standards were returned to the keyers to be redone. After proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. Any remaining illegibles were encoded as <gap>s. Understanding these processes should make clear that, while the overall quality of TCP data is very good, some errors will remain and some readable characters will be marked as illegible. Users should bear in mind that in all likelihood such instances will never have been looked at by a TCP editor. The texts were encoded and linked to page images in accordance with level 4 of the TEI in Libraries guidelines. Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Stars, New. Astronomy -- Early works to 1800. 2006-05 TCP Assigned for keying and markup 2006-05 Apex CoVantage Keyed and coded from ProQuest page images 2006-09 Jonathan Blaney Sampled and proofread 2006-09 Jonathan Blaney Text and markup reviewed and edited 2007-02 pfs Batch review (QC) and XML conversion Learned Tico Brahae his Astronomicall Coniectur of the new and much Admired ⋆ Which Appered in the year 1572 Non Haberi Sed Esse portrait of Tycho Brahe EFFIGIES TYCHONIS BRAHE OTTONIDIS DAN●… DN̄IDE KNVDSTRVP ET ARCIS VRANIENBVRG IN INSVLA HELLISPONTI DANICI HVENNA ▪ Aetatis suae 40 Ann● DN̄I . 1580 diagram of new star found in Cassiopeia Printed at London by BA and T F for Michaell depiction of 'Spark (s)' and Samuell Nealand 1632 TO The High and Mighty Emperour , RVDOLPHVS the II. The Preface of the Heyres to TYCHO BRAHE . AN Orphant Worke ( most mighty Emperour ) we doe now present unto the view of your Sacred Maiesty , and doe dedicate it to your renowned name , being the Astronomicall exercises of our Parent of late approved memory , which by the leysurable studies of the Author are increased to so large a volume , that so they may be more commodious to Posterity , than the bare title of Exercises doth promise . For if ever HORACES Law were observed , it is in this Booke , which commeth forth after Three times nine yeares are expired . For when our Parent at the first , had onely purposed to treat in this Booke of that wonderfull new Starre , which was seene in the yeare of seventy two , and diligently to examine the opinions of others concerning the same , and had begun to print it at Vraniburg , ( all things going forward according to his owne desire ) it happened in the mean time , that he began to make a new and exact description of the course of the Sunne , and to assigne and point out the severall places of the fixed Starres , even to halfe a minute , according to their Latitude and Longitude , and lastly to search out the intricate motions of the Moone , all which at length be performed , and hate heere added to this Volume ; so that we may truly affirme , that this Booke in respect of the worthinesse of the matter , deserveth a more famous title , than to be called Astronomicall exercises . How difficult it was to performe , in respect that things lay deeply hidden , and therefore required the more labour to find out , having beene before in paine attempted by others in former ages , I leave to their consideration , that have any the least knowledge in Astronomy . Now this incomparable labour , which is above the envy of malevolent persons , seeing that our Parent in the last yeares of his life , together with his other studies , hath devoted to your sacred Maiestie , we therefore his surviving heyres , having Printed it after his decease , doe now most humbly offer it to your Highnesse : Which wee have done to the end , that we might give an account of his studies to the chiefe Monarch of the Christian world , and might take away all occasion of detraction from the envious , whom eyther their owne malitious natures have stirred up against him , or their evill dispositions and ignorance have so corrupted and blinded their iudgments , that they should thinke it all lost , which was bestowed on these royall Sciences ; which was very little , in respect of that which was necessary , and in regard of the honour and glory which redoundeth from thence . But in this Complaint , the most learned and excellent men of all ages , may beare us cōpany , who were envyed while they lived . Since no age hath wanted some who with ARISTIPPVS and EPICVRVS , have disdained Mathematicall learning as vaine and idle , and have hated the Professors thereof with more than barbarous malice . Neverthelesse , most mighty Emperor , we being held up and sustained by the authority of your Imperiall Maiesty , who are placed on the highest Pinacle of honour , have no reason to regard the envy of others . But have cause not to dispise such idle censures , and call to minde the examples of your Maiesties Ancestors ; namely , ALPHONSVS King of Aragon and Castell , ALBERTVS of Austria , FREDERICK , CHARLES the fifth , and the like , who were all favourers of this noble study , and did extend their munificence and bounty to the professors thereof . For ( that I may instance one of many ) who could be more magnificent than ALPHONSVS , who out of his owne praise-worthy and memorable bounty , did bestow upon the Tables of the Coelestiall motions , above fodre hundred thousand Ducats . Notwithstanding the Aristippusses of our time , doe thinke it might better have beene bestowed on sports and idle pleasures . But yet these men doe not consider that ALPHONSVS by this meanes hath gotten to himselfe everlasting glory , while the fame of other Kings is buried in obscurity . But yet how lame and defective are these costly Tables ! And not to be compared with the labours of our Parent . Because they never made any observation from the Heavens , but by comparing the observations of the ancients , and noting the Progresse of the Starres , they have pacthed up this bundle of Tables . This defect divers learned men have endeavoured to supply , and especially the most famous COPERNICVS , who yet was much hindred by wanting fit Instruments , so that hee could not attaine to his desire , although he hath more perfectly rectified the motions than any of his Predecessors . Wherefore with consident modesty we dare affirme , that our . Parene hath excelled all the Astronomers of former ages , in the accurate restoring of the motions , and that neyther any King or Prince except ALPHONSVS , hath bestowed so much upon Astronomy , so that he did not onely employ his whole Revenewes , arising from his Lands and offices which he held under the King of Denmarke , but also of his owne proper stocke , he layd out aboue a hundred thousand Thaleri . But when after the death of this praise-worthy King , the charges grew so great , that he was almost tyred therwith , being sent for out of his Country by your Maiesties command , he endeavored to make the Tables of the Coelestiall motions dedicated to RVDOLPHVS , to exceed the Tables of ALPHONSVS and COPERNICVS , that so your Maiesty ( having promised to helpe him in the charges thereof Astronomy might live by your Maiesties liberality , and your Maiesties name might live eternally by Astronomy . When having thus intended to doe , God tooke him away both in the middle of his age and Worke , to the great hinderance of Learning , and the losse of us his heyres . Now therefore , that we may benefit Posterity , whereof we ought to have especiall regard , we beseech your Maiesty by the holy rites of Vrania the heavenly Muse , that you would not in these trouble some times of Warre , neglect the opportunity of gaining eternall praise , by finishing those I ables , which albeit they require some charge , yet it is a worke that may well beseeme your Imperiall Maiesty . For as the Poet said , Sint Maejenates , non dierunt , Flacce , Marones . So we may say , that if we could have such Patrons as ALBERTVS , FREDERICK , and CHARLES the Great , there will not be wanting such , who will cheerefully undertake this labour , and finish that which remaineth . Whereby we dare promise , that your Maiestie by rectifying the study of Astronomy , shall gaine perpetuall fame and glory , which shall continue as long as the Starres endure . And so to conclude this our Dedication , wee commend your most sacred Maiesty to the Protection of Almighty God , and our selves as beeing the heyres of TYCHO BRAHE to your Maiesties protection . From Prague the day before the Calends of August , in the yeare of Christ , 1602. Your Majesties most obedient Servants The Heyres of TYCHO BRAHE . THE TRANSLATOVR TO THE READER . THis Books like to a Commet will appeare For to be gaz'd at in the following yeare , Which though * in time perhaps it come behind , Yet heere the Reader shall most amply find Renowned TYCHO's owne Prognostication Of the new Starre in this same new Translation . Whereof a Learned and most grave Divine Hath made some observations for this Time. But wee make TYCHO speake even word forword . Yet with that leave which * HORACE doth afford , Who thinkes it merits a Translators name To change the wordes , and yet the sence retaine , For this same Starre it selfe before did shroud Within the Latine , hid as in a Cloud , But now it is unvayl'd , and heere in sight It shineth forth againe , as cleere and bright As when it first appeared in the Skie , And was the object of each wandring Eye . * Astrologie is but the speech of Starres , Which doe fore-tell vs both of Peace and Warres , And by this Starre great TYCHO did intend To shew the World was comming to an end . It was no nine dayes wonder , but , shall last Vntill old * Cronos with his Sythe be past , And all thinges bee into a Chaos hurl'd , And that an end doe come upon the World : The thought whereof , should still a motive bee To make vs thinke on our Eternitie . Mens super astra valet . Interp : V. V. S. An Elogie made and written by IAMES the VI. King of Scots , in Commendation of TYCHO BRAHE his Workes , and worth . QVam temerè est ausus Phaëton , vel praestat Apollo Qui regit ignivomos Aethere anhelus equos . Plus TYCHO ; cuncta astra regis : tibi cedit Apollo Charus & Vraniae es hospes , alumnus , amor . IACOBVS REX . WHat Phaeton dar'd , was by Apollo done Who rul'd the fiery Horses of the Sunne . More Tycho doth ; hee rules the Starres above And is Vrania's Favorite , and Love. LEARNED Ticho Brahe his Propheticall Conclusion of the New and much admired Starre of the North , 1572. Translated according to his Originall Astronomicall Prediction . THat which I intended to deliver to posterity , concerning the New and admirable Starre which appeared in the yeare 1572. in the beginning of November , and neare unto the Constellation of Cassiopeae , I have now finished , and by Gods assistance ( from whom wee acknowledge all things to bee received ) brought it to a desired end . And I thinke that in those things which I have propounded and explained , no materiall point is omitted , having taken such paines in finding out the truth and clearing it from the pollutions of error , that all those who understand the Mathematickes , and will consider of things with a sincere judgment , shall find no occasion eyther to doubt or contradict . But yet to the end that those things which I purposed to divulge concerning this strange and wonderfull Starre , being written according to the Rules of Astronomy , and compared with other mens opinions , might attaine to the greater perfection ; I thought it meet in the former part of this Booke , to intreat of some things in generall , thereby to lay a ground-worke , not onely to the Explanation of this Starre , but also to the whole Science of Astronomy . Therefore in the first two Chapters , we have handled all matters appertaining to the exact rectifying and renewing of the course of the Sunne , & of the Moone his Sister , according to their own motions in the Heavens . After this , I have described no lesse than eight hundred of the fixed Starres , and have assigned them their severall places , according to their Longitude and Latitude . For by that amiable bright morning and evening Starre of Venus , wee have set forth by many approved trials , the limits of the fixed Starres , in respect of the Aequinoctiall points and have added to these all the other chiefe Starres , which doe appeare neare the Zodiacke : and so at last we discended to the rectification of the Starres belonging to the Constellation of Cassiopea , the knowledge whereof , we knew would availe much to our present purpose . And now albeit , the performance hereof in due manner required more study and labour , then the unexperienced can judge , who are ready to alledge that I have tooke more paines in searching out and declaring the nature of this Starre according to the fundamentall Rules of Astronomie , then indeed was necessary . Yet to the end , that some solid and certaine truth might bee knowne concerning this unusuall appearance , I thought fit to lay a sound and firme foundation to build upon , which could not be performed without the rectification of the course of the Sunne , and the fixed Starres . So that I doubt not , but I shall obtaine pardon of those which will consider things with an equall and favorable judgement ; But if I seeme to have heaped divers matters together , in more ample manner , than the proper attributes of this Starre did require , I have done it to that end , that so I might profit the whole Art of Astronomy , and might vindicate it from divers faults as occasion was offered ; for which I hope I shall rather deserve thankes , than the envie of those which are studious of this Sublime Science . And moreover this Starre , of which I purposed chiefly to intreat , albeit it were ascitious and chanceable ; yet because it shined forth most miraculously , and contrary to the Lawes of Nature , even in the highest Firmament , like to the other Naturall Starres , and stood there fixed and immoveable for the space of a whole yeare and more , it seemed fit that some diligent paines should be taken , in considering and unfolding the circumstances belonging thereunto . Besides , we shall alwayes gratefully acknowledge the labour of Hypparchus ; who with great diligence hath noted out unto us , the places of all the Starres which are seene in the Eight Sphaere , which hee hath left unto us by his Will , by the occasion onely of one new Starre which was seene in his time , although it is likely that it was not to be cōpared with that which appeared in our dayes , neither in magnitude , nor shining brightnesse , not yet in the duration , and continuance thereof . For albeit , it shined without a taile or any scattered beames , ( for then it had beene a Comet ) yet neverthelesse it might be likened to some of those appearances , which are beheld in the forme of obscure starres without any streaming beard at all , and so doe exercise some proper motion , as that did which was seene in the yeare 1585. But howsoever , it doth not repent us of our labour which we have bestowed , according as our time and leysure would permit us ; in asmuch as we trust that those things which we have delivered will be much availeable , not onely to point out the due place and position of this novell Starre , but also of all the other starres in the firmament , and likewise for the exact measuring of the course of the Planets . For if our Ancestors had used that diligence which they ought to have done , in decyphering the motions of the Sunne , and in rectifying the true places of the fixed starres according to their Longitude and Latitude , we might then have spared that labour , which we bestowed in the two first Chapters , and might presently have declared those things which concerned the Starre it selfe , whose description we had undertaken . Therefore , I thought it fit to prefixe some observations concerning the Sunne , the Moone , and the fixed starres ; because we shall have occasion to mention them hereafter . Now in the other part of this Booke , I have faithfully and accurately exhibited out of our owne observations , these things which properly appertaine to this new Starre , and after that I had declared these observations which could be gathered eyther by ocular animadversion , or by the extrinsecall adjuncts thereunto belonging , I have also set downe the forme and use of those Instruments , that so the certainty thereof might appeare . After this , I demonstrated the very place of the Starre , in respect of the Eclipticke , and Equator , and by working of the small divisions , at last reduc'd them into whole numbers . And so passing to the unfolding of the Paralax , I have cleerely prooved by divers invincible reasons that it had none at all , and that it was exalted , not onely above the Elementary Region , and the confines of the Moone , but farre beyond the Orbes of the Planets , even to the highest Spheare of the fixed starres , and so at last I have measured his true magnitude , and that I might the more truly compare it both to the Earth , and to the Celestial bodies , I have also prescribed the orders , and quantities of the Planets , and fixed starres , according as they are placed in the Heavens , though somewhat different from my Predecessors in the same kinde . Lastly , in the third Partition , I have compared the opinions of other men concerning this matter , and have examined them by the Touchstone of truth . And first , I have shewed their consents , who in this did agree with us , that this Starre did admit of no Particular ; and next their assertions , who did attribute unto it some diversitie of aspect , yet not so great as to make it sublunary . In the third place , I have searched out their suppositions , who have determined nothing Mathematically concerning it , but have brought in some absurd coniectures farre differing from the truth ; namely , that it was not a new Starre , but that it received an accidentall light from some of the old Starres , while some againe indeavored to thrust it out of the Heavens , and to place it nearer the Moone , have drawne it downe to the Aethereall Element . And so in the three last Chapters , I have weighed their opinions who have eyther come neere unto the truth , or wādred frō it concerning this new Starre , which I have done , that so the truth might appeare and shine forth , more clearely , and not by flattery to obtaine the favour of any one , by reciting their opinions , who have iudged somewhat neare the matter , nor yet to enveigh against those who have produced strange conceits very wide from the purpose ; but I have onely tooke care , that the truth might not be violated in any thing , but have endeavoured to suppresse their boasting endeavours , who eyther through ignorance , or wilfulnesse have opposed themselves against it , and have openly reiected and confuted their erronious opinions . For so the truth shall bee more easily brought to light , not onely by inducing probable conceits , but also by removing contrary and erronious supponsions . But when I consider with my selfe , how many vaine opinions there have beene concerning this Starre , both in respect of his scituation and distance from the Earth ( when yet they were more easie to be found out , in regard of the immobilitie of the Starre , and in that it appeared alwayes aboue the Horizon , than in Commets which are alotted some motion ) I doe not so much wonder at it , seeing not onely the motions of the Starres are not hitherto declared in such an accurate manner as is fitting ; but also , that there doe so many questions and controversies arise in Philosophy and Divinity . For if that which plainely appeared to the sight , and might easily be measured and demonstrated Geometrically by fit Instruments , was yet subject to so great variety and difference of Iudgements : how much more those things which are not discernable by the senses , nor subject to humaine industry , but are so full of doubts and perplexities , that truth ( which is alwayes but one , as the center in the Circie ) is very hardly or never found out . Hence arises so great a confusion of opinions in every Science , and divers severall questions are discussed , not onely in naturall Philosophy , but also in Divine and Morall matters , that it is hard to find out , and firmely to establish any certainty , which may bee equall to Geometricall demonstrations , or which cannot bee contradicted . Such are the blind apprehension of mans nature , and in such a darknesse of error doe we spend our dayes heere on Earth . And therefore moved by these considerations , I have illustrated and discovered whatsoever I thought did belong to the consideration of the unusuall Starre , both by declaring the true nature thereof , as also by detecting the errours of divers and sundry Writers : Now there remaineth yet two other questions to bee unfolded , whereof the one is Physicall , concerning the matter and procreation of this Starre ; the other Astrologicall , concerning the effects and signification thereof , whereof I purposed not to intreat seriously , or by way of iudiciall divination to set downe any certainty in this present Worke , in as much as they are not subiect to the senses nor to any Geometriall demonstration , but are onely grounded upon probable coniectures , and not on Mathematicall Principles : Yet neverthelesse , because many doe desire a Physicall and Prognosticall explanation of this Starre , and are very desirous to see them set forth , especially , the latter : therefore for the satisfaction of their minds , I will declare my opinion concerning this Starre , but yet with this caution ; that those things which I shall disclose are not to be compared in respect of their indubitable certainty , with that which I have propounded demonstratively in the former part of my Booke ; for these Prognostick matters are grounded onely upon conjecturall probabilitie . Therefore I will not insist long upon them , but speake of them as briefely as I may ; and for this purpose I have reserved them to be handled here in the conclusion of my whole Booke , that so I might the more sparingly intreat of them . Therefore , concerning the matter of this adventitious Starre , that I may first give you my opinion , I thinke it was Coelestiall , not differing from the matter of the other Starres , but yet in this it did admit of some diversitie , that it was not exalted to such a perfection , nor solid composition of the parts , as appeareth in the everlasting and continuing Starres : and therefore it had no perpetuall duration , as these have , but was subiect in processe of time to dissolution ; forasmuch as this Starre could not consist of any elementary matter , sith that cannot be carried into the highest part of the ayre , nor can obtaine there any firme place of abiding . Besides , this Starre did at the first in his magnitude exceed the whole Globe of the Earth , and was three hundred times bigger then the whole circumference thereof , and therefore what sublunary matter could be sufficient to the conformation of it ? But some may say , how or whence could it bee framed of Coelestiall matter ; I answere that the Heavens did afford it themselves , in like manner as the Earth the Sea , and the Ayre ; if at any time they exhibite some strange sight , doe produce it out of their owne proper substance . For although the Heaven it selfe be thinne and pervious , giving way to the motion of the Starres without any hinderance , yet it is not altogether incorporeall , for then it should be infinite and without place . Therefore the very matter of Heaven , though it be subtile , and possible to the courses of the Planets , yet being compacted and condens●ted into one Globe , and being illustrated by the light of the Sunne , might give forme and fashion to this Starre . Which because it had not his beginning from the common order of nature , therefore it could not have a continuall duration equall to the rest ; as in like manner , new and monstrous generations arising and compounded out of the Elements cannot long endure . And albeit the large vastnesse of the Coelestiall world may afford sufficient matter for the conformation of any adventitious Starre , yet there is no where more plenty then neere unto Vialactea or the Milkie way , which I suppose to be a certaine heavenly substance not differing from the matter of the other Starres , but diffus'd , and spread abroad , yet not distinctly conglobated in one body , as the Starres are : and hence I conjecture it came to passe , that this Starre appeared in the edge of the milkie way , and had the same substance as the Galaxia hath . Besides , there is discerned a certain marke or scarre as it were in that part of the Galaxia , wherein this Starre was seated , as in a cleare night when the milkie way is not vailed with cloudes we may easily perceive . Which marke or scarre I never saw before this Starre did arise , neither did I ever reade of it . But howsoever , the substance of the milkie Zone is able to supply matter for the framing of this Starre , which because it had not attained so excellent a consummation , and solid existence , as the genuine and naturall Starres have , therefore it was subiect to dissolution and dissipation , eyther by its owne nature , or by the multiplicitie of the beames of the Sunne and other Starres . Neither is Aristotle here to be allowed of , who disapproving of the opinions of others , doth himselfe bring in no lesse absurdities , while hee maketh the Galaxia to be a certaine sublunary concretion attracted and formed out of the Starres which are above it ; so that it becommeth a Meteor , in the highest part of the Ayre , not unlike to the Comets , which he ( grounding one absurdity upon another ) supposeth to be generated there . For if it were so , the Milkie way would not have continued in the same forme , place , and Magnitude , as it hath done from the beginning of the world . And besides , other Starres would attaine unto the like Luminous concretion ; And moreover , this Galaxia of Aristotle , would then admit of a Paralax , and according to the opticke consideration , by the shining of the fixed Starres through it , it would beget a strange refraction , differing from that which is occasion'd by the vapors that are seene about the Horizon , which seldome riseth to the twentieth degree of Altitude , when this proceeding from the Via lactea would reach to the greatest height . All which , Aristotle rather guested at , grounding it upon coniecture rather than on the doctrine of the Mathematicks & opticks ; and therefore it is no marvell , if he hath endeavoured , to banish those seldome appearing Cornets out of the heaven , and to equall them to sublunary Meteors , whereby he hath thrust downe the Galaxi● beneath the Moone , and hath made it participant of a sublunary nature . Hence it is , that Aristotle and other Philosophers , have ioyned the description and explication of the Galaxia , together with the Commets , because they knew not , the affinity which is betweene , having onely learned by experience , or by the relation of ancient writers , that these beamy Starrs have their originall and beginning neere to the Milkie way . Neither can it be a Solaecisine , in that I affirme , that this new Starre was framed of Coelestiall matter , being the same whereof the Galaxia and other Starres doe consist , yet not so well compacted ; when we may discerne the like productions in the Earth , which bringeth forth mettals and precious stones . Yet though all mettals and Iems have one and the same matter , yet all are not concocted and brought to the same subtility , and maturity by the powerfull working of nature ; hence it is , that some are sooner corrupted ; others very hardly ; so that pure gold and silver , in respect of the homogemly and perfection of their parts , are able to resist the violence of the fire , without any losse or detriment at all , when more imperfect mettals , as Lead and Tinne , are soone calcinated into ashes , or else vanish into smoake ; In like manner , this Starre might bee framed of Coelestiall marter , although it had not attained to such a perfect existence as the naturall Starres ; and therefore , it could not with them be able to endure the beames of the Sunne and Starres , and the motion of the Heaven , and with all it was subiect to a successiue alteration , untill at last it was quite dissolu'd . But why this Starre although it had the same matter with the Galaxia , which is not obnoxious to corruption , yet was in time extinct , I wil declare some reasons hereafter . Wherfore having spoken sufficiently of the first part , namely of the Physicall nature of this Starre , I will now discend to give you my coniecturall opinion , concerning the signification of this Starre as it did betoken some thing that was to come . I know there were some ( otherwise learned men ) who did hold , that these new appearances which are sometimes seene in the Heavens , have no effectuall operation , or signification , being ( it may be ) led unto that opinion , because those things which Astrologers foretell concerning the effects of such adventitious Starres , are full of vanity , and doe seldome come to passe , or prove true in the end . Yet notwithstanding in my opinion , we should not take away all power of Divination , from such admirable and strange appearances , because Astrologers cannot by evident demonstration presage of their events . But rather , such are to be taxed , who rashly deliver their uncertaine conjectures ; and the weaknesse of mans judgment , which is ready to wander from the truth is to be pardoned , but we ought not to imagine that God and Nature doth vainely mocke us , with such new formed bodies , which doe presage nothing to the world . Yet truly the Prognostication and fore-knowledge of and concerning such strange appearances in the heavens , is very hard to finde out , and doth oftentimes delude the understanding of man , seeing we doe not certainly know the influences of the other Starres . Whence it may come to passe , that Astrology , which entreateth of the effects of the Starres , may deliver that which is true , as well as Astronomy , which onely declareth their motions and appearances , since the cause cannot want an effect , whether it is to be knowne or not . Neither hath humaine industry beene able to search out the motions of the Starres , although they are most certain . So that it is lesse marvaile , that their effects which are not obvious to the sense should lye so deeply hidden , and oftentimes deceive mens judgements . For if there were ever any difficulty in discerning , and foretelling the significations of the Starres , truly this new Starre , which appeared in our age for a whole yeare together , doth require much labour and diligence , in revealing the Portent thereof , and in shewing what it might signifie . Especially , since there were never any apparitions like unto it , from whence any knowledge might be gathered by the likenesse of events , for Arts of divination are not grounded on any Principles , but upon experimentall observation . But no apparition like this was ever testified by any monument of antiquity , to have beene seene and beheld of men , except that which Pliny mentioneth to have beene observed by Hypparchus , which in regard it had a proper motion ( as wee may gather from the words of Pliny ) cannot be compared with this new Star , which alwayes stood fixed in one place . Yet it is probable , that as the Starre which Hypparchus beheld , did fore-signifie the declining of the Graecian Monarchy , and the enlarging of the Roman Empire . So farre , that the whole world should be in subjection to this one City ; so likewise , some strange alteration in the publike government of Estates and Commmon-weales , shall ensue in the following yeares . For , as this was a rare and wonderfull Starre , shining forth in the heavens unexpectedly , so it is likely and probable , that it will produce strange , great , and wonderfull effects , but what they shall be in particular , I thinke no mortall man is able to guesse , being as farre distant from our knowledge , as the rising of this Starre was before it did appeare . Yet the forme of it , when it shewed it selfe from the beginning , shining forth with a joviall , cleere , and bright lustre , doth seeme to fore-shew a prosperous and pe●c●able estate of humane affaires ; but yet the Martiall fiery glistering thereof , doth foresignifie that some violence and trouble shall be intermingled with it . And besides , by this joviall figure , it seemeth to portend , a great alteration , if not an utter subversiō of Religion ; so that those devices which by outward shewes and Pharisaicall Hypocrisie , have long time bewitched ignorant people , shall now come to their full point and end : and even as this new false Starre shined foorth at the beginning , with a cleare and amiable aspect , but yet at last did change in colour , and lessen in proportion , untill at length it vanished quite away : So those false Planets , which by an outward plausible appearance , doe seduce and leade men from the light of the truth , shall be quite extinguished . Also , it is worthy of consideration , that albeit this Starre was so neare to the Semicircle of the Colure , that his beames almost touched it , yet his whole body was seated toward the Vernall Quarter , and in respect of the Poles of the world , in the middle of the first degree of Aries , which may seeme to declare , that some great Light is now at hand , which shall enlighten and by degrees expell the former darknesse ; as the Sunne having passed the Vernall poynt of the Aequinoctiall , doth make the day longer than the night , which before had the advantage of the day . And as this Starre appeared in the highest heavens , to the view of the whole world , so it is credible , that there shall happen a great Catastrophe and universall change throughout all the chiefe Nations of the Earth , especially those which are scituated Northward from the Aequinoctiall . Moreover , forasmuch as this Starre was placed in the eight Spheare , above the Orbes of the Planets , it seemeth that the predictions issuing from it , do not only concerne one peculiar tract of Land , but all the Nations of the world ; and therefore it will bee the longer before the effects will be declared by succeeding events . Which , as they shall not begin , untill some yeares after the apparition , so they shall continue for a long time afterward . And if wee may take leave to conjecture by Astrologicall computation of time , concerning the first beginning of that which is portended , we may guesse it will be nine yeares after the great conjunction , whereof this Starre was the Prodromus or fore-runner . If therefore wee frame our Astrologicall direction by the place of this Cōjunction which was in the one and twentieth degree of Aquarius , the events of this Starre shall begin to shew themselves , nine yeares after this Conjunction . And when this is finished , in the yeare of Christ 1583. and in the latter end of the Moneth of Aprill , the confirmation and end of this Equinoctiall progression to the place of the new Starre , will fall out in the yeare 1592. when the third Septinary of yeares after the first appearing of the Starre shall be accomplished . And those Noble Heroes which shall happen to be borne at the first rising of this Starre , being ordained to be the Authors and atchievers of those great mutations , shall about that time come to full ripenesse of age , that they may be fit and able for the performance of such great enterprises , and for the reducing of these Predictions into act . And in the fourth Septenary of yeares , when they have attained to their chiefe strength , they shall make the truth of these conjectures appeare most plainly ▪ But if we take our direction by comparing the place of this Conjunction from the Zodiacke , or the degrees of the Eclipticke , unto the place of this new Starre , then it is likely that the force and influence of this Starre , will chiefly shew it selfe in the yeare of our Lord 1632. for all the significations of this Star doe depend on the Trigonall revolution and tansmutation of the Planets . And therefore if this rbee the seventh revolution of the Planets , the first whereof was in the dayes of Enoch , the second in Noahs time , and at the Vniversall Deluge , the third in the dayes of Moses , when the people were freed from the Egyptian servitude , the fourth in the dayes of the Kings of Israel , the fift in the time of Christs Incarnation , when the Roman Empire was at the highest , and the sixt in the dayes of Charles the Great , when the Empire was translated to the Germanes , this last and seventh , is as it were the Sabbath to all the rest , and doth foreshew something of greater consequence than all the former , wherein it is worthy of observation , that all the trigonall revolutions , as the first , third , and fift , were very profitable and advantagious to the world ; and so it is not unlikely that this seventh revolution being an unequall number , doth point out and fore-signifie the happy estate of things which is to come . Neyther doth this conjecture differ from the Prophesies of wise men which were illuminated with divine knowledge , who have foretold , that before the universall consummation & end of all things , there shall be a peaceable and quiet age , wherein the divers formes of Religions and politike government , shall be changed and be made agreeable and conformable to the will of God. Which assertion we may collect out of the Prophets , who did fore-tell , that at last there should be a golden age ; In which they shall breake their swords into Plough-shares , and their speares into pruning-hookes , Nation shall not life up a sword against Nation , neither shall they learne Warre any more : But they shall sit every man vnder his Vine , and vnder his Fig-tree , and none shall make them afraid : As the Prophet Micah hath it . Chap. 4. And Isaiah , Chap. 11. doth foretell of it , in this manner : The Woolfe also shall dwell with the Lambe , and the Leopard shall lye downe with the Kid , and the Calfe and the young Lyon , and the Fatling together , and a little Childe shall leade them , and the Cow and the Beare shall feed ; their young ones shall lye downe together : and the Lyon shall eate straw like an Oxe . And the sucking child shall play on the hole of the Aspe , and the weaned child shall put his hand on the Cockatrice Den , they shall not hurt nor destroy in all my holy mountaine : for the Earth shall be full of the knowledge of the Lord , as the waters cover the Sea. Also , in the sixty Chapter of Isaiah , speaking of the mysticall Hierusalem , and perfect state of Christianity , he saith , For brasse I will bring gold , and for yron I will bring silver , and for wood brasse , and for stones yron ▪ I will also make thy Officers peace , and thine exactor ▪ Righteousnesse : Violence shall no more be heard in thy land , wasting nor destruction within thy borders , but thou shalt call thy walls Salvation , and thy gates praise ; & at length he concluded thus ; for , I the Lord will hasten it in his time . Besides , many other places are found both in the Prophets , and the Revelation , which doe promise this unexpected happinesse . Therefore that this Prophesie may be fulfilled , which was delivered by divine inspiration , it must needs come to passe , even before the end and consummation of the world . But seeing the event of these things shall come to passe in the new revolution of the Planets , before which this Starre appeared , some doe suppose , that the light of Religion doth now shine out cleerely having over come the darknes of Error ; but if it were so , whence are then those Controversies , and varieties of opinions which are defended by Learned men ; insomuch that the warre of Pennes , is more dangerous than that of Swords . Truely , it is rather to bee feared , least wee take this dawning and breake of day , to be the cleere noone-light . Therefore , I suppose that this Starre doth signifie , that there shall be a new change both in Religion , and the estate of humaine affaires . Ventum ad supremum est patientur summā ruinam , qui Deus in Coelis regit & reget omnia terris . That is to say , Wee are come now to the highest perfection , the power of Antichrist and the Pope shall decay and bee brought to ruine , and GOD who ruleth in Heaven shall rule all thinges on Earth . But if any doe obiect , that the end of the world is at hand , and that therefore there will not be sufficient time to bring about a new Change. I answere , that Saint Paul doth assure us , that the Iewes shall be engraffed into the Church , before the finall consummation of the world , which ( by humaine coniecture ) must needs require some time before , they being scattered over the whole face of the Earth , shall be gathered into one Nation . Yet I thinke it not unnecessary to admonish and stirre up the mindes of men to thinke upon the end of the world , that so they may remember the Eternity which shall follow after it . But yet it is impossible to limit and set forth a certaine time for the consummation of the world , which only dependeth upon the good-will and pleasure of God , and is not reuealed to the Angels , and therfore cānot be knowne by any humain prescience ▪ But if some doe suppose , that the tract of Hand to which this Starre was verticall , is ominous aboue the rest , as if from thence the occasion and author of so great mutations are to bee expected , we must then chuse out those parts of the Earth , which had the new Starre in their Meridian at the time of the new Moone next following , which fel out , accounting the time by our Meridian , upon the fifteenth of November , seaven houres , thirteene minutes ⅔ . in the afternoone ; to which if we apply , the latitude or distance from the Equinoctiall agreeable to the declination of the Starre which was in 61. ¾ . so that the place on the Earth answerable thereunto , must needs be Russia or Moschovia , especially that part thereof which is ioyned unto Finland ; for in that tract of Earth this new Starre in the new Moone following , was in their Zenith , and iust over their heads , where it stood equally distant from the Horizon , and with a right angled aspect beheld this Countrey . Therefore , if this position of the Starre doe point out the place of the Earth , from whence these events shall arise , Moschovia seemes especially to be designed , before any other Regions , which are scituated towards the North , to whom this new Starre was every day Verticall . Whither therefore , the first occasions of so great disturbances and mutations shall arise from hence which afterward shall be sowed and dispersed into other parts of the world , I leave it to be decided by others . Truely ▪ that Gogus , whereof mention is made in the eight and thirtieth Chapter of Ezekiel , and to whom Esay Chapter 17. 56. and Micha Chap. 5. doe allude , and with whom Magog is named in the Revelation , Chap. 20. may be rightly understood of the Msochovite , as Castellio hath interpreted it in the 38. and 39. of Ezekiel ; That Gog should be the leader of the Moscovites and Iberians , because the old translation reades it , that he should be the Prince of Mosoch ; and Thubal . For seeing the Hebrewes reade it Mesech , and the Greekes and Latine interpreters doe reade it Mosoch , it is probable that the Moschovites are signified heereby ; or else by this name , the whole Northerne tract of Earth is included . Therefore it is very likely , that Moschovia is principally denoted by this Starre , and Gogus the leader of the Moschovites , of whom it is foretold in the Prophets and the Revelation , who having made great slaughters in Europe , hee at last with his whole army shall be overthrowne , and so the Earth shall be disburthened of her wicked inhabitants . For it is probable , that there must be a great clensing and extirpation of all Earthly impurities , before that peaceable and happie age ( whereof the Prophets have spoken ) shall come , but to shew the particular manner thereof is above humaine knowledge ; wee purpose onely to make some coniectures in generall , for the event will shew it selfe . Moreover , because a certaine ancient Prophesie of Sibylla Tiburtina , which was found in the yeare 1520. in Switzerland , engraven in a Marble stone in old latine Characters , which was discovered by the force of the water washing away the earth , may be fitly applyed to this Starre , I will heere insert it and ioyne it to our coniectures , for it is worthy of observation , beeing recited by Cornelius Gemma in his Treatise of Supernaturall Apparitions , in these words . The Sybils Prophesie . A Starre shall arise in Europe over the Iberians , at the great house of the North , whose beames shall vnexpectly inlighten the whole World. And this shall bee in a most desired time , when all Nations shall lay by their weapons and imbrace Peace ; but they shall contend during the Interregnum , and strive to obtaine the reynes of Government ; yet the ancient House shall prevaile , and shall be prosperous in Warre , vntill contrary fates shall encounter one with another . For in the same time after this Starre is gone , another great Light shall shine foorth with Martiall sparkling beames , and shall inlarge his Empire even to the bounds of the Antipodes . After this there shall bee bloudy Comets , and flashings of fire seene in the Heavens , so that there shall be no safety any where . The firmament of Heaven shall bee dissolved , the Planets shall forget their courses , and the Spheares shall iustle one another , the fixed Starres shall out-goe the Planets . The Heavens shall bee leveld with the Seas , and after these thinges come to passe , there shall be continuall Night , destruction , ruine , condemnation and eternall darknesse . G. S. G. There were divers expositions of this Prophesie , at that time when it was first found out , some interpreting it of CHARLES the Fift , others drew the meaning of it to PHILIP King of Spaine , and some thought that the King of France was meant thereby ; but I thinke , that it doth rather point out those Iberi , which inhabite Northward toward Moschovia . So that this Oracle of Sibilla Tiburtina , did not denote the Spaniards , but those Iberians , which are neare unto the Moschovites ; especially , when she useth these words ; Supra Iberos ad magnam Septentrionis domum : Over the Iberi at the great house of the North. And truly Moschovia , Scythia , and Tartaria , doe make a great part of Europe , so that it may well be called the great house of the North. And therefore , seeing we have formerly shewed , that this unusuall Starre did cast his perpendicular beames and influence on the Country of Moschovia , it is not to be doubted but that this Starre , together with that tract of Land , doth agree with the Sybilline Oracle . But concerning the other matters which are mentioned , I will not touch upon them in particular , but leave them to other mens judgments . Moreover , some of the other Sybils , have prophesied concerning Gog and Magog , who should come in the latter times , and have expresly foretold of the rising of this Starre , and among the rest Sybilla Babilonica , thus saith : Then a great Signe , shall from above be given , And a bright Starre shall then arise in Heaven : Which shall like to a glistring Crowne appeare , And many dayes it shall stand fixed there . What can be more evident , concerning this cleere Starre which was beheld in our time , for that was more bright and shining than any of the rest , and was round in forme like unto a Crowne , having no beames right shooting from it as Comets have , besides it continued for a whole yeare and kept his Station in the Firmament with the other Starres . And therefore , this Sybilline prediction , doth fitly describe the forme , light , scituation , duration , and consumption of this Starre , as if it had beene then seene . Besides , shee speaketh , of that great Commet , which immediatly followed after this Starre , in these word ▪ Within the West , a Blazing-Starre ▪ Shall rise , which named Comets are ▪ And in another place , thus ▪ After this Starre within the fourth yeare ▪ A flaming Comet shall appeare , Which on the deepest Seas below , His gloring beames abroad shall throw , Behold , how iustly we doth limit out the time betweene the apparition of this new Starre , and the Comet following ; for there were almost foure yeares betweene the vanishing of this new Starre and the rising of the Comet which followed . And by the Sea shore , meaneth the Westerne Ocean , for in this part of the world , presently after the setting of the Sunne , this Comet was seene ; those who would know more concerning these predictions , let them reade the bookes of the Sybils , in which it doth appeare , that there shall bea Catastrophe and change of things before the vniversall consummation of the world . Yet in what order things shall come to passe , it is hard to guesse , either by the signification of this Starre , or by the Sybilline Oracles , or by Divine Prophesies . But yet is likely , that those happy times shall not preceed , but follow after a more troublesome time ; even as this Starre at the first , did shine with a bright and cleare lustre and with a Ioviall light , but afterward did assume a Martiall sparkling colour , as may bee gathered out of the words of the same Sybilla . And God who dwelleth in the Heavens shall then Save the remainder of the Sonnes of men , Then Peace and knowledge of the truth shall flourish The Earth her plentious fruits shall likewise cherish It shall not bee devided as before Nor to the plough be subiect any more . Which also , the holy Prophets doe seeme to intimate , who foretell that the happy & peaceable estate of the Church , shall be after the destruction of this Gogus . But I thinke it not fit , to proceed any further in unfolding these mysteries , having promised to handle them sparingly ; as also in regard , that these Prophesies , are not to be declared by humaine coniecture , neither can be Geometricially demonstrated , as those matters which belong to the knowledge of Astronomie . And so leaving these my coniectures , to the consideration of the Reader : I will heere leave of to entreat any further concerning this Starre . FINIS . LONDON . Printed by B. A. and T. F. for Michael Sparke , at the blue Bible in Greene-Arbor . 1632. Deus & Rex . This King of Swed , Gustavus is by Name , And both words doe include an Anagram . For SVVED is DEVS , GVSTAVVS , it doth make Augustus , shewing that hee doth pertake Of Gods great power , and of Augustus Fame Which both this Starre , and Titles doe proclaime , Besides God-acre-field , which hee did winne Where God did give the Victorie to the King. Deus & Rex . Notes, typically marginal, from the original text Notes for div A16631-e510 Tempore posterior . Nec verbum verbo curabis reddere , fidus Interpres . Astrologie is a word compounded of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 signifying ; The speech of the Starres . Or Time. 
A59618	----	An essay on the certainty and causes of the earth's motion on its axis, &c. Sheeres, Henry, Sir, d. 1710. 1698 Approx. 42 KB of XML-encoded text transcribed from 16 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2003-07 (EEBO-TCP Phase 1). A59618 Wing S3059 ESTC R9477 12029871 ocm 12029871 52738 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A59618) Transcribed from: (Early English Books Online ; image set 52738) Images scanned from microfilm: (Early English books, 1641-1700 ; 877:41) An essay on the certainty and causes of the earth's motion on its axis, &c. Sheeres, Henry, Sir, d. 1710. 30 p. Printed for Jacob Tonson ..., London : 1698. Reproduction of original in Huntington Library. Attributed to Sir Henry Sheeres. cf. NUC pre-1956. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. 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Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Astronomy -- Early works to 1800. Earth -- Rotation. 2003-02 TCP Assigned for keying and markup 2003-03 SPi Global Keyed and coded from ProQuest page images 2003-04 Jennifer Kietzman Sampled and proofread 2003-04 Jennifer Kietzman Text and markup reviewed and edited 2003-06 pfs Batch review (QC) and XML conversion AN ESSAY ON THE Certainty and Causes OF THE Earth's Motion On its Axis , &c. LONDON : Printed for Iacob Tonson , at the Iudge's-Head in Fleetstreet . MDCXCVIII . An Essay on the Certainty and Causes of the Earth's Motion on its Axis , &c. IN an Essay so new and difficult , it may become me to begin with some Apologie to Men of Learning in Mathematical Science ; wherein I profess to have never aim'd higher than to be competently furnish'd for Business and Practice in an Active life . Wherefore to those Gentlemen , ( for whose merits no man has a greater value ) I make this short excuse for treating my Subject in so plain and familiar a manner : Namely , That being conscious of my insufficiency , by any show of Learning to add to their Stature ; it sorts better with my Talents and choice to speak my mind intelligibly to common Capacities , whereby increasing the number of my Judges , the Truth , Probabillity or Error of my Conceptions will be better sifted and discern'd ; for it shou'd be no mortification to consider with the Wise Man , that Chance has a great hand in every thing we do or think ; which by a kind of Revelation often leads us to the retreats of Truth through unaccountable Labyrinths and long obscurity of Causes . On which reflection if I ( who am best acquainted with my self ) ascribe nothing to my own forces of Learning , or penetration in my attempt to untie so hard a knot , may thereby have a better claim to the candour of my Readers , and they shall but barely allow me the priviledge of having stumbled on a new and profitable Notion , capable of Cultivation by the Learn'd , and of yeilding matter of Speculation to others ; I shall reap all the pleasure I look for , and as much honour as comes to my share . Thus bespeaking the candour of my Readers , I proceed ; by first imparting a few Articles of my Physical Creed , viz. So far as I conceive it may concern my Subject ; which till I shall be better inform'd , bear great sway with me , as being gather'd from the best Collections ( and my Meditations thereupon ) that I have been able to make from Experiments and Observations of Matters of Fact. Which Articles being first known , as conceiving them a necessary Introduction towards clearing the ground whereon I am to build ; I shall then proceed to my Hypothesis for solving the Earth's Motion on its Axis &c. by Explaining the Causes by which I conceive it may fairly and by Mechanical Laws be prov'd . And lastly ( in a discourse by it self ) I shall come to the Proofs and thereby show by what Clue of Deductions from natural Causes I came to be Establish'd in the perswasion I profess to be of touching this hard Question ; Wherein I have the rather ingag'd from my Observation of Late of so many unprofitable attempts in new Theories on Philosophical Subjects ; where with Ostentation of Erudition and Elocution , Authors obtrude strange Opinions , dangerous in their consequence to our Common Faith , and of no manner of Instruction to human Life ; Neglecting the while ( as perhaps thinking it beneath them ) to ingage in Studies of Utility ; whereby to improve our Knowledge in Nature , which wou'd inable us to see better before us in our way through this darksom Vale of Mortality wherein we Sojourn ; conduct us with more pleasure and Assurance in our Passage , and bring us with more safety to our Port , where all Speculation about doubtful Subjects will be resolv'd into Certainty . First , I believe that we neither have , nor can attain any clear Knowledge of the Effects of Matter and Motion , otherwise than as we become inlightned by their Operations on our Senses , which by means of the impressions made on them , make report thereof to the Mind , which gives Sentence true or false therein . I Hold also that the remoter the Situation of any cause is , the lighter or weaker the action and impressions thereof must needs be on our Organs of Sensation ; and consequently the reports made by them to the Understanding are proportionably ( as I may say ) doubtful and inarticulate , and the Judgment thereupon to be made necessarily more confus'd and uncertain : 'till at length by a Scale ( as it were ) of Cessation , the force of such cause gradually Expiring ; all Reasoning thereupon must needs there be at an End too . I say , that this is my belief , built on a rigid Examination of my own Heart , touching the objects of natural Knowledge and our Speculations about them ; from whence I have Determin'd with my self , that while I can by this rule conceive ( without much difficulty ) how a period of any Action whatsoever may be collected from such a sensible Gradation of stronger and weaker Power in the Agent , ( which our Senses inable us to distinguish ) I may I think safely and Mechanically thence infer , that such Power so working must have some certain Boundaries which it cannot Exceed ; and beyond which it is Idle and of no Effect . Wherefore I hence conclude , that all rational Reflection must needs there Expire , where the Powers by which those Images are stamp'd which furnish the matter of our Argument determine ; and that all Speculation , Refining and Excogitation about any thing whatsoever beyond or without this Sphere of Action , ( which I shall have occasion further to Explain ) is Vain and Fabulous . This Reflection , tho' it may humble us by Correcting the Enthusiasm of human Imagination , which is apt licentiously to soar and wander without Light or Guide ; yet the fruit may be profitable ; for by thus containing our Inquiries within that Circle which holds all things that are adequate to , and may yield proper matter for our Contemplation ; We shall have leisure to turn our Minds with greater attention and effect on Subjects of Publick Utility , which may at once avail us in the Conduct of our Life , and do good in our Generation ; than which no study is more Praise-worthy , nor can we by any means better fulfill the Ends of our Being . Pursuant to this reflection , Let us take into our View , and thence frame an Argument for our Meditation , some of the most remarkable Objects of the Creation , or of this Visible Material World : Namely , such as seem to us to share the greatest Power of Action on this our Globe . Among which , after sorting the whole Species of Things , and as I may say , ransacking Nature over and over , I believe I may challenge the most Sceptical man Living , to specify or point us out to any one single Instance of a Visible Being that may claim any Degree of Comparison with the Sun ; Whether we consider it in its Beauty and Glory , ( surpasing every thing we see ) or in its Situation in the Center of the Planetary World , a Position the most proper to dispense its ruling Power and Influence ; Or in its plain and sensible Effects , as being the Visible cause of Day and Night , Winter and Summer ; of Animation , Vegetation &c. All which are the indisputed Product of that Planet's Motion and Virtue . From these so many shining Evidences ( handed to us by our Senses ) of the Sun's force and predominancy , we are compell'd or taught as by Instinct , to ascribe a yet greater Extent of Power to its Operations , and to Collect and infer from what we see and feel ( and thereby know ) that the Sun has a greater Right than any visible Being , to be the Cause also productive of many of those other Appearences , which being eminent Subjects of our Observation are so much the greater Objects of our wonder , by how much they are effected more in the Dark ; namely , by means more remote , as acting on a Medium not so familiar to our Senses ; whereby the cause lies more hid and out of the reach of our Knowledge — Among these Phoenomena , that of the Earth's Motion on its Axis is one , which to prove and give some Aim at the Certainty and Cause thereof , in regard it may be of publick benefit in the Consequence , I have therefore chosen it for the Subject of this Essay . I hold then ( as being taught and confirm'd by Observation , and the Proofs I shall produce ) that the Sun is both the Cause and Center of Motion and gravity of the Earth and the rest of the Planets ; whose Motions and Periods tho' We may calculate and arrive at a degree of Certainty therein , yet perhaps while we continue in the dark , touching the reason of such motion , we shall remain to seek in our Conclusions , about many useful points of Knowledge , and by searching and penetrating with but never so little success into the Cloud that seems to cover the cause ; such sparks may by chance be struck out , as may suffice at least to light others quicker sighted ( whose Heads are better turn'd for such Subjects ) to a nearer View of Truth therein . I further hold , That by the Sun's Action and influence on the universal Fluid , wherein that luminary presides ; all the Heavenly Bodies , within the solar System , ( whose motion I take to be owing to his Virtue ) are bound also to that determin'd and unerring distance from him their Common Center , by such Laws of Mechanism , as in the proofs to be produc'd will not I hope appear frivolous , borrow'd , or any way inconsistent with the Principles I have laid down , wherein I shall endeavour to show that the Planets respective Ranck and Positions also in Heaven are by Mechanick Laws assign'd them , and Explain not only why , and how they move , but in what manner also the Poles of their Verticity are obtain'd ; and how it comes to pass that their Motions are so Regulated both on their Axes and in their Respective Orbits , so as they cannot be thought to Err and Wander in the Ocean of Fluid wherein they Float ; fareing like a Ship becalm'd , of whose Fluctuation no Pilot can keep any Account . In which Argument , I have some Hope , that a glimmering at least of Light may Shine forth to show us how the Harmony of the Heavenly Motions is Establish'd and Preserv'd . I Believe also , ( and Hope by intelligible means to show ) that my granting the Sun to be the Universal cause and Center of Motion and Gravity in the Planets , ( among which this our own Globe is compriz'd ) whereby their Verticity on their Axes and Revolutions in their Orbits are made and Govern'd ; that this Original Virtue of the Sun acting immediately on those Bodies , namely , the Planets , does not gainsay or oppugn , but infer and prove the like Effects of Motion and Gravity belonging to and producible by themselves also , as proceeding from the same Cause in Nature by which those first greater Bodies are mov'd . By means of which Motions , I conceive , that New and By-Laws of Gravity ( as I may say ) are obtain'd and Establish'd , to which all Matter and every Being which belongs to , Exists , or resides within the Circle of their Jurisdiction , viz. The reach of their Action respectively becomes liable . Which for a present Interpretation of my meaning , I thus Exemplifie , viz. The Globe of this Earth , Gravitates , towards , or has a tendency to the Sun : Iron or a Stone Gravitate ; the one towards the Magnet , rather than towards the Earth ; the other towards the Earth , more than towards the Magnet ; The like may be said also of the Moon , with respect to our Globe , and of the other Secondaries with regard to the Planets to which they belong ; so that this Diversity of Gravitation here produc'd to give an Image of my meaning , tho' it grows from one and the same cause , if we respect the Original impression ; yet springing from Collateral Agents , ( Acting as I may say by Subaltern Powers ) becomes thus Diversify'd , and thence those By-Laws of Gravity ( as I term them ) are begotten , as an Effect of nearer and more Prevalent Impressions on the Fluid that Surrounds them Respectively ; caus'd by their Verticity on their Poles ; Which Verticity acts in such manner on the Fluid that Surrounds them , as absolves , ( if I may use that form of Speech ) those lesser Bodies that are Creatures ; Beings or Inhabitants of the Planets themselves , from any Obedience to those General Laws of Gravity and Motion , to which the Primary Bodies their Principals are subject ; which I shall elsewhere further Explain . And thus in a word I am taught to believe , That Gravity is of manifold Production , and that there is a Devolution , Descent or Lineage thereof from the Sun , the First cause which Acts immediately on the Greatest and most Dignify'd Bodies , by a chain of Relation and Dependancy , down to the nearest and least particle of Matter and product of Motion Existing in this World of Matter and Motion . Lastly , From my conjecture that the Sun has no Dominion beyond those Circles , whereof he is the Center and cause of Motion , which we call the Planetary Heaven wherein he presides : From this belief , I say , touching the Extent and Boundaries of that Planets Action and Influence , ( which I conceive prescribes Limits to all sound Reasoning and Reflection about his Effects ) I am taught in like manner to Believe , that this Race of Thought , or course of Philosophizing here with us , must needs , as it is bounded in its extent , have a Beginning too from some certain Point or place or other ; Wherefore I conceive , that the Center of this Circle which is the Scene of Action , and contains all those Operations which by Mediation of our Senses is reveal'd , more or less to the Mind ; ( and which I observe to be the Sun ) , must necessarily assign also a Beginning to our Meditations about them ; further than which , or beyond that Center , our chain of Thought has no Linck , but is there fastn'd and lock'd up in Darkness ; for as it is Impossible to conceive the Harmony of a Lute by all that my Sight can impart to me ; Which tho' it may plainly tell me at a Distance , that the Fingers of the Artist move with great quickness and variety , yet the proper Organs of Sensation not being within the reach of the Sound ; all that Action which I behold , may for ought I know , be no other than Grimace , and playing the Fool — So , Tho' we can see the fix'd Stars and perhaps other Objects , without or beyond the bounds of the Suns Action or Dominion , yet being our selves Creatures whose Organs are Fram'd and Tun'd to his Operations , to whose unfluence ( by the Decree of the Almighty , ) we manifestly owe our Life and Being ; I say , that while we inhabit this mortal Tabernacle of Flesh and Blood , and have no Motion , Animation or Sensation ; that we cannot by fair Reasoning derive from the Force and Impressions of this Planets Virtue , by what Clue of Reason or Deduction , ( when our Reason it self has neither Tools , nor Materials , whereby to build any Scheme or Notion about natural Knowledge , that is not deriv'd from this Fountain ) can we be thought to have any Radical reflection or sound imagination beyond this Being ; or in a word by what Method of thinking can we go about ( Mechanically speaking ) to inquire into the cause of that Power to whose Action alone we owe the means of thinking at all . After this first Necessary Account of some Notions and Opinions about general Causes that have obtain'd with me , as I conceive they may somewhere or other relate to my Subject ; I come now to my Argument ; namely , a Mechanical Solution of the Earths Motion on its Axis ; by Explaining the causes by which I conceive that Motion is produc'd . First , By granting the Sun to be the Center of gravity of the Earth , and the rest of the Planets ; I am from thence Taught , to conclude that the Tendency or Gravitation of this Globe towards that Center , ought to yield the like Effects and produce the same Appearances ( Mechanicaly discoursing , ) that we find to be brought to pass by any solid Body here with us by means of our Center of Gravity : As namely , If any solid matter be fram'd or cast into a Sphaerical form , whereby it Recieves perhaps a Resemblance of the Earths Globe ; This Sphear being fitted with Poles , nicely plac'd and exactly poiz'd , shall by the least Addition of Weight duly apply'd , or the Application of any proper degree of Force , presently acquire a Motion on its Axis : viz. A Verticity or turning on its Poles . Secondly , Among the many great Effects I have observ'd to be produc'd by the Suns Virtue on this our Globe , I have remark'd that the Power of that Planets Influence is hardly any where , or on any thing more Conspicuous than by his Action on Fluids , on which Bodies it works so suddenly , so apparently , and with such force , that by my frequent Meditation thereupon , I came at Length to think it might be no unprofitable attempt , to inquire after some yet remoter than the Common and visible Effects of its Power , acting on that matter by that Medium : Having I thought some Hints from the Ordinary and Familiar Lights his daily Operations afforded , that the Sun might also be the cause of manifold other great Productions , which seem hitherto to want a clear Solution ; among which , this of the Earth's Motion on its Axis I conceiv'd might possibly be one . I observ'd , that tho' there might be many other causes of the Production and Variation of Winds ; yet that the Sun was manifestly the cause of all those we call Periodical Winds , as the Trade-Winds , Munsons , &c. as also of the Sea and Land Breezes , in warm Countries in the Summer time . That the Sun Visibly wrought the like Effects in many parts of the Globe on the Watery Element , by Currents in the Ocean ; Spouts , &c. That what I had observ'd for many Years together of the production and Force of the Levant-Winds , which will be calm in the Morning , and by Noon , will often blow with such impetuosity as to become a Storm ; and so die away again , as the Sun withdraws ; and become still and quiet all Night , till his return to the Meridian again : For thus have I beheld the Scene shift , and the Sun Act this part daily in those Countries about the Summer solstice for a Month or six Weeks together . From which Observation , ( when I came to turn my Thoughts to this Subject , of the Earths Motion , and the Causes thereof ) I gathered such Materials as in the Issue of the question will not I Trust be thought to have been Impertinently apply'd . But to hasten to the most prevalent Reasons occurring to my Understanding , How the Sun might be the cause of the Earth's Motion on its Axis ? take them as followeth , viz. By my Observation and Calculation ( as I have been able ) of the Effects of the Suns force in general , acting on different Subjects in divers manners : I conciev'd nevertheless that his power by Rarifaction was of all others the most Remarkable , and Seem'd to me not Obscurely to intimate that by that Action alone , having so Spacious a Field as the Globe of Earth , Sea and Air , wherein to display his Power , I cou'd discern cause enough whereby to determine a good deal towards the Solution of this notable Question . And first , I consider'd , ( and have no need at all to doubt it ) that the Hemisphere of this Globe , wheresoever the Sun chances to be in the Meridian ; ( that is , where his Virtue is in greatest Force ; ) must needs be the most rarifi'd part thereof , whither we consider'd it in the solid and Consistent parts thereof , or in the Fluid that surrounds it ; Which Fluid ( namely , that portion thereof that resides nearest the Earth , ( which we call the Atmosphere ) being imbu'd with infinite Variety of combustible and inflamable particles Steaming from the Earth ; is as I may say the Storehouse of those Materials , which by the Suns Action thereon produces all that Variety of Appearances which we behold , and daily converse with on this our Globe ; such as Heat and Cold , Wind and Rain , Storms and Calms , Hail , Frost and Snow ; Foggs , Vapours , Meteors , Exhalations , Thunder and Lightning ; &c. all which are Legible instances of that Planets power working on matter furnish'd from this Globe ; Whereof we can have no doubt from our Knowledge of many Situations and Heights , that are above all this Hurry and Variety of Action and Motion ; as namely , some part of Mount-Atlas ; the Peak of Teneriffe , Mount Arrarat ; a long Chain of Mountains in America , called , the Andes &c. which places are known to injoy a perpetual Serenity ; from whence Men can look down and Contemplate as in a Gallery the whole Action and Shifting of those Scenes that by the Suns Predominancy is produc'd on the Stage of the World below ; from whence I gather , and make two Remarkable Observations thereupon , viz. First , That the several Species of things that furnish Subject matter for this Action , are for the most part of the Earths product : Secondly , That the Effects reach not beyond a certain Limited distance from its Surface . Which Observation of Fact may save us the pains and words , of Philosophizing by the Laws of Gravity , about Limiting the Action of the Surrounding Fluid , which by the Sun's rarifiing Virtue is put is put into Motion . Wherefore having noted , that the Earth furnishes the Materials for this Motion ; and that the Action it self , is contain'd within Conceivable bounds ; it remains , That we determine how , and which way , this Fluid put into Motion , may be thought to take its Flight . I say then , that the Fluid , investing that Hemisphere wherein the Sun's Fire chances to be in its Greatest Vigour , is directed in its course by Lines drawn or produc'd from the cause that Acts thereon ; Namely , the Sun , and this by the same Mechanick Laws , by which any body is found to move , that is , impell'd and driven out of its Place , by another Body that has force enough to do it ; namely , by right Angles from the Plane of the cause that Acts : Wherefore remarking barely that a Line Conceiv'd to be at any time , drawn from the Body of the Sun , through the Axis of the Earth any where betwixt the Tropicks , will not vary much from East and West ; this single note , may suffice to show , that the Course or Tendency of the moving Matter or Fluid must be that way , namely by right Angles , or thereabouts , from the Axis of the Globe , or ( which better Expresses it ) by Circles parallel a little more or less to the Aequator , and not towards the Poles . Thus stating the Boundaries and Tendency of the Action or Course by which the Fluid wings it's way , that Surrounds this Earth , I mean that Portion thereof which we call the Atmosphere : I come Lastly to make a short necessary note or two , touching the Effects of Rarifaction , and Condensation , ( viz. According to common acceptation ) where I observe that the same Body or Quantity of Matter , when it is Rarifi'd becomes bigger , or is Extended in all its Dimensions , and so comes to require more space , wherein to be contain'd than it did before ; and ( on the contrary ) when the same Body comes to be Condens'd or Compress'd , it needs Consequently a less Space to contain it ; by which means any Body so alter'd , becomes Lighter , or Heavier , with Respect to the Fluid or Medium , wherein it has its Residence . But this Alteration by Extension or Contraction , can by no means come to pass but by being the cause of some certain Motion ; for whatsoever Thing requires a greater Space to contain it , than it did the Instant before ; must needs in the same Moment remove some other thing to obtain such new space ; and whatsoever Thing becomes on the Sudden lessen'd or contracted , must occasion the Motion of something or other , at the same time , to Replenish the Space it deserted , by such contraction or shrinking into narrower bounds . Having in some degree , clear'd the way , and conducted the Reader by those steps , and that train of Reflection , by which I became Establish'd in my Opinion touching the Certainty and Causes ( as they seem to me to be ) of the Earth's Motion , on its Axis , &c. I come now to interpret that Motion as I conceive it to be an Effect of those Causes . First , Then I take for Granted , ( and hope in due place to give probable Proof thereof ) that the Sun is the Center of the Earth's Gravity , towards which it tends . Secondly , I have observ'd that the Fluid which Invirons the Earth's Globe , by the Concurrence of proper admixtures of Matter , furnish'd from thence , is dispos'd for Motion , and by a Posture of Obedience to proper Causes , cannot but be deem'd to be Actually ever in a ready State of Mobillity . Thirdly , I have noted , that Rarifaction and Condensation are causes of Motion , and that the same quantity of Matter , rarifi'd or condens'd becomes Lighter and Heavier as an Effect of such Causes . Fourthly , I note that every Action of Fire ( be it more or less ) breaks or alters the Aequilibrium of the Neighbouring Fluid , which we see verifi'd every Moment , by the Fire in our Chimneys , which is the cause of that noise and whistling of the Wind through the Crannies and Key-holes of a close shut Room , where a good Fire is Kept ; the Air tending and rushing thitherwards , by stronger or weaker impulses , ratably to the strength or weakness of the cause Acting thereon . Fifthly , I am in no great doubt but the Sun is the universal Fountain of Fire , ( by whose Transcendent Masculine Force I conceive , all the Seeds or Sparks of that Element existing every where here below , is disseminated and propagated , through out the World ) which Planet I conceive , Acts in the fame manner on this whole Globe , and the Fluid that surrounds it , as any part or particle of its Fire , is found to do on any Fragment of the same matter . We see and know that a very small parcel of his Beams united or contracted by a glass , will as certainly burn , and therefore as certainly Act in proportion by Rarifaction , as any Body of Fire of never so much Greater dimentions can be thought to do : Whence we may I think safely conclude from the uniformity : We find in the Operations of Nature ; that the Sun ( which is an immense Body of Fire , whose Magnitude we know to be such as to Imbrace with his Heat , and Inlighten with his Beams more than Half the Earth's Globe at once ) Acts in like manner and Proportion on the universal Mass , as a Spark of his Fire shot through a Burning Glass , does on a drop of Water , or any other visible Fluid ; which we are sure it will Exhale and cause to disappear in a Moment . I say , that since we are certain , that there can be no very great disparity of Proportion betwixt such drop of Water and the least spark of the Sun's Fire , Acting thereon , and that of this Globe of the Earth , and Fluid compar'd with the Collected force of his Universal Influence , on the whole Terrestrial Mass ; We can hardly withstand the Evidence of this Truth , namely , that the entire Hemisphere which is at once imbrac'd , illumin'd and warm'd , by that Planets Virtue , cannot chuse but be Affected in the same Degree , and be Lyable to all those Motions , and Alterations which we behold and know to be the Effect of the like Action , on the like Subject in lesser Proportions . Sixthly , We may determine from a bare Guess by what we see and observe , That there is an unspeakable Store , or Reserve , of combustible , and proper Matter , contain'd on the Surface and in the Bowels of the Earth , prepar'd to obey the Sun's Action and Impression thereon , and we shall not I hope be Thought to Resolve too boldly , if we conclude , that as far as that Planets Force penetrates and warms , so far he may be Computed to act by Exhalation , ( or Rarifaction ) call it what you please on the Universal Mass of matter . So that by this Mighty force employ'd on a Sufficient Proportion of Subject matter , we may be taught to Expect proportionable Effects . Wherefore I believe it will be hard to gainsay but that the enlighten'd Hemisphere or that Face of the Globe , which is at any time the Scene of this Action , must unquestionably Suffer a manifest dimunition of Matter , and consequently of weight , by the Transpiration , Extension and Motion , of the Volatile parts , which ever Wing their way from the Light , to the Dark side of the Globe ; where by the same Laws , by which they mov'd , they must also cease from Motion ; and there Subside and be at rest , till actuated anew , and put on the wing again by the return of the cause ; by which means , namely this Revolution of Action , we may conceive a constant course of Diminution , and Restitution of Matter ; or an alternate Gravitation , and Alleviation thereof on the Earth's Globe , which by plain Mechanick Laws , urges a manifest Succession of Change in the Aequilibrium thereof ; and that in a Double Proportion , viz. By borrowing from one Scale , to lend to the other . Whereby the Preponderancy of the dark Hemisphere , or Alteration of the Aequilibrium of the Globe , becomes I say so much the Greater : And thus I conceive how by the Laws and Action of Gravity , we may discern with some Evidence , a Proclivity in the Earth's Globe towards a Motion of Verticity , or turning round ; and that from a Cause , as Familiar and Intelligible , as a Bird 's ringing the Chimes , in a Cage . Lastly , Having produc'd and assign'd the Causes , how I imagine the Earth's revolving Motion , may by Mechanick Laws be obtain'd ; I come now to inquire after the Poles of this Motion without which , we shall be at a loss , and want a Sound Footing of Reason , whereon to Build , and Govern this Motion ; which , while we consider its Regular and stated Periods , it cannot be thought to be fortuitous , but founded and stated on Adequate Causes . The Earth's Globe being as I have noted , immers'd in the Great Fluid or Aether , wherein both that and the rest of the Planets , are Granted to move : This Fluid according to its Nature , and Property , Claspes and Embraces it universally ; pressing or Gravitating on the Surface therefore equally every where ; ( I say equally because I wou'd not ingage here in any Statical questions ) but Subject and Obedient still to certain Adventitious Causes , which may alter , and Diversify such pressure or Gravitation . Let it be permitted me then to conceive , that this Fluid being simply Consider'd , and in its own Native purity ; namely , clean from all whatsoever Admixtures ; I say this Elemental Aether , ( if I may so call it , ) Nakedly understood , viz. stripp'd of all Foreign and Heterogenius Ingredients , ( which by there Inflamable and Explosive Virtue , may be conceiv'd to Act thereon ) is of it self , a Passive Lifeless matter ; destitute of any Intrinsick Force of Action , and is no other in short than the Vehicle of those Powers or Ingredients that swim and reside in it ; which matter or Fluid becomes Lighter and Heavier , Slow , Swift , Rappid , and at rest , just as it is Impregnated Inspirrited , or Deserted by those Forreign Agents ; or any Heterogenius Body casually Mixing or Floating therein ; to which I say the Fluid or Aether is nothing else but the meer Vehicle . This remark being duly weigh'd , we need but recurr to the cause of that Variety of Action and Motion , which we have Observ'd to Exist on the Earth's Surface , which I observe to be the Sun , by whose force ( Acting on proper Matter ) all that tumult of Action is rais'd and begotten ; in proof whereof we need not go further , than to note that the greatest Storms and Hurrican's are ever found where that Planets power reigns with greatest force . From a reflection on the Power , let us go to the Situation or Position of the Agent , with respect to the Earth's Globe , which furnishes the Materials whereon it works : And therein may be considered , that the greatest Vigour of the Sun's Action is contain'd betwixt the Tropicks ; his Beams ever darting somewhere or other within or between those two Circles , ( and no where else ) at right Angles on the Earth's surface ; and from or without the Tropicks , ( viz. towards the Poles ) the Angles of insidence become oblique , and ever fall with greatest obliquity at the Poles . The use I wou'd make of this observation is , That since we can determine where , and on what part of the Earth's Globe , the Sun's Beams fall with least Obliquity , we may resolve also that it is on that part , and within those boundaries , that his Fire acts with greatest fervour . But this force of the Sun's Virtue is found to be greatest betwixt the Tropicks ; where by his Action on the greater Circles of the Globe , the Effect becomes so much the surer , by how much we observe a greater Wheel , or a longer Lever , to Act more forcibly than a lesser ; which as it fortifies the Reasons already offer'd for the Earth's Verticity , by assigning such a position to the Cause as may render the Effect so much the more Probable , so it leads us not obscurely to concieve , how the Poles of this Motion also are begotton . For if there shall appear , any Evidence from the Causes we have assign'd , for the Fluids pressing or Gravitating less on the Earth's Globe on the greater Circles , ( namely betwixt the Tropicks ) which cannot ▪ fairly be gainsaid ; the Alleviation thereof , being greatest where the Rarifaction and Motion is granted to be Greatest ; It will not then be hard to allow , that every degree of Remission of the Power , of the Agent ( viz. the Sun , ) must produce a proportionable Diminution of the Effect . But I have shown ( or lead the Reader to conceive , ) how it comes to pass , that the surrounding Fluid presses Lightest on the Surface of that Region of the Globe , that shall be found remotest from the Poles , and therefore there will be no difficulty to infer , That as the Angles of incidence of the Sun's Beams ( by whose Action that Alleviation of the Fluids pressure is begotten , which we have endeavour'd to explain ) grow more and more Oblique , the Effect becomes more and more diminish'd . So that by a Scale , as I may say of Diminution , or by the Gradual Obliquity of the Angles of incidence , which begins at the Tropicks , and are ever most Oblique at the Poles ; we may be taught to discern how the Fluid ( by this Remission of the Sun's Action thereon ) comes to press harder or Gravitate more on the Globe at the Poles than elsewhere ; or rather infer , that by this necessary Superiour pressure , the Poles of the Earth's Verticity are begotten . For in a word the Fluid ( which I have over and above , Endeavour'd to show ) being heaviest or pressing Hardest , when in its native purity ; must needs abide there above all other parts of the Globe , most clean and unmix'd from all such Heterogenius matter ; those two points of the Earth's Surface , being the most absent from that active and Rarifying Force by which , by means of such matter , it is put into Motion , as I have shewn how . And I am in no doubt , but all those combustible and Inflamable Ingredients , which in other Regions of the Globe , are the cause ( cooperating with the Sun ) of all that Agitation we have observ'd ; remain here Lazy , and Lifeless on the Surface , and in the Bowels of the Earth , and like a Snake in Winter benum'd , and bereft of all Power of Motion , through the Absence of that inlivening Virtue to which it owes all its Power of Motion and Action ; by which means the Fluid or Aether , which invirons the Globe ; abides there in a perfect State of Tranquillity , and ( unmolested by any Foreign force ) has leave to rest , press or gravitate by its own Laws , and according to its native Tendency ; which Liberty I say it doth not injoy on other parts of the Globe , where the Sun's Action is more in Force . Thus then , I concieve , and have as well as I can Explain'd how the Poles of the Earth's Verticity are obtain'd ; the Surrounding Fluid leaning or Gravitating on the Surface thereof , by a stronger Pressure in those two points of the Globe , than it can be thought to do in any other part whatsoever : Which pressure like two Fulciments , props , holds and sustains it in that Regular posture wherein we find it to move ; or to give a plainer similitude of my meaning , by the stronger resting of the Fluid , in and about these two Opposite points ; whereby cliping as I may say , and embracing the Globe by a Superiour pressure there , those Two points become by that means , the Centers of the Earth's Revolving Motion , as intellibly as a polish'd Ball , or Sphere , being held and press'd betwixt the Finger , and the Thumb on the two Centers by which it was turn'd , is thereby dispos'd to a motion of Verticity , by means of any competent Force in a proper manner apply'd to produce it . When I Enter'd on this Discourse , I thought to have pursu'd my Argument through all the Difficulties , that seem'd to occur to me and had been fairly hitherto suggested , by others to my Hypothesis as I have here simply Explain'd it . But being inform'd that I am to Expect farther , and more material Objections than I may be aware of , I have therefore Consented to Publish the First naked Draught , of my Conjectures on this Subject in a single Essay , which containing my Principles , and the Out-lines of my Design , the Reader being thereby Furnish'd with Light into the Proportions and Consistency , at least of my Meaning , will have more room and liesure , for his Reflection and to impart his Doubts , which I shall recieve with Gratitude , and Consider with my utmost care — Truth is painted Naked , because in that Simplicity of Appearance , she is best known , and the more we beg or borrow , or are driven for Supplies to Wit or Art , to imbelish her , the more we seem to disguise Her , and bewray the uncertainty of our Knowledge about her — Her abode to ( as in our Case ) is often in the Clouds , so that He who attempts to shew her in the greatest undress , may be thought to do most Right to her Charms , and whosoever shall give the best Aim at the means of Resolving distant and doubtful Causes , by the plainest and most Familiar Methods , such as Nature by the Laws of Mechanism seems to Approve , may be deem'd to be more in the way , and to make the Approaches to Truth more Lightsom and intelligible , than by remote and Metaphysical Speculations , wherein we know the greatest Wits have wander'd , who according to their different Modes of thinking , have compass'd to solve Appearances so many different ways ; whereby we are taught Just so much Truth as to be sure that their Systems may be all false , because we are most certain , there can be but one True. In a word , Whatever may be the Destiny of this Essay , the Author trusts to have some title to Excuse , both from the Learn'd and others , for his attempt : From the One for Propounding so much a nearer , and more likely way to the unravelling this Skain , which hath been left more intangl'd and perplex'd by Dispute , and the Diversity of Learn'd men's Opinions about it , which infaelicity may perhaps have sprung from their Speculating so far after distant and obscure Causes , that they have thereby miss'd and overlook'd the True. To these Gentlemen , if any thing in this Theory has been started new , or of Moment enough to be consider'd , I may have given an occasion of meriting from the World , by my laying this rude Foundation whereon by their better Abilities some useful Structure of Knowledge may perhaps be rais'd . From the rest who are much the Majority , I will not doubt of Acceptance while I do my best , to shorten and Ascertain the way to Truth , by calling in our Senses more to our Aid , which being the surest Succours , and clearest Conduits of Knowledge , our Researches and Reasonings , on these dark Phaenomena , will thereby stand on a Surer Basis ; and to conclude with one single Instance here , of my Method in this pursuit ; I Note , That to obtain a Proof of my seeming at least to have Reason'd right , about this Problem of the Earth's Motion on its Axis , I fram'd a Machine , with all the accuracy possible ; wherein I imitated , according to my best Knowledge , the Earth's Globe with its Atmosphaere , &c. Which being poiz'd very nicely , and tenderly sustain'd on its Poles to adapt it for Motion , and then fairly substituting and applying the Causes , which I conceive , by the Laws of Gravity , are productive of the Earth's diurnal Motion : I reap'd the Contentment , to behold the Effect of such causes working on the said Matter , to give credit in every Article to what I had thereupon before imagin'd : The Machine so fram'd and fitted , visibly Revolving on its Axis ; Each Revolution finishing in about the space of Three Hours . Which Experiment beheld by my Friends , who were not presently aware of the Springs of such Motion , they were no less pleas'd than surpriz'd . FINIS . 
A40034	----	Posthuma Fosteri the description of a ruler, upon which is inscribed divers scales: and the uses thereof: invented and written by Mr. Samuel Foster, late professor of astronomie in Gresham-Colledg. By which the most usual propositions in astronomy, navigation, and dialling, are facily performed. Also, a further use of the said scales in deliniating of far declining dials; and of those that decline and recline, three severall wayes. With the deliniating of all horizontall dials, between 30 and 60 gr. of latitude, without drawing any lines but the houres themselves. Foster, Samuel, d. 1652. This text is an enriched version of the TCP digital transcription A40034 of text R218296 in the English Short Title Catalog (Wing F1635A). Textual changes and metadata enrichments aim at making the text more computationally tractable, easier to read, and suitable for network-based collaborative curation by amateur and professional end users from many walks of life. The text has been tokenized and linguistically annotated with MorphAdorner. The annotation includes standard spellings that support the display of a text in a standardized format that preserves archaic forms ('loveth', 'seekest'). Textual changes aim at restoring the text the author or stationer meant to publish. This text has not been fully proofread Approx. 85 KB of XML-encoded text transcribed from 46 1-bit group-IV TIFF page images. EarlyPrint Project Evanston,IL, Notre Dame, IN, St. Louis, MO 2017 A40034 Wing F1635A ESTC R218296 99829904 99829904 34351 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A40034) Transcribed from: (Early English Books Online ; image set 34351) Images scanned from microfilm: (Early English books, 1641-1700 ; 2029:21) Posthuma Fosteri the description of a ruler, upon which is inscribed divers scales: and the uses thereof: invented and written by Mr. Samuel Foster, late professor of astronomie in Gresham-Colledg. By which the most usual propositions in astronomy, navigation, and dialling, are facily performed. Also, a further use of the said scales in deliniating of far declining dials; and of those that decline and recline, three severall wayes. With the deliniating of all horizontall dials, between 30 and 60 gr. of latitude, without drawing any lines but the houres themselves. Foster, Samuel, d. 1652. [8], 80, [2] p. : ill. printed by Robert & William Leybourn, for Nicholas Bourn, at the South entrance into the Royall Exchange, London : 1654. With final page of errata. Reproduction of the original in the British Library. eng Astronomy -- Early works to 1800. Nautical astronomy -- Early works to 1800. Navigation -- Instruments -- Early works to 1800. A40034 R218296 (Wing F1635A). civilwar no Posthuma Fosteri: the description of a ruler, upon which is inscribed divers scales: and the uses thereof: invented and written by Mr. Samue Foster, Samuel 1654 13737 3 0 0 0 0 0 2 B The rate of 2 defects per 10,000 words puts this text in the B category of texts with fewer than 10 defects per 10,000 words. 2003-06 TCP Assigned for keying and markup 2003-06 Aptara Keyed and coded from ProQuest page images 2003-07 Marika Ismail Sampled and proofread 2003-07 Marika Ismail Text and markup reviewed and edited 2003-08 pfs Batch review (QC) and XML conversion Posthuma Fosteri : THE DESCRIPTION OF A RULER , Upon which is inscribed divers SCALES : AND The Vses thereof : Invented and written by Mr. SAMVEL FOSTER , Late Professor of ASTRONOMIE in GRESHAM-COLLEDG . By which the most usual Propositions in Astronomy , Navigation , and Dialling , are facily performed . Also , a further use of the said Scales in delineating of far declining Dials ; and of those that Decline and Recline three severall wayes . With the delineating of all Horizontall Dials , between 30 and 60 gr. of Latitude , without drawing any lines but the Houres themselves . LONDON : Printed by ROBERT & WILLIAM LEYBOURN , for NICHOLAS BOURN , at the South entrance into the Royall Exchange , 1654. TO THE READER . COURTEOUS READER , WE here present to thy view , this short TREATISE , ( written by that learned Professor of ASTRONOMIE in Gresham Colledge , Mr. SAMUEL FOSTER deceased ) containing in it the Description and Vse of certain Lines to be put upon a streight Ruler , in the ready solution of many necessary Questions , as well Geometricall , as belonging to Astronomie , Navigation , and Dialling . We should not thus hastily have thrust this into the World without its fellows , had we not been assuredly informed that some people , greedy rather of unjust gain to themselves , then with honesty to sit still , had prepared one for the Presse , from a spurious and imperfect Copie , both to the abuse of thee , and discredit of the industrious Author : who had he thought such things as these worthy him or the Presse , could have daily cram'd thee with them , to his own losse of time , and thy satiety . However , such as it now is , we assure thee was his own , and doubt not , but thou wilt finde it pleasant in the use , profitable to thee , and portable in it selfe . We thought fit farther to advertise thee , that there are abroad in particular hands , imperfect Copies of some other Treatises of the same Author : Namely , An easie Geometrical way of Dialling . Another most easie way to project houre-lines upon all kinde of Superficies , without respect had to their standing , either in respect of Declination or Inclination . A Quadrant fitted with lines for the solution of most Questions of the Sphere : with some other things of the like nature . We fear least sinister ends of some mean Artists , or ignorant Mechanicks , ( for those of ingenuity in whose hands they may be , we no way distrust ) may engage them to father these things as their own , or at least under the Authors name put out lame and imperfect Copies of otherwise good things : To prevent which we give thee this timely notice , assuring thee , that these , together with divers other pieces never yet seen , except by very few , and if we deceive not our selves , of much greater weight , are making ready for the Presse by the Authors approbation , and from his own Copie in our command , with his other papers , of which thou shalt be made partaker within few moneths . In the mean time , we desire thee not to lose thy time in reading , or money in buying any the forementioned Treatises put out by any other , either under their own , or our Authors name , except such as shall be attested by me , who am one of those intrusted for that purpose , and who shall be ever studious of thy good . Grayes Inne , July 26 , 1652. Edm. Wingate . The description of the Scales on the Ruler . THere are 9 Scales upon the Ruler . 1. Of Inches or equall parts . 2. Of Horizontall spaces : with 3. A Scale of 60 Chords fitted to the same Radius , proper to that Horizontall Scale . 4. A Scale of Sines , to a Radius of two Inches . 5. A Scale of Secants : and 6. Of Tangents , both of the same Radius with the Sines . All these are upon one side . On the other side is , 7. A little Scale of 60 Chords , of the same length with the common Radius of Sines , Secants , Tangents , and common in use to them all . 8. A large Scale of Versed-Sines of the whole length of the Ruler , with a Zodiac annexed to it . 9. A Scale of unequall parts divided into 90 , noted with ☉ , of two Inches Radius as is the line of Sines . THE Vses of the SCALES on the RULER . CHAP. I. Of the Scale of equall parts . THe Scale of Inches is a Scale of equall parts , and will performe ( by protraction upon paper ) such conclusions as are usually wrought in Lines and Numbers , as in Master Gunters 10. Prop. 2. Chap. Sector , may be seen , and in others that have written in the same kinde . An Example in Numbers like his 10th . Prop. As 15 to 5 , So 7 to what ? But if your second terme shall be greater than the first , then the form of working must be changed ; as in this Example . As 5 to 15 , So 20 to what ? Upon the line AB , I set the second terme 15 , which here suppose to be AD : then with the first terme 5 , upon the center D , I describe the arke GH , and draw AG that may just touch it . Again , having taken 20 the third term , out of the same Scale , I set one foot of that extent upon the line AB , removing it till it fall into such a place , as that the other foot being turned about will justly touch the line AG before drawn , and where ( upon such conditions ) it resteth , I make the point C. Then measuring AC upon your Scale , you shall finde it to reach 60 parts , which is the fourth number required . The form of work ( though not so Geometricall ) is here given because it is more expedite than the other by drawing parallel lines . But in some practises , the other may be used . I have been the more large upon this , because the solutions of proportions which follow must be referred hither , the forme of their operations being the same with this . In them therefore shall only be intimated what must be done in generall , the particular way of working being here explicated . CHAP. II. Of the Scales of Chords . THe Scales of Chords are to protract and measure angles . The manner how they must be used is well enough known . Only note here , that you may make the line of Sines , the line of Versed Sines , or the Zodiacke , ( beginning at the middle of these two last mentioned ) to serve for Chords of severall extents , if you count each halfe degree for a whole degree , and so double all the numbers , accounting 10 to be 20 ; and 30 to be 60 , 45 to be 90 , &c. By this you are fitted with severall Scales of Chords which are of different lengths , and may be used , each of them , as occasion shall require . And ( by the way ) the Versed Scale being taken for Chords , it will be of the same Radius or length with the Sines , Tangents and Secants and so will protract Angles to a Circle of their Radius , which is usefull in Projections , and many other things : and so the little Scale of 60 Chords might be spared . CHAP. III. The joynt use of equall parts and Chords . BY these two together , may be resolved all Cases in Plaine Triangles without proportionall work , if the three quantities given be protracted by help of these two Scales . For their principall uses are to measure lines and angles . Here must be remembered . First , that if the three angles alone be given , then will the proportions only of the sides be found , but not the sides themselves . Secondly , that if two angles be known , then is the third also known ; because it is the residue of the sum of the other two to 180 gr. Then with a line of Chords protract the angles at A and B according to their known quantities , so shall the two legges of the same angles meet at C : And if the length AC be taken and measured upon your Scale of equall parts , the same will shew about 1004 , intimating that C is from A 1004 feet . So again BC being measured in the same Scale will give 1120 ; shewing that from B to C are about 1120 feet . In this manner may perpendicular altitudes ( as of Towers or such like ) be measured , though no accesse can be had to them ; and that much better than by the Geometricall Square . For it is not here requisite that the ground whereon the mensuration is made , should be levell , as if you work by the Square it is most commonly required ; neither are you tyed to right angled Triangles here , as there you are . As for example , If one station be at A , and the other at B , you may , by the precedent work get the distance AD . Then ( standing at A ) observe the altitude of C , the complement of that altitude gives the angle ACD . And again from A , if you observe the altitude of D , the difference of these two altitudes observed , gives the angle CAD . Or if D had appeared lower then your station , then the summe of your two observed altitudes had made the angle CAD . However , you have now the three angles and side AD ; you may therefore , by help of them , finde the length of CD . In such manner may all cases in plain Trigonometry be resolved . CHAP. IV. Of the Scales of Sines , Secants , and Tangents . THese being joyntly used with a Scale of equall parts , will resolve all things in plain Triangles , by working such proportions as are usually given for that purpose . The manner of the work may be gathered by the former delineation in the 1 Chapt. For if AC and AD had been taken out of the Scale of Sines , or Tangents , or Secants ; and CE , DG , out of the Scale of equal parts ; then had the work been resolved in Sines and equall parts , or Tangents and equall parts , &c. And so this kinde of work will produce the quantity required ; although there be no delineation of the particular parts of the Triangle , as was before done by protraction . By these same three Scales of Sines , Tangents , and Secants , may be wrought all things pertaining to Sphericall Triangles . That is to say . 1. Proportions in Sines alone . 2. Proportions in Tangents alone . 3. Proportions in Secants alone . 4. Proportions in Sines and Tangents together . By naturall Sines and Tangents . By ☉ and Versed-Sines . 5. Proportions in Sines and Secants together . 6. Proportions in Tangents and Secants together . An Example in Sines alone What Declination shall the Sun have in the 10 gr. of Aries ? Upon the line AB ( see Chap. 1. ) set the Radius or Sine of 90 AC : and make AD equall to the Sine of 10 gr. ( which is the Suns distance from the next Equinoctiall point . ) Then with the Sine of 23½ ( taken out of the same Scale of Sines ) upon the center C , describe the arke EF ; to which , from A , draw the Tangent line AE . Lastly , from D , to this line AE , take the least distance , the same measured in the line of Sines , gives about 4 gr. for the declination required . The proportion that is here wrought stands thus . As the Radius , to the Sine of 23 ½ ; So the Sine of 10 , to the Sine of 4 gr. The like manner of work is to be used in Sines and Tangents ( or any of the other two ) joyned together ; if it be remembred that the greater terms be kept upon the line AB ; as was before prescribed in the first Chapter . CHAP. V. OF NAVIGATION . Some things in this kinde will be performed very conveniently by these lines : As , SECT. 1. To make a Sea-chart after Mercators projection . A Sea-chart may be made either generall or particular ; I call that a generall Sea-chart , whose line AE , in the following figure , represents the Equinoctiall , as the line AE there doth the parallel of 50 gr. and so containeth all the parallels successively from the Equinoctiall towards either Pole : but they can never be extended very neere the Pole because the distances of the parallels increase so much , as the Secants doe . But notwithstanding this , it may be termed generall , because that a more generall Chart cannot be contrived in plano , except a true Projection of the Sphere it selfe . And I call that a particular Chart which is made properly for one particular Navigation , as if a man were to sail between the Latitude of 50 and 55 gr. and his difference of Longitude were not to exceed 6 gr. then a Chart made ( as the figure following is ) for such a Voyage , may be called particular . Now the making of such a Chart , is Master Gunters first proposition page 104 of the Sector , and this the line of Secants will sufficiently perform . For it were required to project such a Chart : Having drawn the line AB , and having crossed it at right angles with another line AE , representing the parallel of 50 gr. you must then take the Secant of 51 from your Scale , and set it from 50 to 51 on both sides the Chart , and draw the parallel 51 51. Again , take the Secant of 52 from your Scale , and set it upon your Chart from 51 to 52 , and so draw the parallel 52 52. And so you are to draw the rest of the parallels . If therefore you take the Radius , and run it above and below , you shall make the spaces or distances of the Meridians such as in the bottome of the Chart are figured with 1 , 2 , 3 , 4 , 5 , 6. These degrees thus set on the Chart , may be sub-divided into equall parts , which in the graduations above and below ought so to be . But in the graduations upon the sides of the Chart , they ought as they goe higher , still to grow greater . Yet the difference is so small that it cannot produce any considerable errour , though the sub-divisions be all equall . Divide them therefore either into 60 minutes , or English miles , or into 20 leagues , or into 100 parts of degrees , as shall best be liked of . It a little more curiosity should be stood upon for the graduations of the Meridian , instead of the Secants of 51 , 52 , 53 , &c. you may take 50½ , 51½ , 52½ , &c. alwayes halfe a degree lesse than is the Latitude that should be put in . Now if each of those divisions at the bottome of the Chart , as A 1 , &c. be made equall to the common Radius of the Sines , Secants , and Tangents , and if a Chart be made to that extent upon a skin of smooth Velame ; well pasted on a board ; you may work upon it many conclusions very exactly . The Vses of the Sea-Chart Are set down in 12 Propositions by Master Gunter , beginning page 121. In each of which Propositions is shewed how to resolve the Question upon the Chart it selfe , which will be direction enough how the work must be performed , without any more words here used . The working of these propositions also may be applyed to the Scales of Sines and Tangents , on the Ruler , and wrought by protraction , according to the rules given in the first Chapter , if the proportions , as he layes them down in the forecited pages , be so applyed . If a Scale of Rumbs be thought more expedient for these operations then is a Scale of Chords , it may be put into some spare place of the Ruler . His two Propositions , page 114. 116 , may be done upon the Chart as is there shewed , but his second Proposition , which is , SECT. 2. To finde how many Leagues doe answer to one degree of Longitude , in every severall Latitude . THis ( I say ) may be done upon the Scales of Sines and equall parts : And for this purpose , the two last inches of the same Scale of equall parts , being equall in length to the Radius or Sine of 90 , are divided into 20 at one end , and into 60 at the other end . Take therefore upon the line of Sines , the complement of the parallels distance from the Equator , ( or the complement of the given Latitude ) and measuring it upon the Scale of 20 parts , it will shew you what number of Leagues make one degree of Longitude in that parallel of Latitude . And being measured upon the Scale of 60 parts , it gives so many of our miles , or so many minutes of the Equinoctiall , or any other great circle , as are answerable to one degree of Longitude in that Latitude . Example , Let it be required to finde how many Leagues doe answer to one degree of Longitude , in the Latitude of 18 gr. 12 ' . Take out of the line of Sines , the complement of the given Latitude , namely . 71 gr. 48 ' . Then applying this distance to the Scale of 20 equall parts , you shall finde it to reach 19 , and so many Leagues doe answer to one degree of Longitude , in the Latitude of 18 gr. 12 ' . And the same distance being measured upon the Scale of 60 equall parts , will give you 57 parts , and so many minutes of the Equator are answerable to one degree of Longitude , in that parallel of Latitude . So likewise , in the Latitude of 25 gr. 15 ' , if you take the complement thereof 64 gr. 45 ' , out of the Scale of Sines , and apply it to the former line of 20 , you shall finde it to reach 18 parts , and so many Leagues doe answer to one degree of Longitude , in the Latitude of 25 gr. 15 ' . ¶ In the Appendix to Master Norwoods Doctrine of Triangles , there is by him laid down 15 Questions of sailing by the plain Sea-chart , and others by Mercators Chart , all which the line of Chords and equall parts will sufficiently perform , if the work of the third Chapter of this Booke be rightly understood . SECT. 3. How to set any place upon your Chart , according to its Longitude and Latitude . IF the two places lie under one parallel , and so differ only in Longitude , then the course leading from one to the other is East or West : As A and E being two places under the parallel of 50 gr. and differing 5½ gr. in Longitude . But if the two places differ only in Latitude , and lie under one Meridian , as A and B , then the course is North or South . CHAP. VI . Of Projections of the Sphere . FOr this purpose chiefely , is the lesser line of Chords added , being made to the same Radius that belongs to the Sines , Secants , and Tangents . For when any Projection is to be made , the fundamentall Circle must be of that common Radius , and then the angles to be inserted upon it may be taken out of this line of Chords which is fitted to it . See the second Book of the Sector , Chap. 3. For these Tangents and Secants will performe the same things in those Stereographicke projections that there are done ; and in all other irregular projections likewise . By this kinde of work may any Sphericall conclusions be performed by protraction in plano . Also true Schemes of the Sphere may be drawn , sutable to any question , which will not a little direct in Sphericall calculations . As suppose it were required to project the Sphere sutable to this Question . Having the Latitude of the place , the declination of the Sun , and the Altitude of the Sun , to finde either the Azimuth or the houre of the day . First , With the Radius of the line of Chords , upon the center C describe the fundamentall Circle ZHNO representing the Meridian , and draw the diameter HO for the Horizon , and ZCN at right angles thereto , ZN being the Zenith and Nadir points . Then by your line of Chords set the Latitude of your place ( which let be 51 gr. 32 ' ) from Z to E , and from N to Q , drawing the line ECQ for the Equinoctiall , and at right angles thereto , the line MP for the axis of the World , P representing the North , and M the South Pole Secondly , Supposing the Sun to have 20 gr. of North Declination , take 10 gr. ( the Semitangent of the Declination ) out of the line of Tangents , and set it from C to G. Likewise , take 20 gr. ( the Declination ) from your line of Chords , and set that distance upon the Meridian from E unto D , and from Q unto K : then describe the arke of a Circle which shall passe directly through the points DGK , the center whereof will alwayes fall in the line CP if it were extended , and this arke DGK shall be the line of the Suns course when his Declination is 20 gr. from the Equinoctiall Northward . ¶ 1. The centers of the parallels of declination , and of the parallels of altitude , may readily be fouud by the Scale it selfe ; as in this projection , having found the point F upon the Line ZC , extend the line ZC without the circle , and because the Suns altitude is 50 gr. take therefore out of your Scale the Secant of 40 gr. ( the complement of the Altitude ) and set that distance from C to I , so shall the point I be the center of the parallel of Altitude . Or take the Tangent of 40 gr. out of your Scale and place it from F to I , either of which will fall in the point I , the center of the parallel of 50 gr. In the same manner may the center of the parallel of Declination be found , by taking out of your Scale the Secant complement of the Declination , and setting it from C , upon the line CP , ( being extended ) and where that distance ends , that is the center of the parallel . ¶ 2. For the finding of the centers of the Hours and Azimuths , the Scales of Secants and Tangents will much help you ; So the Azimuth from the South being 49 gr. 52 ' , if you take the Tangent thereof out of the Scale of Tangents , & set it upon the Horizon from C to L : the point L shall be the center of the circle NTZ. Or the Secant of 49 gr. 52 ' being set from T , that also shall give you the center Las before . The center of the Houre-circle is found in the same manner , for the houre from the Meridian being 31 gr. 28 ' , if you take the Tangent thereof our of your Scale , it shall reach from C to R , the point R being the center of the Houre-circle MVSP . Or the Secant of 31 gr. 28 ' , being set from V , shall give the point R for the center of the same houre . And in this manner may any Houre or Azimuth whatsoever be drawn . Many other propositions in Astronomie , may be wrought upon this projection , and indeed any of the 28 cales of Sphericall Trigonometry , may by this kinde of projection be easily illustrated and resolved , which will cleerely informe the fancie in the resolving of Sphericall Triangles . An Example or two for practise shall be , 1. To finde the Suns Amplitude . In this projection , the Amplitude from the East or West is represented by the line CX , take therefore the distance CX in your compasses , and apply it to the line of Tangents , ( counting every degree of the Tangents to be two degrees ) and where it resteth , that shall be the Amplitude from the East or West , which will be found to be 33 gr. 22x . Or if you lay a Ruler upon Z and X , it will cut the Circle in Y , and the distance NY being measured on the line of Chords , shall give the Amplitude also . 2. To finde the distance of the Sun from the Zenith . The distance of the Sun from the Zenith is the arke Z S , therefore to finde the quantity thereof , you must first finde the pole of the circle NS Z , which is done after this manner . Lay a Ruler from Z to T , and it will cut the circle in a , then take in your compasses a quadrant of the outward circle , and set it from a to b , then lay a ruler from Z to b , and it shall cut the Horizon in e , which point e is the pole of the circle ZTN. Now to measure the arke Z S , you must lay a ruler upon e and S ; which will cut the outward circle in the point A , so shall A Z , being measured upon the line of Chords , give you the quantity of degrees contained in the arke Z S , which will be 40 , equall to the complement of the Suns Altitude . ¶ This latter proposition was inserted rather to shew how the arke of any great Circle of the Sphere ( the sides of all Sphericall Triangles being such ) may be measured , then for any need there was to finde the distance of the Sun from the Zenith , for that mighe have been more easily effected , it being only the complement of the Suns Altitude ; but according to this operation , may the side of any Sphericall Triangle whatsoever be measured . The line of Sines also will project the Analemma , as Master Gunter sheweth , if this proposition be added . How to divide any line given , into such parts as the Scale of Sines is divided . Which proposition may be done by that which is set down in the 1 Chapt. For if AD mn C were parts or divisions made equall to those upon the Scale of Sines , and CE were a line in the same manner to be divided : After you have prepared your work as is there prescribed , you need only to take the least distances between the points C nm D and the line AE , and insert the same into your given line , so shall the divisions thereof be proportionall to the line of Sines . CHAP. VII . Of the line of Versed-Sines . THe generall use of this Scale is principally to resolve these two Sphericall Cases . First , By having three sides of a Sphericall Triangle , to finde an angle . Secondly , By having two sides and the angle comprehended , to finde the third side . According to which two generall cases you shall finde particular examples ; namely , the first and third Sections of this Chapter sutable to the first Case : and the 5 Section answerable to the second . SECT. 1. To finde the Suns Azimuth . FIrst , Finde the summe and difference of the complement of your Latitude , and complement of the Suns altitude . Then having made AB equall to the length of the whole Scale , count upon the same Scale the summe and difference before found . After this , take with your Compasses the distance from the Suns place to the summe , and setting one foot of that extent upon B , with the other describe the arke CD . So again , take the distance upon the Scale from the Suns place to the difference , and with that extent upon the center A , describe the arke EF : Which done , draw the streight line DE , so as it may justly touch those two arks , cutting the line AB in G : so shall BG ( being measured upon the Scale , from the beginning of it ) shew the Azimuth from the South . And AG measured upon the same Scale will give the Azimuth from the North . SECT. 2. To finde the Amplitude of the Suns Rising or Setting . IF you suppose the Sun to be in the Horizon , or 00 gr. high , and so the complement of the Altitude to be 90 , and if ( upon these suppositions ) you work as in the last Section is shewed , then shall BG give the graduall distance of the Suns rising or setting from the South ; AG from the North , and from the midst of the line to G , is the Amplitude from East or West . SECT. 3. To finde the houre of the Day . MAke AB equall to the whole Scale , as before : and count from the beginning of the Scale to the Suns place what number of degrees there are ; the same number shews the graduall distance of the Sun from the North Pole . Of this distance and the complement of your Latitude , finde the sum and difference , and count them both upon the Scale , as was done before . Then again , count thereon also the complement of the Suns altitude : Upon which point , setting one foot of your Compasses , extend the other to the forenamed summe ; and with that extent upon the center B describe the arke CD . Again , setting one foot of your Compasses upon the complement of the Suns altitude , extend the other to the forenamed difference , and with that extent upon the center A , describe the ark EF. Lastly , draw the streight line DE , which only touching the two former arks , may cut the line AB in G : so shall AG ( measured on the Scale , from the beginning of it ) give the degrees of the Suns distance from the South . These may be turned into houres , counting 15 gr. for one houre , and 1 gr. for 4 minutes of an houre . SECT. 4. To finde the Semidiurnall and Seminocturnall arks . IF you suppose the Suns altitude to be 00 gr. and so the complement of it to be 90 , and then work as is directed in the 3. Sect. of this Chap. then shall AG give the Semidiurnall arke , and BG the Seminocturnall arke : Each of these turned into Houres and minutes , and doubled , will give the length of the Day and Night . SECT. 5. The Suns place being assigned in any point of the Ecliptick , to finde his Altitude at all houres . BY this , may Tables of the Suns Altitude be made to all houres , the Sun being in any Signe of the Zodiacke , whereby many particular Instruments for finding the houre of the day , may be made , as Rings , Quadrants , Cylinders ▪ and such like . [ This alwayes , and then only , happens , when the sum ( found at first ) is greater than 90 gr. ] Look then how much it is beyond , for so many degrees is the Sun below the Horizon at that houre of the night : Or ( which is all one ) so many degrees is the Sun elevated above the Horizon in that Signe or point of the Eclipticke which is so much on the other part of the Equinoctiall . That is , If the Suns place given were the beginning of Taurus or Virgo , and your Compasses ( suppose at the 9th . houre ) goe beyond the 90th gr. of the Scale , you shall there see how low the Sun is under the Horizon at 9 a clock at night , or at 3 in the morning . And the same also sheweth how high the Sun is at 9 in the morning , or at 3 afternoon , if his place were in the entrance of Scorpio or Pisces , which two Signes are so much beyond the Equinoctiall on the other part , as Taurus and Virgo are on this side . SECT. 6. All Proportions in Sines alone , where the Radius stands first , may be wrought upon this Scale , without any protraction at all . THe manner of the work will best appear by an Example . Let the proportion set down before in Sines alone be here repeated . The terms stand thus : As the Radius , to the Sine of 23½ ; So the Sine of 10 , to the Sine of what ? Take the sum and difference of the second and third arks , the sum is 33½ the difference is 13½ : count these both upon the Scale , and there take their distance : apply the same to the middle of the Scale ; so as that the same number of degrees may be above 90 , that is below ; so shall the degrees either above or below , be about 4 ; and this is the Sine required for a fourth proportionall to the former . CHAP. VIII . How to work proportions in Sines and Tangents , by the lines of Versed-Sines and ⊙ . Let the Sines ( given or required ) be measured out of ⊙ , and let them be set upon the Radius from A , to AC or AE . Let the Tangents ( given or required ) be measured out of the Versed Scale , from 90 to 00 , or to 180 , which are 90 Chords belonging to 90 equall parts of the Semicircle ABDP , and the same Tangents must ever be set upon the Circle from A , as AB , AD : Then draw a right line through the first and third of the given terms , as from B and C to O ; and another right line from O to D or to E. So the fourth terme required shall be either the Sine AE , or the Tangent AD , each to be measured in its proper Scale . The further use of this line is shewn afterwards in the making of declining reclining Dials . CHAP. IX . To finde the declination of a Plain . TO effect this , there are required two observations : the first is of the Horizontall distance of the Sun from the pole of the plain , the second is of the Suns Altitude , thereby to get the Azimuth . And these two observations must be made at one instant of time , as neer as may be , that the parts of the work may agree together the better . 1 For the horizontall distance of the Sun from the pole of the plain : Apply one edge of a Quadrant to the plain , so that the other may be perpendicular to it , and the limbe may be towards the Sun , and hold the whole Quadrant horizontall as neer as you can conjecture : Then holding a threed and plummet at full liberty , so that the shadow of the threed may passe through the center and limbe of the Quadrant , observe then the degrees cut off by the shadow of the threed , and number them from that side of the Quadrant that standeth square to the plain , for those degrees are the distance required . 2 At the same instant observe the Altitude of the Sun , these two will help you to the plains declination by the rules following . First , By having the Altitude , you may finde the Azimuth by the 1. Sect. of the 8. Chap. then by comparing the Azimuth and distance together , you may finde the plains declination in this manner . When you make your observation of the Suns horizontall distance , marke whether the shadow of the threed fall between the South and that side of the Quadrant which is perpendicular to the plain . For , 1. If the shadow fall between them , then the distance and Azimuth added together , do make the declination of the plain , and in this case , the declination is upon the same coast whereon the Suns Azimuth is . 2. If the shadow fall not between them , then the difference of the distance and Azimuth is the declination of the plain , and if the Azimuth be the greater of the two , then the plain declineth to the same Coast whereon the Azimuth is : Otherwise , if the distance be the greater then the plain declineth to the contrary Coast to that whereon the Suns Azimuth is . ¶ Note here further , that the Declination so found is alwayes accounted from the South , and that all Declinations are numbred from either South or North towards either East or West , and must not exceed 90 gr. 1. If therefore the number of declination exceed 90 , you must take the residue of that number to 180 gr. and the same shall be the declination of the plain from the North . 2. If the number of declination doe exceed 180 gr. then the excesse above 180 gives the plains declination from the North , towards that Coast which is contrary to the Coast whereon the Sun is . ¶ And here note , that wheresoever in this Chapter the use of a Quadrant is required , the Scale of Chords will effect the same ; if upon a piece of plain board you describe a Quadrant , whose sides may be parallel to the edges of the board , upon which you may set off the Horizontall distance and Altitude , which will performe the work thereof when a Quadrant is not at hand . CHAP. X. OF DIALS . To draw upright declining Dials , by the lines of Sines and Tangents . THe declination of the plain being found by the last Chap. Upon your plain describe a rectangled parallelogram , in which let the sides AB and CD be perpendicular to the Horizon , and each of them equall to the Tangent of your Latitude : and let AC and BD be equall each of them to the co-tangent of your Latitude , and let BD be prolonged if need be . Then taking that side of the parallelogram ( for the houre of 12 ) which looketh towards that coast unto which the plain declineth , as here namely , the side AB ; and on that line having assumed the superiour angle A in South-declining-plains , or the inferiour in North-decliners , for the center of your Diall : Let BE and CG be made equall to the Sine of the plains declination , so AE being drawn , shall be the substilar , and AG shall be the houre of 6. Then from E , raise EF perpendicular to AE , and make A 12 and EF equall to the co-sine of the declination : and if you draw AF , the same shall represent the Axis , and the angle FAE sheweth how much the same is to be elevated above the substylar . Again , make AH equall to the co-sine of your Latitude , and draw H6 parallel to AB ; which will cut AG in the point noted with 6. To this A6 , let A6 also beyond the center be made equall , and then draw the lines 12 6 and 12 6 , which lines must have the houre points set upon them ; and to performe that worke doe thus . Draw upon paper , or some other plaine , the line LM , upon which set LR and RM , each of them equall to your Tangent of 45 gr. Then make RN equall to the Tangent of 30 , and RO equall to the Tangent of 15 , so shall you have points to finde all the houres , and if you desire halves and quarters , you must also put their Tangents into the same line RM. Being thus prepared , if you would divide the lesser line 12 6 into its requisite parts , take the same line in your Compasses , and with it , upon L as a center describe the arke PQ , and from M draw MP , which may only touch the same arke . Then from N take the least distance to the line MP , and the same will reach from 12 to 11 , and from 6 to 7 ; so the least distance from O to the line MP , will give from 12 to 10 , and from 6 to 8. And the least distance from R will reach from 12 or 6 to 9. In the same manner you must divide the larger line 12 6. Take it out of your Diall , and with it describe the arke ST from the same center L , and draw MS touching only the same arke . Then the least distances from N , O , R , to the line MS , will give the points or distances 12 1 ; 6 5 ; and 12 2 ; 6 4 ; and 12 3 ; or 6 3. These upon the South-decliner ; the like may be done upon the North-decliner . Lastly , from the center A , through these points you must draw the Houre-lines . An upright plain declining from the South towards the East , 30 gr. An upright plain declining from the North towards the East , 30 gr. In both these Plains . a rectangle parallelog . AB = tang . Lat. BD = co-tang . lat . BE = CG = sine declination . A12 = EF = co-sine declina . AH = co-sine lat . A6 = A6 . RL = RM = tang . 45. RN = tang . 30. RO = tang . 15. CHAP. XI . Of the Horizontall and full South Dials . The upright North plain is the same with the South , only turned upside down , and the course of the figures altered . The East and West upright plains may be made by the Tangent line , in such manner as others have prescribed . CHAP. XII . Of the Scale of Horizontall Spaces . FOr the Horizontall plains in speciall , there is a peculiar Scale by which the houres may sodainly be described , to any Latitude between 30 and 60 degrees . The manner of which work is easie . For you have the numbers from 30 to 60 five times repeated , serving for the five houres in so many Latitudes . Suppose then a Horizontall Diall were to be described for the Latitude of 51½ gr. First , by the Radius ( which is from the beginning of the line to R ) describe a Circle , and draw the line of 12 from the center . Then take from the beginning of the line to VI , and set it in the Circle both wayes from 12 , these two are the points of the two sixes . Again out of the same Scale take the length from the beginning to 51½ in the remotest numbers , and set that upon the Circle on both sides 12 , these are the points of 5 and 7. So from the beginning of the Scale to 51½ in the next remotest numbers , being set as the other were , will give the points of 4 and 8. The third 51½ will give the points of 3 and 9. And the fourth gives 2 and ●0 . The last gives 1 and 11. ¶ The Chord line that is fitted to this Horizontall Scale , is of good use in other delineations : But the further use of these two joyntly , must be referred to another place . CHAP. XIII . How to draw upright declining Dials when the Latitude of the place is very little or very great . IN the work of the 10 Chap. it may fall out that either the Tangent or co-tangent of the Latitude may be too great , such as the Scale wil not afford . This will frequently fall out in the new Latitude of re-in-cliners : to remedy that inconvenience , I have added these helps . Where the Latitude is but small A rectangle parallelo . 1. AB = CD = tang . of Latit . 2. BD = AC = Radius . 3. BE = CG = Sine declination . 4. A12 = EF = cosine of declination . 5. AH = consine of Latitude . 6. H m ♒ AB . 7. Draw EG , it will cut CD in K. AK is the line of six : it cuts H m at 6 , make A6 = A6 , on both sides , and draw 12 6 ; 12 6 ; and divide them as the other are in the 10 Chap. Or you may draw BC the Diagonall , and EK ♒ thereto , and so omit CG . Or you may make the ∠ DEK = to your Latitude , and so omit the two former . Or thus . After the 1 , 2 , 3 , 4 , 5 , you may omit the 6. Then 7thly . Draw EG it will cut CD in K , and AK is the line of six . Then lay a Ruler from 12 to H , cutting DC in L. Make 12M = CL , and AN = AK . So shall KM , MN , be ♒ to the two former lines 6 12 ; 6 12 ; and may supply their Offices somwhat better , because they are larger . Where the Latitude is great . a rectangle parallelogr . 1. AB = CD = Radius , 2. BD = AC = co-tang . lat . 3. BR = CG = Sine declination . GR a right line cutting DB in E. AE Substilar . AG houre of 6. 4. GP = RT = A12 = co-sine of declination . TP a right line , cutting BD in O. AEF a right angle . 5. EF = EO . AF the Style . 6. AH = co-sine Latitude . Hm ♒ AB , cuts AG in 6. A6 = A6 , on both sides . Draw 6 12 ; 6 12 , &c. Or after the 1 , 2 , 3 , 4 , 5. 6. Draw 12 H , it cuts DC in L. Make 12 M = LC : and AN = AG. Then GM , MN shall be ♒ to 6 12 ; 6 12 : and may therefore supply their uses . CHAP. XIIII . Concerning Reclining and Inclining Plains , how to draw houres upon them . THey may be referred to a new Latitude , in which they shall stand as upright plaines : and then the delineation will be the same with those in the 10 Chap. The Meridian line is not here to be taken for the line of 12 at mid-day ( for it often represents the mid-night ) but for that part which helps to describe the Diall . 1. The first thing to be done upon these plains , is ( by some levell ) to draw the Horizontall , and then the Verticall line perpendicular thereto . 2. Next is the placing of the Meridian upon the plain , in a true position . In direct plains that re / in-cline , and in upright decliners , the Meridian is the same with the plains Verticall line . In East and West re / in-cliners , it is the same with the horizontall line . In the rest , it ascendeth or descendeth from the horizontall line , and must be placed according to the rules hereafter given . I. ZB iein-clination . BG ♒ ZO OC co-sine of declination . RC ♒ FO. ORD Radius . DS ♒ BO . Out of this Structure will follow . DAE new Latitude lesse than 90. OR co-sine of new Declination . DS Sine of Meridians ascension or descension . II. ZB rein-clination . BG ♒ ZO . OA Sine of declination . HAI ♒ FO. IO Radius . AM ♒ IO . Out of this Structure will follow . OK is the sine of ZD or ND in the former figure , where the new Latitude DAE will be found . HO Sine of new declination . AM co-sine of Meridians ascension or descension . ¶ How all re/in-clining plains ( being counted as upright in their new Latitude ) are to be taken ; whether as North or South decliners . As also , ¶ How the Meridian line is to be placed , whether ascending above , or descending below the horizontall line : and from which end of that line , whether that which looks the same way with the declination of the plain , or that which looks the contrary way . In North re / in-cliners . If D fall below P , the Recliners are North plains , and the Meridian ascends above the horizontall line , from that end of it which looks to the same Coast of declination . Incliners are South plains , and the Meridian descends below that end of the horizontall line , which looks to the contrary Coast of declination . If D fall above P , the Recliners are South plains , and the Meridian goes below : contrary , Incliners are North plains , and the Meridian goes above the end looking the same way with declination . In South re / in-cliners If D fall above AE , the Recliners are North plains , and the Meridian goes above the horizontall line , from the same end with the Coast of declination . Incliners are South plains , and the Meridian goes below the horizontall line , from that end which is contrary to the Coast of declination . If D fall below AE , the Recliners are North plains , and the Meridian goes below the horizontall line : contrary , Incliners are South plains , and the Meridian goes above the horizontall line , from that end which looks to the Coast of declination . If D fall into P , both re / in-cliners , are called Polar plains , and the Meridian , in both , ascends from the Same end in Recliners . contrary end in Incliners . If D fall into E , the Recliners are North plains , and the Meridian ascends from the same ; descends from the contrary end to that which looks upon the Coast of declination . Incliners are South plains , and the Meridian ascends from the contrary ; descends from the same end that looks upon the Coast of declination . ¶ East & West Recliners are North plains , declining from North , So much as the complement of their re / in-clination comes to . This is their new declination , & their new Latitude is the complement of the Latitude of your place . Incliners are South plains , declining from South , 4. For that which follows , take notice of these four things . First , That from D to the neerest AE ( measured by the line of Chords ) gives the new Latitude , in which the re / in-clining plain , is an upright declining plain . Secondly , That OR ( measured upon the line of Sines ) gives the complement of the plains new declination in that new Latitude : this New declination is to the same Coast with the Old , but alwayes lesse in quantity than it . Thirdly , That DS ( measured upon the Sines ) gives the quantity of the Meridians ascension or descension . This gives the quantity , the former rules gave the Coast . Fourthly , That in the description of the Diall , you must only make use of the new Latitude , and new Declination : having nothing to doe with the other . 5. Having the former things known , you must ( by the Tangent and co-tangent of the new Latitude ) describe your Rectangled Parallelogram ( as in the 10 Chap. ) and according as the plain was discovered to be a decliner from the North or South , you must make choice of your center , place the substylar , style , and six a clock line , by help of the Sine and co-sine of the new declination , and new Latitude , and then prick down and draw the houres , all in the same form that was before shewed in the 10 Chap. for upright decliners . This for the Dials description . 6. Lastly , for placing your Diall . First , Consider which way , and how much , your Meridian ascended or descended from the horizontall line . Then goe to your plain , and there draw the same Meridian line answerably , setting off so many degrees by your Scale of Chords . When this is done , take your paper description , and lay the Meridian of it , either upon , or else parallel to , the Meridian drawn upon the plain , and take care to place it the right way ; namely so , as that the imaginary style of your paper ( or a reall pattern of the style cut fit and set upon the paper Diall ) may point into the North or South Pole , according as the plain is esteemed to be a North or South plain . After this is performed , you may transfer each houre from the paper to the plain , and so finish all the work . CHAP. XV . Concerning full East and West re-in-clining plains . HEre in this sort of plain , you are only to take notice , that the new Latitude ( wherein they stand as erect plains ) is ever the complement of your own Latitude . And the new declination ( in that Latitude ) is the complement of their re / in-clination . By knowing these , you may describe the diall according to the 10 Chap. The Meridian line ( in all these ) lyeth in ( or parallel to ) the horizontall line . All which things will appear also out of the former figures , if according to them you should make a draught , and suppose your plain to decline 90 degrees , as all these East and West plains do . All other things will follow of themselves , agreeable to other plains . CHAP. XVI . Concerning re-in-cliners , that are direct , or have no declination . IF the line CB be placed ( as is prescribed in the former figure ) and drawn quite through , it will represent your plain that is re / in-clining towards the North , and without any declination . So also BL , if it be drawn quite through , will represent such plains as re / in-cline towards the South , and have no declination . For which lines so drawn ( or imagined only ) you may gather ( according to the former rules ) which of the Poles ( A or X ) is elevated , and how much it is elevated ( which is shewed by the arke CA or LX . ) You may also see which end of the Meridian is to be taken for the substilar line , over which ( in these direct plains ) the stile is ever to be erected , and must stand . Then for drawing the houres , you have no more to doe , but to describe an Horizontall Diall to that elevation , which is due to the plain . The manner whereof is shewed before in the 11 Chap. CHAP. XVII . How to deal with those plains , where the Pole is but of small elevation . SUch plains whose styles lie low , cannot have the houre-lines distinctly severed , unlesse the center of the Diall be cast out of the plain . In such cases therefore the Diall is to be made without a center , in this manner . 1. Place AB the Meridian , A● the substilar , AF the style , by the rules before given in the 10 and 13 Chapt. omitting what is done for the line of six , being here of no consequence . 2. Finde the plains difference of Longitude by the 18 Chap. following . 3. Assume any two points in the substilar AE , as at R and S , and through them draw two infinite right lines , at right angles to AE . 4. To the style AF , draw the parallel GH , at any convenient distance , such as you shall think fit , for your new style to stand from your plain . 5. Take the least distance from R to GH , and set it upon the substilar from R to K. So from S to GH , set from S to L. 6. Upon the two centers K and L , describe two Circles : And in them both , make the two angles RKM , SLM , equall to the plains difference of Longitude ; and set it on that side the substilar RS , upon which the Meridian AB standeth . 7. The rest of the work will be easie to finish , if you begin ( in each circle ) from the points at M , to divide them into 24 equall houres ; and from the centers to those equall divisions , draw out lines to cut their respective contingent lines in 12 , 11 , 10 , &c. And from each correspondent houre , you must draw the lines 12 12 , 11 11 , 10 10 , &c. An Vpright Plaine declining from South towards East 80 gr. Difference of Longitude 82d 08 ' South Pole elevated 6 12 CHAP. XVIII . Having the Latitude of the place , and the plains declination , to finde the plains difference of Longitude . IT must be understood , that the plain is supposed ( in this work ) to be alwayes erect ; and that therefore for re / in-clining plains , the Latitude and declination here mentioned is meant of the new Latitude and new declination . Two wayes to doe it . Make ABC a right angle . I. AB Sine of new Latitude . BC Tangent of new declination . BAC is the difference of the plains Longitude from your Meridian . Make DEF a right angle . II. DE Radius . EG Sine of new Latitude . EF Co-tangent of plains new declination . Draw GH parallel to DF. HDE is the complement of the difference of Longitude . Or DHE is the difference it felfe . If this work be done for upright plains in your own Latitude , which will be needfull in far decliners , then instead of the new Latitude and new Declination here mentioned , you are to use your own Latitude , and the upright plains Declination . The new Latitude and Declination are for re-in-clining plains . CHAP. XIX . Of Polar Plains , on which the Pole is not elevated at all . THose are called Polar plains , upon which neither of the two Poles is elevated at all , but the plaine lies parallel to the Axis , such are the upright East and West : and in every declination from the South some one recliner : in every declination from the North some one Incliner . The new declination of all Polar plains is their difference of Longitude , in these you must work by the 10 and 14 Chap. to place AB the Meridian , AE the substilar ; & for the style AF , it hath no elevation from the substilar , but is the same with it . So that the work will be much like that in the 17 Chap. Make GH for the style , parallel to the substyle AE , at some convenient distance . Then assigning any point in the line AE , as S , through it draw an infinite right line perpendicular to AE . And take the least distance from S to GH , make SL equall thereto . Upon L describe a circle , and make SLM equall to the difference of Longitude , on the same Coast from SL unto which the plain declineth , or to the same Coast upon which the first line of 12 namely AB standeth . Then having found the houre points upon the line which passeth through S , namely , 6 , 7 , 8 , 9 , 10 , &c. draw lines through them , all parallel to thē substilar AESL . CHAP. XX . Another way to prick down the hourepoints , by the Tangent line on the Scale . LEt the first four Sections of the 17 Chap. be performed according to the directions there given . After them , you must gather the angles at the Pole , by help of the plains difference of Longitude in this manner . Let the former example serve . The difference of that plains Longitude will be 82 gr. 08 ' . Out of this , take the greatest number of some just houre ; viz. 75 gr. The remainder is 7 gr. 8 ' . Having then set down the substile 00 00 , as in the Margin , write this 7 gr. 8 ' . next under it , to which adde 15 gr. continually , and you shall produce all the following numbers as you there see them . And note , that in this work 82 gr. 8 ' . the difference of Longitude will ever stand against the houre of 12 , if you work right . Then take the first number 7 gr. 8 ' . out of 15 gr. the remainder is 7 gr. 52 ' ; set this above the substyle , and to this number adde continually 15 gr. ( or one houre ) the numbers will be produced such as you here see .   gr. ' 3 52 52 4 37 52 5 22 52 6 7 52 Substyle 00 00 7 7 08 8 22 08 9 37 08 10 52 08 11 67 08 12 82 08 When this is done , draw a right line , therein assuming the point S or R. Then upon your Scale of Tangents , count the numbers 7 08 , 22 08 , &c. in the Table , and take them off from the same Scale , setting them severally from S to a , b , c , d , e. So again , upon the same Scale of Tangents count the other numbers , 7 52 , 22 52 , 37 52 , &c. and take them off thence severally , and place them from Sat f , g , h , i. But because the tangents upon the Scale goe but to 63 gr. 26 ' , it must therefore here be shewed how those that exceed that quantity may be supplyed . Namely thus , Double the number of degrees and minutes , and from the sum take 90 gr. so shall the Tangent and Secant of the remaining arke ( both of them put together ) give the Tangent required . As if in the former example , it were required to finde the Tangent of 67 gr. 8 ' noted upon the line by the length S e , we must doe thus . The double of 67 gr. 8 ' is 134 gr. 16 ' , from which takeing 90 gr. the remainder will be 44 gr. 16 ' . Accordingly we must first take the Secant of 44 gr. 16 ' , and set it from S to y ; then take the Tangent of the same 44 gr. 16 ' . and set it also forward from y to e , so shall you have S e the whole Tangent of 67 gr. 8 ' . as is required . Thus doe for any other which shall goe beyond the Scale . CHAP. XXI . A second way for re-in-cliners . TAke notice of these terms . 1. Verticall distance , is the distance of the plains pole from the Vertex or Zenith of the place . 2. Polar distance , is the distance of the plains pole from the North pole . Preparatory works . 1. Draw the horizontall line upon the plain , and crosse it at right angles with a Verticall line . 2. Get the plains re / in-clination , and consequently the distance of the plains Pole from the Zenith of the place : which is here called the Verticall distance . 3. Get the plains declination , and alwayes account how much it is from the North . For that is here called the angle of Declination . SECT. 1. By the Scale of Versed Sines , how to finde the elevation of the Pole above the plain : and which Pole it is , whether North or South , that is elevated . First , finde the summe and difference of The complement of your Latitude , The plains Verticall distance . And observe likewise , that If the point of your Compasses ( applyed to the Scale ) doe fall just upon 90 , then is your plain a Meridionall or Polar plain , and hath no pole elevated above it . If it fall short of 90 then is the North Pole elevated ; and the elevation is so much as the point fals short of 90. If it fall beyond 90 , so much as it falls beyond , so much is the South Pole elevated . SECT. 2. To finde the plains difference of Longitude from the South part of your Meridian , and which way the said difference of Longitude is to be taken . First , finde the sum and difference of The complement of your Latitude , The fore-mentioned polar distance . Then make AB equall to your whole line of Versed Sines . And upon your Scale count your difference now found , and the fore-mentioned verticall distance , taking the distance of these two as they are numbered upon the Scale . With which length upon A , describe the arch CD . Take also upon the Scale , from the verticall distance to the fore-mentioned sum , and with that length upon B , describe the arke EF. Then draw the line FC , so as to touch both these arks , cutting the line AB in G : so shall AG ( being measured upon the Scale ) give the plains difference of Longitude from the South , which is here required . ¶ This difference of Longitude is to be taken to the same Coast in the heavens unto which the plain declineth , and may afterwards , in the description of the Diall , be easily accounted either from the South or North part of the Meridian , viz. so as that the said difference may be alwayes lesso than 90 gr. SECT. 3. To finde how much the Substilar ( or plains proper Meridian ) must lie from the Verticall line of the plain , and which way . Frist , Finde the summe and difference of The Polar distance , The Verticall distance . Then make AB equall to your whole Versed Scale . And on the same Scale , take the extent from the complement of your Latitude to the difference now before found , with which length , upon A as the center , describe the arke CD . Also upon the Scale , take from the complement of your Latitude to the summe here before found , and with that length , upon the center B , describe the arke EF. then draw the line FC , justly touching both these arks , and cutting the line AB in G , so shall AG ( being applyed to the Scale ) give the quantity of the angle here required . According to this angle the substylar line must alwayes stand off from the verticall line of the plain . Which way must the Substilar lie from the Verticall line . If the plain hath the North Pole elevated upon it , then must the substilar alwayes lie from the upper end of the Verticall line towards the North Pole , so much as the angle was ( in the last Section ) found to be . If the South Pole be elevated , then the substilar lyeth alwayes from the lower end of the verticall line towards the same South Pole , according to the forenamed angle . If the plain be Meridionall ( upon which neither of the Poles is elevated ) then the substilar must doe either , or both ; these two : according to the angle before found . According to these Rules you may place the substilar line upon the plain in its true position requisite . SECT. 4. To draw the houre-lines upon the plain . FIrst , consider by the first of these Sections , whether it is the North or South pole that is elevated upon your plain . If it be the North pole , then must the center of your Diall stand downward , and the style must point upward to the said North pole . But if the South pole be elevated , then the center of the Diall is to be set upward , and the style comming from thence must point downwards into the South Pole . Lastly , From the center of the Diall A or B , and through the said unequall parts , draw right lines . These last lines shall give you 12 of your houres required : And if you draw each of them quite through the center , you shall have the whole number of 24 , of which , you may take such as are sutable and necessary for your plain . When your paper Diall is thus finished , you may transfer it to your plain , by laying the substilar upon ( or parallel to ) the substilar before placed upon the plain , and so insert all the houres from the paper to the plain . After all this , you may make the style to the angle of the Poles elevation , and fit it in according to its requisite place and position . ¶ Note , that because some of the houre points found in the Circle will happen so neere to the center of the Diall that you cannot well draw the houre-lines true ; you may therefore help your selfe by that direction which I have given in my Geometricall way . [ This Geometricall way shall shortly be published by the Authors own copie , with his own Demonstrations of the whole work . ] For drawing houres upon plains that have small elevations , and upon Polar plains , use the former directions . CHAP. XXII . A third way for all re-in-clining Dials . SECT. 1. To finde a re-in-clining plains difference of Longitude from the South part of your Meridian : and how much the plains Meridian or ( substyle ) must lie from the Verticall line of the plain .   I. II. III. Complement of your Latit . 38 30 K 38 30 K 38 30 K Plains verticall distance . 100 00 Z 60 00 Z 30 00 Z Their Summe . 138 30 98 30 68 30 Their Difference . 61 30 21 30 8 30 Their halfe Summe . 69. 15 R compl. 20 45 V 49. 15 R comp. 40. 45 V 34. 15 R compl. 55. 45 V Their halfe difference . 30. 45 S. compl. 59. 15 X 10. 45 S compl. 79. 15 X 4. 15 S compl. 85. 45. X Plains declinat . from Sou. 50. 00 Y 140 00 Y 160 00 Y Describe a Circle with your common ( or lesser ) Scale of Chords . And out of the same Scale make A Y = plains declination from South . Out of the line ⊙ make A R = R , and A S = S , & draw Y R M and M S B and make A D = A B. Out of the same line ⊙ make A V = V , and A X = X , and draw Y V N , and N X C. ¶ Then if K be lesse than Z C A D is the differ . of Longitude required . and C B is the angle between the substile & the verticall line . ¶ But if K be greater than Z C A D is the forementioned angle . and C B is the difference of Longitude . These two arks C D and C B , must be measured from 90 in the line of Versed Sines , and looke what number of degrees they there cut , the same must be accounted for their quantities . SECT. 2. To finde the elevation of the Pole above the plain : and which of the Poles it is , whether North or South , that is elevated . MEasure A B upon the Versed Sines ( from 90 ) as before : the complement of that is E B. Measure also E C upon the same Scale , in the same manner . Count these quantities E B and E C ( so found ) upon the line ⊙ , and set them from E , to F and G , and make Er = R ( taking E r out of the Scale of Versed Sines from 90 ) Draw r F O , and O G P. Measure E P upon your Scale of Chords , it will there give you the polar distance . If E P fall to be 90 , it is a Meridionall plain , and hath no Pole elevated . If it be lesse than 90 , the complement of it is the elevation of the North Pole . If it be greater than 90. the excesse is the elevation of the South Pole . ¶ Note , that the three figures following have relation to the three Columns of the foregoing Table ; and to these rules last delivered . Figure I. In this first Figure C A D 62 49 C B 34 13 E P 122 00 Figure II. In this second Figure C A D 110 29 C B 42 19 E P 36 28 Figure III. In this third Figure C A D 118 26 C B 44 56 E P 14 00 SECT. 3. Which way must the Substilar lie from the Verticall line ? THe Rules are the same with those before in the second way of Dialling , where the same Question is propounded . You may therefore have recourse to them . Or thus . Upon all plains whereon the North pole South pole is elevated ; the substilar must lie from the upper end lower end of the Verticall line towards the full North . South . For drawing the houres , and finishing the Diall , you must doe as is prescribed in the 4th . Sect. of the former second way . For , having placed the Substilar , and knowing the plains difference of Longitude , you are to use the same course here that was there given . It will be easie to doe these things in plains that are upright , and have no re-in-clination . Note in all these three wayes of Dialling . All directions here given suppose you to be in the Northern Hemisphere of the world . If therefore you should be in the Southern Hemisphere , you may easily make these precepts serve there too , by only altering the name of North , Northen , &c. and South Southern , &c. one into the other . FINIS . This Scheme hath relation to the 16th . Chapter , page 54. Errata . Page 32 , in the Diagram , for H P G , read H F G. Page 51 , for , If D fall into E , read , If D fall into Ae . Page 54 , line 16 , for For , read From . In the Diall Page 57 , at the other end of the line M , place the letter K upon the Substilar . Page 62 , line 19 , for L P , read S P. In the Diagram page 76 , the letter R is wanting , at the intersection of the line Y M , with the line A E. Notes, typically marginal, from the original text Notes for div A40034e-1660 The wayes how to effect these are shewed other-where , and are here taken as known . 
A85919	----	The first lecture of an introduction to cosmographie: being a description of all the vvorld. Read publiquely at Sr. Balthazar Gerbiers academy. Imprimatur, Hen: Scobell, Cleric: Parliamenti. Gerbier, Balthazar, Sir, 1592?-1667. This text is an enriched version of the TCP digital transcription A85919 of text R206228 in the English Short Title Catalog (Thomason E584_6). Textual changes and metadata enrichments aim at making the text more computationally tractable, easier to read, and suitable for network-based collaborative curation by amateur and professional end users from many walks of life. The text has been tokenized and linguistically annotated with MorphAdorner. The annotation includes standard spellings that support the display of a text in a standardized format that preserves archaic forms ('loveth', 'seekest'). Textual changes aim at restoring the text the author or stationer meant to publish. This text has not been fully proofread Approx. 29 KB of XML-encoded text transcribed from 11 1-bit group-IV TIFF page images. EarlyPrint Project Evanston,IL, Notre Dame, IN, St. Louis, MO 2017 A85919 Wing G558 Thomason E584_6 ESTC R206228 99865402 99865402 117642 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A85919) Transcribed from: (Early English Books Online ; image set 117642) Images scanned from microfilm: (Thomason Tracts ; 89:E584[6]) The first lecture of an introduction to cosmographie: being a description of all the vvorld. Read publiquely at Sr. Balthazar Gerbiers academy. Imprimatur, Hen: Scobell, Cleric: Parliamenti. Gerbier, Balthazar, Sir, 1592?-1667. England and Wales. Parliament. [4], 16, [2] p. for Robert Ibbitson dwelling in Smithfield neer Hosier Lane, Printed at London : 1649. The last leaf is blank. Annotation on Thomason copy: "Decemb: 1st". Reproduction of the original in the British Library. eng Astronomy -- Early works to 1800. Cosmography -- Early works to 1800. A85919 R206228 (Thomason E584_6). civilwar no The first lecture of an introduction to cosmographie:: being a description of all the vvorld. Read publiquely at Sr. Balthazar Gerbiers aca Gerbier, Balthazar, Sir 1649 5330 4 0 0 0 0 0 8 B The rate of 8 defects per 10,000 words puts this text in the B category of texts with fewer than 10 defects per 10,000 words. 2007-04 TCP Assigned for keying and markup 2007-06 Apex CoVantage Keyed and coded from ProQuest page images 2007-08 Angela Berkley Sampled and proofread 2007-08 Angela Berkley Text and markup reviewed and edited 2008-02 pfs Batch review (QC) and XML conversion The FIRST LECTURE of an Introduction to COSMOGRAPHIE : BEING A Description of all the VVORLD . Read Publiquely at Sr. Balthazar Gerbiers ACADEMY . PSALM . 8. ver. 3. 4. When I consider the Heavens , the work of thy fingers , the Moon and the Starres which thou hast ordained : What is man , that thou art mindfull of him , and the Son of man that thou visitest him ? Imprimatur , Hen : Scobell , Cleric : Parliamenti . Printed at London for Robert Ibbitson dwelling in Smithfield neer Hosier Lane , 1649. To the Right Honorable William Lenthall Esq ; SPEAKER Of the most Honourable Assembly of PARLIAMENT . Right Honourable , I Shall not need ( as I humbly conceive ) to seek farre for a just argument that the Dedication of this Lecture ( being an Introduction to Cosmography , read in the Academy , which I doe zealously labour to settle , for the glory of God , the honor of this Nation , the encouragement and improvement of all Lovers of Vertue : ) belongs to your eminent place of Trust , And from whose determinations , as from the highest Influences of so many Stars , guide , direct , move , and preserve the whole Body of this Common wealth . My Academy-Reader in part to make good my more large intentions , having begun with Cosmography ( as the most noble subject to read on ) presents therefore these his first productions to your honourable hands , as an unquestionable duty , and with all Submissivenesse , and possible reverence , wishing that the State may please not only to protect these hopefull beginnings , but likewise to cherish and promote them . That all Lovers of Vertue may receive content and profit thereby , and the Nation glory , that such capable spirits need not to runne unto Salamanca in Spaine , to Padua in Italy , no● to Paris in France , there to seek ( with hazard of their godlinesse , goodnesse and Loyalty to their Native Country ) that which they may have at home , with more ease and safety , and with lesse charge to themselves . And if in this case the lawfull interest of a particular zealous well-wisher to the State may be comprehended , I shall with a joyfull confidence conclude , that I have not been ill-perswaded thereunto , nor can I have a greater hope , or reap a greater contentment , than by putting my hand to so good a work , which giving me an assured confidence that my indeavours may meet with a favourable acceptance from Your Honour , unto whom I shall remaine as I was long since , Your Honours most humble and most obedient Servant , Balthazar Gerbier . From the Academy this 28 of Novemb. 1649. The First Introduction to COSMOGRAPHY . COSMOGRAPHY is the description of the celestiall and elementary Region . In the celestiall Region , we learne to know Heaven , its matter , its qualities ; The Planets , their motions , and their order , &c. In the Elementary Region , we see the most admirable construction of the Elements , the which by their unequall proportioned assemblings , do compose the severall sorts of kindes , of mixt ones , which wee see here below . All this we shall particularly describe with their qualities , properties , and scituations . And in that Region which seemes for a Center unto the universall world , we shall see an innumerable number of most remarkable , satisfying and most necessary things to be observed , viz. The proofes of its circular forme : whether the Earth or Water exceeds the one or the other in quantity : The scourses or heads of Springs and Floods , the smallnesse of the terrestriall globe , not onely in comparison of the Heavens , but also of the Sun , and of the Stars : And how that the said Earth may be measured , both on its superficies , and on its solidity . Afterwards we shall describe the circles which are to be imagined in the Heavens , That so we may learn the course of the Planets , and the various effects which we feele by them . As the causes of their rising and setting , of the Summer and Winter , of the long and the short dayes , So also we must have regard to the Solstices , and Equinoxes , from whence the different constitutions of the Earth do proceed , and severall other things , the curiosity whereof , as its extreame commendable , so its familiar incidents prove altogether necessary unto those who are desirous to passe for men of knowledge and understanding . And that we may end in our owne sphere , we will finish with a Lecture on the Meteors , wherein all the impressions that are made as well of Fire , as of the Aire , and of the water ; both in the high , middle , and low Region of the Aire , shall be clearly shewed and set forth unto our view . That is to say , whence the fiery impressions proceed , and how those impressions are framed which are seen in the high Region of the Ayre , viz. Like unto fiery Darts , Launces , Flying Stars , and Commets , and how it happens that the Heavens themselves seem to be sometimes al on fire , whence the lightening , thunder and thunderbolts proceeds : whence the wild fire , glow-wormes , and such like , have their being : And so consequently , we will treate of the impressions framed in the Aire , as the winds , stormes , and the whirlewindes : Those of the Waters , as the Clouds , Raine , Snow , and Hail , which are framed in the middlemost Region . Then we will proceed to describe other impressions which are not real ones , as that Crown of resplendant rayes , which seems to be about the Sun , the Rain-bow , and the like ; from thence we shall descend lower , and observe from whence all Fogs , Dewes , Mists , Frosts , and Ice proceeds . Finally , we will end with the three kinds or species contained in the Earth , as Mineralls , Vegetables , and Animalls ; observing in the Mineralls , their generation in the bowells of the Earth , their qualities , and connexions , and how they chance to be seven , correspondent to the seven Planets . Moreover we will treate of all kind of Stones , as also of the sappes conducing in the Mines , like unto Vitriol , Allum , and such like , which depend of these . In the ingendering of the vegetables , we are to consider the nature of plants , their faculties in producing their severall effects , and their multiplying by their seed ; after all , wee will conclude with the Animalls , the which besides their vegetating Soule and faculty of budding , and shooting forth , have over and above the sensitive part , which gives them both feeling and motion , and these are much esteemed above the Plants , all their organs , and naturall parts being much perfecter then those of the others . But of these these are two sorts , the rationall and irrationall , Man and Beast ; but we shall leave the beasts , for to speake of rationall creatures , it being more proper in this place , Let us then say that man , far more worthy then all other things , was created by God , for that by his word all things were made , fiat lux , Genesis the second , and the light straight appeared : But when God came to make man , he formed him , Formavit Dominus Deus Hominem de Lima Terrae : Et inspiravit in faciem ejus spiraculum vitae , & factus est homo in animam viventem , And both animated and endowed him ( besides the precedent said qualities ) with an intellectual soule , of which both the understanding and wil of man depends . Now let us consider I beseech you , how the Mercy of God hath alwayes augmented some degree of perfection in each Body , for to compleate in man a fulnesse of the perfection of all his workes , and how hee hath placed him as a King to command over , and to make use of the aforesaid things , Et praesit piscibus Maris , & volatilibus Coeli , & bestiis universaque Terra , omnique reptili quod movetur in Terra . All which are only made for mans use and advantage . For God was no lesse before the world then he is now , and hath no need of any of the creatures to bee more glorious , wee ought therefore to have a great and deep sense of acknowledgement . And that our labour be not in vaine , we must consider that great Architector in his wisdom , in his power , in his liberality , and in his bounty , we must adore him , honour him , and admire him in all his Attributes , and thanke him incessantly , not onely for the present meanes ( the vicissitude of which sufficiently shew their vanity ) but for the hope of eternall blessings , to which hee hath designed us , provided that we prove true by faith , and that we make good by our workes , that we acknowledge him above all things ; but alas ! unhappy men as we are , in what an Age doe we live ? wherein the creature is more praised then the Creator , the gift is perfected to the giver ; and that which we should but take notice of , as a transitory thing , we do abuse oft ( Christian prudence permitting and willing it ) by a most horrid blindnesse , preferring those things unto the Author of them , which are but created in order according to Nature . Therefore the most insensible things , and most inanimate ones , both dictate unto , and convince those with a most horrid shame and confusion , who dare so boldly and impudently abuse that great Author , Guider and preserver of all things . But he will not be abused doe what thou canst , O inraged Atheist , thou perverse wit , of the most perverse times ; for he will make thee confesse thy wilfull malice in the day of vengeance , when thou shalt not be able to pleade ignorance ; since as thy senses condemne thee , so doe likewise the Elements , which at all times seek their proper places , the Fire being light , ascends ; the Aire not so light , remaines in the lower sphere ; the Earth , the heaviest of the foure , keepes to its Center ; and the Water lesse heavy , swims above it . Now as those things that are mixt , have one of the Elementary qualities in one eminent degree above the other , so they seek their sphere , & do not rest til they have attained unto it : For a ston would descend even to the center of the Earth , if there were an overture in it , as being the most properest place of its abode , being its altogether terrestriall . We see that wood swims above the water , and the reason is , that there is more Aire and Fire in its composition , then either in the Water or in the Stone . And let man do what he will , it shall ever be so , because that God hath created them , and bestowed on them those properties , of lightnesse and heavinesse , which causeth those motions , making the light things to ascend , and the heavy ones to descend , and since Gods will is inviolable , all things must obey it . Now let us come to Man , made by God as well as all the other Elements , and likewise all other things , and to what end made God Man ? only to admire his greatnesse , and to adore him , which certainly is the sole reason why God made man according to his owne resemblance , and indued him with a rationall soule , and a sensible appetite or desire . Unto what can man then more fitly apply that sensible appetite or desire , but to follow in all things , the designe and intent of his Maker , from the beginning to the very end of his life : And this doubtlesse is the true reason of mans being , and the true vocation man ought to apply himselfe unto : And no more to vary therein , then the Stones change their property of descending , nor the Fire its course of ascending : God hath created thee Oh man to this effect , and intent , but if thou wilt not follow his dictates , to what serveth thy intellectuals , thy knowledge , and thy will , save only to harden thy heart against God , and against his will , far more then all inanimate creatures do , and hereby to hinder the effect of his graces in thee ; wherfore we ought seriously to meditate hereon , and to rest assured , that if so bee wee doe abuse the Tallent , which we have received , by rendring more honour unto vice , and unto our stubborne , lawlesse senses , than unto God ; we shall render our selves unworthy to be placed even beneath the insensible things , and that instead of an eternall blisse , for the which we were created , we shall most justly deserve to indure eternall torments , from which God in his mercy preserve us all , and grant unto us that true sense of reason , which may preserve his true Image and workemanship in us , and inable us to destroy our owne , voide of sensuality . Dele quod fecisti , ut Deus salvet , quod secit : saith Augustine . Now let us enter into some particulars , concerning the treaty of the severall parts of the Universe , or World ; particularly described by this Science of Cosmography , which may stand us in stead for the present , and so enable us for the future , that we may be the better disposed , to contemplate the same from above . What the Sphere is . THe Science or understanding of the Sphere , is the knowledge , or the being acquainted with the particulars of this worlds parts , and properties : The world is the assembling , and ordering of all that God hath created , it s the composure of Heaven , and of Earth , or of the Celestiall and Elementary Region , and therefore it is called the Universe : And to the end that we might have a more particular insight in this Science , an Artificial Sphere hath been framed , being of a round forme , composed of sundry circles , by the which , though imaginary ones , the motion of the Heavens are described : The reasons of the severall changes in the seasons of the yeare ; that of the difference of dayes and nights , according to the severall places and scituations or the terrestriall Globe . Finally by the Sphere , you may observe the whole course of the world , being it was made according to the worlds resemblance . What the Heaven is . AS we are not resolved to build Castles in the Aire , nor to entertaine our Auditory with imaginary things , but to give most evident proofes of what we alledge , so it will be necessary to make appeare unto you that there is a Heaven , before we come to distinguish its qualities , and herein we shall meet with no great difficulties ; since that Nature admitting of no emptines , that space which is between , the Firmament , the Imperial Orbe , and the lowermost of the Planets , to wit , the Moon , must of necessity be filled with some matter ; And this matter is called Heaven , which is both simple , sollide , fixt , shining , transparent , incorruptible , and exempted from any changes . Of the qualities of Heaven . ALL naturall things have two principles , first God , secondly Nature , unto which hee hath given full power to work by a certaine universall spirit , which he hath inclosed in her . All naturall things are corporall essences , which subsist of themselves , and result from the union of the substance , and of the forme : So that Nature then consisting in these two points , substance , and forme , all naturall bodies are ingendred by the substance of it , and the forme makes them to be what they are . But the matter being susceptible , of divers formes , having not so soone quitted one , but that it receives another : And for as much as it cannot receive a second , before it be deprived of the precedent , therefore the Philosophers have establisht three principles ; the substance , forme , and privation : Now there are two sorts of natural bodies , the one simple , the other mixt : The simple bodies are the Heavens , and the Elements , because that in their creation they are simple , and never admit of severall formes , on the contrary , the mixt ones , are such as receive their composition from the Elementary qualities , and are susceptible of divers formes . The matter of the Heaven is therefore simple , as likewise solide and fixt . Because that the Starres , which though they do turne , and have moved since the beginning of the World , yet they never change nor vary their figures , nor the distances which they observe betwixt each other : Now this order could never have been kept , unlesse some solide matter had constrained them thereunto , which cannot be by any other thing , then by the solide and fixt matter of the Heaven : Likewise it 's the opinion of the most learnedest ancient Astronomers , and all those who have written on this subject , besides the most approved Authorities , That the Stars are of the same matter that Heaven is of , save of a more dusky and danky substance , which they have adjudged them to be of , by reason that they stop , and as it were , hinder the light of the Sunne ; the which Heaven doth not , as we shall shew hereafter : Moreover they alledge the Stars are just in Heaven , as knots are in boards ; others deem the Stars and Planets to be in a continued Aire like as the birds are : But then there ought to be many particular properties for to maintain the Stars in so permanent and immutable an order , against the violent swiftnesse of so many contrary motions , which opinion I shall wave , as well as the flight of their Birdes . The matter of the Heaven may bee said to bee of an abundant luster : since that the Sunne , the Moon , and the Stars are so , all which are comprehended of the same matter : But to speak more properly , the matter of Heaven is transparent , and the Sun and the Stars are not . That the Heavens are transparent , is very easie to prove , since experience sufficiently denotes it unto us : For if the Heaven of the Moon were dusky , it would hinder us from seeing of the Sunne , and the rest of the Stars which are about it . That the Sun , the Moon and the Stars are dusky , is apparent by their Eclipses : This matter is also incorruptible , and consequently exempted from all changes , since that it 's simple , and that in those Scituations , or Regions , generation finds no imployment . Of the Celestiall Region . THe Celestiall Region , is the assembling of all the Heavens , and comprehends them all intirely , the order and course whereof shall be shewn in its proper place . Their matter or substance as we have proved , is sollide , so is that of the Stars , and Planets , but more dusky and danky , that is to say , their matter is more close and compacted , and since they are most pure and polished bodies , they receive , and cause the light which they borrow from the Sun , to reverberate , as shall be proved hereafter , but as for the Heaven it 's altogether transparent . Now in the Celestiall Region , there are two sorts of Stars , Fixt , and Errants ; the Fixt are those that never change their figures , but have all one and the same motion , which is that of the Firmament : The Errant Stars are the Planets , which have all different motions from that of the Firmament , and they are seven in number ; unto which the Ancients have given the names of their Deities , viz. Saturne , Jupiter , Mars , Sol , Mercury , Venus , and the Moone , which names were likewise appropriated unto them , because of their powerfull influences . The duskey matter , is that which gives no passage to the sight , as you may perceive in Wood , and in the Stones . The solide and fixed matter is that which will not suffer any very easie penetration , as you may observe in Chrystall , or in glasse . But the penetrable matter is that which suffers the peircing with ease , as the Aire doth , the Water and the Fire . The transparent matter is that which gives passage to the light , as Chrystall , and Glasse doth : And so consequently , we may justly infer , that the Heavenly Matter or Substance , is both solide , fixt , impenetrable , and transparent That there are many Heavens . BY the diversities of the Motions , we prove that there are many Heavens , thus ; since the matter is solide , two Planets having different motions , cannot be in the same Heaven , or Orbe , and by this same reason you may observe , that it s not the Planet which moves , but its Orbe , or Heaven ; for otherwise they would penetrate the matter , which is both fixt and solide : But the Sun and the Moon have different Motions , for that the Sunne accomplishes its course in a day , and the Moone in a Month ; then the Sun and the Moon cannot be in one and the same Orbe , or Heaven : And by the same reason , no two of al the seven Planets having the self-same Motion , there must then of necessity be seven Orbes , or Heavens , requisite for the seven Planets : since also the matter of Heaven is fixt , and impenetrable : Against this may be objected , that there might be but one Heaven of an impenetrable matter , in the which many spaces may be imagined , and by which the Planets having different Motions , may make their courses . And let them say what they please , yet it will alwayes come to this period , That of necessity there must be seven spaces for the seven Planets , to move in , which must be filled by seven bodies , and these are by Astronomers called the Planets attributes , and these we call Orbes , joyning close the one to the other . Of the Firmament or eight Heaven . HAving demonstrated that there are seven Orbes for the seven Planets ; it will be necessary to shew how that its requisite that there be also another Heaven , for all the fixed Stars are differing from the seven others : for the Ancient Astronomers observing that the Motion of the Stars was very slow , not advancing above a degree from one hundred to a hundred years , concluded , that it was most necessary to admit an eight Orbe , in the which al the fixed Stars are , and the which never vary their scituation , distance , nor figure , or shape , and this Heaven is called by them , the Firmament . How the Astronomers divide the Stars , or whether they be numberlesse or no . AS for the fixed Stars we hold them to be numberlesse , the Holy Scriptures giving us a testimony thereof , I meane , that besides the great infinite number that we see , there are yet a far more infinit number of lesserstars which are by us not seen , as hath been observed by certain Prospective Glasses , made in Italy , and though the Ancients have not marked above 1022. their meaning was not , that there were no more Stars , but that they had observed none but those , as being only the cheifest which they had need of ; And those thousand twenty two Stars , are divided into forty eight Constellations , or Figures of Animalls , which the Ancients have supposed , for to discerne the one from the other ; and have separated and disposed of them into three ranks , as Septentrionalls , Zodiackes , and Meridionalls . Moreover , the Stars are distinguisht by their severall Magnitudes , or Bignesses , which have been found to be six : So that all the great Stars are of the first Bignesse , the lesser of the second , third , fourth , fifth , and sixth magnitude or bignesse , in which the least of them all are comprehended . Whether or no the Stars be translucent of themselves , and transparent . THe Stars have no proper light of themselves , save in this manner , all the Stars and Planets are of one and the selfe-same Nature . But the Moone hath no other light then what she borroweth of the Sunne , so no more can any of the other Stars have any other light but from the Sun . But suppose it be objected , that the Moon loseth not altogether its light , though she Eclipses in the shadow of the Earth ; because that in the Eclipsed party there appears a rednesse , and that such a rednesse for ought we know , might be her natural light . I answer , That that rednes cannot be her natural , because that if it were so , she would never quit that rednes , save when she increases , or that she is in her first quarter , And then that part of the Moon which is not illuminated by the Sun , ought to have that rednesse , which is not so , as we see by experience : And therefore all rednesse is not naturall to the Moon : Moreover , if it be demanded from whence that rednesse proceeds ? its from the reflection of the lig 〈…〉 is encountered by the Moone in the shado 〈…〉 Earth : For as the Moone is a polisht body , 〈…〉 the shadow of the Earth is never destitute of some little light , so it 's that little light which causes the rednesse in her . So that by what is aforesaid , it clearly appeares that the Sunne is the Principle of light , it being Gods pleasure to adorn it with such an eminent quality . Furthermore , we say that the Stars are not so transparent as the Heaven is , which may be seen by the Moon and Mercury , when they are interposed , between our eyes and the Sunne , and that they Eclipse her ; And so its apparent that the Stars are both dusky and danky . That the Heavens are round , and that they move the one within the other , from the East to the West , their usuall course . AS we have hitherto proved , that there are eight Heavens , so must we prove that they are round , and that they turne the one within the other , from East to West , the which may appear unto us most manifestly , for we see that the Sun , the Planets , and all the other Stars , do rise first in the East , on our Horizon , then little by little they advance toward the South , and that finally , they set in the West , so next againe they rise all in the East . We will but instance in the Sun , And say that it must be either the selfe same Sun , or another which we daily see to rise , and set , It cannot be any other , for that then every day would require a new one : And if it be the same Sun , it must either have past over , within , or underneath the Earth : Over the Earth it cannot have past , for as much as then there would have been no night , the presence of the Sun causing the day ; neither can it have past within the Earth , because , as we shall see hereafter , its greater then the Earth , It remains then , that it must have past underneath the Earth , and that consequently its Orbe , or Heaven turnes about the Earth ; And since all the Heavens turne , the one within the other , about the Earth , and that from the East to the West , we may justly then say that the Heavens are round . It s also granted that the Heavens are round , because that being they are the most noble part of the world , and in which all the rest are contained ; it is most necessary , that they should be of a round forme , which is the most capablest and most perfectest of al others . For if the Heavens had any other Figure or Forme , those which are inferiour to the others , could not possibly transport their Planets from the East to the West , because of their Angles , or else we must grant that they penetrate each other , and so there would chance to be a penetration in the matter of the Heavens , which would contradict what hath been formerly proved , to wit , that its matter or substance , is both solide and fixt , &c. The End of the first Lecture , concerning COSMOGRAPHY . 
A65673	----	A second defence of the New theory of the earth from the exceptions of Mr. John Keill. By William Whiston, M.A. vicar of Lowestoft, Suffolk; and chaplain to the Right Reverend Father in God, John Lord Bishop of Norwich Whiston, William, 1667-1752. 1700 Approx. 38 KB of XML-encoded text transcribed from 14 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2003-01 (EEBO-TCP Phase 1). A65673 Wing W1697 ESTC R220939 99832323 99832323 36795 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A65673) Transcribed from: (Early English Books Online ; image set 36795) Images scanned from microfilm: (Early English books, 1641-1700 ; 2103:07) A second defence of the New theory of the earth from the exceptions of Mr. John Keill. By William Whiston, M.A. vicar of Lowestoft, Suffolk; and chaplain to the Right Reverend Father in God, John Lord Bishop of Norwich Whiston, William, 1667-1752. [2], 22 p. printed for Benj. Tooke at the Middle-Temple-Gate in Fleetstreet, London : 1700. A response to John Keill's "Examination of Dr. Burnet's theory of the earth", in which Keill, an astronomer, attacked Whiston as well as Burnet. Reproduction of the original in the Henry E. Huntingon Library and Art Gallery. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. 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Understanding these processes should make clear that, while the overall quality of TCP data is very good, some errors will remain and some readable characters will be marked as illegible. Users should bear in mind that in all likelihood such instances will never have been looked at by a TCP editor. The texts were encoded and linked to page images in accordance with level 4 of the TEI in Libraries guidelines. Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Keill, John, 1671-1721. -- Examination of Dr. Burnet's theory of the earth -- Controversial literature -- Early works to 1800. New theory of the earth -- Apologetic works -- Early works to 1800. Astronomy -- Religious aspects -- Early works to 1800. 2000-00 TCP Assigned for keying and markup 2001-10 SPi Global Keyed and coded from ProQuest page images 2001-11 TCP Staff (Michigan) Sampled and proofread 2001-11 TCP Staff (Michigan) Text and markup reviewed and edited 2001-12 pfs Batch review (QC) and XML conversion A SECOND DEFENCE OF THE New Theory of the Earth FROM THE EXCEPTIONS OF Mr. IOHN KEILL . By WILLIAM WHISTON , M. A. Vicar of Lowestoft , Suffolk ; and Chaplain to the Right Reverend Father in God , IOHN , Lord Bishop of Norwich . LONDON : Printed for Benj. Tooke at the Middle-Temple-Gate in Fleetstreet . 1700. A SECOND DEFENCE OF THE New Theory of the Earth , &c. SINCE I have resolv'd to be as short as possible in this Rejoinder , and have ever determin'd with my self to avoid all Heat and Passion ; all Recriminations and personal Reflections ; which I look upon as Things unworthy of the Professors of the Peaceable and Charitable Religion of our Saviour ; as Immoralities in Philosophers , and Crimes in Christians : I shall therefore wave all things in Mr. Keill's Defence which might occasion any Reflections of that nature , and endeavour only to debate the Matters in dispute between us with all the Calmness and Fairness possible . And as wherever I am convinc'd by his Reasons , I shall freely own it ; so it is but Equal that I expect the same of him upon the same Occasions . Only He must give me leave to say , That the Reason of my Surprize at His appearing in Publick against me , was not any Special Obligations I thought him under to me ; but his having declar'd his Satisfaction with the principal Assertion , nay the main Foundation of my Theory , viz. That a Comet pass'd by the Earth at the Deluge . After which Concession I could not , I thought , expect an Opposition in Print to my Book from him . I will repeat Mr. Keill's Words at large , in the beginning of his former Remarks , and Appeal to the Candid Reader , whether I had not some reason to be surpriz'd . I cannot but acknowledge , says Mr. Keill , that the Author of the New Theory of the Earth , has made greater Discoveries , and proceeded on more Philosophical Principles , than all the Theorists before him have done . In his Theory there are some very strange Co-incidents , which make it indeed probable , That a Comet at the time of the Deluge pass'd by the Earth . It is surprizing to observe the exact Correspondence between the Lunar and Solar Year , upon the Supposition of a Circular Orbit , in which the Earth mov'd before the Deluge . It cannot but raise admiration in us , when we consider , that the Earth at the Time of the Deluge was in its Perihelion , which would be the necessary Effect of a Comet that passed by at that time , in drawing it from a Circular to an Elliptical Orbit . This , together with the Consideration that the Moon was exactly in such a place of its Orbit at that time , as equally attracted with the Earth , when the Comet pass'd by , seems to be a very convincing Argument that a Comet really came very near , and pass'd by the Earth , on the day the Deluge began . But to leave this Preface , and to come to the Matters themselves in dispute between us . In the First place therefore , because Moses at the beginning of the Six days Creation , says , That Darkness was upon the face of the Deep ; whereas the Atmosphere of a Comet , which I suppose to be the Chaos here meant , is a transparent Fluid while it is such : Mr. Keill argued , that this transparent Atmosphere could not be the dark Abyss of Moses . Now what I answer'd was , That Moses did not concern himself with the ancient State of the Chaos , but only with its State at the Commencing of his Creation : at which time it would be a dark Abyss in the properest sense , and highest degree imaginable . Now all that Mr. Keill adds about this matter ( whether as to the light and shining of the Central Solid , and his Calculations thereto relating : As to the Change from a Pellucid to an Opake Fluid : or as to the Restraint of the word Abyss to the Dense Fluid alone ) might have been omitted , if he had first rightly understood and consider'd the Propositions in the New Theory , where these Matters were explain'd already . For certainly , though the Central Solid were as luminous as the Sun it self ; yet to a Spectator , plac'd in so thick a Mist , there could no more of its Light from within , than of the Sun 's from without , appear : Though truly the Calculations here suppose ( 1. ) the Earth , when a Comet to have mov'd as near the Sun as the last ; whereas perhaps no other ever did so besides . ( 2. ) The Heat of its own Nucleus the main Cause of its Tail ; which is utterly false , and never imagin'd by me . And ( 3. ) The Spectator at only Ten Miles distance from the Nucleus , when he must have been as many Hundreds at least : and so are wholly groundless , and my Theory not at all concern'd in them . Besides ; though All the Upper parts of the Atmosphere of a Comet , through which we see the Fix'd Stars , is Transparent ; yet the Lowest part next the Nucleus , or Dense Body , seems Opake and Dark ; like a very thick Mist ; so as to hide the Nucleus it self from our sight , and cause Darkness upon the Face of the Deep . For the Changes which some observe in the Nucleus of Comets , are to be suppos'd not in the Solid Body , but in the Cloudy Bottom of the Atmosphere , which next encompasses the Nucleus . And this Darkness upon the Face of the Deep might continue till the Comet was grown Cold , and all the Denser part of the Atmosphere was Subsided : and be greatest while those Denser parts were in a State of Coagulation and Subsiding . 'T is also evident in my Book that I ascribe the Changes of the Chaos to the Operations of the Spirit of God introducing such Laws of Bodies by which the Earth would first be form'd , and its Phaenomena ever after be govern'd . And 't is sure no hard interpretation to include all that Fluid Region beneath the Earth's Future Surface under the term Abyss ; though after the Separation of the Earthy Parts , and their Consolidation , the Dense Fluid may most properly go by that Name : And upon the Face of the Abyss there was at first Darkness , and that succeeded by Light , according to the exact Description of Moses ; and according to the Solution of the First Day 's work in the New Theory . My next Answer was to Mr. Keill's Objection against the sudden Formation of the Earth in a few years time by the Laws of Mechanism . For since , says he , the Confusions of the Comet 's Atmosphere seem to arise from the Violence of the Heat in its Perihelion ; as that Heat gradually decreas'd , ( which would not be under many Hundreds , or perhaps Thousands of Years ) the Confusions would cease also ; and the Subsidence and Mechanical Formation be compleated proportionably in the same time , and not sooner ; contrary to my Theory . My Answer to this was , it seems , by me so obscurely express'd , that Mr. Keill could not apprehend my meaning : Which therefore I shall endeavour to explain more distinctly thus . I deny that all the Confusions of a Comet 's Atmosphere are owing to the Heat at the Perihelion ; and I also affirm , That since Astronomers find by Observation , that upon a Comet 's return to the Solar Regions , the Atmosphere does still return , and is not at all settled and formed like a Planet , I must have contradicted that Observation if I had ascrib'd the Formation of our Earth to such a gradual and tedious Operation . In short : My Chaos was a Comet 's Atmosphere . Such an Atmosphere does not Subside in the Period about the Sun ; and consequently Mr. Keill , who makes that an Objection against me , is mistaken , and the Formation of the Earth is to be ascribed to other Causes , and perfected by other Measures than he here imagines ; and so for ought that appears , by those assign'd in my Theory . I had said , that All the same Laws , Properties , and Operations of Bodies , which we find establish'd here on Earth , do not so Universally obtain in the Atmosphere of Comets . Which Assertion Mr. Keill is surpriz'd at , and endeavours to Expose . Now in this Case I would desire Mr. Keill to shew how , according to the Laws of Bodies with us , that so Thin Atmosphere of a Comet can sustain , at the distance of so many Thousand Miles from its Center , such Clouds or Opake Masses as it frequently does . Nay , if we come to the Planets , which appear to be Bodies so like to our Earth , as to require the same general Measures and Laws in them ; we may find such a Ring about Saturn , as 't will be hard to account for by the Mechanical Laws upon our Earth . Sure there is no reason to imagine that , because God has been pleas'd to fix several arbitrary Laws , and Powers of Bodies resulting from them , in our little System ; that therefore he has confin'd himself to ordain no others in different ones . To give an instance : The Particles of our Elastical Fluid , or Air , may be preserv'd from coming close together , as Mr. Keill , I suppose , will not deny , by a Special Law directly opposite to that of Gravity ; or by a particular vis centrifuga belonging alone to such Particles of Matter as the Air is composed of . Now I believe Mr. Keill will hardly affirm this to be an Universal Law , obtaining all over the Universe , but confin'd to some parts of it at pleasure . And many such Laws there may be in the Opinion of that Great Man , whose very Name is enough to defend one ( as Mr. Keill justly speaks : ) upon which the particular Phaenomena among us do generally depend . Now though I believe such Laws as these various in various Systems , yet I never imagin'd that the Mechanical Powers demonstrable from the Necessary Laws of Motion are at all so ; whatsoever , for the diversion of his Readers , Mr. Keill is pleas'd to suppose . However , By this Answer I not only , it seems , have prevented all possible Objections against my Theory : [ a thing , to be sure , I cannot but be very fond of : ] But I have Granted Mr. Keill all he design'd to prove , viz. That the Earth was not form'd according to the known Laws of Mechanism , but by the Efficacy of the Divine Spirit , which moved on the Face of the Waters . Now I must here deny the Opposition , and affirm , That in my Opinion the Earth was form'd according to the known Laws of Mechanism , some of them introduc'd then by the Efficacy of the Divine Spirit , which mov'd on the Face of the Waters ; and ever since continu'd among us . For Almighty God to introduce New and Regular Laws at the beginning of a New World , which are to be ever afterward observ'd in it , I take to be a Miraculous Interposition very worthy of God , and very accountable to our Reason . But to suppose him by a Multitude of Miracles acting so disproportionably and disorderly , as the common Scheme of the Creation obliges one to do , is to introduce Miracles sufficiently strange and unaccountable to me : and such as I can't be persuaded of by such Reasonings as I have yet met with upon this Occasion . Though to Mr. Keill , who finds so little difficulty in this matter ; and without Authority , can admit the Creation , and , I suppose , the Annihilation of the Waters of the Deluge ; I little expect to shew that any Miracle can be strange and unaccountable . As to the Internal Heat in the Earth , which is allow'd by Mr. Keill ; and by reason of some Earthquakes , of a very large Compass deriv'd from it , can't but Reach downwards to a mighty Depth ; It must be accounted for , whether it be a Cause of Fountains or not . And if Mr. Keill think it more easily ascrib'd to the Mixture of Sulphureous , Nitrous , and Mineral Principles , than to a Hot Central Solid ; He must give me leave to retain my former Opinion , for these two Reasons : Viz. Because the Earth , at the Depth necessary for the Mixture , is too close and fast , and has no Caverns or Hollows requisite thereto : And Because such a Mixture it self supposes that Heat and Motion of Parts as Causes , which ought only to be the Effects thereof : Besides ; I am still inclinable to ascribe the Origin of Springs in great part to the Vapors ascending , and elevated by the Subterranean Heat , for this particular , and to me substantial Reason , among others , That the Springs break forth extraordinarily , and run the fastest in a Frost , as they ought to do in this Hypothesis : when the Vapors in the Air seem most at rest and quiet ; as is commonly observ'd , and particularly in the great Frost , by the Excellent Mr. Ray. To some other of whose Reasonings also I refer him upon this Occasion . As to my Receding , without Reason , from the Letter of Moses in the Fourth Day 's work ; Mr. Keill has so little still to say against those large Accounts I have given of that Matter , that I shall venture the Reasons I have already alledg'd with the Impartial and Considering , without any addition . Only his Argument against the Nature of the Hexaemeron , viz. that of an Historical Iournal , such as a Spectator on the Earth would have made : Because there was , in his Opinion , no such Spectator in being to make it ; Is , I think , neither Conclusive , nor True. For though there were no real Spectator at first , yet the Nature of the History might , for good Reasons , be such as I assign notwithstanding . But , to tell him my Mind freely , I believe that the Messias was there actually present : That He made the Journal : that He deliver'd it afterwards to Moses on Mount Sinai : and , That from thence it appears in the Front of his Pentateuch at this day . In the next place Mr. Keill endeavours to Vindicate his Assertion , That the Heat of the Sun for half the Second Day , or Year of the Creation , could not elevate Vapors enow to fill the Seas of the Primitive Earth . I had told him that I did not suppose the Waters in the Small Seas and Lakes of the Primitive Earth much above the Thousandth part of those in the present Seas and Ocean ; and so there was no need of the raising of so many Vapors that day as he imagin'd . Now to confute this , he says , that so little Water would necessarily render that Earth dry , barren , and unfruitful . For since the quantity of Vapor rais'd is proportionable to the Surface of those Waters from whence 't is rais'd ; and since the Thousandth part of the present Water must have only the Thousandth part of the present Surface ( which he must say , or say nothing : ) It will follow that the Rains and Dews before the Flood were but the Thousandth part of those at present in a year's time : And since by the Absence of the Ocean the dry Land then was near double to that now , and to be supply'd with only the Thousandth part of its Water , every Region would have in particular little more than the Two thousandth part as much Moisture as it has at present . Now this looks like a very formidable Calculation , and sufficient to destroy a main Foundation of the New Theory . But for Answer : How comes it about that Mr. Keill , who knows it so well , should forget the different Proportions between Solids and Superficies ? between the quantity of Water for Use , and the quantity of its Surface for Evaporation ? 'T is certain , that though the Channels of the Primitive Seas and Lakes were Similar to those at present , yet a little more than a Thousandth part of the present Waters would have near an Eightieth part of the present Surface : Besides , 'T is evident , that as our Ocean affords vast Quantities for Vapor , so the much greatest part of those Vapors return upon it self again , and are of no Use to the dry Land , especially in the Middle parts ; from whence the Clouds seldom or never march so far as is necessary for that purpose : Nay , I will venture to say , that near the Thousandth part of the Waters of our present Ocean might be so dispos'd of in the Plains and smaller Valleys of our present Earth , as to afford not much less Surface , and so not much less Vapor than it does at present ; if once all those Middle parts were away , whence little or nothing does accrue to the dry Land , which alone stands in need of it . Which things being suppos'd , as they are , I think , undeniably true ; I answer thus ; ( 1. ) I never assign the Sun as the Sole Cause of the Ascent of the Vapors at the Time referr'd to . My Words are , The Heat of the Sun , with the continual Assistance of the Central Heat . From which Assistance Mr. Keill may imagin , that I believe vast Quantities of Vapors would be rais'd , at a time when it was really greater , and had a much freer passage ; since I still derive so much of the Vapors of our present Rivers from it , even after its inclosure within the Crust of Earth consolidated together . ( 2. ) I fear not to assert that a small part of the Water now rais'd in a year , when it fell regularly and constantly in equal Dews , and went not off in violent Rains and Torrents , not insufficient for the Antediluvian Earth . ( 3. ) At a time when the Ground was every Night very wet with a mighty Dew , the Surface of the dry Land did afford much more Vapor than the present Surface ; which is only sometimes wet with some uncertain Showers , and that in some particular places only . ( 4. ) The Channels or Receptacles of the Waters would scarcely then be Similar to the Channel of the Ocean now , but more level and shallow ; which would still make the Surface larger in proportion to the Solid Content ; and so afford much more Vapor for the supply of the Earth proportionably . ( 5. ) If all my own Computations fail , I will for once beg one of Mr. Keill ; which will certainly help us over this difficulty , [ though it increase upon us by his next , which takes away Nine Tenths of our former quantity by the Interposition of the Atmosphere : ] And that is from his Assertion , which we shall come to by and by ; That the Heat of the Sun , at the time assign'd , was several Hundreds of times as great as at present . Now though I shall shew anon that this Computation is much too great ; yet let us allow but a small part of that , and it will set us over this difficulty . For if the Heat were but Twenty times as great , it would in the same Space elevate Twenty times as many Vapors : which I hope will satisfy even Mr. Keill's own Expectations ; and being from his own Assertion , will be allow'd as satisfactory in the present Case . But after all ; Sure Mr. Keill has forgotten that Solution in my Theory , whence all this Objection is rais'd : Otherwise He would have seen , that the vast Quantity of Vapors in the Air , on the Second Day of the Creation , came thither in Ways very different from that of the Raising of them now by the Heat of the Sun upon the Surface of our present Ocean , at a time when neither its Surface nor itself was in being . Which therefore has little to do with all the Computations us'd by Mr. Keill upon this Occasion . Neither has the next Objection any more weight in it : That the Waters in the Seas are call'd by Moses , Waters under the Firmament : and so are of a different Nature and Original from those in the Air , which are Waters above the Firmament : Whereas I derive the one from the other , and suppose the Seas to have once been Vapor , and so part of the other Waters . For certainly if Vapors in the Air , or Waters above the Firmament , fall down , become Water , and run into the Seas , they must be allow'd to change their Name , and become Waters below the Firmament . I am sure this Change is no new thing , but has been continual from the Creation till our Times . Every day Vapors become Rain , and run into the Seas ; and the Seas are every day resolving into small Parts , and become Vapors : and so the Inferior and the Superior Waters still communicate with , and supply each other , and accordingly change their Denomination perpetually . And truly this , and the next Shadow of a Difficulty about the Appearance of the Dry Land , might have been so easily avoided by a little more careful perusal of a Solution or two in my Theory , that Mr. Keill need not have desir'd a farther Answer . We are now come to the great Point of the Inconveniences which would arise from the long Days and Nights in my first Hypothesis ; and how entirely they all vanish upon that Additional one of the Elliptick Orbit till the Fall. Now though Mr. Keill does not disown that his former Objections are of no force against me now ; yet because this Additional Hypothesis did not appear before in my Theory , He thinks it not worth while to confute it : which is truly a short and easy way of Answering . Now for my part , I am far from thinking worse of any Discovery upon the account of the Time in which it was made : And if I can shew good Reason for this , as I think I can , I shall not be much concern'd at Mr. Keill's passing it over untouch'd . For the only thing he says , viz. That 't will hardly be allow'd that but one half of the Primitive Earth was Habitable before the Fall , seems to me too inconsiderable to be made an Objection . I should think it no great matter if all the Earth , excepting the Regions about Paradise , were uninhabitable at a time when they were not to be inhabited . For to what great Purpose is it that all proper provision be made for the Entertainment of a Company of Guests at a Table , when 't is certainly known that not one Guest will be there ? Providence does ever wonderfully provide for the Accommodation of his Creatures wherever it places them : But that a suitable Provision is made for them where they will never be plac'd , I see no reason to imagin . If I ever attempt another Edition of my Book , this Hypothesis , with several other Discoveries since made , will be inserted ; and will , I believe , with fair and considering Persons , be thought far from spoiling the Beauty of the Theory ; whatsoever Mr. Keill , who is no friend to Theories in general , may think to the contrary . But to proceed . Mr. Keill still asserts , that the Heat in my Hypothesis before the Fall , when the Sun was half a year at least above the Horizon at once , was several Hundred times greater than that with us at present . Now in answer to this , I alledg'd , That if we compute the Quantity of Heat from that of the Sun's Rays , it will be equal in both Cases , and so his Assertion must be a plain Error . But it seems he meant quite otherwise than I imagin ; viz. That the Degree of Heat , produc'd by so long continuance of the Sun's presence , would at last be several Hundred times as great as with us at present . I answer , That in this sense the Assertion is not much truer than in the other . The Heat produc'd by the Fire , or the Sun , for some time continually increases ; and perhaps pretty nearly in proportion to the time . But this only for a while , till a suitable or competent Degree of Heat be produc'd ; but no longer . Let us try this by Calculation . A piece of Wax will melt in a Second of Time , suppose , at the distance of an Inch from the Fire ; because the Degree of Heat there is sufficient to dissolve its Texture immediately . Let us remove it to the Distance of a Hundred Inches , where the Heat is Ten Thousand times weaker ; for Ten Thousand Seconds , or near Three Hours Space , the Quantity of Heat is therefore ( as the Rectangle , contain'd betwixt the Sine of the Angle of Incidence ( the same in both Cases here ) and the time of continuance ) exactly equal to the former Heat ; and must therefore have the same effect : Which yet , I presume , Mr. Keill does not believe it will. Thus let us compare the Heat of the Sun at the Equator , and near the Poles ; where the Sines of the Sun's Angle of Incidence are as 10 to 1 , [ for the Day-time , or 12 Hours at the Equator ; and for the 12 Hours at the Conclusion of the Half-year-day near the Poles ] Which will , according to Mr. Keill , be as 10 + 12 to 1 + 4320 ; or as 120 to 4320 ; and so the Heat near the Pole 36 times as great as that at the Equator : Which , I presume , Experience does not attest . But after all , This Objection , if it were true , only refers to the Circular Orbit before the Fall : But as my Theory stands at present , with the Hypothesis of an Elliptick Orbit , 't is no way concern'd in it . But now we are come to a Point of much greater Consequence , Whether the Dense Fluid , on the Approach of the Comet at the Deluge , would have force enough to burst the Earth , or that upper Crust which is situate upon the Surface of the Dense Fluid . For Mr. Keill , with no mean Appearance of Demonstration , urges , That since the first Impetus of the Dense Fluid is infinitely less than any succeeding Impetus acquir'd by Motion ; and since here is no room for Actual Motion , here cannot be Impetus sufficient to break the Crust , which otherwise Mr. Keill owns it would easily do . In answer to this I say , That since Mr. Keill does not disown the first Original of the Earth's Fissures , and the breaking of the Crust by the Diurnal Rotation ; he ought much less to scruple it here . A Plank or Board , when once 't is cut into several pieces , let the pieces be laid as true and close as possible , will be separated without any difficulty upon all Occasions . And just thus it is here . The Strata having been formerly separated , and by the continuance of the Diurnal Motion not permitted to join or close afterward upon any Impetus of the Fluid below , they will open again ; as I have asserted in the New Theory . But because Mr. Keill imagines that the Upper Crust of Earth would hinder the force of the Fluid below from breaking open its Fissures ; let us compute the force of the Comet 's attraction upon it self , and see whether even that alone , without the assistance of the Dense Fluid , would not be sufficient to break it in the manner I have assign'd . Mr. Keill may remember , that I suppose the Comet at the Deluge about half as big as the Earth ; and the nearest distance of its Center to that of the Earth about 30000 Miles . Let us see what force this will afford towards breaking the Earth . At the nearest distance the Gravity of the Parts of our Earth nearest the Comet , towards the Comet 's Center , would be near 1 / 100 of their Gravity towards the Center of the Earth ; and the difference between the Gravity of those Parts towards the Comet , and of the Middle Parts or Center of our Earth towards the same , would be the difference of the Squares of their several Distances , or about a quarter of the former Force 1 / 400 So that the Parts nearest to the Comet , and farthest off it , [ the Regions about b and a in my 7 Fig. ] if the Crust be suppos'd 400 Miles thick , will have a Force upon them equal to the Weight of an entire Mile of Earth : and this sure will be more than sufficient to break and separate those Strata which are already broken and separated ; and which therefore , at the first Impulse , would yield to that powerful Attraction which the Neighbourhood of so mighty a Body would occasion in the Case before us . As to the sudden Condensation of the Vapors from the Comet , upon their first Fall , whether by the Air or Earth , were it never so evident and universal , 't is of very small consequence to me ; since , as Mr. Keill does not deny , their own Heat would ratify vast Quantities of them again , and occasion their Elevation into the Air immediately : which is all I desire of him . But still he urges , That then the first Violent Fall would it self do the Business of the Deluge , without any occasion for the great and long Rains : And so the Forty days Rain , which occasion'd the Flood in Moses , can't be accounted for , and is almost wholly superseded by us . In answer to which I say , That though the primary violent Fall of the Vapors were in less than a Day 's time , as I have shewn in my Theory ; yet because as many would immediately arise again as the Air could hold , here is a Fund abundantly sufficient for the most violent Forty days Rain imaginable . And though the Vapors did Originally fall in so short a time , and with such Violence , on that Hemisphere of the Earth exposed to them , as there to do the Business of the Deluge immediately : Yet because the Regions near the Ark were not in that Hemisphere , their Deluge must arise from the Forty days Rain succeeding , and from the flowing in of the Waters from those other Parts of the Earth on which they first fell : according as this Matter is already stated in the New Theory ; and , I think , need not be alter'd from any thing here suggested . We are now got to the principal Thing considerable in Mr. Keill's Objections ; and that is his Demonstrations , that the Pressure of the incumbent Fluid could not raise the Subterranean Waters to the Surface of the Earth . And I must own , that I see the force of his Demonstrations now , which I did not before . And I heartily thank Mr. Keill for correcting so considerable a mistake in the New Theory ; and a mistake that before was the only Obstacle to as remarkable a Confirmation of the main Parts of it , as perhaps any other whatsoever ; which in due time shall appear . All that Moses says relating to this matter , is , That the Fountains of the Great Deep were broken up at the beginning , and shut up at the Conclusion of the Deluge , without the least Affirmation that any Waters issued out of them ; as has hitherto been universally suppos'd , and as I accordingly believed also . Though , in truth , I am now so far from that Opinion , that I believe the use of that disruption of the Fissures was only to drain off , and not at all to send out the Waters of the Deluge , as will more distinctly be shewn upon a proper Occasion hereafter . But if Mr. Keill's Reasoning under this last Head appear so strong , what follows , touching the Removing of the Waters of the Deluge , seems to me of a very different Character . For ( 1. ) Let the Cracks and Fissures be full during the Deluge ; nay , let the Waters be draining away by them continually into the Bowels of the Earth : Yet till this Drain took away more than the Rains and the Running in of the Waters brought , the Flood would continually increase notwithstanding . ( 2. ) I say still , Certainly the Pores and Interstices of 30 or 40 , I might say of 60 or 80 Miles of dry Earth , or Earth that can still admit vast Quantities of Water , are capable of receiving 3 , 4 , or more Miles of Water into them . ( 3. ) Mr. Keill's Assertion , That the inward Strata of the Earth are almost wholly compos'd of a tough Clay , common Stone , Whinstone , Coal , Metalline Ores , and the like , uncapable of containing any Water considerable , is not generally true . I appeal to the following Table of the several Strata of a Well at Amsterdam , mention'd by Varenius , which is the best and deepest that I know where readily to meet with . And let the Reader judge whether all the Strata are such as will exclude Water or not , or such as Mr. Keill supposes the whole Body of the Earth below compos'd of . Feet . Garden-Mould 7 Turf 9 Soft Clay 9 Sand 8 Earth 4 Clay 10 Earth 4 Sand in which the Piles for the Amsterdam Buildings are fix'd 10 Clay 2 White Gravel 4 Dry Earth 5 Mud 1 Sand 14 Sandy Clay 3 Sand mix'd with Clay 5 Sand mix'd with Sea-shells 4 A Clayey Bottom 102 Gravel 31 In all 232 ( 4. ) I look upon his last Argument , viz. That these Fissures would not drain off the Waters in half a year , nor indeed under several Hundred years ; as so far from affecting me , that I heartily thank Mr. Keill for so considerable a Confirmation of my Conjecture to this purpose at the End of my former Vindication . For though I think his Computation of the Time much too long , because the Fissures were then very much more open than now ; and because the vast weight of the Waters , at first especially , would hasten the Velocity of their Descent : yet in general I am fully of his mind ; that the Waters of the Deluge could not be Mechanically drain'd off so soon as the common Opinion is ; as he may see in the place referr'd to , which 't is a little strange he should not discover before , and so perceive that he was , by the last Computation , but confirming one of the Points I had observ'd since the publishing of the New Theory . In short ; The Remarks and Objections Mr. Keill and Others have made against some Branches of the New Theory , have occasion'd me to correct some Parts , to confirm others , and to improve the whole . But so little do I esteem the principal Foundations of that Book destroy'd by all that has been hitherto said , ( Though Mr. Keill is pleas'd to presume , that by those few Objections he before made against a few particulars in it ; And this after he had granted me the principal Point of all , it was in general already confuted : ) That I may venture to say , I am prepar'd , upon a Second Edition , more fully to confirm and establish the main Conclusions in it than ever ; as I hope will appear in due time . I shall add no more : But because the two concluding Questions I put to Mr. Keill before , are wholly past over in silence , I shall Reprint them here again ; and if he make another Rejoinder , again desire his free and ingenuous Answer : and so take my Leave . ( 1. ) Since Mr. Keill grants that a Comet pass'd by at the Deluge , and yet contends that the Flood is not to be solv'd therefrom , but is to be believ'd wholly miraculous ; To what purpose did the Comet so providentially pass by just at that time , if it had no relation to the Deluge ? Does Mr. Keill imagine , That the same miraculous power which caus'd the Deluge , could not also , without the attraction of a Comet , make the Earth's Orbit Elliptical ? A strange , unheard-of , and most surprizing Phaenomenon happens in the World ! A Blazing Star , which we but seldom discover at a vast distance in the Heavens , descends hard by the body of our Earth : which without the greatest exactness in the Chain of Providence does not happen in thousands , nay millions of years : and as soon as ever 't is pass'd by , a wonderful , and incredible Deluge of Waters overflows the whole Earth , and drowns all its Inhabitants without any other visible or imaginable occasion in the World : and yet , as it seems , the Comet only accidentally pass'd by , and had no hand at all in the Deluge ! — Credat Iudaeus Apella . ( 2. ) How could those effects I have mention'd be avoided upon the passing by of the Comet ? We are not now in a Cartesian Vortex , where Fancy and Contrivance can introduce or hinder any effect at pleasure : But we are in Mechanical and Experimental Philosophy , which is an inflexible thing , and not at all subject to our inclinations . When the Comet therefore was just pass'd by us , I desire to know how the Earth could possibly avoid passing through its Atmosphere and Tail : If it could not , Pray what could prevent the acquiring that Column of Vapours I , by computation , find would fall on its Surface ? And if such a Column of Vapours was left on the Earth , what could hinder their becoming Water , and drowning the Earth ? I shall not , though I easily might , carry on the Chain of Queries any longer . But if Mr. Keill can fairly Answer me these few leading Questions , I shall then believe him alike able to Answer the rest : and so I shall not pursue this particular any farther , but leave it and this whole matter to his and the Reader 's leisure and consideration . Lowestoft , Suffolk , Octob. 4. — 99. FINIS . Notes, typically marginal, from the original text Notes for div A65673-e140 Vind. p. 4 , 5. Vid Newt . p. 301. Vid. Verb. Newt . N.T. pag. 225. marg . p. 134. Pag. 4 , 5. 3. Disc. 2 d Edit . p. 109. N. T. p. 242. P. 181 , 182. Coroll . 8. post Hyp. 10. New Theor. Fig. 7. Gen. 7.11 . & 8. 1. Varen . Greg. p. 46. Vind. p. 46 , 47,48 . 
A51558	----	The use of the astronomical playing-cards teaching any ordinary capacity by them to be acquainted with all the stars in heaven, to know their place in heaven, colour, nature, and bigness. As also the poetical reasons for every constellation, very useful, and pleasant, and delightful for all lovers of ingeniety. By Joseph Moxon hydrographer to the Kings most Excellent Majesty. Moxon, Joseph. 1692 Approx. 101 KB of XML-encoded text transcribed from 31 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2005-12 (EEBO-TCP Phase 1). A51558 Wing M3027A ESTC N66308 99834803 99834803 39340 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A51558) Transcribed from: (Early English Books Online ; image set 39340) Images scanned from microfilm: (Early English books, 1641-1700 ; 1837:7) The use of the astronomical playing-cards teaching any ordinary capacity by them to be acquainted with all the stars in heaven, to know their place in heaven, colour, nature, and bigness. As also the poetical reasons for every constellation, very useful, and pleasant, and delightful for all lovers of ingeniety. By Joseph Moxon hydrographer to the Kings most Excellent Majesty. Moxon, Joseph. Hood, Thomas, fl. 1582-1598. aut [2], 50, [9] p. printed by J. Moxon, and are to be sold at the sign of the Atlas in Warwick Lane, London : 1692. With a caption title on p.15: Here follows the ancient stories of the several stars and constellations. Shewing the poetical reasons why such various figures are places in heaven. Collected from Dr. Hood. Signatures: A-D(-D8). Reproduction of the original in the Harvard University Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. EEBO-TCP is a partnership between the Universities of Michigan and Oxford and the publisher ProQuest to create accurately transcribed and encoded texts based on the image sets published by ProQuest via their Early English Books Online (EEBO) database (http://eebo.chadwyck.com). The general aim of EEBO-TCP is to encode one copy (usually the first edition) of every monographic English-language title published between 1473 and 1700 available in EEBO. 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Understanding these processes should make clear that, while the overall quality of TCP data is very good, some errors will remain and some readable characters will be marked as illegible. Users should bear in mind that in all likelihood such instances will never have been looked at by a TCP editor. The texts were encoded and linked to page images in accordance with level 4 of the TEI in Libraries guidelines. Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Astronomy -- Early works to 1800. Sky -- Early works to 1800. Constellations -- Early works to 1800. 2005-02 TCP Assigned for keying and markup 2005-03 SPi Global Keyed and coded from ProQuest page images 2005-04 Andrew Kuster Sampled and proofread 2005-04 Andrew Kuster Text and markup reviewed and edited 2005-10 pfs Batch review (QC) and XML conversion THE USE Of the ASTRONOMICAL Playing-Cards , Teaching any Ordinary Capacity by them to be acquainted with all the STARS in HEAVEN , To know their Place in Heaven , Colour , Nature , and Bigness . As also the Poetical Reasons for every CONSTELLATION , Very Useful , Pleasant , and Delightful for all Lovers of INGENIETY . By Joseph Moxon Hydrographer to the Kings most Excellent Majesty . LONDON : Printed by J. Moxon , and are to be Sold at his Shop at the Sign of the Atlas in Warwick Lane. 1692. OF THE Stars in HEAVEN . THE Stars are divided into six sorts or sizes called Magnitudes , ( which are you may see ) distinguisht with six several sizes of Asterisks made like Stars , as sēt down in a Table on the Card over Dorado , whither I ●efer you . Astronomers have computed the sizes of these Stars by comparing them either to the Diameter , or ●lse to the whole Globe of the Earth . The Diame●…er of the Earth is 6872 of our common Miles , viz. ●uch Miles , as the whole Circumference of the Earth ●nd Water makes 21600 Miles ; allowing for every ●egree of the greatest Circle 60 Miles . Now the Diameter of a Star of the first Magnitude compared with the Diameter of the Earth hath such proporti●…n to it as 19 hath to 4 ; therefore it containeth ●he Diameter of the Earth 4 times and ¾ . The Diameter of a Star of the second Magnitude ●s unto the Diameter of the Earth as 269 is to 60 : ●herefore it containeth it 4 28 / 90 times . The Diameter of a fixed Star of the third Magni●ude is unto the Diameter of the Earth as 25 unto 6 : ●herefore it containeth it 4 ⅙ times . The Diameter of a fixed Star of the fourth mag●itude is unto the Diameter of the Earth as 19 unto 〈◊〉 : therefore it containeth it 3 ⅘ times . The Diameter of a fixed Star of the fifth Magnitude is unto the Diameter of the Earth , as 119 unto 36 , therefore it containeth it 3 11 / 36 times . The Diameter of a fixed Star of the sixth magnitude is unto the Diameter of the Earth as 21 unto 8 therefore it containeth it ⅝ times . As for the proportions of the cloudy and obscure Stars , they are not expressed , because they are but few , and of no great account in respect of their smalness . The proportions of the fixed Stars compared with the Globe of the Earth , are as follow . A Star of the first Magnitude is to the Globe o● the Earth , as 6859 to 64 , therefore it containeth the Globe of the Earth 107 ⅙ times . A Star of the second Magnitude is to the Globe o● the Earth , as 19465109 is to 216000 , therefore i● containeth it 90 ⅛ times . A Star of the third Magnitude is to the Globe o● the Earth ▪ as 15625 is unto 216 , therefore it containeth it 72 ⅓ times . A Star of the fourth Magnitude is to the Globe o● the Earth , as 6850 is unto 125 : therefore it containeth the Globe of the Earth 54 11 / 12 times . A Star of the fifth Magnitude is to the Globe o● the Earth , as 1685159 is unto 46656 , therefore i● containeth the Globe of the Earth 36 8 / 1 times . A Star of the sixth Magnitude is to the Globe o● the Earth as 9261 is unto 511 , therefore it containeth the Globe of the Earth 18 1 / 10 times . I confess all this may seem matter of incredulity to those whose understanding is swayed by their visual sence , because they cannot perhaps conceive it possible that the Heaven which appears so small to the bare eye should be able to contain so great a number of such great bodies as is here spoken of ; yet if those be capable to consider the vast distance of this Heaven , and consequently of the Stars placed in it from the face of the Earth , and also the Diminutive quality of distance , their reason will be rectified , and their incredulity turn'd into an acknowledgment of the unspeakable wisdom of Almighty God ; and they will say with the Psalmist , Great is our Lord , Great is his Power , his Wisdom is Infinite , Psal. 147.5 . The distance of the Stars therefore from the Earth , is according to Mr. John Dee's computation , 2008 1 ½ semidiameters of the Earth . The semidiameter of the Earth containeth of our common miles 3436 4 / 11 , such miles as the whole Earth and Sea round about is 21600 : allowing for every degree of the greatest circle 60 miles , so that the distance of the Stars from the Earth is in miles 69006540 , a distance so vastly great , that were there a path for a Footman to walk in of that length , he must have set forth 9452 years 347 days ago , and have travelled 20 miles every day to have been just now at his Journeys end . Now as Mr. Dee saith ( almost in the same words ) if you weigh well with your self this little parcel of fruit Astronomical , as concerning the bigness and distance of the Stars , &c. and the huge massiness of the Starry Heaven , you will find your Consciences moved with the Kingly Prophet to sing the confession of Gods Glory ; and say , The Heavens declare the Glory of God , and the Firmament sheweth the works of his Hands . Of the Constellations in Heaven . A Constellation is a certain number of Stars placed by God Almighty neer one another in Heaven , and by Astronomers circumscribed in one Figure depicted about them , as Aries the Ram is a Constellation . Taurus the Bull is another Constellation , &c. Astronomers brought them into these figures , for instructions sake , things cannot be taught without names ▪ to give a name to every Star had been troublesom to the Master , and for the Schollar , for the Master to devise , and for the Schollar to remember ; and therefore the Astronomers have reduced many Stars into one Constellation , that thereby they may tell the better where to seek them , and being sought , how to express them . And they brought them into these figures , and none other , being moved thereto by these three Reasons : first these figures express some properties of the Stars that are in them ; as those of the Ram to be hot and dry , Andromeda chained betokeneth imprisonment : the head of Medusa cut off , signifieth the loss of that part : Orion with his terrible and threatning gesture , importeth tempest , and terrible effects : The Serpent , the Scorpion , and the Dragon signifie poyson : The Bull , insinuateth a melancholly passion : The Bear inferreth cruelty , &c. Secondly , the Stars ( if not precisely , yet after a sort ) do represent such a figure , and therefore that figure was assigned them : as for example , the Crown , both North and South ; the Scorpion and the Triangle , represent the figures which they have . The third cause was the continuance of the memory of some notable men , who either in regard of their singular pains taken in Astronomy , or in regard of some other notable deed , had well deserved of mankind . The first Author of every particular Constellation is uncertain ; yet are they of great antiquity ; we receive them from Ptolomy , and he followed the Platonicks ; so that their antiquity is great . Moreover we may perceive them to be ancient by the Scriptures , and by the Poets . In the 38 Chapter of Job there is mention made of the Pleiades , Orion , and Arcturus , and Mazzaroth , which some interpret the 12 Signs : Job lived in the time of Abraham , as Syderocotes maketh mention in his Book de Commensurandis locorum distantiis . Now besides all this , touching the reason of the invention of these Constellations the Poets had this purpose , viz. to make men fall in love with Astronomy : And to that intent have to every Constellation invented strange conceited stories , ( as you may read hereafter , therein imitating Demosthenes , who when he could not get the people of Athens to hear him in a matter of great moment , and profitable for the Common-wealth , he began to tell them a tale of a fellow that sold an Ass ; by which tale he so brought on the Athenians , that they were both willing to hear his whole Oration , and to put in practice what he exhorted them to . The like intent had the Poets in inventing of those stories : they saw that Astronomy being for its commodity singular in the life of man , was almost of all men utterly neglected : Hereupon they began to set forth that Art under Fictions , that thereby such as could not be perswaded by commodity might by the pleasure be induced to take a view of these matters ; and thereby at length fall in love with them . For commonly you shall note this , that he that is ready to read the stories , cannot content himself therewith , but desireth also to know the Constellation , or at leastwise some principal Star therein . All the Constellations formerly notified by the Antients , were in number 48 , because no more were seen in our Hemisphere , though in this latter Age there are 12 more discovered about the South Pole , which because it may be somewhat more pleasant for reading , and much more helpful for your memory , I shall give you their Names in plain English Rhythmes . The Constellations of the Fixed Stars . THE Army of the Starry Skie Declares the Glory of God most high ; Seen and perceived of all Nations In eight and fourty Constellations . First near unto the Northern Pole The Dragon and two Bears do role ; Whose hinder parts and Tails contain The lesser and the greater Wain . The Hair , the Bear-ward , and the Crown , And then comes Hercules kneeling down . And next below a place doth take Great Serpentarius with his Snake . Under the Harp of Orpheus The Eagle and Antinous . The Silver Swan her Wings doth spread Above the Dart and Dolphins head . Then Pegasus comes on amain , Andromeda follows in her Chain . The Triangle below her stands ; And at her feet in Perseus hands The Gorgon's head . Above are seen Her Parents Cepheus , with his Queen Cassiope . Not far below Heniochus his Goat doth show On his left shoulder : in his hand He doth the stormy Kids command . Of the Zodiack . Here in the Zodiaque begins The Ram , the Bull , the Loving Twins ; The Crab , the Lyon , and Virgin tender , The Ballance , Scorpion , and Bow-bender ; Goat , Waterman , then Fishes twain Shall bring you round to th' Ram again . Fifteen Images appear In the Southern Hemisphere . The Monstrous Whale before the rest , Eridanus scarce wets his brest : Over the Hare Orion bright Sparkles in a Winters night . Then comes the Great Dog , at whose tail The famous Argo spreads her sail . Above the Little Dog doth flame , For whom the Latines had no name : Long Hydra on her tail allow Carries the Pitcher and the Crow . The Centaure holds the Wolf by th' heel . The Altar , and Ixions Wheel Are never seen of us : but here The Southern Fish brings up the rear . Southern Constellations . About the Southern Pole there be Twelve Constellations we can't see , Which Frederick Houtman did survay Upon the Island Sumatrae : They 'r call'd the Crane , the Phoenix , and The Indian , with three Darts in 's hand , The Bird of Paradice , the Fly , The Peacock , the Camelion sly , The South Triangle , and South Snake , The Toucan Goose with its long Beak , The Flying Fish and Dorado : Two Magellanick Clouds also . Of the Nature of the Stars . To many of the Principal Stars there is in planetical Characters prefixed their Planetical Natures . The Astrologers make great use of them for knowing the nature of the Stars ; for those Stars that have the character of ♄ adjoined , are said to be of the nature of ♄ ; those that have ♃ adjoyned , are of the nature of ♃ , and so of the rest . If a Star have the characters of two Planets adjoyned , that Star participates of both their Natures , but most of that Planets whose character is first placed . The use Astronomers make of those characters , is for knowing the colour of any Star ; as if a Star have ♄ adjoyned , it is of the colour of ♄ ; if ♃ , it is the colour of ♃ , &c. The fixed Stars are known from the Planets by their continual twinckling , for the Planets never twinckle , but the fixed Stars do . How you may learn to know all the Stars in Heaven by these Playing Cards . To each of these Cards I have set down the day of the month that the Constellation in it rises at the Time of Sun-setting , as also the point of the Compass it rises on , so that if you will observe it , when the Sun sets , you will see the Constellation rising upon that point of the Compass set down on the Card with the letters of the point of the Compass . For Example . If you would know when the Little Dog rises in the Evening , look in the bottom of the Card , and you will find Jan. 11. E. by N. which shews that on the 11 th . of January at Sun-set the Constellation of the Little Dog rises East and by North ; therefore looking into that part of Heaven , you shall see the Constellation rising , and the Stars placed in Heaven , just as you find them placed on the Card. But if the Constellation be risen some considerable time , you must know the time since it rose , and estimate how high it may be above the Earth , by allowing about the twelfth part of Heaven for every hour since Sun-set , and about that esteemed height look for it , and when you find a number of Stars placed in Heaven like those on your Card , you may conclude that to be the Constellation , and to your great delight and satisfaction . See in what part of the Constellation each particular Star lies , and of what Nature , Colour , and magnitude it is . These Cards are divided into four Suits , as other Playing Cards are , viz. Spades , Hearts , Diamonds , Clubs : And Astronomers have divided the whole face of Heaven into four Colures , viz. The Vernal Colure , or Spring , The Aestival Colure , or Summer , The Autumnal Colure , or Autumne , The Hyemnal Colure , or Winter . Because when the Sun comes to any of these Colures , the Season of the year alters into Spring , Summer , Autumn , Winter ; and so have I divided these Cards ; for all the Constellations that are in the Vernal Colure are known by the suit of Spades , in the Aestiral Colure are Hearts , in the Autumnal Colure Diamonds , and in the Hyemnal Colure are Clubs , which are placed on the top at the left hand of every Card ; and the number of each suit is marked on the top of the Card close by it with Numerical Letters thus , I , II , III , IV , V , &c. to X , and the Kings , Queens , and Knaves of each suite are also depicted on the top in the middle of the Card. Of Via Lactea , or the Milky-way . This Circle is not set down on the Cards , because it takes up the whole compass of Heaven , but it is so plain to be seen every clear night , that it needs no picture : Yet I shall tell you what Constellations it passeth through , so that you may easily find any part of it that is above the Horizon when you please . VIA LACTEA , or Circulus Lacteus by the Latines so called ; and by the Greeks Galaxia , and by the English the Milkey way . It is a broad white Circle that is seen in the Heaven : In the North Hemisphere , it beginneth at Cancer , on each side the head thereof , and passeth by Auriga , by Perseus , and Cassiopeia , the Swan , and the head of Capricorn , the tail of Scorpio , and the feet of Centaur , Argo the Ship , and so unto the head of Cancer . Some in a sporting manner do call it Watling-street , but why they call it so , I cannot tell , except it be in regard of the narrowness that it seemeth to have , or else in respect of that great High-way that lyeth between Dover and St. Albans , which is called by our men Watling-street . Concerning this Circle as there are sundry opinions , so there is great difference among some writers , both touching the place , matter , and efficient cause thereof : Aristotle dissenteth from all other , both Philosophers and Poets , in the place , matter , and cause of this Circle ; saying that it is a Meteor ingendred in the Air , made of the vapors of the earth , drawn up thither by the heat of the Sun , and there set on fire . But his opinion is of all men confuted . First , touching the place , it cannot be in the Air , whatsoever is in the Air , is not seen of all men , at all times , to be under one and the same part of Heaven ; If we see it in the South , they that are in the West shall see it under the East side of the Heaven ; and they that are in the East , shall see it in the West part of the Heaven , but this Circle is of all men seen always under the same part of Heaven , and to be joined with the same Stars : therefore it cannot be in the Air. Again , for the matter , it cannot be made of that which Aristotle nameth ( i. e ) the vapours of the Earth because of the long continuance of the thing , and that without any alteration : for it is impossible that any Meteor made of vapours drawn up from the Water , or exhalations from the Earth , should last so long ; as may be seen in Blazing Stars ; which though they have continued long , as namely 16 months , some more , some less ; yet at the length they have vanished away ; whereas this Circle hath continued from the beginning unto this day . Besides , put case it were made of these exhalations ; whence will they infer the uniformity thereof ? The Comets do alter diversly , both in the fashion of their Blazing , and also in their several quantities , whereas in this Circle there is nothing but the same part , always of one form , and of one bigness . In the efficient cause thereof he must needs erre : for if it be neither in the Air , nor made of the exhalations of the Earth , it cannot be caused by the Sun ; for the one is the place , and the other the matter , wherein , and whereupon the Sun sheweth his power . All other ( besides Aristotle ) agree in the place , but differ in the efficient cause thereof : and rhey are either Philosophers , or Poets . Both these affirm that it is in the Firmament , ( i. e. ) in the eight Sphere ; but they disagree in the cause thereof . The Philosophers , ( and chiefly Democritus ) affirm the cause of the thing , to be the exceeding great number of Stars in that part of Heaven , whose beams meeting together so confusedly , and not coming distinctly to the eye , causeth us to imagine such a whiteness as is seen . But the best opinion is this , that this Milkey way is a part of the Firmament , neither so thin as the other parts thereof are , nor yet so thick as the Stars themselves . If it were as thin as the other parts of the Heaven besides the Stars , then could it not retain the light , but the light would pass through it and not be seen ; if it were as thick as the Stars , then would the light be so doubled in it , that it would glister and shine , as the Stars themselves do : but being neither so thin as the one , nor so thick as the other , it becometh of that whiteness we see . Thus far Dr. Hood . But Our modern Philosophers conceive this Lactean whiteness ariseth from a great number of little Stars constipated in that part of Heaven , flying so swiftly from the sight of our eyes , that we can perceive nothing but a confused light ; this the Telescope ( more lately found out ) doth evidently demonstrate to us : by the benefit of which , little Stars ( otherwise inconspicuous to our eyes ) are there clearly discerned . About the Southern Pole are seen two white spots , like little Clouds , coloured like the Via Lactea . One of which is trebble the latitude of the other ; some Mariners call them Nubeculae Magellani . Here follows the ANCIENT STORIES Of the several Stars and Constellations . Shewing the Poetical Reasons why such Various FIGURES are placed in HEAVEN . Collected from Dr. HOOD . And First , Of the Northern Constellations . URSA MINOR , This Constellation hath the preheminence , because it is nearest of all the rest unto the North Pole ; and is called of the Greeks Arctos , whereupon the Pole is called the Pole Artick , for that it is near unto this Constellation . It is also called Helice minor , because of the small Revolution which it maketh round about the Pole : or rather of Elice , a Town in Arcadia , wherein Calisto the great Bear , and Mother to the less , was bred . It is called Cynosura , because this Constellation , though it carry the name of a Bear , yet it hath the tail of a Dog : Last of all , it is termed Phaenice , because that Thales , who first gave the name to this Constellation , was a Phaenician : And therefore the Phaenicians being taught how to use it in their Navigations , did call it by the name of the Countrey wherein Thales was born : It consisteth of Seven Stars , which the Latines call Septentriones , because by their continual motions those Seven Stars do as it were wear the Heaven . The Spaniards do call them all Bosina , that is an Horn ; because they may be very well brought into that form ; whereof that which is the end of the Tail is called the Pole-Star , by reason of the nearness thereof unto the Pole of the World ; for it is distant ( according to the opinion of most ) from the true Pole , but 3 degrees 30 minutes . The Arabians call it Alrukaba . And of the Scythians it is said to be an Iron nail , and is worshipped by them as a God. The two Stars that are in the shoulders of the Bear , are called the Guards , of the Spanish word Guardare , which is to behold ; because they are diligently to be looked unto , in regard of their singular use which they have in Navigation . The reason why this Constellation was brought into the Heavens is diversly set down , and first in this manner ; Saturn having received of the Oracle that one of his Sons should banish him out of his Kingdom , determined with himself to kill all the Men-children that he should beget ; whereupon he gave command to Ops his Wife , being then great , that she should shew him the Child so soon as ever it was born : But she bringing forth Jupiter , and being greatly delighted with his hair , gave the Child unto two Nymphs of Creet , dwelling in the Mount Dicte , whereof this was one , and was called Cynosura , the other was Helice . Jupiter , after that ( according to the Oracle ) he had bereft his Father of his Kingdom , in recompence of their pains and curtesy , translated them both into the Heavens , and made of them two Constellations , the lesser Bear , and the greater Bear. Other-some say , that it was Arcas the son of Calisto , and they tell the Tale on this manner ; Calisto a Nymph of singular Beauty , Daughter to Lycaon King of Arcadia , induced by the great desire she had of hunting , became a follower of the Goddess Diana . After this , Jupiter being enamoured with her Beauty , and out of hope , by reason of her profession , to win her love , in his own person , counterfeited the shape of Diana , lay with Calista , and got her with Child , of whom was born a Son which was called Arcas . Diana , or rather Juno , being very much offended herewith , turned Calisto into a Bear. Arcas her Son at the age of fifteen , hunting in the Woods , by chance lighted on his Mother in the shape of a Bear , who knowing her Son Arcas , stood still that he might come near unto her , and not be afraid : but he fearing the shape of so cruel a Beast , bent his Bow of purpose to have slain her : whereupon Jupiter to prevent the mischief , translated them both into Heaven , and of them made two several Constellations : unto the Lesser Bear there belongs but one Star unformed . 2. VRSA MAJOR , the Greater Bear , called also of the Greeks Arctos , and Helice , consisteth of 27 Stars ; Among the which , those seven that are in the hinder part and tail of the Bear are most observed ; the Latines call them Plaustrum , and of our met they are called Charles Wayn ; because the Stars do stand in such sort , that the three which are in the tai● resemble the Horses , and the other four which are in the flank of the Bear , stand ( after a manner ) like the Wheels of a wagon , or Chariot ; and they are supposed by some to be greater than the Sun. The reason of the translation of this Constellation into the Heaven , is at large set down in the other Constellation● and therefore needs not here to be repeated . This Constellation was first invented by Nauplius , the Father of Palamedes the Greek ; and in great use among the Grecians ; and this is to be noted both in this and the former Constellation , that they never set under the Horizon in any part of Europe : which though it fal● out by reason of their scituation in the Heavens ; Ye● the Poets say , that it came to pass through the displeasure and hatred of Juno , who for that she was by Calisto made a Cuckquean , and they notwithstanding ( as she took it ) in despight of her ' were Translated into Heaven , requested her brother Neptune , that h● should never suffer those Stars to set within hi● Kingdom , To which request Neptune condescended● so that in all Europe they never come near unto th● Sea , or touch the Horizon . If any one marvel , tha● ( seeing she hath the form of a Bear ) she should have a tail so long ; imagine that Jupiter fearing to come too nigh unto her teeth , laid hold on her tail , and thereby drew her up into Heaven ; so that she of her self being very weighty , and the distance from the Earth to the Heaven very great , there was great likelyhood that her tail must stretch . The Unformed Stars belonging to this Constellation are Eight . 3. DRACO , the Dragon , of some named the Serpent ; of others the Snake , by the Arabians , Aben , and by Junctinus Florentinus , Vrago ; because he windeth his tail round about the Ecliptick Pole ; it containeth 31 Stars . This was the Dragon that kept the Golden Apples in the Orchard of the Hesperides , ( now thought to be the Islands of Cape de Virde ) and for his diligence and watchfulness , was afterwards Translated into Heaven : Yet others say that he came into Heaven by this occasion ; when Minerva withstood the Gyants fighting against the Gods ; they to terrifie her , threw at her a mighty Dragon , but she catching him in her hands , threw him presently up into Heaven , and placed him there , as a memorial of that her resistance . Others would have it to be the Serpent Python , whom Apollo slew , after the Deluge . 4. CEPHEVS , containeth in him 11 Stars , and hath two unformed . This was a King of the Aethiopians , and Husband unto Cassiopeia , and Father of Andromeda , whom Perseus married : He was taken up into Heaven , with his Wife and Daughter , for the good Deeds of Perseus his Son in Law , that he and his whole stock might be had in remembrance for ever . The Star which is in his right shoulder is called by the Arabians Alderahiemin ( i. e. ) his right Arm. 5. BOOTES , the driver of the Oxen ( for so I suppose the name to signifie , rather than an Herdsman , for he hath not his name because he hath the care of any Cattel , but only because he is supposed to drive Charles his Wain , which is drawn by 3 Oxen ) he is also called Arctophilax , the keeper of the Bear , as tho' the care of her were committed to him : This Constellation consisteth of 22 Stars . Some will have Bootes to be Arcas , the Son of her who before was turned into the Great Bear ; and they tell the Tale thus : Lycaon the Father of Calisto , receiving Jupiter into his house as a Guest , took Arcas his Daughters Son , and cut him in pieces ; and among other Services , set him before Jupiter to be eaten ; for by this means he thought to prove if his Guest were a God , as he pretended to be Jupiter perceiving this heinous fact , overthrew the Table , fired the house with lightning , and turned Lycaon into a Wolf : but gathering , & setting together again the limbs of the child , he committed him to a Nimph of Aetolia to be kept : Arcas afterwards coming to mans estate , and hunting in the Woods , lighted at un-awares upon his Mother , transformed by Juno into the shape of a Bear , whom he pursued into the Temple of Jupiter Lycaeus , whereunto by the Law of the Arcadians , it was death for any man to come . For as much therefore as they must of likelihood be both slain , Calisto by her Son , and he by the Law , Jupiter to avoid this mischief , of meer pity took them both up into Heaven . Unto this Constellation belongeth but one Star unformed , and it is between the legs of Bootes , and by the Grecians it is called Arcturus , because of all the stars near the great Bear named Arctos , this star is first seen near her tail in the evening . The Poetical invention is thus . Icarus the Father of Erigone , having received of the God Bacchus a Flagon of Wine , to declare how good it was for mortal men , travelled therewith into the Territoires of Athens , and there began to carouse with certain shepheards , they being greatly delighted with the pleasantness of the wine , being a new kind of Liquor , began to draw so hard at it , that er'e they left off , they were past one and thirty ; and in the end , were fain to lay their heads to rest . But coming unto themselves again , and finding their brains scarce in good temper , they kil'd Icarus , thinking indeed that he had either poysoned them , or at the least-wise made their brains intoxicate . Erigone was ready to dye for grief , and so was Mera her little dog . But Jupiter to allay their grief , placed her Father in Heaven , between the legs of Arctophilax . 6. CORONA BOREA , the Northern Garland , consisteth of Eight Stars ; yet Ovid saith , that it hath nine . This was the Garland that Venus gave unto Ariadne , when she was Married unto Bacchus , in the Isle Naxus , after that Theseus had forsaken her : which garland Bacchus placed in the Heaven ; as a token of his love . Novidius will have it to be the Crown of the Virgin Mary . 7. ENGON ASIS ; This Constellation hath the name , because it is expressed under the shape of a man kneeling upon the one knee , and is therefore by the Latines called Ingeniculum It containeth 29 Stars and wanteth a proper Name , because of the great diversity of Opinions concerning the same . For some will have it to be Hercules , that mighty Conqueror who for his 12 Labours was thought worthy to be placed in the Heaven , and nigh unto the Dragon whom he overcame . Others tell the tale thus : That when the Tytans fought against the Gods , they for fear of the Gyants , ran all unto the one side of the Heaven : whereupon the Heaven was ready to have fallen , had not Hercules together with Atlas , set his neck unto it , and stayed the fall : and for his Desert he was placed in Heaven . 8. LYRA , the Harp , it containeth 10 Stars , whereof thus goeth the Fable . The River Nilus swelling above his banks , over-flowed the Country of Egypt ; after the fall whereof there were left in the fields divers kinds of living things , and amongst the rest a Tortoise ; Mercury , after the flesh thereof was consumed , the sinews still remaining , found the same , and striking it , he made it yield a certain sound ; whereupon he made an Harp like unto it , having Three strings , and gave it unto Orpheus the Son of Cassiopea . This Harp was of such excellent sound , that Trees , Stones , Fowls , and Wild Beasts are said to follow the sound thereof . After such time therefore that Orpheus was slain by the Women of Thrace the Muses by the good leave of Jupiter , and at the request of Apollo , placed this Harp in Heaven . Novidius will have it to be the Harp of David , where by he pacified the Evil spirit of Saul . This Constellation was afterwards called Vultur Cadens , the falling Grype : and Falco the Falcon ; or Timpanum the Timbrel . 9. OLOR , or Cygnus the Swan , called of the Chaldaeans Adigege , it hath 17 Stars : of this Constellation the Poets Fable in this manner . Jupiter being overtaken with the love of Laeda the wife of Tyndarus King of Oebabia , and knowing no honester way to accomplish his desire , procured Venus to turn her self into an Eagle , and himselfe he turned into the shape of a Swan . Flying therefore from the Eagle , as from his natural Enemy that earnestly pursued him he lighted of purpose in the lap of Laeda , and as it were , for his more safety crept into her bosom , The Woman not knowing who it was under that shape , but holding ( as she thought ) the Swan fast in her arms , fell asleep . In the mean while Jupiter enjoyed his pleasure , and having obtained that he came for , betook him again unto his wings ; and in memorial of his purpose ( attained under that form ) he placed the Swan among the Stars . Ovid calleth this Constellation Milvius , the Kite and telleth the Tale thus . The Earth being greatly offended with Jupiter , because he had driven Saturn his Father out of his kingdom , brought forth a monstrous Bull , which in his hinder parts was like a Serpent ; and was afterwards called the Fatal Bull , because the Destinies had thus decreed , that whosoever could slay him and offer up his Entrails upon an Altar , should overcome the eternal Gods , Briareus that mighty Gyant , and ancient enemy of the Gods , overcame the Bull , and was ready to have offered up his Entrails according to the decree of the Destinies : but Jupiter fearing the event , commanded the Fowls of the Air to snatch them away : which although to their power they endeavour'd , yet there was none of them found so forward and apt to that action as the Kite , and for that cause he was accordingly rewarded with a place in Heaven . Some call this Constellation Orvis , that is the Bird : others call it Vultur Volans , the Flying Grype : It is called Gallina , the Hen. Unto this Constellation do belong two unformed Stars . 10. CASSIOPEIA , She consisteth of 13 Stars . This was the Wife of Cepheus , and the mother of Andromeda , whom Perseus married , and for his sake was translated into Heaven , as some write . others say that her beauty being singular she waxed so proud , that she preferred her self before the Nereides , which were the Nymphs of the Sea : for which cause , unto her disgrace , & the example of all others that in Pride of their hearts would advance themselves above their betters , she was placed in the Heaven with her head as it were downwards ; so that in the revolution the Heavens she seemeth to be carried head-long . 11. PERSEVS , he hath 26 Stars . This was the Son of Jupiter , whom he in the likeness of a Golden-shower begat upon Danae , the daughter of Acrisius . This Perseus coming unto mans estate , and being furnished with the Sword , Hat , and Wings of his brother Mercury , and the Shield of his Sister Minerva , was sent by his Foster-father Polidectes , to kill the Monster Medusa , whom he slew ; and cutting off her head , carried it away with him : But as he was hasting homewards , flying in the Air , he espied Andromeda the daughter of Cepheus and Cassiopea , for the pride of her mother , bound with a Chain unto a Rock , by the Sea side , there to be devoured by a Whale : Perseus taking notice and pity of the case undertook to fight with the Monster , upon condition that Andromeda might be his Wife , to be short , he deliver'd Andromeda , married her , and returning homeward unto the Isle Seriphus , he found there his Grand-father Acrisius , whom by mischance and unadvisedly he slew with a quoit : ( or as Ovid reporteth ) with the terrible sight the horrible head of Medusa not knowing that it was his Grand-father : but afterwards understanding whom he had slain , he pined away through extream sorrow whereupon Jupiter his father pitying his grief took him up into Heaven : and there placed him in that form wherein he overcame Medusa with the Sword in one hand , and the head of Medusa in the other , and the wings of Mercury at his Heels . This Constellation because of the unluckiness thereof , is called by Astrologers Cacodaemon ( i. e. ) Vnlucky , and Vnfortunate . For ( as they say ) they have observed it that whatsoever is born under this Constellation , having an evil aspect , shall be stricken with Sword , or lose his Head. Novidius saith that it is David with Goliah his head in one hand , and his Sword in the other . The unformed Stars belonging unto this Constellation , are three . 12. AVRIGA , the Wagoner , or Carter : he consisteth of 14 Stars : the Arabians call him Alaiot ; the Greeks Heniochus , ( i. e. ) a man holding a bridle in his hand and so is he pictur'd . Eratostenes affirmeth him to be Ericthonius King of Athens , the son of Vulcan : who having most deformed feet , devised first the use of the Waggon or Chariot , and joyned horses together to draw the same , to the end that he sitting therein might the better conceal his deformities . For which invention , Jupiter translated him into the Heavens . In this Constellation there are two other particular Constellations to be noted ; whereof the one consisteth but of one Star alone , which is in the left-shoulder of Auriga , and is called Hircus , or Capra the Goat ; the Arabians call it Alhajoth : The other consisteth of 2 little Stars a little beneath the others , standing as it were in the hand of Auriga ; this Constellation is called Haedi , the Kids . The tale is thus ; Saturn ( as you heard before ) had received of the Oracle , that one of his Sons should put him out of his Kingdom , whereupon he determined to devour them all : Ops by stealth conveyed away Jupiter , and sent him to Melissus King of Crete , to be nourished . Melissus having 2 daughters , Amalthaea , and Melissa , committed Jupiter unto their Nursery ; Amalthaea had a Goat that gave suck unto 2 Kids , so that by the milk of this Goat , she nourished Jupiter very well : To requite this her care and courtesie , Jupiter ( after he had put his Father out of his Kingdom ) translated her Goat and her two Kids into Heaven , and in remembrance of the Nurse , the Goat is called Capra Amalthaea . Novidius saith , that when Christ was born , and his birth made manifest by the Angels unto the Shepherds , one of them brought with him for a Present , a Goat and two young Kids ; which in token of his good will , were placed in Heaven . 13. OPHIVCVS , or SERPENTARIVS , That is the Serpent bearer . This Constellation hath no proper name , but is thus entituled , because he holdeth a Serpent in his hands . It containeth 24 Stars . Some say that it is Hercules , and report the Tale on this manner . Juno being a great enemy to Hercules , sent two Snakes to kill him as he lay sleeping in his Cradle : but Hercules being a lusty Child ( for Jupiter had spent two days in begetting him ) without much ado strangled them both : In memorial of so strange an event , Jupiter placed him in the Heavens , with a Serpent in his hands . 14. SERPENS , the Serpent of Ophiuchus , which consisteth of 18 Stars . Some say that it is one of the Serpents that should have slain Hercules in his Cradle . Novidius saith , it is the Viper that bit Paul by the hand . Others deliver the Tale in these words ; Glaucus the son of Minos King of Crete , was by misfortune drowned in a Barrel of Honey : Minas his Father craved the help of Aesculapius the Physician : and that he might be driven perforce to help the Child , he shut him up in a secret place , together with the dead Carcass : whiles Esculapius stood in a great maze with himself what were best to be done , upon a sudden there came a Serpent creeping towards him , the which Serpent he slew with the Staff which he had in his hand . After this there came another Serpent in , bringing in his mouth a certain herb , which he laid upon the head of the dead Serpent , whereby he restored him unto life again . Esculapius using the same herb , wrought the same effect upon Glaucus . Whereupon ( after that ) Esculapius ( whom some affirm to be Ophiucus ) was placed in the Heaven and the Serpent with him . 15. SAGITA , or Telum ; the Arrow or Dart. This was that Arrow wherewith Hercules slew the Eagle or Grype that fed upon the Liver of Prometheus being tyed with Chains to the top of Mount Caucasus , and in memorial of that deed , was translated into Heaven . Others will have it to be one of those Arrows which Hercules at his death gave unto Phyloctetes , upon which the Destiny of Troy did depend . The whole Constellation containeth five Stars . 16. AQVILA , the Eagle , which is called Vultur Volans , the flying Grype . It hath in it 9 Stars . The Poetical reason of this Constellation , is this ; Jupiter transforming himself into the form of an Eagle took Ganimedes the Trojan Boy , whom he greatly loved up into Heaven , and therefore in sign thereof : ( because by that means he performed his purpose ) he placed the figure of the Eagle in Heaven . There belong unto this Constellation 6 Stars ( before time ) unformed , but now brought into the Constellation of Antinous . But whereupon that name should come , I know not , except it were that some man devised it there to curry favour with the Emperour Adrian , who loved one Antinous Bithynicus so well , that he builded a Temple in his honour at Mantinea . 17. DELPHINVS , the Dolphin : it containeth 10 Stars ; yet Ovid in his second Book de Fastis , saith that it hath but nine . Neither did the ancient Astronomers attribute unto it any more , according to the number of the Muses ; because of all other Fishes the Dolphin is said to be delighted with Musick . The Tale goeth thus concerning this Constellation . When Neptune the God of the Sea greatly desired to match with Amphitrite , she being very modest and shame-faced , hid her self ; whereupon he sent many messengers to seek her out , among whom , the Dolphin by his good hap , did first find her ; and perswaded her also to match with Neptune : For which his good and trusty service , Neptune placed him in the Heavens . Others say , that when Bacchus had transformed the Marriners that would have betrayed him , into Dolphins , he placed one of them in Heaven , that it might be a lesson for others to take heed how they carried any one out of his way , contrary both to his desire , and their own promise . Novidius referreth this Constellation unto the Fish that saved Jonas from drowning . 18. EQVICVLUS , is the little Horse , and it consisteth of 4 Stars . This Constellation is named almost of no Writer , saving Ptolomeus , and Alphonsus who followed Ptolemy , and therefore no certain Tale or History is delivered thereof by what means he came into Heaven . 19. EQUUS ALATUS , the Winged Horse , or Pegasus , it containeth 20 Stars . This Horse was bred of the blood of Medusa , after that Perseus had cut off her head , and was afterwards taken and tamed by Bellerophon , whiles he drank of the River Pirene by Corinth , and was used by him in the conquest of Chimera ; after which exploit Bellerophon being weary of the earthly affairs , endeavoured to fly up into Heaven . But being amazed in his flight , by looking down to the earth , he fell from his Horse , Pegasus notwithstanding continuing his course ( as they feign ) entred into Heaven , and there obtained a place among the other Constellations . 20. ANDROMEDA , She consteth of 23 Stars ; but one of them is common both unto her and Pegasus . This was the daughter of Cepheus and Cassiopeia , and the Wife of Perseus ; the reason why Minerva or Jupiter placed her in the Heavens , is before expressed . Novidius referreth this Constellation unto Alexandria the Virgin , whom S. George through the good help of his Horse delivered from the Dragon . 21. TRIANGULUM , the Triangle , called also Deltoton , because it is like the fourth Letter of the Greek Alphabet Δ , which they call Delta ; it consisteth of four stars . They say it was placed in Heaven by Mercury , that thereby the head of the Ram might be the better known . Others say , that it was placed there in honour of the Geometricians , among whom , the Triangle is of no small importance . Others affirm , that Ceres in times past requested Jupiter that there might be placed in Heaven some Figure representing the form of Sicily an Island greatly beloved of Ceres for the fruitfulness thereof : now this Island being triangular ( at her request ) was represented in the Heaven under that form . Thus much concerning the Constellations of the Northern Hemisphere . Now follow the Poetical Stories of the Constellations of the Southern Hemisphere . Secondly , Of the Southern Constellations . 1 CETUS , the Whale , it is also called the Lyon , or Bear of the Sea. This is that monstrous Fish that should have devoured Andromeda , but being overcome by Perseus , was afterwards translated into Heaven by Jupiter , as well for a token of Perseus his manhood , as for the bigness of the Fish it self . This Constellation consisteth of 22 Stars . 2. ORION , this hath 38 Stars . The Poetical reason of his translation into the Heavens , shall be shewn in the Scorpion amongst the Zodiacal Constellations . The Ancient Romans called this Constellation Jugala , because it is most pestiferous unto Cattel , and as it were the very cut-throat of them . There are bright Stars in his girdle , which we commonly call our Ladies yard , or wand . Novidius , applying this sword of Orion unto Scripture , will have it to be the Sword of Saul , afterwards called Paul , wherewith he persecuted the Members of Christ : which after his Conversion was placed in Heaven . In his left shoulder there is a very bright Star , which in Latine is called Bellatrix the Warriour , in the Faeminine Gender . I cannot find the reason except it be this ; that Women born under this Constellation shall have mighty tongues : the reason of the Ox hide which he hath in his hand , may be Gathered out of the next story . 3. FLUVIUS , the River ; it comprehendeth 34 Stars : It is called by some Eridanus , or Pagus ; they say that it was placed in Heaven in remembrance of Phaeton , who having set the whole Earth on fire by reason of misguiding his Father Phoebus his Chariot , was slain by Jupiter with a thunder-bolt , and tumbling down from Heaven , fell into the River Eridanus , or Padus , which the Italians call Po. Others say that it is Nilus , and that that figure was placed in Heaven because of the excellency of that River , which by the Divines is called Gihon , and is one of the Rivers of Paradice . Others call it Flumen Orionis the flood of Orion ; and say that it was placed there , to betoken the off-spring from whence Orion came : for the tale is thus reported of him . Jupiter , Neptune , and Mercury , travelling upon the Earth in the likness of Men , were requested by Hyerus to take a poor lodging at his house for a Night : they being overtaken with the evening , yeilded unto his request ; Hyreus made them good cheer , killing an Ox for their better entertainment : The Gods seeing the good heart of the old man , willed him to demand what he would in recompence of his so friendly cheer . Hyerus and his Wife being old , requested the Gods to gratify them with a Son. They to fulfil his desire , called for the hide of the Ox that was slain , and having received it , they put it into the Earth , and made water into it all three together , and covering it , willed Hyreus within ten months after to dig it out of the Earth again ; which he did and found therein a Man-child ; whom he called Ourion , ab Urania , of piss ; although afterwards by leaving out the second letter , he was named Orion . At such time therefore as he was placed in Heaven , this flood was joyned hard to his heels , and the Ox hide wherein the Gods did piss , was set in the left hand , in memorial of his Off-spring . 4. LEPUS , the Hare , which consisteth of 12 Stars . This Constellation was placed in Heaven between the legs of Orion , to signifie the great delight in hunting which he had in his life time : but others think it was a frivolous thing , to say that so notable a fellow as Orion would trouble himself with so small and timorous a Beast as the Hare ; and therefore they tell the tale thus . In times past there was not a Hare left in the Isle Leros ; a certain youth therefore of that Island , being very desirous of that kind of beast , brought with him from another Country thereabout , an Hare great with young ; which when she had brought forth , they in time became so acceptable unto the other Country men , that every one almost desired to have and keep a Hare . By reason whereof , the number of them grew to be so great , within a short space after , that the whole Island became full of Hares , so that their Masters were not able to find them meat : whereupon the Hares breaking forth into the fields , devoured their Corn. Wherefore the Inhabitants being bitten with hunger ; joyned together with one consent , and ( though with much adoe ) destroyed the Hares . Jupiter therefore placed this Constellation in the Heavens ; as well to express the exceeding fearfulness of the Beast , as also to teach men this lesson ; that there is nothing so much to be desired in this life , but that at one time or another bringeth with it more grief than pleasure . Some say , that it was placed in Heaven at the request of Ganimedes , who was greatly delighted with hunting the Hare . 5. CANIS MAJOR , the Great Dog , it consisteth of 18 Stars . It is called Sirius Canis , because he causeth a mighty drought by reason of his heat . This is the Constellation that giveth name unto the Canical or Dog days ; whose beginning and end is not alike in all places , but hath a difference according to the Countrey and time : as in the Time of Hippocrates the Physitian , who lived before the time of Christ 400 years , the Canicular days began 13 or 14 of July . In the time of Avicenna , the Spaniard , who lived in the year of Lord 1100. the Canicular days began the 15 , 16 , or 17 of July . In our Country ; they begin about St. James-tide , but we use to account from the 6 of July , to the 17 of August ; which is the time when the Sun beginneth to come near unto and to depart from this Constellation . Novidius will have it to be referred to Tobias Dog which may very well be , because he hath a tail ; Tobias Dog had one ; as a certain fellow once concluded , because it is written that Tobias his Dog fawned upon his Master , therefore it is to be noted ( said he ) that he had a tail . The Poets say , that this is the Dog whom Jupiter set to keep Europa , after he had stolen her away , and conveyed her into Creet , and for his good service was placed in Heaven . Others say , that it was one of Orion his Dogs . There belong unto this Constellation 11 Stars unformed . 6. CANIS MINOR , the Lesser Dog ; this of the Greeks is called Procyon , of the Latines Antecanis ; it containeth but two Stars . Some say , that this was also one of Orion's Dogs . Others rather affirm it to be Mera the Dog of Origone , or rather of Icarius her Father , of whom mention is made in the Constellation of Bootes and Virgo . This Dog of meer love to his Master , being slain , as aforesaid , threw himself into the River Anygrus , but was afterward translated into Heaven , with Origone . Among the Poets there is great dissention which of the two should be the Dog of Origone , some saying one , and some the other , and therefore they do many times take the one for the ●●her . 7. ARGO NAVIS , the Ship Argo which comprehendeth 41 Stars ; this is the Ship wherein Jason did fetch the golden fleece from Colchis , which was afterward placed in Heaven as a memorial , not only because of the great Voyage , but also , because ( as some will have it ) it was the first Ship wherein any man sailed . Their reason why this Ship is not made whole is that thereby men might be put in mind not to despair , albeit that their Ship miscarry'd in some part now and then : some avouch it to be the Ark of Noah . Novidius saith it is the Ship wherein the Apostles were , when Christ appeared unto them walking on the Sea. In one of the Oars of this Ship there is a great Star , called Canopus , or Canobus , which the Arabians called Shuel , as it were a bone-fire because of the greatness thereof . It is not seen in Italy , nor in any Country on this side of Italy : Some say that Canobus the Master of Menelaus , his Ship was transformed into this Star. 8. HYDRA , the Hydra , that hath 25 Stars and two unformed . 9. CRATER , the Cup , or Standing-piece ; that hath seven Stars , some say that this was the Cup where in Tagathon , that is the chief God , mingled the Stuff whereof he made the Souls of Men. 10. CORVUS , the Crow ; this hath seven Stars . These 3 Constellations are to be joyned together , because they depend upon one History , which is this . Upon a time Apollo made a solemn feast to Jupiter , and wanting water to serve his turn , he delivered a Cup to the Crow ( the bird wherein he chiefly delighted ) and sent him to fetch water therein . The Crow flying towards the River , espied a Fig-tree , fell in hand with the Figs , and abode there till they were ripe : In the end when , he had fed his fill of them , and satisfied his longing , he bethought himself of his errand , and by reason of his long delay , fearing a Check , he caught up a snake in his bill , brought it to Apollo , and told him that the snake would not let him fill the Cup with water , Apollo seeing the impudence of the bird , gave him this gift , that as long as the Figs were not ripe upon the Tree so long he should never drink : and for a memorial of the silly excuse that she made , he placed both the Crow , Cup , and Snake , in Heaven . 11. CENTAURUS , the Centaure , which comprehendeth 37 Stars . Some say , that this is Typhon , others call him Chiron , the Schoolmaster of those three excellent men , Hercules , Achilles , and Esculapius : unto Hercules he read Astronomy , he trained Achilles in Musick , and Aesculapius , in Physick : and for his upright life he was turned into this Constellation , Yet Virgil calleth Sagittarius by the name of Chiron . In the hinder feet of this Constellation , those Stars are set which are called the Crosiers , appearing to the Marriners as they sail towards the South Sea , in the form of a Cross , whereupon they have their name . The four Stars which are in the Garnish of the Centaurs Spear , are accounted by Proclus as a peculiar Constellation , and are called by him Thyrsilochus which was a Spear compassed about with vine leaves : but they are called by Copernicus , and Clavius , and other Astronomers , the Stars of his Target . It should seem that they were deceived by the old translation of Ptolomy , wherein Scutum is put for Hasta ( i. e. ) the Target , for the Spear , as it is well noted by our Country-man Mr. R. Record , in his Book entituled The Castle of Knowledge . 12. LUPUS , the Wolfe , or the beast which the Centaur holdeth in his hand , contaneth 19 Stars ; the Poetical reason is this , Chiron the Centaur being a just man , was greatly given to the worship of the Gods : for which thing , that it might be notified to all posterity , they placed him by this beast , which he seemeth to stick and thrust through with his Spear ( as it were ) ready to kill for Sacrifice . 13. ARA , the Altar , it is also called Lar , or Thuribulum ( i. e. ) a Chimney with the fire , or a Censor . It consisteth of seven Stars , and is affirmed of some Poets to be the Altar whereon the Centaur was wont to offer up his sacrifice . But others tell the tale thus . When as the great Gyants called the Tytans laboured as much as might be to pull Jupiter out of Heaven , the Gods thought it good to lay their heads together , to advise what was best to be done : Their conclusion was , that they should all with one consent join hands together to keep out such fellows , and that this their league might be confirmed , and throughly ratified , they caused the Cyclops ( which were workmen of Vulcan ) to make them an Altar : about this Altar all the Gods assembled , and there sware , that with one consent they would withstand their enemies ; afterwards , having gotten the Victory it pleased them to place this Altar in Heaven as a memorial of their League , and a token of that good which unity doth breed . 14. CORONA AUSTRINA , the South Garland , it hath 13 Stars . Some say that it is some trifling Garland which Sagittarius was wont to wear , but he cast it away from him in jest , and therefore it was placed between his legs ; others call it the Wheel of Ixon , whereupon he was tormented for that great discourtesie he would have offered unto Juno , thinking indeed to have gotten up her Belly : but Jupiter seeing the impudency of the man , tumbled him out of Heaven ( where by the license of the gods he was sometimes admitted as a guest ) into Hell there to be continually tormented upon a Wheel : The Figure of which Wheel was afterwards placed in Heaven , to teach men to take heed how they be too saucie to make such courteous proffers unto other mens wives . The Greeks call this Constellation by the name of Vraniscus , because of the Figure thereof : For it representeth the palate or roof of the mouth , which they call Vraniscus . 15. The last is PISCIS AUSTRINUS , or Notius , the South Fish , which comprehendeth 11 Stars , besides that which is in the mouth thereof , belonging to the water , which runneth from Aquarius , and is called by the Arabians Fomahant . The reason why this Fish was placed in the Heaven , is uncertain : yet some affirm , that the daughter of Venus going into a water to wash her self , was suddenly transformed into a Fish the which Fish was afterwards translated into Heaven . The unformed Stars belonging unto this Constellation are six . Thus much concerning the Constellation of the Northern and Southern Hemispheres ; now follow the Poetical Stories of the Zodiacal Constellations . Thirdly , Of the Zodiacal Constellations . 1. ARIES , the Ram , it is called by the Greeks Criot , it containeth in it 13 Stars , which were brought into this Constellation by Thyestes , the son of Pelops , and brother of A●reus . This is the Ram , upon which Phr●xus , and H●lle his sister , the children of Athamas did sit , when they fled from their step-mother Ino , over the Sea of Hellespont : which Ram was afterwards for his good service , translated to Heaven ven by Jupiter Others say , that it was that Ram which brought Bacchus unto the spring of water , when through drought he was likely to have perished in the desert of Lybia . Novidius will have this to be the Ram , which Abraham offered up instead of his Son Isaac . The Star that is first in the head of the Ram , is that from whence our later Astronomers do account the Longitude of all the rest , and it is distant from the head of Aries , in the tenth Sphere , 27 degrees 53 minutes . The unformed Stars belonging unto this Constellation , are five . 2. TAVRVS , the Bull , which consisteth of 23 Stars . This was translated into Heaven in memorial of the Rape committed by Jupiter on Europa the daughter of Agenor , King of Sidon ; whom Jupiter in the likeness of a white Bull stole away , and transported into Candia . Others say , That it was Io the daughter of Inacus , whom Jupiter loved , and turned into the form of a Cow , to the intent that Juno coming at unawares , should not perceive what a part he had played : Jupiter afterward in memorial of that crafty conveyance , placed that Figure in Heaven ; The reason why the Poets name not certainly whether it be a Cow or a Bull , is because it wanteth the hinder parts ; yet of the most of them it is called a Bull. In the Neck of the Bull there are certain Stars standing together in a cluster , which are commonly called the seven Stars ; although there can hardly be discerned any more than six , these are reported to be the seven daughters of Atlas , called Atlantiades , whereof 6 had company with the immortal Gods , but the 7 th . ( whose name was Merope ) being married unto Sysiphus a mortal man , did therefore withdraw and hide her self , as being ashamed that she was not so fortunate in matching herself as her sisters were . Some say that that star which is wanting is Electra , eldest Daughter of Atlas , and that therefore it is so dim , because she could not abide to behold the destruction of Troy ; but at that time and ever since , she hid her face . The reason why they were taken up into Heaven , was their great pity towards their Father , whose mishap they bewailed with continual tears . Others say , that whereas they had vowed perpetual Virginity , and were in danger to lose it , by reason of Orion , who greatly assailed them , being overtaken with their love ; they requested Jupiter to stand their friend ; who translated them into Stars , and placed them in that part of Heaven . The Poets call them Pleiades , because when they rise with the Sun , the Mariners may commit themselves to the Sea. Others will have them to be so termed a pluendo , because they procure rain . Others give them this name , of the Greek word Cleiones , because they be many in number ; they be also called Virgiliae , because they rise with the Sun in the Spring time : likewise Athoraiae , because they stand so thick together . Our men call them by the name of the seven Stars , or Brood Hen. The Astronomers note this as a special thing concerning these stars , that when the Moon and these Stars do meet together , the eyes are not to be medled withal , or cured if they before : their reason is , because they be of the nature of Mars and the Moon . Moreover , there be five stars in the face of the Bull , representing the form of the Roman letter V , whereof one ( which is the greatest ) is called the Bulls Eye , They be called Hyades , and were also the daughters of Atlas , who so long bewailed the death of Hyas their Brother , slain by a Lyon , that they died for sorrow , and were afterwards placed in Heaven , for a memorial of that great love they bare to their Brother . The ancient Romans call the Bulls Eye Parilicium , or Palelicium ; of Pales their goddess , whose feast they celebrated after the conjunction of this Star and the Sun. The unformed Stars belonging unto this Constellation , are eleven . 3. GEMINI , the Twins consisteth of 18 stars . The Poets say , they are Castor and Pollux , the sons of Leda , brethren most loving , whom therefore Jupiter translated into Heaven . Some say that one of them is Apollo , and the other Hercules : but the most affirm the former . The unformed Stars of this Constellation are seven , whereof one is called Tropus , because it is placed next before the foot of Castor . 4. CANCER , the Crab , it hath 9 Stars . This is that Crab which bit Hercules by the heel as he fought with the Serpent Hydra in the Fen Lerna , and for his forward service , was placed in Heaven by Juno , the utter enemy of Hercules . In this Constellation there are Stars much spoken of by the Poets ; although they be but small , whereof one is called the Crib , other two are the two Asses , whereof one was the Ass of Bacchus , the other of Vulcan , whereon they rode to Battel , when as the Gyants made War with the Gods ; with whose braying and strange noise , the Gyants were so scared upon the sudden , that they forsook the field , and fled . The Gods getting the Victory , in triumphing manner translated both the Asses , and their manger into Heaven . The unformed Stars of this Constellation are four . It is called animal Rerrogradum , for when the Sun cometh into this Sign , he maketh Retrogradation . 5. LEO , the Lyon ; it hath 27 Stars , this is that Lion which Hercules overcame in the wood Nemaea , and was placed in Heaven in remembrance of so notable a deed . Novidius saith , this was one of the Lyons that were in the den into which Daniel was cast , and was therefore placed in Heaven , because of all other he was most friendly unto Daniel . In the breast of this Constellation is that notable great Star , the light whereof is such , as that therefore it is called by Astronomers Bazileus or Regulus ( i. e. ) the Viceroy or little King among the rest . The unformed Stars belonging to the Lyon are eight , whereof three make the Constellation which is now called Coma Berenices that is , the hair of Berenice . This Constellation was first found out and invented by Canon the Mathematician , but described by Calimachus the Poet. The occasion of the story was this . Ptolomeus Euergetes having married his sister Berenice , was shortly after enforced to depart from her , by reason of the Wars he had begun in Asia : whereupon Berenice made this Vow , that if he returned home again in safety , she would offer up her hair in Venus Temple . Ptolomy returned safe ; and Berenice , according to her Vow , cut off her hair and hung it up . After certain days , the hair was not to be found ; whereupon Ptolomy the King was greatly displeased ; but Canon , to please the humor of the King , and to curry favour with him , perswaded him that Venus had conveyed the Hair into Heaven . Canon attributeth seven Stars unto it , but Ptolomy allotteth it but three , because the other be insensible . 6. VIRGO , the Virgin , it hath 26 Stars . This is affirmed to be Justice , which among all the Gods sometime living upon the Earth , did last of all forsake the same , because of the wickedness that began to multiply therein , and chose this place for her seat in Heaven . Others say , that it was Astrea , the daughter of Astreus , one of the Gyants that were called Titans , who fighting against the Gods , Astraea took their parts against her own Father , and was therefore after her death commended unto the Heavens , and made one of the 12 Signs . Others say , that it was Origone , the daughter of Icarius , who for that her Father was slain by certain drunken men , for very grief thereof hanged her self : but Jupiter taking pity of the Virgin for her natural affection , translated her into Heaven . In her right wing there is one Star of special note , which by the Astronomers is called Vindemiator , ( i. e. ) the gatherer of Grapes . This was Ampulos the son of a Satyr and a Nymph , and greatly beloved of Bacchus unto whom in token of his love , Bacchus gave a singular fair Vine , planted at the foot of an Elm ( as the manner was in old time . ) But Ampelos in Harvest gathering Grapes , and taking little heed to his footing , fell down out of the Vine , and brake his neck . Bacchus in memorial of his former affection , translated him into Heaven , and made him one of the principal Stars in this Constellation . There is another great Star in the hand of the Virgin , called of the Latines Spica , of the Greeks Stachus , of the Arabians Azimech ( i. e. ) the Ear of Corn : whereby they signifie , that when the Sun cometh to this Sign , the Corn waxeth ripe . Albumazar the Arabian , and Novidius , take this Constellation for the Virgin Mary . The unformed Stars in this Constellation are six . 7. LIBRA the Ballance , it containeth eight Stars , Cicero calleth Jugum the Yoke , and here it is to be noted , that the ancient Astronomers that first set down the number of the Constellations contained in the Zodiack , did account but eleven therein , so that the Sign , which now is called Libra , was heretofore called Chelai , that is to say , the Claws of the Scorpion , which possesseth the space of two whole Signs . But the latter Astronomers , being desirous to have 12 Signs in the Zodiack , called those eight , whereof the Claws of the Scorpion do consist , by the name of Libra , not that there was any Poetical Fiction to induce them thereto , but only moved by this reason , because the Sun joyning with this Constellation , the Day and the Night are of an equal length , and are ( as it were ) equally poized in a pair of Ballances . Yet ( as I remember ) some will have this to be the Ballance , wherein Justice , called also Astraea , weighed the deeds of mortal men , and therein presented them unto Jupiter . It hath 9 unformed Stars appertaining unto it . 8. SCORPIO , the Scorpion , called of the Arabians , Alatrab ; of Cicero , Nepa . It consisteth of 21 Stars . The Fiction is thus ; Orion the son of Hyreus greatly beloved of Diana , was wont to make his boast : that he was able to overcome what Beast soever was bred upon the Earth : the Earth being moved with this speech brought forth the Scorpion , whereby Orion was stung to death . Jupiter thereupon ( at the request of the Earth ) translated both the Scorpion and Orion into Heaven ; to make it a lesson for ever , for mortal men not to trust too much unto their own strength ; and to the end he might signify the great enmity between them , he placed them so in Heaven , that whensoever the one ariseth , the other setteth ; and they are never both of them seen together above the Horizon at once : Gulielmus Postellus will have it to be the Serpent which beguiled Eve in Paradise . The unformed Stars about this Scorpion are three . 9. SAGITTARIVS , the Archer . It hath 31 Stars . Touching this Sign , there are among the Poets many and sundry opinions . Some say that it is Crocus , the son of Paphene , that was Nurse unto the Muses . This Crocus was so forward in learning of the Liberal Sciences , and in the practice of feats of Activity , that the Muses entreated Jupiter that he might have a place in Heaven . To whose request Jupiter inclining , made him one of the 12 Signs : And to the end that he might express the excellent qualities of the Man , he made his hinder parts like unto a Horse , thereby to signifie his singular knowledge in Horsemanship : and by his Bow and Arrow , he declared the sharpness of his Wit. Whereupon the Astrologers have this conceit , that he that is born under Sagittarius , shall attain to the knowledge of many Arts , and be of prompt wit , and great courage . Virgil affirmeth this to be Chiron the Centaur , who for his singular Learning and Justice was made the Master of Achilles . At which time Hercules coming to visit him ( for he had heard both of the worthiness of the School-master , and of the great hopes of the Scholar ) brought with him his quiver of Arrows dipped in the blood of the Serpent Hydra ; but Chiron being desirous to see his shafts , and not taking heed of them being in his hand , let one of them fall upon his foot , and being greatly tormented , not only by the anguish of the Poyson working in the Wound , but much more because he knew himself to be immortal , and his wound not to be recovered by Medicine , he was enforced to make request unto the Gods , that he might be taken out of the World , who pitying his case , took him up into Heaven , and made him one of the 12 Signs . 10. CAPRICORNVS , the Goat , it consisteth of 28 Stars . The Poets say , that this was Pan the God of the Shepherds , of whom they feign in this manner : The Gods having War with the Gyants , gathered themselves together into Aegypt , Typhon the Gyant pursued them thither , whereby the Gods were brought into a quandary , that well was he that by changing his shape might shift for himself . Jupiter turned himself into a Ram : Apollo became a Crow : Bacchus a Goat : Diana lurked under the form of a Cat : Juno transformed her self into a Cow : Venus into a Fish : Pan leaping into the River Nilus , turneth the upper part of his body into a Goat , and the lower part into a Fish. Jupiter wondring at the strange device , would needs have that Image and Picture translated into Heaven , and made one of the 12 Signs . In that the hinder part of this Sign is like a Fish. It betokeneth that the latter part of the month wherein the Sun possesseth this Sign , inclineth unto Rain . 11. AQVARIVS , the Waterman : it hath 42 Stars , whereof some make the Figure of the Man : othersome the Water-pot ; and some , the stream of water that runneth out of the pot . This is feigned to be Ganimedes the Trojan , the son of Oros and Callirhoe , whom Jupiter did greatly love for his excellent favour and beauty , and by the service of his Eagle carried him up into Heaven , where he made him his Cup-bearer , and called him Aquarius . Others notwithstanding think it to be Deucalion the son of Prometheus whom the Gods translated into Heaven , in remembrance of that mighty deluge which hapned in his time ; whereby mankind was almost utterly taken away from the face of the earth . The unformed stars belonging unto this Sign are three . 12. PISCES , the Fishes : these together with the line that knitteth them together , contain 24 Stars . The Poets say , that Venus and Cupid her son coming upon a certain time unto the River Euphrates , and sitting upon the bank thereof , upon a sudden espied Typhon the Gyant , that mighty and fearful enemy of the gods coming towards them ; upon whose sight , they being stricken with exceeding fear , lept into the River , where they were received by two Fishes , and by them saved from drowning . Venus for this good turn , translated them into Heaven . Gulielmus Postellus would have them to be the two Fishes wherewith Christ fed the 5000 Men. The unformed Stars of this Constellation are four . Thus have I briefly run over the Poetical reasons of the Constellations : It remains now that I speak of the Milky Way . VIA LACTEA , or Circulus Lacteus ▪ by the Latines so called ; and by the Greeks Galaxia ; and by the English the Milkey Way . It is a broad white Circle that is seen in the Heaven : In the North Hemisphere , it beginneth at Cancer , on each side the head thereof , and passeth by Auriga , Perseus , Cassiopeia , the Swan , and the head of Capricorn , the tail of Scorpio ▪ the feet of Centaur , Argo the Ship , and so to the head of Cancer . Some in a sporting manner do call it Watling-street , but why they call it so , I cannot tell ; except it be in regard of the narrowness that it seemeth to have ; or else in respect of that great high way that lyeth between Dover and St. Albons , which is called by our men Watling-street . Ovid saith , it is the great Causey , and High-way that leadeth unto the Pallace of Jupiter , but he alledgeth not the cause of the whiteness ; belike he would have us imagine that it is made of White Marble . Others therefore alledg these causes : Jupiter having begotten Mercury of Maia the daughter of Atlas ▪ brought the child when he was born , to the breast o● Juno lying asleep : But Juno awaking threw the child out of her lap , and let the milk run out of her breast in such abundance , that ( spreading it self about the Heaven ) it made that Circle which we see . Others say , that it was not Mercury , but Hercules ; and that Juno did not let the milk run out of her breast , but that Hercules suckt them so earnestly , that his mouth run over , and so this Circle was made . Others say , that Saturn being desirous to devour his children , his wife Ops presented him with a stone wrapped in a clout , instead of his Child : This stone stuck so fast in Saturn's Throat as he would have swallowed it , that without doubt he had therewith been choaked , had he not been relieved by his wife ▪ who by pressing the milk out of her breasts saved his life : the milk that missed his mouth ( whereof you must suppose some sufficient quantity ) fell on the Heavens , and running along made this Circle . Dr. Hood Commenting upon Constellations saith ; the Stars are brought into Constellations , for Instruction sake , things cannot be taught without names ; to give a name to every Star had been troublesome to the Master , and for the Scholar ; for the Master to devise , and for the Scholar to remember ; and therefore the Astronomers have reduced many Stars into one Constellation ; that thereby they may tell the better where to seek them ; and being sought , how to express them . Now the Astronomers did bring them into these Figures , and not into other , being moved thereto by these three reasons : first , these Figures express some properties of the Stars that are in them ; as those in the Ram to be hot and dry ; Andromeda chained betokeneth imprisonment , the head of Medusa cut off signifieth the loss of that part : Orion with his terrible and threatning gesture , importeth tempest and terrible effects . The Serpent , the Scorpion , and the Dragon , signifie Poyson : The Bull insinuateth a melancholy passion : The Bear inferreth cruelty , &c. Secondly , the Stars ( if not precisely , yet after a sort ) do represent such a Figure , and therefore that Figure was assigned them , as for example , the Crown , both North and South , the Scorpion and Triangle , represent the figures which they have . The third cause was the continuance of the memory of some notable Men , who either in regard of their singular pains taken in Astronomy , or in regard of some other notable deed , had well deserved of Mankind . The first Author of every particular Constellation is uncertain ; yet are they of great antiquity ; we receive them from Ptolomy , and he followed the Platonicks ; so that their antiquity is great . Moreover , we may perceive them to be ancient by the Scriptures , and by the Poets . In the 38 Chapter of Job there is mention made of the Pleiades , Orion , and Arcturus , & Mazzaroth , which some interpret the 12 Signs : Job lived in the time of Abraham , as Syderocrates maketh mention in his Book de Commensurandis locorum distantiis . Now besides all this , touching the reason of invention of these Constellations , the Poets in setting forth those Stories , had this purpose , to make men fall in love with Astronomy : When Demosthenes could not get the people of Athens to hear him in a matter of great moment , and profitable to the Common-wealth he began to tell them a Tale of a fellow that sold an Ass ; by which Tale he so wrought on the Athenians , that they were both willing to hear his whole Oration , and to put in practise that whereunto he exhorted them . The like intent had the Poets in these Stories : They saw that Astronomy being for commodity singular in the life of Man , was almost of all men utterly neglected : Hereupon they began to set forth that Art under these Fictions ; that thereby such as could not be perswaded by commodity , might by the Pleasure be induced to take a view of these matters , and thereby at length fall in love with them . For commonly note this , that he that is ready to read the Stories , cannot content himself therewith , but desireth also to know the Constellations , or at least wise some principal Star therein . FINIS . A Catalogue of GLOBES Coel●stial and Terrestrial , Spheres , Maps , Sea-Plats , Mathematical Instruments , and Books , with the●r Prizes , Made and Sold by J. Moxon at the Sign of Atlas in Warwick Lane. GLOBES 26 Inches the Diameter . The price 20 l. the pair . GLOBES near 15 Inches Diameter . The price 4 l. GLOBES 8 Inches Diameter . The price 2 l. GLOBES 6 Inches Diameter . 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A28817	----	A new treatise proving a multiplicity of worlds that the planets are regions inhabited and the earth a star, and that it is out of the center of the world in a third heaven, and turns round before the sun which is fixed : and other most rare and curious things / by Peter Borell ... Discours nouveau prouvant la pluralité des mondes. English Borel, Pierre, 1620?-1671. This text is an enriched version of the TCP digital transcription A28817 of text R19665 in the English Short Title Catalog (Wing B3753). Textual changes and metadata enrichments aim at making the text more computationally tractable, easier to read, and suitable for network-based collaborative curation by amateur and professional end users from many walks of life. The text has been tokenized and linguistically annotated with MorphAdorner. The annotation includes standard spellings that support the display of a text in a standardized format that preserves archaic forms ('loveth', 'seekest'). Textual changes aim at restoring the text the author or stationer meant to publish. This text has not been fully proofread Approx. 124 KB of XML-encoded text transcribed from 112 1-bit group-IV TIFF page images. EarlyPrint Project Evanston,IL, Notre Dame, IN, St. Louis, MO 2017 A28817 Wing B3753 ESTC R19665 12221681 ocm 12221681 56411 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A28817) Transcribed from: (Early English Books Online ; image set 56411) Images scanned from microfilm: (Early English books, 1641-1700 ; 128:1) A new treatise proving a multiplicity of worlds that the planets are regions inhabited and the earth a star, and that it is out of the center of the world in a third heaven, and turns round before the sun which is fixed : and other most rare and curious things / by Peter Borell ... Discours nouveau prouvant la pluralité des mondes. English Borel, Pierre, 1620?-1671. Sashott, D. [10], 200 p. Printed by John Streater, London : 1658. Translation by D. Sashott of: Discours nouveau prouvant la pluralité des mondes. Reproduction of original in Thomason Collection, British Library. Imperfect: introductory material on film difficult to read; t.p. is illegible. eng Cosmology -- Early works to 1800. Astronomy -- Early works to 1800. A28817 R19665 (Wing B3753). civilwar no A new treatise, proving a multiplicity of worlds. That the planets are regions inhabited, and the earth a star, and that it is out of the ce Borel, Pierre 1658 21950 8 0 0 0 0 0 4 B The rate of 4 defects per 10,000 words puts this text in the B category of texts with fewer than 10 defects per 10,000 words. 2006-06 TCP Assigned for keying and markup 2006-06 Apex CoVantage Keyed and coded from ProQuest page images 2006-07 Andrew Kuster Sampled and proofread 2006-07 Andrew Kuster Text and markup reviewed and edited 2006-09 pfs Batch review (QC) and XML conversion A NEW TREATISE , PROVING A Multiplicity OF WORLDS . That the Planets are Regions Inhabited , and the Earth a Star , and that it is out of the Center of the World in the third Heaven , and turns round before the Sun which is fixed . And other most Rare and Curious Things . By PETER BORELL , Counsellor and Physitian to the King of France . London , Printed by John Streater ▪ 1658. TO The Vertuous , AND Most Renowned Gentleman , Mr. Frederick Clodius , Doctor in Physick , His truly honoured Friend . Worthy SIR , THree considerations have induced me to offer these rude and unpolished lines to your Patronage and favourable acceptance . The first is , the Learning and fame of the Author of this Treatise , who carrieth the same Title as Your Self . The second is , the worthinesse and great esteem and acuity of spirit of that Person of Honour , Sir Kenelm Digby , to whom it was offered by the Author . The third is , the worthiness , wisdom and deep Learning wherewith You are indued & adorned , which that Noble Knight well knowing , for an acknowledgment thereof , hath presented this Book to your view , as a piece of great novelty . I shall not presume to implore your Protection for the subject , but onely for this my rash attempt in the translating of it ; which if it may auspiciously be admitted into Your friendly estimation , doubtlesse 't will find an universall acceptance amongst Persons of greatest Eminency ; All I humbly crave for the present is , my boldnesse might be favourably excused , since 't was my lawfull Ambition thereby to avoid Ingratitude ; However this Work be esteemed , may your deserved good name and honor encrease more and more ; which is and shall be the constant Vote of , Sir , Your humbly devoted Servant , D. Sashott . A NEW TREATISE , PROVING A Multiplicity OF WORLDS . CHAP. I. Of the Plurality of Worlds in general , being as a Preface to the following Chapters . WE may truly say , that Preoccupation is an horrid Monster , which makes a strange havock in the spirits of Men , hinders the progress of Sciences , and causes Men to droop in a constant ignorance ; for they who by it are once prepossessed , can judge of nothing by themselves , censure the best opinions that are , assert those of their Masters , whether good or bad ; and having conceived a distaste of whatsoever checks what is contrary to their belief , though grosse and ignorant , bring forth nothing but contempts and blames against those who endeavour to open their eyes , and root them out of the darknesse of their ignorance , to draw them to the enjoyment of the true light and knowledg of things . The which is more particularly practised now in this Age wherein we live , wherein Men live but by imitation , wherein learned Men are despised , wherein they who have some particular and rare notions upon subject matters of great moment and concernment to mens knowledge , are esteemed extravagant and ridiculous , wherein no new proposition can be admitted . But alas , what may I hope , seeing this evill is like a gangrene , and hath taken so deep root , that it hath robb'd men of their senses and feeling , who by it are infected , Considering , that those who are most possess'd with it , do not think so themselves to be ; What then may I expect , who am going to propose some Novelties , not of things that are in the Earth , but even in the Heavens ; and not onely in the Heavens , but also in the bodies of the Stars . As soon as the Title of this Discourse shall appear to the eyes of Men , they will condemn me before they hear me ; neither will they so much as read my Reasons , and will rather live in ignorance , then change their opinion ; and be as beasts in the World , than know the secrets thereof . Most men think it a shame to confesse , that they are ignorant of some thing , and that they are in the wrong ; for on the contrary , it 's the way to find out the truth , considering , that new reasons are alwayes sought for what we esteem our selves ignorant of . Mens ignorance is so great , that the holy Scriptures have declared Mens knowledg to be nothing else but vanity ; and if we do not flatter our selves , we shall find , that we know nothing but is or may be controverted . Divinity it self is not exempted from it ; and as for the other Sciences and Arts , those great & many Volumes that we have of them , sufficiently testifie the same . And this hath moved the Pyrrhonians and Scepticks , to doubt and question all things , and hath brought forth severall Books of the vanity of Sciences , the Astrology , the Medicine , the Jurisprudence , and the naturall Physick are daily moved and shaken , and see their foundations totter ; Ramus did overthrow Aristotle's Philosophy ; Copernicus , Ptolomey's Astrologie ; Paracelsus , Galen's Physick ; So that every one hath followers and disciples , and all appearing plausible . We have much ado whom to believe , and thereby are constrained to confesse , that what we know , is much lesse then what we know not . I greatly esteem Michael Mountanus's Judgment , who is the honour of our Age upon this point ; for it is consonant to reason , and my opinion hereupon is for the most part agreeing with his ; and especially with that is the subject matter of this Treatise : Amongst a thousand rare thoughts that he hath upon it , he alledges a most exquisite similitude , by which he compares learned persons to the ears of corn , which being well fill'd , do bow down their heads ; for after they have learned all Sciences , and have consumed themselves in them , they are constrained to confesse , that they know nothing by the acknowledgment of that great Philosopher , in these words ; Hoc unum scio , quòd nihil scio , I know this one thing , that I know nothing . If then we be ignorant of all things , may we not yield , that we can be ignorant of heavenly things especially , and that they are praise-worthy , who have endeavoured to raise their contemplations and meditations up into Heaven ; and having , as it were , loosened their Souls from their bodies , have made it to wander and run through the Vaults and concavities of Heaven , there to observe those things which were above our reach ? Our understanding being heavenly , and our Soul full of knowledg & perfection , is not ignorant of these things ; but the lump & corpulency of the body , which is its prison , hinders it freely to perform its functions ; it would willingly rise up , and at every moment lenche it self up towards the place of its original ; but the weight of its body keeps it low and under , and the mixture of the Elements wherewith the body is composed , makes its agility dull and heavy . If , before the Invention of Artillery , of Printing , of Prospect-glasses , and of infinite number of other Inventions , that in these times are practised , their effects had been told to us , we had never believed them ; for if it had been asserted , That with the powder , without stirring , we might kill beasts distant from us ; and not onely the beasts on the earth , but also the fowls and birds flying high through the ayr , throw down walls of Cities , and batter and thunder down the strongest places ; and that in a moment those instruments should execute our will : That by printing , and the letters , we might communicate our thoughts to another , and write in a short time a number infinite of books , and even write a thousand times faster then we speak , transmit and leave to our posterity our exquisite conceptions , and get an immortal name ; And that by the prospective glasses , we might approach to objects far distant , strengthen our sight , and make us distinctly to see things sar remote ; If these things ( I say ) had been proposed to us in a time , wherein farther speech and enquire had never more been made of it , who had believed them ? but rather who had not laughed at them , and derided the first motioner of them ? and yet experience daily sheweth the effects of these Inventions to be true . So the former Ages did condemne as hereticks , those who believed the ▪ Antipodes ; and this belief was a long time held for a false and ridiculous opinion ; Christophorus Columbus was rejected of divers Kings , when he proposed to them the discovery of the West-Indies ; and yet his propositions have been found very true , and have immortalised their Author . So likewise do I hope , that time will bring forth the truth of this my opinion , which I do not produce to the light , without many strong Reasons , and the authority of the most learned men , the holy Scripture it self is not repugnant and contradictory to it , but rather leans much towards my opinion : And as touching those Philosophers , who grant it not , some deny not , but that this may be ; others dare not contradict it ; and others have so ridiculous reasons , that I cannot imagine weaker can be found ; and considering all they , no more then I , have ascended into Heaven , and therefore who ever hath the best Reasons , ought to be believed ; which being doubtlesse on my side , my opinion ought not at all to be esteemed ridiculous . Democritus , King of the Abderitanes , constantly smiled , because the World could not apprehend the multiplicity of Worlds ; I , like him , have also sufficient occasion to smile , and laugh at those , who are ignorant of the plurality of the Worlds , and even to compare them to bruit beasts , which eat the fruits of the Earth , without considering whence they come to them : for Man is lodged in this World , to contemplate in it the wonders that God exposes to the sight of his eyes , and to which end he hath given him a face looking upward , for to look up to Heaven ; but he will not make use of his gifts , nor enquire after the place of their habitation . Why open ye not your eyes , O ye learned and wise Men ? and why awake ye not out of your slumber , and deep sleep ? Awake up the eyes of your Understanding and Reason towards the Heavens , contemplating the wonderfull things thereof ; despise the earthly things ; and as true Philosophers , consider the rest of Men in a dunghill , having their thoughts low , and Earthly Souls , which not being able to stretch themselves beyond the limit of their weak activity , dare even accuse those who by noble projects desire to lend them their hands , for to draw them out of their ignorance . Having then so many , and so good Reasons and authority on my behalf , I shall not longer fear those , who scarce can find any for the confirmation of their opinion , or what they have is so weak , that the building , that the edifice is upon , tottereth and leans on every side ; therefore will I not fear those backbiting tongues which envy anothers good repute and fame , which I already foresee in great number opened against me ; but I shall justly say , that they accuse God and Nature of weaknesse and insufficiency , and their own proper reason of incapacity ; Can it be possible , that so many rare and great persons , who in former Ages did believe it , and whose memory is by us honoured and reverenced , had erroneous opinions ? and that so many pertinent reasons should have no solid ground ? Could it be possible , that you would not willingly hearken to those who desire to free you from your mistakes ? nor suffer your eyes to be unfolded , when they be folded with the vail of Preoccupation ? No , I hope , that some of the most reasonable at least will be found , who will adhere to me , and take my part against the assaults of the ignorants , who endeavour to discredit me , thinking to obtain great glory , for the endeavouring the overthrow of so great a project ; for that is their ordinary scope ; Alta petit livor , praestant altissima venti , Alta petunt dextrâ fulmina miss a Jovis . That is , Envy , nothing but high things emulates , As by the whirlwinds shaken are high States ; And the thunders of great Jupiter the god of gods , Fall upon the Steeples , and not upon the Valleys . But I shall smile at them in my heart , and applaud my self , if none can be found to second me , hoping that the Ages to come will produce men more reasonable ; and who , better esteeming my conceptions , will accuse this present Age of great ingratitude . Chap. II. Proving the plurality of the Worlds , by a reason taken from the place wherein are ingendred the Comets . PRoclus , Cardanus , Telessius , and others have observed , That most of the Comets are formed not onely out of the Region of the Meteors , but even far above the Moon ; and Tycho Brabe , that great Astrologian , who by his exquisite and rare Observations , hath gotten an everlasting name , discoursing of it , hath asserted , That all the Comets are formed above the Moon , even according to Kepler , as high as the Sun . Now it 's Impossible for the vapours to pierce and penetrate into the fiery Region , there to be changed into Comets even far above it , considering , that according to all the Philosophers Judgment , the fiery Region is under the concavity of the Moon , and so these Comets are formed out of the exhalations of other Lands which are the Starres ; it 's so clear and perspicuous , that I cannot believe that any Man is so void of Reason as to deny it . If it be objected , That it cannot positively and certainly be known , that the Comets are above the region of the Moon ; I shall send them to the School of Astrologie , which teaches by true Rules and Demonstrations , the way to measure all the bodies , and their far distances from the earth ; the which Galileus , a Person of great fame and renown in this our Age , hath confirmed by such like Observations . Chap. III. Proving the same , by another Argument taken from the bignesse and continuancy of the Comets . THE same Astrologers have observed , That some Comets have so vaste and great bodies , that it 's impossible to believe , that the exhalations of this Earth could furnish them sufficiently with matter ; but I shall dare to go beyond , and shall say , That though all the Earth should be dissolved into vapours and exhalations , yet it could not form so great Comets , and of such long continuancy , as those which sometimes have been seen , although it should all be burned ; insomuch , that it 's needful to say , That the other Stars , whose body is so great in comparison of this our little Globe , did furnish it with matter . Chap. IV. Proving the multiplicity of the Worlds , by a reason drawn from the conformity of the Moon with the Earth . ALL Philosophers and Astrologers are agreed , That the Earth and Moon have this commune between them , that they both are thick , grosse , dark , and solid bodies , able to receive and refresh the light of the Sun ; this being granted , What is easier than to conclude , That the Earth reverberating the beams of the Sun , would appear lightsome to them who should be raised high towards Heaven ? that it would seem so little and small by its far distance from us , that it would be almost like the Moon , both in light and bignesse ; and that it would even have its spots , because of the waters which bury and smother the Sun beams ; and do not reverberate them . We might discover in it by prospective glasses some of the chiefest Mountains , whereby we might soon be perswaded to believe , that those Seas and Mountains are inhabited and filled with living Creatures . And if we turn what we have said of the Earth , to the Moon , shall we not say the same of it ? Wherein we discover those spots , that by Galileus's prospective-glasses helps us so naisty to distinguish , that we see in it , as in a Table and Mapp , some Seas , some straights , some Lakes , some Rivers , and some Islands , some Rocks and Mountains , that are perceived to swell out , especially at the new Moon . And if it be true of the Moon , can it not be true also of the other Stars ? but their far distance stealing from our eyes their spots , we must judge of it by the Moon , which though lesser , is nearer to us , and appears greater to our eyes ; and that we may not think , that the same things that are seen in the Moon , cannot appear in the other Stars , the Telescope sheweth us a Mountain in Mars , some spots in other Stars , and that Venus increaseth and diminisheth even as the Moon . Chap. V. Wherein is proved , this Opinion of divers Worlds , in that the Earth is a Starre , as the others . THe foregoing Chapter declaring to us , how the Earth would appear lightsome to us , if we were once high raised up from it , because it reflects the beams of the Sun , which according to the divers places by it inlightned , would cause it to increase and decrease ; considering also , that Mountains seen from far are bright and shining ; and that , as Milchius saith , the fields adjacent to mount Hesperides , shine at night as the Stars ; and seeing also that the Earth is moveable , as hereafter we shall prove it , that it is situated in the Ayr , and weighed and counterpois'd in its proper weight , and that the Ayr is the Heavens , as the Holy Scriptures do sufficiently prove it , when at every moment they confound the Ayr with the Heavens , Shall we not then say , That the Earth is a Star situated in Heaven , as well as the other Starres ? That this at the first sight will amuse the Readers , but they shall be pleased to yield , That the yolk of an egg is in its shell , neither can they deny , that the Earth is in Heaven , which wraps and compasses it on every side as an egg-shell ; and that the infinite spaces of the Aires , which are the Heavens , do not contain divers bodies far distant one from the other , and so consequently the earth seeming from on high little and lightsome , may be a Star inhabited . But if the Earth be a Star inhabited , the others may be Earths inhabited , being they , as well as the Earth , seem and appear to be great and lightsome bodies to those who are far remote from them . And that no Man may object , that the Heaven is a place coloured , solid and separated from their aire , I beseech him to consider , that things far remote from us , appear as the Skie , even the Mountains and Seas seen from far , seem blewish ; so that this skie-colour'd Heaven that we see , is not a solid and reall thing , but the limit of our sight in a certain place of the infinite spaces of the Aire , which are the common place , wherein are lodged an infinite number of great globes of divers natures , or inhabited by several living creatures , which the Sun being in the middle , equally inlightens ; as a great Torch set in the midst of a Chamber , shines in every corner of it , with the brightnesse of its light . Chap. VI . Proving the same , by the great number of the Stars , and by their noblenesse . THose who imagine , that the infinite number of the heavenly bodies are created for the globe of the earth , and for the advantage of its Inhabitants , are much mistaken : for natural reason doth sufficiently disswade us to believe , that the greater things serve the lesser ; and that those that are the noblest , serve the vilest , and that are of lesse consequence and moment ; Is it not very like , that every Globe makes a World , or a particular Earth ? and that this great number is suspended in the Air , whereof the vast space conjoyns them all as so many dependances from the everlasting and divine Empire : the greatnesse and bignesse of the whole World is composed of divers creatures , which though far remote and differing one from the other , as well by their nature , as by their place , do notwithstanding so well agree in a mutual love , that they compose and make up a perfect harmony in the World , where the Heaven or the Air is their common space , and the Sea , whereof the Earths or Stars are the Islands , which doth so joyn and separate them , and therefore is this Ayr purest , near the perfectest bodies ; neverthelesse , this spiritual body of the Air equally receives the influences and operations of every Globe , and communicates with great speed to every one those of all the others . Chap. VII . Wherein the same is proved , by a reason drawn from the bignesse of the Stars . PYthagoras did often call the Earth a Moon ; and , all well considered , What hinders , that the Earth be not as well reckoned in the number of the Stars , as the Moon , seeing that ( as we have said ) the body of both of them is of a thick , dark , and heavy matter , that both do borrow their light from the Sun , that they are both solid , and reverberate the beams of this light of the World , that both produce vertues and spirits of themselves , and that both are heng'd and suspended each in its aire or heaven , and upon its center : and having all these things common together , may not the Moon , and so consequently the other Stars , infinitely bigger then it self , have Inhabitants ? And indeed this exceeds all belief , that so great bodies as the Stars , which many times over exceed the Earth in bignesse , should be so idle and barren , that no creature should dwell in them , and that their motions , labours , and actions , should onely redound to the advantage of this Terrestriall Globe alone , which is the least and meanest of all . Chap. VIII . Proving the same , by the Creation , multitude , and society of things . God ( with respect be it spoken ) finding himself weary of solitarinesse , did in a manner go out of himself , by the Creation , and poured himself , as if it were wholly , into Creatures , and commanded them to multiply ; and is it not also more meet and convenient to his goodnesse and Divine glory , to have made one whole world alone , as an Empire adorned with varieties of worlds , as with Provinces and Cities ; and that these divers worlds be the habitations of so many Citizens and numberlesse Inhabitants of divers kinds , and that all these things be created for the praise and everlasting glory of their Maker , and that the Sun be in the midst of them , to inlighten them all equally . Chap. IX . Confirming the Plurality of the Worlds , by the privation of Mens Sciences and Knowledg after Adam's Sin . THis Doctrine of many Worlds or Globes inhabited , is not repugnant to the holy Scriptures , which do onely discover to us the Creation of that which we inhabit ; of which they even speak what they mention , in a discourse more mystical then clear ; onely briefly mentioning the other creatures of the world , for to yield greater occasion of admiration , then of knowledg to mens weak spirits , of old fallen from the knowledg of Sciences ; this obscurity of the truth , and these darknesses of Mens understanding have been part of the pains and miseries that Adams sin drew upon us , by reason whereof Man was excluded from the delights of Paradise , from the satisfaction that is in the knowledg of Sciences , from the true knowledg of the nature of heavenly things , that he who had raised himself up to the wicked desire and appetite of forbidden things , might justly be deprived of the knowledg that had been granted him . Chap. X. Containing a Reason drawn from this , That the Earth is not the Center of the World , but the Sun ; With a description of Copernicus his Sphere . THeophrastes writes , That Plato in his old age repented , to have placed the Earth in the Center of the World ; and St. Chrysostome saith , That the seat and scituation of the earth is not known : and after him Nicolas Copernicus , that great Astrologer , who after long study in Astrology , hath thereof known the falshood , did so well confirm this opinion , and unto this day hath rendred it approved by the best and rarest spirits of these Ages , that I doubt not , but that the Reason I thence intend to draw , will be sufficient and pertinent enough : he hath grounded his opinion upon admirable demonstrations which have overthrown the ancient Astrology ; yet without overturning the Science ; but he did onely find the truth , and the same predictions , aspects , and other needful things with his new Maximes , which have established this Science : with much more perspicuity and certainty , he settles the Sun in the Center of the World , where it is immoveable as a great Torch in the middle of the world , as a great King upon his Throne , whence he rules all the heavenly Globes , which are nothing but Earths , like unto that we inhabit ; and round the earth he causes the Moon to move alone ; and round about the Sun , Venus and Mercury ; then Mars , Jupiter , and Saturn , and the other Spheres wrap all that in ; and so the Earth is found to be distant from the Center of the World , and in the third Heaven ; so that being distant from the Center , it may easily be said , That the other Globes of equall , or even , of more vaste extension , that are in equal distance from the center of the World , which is the Sun ; may be Globes inhabited with Creatures , whose true descriptions we know not : the Figure of this may be seen in Campanella , Gassendi , and other Authors . Chap. XI . Proving the same thing , by the motion of the Earth . THe same Copernicus , who after Philolaus , Crotoniatus , E●phantes , Ponticus , Heraclides , Nicetas , Syracusius , Democritus , Timeus , Aristarchus , and Seleucus , hath confirmed and renewed the opinion concerning the motion of the Earth : and the immobility of the Sun , gives us by this motion yet one means to prove our opinion ; for if the Earth be moved in the Aire , and doth its course as the Stars far distant from the Center of the World , what hinders , that it be not put in the number of the Stars ? and contrariwise , that the Stars which have such a motion , be not earths ; and if they be Lands , to what purpose , if they be not inhabited ; and that we may say nothing without proof , the next following Chapter shall prove the motion of the Earth . Chap. XII . Proving the Motion of the Earth . WEe have here above promised to prove , that the Earth moves , because we have hence drawn an argument to confirm our Opinion ; though most men of understanding now adayes believe this motion of the Earth as better clearing the course of the Stars , the order of the Heavens , and the ebbing and flowing of the Sea , yet I shall speak something of it . The Heavens and the Stars had cheaten three thousand years , all the World did so believe it ; untill that Cleanthes the Samian , or , as Theophrastes saith , Nicetas of Syracuse , was resolved , that the Earth moved upon its prop. And in our Age , Copernicus hath so well grounded this doctrine , that he makes use of it for a rule to the consequences of Astrologie , and freeth our spirit from those impossibilities , that the Astrologians of old would make us believe ; for , according to their judgment , the first mobile should run in one minute 706640 miles and a half , and that one and the same body had contrary motions ; Is it not more probable , that the Earth turns round in 24. hours from the West to the East , as in former Ages , Timeus Locrenfis , Philolaus , Aristarchus , Franciscus Marius , and others , did believe it ? Keplerus , Longomonus , Origanus , Campanella , and others of our Age have acknowledged this truth ; Galileus also seems to be of the same opinion , when he saith , That if the Earth did not move and turn , the Sea could not have its flux and reflux . We are as those who are in floating Islands , or in a Ship , who think that they move not , but that , on the contrary , Sea-banks seem to flye from them ; for we cannot perceive the motion of the Earth , as well because of its bignesse , as because that we are not loosed from it . But if in opposition to this , be alledged those Texts of the Word of God , which say , that the Sun is moveable , and the Earth fixt ; may it not suffice to answer , That God speaks according to mens belief , as he hath done upon a thousand of other subject matters ; as when he calls the Moon the great light , though an infinite number of others are greater . As for the Argument that is alledged from a stone cast down from high far from us , if the Earth turn ; I answer , That the Ayr roles and turns with the Earth , and that a ponderous body falls down in so short a time , that the Earth cannot by its motion in 24. houres be alienated from it . It 's also objected , That the Towers would fall , and that the Clouds and Rivers would all follow the course of the Earth . But I answer , That the Clowds are agitated by the winds , and therefore cannot follow the course of the earth ; and as for the Towers , they cannot fall , considering that the Earth's motion is not violent , and that the Towers , by reason of their ponderosity , bend still towards the Center of the earth , and are not removed from their situation ; And as touching the Rivers , the earth being as a gall-nut , a River may run towards the East , by the bending of its Seats towards the center of the earth , although the Earth tends towards the West ; which may easily be apprehended , if we conceive , that a man walking in a Ship , directs his steps towards the East , whilest that the Ship sayles to the West . Many severall other Reasons are objected , which are but weak ; but because there are divers Discourses touching the Earth's motion , which resolve them , and reconcile the places of the holy Scripture upon this subject matter , amongst whom are Foscarinus , and Barantzanus ; I shall desire the curious Readers to read them , and shall content my self with what I have said . Chap. XIII . Proving the Plurality of the Worlds , by the variety of all natural things : NAture is various in all its operations ▪ and God hath put such variety in all his Works , that we can find nothing uniform in this world ; all things in it are various and different : and this great diversity causes us the more to admire the Creator of this whole Fabrick . If it be so concerning the earth , which is near-upon the smallest of all the Globes , what will it not be of the heavenly , which are incomparably greater ? For this cause did Campanella say , That though God and Nature do nothing in vain , yet such a great number of Stars , greater then the earth , would be in vain , if there was not in them divers demonstrations of the Idea's of God ; It 's then consonant to reason , that not only the four Elements be in every one of the Starres , but also that Men , Bsasts and Plants , and all whatsoever is seen amongst us , be in them . And thus did this famous Person of our time speak . Chap. XIV . Of the measures and dimensions of the Stars , and their distance from the Earth , and proportions with it ; with an argument taken from those distances , for to prove the multiplicity of Worlds . BUt because we have often mentioned the bignesse of the Stars , and how they exceed the Earth in extension , and also spoken of their infinite distances ; It will not be out of purpose , and beyond our present Discourse , to insert them in this Chapter . These distances are somewhat variously given by divers Authors ; but the difference being but small , is not of great concernment to us : Charles Rapineus gives these distances in his book , called Nucleus Philosophiae . The Moon is lesser then the Earth 39 times ; and according to Cardan , thirty nine times and a half . Mercury is lesser then the Earth by 1100 times . Venus by 37 times . The Sun is greater then the Earth , by 166 times . Mars by 1 time . Jupiter by 95 times . Saturn by 91 times . The fixt Stars are innumerable , but those that are observed by the Astrologians , are 1022 , and are of proportions of bignesse : Those of the first magnitude , are 15 in number , and are bigger then the Earth by 117 times . Those of the second magnitude are 45 , and are bigger then the Earth by 90 times . Those of the third , are 208 , and are bigger then the earth by 70 times . Those of the fourth , are 472 , and are bigger then the Earth , by 54 times . Those of the fifth , are 17 , and are bigger then the Earth , by 37 times . Those of the sixth , are 49 , and 5 dark , and 9 bright ones , and are all bigger then the Earth by 18 times . The concavity of the Moon is distant from the Center of the Earth 14291 leagues , which are 28541 miles . From the Center of the Earth to Venus , there is 542749 miles . To the Sun , 3640000 miles . To Mars , 3965000 miles . To Jupiter , 28845000 miles . To Saturn , 46816250 miles . To the Concavity of the Firmament , 65357500 miles . The thicknesse of the Moons round , is of 99504 miles . Mercury's round is of 334208 miles . That of Venus , of 3097251 miles . That of the Sun , 32500 miles . That of Mars , 248820000 miles . That of Jupiter , 17969250 miles . That of Saturn , 18541250 miles . That of the Firmament , 55357500 miles . The diameter of the Earth is of ten thousand and eight hundred miles ; But Cardanus saith , of 10000 miles . It s circumference is of 32400 miles ; and according to Cardanus , of 31000 miles and a half . It s semidiameter , or half diameter , is of 5000 miles . These things being thus , is it not very like , that so huge and vaste bodies , so distant one from the other , should hide and contain in themselves something , as well as the Earth ? at least those that move , and are Planets , as It is ; and that turn round the bright body of the Sun , which communicates his light to them all ? Chap. XV . Wherein the plurality of Worlds is proved , by a Reason drawn from the colour of the Stars . IF we see , and punctually discern , not onely with Jacob's staffe , but also with our own sight , without the help of any instrument , a great diversity in the Stars in their bignesse , colour , light , and other circumstances ; Shall we not say , That those various colours do testifie their various nature , and their bodily mixtures ; and that they may consequently be bodies , as well as the Earth ? Chap. XVI . Proving the same , because that there is nothing empty nor vain in nature . WE cannot remark any thing empty in the whole Nature ; this passes for a sure Maxim : therefore did Hermes in his Asclepe say , That all the parts of the World are very full , the whole World is full of Globes or Stars ; these Stars , and especially the Earth which we inhabit , is filled with Seas , Rivers , four-footed Beasts , Men , Birds , Minerals ; the waters are filled with Fishes ; these things have yet in themselves , and unto their very Center , so great a variety , that their anatomy drawes us to admiration : In a word , we may lose our selves in the subdividing of them ; And why may not the Stars be so too , seeing that , as it hath already been proved in the foregoing Chapter , we may see and observe in them some certain variety ? especially in the Moon , where Mountains and Waters evidently appear , and may very well be discerned with a good Prospective glasse , with which Instrument is a notable Mountain discerned in Mars . Chap. XVII . Proving the plurality of Worlds , by the plurality of Men , and because things above , are as things below . GReat Mercurius Trismegistus , who for his eximious Learning , hath obtained the name of Thrice most Great , hath left us this notable Aphorism , That things below , are as things above ; and , vice versa , those above , as them below ; the meaning is , That this World is an example to us , without any need to go out of it , for to know those things that role over our head ; and God hath even bestowed upon us sufficient capacity to draw reason from every thing ; If we consider our own selves , we shall see by a generall approbation , that Man is a little World ; so that Men being infinite in number , who are Microcosms ; likewise ought the Macrocosms or great Worlds , to be many , after whose Idea's and images he is built ; as may appear by the conformity of one with the other : But here might we speak of this conformity , had it not been fully described by many Philosophers of note ; therefore omitting it , we shall proceed . Chap. XVIII . Wherein the same is proved , by some Reasons taken from God's Power , from Man's Reason , from hence , That there is nothing onely one , and such other considerations . I Shall not fear to say , That those who deny this exquisite Opinion , seem to be offended against themselves , to accuse God of impotency , and their own Reason of falshood : and that I may bring them to passe sentence of condemnation by another mouth then mine , I would have them to hearken to great Michael Montanus , who is esteemed one of the wisest , and reasonablest Men of his Age ; he hath these words in his Apologie for Raymond of Sebone ; Thy Reason hath in nothing else more likely truth and foundation , then in that , wherein it perswades thee of the plurality of Worlds . Terramque et Solem Lunamque et caetera quae sunt Non esse unica sed numero magis innumerabilia . That is to say , The Earth , the Sun , and the Moon , are not one alone , but many in number . The ratest spirits of former Ages did believe , yea , even some of our Age , constrained to it by humane reason , because that in this building and fabrick that we see , there is nothing alone and one . Cùn , in summa , res nulla sit una , Vnica quae gignatur , et unica solaque crescat . That is to say , Being there is nothing that is onely one in this World , that is engendred alone , nor in the Sea , nor in the Earth . And every species is multiplyed in some reasonable number ; whence it appears , that it 's not likely that God hath formed this work alone , without some more , and that all the matter of this form was spent in this Individual alone . Quare etiam atque etiam tales fate are necesse est , Esse alios alibi congressus materiai : Qualis hic est avido complexu quem tenet aether . Wherefore it must be confessed , that some where else there are heaps of matter , as that which is wrapt up in this our Aire . Especially , if it be a living creature , as by its motions we may be perswaded it is , as Plato asserts it ; and many of the Learned of our time either do confirm it , or dare not deny it . Now if there be many Worlds , as Democritus , and almost all the Philosophers did judge , what do we know , whether the principles and rules of this do concern particularly the others ? perhaps they may have another face and policy ; but being all things are divers in this , yea in a small distance , we may believe , that the other worlds ought to be divers and various ; For why should God , who is Almighty , have limited and restrained his power and virtue ? Chap. XIX . By what reason , the World may be proved to have a Soul . VVHereas Montanus hath here above spoken of the Soul of the World , It will be meet for our present subject , to demonstrate those Arguments by which this Opinion may be proved , that he may not be judged to have incongruously spoken of it , it being also advantageous for our Discourse . If the World is a reasonable Creature , as divers Learned Persons have proved , It may not be strange and ridiculous to believe . That the Earth hath a motion , nor consequently that it is a moving Star or Planet inhabited , and that so likewise all the others may be inhabited : Now if the Earth turns and moves ; is it not also needfull to grant , that that whereby it is moved , is as it were , its soul moving it , as our soul moves our body ? Some have thought , that God is the soul of the World , and that he is in the World , as the soul in man's body ; that is to say , all in all , and all in each part ; and that therefore the World might have a soul , and be called a living creature , great and round , and as Montanus saith , Is it not more likely , that this great body by us called the World , is a thing quite contrary then we esteem ? The Pythagorians , Xenophon , Plato , and all his Schollers , have taught and believed this opinion ; and since them Marsilius Ficinus , and Hierome Fracaster , most renowned Doctors of Physick ; and in our Age Campanella , who alledges Seneca , Origenes , Eusebius , and Gregorius Nazianzenus , as witnesses of it . But if any one should say , That the World cannot be a living creature , seeing it hath nor feet , nor eyes , nor hands , nor any such member as living creatures have ; I beseech him to consider , that it s not requisite it should have some feets , being it treads not upon the other living creatures ; nor eyes , nor ears , because it can neither see nor hear any thing out of it self ; but the hands of this living Creature , as those that in it are contained , and we have , are its beams and virtues ; its eyes , the Stars ; its bloud , the Waters ; and so hath other things besides , consonant and correspondent to our members , without having need of the same as we have ; Are there not strange and monstrous beasts in respect of us , and yet live well , and are perfect in their kind , doing well enough without such members as we have , though they have not the same situation with us . How many Fishes is there , that have their mouth in the belly , the eyes and other members in extravagant places ? Some Creatures have the gall in their head , and some in their tail ; yea , there are some Men , whose head is in their bosome ; some likewise may be formed , so as we cannot comprehend nor know how . Its motion sets forth its life ; and the flux and reflux of the waters its breath and respiration . There are divers such Reasons to prove the same : but I shall desire the curious Reader to peruse Plato , Sextus , Empiricus , Ficus , Macrobius , Campanella , and others , to avoid tediousnesse . Chap. XX . Proving the multiplicity of Worlds , by a Reason drawn from infinite number of causes , and by the spots of the Moon . THe spots in the Moon , touching which Plutarch hath made a whole Discourse , whereof we might here alledge divers Observations ; are to us a sufficient testimony , that the Moon is as the Earth , filled with Rivers and Seas , Mountains , Valleys , Plains , and other such things ; for its Spots are not the shadow of the Earth , as some have thought ; considering , that they never change their shape , as they would do , according unto the divers parts of the Earth , to whom the Moon by its motion would answer , and having no conformity at all with the Earth , nor with the Sea ; and lastly , because that our sight holpen by the Prospective-glasses , observes in it some Seas , and the tops of divers Mountains , and such like remarkable things , whereof the Maps and figures may be seen in Hevelius , Argolius , and several others , and in our Book de Telescopio . These Spots shew , that the Moon is partaker of the Elementary and Terrestriall nature , and consequently of the rest of the Elements . This did move Plato to say , That the Stars are composed of fire and earth , by reason of their splendour , and of their great and lumpish body . This plurality of Worlds may again be proved by the variety of the causes that compose it , and by the divers combinations that may thence be made ; which is the argument used by Morodorus in Plutarch , in his book of the Philosophers opinion , wherein it 's said , That where the causes are , there the effects ought to be also ; and the causes of the World being a great many , so also ought the Worlds to be many ; the causes of the world are the four Elements , and others that may yet be unknown to us , or the infinite number of Democritus Atomes ; unlesse we had rather say , That its God , who being infinite , so likewise hath created an infinite not onely of Worlds , but of all things : And indeed , as the same Philosopher saith , it would be a sad spectacle , if there were but an ear of corn in a great field ; the same would it be of Heaven , if it were true , that there is no more Earth but one . Chap. XXI . Wherein is the same proved , by certain Reasons drawn from Galileus's Observations , and others ; as of the Stars of Jupiter , and of the Spots in the Sun . THat great Galileus , who seemed onely to be in the World for to resolve the doubts in Astrologie , hath discovered with his admirable invention of Prospective-glasses , which immortalize his name , by the discovery of what is contained in the Stars ; he is the first who hath directed his Telescopes or Prospective-glasses towards Heaven , and by help of them , that the milky line were small Stars , which by reason of their proximity and great number , do confound their light : he also hath discovered the Moons superficies , not smooth , but rugged , and full of risings of Hills , and hollownesse of Valleys . He also hath observed , that the Star Venus doth imitate the course of the Moon , being now full , then half , then in the first quarter as a sithe ; and hath observed the perspicuous change of bignesse in Venus and Mars's diameters ; things of great concernment and note , for the theories of Copernicus and Tycho Brahe . He hath ashamed the Sun , discovering in him those Spots , which for so many Ages he had buried and hid in his bright obscurity , and hath discerned , that those Spots were not fixed , and alwayes lasting , as those in the Moon , but that they disappear & appear again , turning round the Sun : he hath also discovered four new Planets , that had not yet bin observed by some of the ancient Astrologers , which he hath called the Planets of Medicis , in favour of his Prince ; these Planets move onely round about Jupiter , which hath induced some to believe , that Jupiter was another world , or another Sun , round about which other Planets do run , as round about that which in lightens us . He hath farther observed , that the Planet Saturn hath three bodies , having two more at his sides ; and that the Planet Jupiter is be spotted with girdles or Zones that do girth it ; the which may plainly and perspicuously be seen by those Telescopes or Prospectives , admirably well made by Torricelli the Florentine . These are those rare Observations of that illustrious Person , who though but little in body , yet so great in ingenuity , and acuity of spirit , that all the World hath suffered by the losse of him ; He became blind , by reason of his too great propensity and labour in these Observations ; and he who had in these things given light to all this world , could not enjoy the light , nor his Invention . Foscarius adds to all these Observations , that Venus hath been seen with three bodies , as well as Saturn , and that Jupiter hath 4. bodies ; But Gassendus Fontana , Neapolitan , hath now the excellentest Telescope in the world , with which he hath seen the four Planets which are adjacent to Jupiter as four Moons ; two about Saturn , which make a figure of a pot handle at each side of it . In the midst of Mars , a little Globe , at his brimmes a darkish circle , and about Venus two Moons or Stars . Chap. XXII . Proving the Plurality of Worlds , by a Reason taken from the Clouds , and the waters above in Heaven . WIth the Prospective-glasse we may see some Clouds flying round about the Sun , which can arise but from the Moon , from other Stars , or from the Sun it self , because they be beyond the Region of the Meteors : Now if the Stars ingender clouds , they have water within themselves ; but if the Element of water is in them , the Element of earth and the rest have as great priviledge to be in them , as it . Now that there is water in them , the first Chapter of Genesis proves it clearly , when he saith , Then God said , Let there be a Firmament in the midst of the waters , and let it divide the waters from the waters ; And God made the Firmament , and divided the waters which were under the Firmament , from the waters which were above the Firmament ; & he called the Firmament , Heaven , and the waters under the Firmament , Seas . Esdras in Chap. 6. of his second Book , saith the same , in these terms , Thou madest the spirit of the Firmament , and commandedst it to part asunder , and to make a division betwixt the waters , that the one part might go up , and the other remain beneath . Where are these waters above , I beseech you , if they are not in the Stars ? For it 's a very weak Reason to say , That they are in the Clouds ; because that , besides that they could not contain the Seas , It s said in the second Chapter of Genesis , that God had not caused it to rain upon the Earth , but there went up a mist from the Earth , and watered the whole face of the Earth ; and so consequently there was no vapour raised up to form them : and what should have raised them , seeing there was yet no Sun created to light the World ? Let us then lift up our eyes to Heaven , and , as the new Gymnosophists , who daily contemplated the Sun , let us observe in them those new Worlds , wherewith it is wonderfully enriched , which are divers and various in bignesse , light , and other qualities ; let us not be as poor simple Countrey fellowes , who having seen no farther then the corner of their own chimney , cannot apprehend , that there can be any Town or City bigger then their Village ; but let us raise our spirits to the contemplation of the remotest and highest things that are ; thereby ennobling our selves , though it be a very high attempt . O how happy is that man , who when he pleaseth , can spiritually loosen his Soul , and by his exquisite Meditations rise up to the meditation and contemplation of these Worlds ! When once we are well acquainted with it , and freed from all Preoccupation , nothing can be found sweeter , pleasanter , and more consonant to truth . What Patents and particular priviledges have they , who believe the contrary , that we should adhere to them ; and our belief should be ruled by them , as if it were under their commands ? Men feign and forge to us five Zones in Heaven , and seen other things , that are nothing but dreams and foolish fancies , as if they had been there above to see it . We may say the same to them , as Diogenes said to such other creatures , How long is it since thou camest from Heaven ? It 's then as lawful for us to establish new Maxims , as for them ; and to believe in the strength of our reason , what we here have attempted , and what others say with reason , or appearance of truth . O that Nature would once open us her bosome , and plainly shew us the direction and Government of its motion , with what is contained in those great and vaste bodies , which sparkle and glister in Heaven ; What abuses and grosse mistakes should we find in all Sciences ? Chap. XXIII . Wherein the same is proved , by an Argument taken from the place where the Clouds stay without going farther . WE have here above spoken of the Clouds , and thence have drawn an Argument to assert this our opinion ; we may yet draw this from them , viz. that the Clouds and vapours being light should ascend without limitation , untill that they were lost from our sight , if there were not some other terrestrial Globes in Heaven , nor any other attraction then that of the Center of the Earth ; but we may observe even in the hottest of Summer , that the Clouds do not ascend above 3. miles , and the strongest vapours that are , not above 30 miles ; whence we must infer , that they ascend unto the limit of the activity and attraction of the center of the Earth , not being able to go beyond , because it would be to bend downward , viz. towards the Center of some other terrestriall Globe . But , that I may better be understood , it 's to be observed , that as the Loadstone hath a certain inward virtue to draw iron , or to move the Needle of the Sea-compasse unto such a distance , and no farther ; so likewise the Earth , which by the opinion of some , is a great Loadstone , whose circumference and activity is extended towards the Moon , unto such a certain heighth ; and the other Stars also have such like circumference , wherunto their virtue & attraction may reach ; Insomuch , that the Clouds having attained unto that distance which makes a middle between us and the Moon , there they are stayed , not being suffered to go beyond it , because then they would descend towards the Moon , or some other Stars , which would be contrary to their nature , which is to rise upward still ; so that if a ponderous body as a stone being cast up , could go beyond the Earth's attractive point , it would not fall back upon the Earth , but upon that Star , whose attractive Center should reach unto that place whither the stone was cast ; therefore hath Bacon said in his Book de progressu Scientiarum , that Gilbert did not doubt incongruously , That the bodies of weight and ponderosity , being at a far distance from the Earth , would by little and little forsake their motion towards things below . Chap. XXIV . Containing a Reason , drawn from the Bird of Paradise . THe new World discovered by our Fathers amongst those infinite riches and rare things it communicates to us , makes us partakers of a Bird , called by the Indians , Manucodiata , that is to say , the Bird of God , or of Paradise ; This Bird is so beautiful , that no one in the Earth is to be compared to it ; its figure is of so rare a form , and so extraordinary , that never the like hath been found ; for it hath neither feet nor wings , but is clothed with a skin of feathers , made otherwise then that of other birds ; it 's not found but dead either upon the Earth , or in the Sea , no body ever saw its eggs , nor its nest ; and it 's asserted , that it lives by the Air ; this Bird never being found upon Earth , is it not confonant to Reason , that it may come from some other Starre , where it lives and breeds , and that having flown higher , and beyond the attractive Center of that earth or Star where he lived ; he dyeth by changing his Ayr , unto that which is not proper and natural , and dying , falls upon this Earth . Now if birds be found in the Stars , there also may other living Creatures be , having all the same right of habitation . And grant , that what some object , be true , that it hath feet , but that they are very short , or that its feet are cut , that it may appear the rarer , yet it hinders not the consequence drawn from it ; provided , that the other circumstances of its nature be true ; for if it hath feet , it must be understood of some of its species onely ; for Aldrovandus mentions five or six sorts of them , whereof some have feet , and some none . Chap. XXV . Wherein is alledged , an Argument taken from the Eclipses . BEfore the Creation of this whole Fabrick , God did inlighten himself , and contemplate himself , he was a sealed Book , which at length is opened , and hath set forth to the view , that which remained in Himself ; wherefore the whole World is nothing else , then an evident image , an Idea of his hidden God-head , he is through it all , as our soul is throughout all our body , and by his will , encompasses all the motions of the spheres , having spread through them all the Aires , as a scrowl ; which folding it self away at the last day , shall be reduced to its former Silence , or rather to Nothing . This wonderful order , thus by him established , may be seen in the constant and unchangeable course of the Planets , upon which the Astrologians make some certain Almanacks for many years together , and foretell the eclipses of Ages to come , without missing a moment of time . These Stars being all of one and the same nature , do eclipse one another ; the Earth eclipses the Moon , the Moon the Sun , and so all the rest , if their small body is not overcome by the bignesse of those they intend to darken , as it s testified by Averroe's Observation , who hath seen Mercury in the center of the Sun , which seemed to grow in it ; its light , if it hath any , being covered and put out . Now from these Eclipses , or want of light in the Stars , we may draw this strong Reason for the assertion of our Position , for it sheweth and verifieth , that they are of an earthly nature , and that their light is borrowed ; the Moon appears black , when the Earth hinders it to receive light from the Sun : and divers Philosophers have believed , that all the Stars do borrow their light of the Sun ; they are then obscure , and thick of their own nature , and consequently earthy , and may have such variety and diversity as the Earth , viz. Men , Beasts , Plants , and whatsoever is seen here amongst us , and the Pythagorians did believe , and to which Copernicus agreeth . Chap. XXVI . Proving the same , because otherwise it were to make God to act by necessity . IF there were not many Worlds in this whole Fabrick , God could not act so powerfully and freely , but that by some certain necessity and constraint ; which would be a great impiety and blasphemy even to imagine it : for God could assuredly , not onely have made other Worlds , but also much more perfect then this ; for his power is neither shortened , nor exhausted , neither the matter , which he could create of nothing , as well as that of this our Earth ; therefore as he hath created this World , could he not also have created others ? Chap. XXVII . How could we see the Earth , if we were far distant from it ? SOme may ask , If the Planets are so many Earths , and the Earth a Planet , how could we see the Earth , if we were far remote from it ? Clavius in his Commentary upon Sacroboscus , hath endeavoured some suppositions upon this question , and hath found , that if any one were in the Globe of the Moon , and should look towards the Earth , it would appear to him three times bigger then the Moon appears to us , and somewhat more ; and if a man were in the Globe of the Sun , it would appear to him twice bigger then Venus seems to us ; and in the Globe of Mars , thence it would appear lightsome , and would seem to be of the bignesse of one of the Stars of the sixth proportion ; and if he were in the highest heavens , he could not see it at all ; And this is ( saith he ) the Astrologers common opinion . Chap. XXVIII . Of the number of the Worlds . IT may also be asked , What number of Worlds there is ? but though it is a thing not certainly known , considering the infinite number of Stars to us perspicuous , besides those that we cannot see by reason of our eyes weaknesse . Yet I shall here alledge the Judgment of some Authors upon this question ; Baruck the Philosopher , and Clemens a disciple of the Apostles , as Origen saith , do mention seven ; perhaps meaning the seven Planets . An ancient Author , according to Plutarch in his book , touching the ceasing of miracles , did believe , that there were an hundred and eighty nine Worlds disposed in a triangle , every side containing sixty three . Petro of Sicily thought the same thing touching the plurality of Worlds . But the Thalmudists going beyond , say , that there are nineteen thousand ; and Democritus did believe , that they were infinite , and innumerable . Chap. XXIX . Touching divers ancient Philosophers , who have believed the plurality of Worlds . Pythagoras , who first called this Fabrick , Worlds , is also one of the chiefest , who believed the plurality of them , and hath had many disciples and Citators , who have continued to establish and maintain this assertion ; for Socrates hath publickly asserted the Worlds to be infinite ; so did also his disciple Archelaus , who perswaded it also to Xenophanes the Colophian , who also did assert , That there are many Moons and Suns in the world . This same Axiome was believed by Melisseus of Samia , Parmenides's disciple ; as also by his School-fellow Zeno of Elis , and his disciple Lucippus of Elis also . Item , by Democritus of Miletum , Pythagoras's hearer , who saith , That in these Worlds the Stars are more beautifull and bright , which I think may be according to their proximity . By reason of which opinion , that King of the Abderitanes was esteemed by his ignorant people , to be out of his wits , and thereupon they sent for Hippocrates to cure him of his disease ; but Hippocrates found him very well in his mind , and said nothing against his opinion ; which moved Democritus perpetually to laugh at them who were ignorant of the same . Joubertus , who hath composed a book concerning laughter , in it hath set down Hippocrates's letter upon this subject . Diogenes of Apollonia , Anaximenes's disciple , together with Seleucus , hath also pronounced their assertion touching the plurality of the worlds . Orpheus , Origines , and Baruck the Philosopher , Anaxagoras , and many Stoicks more , do a vouch the same ; Plinius also seems to have been of this opinion ; but Anaximander , Anaximenes , Epicureus , and others , following Francis I. Picus Mirandulanus , have fully asserted it . Mahomet , who though an Infidel , wanted not wit and knowledg to establish his belief , did believe the same thing , and in his Alcoran mentions several Earths and Seas to be in Heaven and the four Elements ; and all that is amongst us to be in every one of the Stars . Epicureus did say , That these Worlds were some of them without Sun or Moon , and some had greater then those that lighten us ; and that others had divers Suns , and that some of them were without living creatures in them , without Plants , and without all moisture , and that at the same that things are thus in our worlds as we see them , so also are they in divers other worlds ; but had he seen how the Indians and we agree in severall things , he would questionlesse have believed it more constantly . Icetes the Pythagorian , together with Philolaus , did believe there were two Earths opposite one to the other ; and Picus Mirandula was forced to say , That he thought that the Moon was an Earth like unto ours ; herein conforming himself to those Pythagorians , who sometimes did call our Earth , Moon ; and the Moon , Earth . Francastor , Physitian at Zerona ( following Eudoxus and Calispus's Judgment ) together with divers others , whom for brevity sake I shall omit , did also believe the same . But whereas so many Philosophers have asserted the Position of this opinion ; it will be answered , That I am not the first author of 〈◊〉 ▪ To this I answer , That it 's sufficient for me to renew it , and plainly professe it , the which hitherto was not yet publickly practised . Chap. XXX . Of those things that are in the Moon , and other Planets . THough the Ancients had not the help of Prospective-glasses , as we have , wherewith we see as new Linxes , the Seas , the Mountains , and other things which are in the Moon ; yet they did inquire and speak of things more particular that are in the Stars ; as the Pythagorians and Orpheus , who did believe that the Moon was not onely of the colour of the Earth , but that it contained Men , Beasts , and Trees , 15 times bigger then we , or 50 times bigger , as Herodotus , who also asserts , that in it are Towns and Cities . Xenophanes did also think , that there are men within the body of the Moon ; Anaxagoras and Democritus have also said , That in it are contained Mountains , Valleys , and Fields . Lucianus in his book of true history , & Aristoteles , have both mentioned some particularities of what is in the Moon ; but we shall not take notice what the first saith , because he relates it as a fable ; though for the composing of his work , he hath made use of a great deal of those ancient Philosophers opinions . Plutarch in his discourse of the Moon , reasons pro and con , whether the Moon is inhabited ? and whether it is an Earth as ours , and inclines sometimes to one , sometimes to the other ; but at length it seems that he did believe it , because he answers to divers objections that might be alledged against this opinion . Bacon desires us seriously to cast our eyes upon the opinions of Pythagoras , Philolaus , Xenophanes , Anaxagoras , Parmenides , Lucippus , and of other ancient Philosophers , indicating to us the truth thereof , and wishes , that some body would compose a book of their opinions ; this present discourse is part of it ; and therefore do we in some measure satisfie the desire of so rare a Person . Lucretius , whom we have here above quoted , did confidently believe the same , and hath testified it in divers places of his works , and especially in these Verses , besides those already alledged in the 18. Chapter . Esse alios alibi terrarum in partibus orbes , Et varias hominum gentes et saecla ferarum , Huc accedit , uti in summa res nulla sit una , Unica quae gignatur et unica solaque crescat . That is to say , There are other new Worlds , wherein is variety of Men and Beasts , and of all other living creatures , because that there is nothing groweth single and alone in this World , nor in the earth , nor in the Sea . And in another place , Praeterea cùn materies est multa parata , Cùn loci est praeslò , nec res nec causa moratur Ulla , geri debet nimirum et confitier res . Whereas there is store of matter , and that the causes and the places do suffice , this therefore ought to be declared , and men must needs grant it so to be . Paracelsus hath said , That there are in Heaven some certain men called Tortelii and Penates , for whom Christ did not die , of whom some are without Soul , and some not composed of the four Elements ; he yet names others , never mentioned but by him . Some of the Stoicks were of opinion , not onely that there are people in the Moon , but also in the body of the Sun ; And Campanella saith , That those lively and bright habitations may have Inhabitants , perhaps more wise and learned then we , and better informed in those things that to us are incomprehensible . But Galileus , who in our Age hath perspicuously seen into the Moon , hath observed , That it may be inhabited , seeing that there are Mountains in it , &c. for those parts in it that are the Plains and Valleys are obscure and dark , and the Mountains are bright and clear . For this cause have some said , That the Stars do not shine , but by reason of their irregularity , asserting , That we could not see them , if they had not Mountains for to reflect and reverberate the light of the Sun . Chap. XXXI . Containing the Solution of some Objections that may be made against this Paradox of the World's Plurality . BUt some may say , There cannot be such Men as we , in the Starres ; for they could not live there , because men are divers , even after the diversity of Countreys ; and those who ascend that high Mount Piracaca in the Indies , dye there by reason of the too subtile ayr of the place . To which I answer , That those men must needs be different from us , or indued with more robust and strong bodies then we ; or so well proportioned in the mixture of the Elements , that that Ayr cannot be obnoxious and hurtful to them ; but that God hath so formed them , that they may well live where he hath placed them , but no where else . And if we had never seen or heard of the Sea , we could not be perswaded , that Fishes could live in salt-water , and that therein they could breed and grow for our food ; nor that those Countreys of the burning and frozen Zones , could be inhabited : So must we believe , that God hath by prevention of inconvenience , ordered all things for the best . Here also might be objected , the Incommodities and incongruences that might befall the Inhabitants of the Moon , viz. the Meteors as the Clouds , and other which would offend them , and would hinder Plants to grow therein . We answer to this , That those Meteors are far enough from it , and that rather they are lesse molested by them then we ; for Galileus did see with the telescope , that it doth not rain upon the Earth of the Moon . But it may be replyed , How then do the plants grow ? To which I answer , That they may grow in it , not only by reason of the Moon 's natural humidity and moisture , but also by the inundations of its Rivers ; as in Egypt , where likewise no rain is seen ; I say farther , That those Inhabitants of the Moon have no more ground to alledge these Objections , being that when they look upon the Earth , through the mists and clouds that incompass it , they might doubt whether any creatures could be contained in it . But hitherto we have answered none but weake objections . Now come we to that with which our Opponents do arm themselves chiefly , which is that of the Prince of the Aristotelists , who as the Otthomans aymed to slay all his brothers , that he might reign more securely , viz. to beat down and suppresse all opinions contrary to his ; now this is his argument ; If there were many worlds , the earth of those worlds would move towards our Earth ; or ours towards that of the other Worlds ; and so the other Elements of the other worlds would reach ours , and so there would be nothing but a great tumult and Chaos . This Argument is so weak , that Magirus is constrained to speak in these terms when he alledges it , not being himself able to find others , because he maintains not the truth ; All these Reasons , ( saith he ) and such like Philosophick Arguments , cannot perspicuously demonstrate , that there is but one World ; and Charles Rapineus speaks thus , That it can but weakly be so perswaded . Aristoteles could not comprehend what we have above said , viz. That each world hath its center , whereunto tend those heavy bodies that are in its sphere ; But he arguments upon a false foundation , making the Earth to be the Center of all the worlds , and allotting but one center for all ; his Argument would be good , if his ground were good : for what he saith was true , it would be requisite that all heavy and ponderous things should tend towards our Center ; but there being many , they also go into divers Centers ; for each Star hath its center that upholds it , and though it be of a ponderous nature , yet is it light , in itself . Having thus answered , and so plainly and fully resolved the Objection of Aristoteles , the grand Prince of Philosophers , what may they expect who have not such pregnant Objections as his . Chap. XXXII . Continuing the Solution of divers Philosophers Objections against the Plurality of Worlds . THese following Arguments are yet objected ; First , That whereas there is but one principle and first Mover , or but one God and first cause , and that the world ought to answer in likenesse to its Architype , there also ought to be but one World . But we have here above shewed the contrary , because that God is infinite , so also ought the Worlds to be infinite . For a second Argument , it 's objected , That if there were more then one World , the Divine Scriptures would have communicated it to us ; but speaking but of one onely , it 's not likely there should be any more . To this I answer , That the holy Scripture speaks clearly of none but of ours ; though yet in severall places it agreeth in the plurality of Worlds , as we shall hereafter demonstrate ; and that it speaks after the manner of men , of all heavenly things , condescending to our weaknesse , and to the common opinion ; as when it saith , That the Sun and Moon are the great Lights , and yet the Moon is one of the smallest Stars ; and there are some others that are as bigg as the Sun , as Canopus Starre , and others , and an infinite number bigger then the Moon : Likewise the Scripture saith , That God is angry , and doth repent , though he is immutable and unchangeable ; and therefore might the Scripture do the like concerning the motion of the Earth , and the plurality of Worlds . For a third Argument , Plato speaks thus ; The matter requisite for the composition of the world is but one , and heaped up together into one lump or body alone , and the Heaven contains within it self all the simple bodies , so that no part of the matter can remain , for therewith to compose and frame other Worlds . To this I answer , That it 's not necessary that all the matter be exhausted and spent in the Creation of this our Earth alone , yea rather in the Creation of the whole Fabrick ; but and if it had been all spent at the creation alone of this our Earth , God could yet create some new : And last of all , concedo totum , I grant the whole Argument , it proving nothing against my assertion ; for I comprehend all the Worlds or Earths to be in Heaven . Plato saith farther against this opinion , That the World would be imperfect , if it should not contain all ; and secondly , would not be like its pattern , if it were not single and onely one , and that it would not be incorruptible , if there was any thing out of it . But we have already answered the Objection touching Unity ; where we have discovered , That God being infinite , there must also be infinite Worlds : for as Sextus Empiricus saith , There is nothing one alone of all whatsoever is numbred in the World . And as for the last , Plutarch answers it , saying thus , That it hinders not the World's perfection , that there are other Worlds besides ; for man is perfect , and yet contains not every thing . And to this answer I adde , That by this word World , Plato did understand the whole Fabrick of all these Earths or Worlds which make up but one whole world ; his Arguments cannot at all overthrow my Position . Timplerus forms yet this Argument , If there were divers Worlds , they would have been made in vain , and to no purpose , because no use of them can be shewed . This his Reason is so weak , that it will suffice to say , for to confute it , That though we may not know for what use they are made , yet they are not made for nothing ; for by this same reason , the Indies , from whence we receive great advantage and profit , and the Northern Countreys that yet are unknown to us , would also have been created in vain . Again , there are some who object , That if the Stars were inhabited , they would have need of the influence of other Stars and Heavens , usque ad infinitum , without number . To this I answer , That I am not much perswaded , that the Starres are advantageous to us , the Sun and Moon excepted ; it 's not possible , that the Stars communicate and serve one another mutually , and therefore there is no need of an infinite number of Heavens . Last of all , Zabarella arguments thus , If there were other Worlds , what in them should be contained , would be either like to what is in this our World , or differing from it ; if it were like it , in vain would individuals be multiplyed ; if differing , it could not be found out how it 's disposed . To this Objection I answer , That men and other things in the Indies , would also have been created in vain , if his Reason was valid ; and that though we knew not what was in those new Lands and Countreys , yet it was in them notwithstanding ; so likewise though we be ignorant of what is in the other Worlds , yet this our ignorance excludes not their being . Chap. XXXIII . Answering Pacius's Argument against this Assertion : IN this whole Fabrick ▪ considered at large , may be observed divers Worlds contained within it ; as the individuals under the species ; but Pacius labours to oppose this Position thus ; That the World , such as it is , comprehends all , and that all the matter was spent in the composition of it , and that therefore there can be no other bodies out of it ; for if there were any , they would be either simple , or composed ; if simple , it would be the Heaven or the Elements : But they cannot be the Heaven , considering it changes not fully its place , but turns round upon it self : Nor likewise can it be an Element , because it would be beyond nature ; nor also a mixt body , because that if there be not some simple bodies , there can be no mixt ones . To which I answer , That , as I have already said , by Worlds , is to be understood Earths onely ; and by the general word of World , or whole Fabrick , are by me understood , All the things of the whole Fabrick , in the frame and composition of which , I yield , that all the matter was spent and employed , and that out of them there is no other Universe or generall World . Chap. XXXIV . Answering Melancthon's Objections , together with others , who say , That this Doctrine tends to Introduce new Maxims against Religion . BUt there may yet some stand up , and say with Melancthon , That God ceased from creating , and rested himself ; but Moses in the second of Genesis speaks , and meaneth onely the Creation of this our World : and truly it 's more consonant , that some end , and others be created of new ; as Empedocles did believe it , together with Democritus ; God hath limited his power , and he is still the same for to create again , as he was afore : and as it 's said in the Book of Wisdome , ch. 11. v. 18. he wanteth not means to create of new unknown wild beasts : Therefore both this and the other Arguments alledged by Melancthon , are weak against this our Position , which he himself being forced to confesse , he saith in his natural Physicks , that though his arguments do not fully conclude , yet they must be considered and weighed , lest that if we believe that there are other worlds , we also should believe other Religions , and other natures of Men . For my part , I see no necessity , that because there are more Worlds , there must also be more Religions ; the increase of this World , through the discovery of the Indies , hath not caused any new Religion ; and it 's very unlike from being capable of introducing Heresie and Atheism ; I confidently believe , that this admirable order of the World , which disperses the confusisions and chaos , which by reason of mens ignorance do yet reign , will even make the greatest Atheists of this world to confesse , That they cannot have their originall but from God alone , who is the Soveraign Creator of all things . Melancthon saith farther , That if there were divers Worlds , it would be requisite , that Jesus Christ should suffer death several times for to save them all : but what do we know , whether those Men in the Stars are better then those that are in this world , whereof Satan is called the Prince , and where he abides ; for which cause St. John saith in Chap. 12. & v. 12. of the Revelations , Therefore rejoyce ye Heavens , and ye that dwell in them ; wo to the Inhabitants of the Earth , and of the Sea , for the Devil is come down unto you . And though we should certainly know , that those men in the Starres have need of salvation , God hath so many means and wayes , to us unknown , for to save them , and to satisfie his Justice , that we need not inform our selves about these things , but believe them in faith , captivating our understandings ; as an ancient Father of the Church hath well spoken . But some may object , Who is he that will believe it ? To whom I shall reply with Plato , No wicked man shall ever know it ; but he onely who shall be found worthy of it . Let then those who are unworthy of so high and sublime knowledge , withdraw hence , their gross spirit cannot apprehend the subtilty of it ; and as Spiders do turn the best food into venome and poyson , they call that which is the true way to the knowledge of God , the high-way to Atheism . Chap. XXXV . Proving the Plurality of Worlds , by a Reason drawn from the place of Hell . SOme scrupulous persons might say , That the Reason of this Chapter seems in something to contradict the doctrine of the Church : But I shall answer him , That if any one should endeavour to prove , that there is no Hell , his Opinion should certainly be esteemed erroneous and pernicious ; but to do nothing but to establish and confirm it , as I do in this Chapter , and to remark the place where it is , being that the Divines cannot certainly point out the place , I find nothing in it repugnant to Christianity . Now whereas our bodies are to rise from the dead , for to be rewarded according to their deserts good or evill , and that the damned are in greater number then the saved , the place of Hell must needs be very spatious and great to contain them all , and solid and firm to uphold them ; but it cannot be anywhere but in one of the Stars , and so consequently the Stars may have Inhabitants in them ; for it 's said , That the Center of the Earth , because it is the center of the World , and the farthest place from Heaven ; but that I cannot find it needful to place it in the Center of the World , considering that God is equally every where , and that men cannot alienate themselves from him ; and also because it 's very easie to prove the contrary , not only in that it could not be sufficient to contain in it self all the damned that have been since the Creation , and shall be unto the end , nor can be penetrated through by their lumpish bodies ; and also because the Earth it self at the day of Judgment must be consumed and done away , as Esdras saith in 4th Chapter , and 42 verse of his second book ; but also in this , that not the earth , but the Sun is the Center of the worlds ; the Sun then by reason of its far distance from the highest Heavens , saith Foscarinus , is the true place of Hell , even as its siery nature required ; for the internall habitations seems to perswade it : but I cannot admit this opinion , though that I hold , that Hell must be in one of the Stars ; but to seat it in so beautiful a Star as the Sun is , I cannot consent to it ; seeing that the damned Souls cannot merit so good and advantagious an habitation . But on the contrary , It may seem more plausible and consonant to truth , to seat the Paradise of God in the Sun , according to that Text in the Psalms , In S●le posuit tabernaculum suum , God hath placed his Tabernacle in the Sun . But to prove more certainly , that Hell is not within the Earth , let us but observe , that it was created before the Earth , seeing that the wicked Angels were banished into it before the Creation of the Earth ; to which agrees the first Chapter , and 14 verse of the Wisdome of Solomon , saying , The Kingdom of death is not upon the Earth . Chap. XXXVI . Proving the plurality of Worlds , by an Argument drawn from the Seat of Paradise both Celestial , and Terrestrial . IT may likewise be proved , That Paradise is no where else but in the Stars : Now it 's most clear and certain , that it 's not this Earth , but a new Earth , wherein is the heavenly Jerusalem , which must needs be a solid place , as well as our Earth , that it may hold us up , wherein all joy and happinesse shall be ; and out of which shall all miseries and torments be banished ; this place is prepared of old for men , and what do we know but that we shall be dispersed into severall Stars ; doth not our Lord Christ Jesus assure us , That in his Fathers house are many Mansions : and Esdras , in the 4. chap. & 7. ver. of his second Book , tels us , How many Springs are above the Firmament , and which are the out-goings of Paradise . It may be that after we have inhabited this Earth of misery and sorrow , wherein death and infirmity are the wages of our sins , we shall be introduced into those high Globes wherein we shall live for ever , in fulnesse of happinesse and joy . Is it not said in Rev. 2. ver. 28. To him that overcomes , will I give the morning Star ? And Job , in the 38. and 7. v. doth see through Faith , the Morning Stars singing together , and all the Sons of Men shouting for joy . This his Vision shall be accomplished , when we shall trample upon these moving wonders , and if by reason of those glorious objects we may remember the things of this Earth , we shall from those vast habitations of glory , look with great contempt and disdain upon this lump of Earth , so highly esteemed of men , and by them divided into so many Regions , and Countreys ; and upon that drop of water , by them divided into so many Seas . May it not also be that the Earthly Paradise , or Garden of Eden , out of which Adam was driven , was the same place whereunto we shall return ; he was driven out of it for his sins , without which he had not tasted death . And now that Jesus Christ by his satisfaction to the Father's Justice , hath blotted them out , we shall be therein introduced . Munster faith , that many ancient Philosophers did imagine it scituated in a high place , encompassed with fire , adjoyning the Circle of the Moon , and that there are Elias and Enoch , those Antients were not far from my opinion , seeing the inconveniencies that would follow , if we did seat it in this our World : for if to believe that this Paradise was upon this Earth , it 's a very hard thing ; for it 's of no moment to rely upon the names of the Rivers , and Countreys , that are named in the translation of the Holy Scripture , considering that the Hebrew names in it are not conforme ; and that the Translators do yeild , that they have Interpreted them but by conjecture , and as nigh as they could guesse . Again , this Paradise can no more be found on the Earth ; nor those Rivers , that are said to be those whom Moses , doth mention , do not issue from one and the same Spring , as it 's recorded of those of Paradise . And lastly , it would be a ridiculous thing , to believe that God hath driven his people from that place , which he suffers the Turks , and other Infidels to enjoy , it being that whole Country , apprehended to have been this Earthly Paradise of delight . Before I conclude this Chapter , I will here alledge two notable things . The first is , that as there is no Book , though never so bad , but there is also some good in it : Neither is there any Religion but hath some good Maxims . The Chineans , and the Turks , being perswaded by appearances do not at all doubt but that after death , they go to inhabit the World of the Moon . The second is , that there are already divers bodies in Hell , and also in Paradise . In Hell are those who have yeilded up their bodies to the unclean spirits , and Daemons ; but in Paradise are Elias and Enoch , which both places to hold up those bodies , must needs be solid , which solidity cannot be but in some Stars , or Star , where God doth manifest himself more clearly and visibly , and where are those Rocks of eternity , whereof it 's spoken by Moses , whereunto we must desire to go , and there to dwell , exchanging this Valley of misery to the great advantage and comfort of our glorious bodies . Chap. XXXVII . Proving the Worlds plurality , by an Answer made by the Daemons . IF any Creature can know the pure and naked truth of things , and that may decide and resolve this question to the full , certainly the evil spirits may ; but how may we enquire of them about it ? Thus it may be done ; for it 's very certain , that Pans , Sylvaines , and other gods , who in former Ages did appear to men , were wicked spirits and Daemons , who required worship from men ; but a certain Silenus , who was one of that nature , suffering Marsias to take possession of him , told him , That there were other Worlds , where men lived as old again as we , and were of higher and greater shape and stature . And in the History of Faustus the Magician , it 's said , that his spirits did walk him amongst the Starres , for the space of eight dayes , and that he was carried 80000 miles high far from us ; and that ascending up very high , he did perceive from far off this Earth , the Cities and other things in it contained ; but this his relation is but in brief . Chap. XXXVIII . Proving the same , by a Reason drawn from the unprofitablenesse of the light of the Sun , and others . IF there were no Globes inhabited above the Sun , for what use would that light be which the Sun casts above him ? It would be altogether unprofitable and uselesse , if it was lost in the Air ; It is then cast upon those bodies that have need of it , which cannot be any thing else but the Starres , which of their nature are dark and obscure , and earthly , as the earth that we inhabit ; for otherwise they would have no need of the Sun's light . Shall not so many Reasons suffice for to overcome that obstinacy and Preoccupation ? Great Alexander may break the Ice , and shew us the way , who having heard Anaxarch the Philosopher , discoursing upon this subject matter , did believe him , and fell a weeping , because that there being other Worlds , he had yet conquered but one . Chap. XXXIX . Proving the same , by the Suns mutual ravishments betwixt the Earth and the Moon ; and by their equal qualities , and by other notable Reasons . WE may say , That the time spoken by Seneca in his Medea , is come now . Quae Typhis novos deteget orbes . Wherein we may learn things unheard , viz. the discovery of new Worlds . Et tabula pictos ediscere mundos . We may say it with better ground then he , seeing he onely spoke of the Indies , and we speak of Worlds distinct and separated , and prove it by so many Arguments , as if we could not come to an end of them ; for it may yet be proved , in that the Earth and the Moon deprive each other mutually of the Sun ; which deed doth testifie their conformity , and that both may suffer Eclipses ; also by their mutual communications , cold qualities , solidity and roughnesse , that help us to see it ; for many think , that we should scarcc see it , were it not for its irregularities , which cause its light better to reverberate the beames of the Sun . I shall add to this , That if God , who could make many Worlds , had not made them , his power might be said , in some respects , to have been idle , unprofitable , and limited ; for though it ayms not so much to the works , as to the end of them , yet it being for his greater glory , though he doth not whatsoever he can , we cannot assert , That he was not willing to make many Worlds ; as we cannot deny , but he had the power to make them . Thirdly , the common and general opinion grants , the four Elements to be in Heaven ; for it believed , that there is the Empyred Heaven , that is the Heaven of fire , the crystal Heaven , that is of a waterish nature ; the Heaven of the Stars , which is solid , and by consequence of an earthly nature ▪ and the Air is apprehended to be amongst those Stars : the four Elements then are in Heaven , and why may not there be also mixt and composed bodies ? and why not the effects as well as the causes , which compose them , are in it ? and why could they not act as well within themselves , as in things far remote ? Fourthly , the Creation of the world , or of many worlds , is a thing that wholly depends from the free Will of God , neither can it be denyed by any natural reason ; for God acts not outwardly by necessity , as to limit himself onely to this our World ; but on the contrary , God willeth whatsoever implyeth not contradiction : But many worlds do not imply contradiction , neither from God , nor from the thing created ; and it seems requisite , that the object be the measure of the power ; but this World not being infinite as God is , there must needs be an infinity of them . Chap. XL . Discoursing of those Stars discovered of late , and of the Spots of the Sun . HAving above mentioned the Spots of the Sun , and some new Starres , and thence having drawn some Arguments , it may not be out of our purpose to speak of them now . As concerning the new Stars , Galileus relates , that in the yeares 1572 , and 1604 , were seen some new Stars , that were higher then any one of the Planets ; whereof the first was in Cassiopeia , as Tycho Brahe , and Campanella declare ; so likewise did Hipparchus observe a new Starre 100 years before Christ's Birth . And as touching the Spots of the Sun , I shall content my self to say , hat Galileus asserts , That these Spots are bigger then all Asia and Africk ; some there are , who believe them to be onely vapours , and some impressions of the Ayr , because that their figures are irregular , and that they are seen in great number disappearing , and again appearing ; but they onely hide themselves in the Sun ; or to say more congruously , they onely disappear by reason of their too nigh approach to the light of the Sun ; and besides , they have a regulated course , according to which they fail not to return at a certain time ; and therefore they are some Stars , touching which I send the Reader to Tardus's book , who calls them the Stars of Bourbon , after the name of the King of France , under whose reign these new Stars were first discovered . Chap. XLI . Containing divers Reasons drawn from several places of Scripture . AS it is said in divers places of the holy Scripture , That the Earth is full of corruption ; or that it sings out the miracles of God by a figure of Rhetorick , that puts the continent for the thing contained ; several Texts of the Scripture do also say , as in Job 25. v. 5 , 6. that the Stars are not clean before God , that they sing his praises , and are his Armies . These are things that very hardly enter into the heart of Men , and very likely part of them that Paul saw in his extasie ; but being he saith , that it never entred into the heart of man , he might mean , unto his time no body had believed it , or at least hath not had the full and particular knowledg of them : wherefore Job saith , chap. 38. v. 37 , 38. Who can number the clouds in wisdom ? or who can stay the bottles of Heaven . And Solomon in the book of Wisdome , ch. 9. v. 16. And hardly do we guesse aright at things that are upon Earth , and with labour do we find the things that are before us ; but the things that are in Heaven , who hath searched out ? And Esdras in his second book , chap. 4. v. 21. They that dwell upon the Earth , may understand nothing but that which is upon the Earth ; and he that dwells above the Heavens , may onely understand the things that are above the heighth of the Heavens . It may be replyed , That these Texts are to be understood of the Angels ; But the Texts alledged in the following Chapter will make it clear , that it 's to be understood of Men onely ; for Campanella hath even observed , that Paul to the Colossians , Chap. 1. verse 20. saith , That by Jesus Christ's blood all things are reconciled to God , whether they be things in Earth , or things in Heaven ; and consequently it will follow , that there are men in Heaven , who have need of Redemption as well as we . Chap. XLII . Containing the Reasons drawn from the Word of God . IF then there be divers Worlds , and that the Stars be inhabited , those worlds may have been created some before the others , and so shall end at divers times ; and perhaps some are ended already , and some are created of new : the believers of those former Worlds seem to speak in Psal. 90. ver. 1 , 2. saying , Lord , thou hast been our dwelling place in all generations , before the Mountains were brought forth , or ever thou hadst formed the Earth and the World . And God seems to be angry against the men of those worlds , in 2. of Esdras , c. 9. v. 18 , 19. because those who were before , were better in these terms . And now when I prepared the World which was not yet made , even for them to dwell in that now live , no man spake against me , for then every one obeyed , but now the manners of them which are created in this World ; that is made , are corrupted by a perpetuall seed , but there is yet one Text more pregnant for to prove that there were other Worlds before this , that are ended , and have been judged as we shall be one day , he speaks in these terms in the 2. Book of Esdras , c. 7. v. 34. And the World shall be turned into the old silence 7. dayes , like as in the former Judgments , so that no man shall remain : And if it be thus , might we not say that those great Comets that remain so long above the Region of the meteor , are the burnings and consummations of some Stars that are ending , and which we had not perceived by reason of their far distance : For as in former ages , new ones have often been seen , yea , even in this our own ; so likewise may some others end : and to all this , we may adde that of the Revelations , viz. that the Stars shall fall , that is to say , shall end . Many ancient Authours were of this Judgment , believing not only that there are divers Worlds at one and the same time , but that there had already been some before . Origenes was of this belief , and that ours shall last seaven thousand years , and that many of the others shall last forty nine thousand years . Campanella differs not much from this judgment , the Wisedome of God speaking in the Proverbs , saith , ch. 8. v. 23. 31. Before the Earth was , I was with God , rejoycing in the habitable part of his Earth , and my delights were with the Sons of Men . And in the 26. v. While as yet he had not made the Earth , nor the Fields , nor the highest part of the dust of the World . Chap. XLIII . which is a sequell of the Texts of the Holy Scripture . THough we have divided these places of Scripture into two chapters for to confirm this opinion ; yet I will not omit some few others , which may in some respects sit this same subject . Paul to the Ephesians , c. 1. v. 10. speaking of Christ Jesus , saith , That in the dispensation of the fullnesse of times , he might gather together in one , all things in Christ , both which are in Heaven , and which are on Earth , even in him . And to the Colos. 1. v. 20. God having made peace through the bloud of Christs Crosse , reconciled all things to himself , whether they be things in Earth or things in Heaven . How may these two Texts be expounded if we do not understand them of these men who are in the Heavens or Stars , whom God hath gathered to himself , and redeemed ? For if it be said that they are those that died before Christ ; It cannot stand with reason , because their Souls were already in Paradise , or in Hell : but where the Soul is , thither also shall the body go after the Resurrection . David speaks thus in the Psal. 112. v. 6. God humbles himself to behold the things that are in Heaven and in Earth , for he dwells on high ; This Text indicates that God is beyond the Heavens , and that in the Heavens whereunto he humbles himself , there are Inhabitants as well as in the Earth . And in the Ps. 148. he bids the Angels , Stars , and Earth , &c. to praise him : That is to say , he spoke thus to the Inhabitants thereof by a figure ; which takes the continent for the thing conteined . Ecclesiasticus , saith in his 16. chap. and 18 , 19 , 20 , 21. verses , Behold the Heaven , and the Heaven of Heavens , the deep , and the Earth , and all that therein is shall be moved , and the Foundations of the Earth shall be shaken with trembling , when he shall visit them , and who can conceive his wayes , for the most part of his works are hid . And in the chap. 43. ver. 32. saith , that There are yet hid greater things then these be , for we have seen but a few of his works . By these two places it plainly appears that those things which we have not seen , and are greater then any that we know , are somewhere else then in this Earth , viz. in the Heavens , and that consequently there is more then one World . I might yet alledge divers other Scriptures , as that of the 2. chap. to the Phillip . verse 10. and Psalm 89. verse 7. But that I may not be too tedious , I shall not make farther mention of others . Chap. XLIV . How the naked truth of the plurality of Worlds may be discovered ; and especially what is in the Moon . BUt being we have neither the wings of birds , nor the eyes of Eagles or Lynxes , nor can heap up Mountains one upon another as Gyants , how can we see perspicuously the things that are in the Moon , and in the other etherial bodies ? To this I answer , That those ancient Ages have shewed us the way , by the Tower of Babel , by Pyramides and Phares , from the top of which , scarce could men be discovered and perceived ; and from those tops were discovered Countreys of far distance , immortalizing the memory of their Authors . It would be requisite , that a King or great Prince , desirous by emulation to immortalize his name , would set poor prisoners , with other Workmen , to the Work , that from it ( being high elevated up into the Ayr ) we might more distinctly behold by the help of the Prospective-glasses , what is within the Stars , and chiefly in the Moon ; no doubt such a Tower would serve much , being built upon a very high Hill . But if it be objected , That there are very high Mountains , from which neverthelesse no new thing can be seen . I answer , That besides that , no body went to try it with a Prospect-glasse , those Mountains , though high , by reason of their crookednesse , are not very high , if we consider them perpendicularly ; and yet it hath been observed , that from the highest Hill of Mount Pyreneus , the Sun appears more majesticall then ordinarily , which cannot proceed but from the heighth of that Mountain . And though nothing could be discovered from such a Tower , which I cannot believe , yet it would be a work of immortal name to that Prince who would do it . And that it may be out of doubt , that from a high Mountain , or some such place high elevated , something may be seen and observed in the Stars , Bethancour in his Travels asserts , That from the top of Tenerisa , a very high Mountain in the Canaries , the Sun may be seen to turn round upon himself , without the help of any Prospective-glasses . Secondly , it 's most certain , That if the Prospective-glasses can be brought to a full perfection , that many things will be discovered new in the Stars , and at the first time that they were invented , divers things have already been discovered ; for Galileus and Descartes declare , that there may be made Prospective-glasses , that shall multiply the object a thousand times in his bignesse : If it be so , what is there in the Firmament that may not perspicuously be seen ? Lastly , some have imagined , that as Man hath imitated the Fishes in swimming , that he may also find out the Art of flying , and that by such an artifice , he may without any other help see the truth of this question ; the Histories relate to us some Examples of men that have flown . Many Philosophers think it feasable , and amongst others Roger Bacon ; I might here relate all those Examples , and divers Reasons for it ; yea , some instruments and engines for that effect : but I shall shew these things in my Book of Naturall Magick ; and in my discourse , de arte volandi ; because though one could attain the Art of flying , yet it would avail him but little for this purpose , because that besides , by reason of his weight he could not rise very high , he could not remain fixt to behold Heaven , or to make use of Prospective-glasses , but would wholly bend his mind to the guiding of his Engine . Chap. XLV . Of Scipio's Dream ; with some new Reason upon this subject-matter . VVE read in several Authors , that Scipio dreamed a very notable dream , wherein he thought that he was carried up high , and that he saw other Worlds in the Stars , whence he perceived the Roman Empire ; and seeing it from very far , found , that it took so little room in this our Terrestrial Globe , that upon that he conceived an exceeding great contempt of those , who despising their life , did venture it , for to get a famous name ( though but vain ) in that little corner of the Earth . Both Cicero and Macrobius have composed Books concerning this Dream , and have doubted under what sort of dreams this was to be entred . For my part , I think that it must be called a Vision , being he saw things that are reall , viz. the airy Lands , and the Stary and Planeticall people . Or it may be , that having such a belief , he was desirous to propose it , as many others in such like case have done , thereby to see how it would be received : And truly , if this was his scope , he hath had no bad successe ; for it hath been embraced by many illustrious Persons , who have found it consonant to Reason . Besides all this , Is it not beyond all reason and appearance , that so many huge and vaste bodies as the Stars are , should remain barren and fruitlesse . I think , that if I should discourse orderly , and gradually with the most opinionative man that is , that I should obtain of him , that those bodies , whereof some are three hundred times bigger then the Earth , do at least bear some plants ; and if this were granted , how could these plants be there , if they were not for the use of some living Creatures : and if it could be granted , that there be some creatures , may it not also be granted , that there are Men for to make use of them , being they are made for them ? And lastly , is it not lawfull and equall , that there be men whither soever their dominion reaches ; but Man rules the Stars , as well as the Earth and Sea , the whole World is made for him ; and consequently there must needs be some Inhabitants in the Stars . Chap. XLVI . Answering the Objection of those , who believe , that the Spots of the Moon are the figure of the Earth . BEfore I conclude this Discourse , I think it yet convenient to answer them , who think that they have hit right on the head of the nayl , when they say , that the Spots in the Moon are nothing else but the figure of the Earth's shadow , which communicate themselves in the Moon , as in a Looking-glasse ; but they do not consider , that there is no analogy nor resemblance between those Spots , and those of our general Mapp ; nor that in dark nights this figure can be communicated to the Moon ; or could it be said , That those Mountains in the Moon , are nothing but some flat and low obscurities ; But I answer , That the shadow of those Mountains appears and turns as the Needle of a Sea-Compasse , proportionably as the Sun inlightens them diversly , which could not be , were they not bodies high elevated ; for they would be without shadow , and Monsieur Gassandus did sometimes say , That he had mathematically measured the heighth of some Mountains and valleys in the Moon by means of their shadows ; and that he had found the heighth of the Mountains in the Moon to be much more remarkable , then of those of the Earth . Chap. XLVII . Containing an Argument drawn from those mountains that are in the Moon . WE must observe that the Moon being half full , more or lesse out of it are seen many little spots , as drops of Water , or Orient Pearls very bright . Now they are the tops of the Mountains , that are lighted by the splendour of the Sun , because they ascend as high as that part of the Moon which is inlightned ; but because the Mountains are broad at the foot , and are dark at the bottome , those drops appear to be somewhat scattered one from the other , and so seem loosed from the Moon , though they be not . So likewise if one should contemplate from above the Mount Pireneus , or the Alps , he would only see their top in the form of so many Pearls , because the top of them would reverberate the splendour of the Sun , and their Snows would encrease the light of it . Observe also that Paul in his 1. to the Cor. c. 15. v. 40. asserts that the Glory of the celestial bodies , is divers from that of the terrestrial , and that there is one glory of the Sun , and another glory of the Moon , and another glory of the Stars . But if they differ in glory , they do so by reason of the variety of creatures that are in them ; in the 47. verse , the Apostle seems to indicate that there are heavenly men , and also earthly men . The Courteous Reader is intreated to consider that this is onely a fragment of the Volume intended by the Authour , for to set forth the life and Philosophy of Democritus , who asserted this opinion : So that I say onely what he himself would have said to confirm his position . But if it seems in any particulars to oppose and contradict the Principles of Religion , and that my Arguments do not give full satisfaction , I shall freely retract and uncloath my self of this opinion , if it be any wayes noxious to Religion : if it be recited and blamed by ignorant persons , who are not able , nor sit to answer to the Objections , and cannot or will not weigh them by reason , I have what I expect . But if learned and wise persons can shew me the contrary with sound proofs , and strong reasons , they shall find me ready to yield up this my opinion to their censures . Though above fifty Authors of this same opinion , going before me , have not yet been contradicted . I hope that I give no more occasion of distaste then they . FINIS . 
A15751	----	The description and vse of the sphaere· Deuided into three principall parts. Whereof the first intreateth especially of the circles of the vppermost moueable sphære, and of the manifold vses of euery one of them seuerally. The second sheweth the plentifull vse of the vppermost sphære, and of the circles thereof joyntly. The third contayneth the description of the orbes whereof the sphæres of the sunne and moone haue been supposed to bee made, with their motions and vses. By Edvvard Wright. The contents of each part are more particularly set downe in the table. Wright, Edward, 1558?-1615. 1627 Approx. 159 KB of XML-encoded text transcribed from 51 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2005-03 (EEBO-TCP Phase 1). A15751 STC 26022 ESTC S120334 99855533 99855533 21028 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A15751) Transcribed from: (Early English Books Online ; image set 21028) Images scanned from microfilm: (Early English books, 1475-1640 ; 1264:9) The description and vse of the sphaere· Deuided into three principall parts. Whereof the first intreateth especially of the circles of the vppermost moueable sphære, and of the manifold vses of euery one of them seuerally. The second sheweth the plentifull vse of the vppermost sphære, and of the circles thereof joyntly. The third contayneth the description of the orbes whereof the sphæres of the sunne and moone haue been supposed to bee made, with their motions and vses. By Edvvard Wright. The contents of each part are more particularly set downe in the table. Wright, Edward, 1558?-1615. [8], 95, [1] p. : ill. (woodcut) Printed by B[ernard] A[lsop] and T. Fawcet, for Iohn Tap, and are to bee sold at his shop at S. Magnus corner, London : 1627. Printer's name from STC. Reproduction of the original in the Henry E. Huntington Library and Art Gallery. Lacks N4. Title page and pages 82-end from the British Library copy filmed at end. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. 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Quality assurance was then carried out by editorial teams in Oxford and Michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet QA standards were returned to the keyers to be redone. After proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. Any remaining illegibles were encoded as <gap>s. Understanding these processes should make clear that, while the overall quality of TCP data is very good, some errors will remain and some readable characters will be marked as illegible. Users should bear in mind that in all likelihood such instances will never have been looked at by a TCP editor. The texts were encoded and linked to page images in accordance with level 4 of the TEI in Libraries guidelines. Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Celestial globes -- Early works to 1800. Astronomy -- Early works to 1800. 2004-10 TCP Assigned for keying and markup 2004-10 Aptara Keyed and coded from ProQuest page images 2004-11 Judith Siefring Sampled and proofread 2004-11 Judith Siefring Text and markup reviewed and edited 2005-01 pfs Batch review (QC) and XML conversion THE DESCRIPTION AND VSE OF THE SPHAERE . Deuided into three principall Parts . WHEREOF The first intreateth especially of the Circles of the vppermost moueable SPHAERE , and of the manifold vses of euery one of them seuerally . The second sheweth the plentifull vse of the vppermost Sphaere , and of the Circles thereof joyntly . The third contayneth the Description of the Orbes whereof the Sphaeres of the Sunne and Moone haue beene supposed to bee made , with their Motions and Vses . By EDVVARD WRIGHT . The Contents of each Part are more particularly set downe in the Table . LONDON , Printed by B. A. and T. Fawcet , for Iohn Tap , and are to bee sold at his Shop at S. Magnus corner . 1627. A TABLE OF THE CONTENTS OF this Booke . The first Part. Of the Circles of the vppermost SPHAERE , and their seuerall vses . THe Definition and deuision of this Sphaere , Chap. 1. The description of the Horizon , Chap. 2. The vses of the Horizon , Chap. 3. The description of the Meridian , Chap. 4. The vses of the Meridian , Chap. 5. The description of the Houre-circle , and Poles of this Sphaere , Chap. 6. Of the Equinoctiall circle , and why it is so called and how diuided , together with his manifold vses , Chap. 7. The description of the Zodiacke of this Sphaere , Chap. 8. The vses of the Zodiacke , Chap. 9. The description of the two Colures , together with the vses common to them both , Chap. 10. The vses of the Equinoctiall colure , Chap. 11. The vses of the Solstitiall colure , Chap. 12. The description of the two Tropickes , Chap. 13. The vses of the Tropickes , Chap. 14. The Polar circles , Chap. 15. Vses of the Polar circles , Chap. 16. Of the Zones , Chap. 17. The difference of shadowes that the Sunne maketh in these Zones , Chap. 18. The second Part. Of the vses of the vppermost Sphaere , and of the Circles thereof joyntly . TO rectifie the Sphaere , that is to sett the Sphaere to the Latitude of that place for which you would vse it , Prop. 1. To know ▪ the place of the Sunne by this Sphaere , Prop. 2. To know the declination of the Sunne , or of any point of the Ecliptick , Prop. 3. To know the right Ascention of the Sunne , or any point of the Zodiack , Prop. 4. To know the oblique ascension of the Sunne , or of any Starre or point in the Zodiack , Prop. 5. To finde the difference of Ascension , Prop. 6. To finde at what time the Sunne riseth or setteth , Prop. 7. To finde the length of the Artificiall Day or Night , Prop. 8. To know the time of the Sunne rising , or Sunne setting , Prop. 9. To find the length of the artificiall Day or Night , otherwise by the Sphaere , Prop. 10. To know the Meridian altitude of the Sunne at any place , whose latitude is knowne , Prop. 11. To know how high the Sunne is about the Horizon at any time of the day , Prop. 12. To find the houre of the day by the height of the Sunne , the place of the Sunne , and height of the Pole being giuen , Prop. 13. To find the bredth of the Sunnes rising or setting , that is , how farre he riseth or setteth from the point of true East or West at any time , Prop. 14. To finde the place of the Sunne , his declination , and the quarter of the yeare being knowne , Prop. 15. To finde what day of the moneth it is by knowledge of the Sunnes declination , Prop. 16. The day of the moneth being knowne to find at what time the day breaketh , Prop. 17. To finde how long the twylight continueth , Prop. 18. To finde how much the declination of the Sunne must alter at any time of the yeare , to make the day one houre longer or shorter , Prop. 19. To finde how many dayes it is ere the day lengthen or shorten an houre , Prop. 20. To make an horizontal Diall by the Sphaere , Prop. 21. How to make a direct murall Diall by the Sphaere , Prop. 22. To make any direct inclining , or direct reclining Dyall by the Sphaere , Prop. 23. To know at what time the Moone , or any other of the Planets , or fixed Starres that are within the bredth of the Zodiack rise or sett , or come to the Meridian : as also with what degree of the ecliptick they rise set or midde Heauen , together with their declinations , and their right and oblique ascensions , and descensions , and their amplitudes or bredths of rising or setting , Prop. 24. To know how long the Moone , or any of the Planets or fixed Starres doe shine , or continue aboue the Horizon , Prop. 25. To find which of the Planets of fixed Starres ( that are within the compasse of the Zodiack ) are aboue or vnder the Horizon at any time of the day or night , Prop. 26. To find in what time any Signe , or part of the Ecliptick , riseth or setteth , Prop. 27. To finde the houre of the Night by any of the Planets , or fixed Starres in the Zodiack , that appeare aboue the Horizon , Prop. 28. To know at any time of the yeare , what Starres in the Zodiack arise or set Cosmically , Achronycally , or Heliacally , Prop. 29. The Meridian Line . Of the vse of the SPHAERE and GLOBE . Pars , 1. The Description of the Sphaere and Globe , diuided into three principall parts .. Whereof this first intreateth specially of the Circles of the vppermost moueable Sphaere and of their peculiar vses . CHAP. I. The definition and diuision of the Sphaere . THis Sphaere , is nothing else but a representation of the Coelestiall orbes and circles , that haue beene imagined for the easier vnderstanding , expressing , and counting of the motions and appa●ences , eyther common to the whole Heauens , or proper to the Sunne and Moone . The circles of this Sphaere are eyther inmoueable , as the two greatest and vtmost circles , the Horizon and Meridian , ( whereto is adioyned the little houre circle that is fixed to the Meridian ) or else moueable ▪ as all the rest contayned within these . CHAP. II. The Description of the Horizon . THe greatest and vtmost circle of the Sphaere that lyeth leuell on all sides from the ground , is called the Horizon , which is deuided into 7. limbs , or borders . The first and vtmost of them conteyneth the 32. points of the Compasse , or the windes ( as they are at this day deuided and vsed by Sea-men ) with their Latine names adjoyned vnto them . The second limbe conteyneth the names and diuisions of the 12. Windes as they were wont to bee deuided in old time . The third is deuided into the moneths and dayes of the new Kalender , first established by Pope GREGORIE the XIII . and now vsed in many places beyond the Seas . In the fourth limbe are set downe the moneths and dayes of the ordinarie Kalender vsed in England . Next within this , are placed the 12. Signes and degrees of the Zodiacke , that so the place of the Sunne might bee presently knowne for any day of the yeare giuen , or contrariwise , that the day of the Moneth might be readily found by the place of the Sunne . After this , followeth the sixt limbe conteyning the 32. Windes or points of the Compasse , with letters representing the names now in vse amongst English Marriners . The seuenth and last limbe next the innermost edge of the Horizon , is deuided into 360. degrees with figures set to euery tenth degree , beginning from the points of East and West , and ending at North and South ; that so the number of any degree of the Horizon might bee the easilier knowne : Which Circle appeareth most plainely to them that are in a plaine Champion Countrie , or vpon the Sea close by the water in a cleare calme day . CHAP. III. The vses of the Horizon . 1. IT deuideth the vpper and visible part of the Heauens from the nether halfe that is hidden out of our sight . 2. It sheweth partly the difference of a right and oblique Sphaere , for when this circle and the Equinoctiall , crosse each other at the right Angles , it is said to be a right Sphaere , otherwise when they make oblique Angles one with another , it is called an oblique Sphaere . 3. In an oblique Sphaere this circle seuereth those Starres which neuer rise nor set , but are alwayes eyther aboue or beneath the Horizon , from such Starres as rise and set in euery 24. houres . For all the Northerly starres that are no further distant from the North pole , then the North pole is from the Horizon , doe neuer set , but are alwayes aboue the Horizon : And contrariwise , those Starres that bee about the South pole , no further distant from it then it is from the Horizon , doe neuer rise , but are alwayes hidden out of sight vnder the Horizon . 4. In respect of this circle , the Sunne , Moone and Starres , or any other part or point of the Heauens , are sayd to rise or set : For when they come vp from vnder the Horizon , they are sayd to rise ; otherwise when they goe from aboue the Horizon downe vnderneath the same , they are sayd to set . 5. And hereof it commeth that the ascendent , and descendent are found by this Circle : for that part of the Ecliptick that is at the East part of the Horizon arising , is the Ascendent ; and the point opposite to this at the West part of the Horizon , may be called the Descendent . 6. This Circle partly sheweth the difference of ascention of any part or point of the Heauens . 7. In this Circle we reckon how farre the Sunne , the Moone , or any Starre , or point of Heauen , ariseth from the point of due East . 8. The Horizon determineth the time of the artificiall day and night : for we call the time w●●rein the Sunne abideth aboue the Horizon , an artificiall day : And the time that he continueth vnder the Horizon , is the artificiall night . 9. This Circle sheweth the reason of the equality of artificiall dayes and nights , in a right Sphaere : and of the inequality of them in an oblique Sphaere . For in a right Sphaere , the Horizon deuideth all the paralels of the Sunne or Circles of the naturall dayes , into equall parts : But in an oblique Sphaere , it deuideth them into vnequall parts . 10. By meanes of this Circle , wee know what Starres , and what Eclipses , Coniunctions , or other aspects of the Planets may bee seene in our Hemisphere at any time . 11. From the Horizon is measured the twilight : For in the morning the Sunne being vnder the Horizon about 18. degrees of the verticall , Circle , the twilight beginneth : And when the Sunne is so much vnder the Horizon at Euening , the twilight endeth . 12. This Circle is of especiall vse in Geography , for from it wee begin to account the eleuation of the Pole , and of the Equinoctiall circle , whereby the Latitude of any place is knowne . 13. In Astrologie for erecting a figure , this Circle sheweth the beginning of the first and seauenth Houses . CHAP. IIII. The description of the Meridian . NExt the Horizon , succeeds the Meridian standing vpright on edge , and crossing the Horizon at right angles in the points of North and South . This circle is diuided on both sides at the inner edge into 360 ▪ Degrees , with figures set to euery tenth degree , beginning at the Equinoctiall , and ending at the Poles with 90. and beginning also at the Poles , and ending at the Equinoctiall with 90. The numbers beginning at the Pole , serue to set the Sphaere readily to any eleuation desired . The other numbers beginning at the Equinoctiall , shew presently the declination of any degree of the Zodiacke , or of any point assigned in the Sphaere , one quarter of the Meridian on eyther side thereof from the Equinoctiall to both Poles , sheweth the Climates , and the quantities of the longest dayes . CHAP. V. The vses of the Meridian . 1. IT deuideth the World into two halfes or Hemisphaeres : that is , the East and the West hemisphaeres . The Easterly hemisphaere is all that part of the world which is on the East-side of the Meridian , and the other halfe may bee called the West hemisphaere . 2. It sheweth the North and South parts of the world , for the two intersections of the Meridian with the Horizon , shew the very points of North and South . The South point is that which is directly vnder the Sunne at noone : And the point right ouer against this , is called the North-point . 3. It deuideth the arches of the Equinoctiall , and of all his Paralels , into two equall parts both aboue and beneath the Horizon . 4. And therefore it deuideth the artificiall Day and Night into two equall parts . 5. And consequently , it sheweth midday and midnight . 6. In an oblique Sphaere it serueth in stead of a right Horizon ( that is ) an Horizon that maketh right angles with the Equinoctiall . 7. Therefore the Astronomers begin their account of times ( which are measured by the equall motion of the Equinoctiall ) from the Meridian : the principall of which times , is the naturall day which is vsually begun from midday , or midnight . 8. This Circle sheweth the highest and lowest heights of the Sunne and Starres , which is most manifest in those Starres that are alwayes aboue the Horizon . These heights are called the Meridian altitudes of the Sun or Starres , which heights are chiefely obserued by Astronomers and Nauigators with great diligence . 9. In this Circle , wee obserue the distance of the Tropickes , and the greatest obliquitie of the Zodiacke . 10. In this Circle , wee obserue and count the Latitudes of places , the height of the Pole , and of the Equinoctiall . For the height of the Pole or Equinoctiall , is nothing else but the arch of the Meridian contained betweene the Pole or Equinoctiall and the Horizon . The height of the Pole is alwayes equall to the Latitude of the place . The height of the Equinoctiall is equall to the Complement of the Latitude and therefore it being substracted out of 90. 〈◊〉 shall remaine the height of the Pole. 11. The Meridian sheweth the longit●●● of places in Geographie . 12. In the Meridian , are measured the bredth of the Zones and Climates . 13. This circle in Astrologie , sheweth the highest and lowest parts of Heauen , which are the beginnings of two principall Houses : that is , the fourth and the tenth houses . CHAP. VI. The description of the Houre-circle , and Poles . THe little Circle fastned to the Meridia● is called the Houre-circle , which is deuided into 24. equall parts , signifying and representi●● vnto vs so many equall houres , whereof both the 〈◊〉 houres are fixed iust vpon the Meridian , becaus●●●hen the Sunne commeth to the Meridian , it is iust twelue a clocke : the vpper XII . serueth for the Day ; and the other XII . beneath serueth for the Night . The Index , or the Painter in forme of an Arrow , fastned vpon the Pinne that commeth through the midst and Center of this circle , is made to shew and point out the said houres as need shall requite , in the vse of the Sphaere . The vse of this houre Circle shall be shewed hereafter , when we shall speake of the common vse of many circles of the Sphaere together . And these two Circles ( that is , the Meridian and Horizon ) are called immoueable , because they keepe themselues alwayes , and in all places ouer the same parts of the Earth ; where as all the rest ( conteyned within these two ) moue round about altogether with one motion in the space of foure and twenty houres . This motion ( being common to the whole Heauens ) is made about two Points or Poles , represented in this Sphaere , by the two Wyre pinnes about which the Sphaere is turned ; whereof the one that commeth through the middest of the little Circle fastned to the Meridian ( which wee call the houre Circle ) representeth vnto vs the Pole Articke or the North Pole : the other because it is opposite to this , is called the Antartick pole , that is the right opposit , to , or right ouer against the North pole , which is also the South pole . CHAP. VII . Of the Equinoctiall Circle . THat Circle which compasseth about the midst of the Sphaere , and is euery where of equall distance from both Poles , is called the Equinoctiall circle , or the Equator ; either because it is equally distant from both Poles of the world ; or ●●se because the Sunne comming vnder this Circle maketh equality of dayes and nights throughout the world . It is deuided at the vtmost edge , or both sides thereof into 360. Degrees , with figures 〈◊〉 to euery tenth degree , beginning at the beginning of Aries , and proceeding Eastwards , till you become about to the same point againe . This Circle hath many vses . 1. It is the measure of the first 〈◊〉 . For this onely amongst all the Circle of the Sphaere is moued equally both in a right and 〈…〉 Sphaere , because ● alone being perpendicular to the 〈…〉 world , about which the Sphaere is equally turned , is deuided into two haltes by euery Horizon in the same points . 2. It is the measure of time ; because it measureth the quantitie of the artificiall and naturall dayes , of which Moneths and Yeares are made : It measureth also the quantitie of Houres and of other times which the Sunne maketh going vnder the Zodiacke . And therefore the degrees of the Equinoctiall are called tempora ( that is ) times . 3. It sheweth the two Equinoctiall points in the Eclipticke , cutting the Ecliptick in two places , which are the beginnings of Aries and Libra : and the Sun when hee commeth to those two points , is equally distant from both Poles of the World , and maketh equalitie of dayes and nights in all places ; which hapneth in our time about the 10. or 11. day of March , and the 13. or 14. of September . 4. The irregularitie of the Zodiacke , and of all the Signes and degrees thereof , is measured by this Circle . For seeing the most part of the apparences of the first motion are referred to the Zodiacke , which is not turned about his owne Poles , but about the Poles of the Sphaere , and therefore must needs bee vnequally turned about ; it was needfull that this inequalitie should be ruled and measured by some other equall motion . 5. It deuideth the Sphaere into two halfes ( which they call Hemisphaeres ) that is , into the North halfe or hemisphaere , wherein is the North pole , and into the South hemisphaere , wherein is the South pole . 6. So it deuideth the Zodiacke into the North halfe , and the South halfe ; or into the North signes , and the South signes . 7. From this Circle are numbred the declinations of the Starres , and of the degrees and parts of the Eclipticke , and of any other point of Heauen . 8. And in this Circle are counted the right ascentions of the same Degrees and Starres , &c. For the right ascention of any starre or point of the Heauens , is nothing else but the Arch of the Equinoctiall circle contained betweene the beginning of Aries and the Meridian , the same Starre or point being first brought vnder the Meridian . 9. In the Equinoctiall is counted the ascentionall difference and the oblique Ascention and Descention of any point of Heauen . And from the same Circle is reckoned the distance of the Sunne rising from the true East point . For the oblique ascention or descention is nothing else but the arch of the Equinoctiall , contained betweene the beginning of Aries , and that point of the Equinoctiall Eastwards , which ariseth or setteth together with the Starre or point that is giuen , in an oblique Sphaere . And the difference ascentionall or descentionall is nought else but the arch of the Equator , whereby the right and oblique ascention or descention of a Starre , or any other point in Heauen doe differ each from other . The distance of the sunnes rising from the true East point ( which in Latine is called Amplitudo ortiua , ) is the arch of the Horizon contayned betweene the Equinoctiall and the paralell of the Sunne , or his Center when he riseth . 10. In Geographie wee count the Longitudes of places in this Circle ; and from it we reckon the Latitudes , in the Globe of the earth , and in Maps , and sea Charts . For the longitude of a place is nothing else but the arch of the Equinoctiall circle contayned betweene two Meridians , whereof one goeth by the canary Ilands , and the other by the place that is giuen , And the latitude of a place is the arch of a Meridian contayned betweene the Equinoctiall , and the Zenith of the place that was giuen . 11. In Dialling this Circle is of especiall vse . For by meanes of it the spaces of the houres are deuided in all kindes of Dials , horizontall , erect , direct , declining , inclining , reclining , &c. 12. In Astrologie the twelue Houses are set out by the equall diuisions of this Circle into twelue parts , according to the way deuised by Regiomontanus , which way is commonly called rationall or reasonable . And this Circle gouerneth the directions , whereby things to come are artificially fore-told . CHAP. VIII . The description of the Zodiacke . THe great broad Circle that compasseth about the Sphaere obliquely , comming nearer the Pole of the Sphaere in one place then in another , is called the Zodiacke . Round about through the middest of this Circle , is drawne the Circumference commonly called the Eclipticke line , deuiding the whole Sphaere , and the whole bredth of the Zodiacke throughout , into two equall parts . In this Sphaere there are represented vnto vs two Eclipticke lines . The one may be called the middle , or fixed Eclipticke , which keepeth alwayes the same distance or obliquitie from the Equinoctiall . The other may bee called the true or moueable Eclipticke , because it maketh not alwayes the same angles of intersection with the Equator , but sometimes greater , sometimes lesse . For the greatest obliquitie of the Zodiacke , which not long before Ptolomees time was obserued to bee 23. Degrees and 52. Minutes ; in Copernicus his time , was hardly found to exceed 23. degrees 28. minutes , according to his obseruation , and therefore hee thought that the difference betweene the greatest and least obliquitie of the Zodiacke , was 24. Minutes : and the middle or meane obliquitie betweene both these , to bee 23. Degrees 40. Minutes . The manner of the variation of this obliquitie may in some sort bee shewed by this Sphaere , if we suppose the fixed Eclipticke drawne round about through the middest of the Zodiack to be 23. degrees 40. min. distant from the Equinoctial at the beginning of Cancer and Capricorne : and the moueable Eclipticke ( fastned as it were vpon two Poles at the beginning of Aries and Libra , and so hauing alwayes the same points of intersection with the middle Eclipticke and Equinoctiall ) to bee moued vp and downe aboue and beneath the middle Eclipticke , by the space of 12. Minutes at the beginning of Cancer and Capricorne : and this motion to finish his reuolution once in 3432. Iulian yeares . The bredth of the Zodiacke is bounded by the greatest latitudes of the Planets , especially of Venus and Mars , which sometimes hath almost 7. degrees of latitude . The Zodiacke is diuided by the Equinoctiall into two semicircles . The one aboue the Equinoctiall is called the Northerly semicircle : the other halfe beneath the Equinoctiall , is the Southerne semicircle of the Zodiacke . So long as the Sunne moueth vnder the first of these semicircles , the dayes are longer then the nights , otherwise they are shorter . Each of these semicircles is againe deuided into two parts , and so the whole Zodiack into foure quarters : the first from Aries to Cancer , may be called the vernall or Spring-quarter , which in this Sphaere is also shewed by the word Ver ( signifying the Spring : ) The next from Cancer to Libra , the Summer quarter , wherein is written the word Ae●tas signifying the Summer . The 3. from Libra to Capricorne , is the Haruest quarter , wherein you shall finde in this Sphaere the word Autumnus which signifieth Autumne or Haruest . The fourth and the last , from the beginning of Capricorne to Aries , is called the winter Quarter , which in this Sphaere is shewed by this word Hiems , which signifieth the Winter . And these foure quarters of the Zodiacke are thus called by the names of the Quarters of the yeare , because the Sunne mouing vnder those quarters of the Zodiacke , maketh those foure Quarters of the yeare . Euery one of these quarters of the Zodiacke is againe deuided into three parts , and so the whole compasse of the Zodiacke into 12. which are called the 12. Signes , whereof euery one contayneth 30. Degrees in length from West to East , and is in bredth equall to the bredth of the Zodiacke . These Signes , and the Zodiacke it selfe haue their beginning from that common meeting , or crossing of the Eclipticke , and the Equinoctiall , where the Eclipticke beginneth to arise aboue the Equinoctiall towards the North pole : and they are called by these names ; Aries , Taurus , Gemini , Cancer , Leo , Virgo , Libra , Scorpio , Sagitarie , Capricorne , Aquarie , Pisces . That is to say , The Ramme , the Bull , the Twinnes , the Crab , the Lyon , the Virgin , the Ballance , the Scorpion , the Shooter , the Goat , the Water-pourer , the Fishes . And they are signified by these Characters , ♈ ♉ , ♊ , ♋ , ♌ , ♍ , ♎ , ♏ , ♐ , ♑ , ♒ , ♓ . This deuision of the Zodiacke into 12. Signes and of euery signe into 30. Degrees , nature it selfe seemeth to haue shewed by the motions of the Sun and Moone . For in what time the Sunne moueth once about the whole compasse of the Zodiacke , the Moone maketh twelue reuolutions through the same . Therefore as the time of a yeare is deuided into 12. Moones , so the Zodiacke is deuided into 12. Signes : And as euery Moneth contayneth 30. dayes , so euery signe is deuided into 30. parts , which they call Degrees , which signifieth as much as steps , because the Sunne steppeth , or goeth forwards almost so much as a degree in euery day , from the West Eastwards vnder the Zodiacke . The Zodiacke is otherwise also deuided into two semicircles , the one ( from Capricorne to Cancer ) ascending , because that so long as the Sunne or any of the Planets are in that semicircle , they still ascend and rise higher and higher aboue the Horizon . The other semicircle of the Zodiacke , from Cancer to Capricorne , is called descending , because the Sunne or Planets being in that semicircle , come downe euery day lower then other . The 12. Signes are by the Astrologians diuersly deuided , first into chiefe , meane , and common signes . The chiefe signes ( which are also called Cardinall , that is the principall signes ) are Aries , Cancer , Libra , and Capricorne , because they come next after the principall points of the Zodiacke , that is , the two Equinoctiall points at the beginnings of Aries , and Libra ; and the two solstitiall points of Cancer and Capricorne . The meane signes ( which are also called fixed ) are Taurus , Leo , Scorpio , and Aquarius . They are called meane , because they are placed betweene the chiefe or principall , and the common signes . They are called fixed signes , because that when the Sunne is in those signes , wee finde a more perfect temperature of the Ayre , then when he is in the other signes . The common signes ( which are also called double bodyed ) are Gemini , Virgo , Sagitarie , and Pisces . They are called common , because they take part of the nature of the fixed signes going before them , and of the Cardinall signes following after them . They are called double bodied , by reason of their Images , as they are imagined in the eight Sphaere , which are compounded of two bodies : For there be two Twinnes ; and the Virgin holdeth an eare of corne in her hand ; Sagitarie is made of a Man and an Horse ; and there are two Fishes . The placing , and nature of these signes brought in this diuision . The Astrologians also deuide the 12. Signes into foure trigons of triplicities , so called because they are distant the third part of a Circle , one from another . The first triplicitie contayneth Aries , Leo , and Sagitarius ; and is called the fiery trigon , or triplicitie : The second triplicitie contayneth Taurus , Virgo , and Capricorne ; and is called the earthly trigon . The third triplicitie contayneth Gemini , Libra , and Aquarius ; and is called the ayrie trigon . The fourth triplicitie contayning Cancer , Scorpio , and Pisces ; is called the watrie trigon . Nature it selfe is the cause of this diuision of the Signes also . For into these Trigons of the signes , shee hath distributed the Coniunctions of the three superiour Planets : especially the coniunctions of Saturne and Iupiter , which the Astrologians call great coniunctions . For examples sake , if there bee a great coniunction in Aries , the same shall be twenty yeares after in Sagitarie , and other twenty yeares after in Leo ; and after as many more yeares , it returneth againe into Aries . The reuolution of one Trigon contayneth almost 200. yeares , after which time the same great conjunctions remoue into the next trigon . CHAP. IX . The vse of the Zodiack . 1. THe Zodiack is the measure of the second motions , as the Equinoctiall is the measure of the first motion . 2. For in this Circle wee reckon the longitudes , and from it we count the latitudes of all the Starres . For the longitude of a Starre is nothing else but the arch of the Ecliptck conteyned betweene the beginning of Aries , and the circle of the Starres latitude . And the latitude is the Arch of a great circle , drawne by the poles of the Ecliptick , conteyned betweene the Starre and the Ecliptick . 3. According to this circle , the whole Heauen , yea , the whole world is deuided into twelue Signes . Whereof it commeth that because of this Circle , aswell the fixed , as the wandring Starres which we call Planets , yea , and those Starres also that appeare of a sudden , as blazing Starres or Comets , and other Meteors , are said to be in this or that signe ; and that three manner of wayes . First , to be in a signe , is to be vnder some one of the 12. parts of the Ecliptick . Thus the Starres which are vnder the Ecliptick , but especially the Sunne which runneth alwayes vnder it , are said to be in the Signes . Secondly , because the Zodiack hath latitude , those Starres are said to be in a signe , which although they be beside the Ecliptick , yet are vnder the Zodiack , and so any of the other Planets , which for the most part wander beside the Ecliptick , may be said to bee in some signe . Thirdly , if we vnderstand six great Circles to bee drawne by the beginnings of the twelue signes , and by the poles of the Eclipticke ; by these circles the whole heauen ( or rather the whole world ) is deuided into twelue parts , which with a generall name are called signes : Thus all the Starres aswell fixed as Planets and Comets , which are without the Zodiacke in any of these parts , may be said to be in some signe . 4. In this circle are noted the degrees of the signes , with which the Starres doe rise and set , as well in a right as in an oblique Sphaere . For because this circle is the chiefest , all Caelestiall apparances ( or at least the most part of them ) are referred vnto it , and not vnto the Equinoctiall . But the Equinoctiall measureth the times of their risings and settings . 5. The obliquitie of the Ecliptick is the cause of the inequalitie , aswell of naturall dayes in both Sphaeres , as of artificiall dayes in an oblique Sphaere . For seeing it is moued vnequally , because it is moued vpon other Poles then his owne , the Sunne which is the author , and maker of times mouing vnder it , must needs make vnequall dayes . 6. The chiefe times are defined by this circle , as the time of a yeare , by the motion of the Sunne ; the time of a moneth by the motion of the Moone , through the whole compasse of this circle . Also the foure quarters of the yeare , Spring , Summer , Autumne , and Winter , whereto may be added Plato his great yeare , which is the time wherein the fixed Starres make one reuolution about the axtree and poles of the Zodiack , if God would haue the world to last so long . 7. The Eclipticke line sheweth the places , and times of the Eclipses : For the Sunne and Moone , are Eclipsed onely vnder it , or neere vnto it . 8. As the description of the Tropicks dependeth on the obliquitie of the Eclipticke , so the polar Circles are described by the Poles thereof . 9. Hereof it commeth , that by reason of the same obliquitie , the Zones and Climats are set forth and bounded . 10. This Circle is of especiall vse in Astrologie , for it distinguisheth the points of the 12. Houses , and in it the Aspects and configurations of the Planets are obserued . The chiefest judgement aswell in casting Figures as in reuolutions and directions is taken from this circle . CHAP. X. The description of the two Colures . THe two circles crossing each other at right Angles in the poles of the Sphaere , are called the Colures : whereof the one that passeth by the common meeting of the Eclipticke and Equinoctiall , is called Colurus aequinoctiorum , that is the Equinoctiall Colure , or the colure of equall dayes and nights . The other passing by the poles of the Eclipticke , and the Solstitiall points , is called Colurus solstitiorum , the Solstitiall colure , or colure of the Sunne-standings . Vses common to both Colures . 1. By meanes of these two Colures , all the mouable circles of the materiall Sphaere are framed together , that so they might be turned about , like as the whole Heauens are moued . 2. The Poles are fastened in the common meeting of these two Circles : and the Poles are also shewed by the same common meetings . 3. They shew the foure principall points of the Eclipticke ; that is , the two Equinoctiall , and the two Solstitiall points . 4. These circles shew those points of the Eclipticke , wherein the Sunne is either equally distant from both poles of the Sphaere , or commeth neerest to either of them : In which points the Sunne maketh the dayes longest or shortest , or of a meane length betweene both these in an oblique Sphaere . 5. They deuide the Ecliptick into foure quarters , in which the Sunne maketh foure quarters of the yeare , the Spring , the Summer , Autumne , and Winter . 6. They deuide the Ecliptick and Equinoctiall into such foure quarters , as in a right Sphaere doe rise together in equall time . CHAP. XI . Vses of the Equinoctiall Colure . 1. THe section of this Circle with the Ecliptick ; sheweth the Equinoctiall points , wherein the Equinoctiall and the Eclipticke doe deuide and crosse each other . In which points the Sunne maketh equality of dayes and nights throughout the whole world : whereof this circle is also called Colurus Aequinoctiorum ; that is , the colure of equall dayes and nights , or the Equinoctiall colure . 2. It deuideth the Eclipticke into the North and South halfes . 3. It deuideth the Signes wherein the Sunne maketh the dayes longer then the nights , from those signes wherein the dayes are made shorter then the nights . 4. It sheweth which halfes of the Eclipticke and Equator , doe arise together in equall time in an oblique Sphaere . 5. It sheweth the two high Sunne-standings in a right Sphaere , in the time of which Sunne-standings , the Sunne passeth by the Zenith . CHAP. XII . Vses of the Solstitiall Colure . 1. THe common meetings of this circle with the Ecliptick , shew the Solstitiall or Tropicall points ; in which points the Sunne seemeth to stand , and then returneth backe againe : for which cause this circle is called the Colure of the Sun-standings . These points are called tropicall ( which is as much to say as turne-points , or points of returne ) because that when the Sunne going alwayes vnder the Eclipticke commeth to these points , which are furthest distant from the Equinoctiall circle , it returneth againe towards the same circle . But they were called Solstitiall or Sun-ding points , because that whilest the Sunne is about those points , the difference of the Sunnes returning is ( for certaine dayes ) insensible . Hereof the Sunne is said to make his station , or to stand , when he commeth to either of those points . They that dwell without the Tropickes , haue two sunne-standings , that is the Summer sun-standing , or high sun-standing ( when the Sunne in Summer time is at the highest , and next vnto our Zenith being in the beginning of Cancer ) and the winterly , or low sun-standing , when the Sunne in Winter time is lowest in the Meridian , and furthest from our Zenith . But they that dwell within the Tropicks ( by a certaine similitude taken from our sun-standings , wherein the Sunne is either highest or lowest ) are said to haue foure sun-standings ; that is two high sun-standings , when the Sunne passeth by their Zenith ( the highest point in the Heauens ) which hapneth twice euery yeare in two places , equally distant from the beginnings of Cancer and Capricorne : and two low sun-standings , when the Sunne is in the beginning of Cancer and Capricorne . 2. In this Circle by the arch conteyned betweene the Equator and Eclipticke , we measure the greatest declination of the Sunne , or obliquity of the Eclipticke , which in Ptolomees time was 23. degrees 51. minutes , and one third part of a minute . But euer since that time it hath beene found by obseruation to decrease ; so as in this our age , it is no more then 23. degrees and one halfe , or little more : Notwithstanding Copernicus thought that the greatest obliquity was 23. degrees 28. minutes . 3. It sheweth the places of the Eclipticke , in which the Sunne ( comming neerest to our Zenith ) maketh the artificiall day longest ; or going furthest from the same point , maketh the same shortest . 4. It deuideth the Zodiacke into two halfes , the one ascending , and the other descending . 5. Hereby also the signes are distinguished , which doe rise rightly , and which rise obliquely in an oblique Sphaere . For the descending halfe riseth rightly , and the ascending halfe riseth obliquely . 6. So the points of the Eclipticke are shewed by this Circle , wherein the greatest difference of right and oblique ascensions happeneth . It distinguisheth those signes in which when the Sunne moueth , the artificiall dayes are increased , and the nights decrease ; from those signes wherein the dayes are diminished , and the nights increase . 7. In this circle are the bredths of the Zones bounded ; for the obliquity of the Eclipticke doubled , sheweth the bredth of the torrid or burnt Zone : the distance of the poles of the Ecliptick , and of the Poles of the Equator , shew the bredth of the cold or frozen Zones ; and the other two Arches remaining , shew the bredths of the temperate Zones . CHAP. XIII The Description of the two Tropickes . THe two smaller Circles Equidistant in all places from the Equinoctiall , and comming vnder these Solstitiall points of the Eclipticke on both sides , are called the Tropicks , that is circles of returne . And they are so called , because that when the Sun commeth to them , it beginneth to returne backe againe towards the Equinoctiall circle . Or else they may be so called , because they are described by the turning about of the Tropicall points of Cancer and Capricorne . They are also called solstitiall Circles ; that is Circles of the sun-standings ; because that by reason of the insensible alteration of the declination of the Ecliptick , for some space both before , and after the Tropicall points , the Sunne ( in respect of his Meridian altitudes , or in respect of the motion he hath towards the North or South , by reason of the obliquity of the Eclipticke ) seemeth to stand ( as it were ) for certaine dayes in those places . There be two Tropicks , the Tropick of Cancer , and the tropicke of Capricorne . The tropick of Cancer , toucheth the Ecliptick in the beginning of Cancer , which is the most northerly point of the Ecliptick : or it is the Tropick described in the first mouable Sphaere , by the Summer solstitiall point . This circle is called the Tropick of Cancer , because it toucheth the Ecliptick in the beginning of Cancer . It is also called the Summer Tropick , and the Tropick of the Summer sun-standing , because that when the Sunne commeth to it , the Summer beginneth . It is called the North tropick , because it is in the North part of the world : and the Circle of the high sunne-standing , because the Sunne comming to it , is highest in the Meridian , and next vnto our Zenith which dwell in the North part of the world , without the Tropicks . The Tropick of Capricorne is the Tropick which toucheth the Ecliptick in the first point of Capricorne . It is called the Tropick of Capricorne , because it toucheth the Ecliptick in the beginning of Capricorne . It is called the winter Tropicke and Tropick of the Winter sun-standing , because the Sunne commeth to it in Winter . It is also called the circle of the lowest Sunne-standing , because that when the Sunne commeth to this Tropicke , it is furthest distant from our Zenith , and hath his lowest height in the Meridian . CHAP. XIIII . Vses of the Tropickes . 1. THe Tropicks shew the Tropicall , or Solstitiall points of the Eclipticke : that is , the points wherein the Sunne seemeth to stand , and beginneth to returne backe againe . 2. They bound out the greatest declinations of the Sunne , which in our times is about 23. degrees and an halfe . 3. Therefore they doe also bound out the obliquity of the Ecliptick , for they are the bounds of the Sunnes way , beyond which the Sunne goeth not at any time . 4. The Sunne comming to either of these circles , is either neerest , or furthest distant from our verticall point . 5. In an oblique Sphaere , they measure out the shortest , and longest artificiall day and night . 6. The Tropicks ( aswell in Heauen as in Earth , conteyne betwixt them the Torrid Zone , and separate it from the temperate . CHAP. XV. The Polar Circles . THe two smallest circles that are next about the poles of the Sphaere , are called the polar circles . They are drawne by the poles of the Eclipticke , and are euery where Equidistant from the Equinoctiall , and from the poles of the Sphaere . They are called polar Circles , either because they are neere the poles of the Sphaere , or else because they are described by the motion of the poles of the Eclipticke . And therefore there be two polar Circles , that is , so many as there are poles of the Ecliptick : the Polar circle Artick , and the Polar Antartick . The Articke polar circle , is that which passeth by the North pole of the Ecliptick , or which is described by the North pole of the Ecliptick being carried about with the motion of the first moueable Sphaere . The Antartick polar circle , is that which goeth by the South pole of the Eclipticke , being described with the first motion by the Antartick pole of the Ecliptick . The distance of these polar Circles from the poles of the Sphaere , is equall to the distance of the tropicks from the Equinoctiall , which in our time is about 23. degr . and an halfe : for so much as is the obliquity of the Zodiack ( whereto the distance of the Tropicks from the Equinoctiall is alwayes equall ) so much are the poles of the Ecliptick distant from the Poles of the world . CHAP. XVI . Vses of the Polar Circles . 1. THe Polar Circles shew the poles of the Zodiack , and shew their distance from the poles of the Equinoctiall . 2. The temperate Zones are bounded by these polar circles ; for the Articke circle boundeth the North side of the North temperate Zone ; and the Antartick circle boundeth out the South side of the South temperate Zone . 3. The Polar circles separate the temperate Zones , from the cold Zones which they compasse round about , and inclose within them . Therefore the foure lesser circles , that is the two Polar circles , and the Tropicks , deuide Heauen and Earth , into fiue Zones . CHAP. XVII . Of the Zones . A Zone is a space of Heauen , or Earth , conteyned betweene two of the smaller Circles ; or inclosed within the compasse of either Polar circle . They are called Zones ( that is as much to say as girdles ) because they compasse about Heauen or Earth like a girdle . The Zones are deuided by auncient Writers into two kindes ; that is into temperate , and vntemperate Zones . A temperate Zone is the space of Heauen or earth , conteyned betweene either of the Tropicks , and the next Polar circle . There be two temperate Zones ; the one North , the other South . The North temperate Zone is conteyned betweene the Tropicke of Cancer , and the Artick polar circle . The South temperate Zone is that which is conteyned betweene the Tropicke of Capricorne , and the Antartick polar circle . They are called temperate Zones , because they haue a better temperature of the ayre for the most part , and more meer for habitation , then the vntemperate Zones . The bredth of eyther temperate Zone is alwayes equall to the complement of the distance of the Tropicks , and therefore in this age is about 43. degrees , that is 2580. English miles . There be two kinde of vntemperate Zones , the one exceeding in heat , the other in cold , for the most part . The hot vntemperate Zone , ( called also the Torrid ; that is , the burnt or broyled zone ) is that space of Heauen or Earth , which is conteyned betweene the tropicks . It is called the burnt Zone , because that by reason of the Sunnes continuall going ouer that zone ; and casting his beames directly downe thereupon , it is scorched with ouer-much heat , and is not so meet to be inhabited as the temperate zones . The bredth of this Zone is alwayes equall to the obliquitie of the Zodiack , or greatest declination of the Sunne , doubled ; which in our time is about 47. degrees , that is 2820. English miles . The cold or frozen zones , are the spaces of Heauen or earth , conteyned within the Polar circles . There be two cold zones , the one North , conteyned within the compasse of the Articke circle : the other South , conteyned within the compasse of the Antartick Polar circle . These zones exceed in cold , because they want the sight of the sunne for a great part of the yeare , and when the Sunne appeareth vnto them , his beames fall so obliquely vpon them , that they can ( in all likelyhood ) receiue but small heat thereby for the most part . The bredth of these Zones is measured from the Poles of the world to the Polar circles , and therefore must alwayes bee so much as the Polar circles are distant from the Poles : that is , in our age about 23. Degrees and a halfe , which make 1410. English miles . CHAP. XVIII . The difference of Shadowes that the Sunne maketh in these Zones . THey that dwell in the torride Zone , doe cast their shadowes which the Sunne maketh at noone ( which we may therefore call their noone shadowes ) both towards the North , and towards the South : towards the North , when the sunne is betwixt their zenith and the south point of the Horizon ; and towards the South , where the sunne is betweene their Zenith and the North. For seeing the zenith of them that dwell in that Zone is betweene the Tropicks , the sunne must needs bee sometimes Northwards from their zenith , and so make a south shadow : and sometime Southwards , and then make a north shadow . For which cause they that inhabite this Zone are called Amphiscij ; that is , such as cast their noone shadowes on both sides . But they that dwell in the temperate Zones , are called Heteroscij ; that is , such as cast their shadowes at noone , one way onely . For they that dwell in the North temperate Zone , haue the Sunne alwayes at noone from their Zenith Southwards , and therefore must needs alwayes cast their noone shadowes Northwards . Whereas contrariwise they that inhabit the South temperate Zone , hauing the Sunne at noone alwayes Northwards from their Zenith , must needs haue their shadowes at noone , alwayes towards the South . And they that are in the cold Zones , are called Periscij ; that is , such as cast their shadowes round about them . For seeing the Sunne continueth euery yeare for certaine dayes together , alwayes aboue their Horizon , and therefore moueth round about them without setting : it must needs bee , that their shadowes also are carried round about them , falling towards all parts of the world in the space of 24. houres . * ⁎ * THE SECOND PART . Of the vses of the vppermost SPHAERE , and of the Circles thereof joyntly . PROP. I. To rectifie the Sphaere to the Latitude . &c. FIrst finde by obseruation , or otherwise the height of the Pole , or Latitude of that place for which you would rectifie the Sphaere . Then ( by turning about the Meridian of the Sphaere ; lift vp or put downe the North Pole of the Sphaere ( about which the houre circle is fastened ) till the arch of the Meridian from the North part of the Horizon vpwards vnto the Pole , be iust so many degrees as the eleuation of the Pole or latitude of the place was found to be : for so haue you the Sphaere duly rectified . As for example , the Latitude of the Citie of London is 51. degrees and 32. minutes , therefore if you lift vp the North Pole of the Sphaere , aboue the North part of the Horizon , so many degrees and minutes you shall haue your Sphaere rectified for that place . PROP. II. To know the place of the Sunne ; &c. LOoke the day of the moneth ( for which you desire to know the place of the Sunne ) in the Horizon , and see what signe and degree of the Zodiacke vpon the Horizon answereth thereto ; for there haue you the place of the Sunne . Take for example the 25. of December : looke this day therefore in the Horizon , and you shall finde answerable thereto 13. degrees , and about 40. minutes of Capricorne , which is the place of the Sunne at that time . PROP. III. To know the declination of the Sunne , &c. BRing the point whose declination you desire to know , vnto the Meridian of the Sphaere , and look what number of degrees and minutes of the Meridian is conteyned betweene that point , and the Equinoctiall , for so much is the declination . As if you would know the declination of the 10. degree of Taurus , bring that degree to the Meridian , and you shall finde the arch of the Meridian between that degree and the Equinoctiall , to be 14. degrees and about 51. minutes . PROP. IIII. To know the right ascention of the Sunne , &c. BRing that point ( as before ) to the Meridian , and see then how many degrees and minutes of the Equinoctiall are conteyned betweene the beginning of Aries and the Meridian : for that is the right ascension of that point . So you shall finde the right ascension of the 10. degr . of Taurus to be 37. degr . 35. min. for if you bring that degree of Taurus to the Meridian , you shall finde so many degrees and min. between the beginning of Aries , and the Meridian . PROP. V. To know the oblique ascension of the Sunne , &c. SEt the Sphaere to the eleuation of the place for which you desire to know the oblique ascension ; then bring the Sunne , Starre , or point whose oblique ascention you would know , vnto the East semicircle of the Horizon , and looke how many degrees and minutes of the Equinoctiall circle , are conteyned between the East point of the Horizon , and the beginning of Aries ; for so much is the oblique ascension desired : As for example , if you see the Sphaere to the Latitude of London 51. degr . 32. min. and then bring the 10. degree of Taurus to the East part of the Horizon , you shall finde about 19. degrees and an halfe of the Equinoctiall , at the same East part of the Horizon ; which is the oblique ascension of that degree of Taurus , for the Latitude of the Citie of London . PROP. VI. To finde the difference of Ascension . COmpare the right and oblique ascensions of the Sunne , ( or of any point of the Zodiacke ) together , and subtract the lesse from the greater , for the remainder shall bee the difference of ascension . As for example , the right ascension of the 10. degree of Taurus , being found by the 4. Propo. to be 37. degrees , 35. min. and the oblique ascention of the same degree at London , by the 5. Prop. 19. degree 30. min. by subtraction of the lesse out of the greater , the difference shall be found to be 18. degr . and 5. minutes , which is the difference of ascension sought for . PROP. VII . To finde at what time the Sunne riseth or setteth . REduce the difference of Ascention into houres and minutes ( taking for euery 15 degrees 1. houre , and for euery one degree that remayneth 4. minutes , and for euery minute of a degree 4 seconds ) for these houres , minutes and seconds , being added to 6. houres , if the Sunne bee in any of the South signes ; or subtracted , if hee be in the North signes , sheweth the time of the Sun-rising . And contrariwise , the same houres and minutes subtracted from sixe houres when the Sunne is in the South signes , or added when he is in the North signes , sheweth the the time of the Sunne-setting . As for example , the Sunne being in the 10. degree of Taurus which happeneth about the 20. or 21. day of Aprill ) I would know at what houre and minute the Sunne riseth , and setteth at London : Hauing therefore found by the former Proposition the difference of ascention to be 18. degr . and 5. minutes I take for 15. degrees thereof one houre , and for the three degr . remaining , 12. minutes of an houre , and for the 5. minutes , 20. seconds of an houre . Which houre , minutes and seconds being subtracted out of 6. houres , because the Sunne is in a North signe , there remaineth the time of the Sunnes rising at 4. a clocke 47. minutes , 40. seconds . And adding the same houre , min. and seconds to 6. houres , you haue the time of the Sun-setting that day at 7. a clocke , 12. min. and 20. seconds . PROP. VIII . To finde the length of the artificiall day or night . THe artificiall day , is the time conteyned between the Sun-rising and the Sun-setting : and the artificiall night is the time betweene Sunne-setting and Sun-rising . The length of both these is found after this manner : hauing found the difference of ascension , and reduced it into houres and minutes ( as in the former Proposition ) double th●se houres and minutes , and adde them to 12. houres if the Sunne be in the North signes , or subtract them from 12. houres if the Sunne be in the South signes , for so shall you haue the length of the day : But ( contrariwise ) subtract the same houres and minutes ( being doubled ) from 12. houres , the Sunne being in the North signes ; and adde them to 12. houres when he is in the South-signes ; so haue you the length of the night . Or else , double the time of the Sun-setting , so haue you the length of the day . And double the time of the Sun-rising , so haue you the length of the right . As the time of the Sun-rising being found by the former Proposition to be 4 houres 48. minutes after mignight at London , the Sunne being in the 10. degr . of Taurus , by doubling the time of the Sun-rising , the length of the night shall be found to be 9. houres and 36. minutes . And doubling the time of the sun-setting that is 7. houres , and 12. minutes , you haue the length of the day , 14. houres ; and 24. minutes . PROP. IX . To know the time of the Sun rising and Sun setting . THe place of the Sunne being found by the 2. Proposition , bring the same to the Meridian , and withall set the point of the Index of the houre circle , to the 12. houre in the same circle : Then bring the place of the Sunne to the Horizon Eastwards ; and the point of the houre Index shall shew you in the houre circle , the time of the Sun-rising . But if you bring the place of the Sunne to the Horizon Westwards , the point of the Index will shew in the houre circle the time of the Sun-setting . As for example , the Sunne being in the 10. degree of Taurus , bring the same degree to the Meridian , and bring the point of the houre Index also to the Meridian : then ( the Sphaere being set to the Latitude of London ) bring the same 10. degree of Taurus to the East part of the Horizon , for then the houre Index will shew you in the houre circle , that the Sunne riseth at 4. of the clocke and 48. minutes . And bringing the same degree to the West semicircle of the Horizon , the same Index will shew the time of the Sun-setting to be 7. houres and 12. min. after noone . PROP. X. To finde the length of the artificiall day or night . BRing the place of the Sun ( being found as before to the East semicircle of the Horizon : set the houre Index 12. a clocke in the Houre circle : turne about the Sphaere from the East Westwards , till the place of the sunne come to the Horizon , and marke how many houres the Index hath runne ouer vpon the Houre circle in the meane time , for so much is the length of the day . And to finde the length of the night : Bring the place of the sunne to the West semicircle of the Horizon , and set the Index to 12. a clocke as before ; Then turning forwards the Sphaere from East Westward till the place of the sunne come to the East semicircle of the Horizon ; see how many houres the Index passeth ouer in the Houre-circle , for so many houres long is the night . As for example ; supposing the Sunne to be as before in the 10. degree of Taurus , bring the same degree to the East part of the Horizon , and the point of the Index to the Meridian : then turning about the Sphaere , till the same degree come to the West part of the Horizon ; you shall finde that in the meane time , the point of the Index shal passe ouer 14. houres and 24. minutes , which is the length of the day . Likewise , if you bring the same 10. degr . of Taurus to the West part of the Horizon , and the Index to the Meridian , and turne about the Sphaere , till that degree come to the East semicircle of the Horizon , the number of houres that the Index runneth ouer in the meane time vpon the Houre circle , shall be found to bee 9. Degrees , and 36. Minutes . PROP. XI . To know the Meridian altitude , or the height of the Sunne at noone , for any time and place . SEt the Sphaere to the latitude of the place where you d●sire to know the Sunnes height at noone : bring the place of the Sunne ( being found as before by the 2. Prop. ) to the Meridian , then see how many degrees of the Meridian , are contayned betweene the Horizon , and the place of the sunne , for so much is the height of the Sunne at noone . In like sort it may be knowne how much the Sunne is vnder the Horizon at midnight , after this manner : Bring the place of the sunne in the Zodiacke to the Meridian vnder the Horizon , and see how many degrees of the Meridian , are contayned betweene the vpper-side of the Horizon , and the place of the Sunne downewards : and so shall you haue that you sought for . Or else if you cannot well come to the Meridian vnder the Horizon : bring that point of the Eclipticke which is opposite to the place of the sunne , vnto the Meridian aboue the Horizon ; for the arch of the Meridian , or the number of degrees and minutes of the Meridian , betweene that point and the Horizon sheweth how much the sunne is vnder the Horizon at midnight . After this manner ▪ the Sunne being in the 10. degr . of Taurus , you shall find that his Meridian altitude at London is 53. degrees , and about one halfe . As also that hee is vnder the Horizon at midnight about 23. degrees and a halfe at London . PROP. XII . To know how high the Sunne is aboue the Horizon at any time of the day . BRing the place of the Sun ( found by the 2. Prop. ) to the Meridian : set the houre Index to 12. a clock vpon the houre circle : turne the Sphaere about till the Index come to the houre at which you desire to know the height of the Sunne aboue the Horizon ; take the distance of the place of the Sunne from the Horizon with a large payre of Compasses : then set both feet of the Compasses in the Ecliptick , and looke how many degrees are conteyned betweene them , for so much is the height of the Sunne . Thus may you finde by the Sphaere , that when the Sunne is in the tenth degree of Taurus , his height at 10. of the clocke in the fore-noone ( the Sphaere being duly rectified by the first Proposition ) shall be about 45. degrees and an halfe at London . PROP. XIII . To finde the houre of the day by the height of the Sunne ; &c. SEt the pole Artick of the Sphaere to his eleuation for that place where you desire to know the houre of the day : bring the place of the Sunne in the Zodiack to the Meridian , and the houre Index to 12. a clocke of the houre circle : take so many degrees of the Ecliptick betweene the feet of your Compasses , as the height of the Sunne amounteth vnto . Then set one foot of your Compasses in the place of the Sunne , and turne the Sphaere about , Eastwards , if it be in the fore-noone , or West-wards , if in the after-noone , till you can but onely touch the Horizon with the other foot of your Compasses ; for then the Index pointeth out the houre of the day in the Houre circle . As suppose you obserue the height of the Sun being in the 10. degr . of Taurus , and find him to bee 30. degrees high in the fore-noone : you shall find ( following the directions prescribed in this Proposition ) that it shall then be about 8. of the clocke in the morning . PROP. XIIII . To finde the Amplitude or bredth of the Sunnes rising , or setting , &c. THe pole of the Sphaere being set to his eleuation , and the place of the Sunne to the East semicircle of the Horizon : see how many degrees of the Horizon , are contayned betweene the place of the Sunne , and the true East point , for so you shall haue the bredth of the sunnes rising . Thus the sunne being in the 10. degree of Taurus , you shall find by the Sphaere , that ( for the latitude of London ) hee riseth about 23. degr . and a halfe Northwards , from the true East point , and that hee setteth as many degrees towards the North , from the true West point . PROP. XV. To finde the place of the Sunne , &c. THe quarter of the yeare being knowne , bring the quarter of the Eclipticke that is answerable thereto , vnder the Meridian ; and turne the Sphaere to or fro , till there bee so many degrees and minutes of the Meridian , conteyned betweene the Ecliptick and the Equator , as the declination commeth to : then looke what degree of the Ecliptick is vnder the Meridian , for that is the place of the Sunne . As suppose the declination of the Sun in some day of the Spring-time of the yeare be found to bee 14. degr . 51. min. ( turning therefore the Sphaere to and fro , till some part of the spring quarter of the Ecliptick , come right vnder that degree and minute of declination in the Meridian ) you may finde that the Sunne is then in the tenth degree of Taurus . PROP. XVI . To finde what day of the moneth it is , &c. THe place of the Sunne being found by his declination ( as is already shewed ) seeke the place of the Sunne in the Horizon of the Sphaere , and looke what day is answerable thereto , for that is the day of the moneth which was sought for . As the place of the Sunne being found by his declination ( as is shewed in the former Proposition ) to be in the 10. degree of Taurus , the day of the moneth shall thus be found to be the 21. of Aprill . PROP. XVII . The day of the moneth being knowne , to finde at what time the day breaketh . FInde the place of the Sunne ( by the 2. Prop. ) and bring it to the Meridian , then bring the houre Index , to 12. a clocke vpon the houre circle . Finde out also the point of the Eclipticke that is right ouer against the place of the Sunne : then take betweene the feet of your Compasses 17. degrees of the Eclipticke , and setting one foot of the Compasses in the point opposite to the place of the Sunne , turne the Sphaere Westwards , till you can but onely touch the Horizon with the other foot , for then the Index sheweth in the houre circle at what time the day breaketh . So the 21. of Aprill , the Sun being in the 10 degr . of Taurus , you shall finde that the day breaketh about halfe an houre past 2. of the clocke in the morning . PROP. XVIII . To finde how long the twylight continueth . FInde out by the former Prop. at what time the day breaketh , and learne also at what time the Sunne riseth by the 7. or 9. Prop. Then subtract the lesser from the greater , and there shall remayne the length of the twylight . Or else thus : hauing brought the point that is opposite to the place of the Sunne to be 17. degrees aboue the Horizon West-wards , in such sort as is shewed in the former Proposition ; and keeping the Sphaere in that position , bring about the point of the houre Index vnto 12. a clocke vpon the houre circle ; then tune the Sphaere Westwards vntill the degree or point of the Eclipticke that is opposite to the place of the sunne come to the Horizon : and see how many houres the point of the Index hath runne ouer in the meane time vpon the houre circle : for so many houres continueth the twylight . By eyther of these wayes , the Sunne being in the 10. degr . of Taurus , you shall finde that the twylight ( that is the time from the breake of the day till Sun-rise ) is about 2. houres and 20. minutes . PROP. XIX . To finde how much the declination of the Sunne must alter at any time of the yeare , to make the day an houre longer or shorter . BRing the place of the Sunne ( found by the second Prop. ) to the East semicircle of the Horizon , and marke what degree or point of the Horizon it falleth vpon ; bring one of the Colures to the same degree or point , and there make a pricke in that colure ; and holding the Sphaere immoueable , ) marke withall what degree of the Equinoctiall , or of eyther of the Tropickes is then at the Horizon : Then turne the Sphaere 7. degrees and an halfe forwards , towards the West , if the dayes shorten : but contrariwise if the dayes lengthen ; and holding the sphaere there immoueable , make another prick in the colure at the Horizon : for the distance of these two prickes in the colure taken with the Compasses and brought to the Ecliptick , or Equinoctiall , sheweth how much the Sunnes declination must alter to make the day an houre longer , if the dayes increase ; or shorter , if they decrease . After this manner you shall finde that the sunne being in the 10. degree of Taurus , his declination must increase about 5. degrees , ( or little more ) to make the day an houre longer ; but when the sunne is in the 20. degree of Pisces , his declination , or rather his Meridian altitude , must increase about 6. degrees to make the day an houre longer : and when hee is in the beginning of Capricorne , his declination decreaseth scarce 5. degrees to make the day an houre longer . PROP. XX. To find how many dayes it is ere the day lengthen or shorten an houre . BRing the foresaid prickes ( made in the Colure by the former Proposition ) vnto the Meridian , and there make two markes iustly answerable vnto those prickes in the Colure : turne about the Sphaere till the Eclipticke line come iust vnder one of those markes , and there make a pricke in the Eclipticke : then againe turne the Sphaere till the Ecliptick come iust vnder the other marke made in the Meridian , and there make another pricke in the Eclipticke : ( But here it is to bee noted , that whereas the Eclipticke may be brought vnder that marke whether way soeuer you turne the Sphaere , it must ( I say be noted that the Sphaere must be turned that way which may soonest bring the Eclipticke vnder that marke . ( Lastly , finde out amongst the signes and degrees described vpon the Horizon , the like arch to this , that is contayned betweene these prickes in the Eclipticke : For the number of dayes answerable to this arch in the Horizon , is the time wherein the day groweth an houre longer or shorter . Thus shall you finde , that when the Sunne is in the beginning of Aries , it will bee about 18. dayes after , ere the day be one houre longer . But when the Sun is in the beginning of Capricorne , you shall finde that it will be almost twice so much , that is neare 34. dayes before the day will be an houre longer . Hereby therefore the error of them manifestly appeareth , which thinke that in euery 15. dayes , the day is lengthened or shortened an houre , whereas indeed the lengthning or shortning of the dayes , keepeth no such rule . For when the Sunne is about the Equinoctiall points , the dayes lenghthen or shorten very fast : but when he is neere the Tropicall points , they grow longer or shorter very slowly . PROP. XXI . To make an Horizontall Diall . SEt the Sphaere to the eleuation of the place for which you would make the Diall turne about the Sphaere , till the solstitiall Colure be 15. degrees ( measured in the Equinoctiall ) from the Meridian ; and where the Colure crosseth the Horizon , there make a prick ; then turne the Colure yet 15. degr . further , that is 30. degrees from the Meridian ; and where the Colure crosseth the Horizon , there make an other prick : againe turne the Colure forwards yet 15. deg . more , ( that is 45. degrees from the Meridian ) and at the common meeting of the Colure and Horizon , make the third prick in the Horizon ; and so proceed with the rest , till you haue made so many pricks on that side of the Horizon as there are houres in halse the longest day . Then looke how many degrees the first , second , third , fourth pricks , &c. are from the Meridian , for so many degrees must the houre lines of 11. a clocke , and one a clocke ; of 10. and 2 , of 9. and 3. of 8. and 4. &c. be from the 12. a clock line in the Horizontall Dyall . After this manner in an Horizontall Diall made for the Latitude of London , ( which is 51. degr . and 32. minutes ( you shall finde the distances of all the rest of the Houre-lines from the 12. a clocke line as followeth : Betwixt twelue and 11. and twelue and 1. are conceyned 12. degrees almost : Betweene 12. and 10. and 12. and 2. there are conteyned 14. degr . and an halfe : Betweene 12. and 9. and 12. and 3. 38. degr . Betweene 12. and 8. and 12. and 4. 53. degr . Betweene 12. and 7. and 12. and 5. 70. degrees and an halfe . Betweene 12. and 6. both before and after noone , 90. degr . The other houre spaces before 6. in the morning ; and after 6. in the euening , are equall to the Houre spaces after sixe in the morning , and before 6. in the afternoone . PROP. XXII . How to make a direct mural Diall . SEt the Pole artick of the Sphaere so much vnder the Horizon as is the complement of the Poles eleuation : the Horizon therefore being thus set as it were to the Zenith of the Sphaere , and so representing the verticall Circle of East and West ( that is the plaine super fices of a direct mural Diall ) you shall finde the distances of all the houre-lines , ( both before and after noone ) from the 12. a clock line , in such sort as you did before for the Horizontall Dial. So you shall finde the distances of the houre-lines in an erect direct murall Dial made for the Latitude of London to bee as followeth : Betweene the twelue a clock line and the lines of 11. and 1. 9 , degr . and about one third part of a degree : Betweene 12. and 10. and 12. and 2. 19. degrees and one quarter ; Betweene 12. and 9. and 12. and 3. 32. degr . or little more : betweene 12. and 8. and 12. and 4. 48. degrees : betweene 12. and 7. and 12. and 5. 67. degr . or little more : betweene 12. and 6. both before and afternoone 90. degrees . PROP. XXIII . How to make any direct inclining , or direct reclining Dial. REckon from the Equinoctiall vpwards in the Meridian , so many degrees as the height of the Pole commeth to at that place where you would make your Diall ; for there is the verticall point or Zenith of that place : from this Zenith reckon Southwards in the Meridian , the inclination of south Dials , and the reclination of North Dialls ; but contrarywise , reckon from the Zenith Northwards the inclination of North Dialls , and the reclination of South Dialls . Then bring that degree of the Meridian , where this reckoning endeth to the Horizon , for so the Horizon representeth vnto you the plaine or the flat superficies of the Diall which you would make . Therefore you shall finde how 〈…〉 euery one of the houre lines should be dist●●● from the 12. a clock line , in such sort as you did before in making the Horizontall Diall . Thus in a South direct Diall inclining 30. degr . or in a North direct reclining 30. degrees made for the Latitude or eleuation of the Pole at London , you may finde the distances of the eleuen a clock line , and of the one a clock line , from the 12. a clock line , to be about 14. degrees . But the houre lines of 10. in the forenoone , and of 2. in the afternoon , are distant from the 12. a clock line 28. degr . & one halfe ; From 12. to 9. and to 3. you shall find 43. deg . From 12. to 8. in the forenoone , and 4. in the afternoone , you shall haue 58. deg . & an halfe : also from 12. to 7. & to 5. shall be about 74. deg . And from 12. to 6. in the morning , & 6. afternoone 90. degrees . Likewise in a South direct reclining , or North direct inclining 20. deg . for the eleuation of London ; the spaces between 12. & 11. & 12. & 1. shall be about 5. deg . or little lesse : Between 12 , & 10. & 12 , & ● . about 10. deg . & ● . third parts . From 12 , to 9. in the forenoone , & 3. in the afternoon , 18. almost ▪ From 12. to 8. & 4. ●g . deg . or little more . From the 1● . a clock line ; to the line of 7. a clock in the forenoone , & 5. in the afternoone , 50. deg . or thereabouts . From 12. to 6. both before and afternooe ▪ 90. deg . as in the former kindes of D● . In all which it is to be noted , that there is alwaies 〈◊〉 distance betweene the houre lines of 5 , & ● . & 4 , & 6. that there is betweene 7 , & 6. and 8 , & 6. in the forenoone , and betweene 5 , & ● . & 4 , & ● . and 7 , & 6. & 8 , & 6. in the afternoone . So as the distances of all the houre lines from the 12. a clock line being found from 6. in the morning , till 6. at night , the distances of the other Houre-lines before 6. in the morning , and after 6. at night shall easily be had . PROP. XXIIII . To know at what time the Moone , or any other of the Planets or fixed Stars , that are within the bredth of the Zodiack ; rise or set , or come to the Meridian , &c. FInde the place of the Moone , or any other of the Planets , both in longitude and Latitude , by the Epheme●ides : and finde the place ( that is , the Longitude and Latitude ) of any of the fixed Star●es in the Zodiack by some table of the fixed Starres , or otherwise ; and marke the same place of the Moone ; Planet or Starre , in the Zodiack of the Sphaere : and hauing set the Sphaere to the Latitude of the place , bring the place of the Sunne ( found by the 2. Proposition ) to the Meridian , and the Houre-index to 12. a clock vpon the houre-circle● , then turne the Sphaere till the place of the Moone , Planet or Starre marked in the Zodiack , come to the East semi-circle of the Horizon ; for then the Index sheweth the time when the Moone , or that Planet or fixed Starre riseth . Al●● the number of degree in the Horizon , contayned betweene the point of the Moones , Planets , or Starres rising , and the point of true East , sheweth the bredth , ●●denesse , or amplitude of rising ; And you may at the same instant , 〈◊〉 , what degree of the Ecliptick riseth with any of them , and what the oblique ascension of any of them is : For if you tell hour many degrees of the Equinoctiall are 〈…〉 betweene the beginning of Aries in the Horizon , proceeding Eastwards , or according to the order of the signes : you shall haue the oblique ascension of the Moone , Planet or Starre , that 〈…〉 for . But bring the same place of the Moone , Planet , or Starre to the Meridian , and the Index sheweth in the houre circle at what time they come to the Meridian : where you may also see , first what degree of the Zodiath middeth Heauen ( that is , 〈◊〉 to the Meridian ) with any of them ; secondly , you may see how much the declination of any of them is ; for count how many degrees of the Meridian are contayned betweene the Equinoctiall and the place of the Moone , Planet , or fixed Starre , and so much is the declination . Thirdly , you may there see what the right ascension of any of them is : for the place of any of them being brought to the Meridian and there 〈◊〉 , r●ckon Eastwards how many degrees of the Equinoctiall are contayned betweene the beginning of Aries and the Meridian , so haue you the right ascension . Lastly , bring the place of the Moone , Planet or Star , to the West semi-circle of the Horizon ; for then the Index sheweth the time of their setting ; and the number of the degrees of the Horizon betweene the point where any of them setteth , and the Equinoctiall , or true West point ( where the Equinoctiall , and Horizon crosse each other ) is the amplitude or bredth of the setting of any of them , shewing how much they set from the true West point . You may there also see what degree ; either of the Ecliptick , or of the Equinoctiall , setteth with any of the● and consequently you may know the oblique descension of any of them , by reckoning how many degr . of the Equinoctiall there are from the beginning of Aries Eastwards , till you come about to the West part of the Horizon . Take for example the great Starre called the Bulls eye , whose place in longitude is about the 4. degr . of Taurus , and his latitude about 5. degrees and an halfe Southwards . Following therefore the directions prescribed in this Proposition , you shall finde that vpon the first day of Aprill this present yeare , 1600. the same Starre riseth here at London about halfe an houre past 7. of the clock in the morning , and setteth about a quarter of an houre past 10. at night , and commeth to the Meridian about 3. a clock afternoone : Also you shall finde that it riseth with the 15. degree of Gemini , and setteth with the last degr . of Taurus , and commeth to the Meridian , or middeth Heauen , with the 5. deg . of Gemini : Thirdly you shall finde his declination to be about 15. deg . and 2. third parts , his right ascension 63. degr . and a quarter , his oblique asce●sion 43. degr . and his oblique descension about 84. deg . and an halfe : and lastly his amplitude of bredth of rising or letting about 25. degr . and an halfe from the true East and West points towards the North. PROP. XXV . To know how long the Moone , or any of the Planets of fixed Stars doe shine or continue aboue the Horizon . THe Sphaere bring set up the latitude of the place , and the place of the Moone , Planet , or fixed Starre , being found and marked in the Zodiack , hoth in Longitude and Latitude , ( as in the 〈◊〉 Prop. ) bring the place of the Moone , Planet , or Star , 〈◊〉 East semi-circle of the Horizon , and the Index of houres to 12. a clock : Then 〈◊〉 about the Sphaere West-wards , till the same place of the Moone , or 〈◊〉 the same Planet , or Starre , come to the West semi-circle of the Horizon , and marke 〈◊〉 how many houres the Index runneth ouer in the meane time vpon the houre circle , for so many houres continueth the Moone , Planet , or Starre aboue the Horizon . Thus shall you finde that the foresaid 〈…〉 The Bulls eye 〈…〉 the Horizon at London , about 14. 〈…〉 and 3. quarters . PROP. XXVI . To finde which of the Planets or fixed Starres are aboue or vnder the Horizon at any time , &c. THe place of the Plantes or fixed Starres being marked in the Zodiack of the Sphaere , as in the former propositions , and the place of the Sunne brought to the Meridian , and then the Index to 12. 〈…〉 Sphaere 〈◊〉 the Index 〈◊〉 to that houre vpon the houre 〈◊〉 at which you desire to know what Planets are aboue or vnder the Horizon ; and then hold still the Sphaere , and marke what Planets or Starres are aboue or vnder the Horizon in the Sphaere for the same Planets or Starres are aboue or vnder the Horizon in the Heauens . As for example : the 1. of Aprill 1600 at 9. of the clocke at night , you may by the Proposition finde ; that the most part of the fixed Starres , that are in the constestation of Taurus , Gemini , Cancer , Leo , Virgo , and Libra , together with the three superiour Planets , 〈◊〉 , ●upiter , & Mars , are at 〈…〉 to be seene aboue the Horizon , and that the rest of the Planets and fixed Stars , that are within the compasse of the Zodiack , are vnder the Horizon , and cannot then be seene . PROP. XXVII . To finde in what time any Signe or part of the Ecliptick riseth or setteth . BRing the beginning of the Signe , or part of the Ecliptick to the East semi-circle of the Horizon , if you would know in how long time it riseth , or to the West part of the Horizon , if you would know in what time it setteth ; then set the Index to 12. a clock , and turne forwards the Sphaere , till the whole signe or part of the zodiack be risen , or set : For then the Index sheweth vpon the houre circle in how long time , that signe or part of the Zodiack riseth or setteth . Thus you may finde ( for example ) that the whole signe of Aries here at London riseth in one houre or somewhat lesse , and setteth in two houres and three quarters , or something more : And that the whole quarter of the Zodiack , from the beginning of Aries to the beginning of Cancer , riseth in lesse then foure houres , but setteth in more then 8. houres . PROP. XXVIII . To finde the houre of the night by any of the Planets or fixed Starres in the Zodiack , &c. THe place ( that is to say , the longitude & latitude ) of any Planet , or fixed Starre in the Zodiacke , that is aboue the Horizon , being first found , and marked in the Zodiack of the Sphaere ; bring the place of the Sunne ( found by the 2. Proposition ) to the Meridian , and the Index to 12. a clocke vpon the houre circle : Then hauing found the height of the Starre , or Planet by obseruation , and the Sphaere also being set to the Latitude of the place of obseruation , take betweene the feet of your Compasses , so many degrees of the Ecliptick , or Equinoctiall , as the height of the Planet , or Starre obserued , commeth to ; and setting one foote of your Compasses in the place of the Planet , or fixed Starre that you obserued in th Zodiack , turne the Sphaere forwards or backwards , till you can but onely touch the Horizon with the other foot : for then the Index in the houre circle , shall shew you the houre of the night . Suppose ( for example ) I should obserue the height of the foresaid Bulles eye , and should finde the same to be 29. degrees the first day of March at euening : finding therefore the place of that Starre in the Zodiack of the Sphaere , and bringing it ( with helpe of the Compasses ) to the height obserued ( hauing first set the place the Sunne and houre-Index both together to the Meridian ) the Index of the houres will shew , that when that Starre hath that height of 29. degrees , it is about 9. of the clock at night . PROP. XXIX . To know at any time of the yeare , what Stars in the Zodiack , arise or set , Cosmically , Achronically , or Heliacally . SVch Stars as rise together with the Sunne , are said to rise cosmically : and such Stars as set when the Sunne riseth , are said to set cosmically ; But those Stars which set together with the Sun , set achronycally ; and those Stars that rise when the Sunne setteth , are said to rise achronically . Lastly , those Starres that rise a little before the Sunne , rise heliacally ; and those that set a little after the Sunne , set heliacally . All which may thus bee found : Bring the place of the sunne to the East semicircle of the Horizon : for the Stars that are then a little aboue the Horizon rise heliacally ; but those that are in the Horizon in the East , rise cosmically ; and they that are in the West semicircle of the Horizon set cosmically : But bring the place of the Sunne to the West semicircle of the Horizon , for those Starres as are at the West part of the Horizon at the same time , set achronycally ; but those that are then in the East semicircle of the Horizon , rise achronycally : and they which are a little aboue the West semicircle of the Horizon set heliacally . Thus you may know that vpon the 26. or 27. day of May ( it our latitude of London ) the Bulles eye riseth cosmically , and the Starres in Serpentarius his right foot , set cosmically , you may see also that the same day the Starre in the Bulls South horne setteth achronycally : and the Northermost starre in Serpentarius his right foot , riseth achronycally : and lastly , you may finde that about the same time the Ple●ades and the Starre in the Bulls North home , rise heliacally , and that the same Starre also , and the former Twinnes feet set heliacally . PROP. XXX . To finde the foure principall or Cardinall points of Heauen ( as the Astrologians call them ) at any time . THese foure Cardinall points are nothing else but foure points of the Ecliptick , whereof one is at the East part of the Horizon , ascending , and is therefore called the Ascendent : another is at the vpper part of the Meridian aboue the Horizon , and is called the midst of Heauen , and the hart of Heauen : the third is at the West part of the Horizon descending , and may be therfore called the descendent : the fourth point is that which is at the nether part of the Meridian vnder the Horizon . Which foure points are the beginnings of the first , tenth , seuenth , and fourth Houses . Therefore to finde these points at any time by the Sphaere , bring the place of the Sunne ( being found for that time by the 2. Proposition ) to the Meridian , and the Index to 12. a clocke : then turne the Sphaere till the Index come to that houre at which you desire to know those foure points , and there hold the Sphaere that it moue not : and looke withall , what points of the Ecliptick are at the East and West semicircle of the Horizon ; and at the vpper and nether parts of the Meridian : for those bee the foure principall or Cardinall points you sought for . Take for example the time of the Sunnes entrance into Aries this present yeare 1600. which was vpon the tenth day of March about eight of the clocke in the morning , or little after with vs here at London , Hauing therefore brought the beginning of Aries together with the houre Index to the Meridian , and then turned back the whole Sphaere till the Index come to 8. of the clocke vpon the houre circle : you shall finde the ascendent at that time , to be the 27. degree of Taurus ; the middest or hart of Heauen , the 27. of Capricorne ▪ the descendent , the 27. deg . of Scorpio ; and the lowest part of Heauen the 27. degree of Cancer . PROP. XXXI . To finde out the bredth of any climate , &c. LIft vp , or put downe the pole of the Sphaere , till you finde that there are 7. deg . and an halfe of the Tropick of Cancer , more or lesse aboue the Horizon , then there were before ; and marke with all how much the pole of the Sphaere is raised , or let fall in the meane time , more then it was before ; for so much is the bredth of that climate . As far example : hauing set the Sphaere to our Latitude of London of 51. deg . and an halfe , with the point of your Compasses , holding and guiding some point of the Tropick of Cancer right vnder the Horizon ; then lifting vp the Pole till you finde 7. degrees and an halfe more aboue the Horizon then were before , you shall finde the Pole eleuated about 2. degr . and an halfe more then it was before . Likewise , if you put downe the Pole till there be 7. degrees and an halfe of the Tropicke of Cancer , fewer aboue the Horizon then was before ; you shall finde the eleuation of the Pole to be about 3. degrees lesse then before . PROP. XXXII . The reason of the inequalitie of naturall dayes , &c. THe reason hereof is shewed partly by the inequality of the differences of right ascentions answerable to equall arcks of the Zodiack ; and partly by the vnequall apparent motion of the Sunne . For the first : the differences of right ascentions answerable to the parts of the Ecliptick , about the Tropicall points of Cancer and Capricorne , are much greater then about the Equinoctiall points of Aries and Libra . In so much that whereas the difference of right ascension answerable to one signe , or 30. degrees taken about those Tropicall points , is more then 32. degrees and an halfe : about the Equinoctiall points it is little more then 27. degrees and an halfe ; as it may appeare by the Sphaere . So as you may hereby gather , that the difference of ascention answerable to one degree , which about the beginning of Capricorne is one degree , and about 6. minutes ; about the beginning of Aries , or Libra , is onely 55 minutes . Secondly , the apparent motion of the Sun is much swifter about his Parig●●● , in the signe of Capricorne , then about his Apogaeum in Cancer , or in other parts of the Zodiacke : so that whereas the Sunne being in Capricorne moueth 61. minutes and something more in a day : in Aries or Libra he moueth but 59. min. or very little more in the same time . Therefore seeing the naturall day is nothing else , but the time wherein the Sunne moueth from the Meridian about , till it returne again to the same part of the Meridian ; it must needs bee that alwayes in one naturall day , there is made one whole reuolution of the Equinoctiall circle , and so much more as is the difference of right ascention answerable to the apparent motion of the Sun in the meane time : which differences of ascention because they be vnequall , for the two causes before alledged ; the naturall dayes must needs also bee vnequall , the motion of the Equinoctiall circle about his owne center being ( as it hath beene alwayes supposed to be ) equall , that is mouing alwayes an equall space in equall time . Which by this example may most plainly appeare : The Sunne being in Capricorne moueth 61. minutes in a naturall day : difference of ascention agreeable thereto is 67. minutes , or something more . Therefore at that time , in the space of one naturall day , the Equinoctial circle must make one full reuolution , and 67. minutes more . But when the Sun is in Aries , mouing onely 59. minutes in a day , and the difference of right ascention answerable thereto , scarce 54. minutes more then one reuolution of the Equinoctiall circle ; there shall passe onely 54. minutes more in a naturall day ; so as here the Equinoctiall circle moueth not about so much in one day as before by 13. minutes . Seeing then that 15. degr . or little more of the Equinoctiall circle doe passe the Meridian in euery houre , and consequently one degree of the Equinoctiall passeth the Meridian in 4. minutes of an houre , and one minute of a degree in 4. seconds of an houre ; therefore 13. minutes of the Equinoctiall shall passe the Meridian in 52. seconds : that is , almost in one minute of an houre : Whereby it manifestly appeareth that the naturall day , that is to say , the space of 24. houres , which is the time wherein the Sunne moueth from the Noone-stead to the same noone-stead againe , is in our age greater almost by one minute of an houre , when the sunne is in Capricorne , then when hee is in Aries or Libra ▪ PROP. XXXIII . To finde by the Sphaere how much the naturall dayes are longer at one time of the yeare then at another . FOr this purpose it will be best to take a good number of dayes together ; as for example , take the whole moneth of December , and the whole moneth of March : both which moneths consist of the same number of 31. naturall dayes : find the place of the Sunne for the beginning and ending of both moneths , which you may finde by the second Proposition to be for the beginning of March this present yeare 1600. about 20. degrees and 13. minutes of Pisces ; and for the ending about 20. degr . 48. minutes of Aries : Also for the beginning of December the same yeare 18. degr . 46. minutes of S●gitarie ; and for the ending , 20. degrees 24. minutes of Capricorne : Then seeke out the right ascensions of the same places of the Sunne for the beginnings and endings of both those moneths by the fourth Proposition , and the differences of ascension answerable to the motion of the Sunne in each moneth , by the sixt Proposition ; which you may finde by the Sphaere to be about 33. degrees , 24 ▪ minutes for December , and 28. degrees , 39. minutes for March. Lastly , finde out the difference of these differences of ascension by substracting the lesser out of the greater ; which in this example is 4. degrees 45. minutes ; which resolued into minutes of an houre , by taking for euery degree 4. minutes of an houre , and for euery 15. minutes of a degree , one minute of an houre shall amount to 19. minutes of an houre , that is a quarter of an houre and 4. minutes . And so much is the moneth of December longer then the moneth of March ; Notwithstanding both of them consist of the same number of 31. naturall dayes . The third Part. Of the Orbes whereof the SPHAERES of the Sunne and Moone haue beene imagined to bee made , and of their Motions and Vses . CHAP. I. Of the Orbes whereof the Sphare of the Sunne is made . WIthin the Sphaere or Orbe contayning all the Circles that wee haue hitherto spoken of , and representing vnto vs the Primum mobile ; that is , the first and highest moueable Heauen , that hath been imagined by the Astronomers , to shew the reason of that daily motion , which appeareth to bee in all the Heauens , and of all the apparences that follow thereupon , are included the Sphaeres and Orbes of the Sunne and Moone . The sphaere of the Sunne contayneth three Orbes : The vppermost of them ( which in this Sphaere is signified by the yellow Circle that commeth next within the compasse of the Zodiacke ) is called Deferens apogaeum Solis ; that is , the Orbe which carrieth about that point , wherein the sunne is furthest distant from the earth . Next within this Orbe is placed the Eccentrick carying about the body of the Sunne ; which in this Sphaere is represented by the greene coloured circle that commeth next vnder the Deferens apogaeum . Againe , within this Eccentrick is included the third Orbe of the Sphaere of the Sunne called Deferens Perigaeum solis ; that is , the Orbe carying about that point wherein the Sun is nearest to the Earth . This is the nethermost of the three Orbes of the sunne , and in this Sphaere is represented vnto you by the yellow coloured circle next vnder the sunnes Eccentricke . CHAP. II. Of the vppermost and nethermost Orbes of the Sphaere of the Sunne , more particularly . IN the vppermost and nethermost of these three Orbes , there be 4. points especially to bee considered : That is , the points where they bee narrowest and where they be broadest , and where they are of a meane bredth betwixt the narrowest and broadest . For at the narrowest part of the vppermost Orbe , where you may see written Aux solis , and the broadest part of the nethermost Orbe , is the place of the sunnes Apogaeum ; so that whensoeuer the Sun commeth there , he is furthest distant from the earth . As you may easily try , if ( with a payre of Compasses , or otherwise ) you take the distance betwixt the Earth and the Sunne , being brought about to that place , and compare the same with the distances that the Sun hath from the Earth in other places . This point is called Aux Solis , and Longitude longior , that is , the point of the sunnes furthest distance from the earth . But vnder the broadest part of the vppermost and vttermost Orbe , where you see printed PERIGAEVM , and right aboue the narrowest part of the nethermost Orbe , is the place where the Sun commeth nearest to the Earth , as you may easily find ( with your Compasses , or otherwise ) in like sort as before was shewed . The point where the Sun commeth nearest to the earth , is called oppositum A●gis , and longitudo propior , that is , the point opposite to the Apogaeum , and the nearest distance . And at those parts of this Orbe , which are in the midst betweene the former ; the Sunne hath a meane distance from the earth : a meane ( I say ) betweene the least , and greatest distance . The very point wherein this meane or middle distance hapneth , is shewed by the points that are iust in the middest betweene the short lines AB , and IK , which are drawne ouerthwart on eyther side of this Orbe . These points are called longitudines media ; that is , the meane distances of the Sunne , because the sunne comming to these points , hath a meane distance betweene the least and the greatest . About these points also , the true motion of the sun , is as it were in a meane between the slowest , which hapneth the sunne being about the Apogaeum , and the swiftest , which hapneth about his Perigaeum . Moreouer the lines A , and K , shew the places wherin there is the greatest Prosthaphaerisis , or Equation of the sunne : that is , the greatest difference betweene the true , and middle , or meane place of the sunne . Lastly , the distance betweene the lines I , and K , or A , and B , shew how much the eccentricitie of the sunnes eccentricke is , that is , how farre the Center of the eccentricke is distant from the Center of Earth . CHAP. III. To finde how much the Sunne is nearer or further from the earth , at one time then at another . BY meanes of this Circle , you may easily find with your Compasses , how much the Sunne is nearer to , or further from the earth at one time , then at another : for hauing set one foot of the Compasses vpon the vtmost edge of the Deferens Apogaeum , vnder the place of the Sunne in the Zodiacke , found by the second Prop. stretch out the other foot , to the innermost edge of the same Orbe ; for then , if you set one foot of your Compasses , vpon the vtmost edge of this Orbe , at the Apogaeum , the other foot turned inwards towards the center of the Sphaere , will shew you how much the Sunne is nearer to the Earth at that time , then when he is in his Apogaeum : for so much as that foot reacheth within the inner edge of the Orbe , so much is the sunne nearer . Likewise if you set one foot of your Compasses , vpon the vttermost edge of this Orbe , at the Perigaeum , and turne the other foot towards the center of the Sphaere , so much as this foot of the Compasse , is from the inner edge of the Deferens Paerigaeum , so much is the Sun further distant from the earth at that time , then when he is in his Paerigaeum . CHAP. IIII. Of the situation and motion of the uppermost , and nethermost Orbes of the Sunne . THe vppermost , and nethermost of these three Orbes , called Deferens Apogaeum , & Perigaeum solis , doe alwayes answer each to other , in such sort that the broadest part of the one , is alwayes against the narrowest part of the other : And therefore both of them are moued thgether , with one motion about the Axtree and poles of the Ecliptick , making one reuolution vnder the Zodiack , in the space of 17000. yeares almost . For in Ptolemee his time ( that is about the yeare of our Lord 134. ) the place of the Sunnes Apogaeum , was about the middest of the 6. deg . of Gemini ; as it may appeare by the 4. Chapter of the 3. booke of his Almagest . But in our time we finde that it cannot exceed the 7. degr . of Cancer , although after the account of Copernicus , and of the Prutenicke tables , it should be in the 9. degr . of Cancer . So as , if the rest of the motion of the Sunnes Apogaeum , that is to come hereafter , be proportionable to that is past , the whole reuolution thereof shal be finished in 1699. yeares vnder the Zodiack . For in 1463. yeares betwixt Ptolemee his time and ours , it hath moued about 31. degn therefore it shall moue 300. degrees , ( that is , the compasse of the whole circle ) in 16990. yeares . Which number of yeares being deuided by 360. it shall appeare that the Apogaeum of the Sunne moueth one degr . in little more then 47. yeares whereby the yearely motion thereof may be sound to be little more then one minute and a quarter . CHAP. V. How to find the place of the Suns Aux or Apogaeum , &c. THerefore the place of the Sunnes Apogaeum , being found for the yeare 1600. to be about 7. degr . in Cancer , the place thereof for any other yeare before or after , may easely be found in our age , onely by subtracting , or adding for euery 4 , yeares 5 , min. and for euery single yeare 1. minute and a quarter , Although indeed we need not stand so precisely neyther vpon quarters of minutes , neither yet vpon whole minutes , in the place of the sunnes Apogaeum , which cannot be by any Art so exactly found , but that the diligentest man that is , may erre many minutes therein . Take for example the yeare of our Lord 1558. ( in which our gracious Q. Elizabeth began her happie reigne , which is now 42. yeares since ) taking therefore for euery 4. yeares 5. minutes , that is , for 40. yeares 50. minutes , and for the two yeares remaining 2. minutes and one halfe ; that is in all 52. minutes and an halfe , and subtracting the same out of 7 , deg of Cancer , there shall remaine the place of the sunnes Apogaeum at the beginning of her Maiesties reigne , in 6. degr . and about 8. min. of Cancer . The vses of these two Orbes are these . 1. First to make the sphaere of the Sunne concentricall ; for these Orbes be framed together , that the narrowest part of the one , answereth alwayes to the broadest part of the other : it commeth to passe by this meanes , that both the out-side , and the in-side of the Sphaere of the sunne , haue alwayes the same center , that the world it selfe hath . 2. The second vse is to shew the reason , and manner of the motion of the Sunnes Apogaeum and Perigaeum . CHAP. VI. Of the eccentrick of the Sunne , &c. THe Orbe conteined betweene the two former , and carying about the body of the Sunne it selfe , is called the eccentricke of the Sunne ; because it hath another center , then the center of the world . The especiall reason , that moued the skilfull in this coelestiall science , to make this Orbe ( wherein the body of the sunne is carryed ) eccentricall , was because they found the apparent motion of the sunne vnder the ecliptick line to be vnequall , that is , swifter in the Southerly Signes : and slower in the Northerly . For Hipparehus , and Ptolemee found in their times , that the sunne continued in the Northerne semicircle of the ecliptick , from Aries to Libra , 187. dayes : and in the other halfe of the Zodiack , that is Southward from Libra to Aries , 178. dayes and a quarter onely . But in our time by diligent obseruation it is sound , that the time of the sunnes continuance in the first of those semicircles from Aries to Libra , is 186. dayes 14. houres and an halfe : and consequently in the other semicircle , from Libra to Aries , 178. dayes 15. houres and an halfe . Taking it therefore for a ground , according to the doctrine of Aristotle , that the motion of the coelestiall bodies is circular and equal ; it must needs follow , that a greater part of the circle described by the proper motion of the sunne must be conteined vnder the Northerly semicircle of the ecliptick , then vnder the Southerly : and consequently that the circle or Orbe that caryeth about the body of the Sunne vnder the ecliptick , hath another center then the center of the Ecliptick . 2. Another reason to proue , that the Sunne is caryed in an eccentricall Circle , is the vnequall apparent , bignes of the Sunnes diameter , the Sunne being of the same height aboue the Horizon and the ayre alike affected , and alike cleare ; so as if there were any refraction by reason of the thicknes of the ayre , it must needs be the same in both places . For in Sommer , when the Sun is at , or neare his Apogaeum , his apparent diameter hath beene found by exquisit obseruation to be 13. minutes 48 seconds . But in winter being about his Perigaeum 33. min. 54. seconds , as it may appeare in Copernicus his reuolutions 4. booke 21. Chapter . Therefore seeing euery visible obiect appeareth greater when it is neare , and lesse when it is further remoued from vs , it is manifest that the Sun appearing greater in winter , then in sommer , must needes be nearer to the earth in winter , then in sommer . The reason of which apparance is most easely shewed , by supposing the Sunne to be moued , in an eccentricall Orbe . 3. A third reason may bee the vnequall greatnesse and continuance of the eclipses of the Moone , euen at those times when she hath had the same latitude , or distance from the Ecliptick , and the same distance from the Center of the earth : which argueth that the conicall sharp pointed shadow of the earth , in the place where the Moone in time of the Eclipse passeth through that shadow , at the same distance from the earth , is sometimes greater , and sometimes lesser : wherof there can no cause be shewed more reasonable then this , that the Sun is sometimes further distant from the earth , and the maketh the shadow greater and sometimes nearer , and so maketh it lesser . Whereby it is also manifestly proued , that the Sun is moued about another center then the center of the earth , and therefore that the circle or Orbe , wherein the Sunne is moued , is an Eccentricke . CHAP. VII . Of the vses of the Sunnes eccentricall Orbe . THerefore the vses of the Sunnes eccentricke may bee these : 1. First to shew the reason of the apparent inequalitie , which seemeth to bee in the motion of the Sunne : for although the Sunne mo●e equally in his owne O●be , and about his owne center ; yet to them that are at the center of the world , or vpon the earth , he shall seeme to moue vnequally ; that is , swiftly when he is in that part of his eccentricke which is nearest vnto the earth ; and slowly when he is farthest from the earth . And therefore in sommer , when the Sunne is about his Apogaeum , and in his greatest distance from the earth , he seemeth to moue little aboue 57. min. in one day . But in winter , being about his Perigaeum and nearest vnto the earth , he seemeth to moue more then 16. minutes : whereas notwithstanding he moueth equally in his Eccentricke , euery day about nine and fifty minutes and 8. seconds ; and so finisheth his reuolution in 365. dayes , and six houres almost . 2. The second vse of the Sunnes Eccentricke , may be to shew the reason why the Sun appeareth greater at one time then at another ; for the Sun being in those parts of the eccentrick that are nearest vnto vs , seemeth greatest , and when he is in those parts of his eccentrick that are furthest from vs , he appeareth to be least . 3. And lastly the inequality of the Sunnes distance from the earth , caused by his eccentrick , is one especiall cause of the inequalitie of the Eclipses , both of the Sunne and Moone . CHAP. VIII . The definitions of certaine Astronomicall wordes of art , for the better vnderstanding of the Theorick of the Sunne . 1. WHat the Aux or Apogaeum of the Sunne is it hath beene partly shewed already : that ●●mely it is that part , or rather point of the Orbe carying the Sunnes Apogaeum , wherein the said Orbe is thinnest , or narrowest : Or it is that point of the eccentrick which is furthest distant from the earth , and is alwayes shewed by a right line vnderstood to be drawn from the center of the world , by the center of the eccentrick , vnto the Orbe carying the Sunnes Apogaeum . Which line is therefore called the line of the Sun his Aux or the line of the Sunnes Apogaeum . 2. The motion of the Aux , or of the Apogaeum of the Sunne ( which is also called the Sunnes Aux in the second signification ) is nothing els but the arch of the Ecliptick , conteyned betweene the beginning of Aries , and the line of the Sunnes Apogaeum , drawne forth to the Zodiack ; where this line also sheweth the place of the Sunnes Apogaeum . 3. The middle or meane place of the Sunne in the Zodiack , is shewed by a line drawne from the center of the world vnto the Zodiack , equidistant from the center of the Eccentricke , and of the Sunne . 4. This line is therefore called the line of the meane or middle place of the Sun. 5. The middle or meane motion of the Sunne is the arch of the ecliptick betweene the beginning of Aries , and the middle place of the Sun. 6. The true place of the Sunne is shewed by a streight line drawne from the center of the earth by the center of the Sun vnto the Zodiack , which line is therefore called the line of the true place of the Sun. 7. The true motion of the Sun is the arch of the eclipticke from the beginning of Aries , vnto the true place of the Sun. 8. The argument of the Sun ( at the 〈◊〉 ●erme it ) or the motion of the Sunnes Anomalie ( as Copernicus calleth it ) is the arch of the ecliptick conteyned betweene the place of the Sunnes Apogaeum and the middle place of the Sunne according to the order and succession of the Signes . This arch is called the argument , or motion of the sunnes Anomalie or irregularitie , because that by it is alwayes found how much the suns true motion which ( is vnequall and irregular ) differeth from his middle motion ; which difference they call the Suns equation , or prosthapheresis . 9. The equation , or prosthapheresis of the Sun is nothing els but the arch of the ecliptick conteyned betweene the true , and middle places of the sunne . This arch is called the sunnes equation , because it maketh the suns middle motion equal to his true motion , being added to it or subtracted from it , as occasion requireth : for which cause it is more significantly and fitly called Prosthaphaeresis , that is as much to say , as that which is to be added to or subtracted from the middle motion , that so we might haue the true motion . For so long as the Sunne is in the semicircle of his eccentrick , discending from his Apogaeum to his ●●●gaeum , so long this Prosthapheresis is to be subtracted from the middle motion : but the Sunne being in the other halfe of his eccentrick ascending , the Prosthapheresis or equation of the Sun must be added to the middle motion , that 〈…〉 motion and place of the Sunne may be found , Because that in the first semicircle of the eccentricke descending , the middle place of the Sunne goeth before the 〈◊〉 , and the middle motion is 〈…〉 greater 〈…〉 the Sun , and therefore the difference of these 〈◊〉 motions , ( that is to say , the 〈◊〉 or Prosthaphaeresis ) must be subtracted , to findeth 〈…〉 for the true place of the Sunne goeth alwaies 〈…〉 motion and place of the same , CHAP. IX . Of the vppermost Orbe of the Sphaere of the Moone carying the Dragons head and tayle . NExt within the Orbes of the Sun in this Sphaere are conteyned the Orbes of the Sphaere of the Moone : which 〈…〉 in number . The vppermost of them ( which in this Sphaere is next vnder the Orbe that caryeth the Suns Perigaeum and is coloured with red ) is called the Caryer of the Dragons head and tayle , or 〈…〉 which is as much to say as the Caryer of the knots , that is of the two intersections , or pointes wherein the rest of the Orbes of the Moone , doe crosse ouer-thwart this Orbe . This Orbe is deuided into foure nineties of degree , for the easier reckoning of the motion and place of the Dragons head or tayle in this Sphaere . And it is moued about in 18. Iulian yeares 224. dayes 3. houres and 5. minutes almost , from the East Westwards , vnder the ecliptick . By reason of this motion it commeth to passe , that the Eclipses , or rather the places wherein the eclipses of the Sunne or Moone doe happen in the Heauens , are remoued continually more backwards in the Zodiack , contrary to the order and succession of the Signes . As for example ; the eclipse of the Moone hapning this present yeare 1600. the 20. of Ianuarie neare vnto the Dragons tayle about the 9. degree and 40. min. of Leo ; the next eclipse that shall happen neare the same intersection of the Dragons taile , in the yeare 1601. the 29. of Nouember , shall be in 17. degrees and an halfe of Gemini ; And that eclipse which shall be the next yeare after neare the same intersection the 19. of Nouember in the morning , shall be about the 6. degree and 40. minutes of Gemini , &c. All this remouing of the Eclipses backwards commeth to passe , by reason of the motion of this Orbe carying the Dragons head and tayle , contrary to the course and order of the Signes . This Orbe continueth alwaies right vnder , and euen with the Orbes of the Sphaere of the Sunne which abide alwaies in all parts iust vnder the ecliptick line , and hath his center agreeing , and all one with the center of the world , and of the ecliptick : And therefore the poles and axtree , about which this Orbe is turned , agree iustly with the axtree of the Ecliptick . The rest of the Orbes of the Moone , that are conteyned within this , haue all theire playnes agreeing in one , and lying euen one with another . But the one halfe of all their playnes , ariseth aboue the playne of the former Orbe , and of the Ecliptick , towards the North pole of the Zodiack : and the other halfe descendeth beneath the playne of the ecliptick , toward the South pole : euen as the one halfe of the Zodiack ariseth aboue the Equinoctiall circle towards the North : and the other halfe descendeth towards the South . And as the angle of intersection , or obliquitie of the ecliptick with the Equinoctiall circle , is 23. degr . and an halfe or little more : so the angle of intersection , or obliquity of the playnes of these Orbes of the Moone , from the plaine of the Ecliptick , and of the former Orbe carying the Dragons head and taile , is 5. degrees , or ( according to Tig●● Brahe his obseruation ) 5. degr . and a quarter almost sometimes , and sometimes lesse then 5. degr . That point or intersection of these Orbes with the former , from which they begin to arise about the playne of the ecliptick towards the North , proceeding East-wards , is called the Dragons head ; and is signified by this character ☊ : and the other point or intersection diametrally opposite vnto this , is called the Dragons tayle , which is also signified by the former character turned vp side downe after this manner , ☋ . The two points of these Orbes that are furthest distant from the plaine of the 〈◊〉 , are called the bounds or limites of the Moones latitude , and they are 90. deg . from the Dragons head and tayle , and 5. deg . and a quarter almost from the playne of the Ecliptick , according to the obliquity , or greatest declination of the playnes of these Orbes , from the playne of the ecliptick : Of these two points , that which is in the north side of the ecliptick , is called the North limit , or bound of the Moones latitude ; and contrariwise , the other point opposit to this on the south side of the Ecliptick , is called the South limite of the Moones latitude . And when the Moone commeth to eyther of these two points , she hath her greatest latitude . CHAP. X. Of the Orbes carying the Moones Apogaeum and Perigaeum . NExt within the Orbe carying the Dragons head and tayle , is contayned the Orbe called Deferens Apogaeum lunae which is the point wherein the Moone is furthest distant from the earth . And vnder this Orbe is placed the Moones Eccentrick , which is also called Deferens Epiculum Lunae ; that is the Orbe carying the Moones Epicycle . Againe within this eccentrick of the Moone , is conteyned the least and lowest Orbe , of all that are in this Sphaere , Which they call Diferens Perigaeum Lunae ; that is , the Orbe carying the Moones Perigaeum , which is the point wherein the Moone commeth nearest to the earth . The vppermost and nethermost of these three Orbes , that is to say , the Orbes carying the Moones Apogaeum and Perigaeum ( both which Orbes in this Sphaere are coloured with blew ) are alwaies placed in such sort , that the nar●●west part of the one , is continually answerable to the broadest part of the other ; whereby it commeth to passe , that the Sphaere of the Moone is made concentricall , that is to say , to haue the same center with the world : which also is one especiall vse , why these Orbes were deuided . Another vse of these Orbes , is to shew the reason of the motion of the Moones Apogaeum and Perigaeum : Therefore both these Orbes are moued togither with one motion equally , about the center of the world , in the same time from the East Westwards , in the space of 32. dayes 3. houres and 5. minutes almost : So mouing in one day 11. deg . 12. min. and 1. third part almost . The axtree , about which these Orbes are moued equally , passeth through the center of the world and of the ecliptick : but the poles of these Orbes differ from the poles of the Ecliptick and of the Orbe carying the Dragons head and tayle , by the space of 5. degr . and a quarter , or thereabouts , which poles are caryed about the poles of the Orbe carying the Dragons head and tayle , with the motion of the same Orbe , in the space of 19. yeares almost . Whereby it commeth to passe , that the poles of the Orbe carying the Apogaeum and Perigaeum of the Moone , describe certaine litle circles about the poles of the Orbe that carieth the Dragons head and taile , euen as the Arctick , and Antarctick circle in the ordinary Sphaere , are described by the motion of the poles of the Ecliptick , caryed about dayly with the motion of the first and highest moueable Sphaere , in the space of 24. houres almost . CHAP. XI . Of the eccentricke of the Moone . THe Eccentrick of the Moone contained betweene the two former Orbes and coloured with a sad yealow colour in this Sphaere , is moued equally about the center of the same Orbes , from the West towards the East , finishing his motion vnder the Zodiack , in the space of 27. dayes , and 8. houres almost : and with this motion , it caryeth about the Moones Epicycle equally , vnder the Zodiack . Therefore the motion of this Orbe , about his owne center , must needs be vnequall , that is to say , swifter in those parts that are about the Apogaeum , and slower in the lower parts about the Perigaeum : Because that greater arches of the Eccentrick , doe answer to equall arches of the Zodiack about the Apogaeum , then about the Perigaeum of the Eccentrick . The axtree about which this Orbe is moued , is alwaies in all places equidistant from the axtree of the Orbe carying the Apogaeum of the Moone : and the poles of the axtree of the Moones eccentrick , are fastned in the Orbe carying the Moones Apogaeum , equidistantly from the poles of the same Orbe : therefore these poles together with the whole axtree of the eccentrick , are caryed and equally moued about the poles and axtree of the Orbe carying the Apogaeum from the East , towards the West . With this motion therefore , the poles and center of the eccentrick , describe certaine litle circles of equall bignes , about the poles , and center of the Orbe carying the Apogaeum , from the East West-wards . And therefore also the Apogaeum of the eccentrick , is moued about equally , vnder the ecliptick , contrary to the order of Signes from the East West-wards . Whereby it commeth to passe , that both the Apogaeum and center of the eccentricke , are somtimes vnder the Ecliptick , that is , when they are vnder the Dragons head or taile : but for the most part they are beside the plaine of the ecliptick , either towards the North , or else towards the South . Hereby also it appeareth , that the plaine of the Ecliptick doth not alwayes deuide the plaine of the eccentricke into epqall parts or halfes ; but then onely , when the Center and Apogaeum of the Eccentrick , is right vnder the Dragons head or tayle ; for then onely the plaine of the Ecliptick deuideth the plaine of the Eccentrick , by the center therof ; and consequently deuideth it precisely into two halfes . Otherwise , if the Apogaeum of the eccentrick , be not vnder the Dragons head or tayle , looke on which side of the plaine of the ecliptick the Apogaeum is , for on the same side of the ecliptick is the greater part of the eccentrick . CHAP. XII . In what proportion the Moones eccentrick , and Orbe , carying her Apogaeum are moued . NOw the Eccentrick of the Moone , and the Orbe carying her Apogaeum , are moued in such sort , that the middle place of the Sunne , is alwayes right in the midst betweene the center of the Epicycle caried in the eccentrick , and the Apogaeum of the Eccentrick ; except it be when the center of the epicycle is in coniunction , or opposition to the middle place of of the Sunne . For in euery middle coniunction and opposition of the Sunne and Moone , the center of the Epicycle , and the Apogaeum of the eccentrick are vnited together ; But in the coniunction they are both conioyned with the middle place of the Sun ; and in the opposition they are both together opposite to the same . Whereof it followeth , that in the first and last quarters of the Moone , the center of her epicycle is diametrally opposite to the Apogaeum of her eccentrick . Hereof it commeth to passe , that although the Moone haue the same position in her epicycle at the time of the new and full Moone , and of the first and last quarters ; yet the equation , or prosthaphaeresis of the Moones Argument ( as they call it ) that is the difference betweene the true , and middle places of the Moone , is alwayes greater in the first and last quarter , then in the full and new Moone . Hereby likewise it appeareth that in the time contayned betweene new Moone and new Moone ( which they call Mensem synodicum , that is the moneth coniunctional , or the time from coniunction to coniunction ) the center of the epicycle maketh two complete reuolutions , vnder the Orbe carying the Apogaeum of the Moones eccentrick . And therefore in euery moneth , the center of the epicycle commeth twise to the Apogaeum and twise to the Perigaeum of the eccentrick ; and so the monthly motion of the center of the epicycle , describeth an oual figure : the ends whereof are alwayes towards the place of the full and new Moone , and the ●ides towards the places of the first and last quarter . By this that hath beene spoken , it is also manifest , that if the middle motion of the Sunne , be subtracted out of the middle motion of the Moone , there remaineth the middle motion of the Moones longitude from the sunne , and that if this longitude againe be doubled , you shall haue the motion of the center of the Moones Epicycle from the Apogaeum of her eccentrick , which motion they call the center of the Moone , CHAP. XIII . Of the Epicycle of the Moone , and how it is moued . THe little Orbe placed in the Eccentrick , is called the Epicycle of the Moone ; in the circumference whereof is also placed the body of the Moone , represented by the round Beade , set into the Moones Epicycle in this Sphaere . The plaine superficies of this epicycle agreeth euen with the plaine of the eccentrick : and the axtree about which it is moued , is perpendicular to the plaine of the eccentrick . This Epicycle is moued equally from his middle Apogaeum , about his owne center and axtree from the East Westwards , contrary to the motion of the eccentrick , carying forwards the body of the Moone with this motion 13. degrees and almost 4. min. euery day , and finishing his reuolution in 27. dayes 13. houres and 19. minutes almost . The middle Apogaeum of the Epicycle is shewed by a right line , imagined to be drawne , from that point of the little circle ( described by the motion of the center of the Moones eccentrick ) which is opposite to the center of the Eccentrick , by the center of the Epicycle vnto the vpper part of the Epicycle . But the true Apogaeum of the Epicycle , is shewed by a right line , vnderstood to be drawne from the Center of the earth by the center of the Epicycle , vnto the vpper part of the circumference thereof . By the motion of this Epicycle it may easily be conceiued why the Moone seemeth to moue sometimes swifter and somteimes slower : For seeing that the vpper part of the Epicycle , moueth contrary to the motion of the Eccentrick from the East Westwards , when the Moone commeth in that part , shee must needs seeme to moue more slowly , to them that are at the center of the world . But when the Moone commeth in the nether part of the Epicycle , the Eccentrick caryeth the Epicycle and the Epicycle caryeth the body of the Moone both one way : that is , from the West East-wards , and therefore at that time the Moone seemeth to moue more swiftly . According as you may see in Ephemerides , the d●●●ne motion of the Moone to be sometimes little more then 11. degrees and sometimes againe little lesse then 15. degrees . The true motion of the Moone seemeth then to be swifter , when the Moone is in the Perigaeum of her Epicycle , and the Epicycle in the Perigaeum of the Eccentrick ; because then she is not onely caryed forwards the same way both by her Epicycle and Eccentrick , but she is also at that time nearest vnto vs for which cause her motion shall seeme swifter , then when the Epicycle is in other parts of the Eccentrick . 〈…〉 CHAP. XIIII . The definitions of certayne Astronomicall wordes of Art , for the better vnderstanding of the Theoricke of the Moone . 1. THe line of the Moones middle motion , is a line vnderstood to be drawne from the center of the earth , by the center of the Moones Epicycle , vnto the Zodiack . 2. This line sheweth the middle place of the Moon in the Zodiack . 3. And the middle motion of the Moone , is the arch of the Zodiack , from the beginning of Aries , vnto the same line . 4. So likewise the line of the true motion , or of the true place of the Moone , is drawne from the center of the world , by the center of the Moone , to the Zodiack . 5. This line therefore sheweth the true place of the Moone in the Zodiack . 6. And the true motion of the Moone , is the arch of the Zodiack , from the beginning of Aries , vnto the true place of the Moone . 7. The middle longitude of the Moone from the Sunne , is the arch of the Zodiack , from the middle place of the Sunne Eastwards vnto the middle place of the Moone . 8. And this arch doubled , is called the doubled longitude of the Moone from the Sunne , or the center of the Moone ( as the Alphonsines call it ) which is nothing else but the arch of the Zodiack , betweene the place of the Apogaeum of the Eccentrick and the middle place of the Moone . It is called the doubled longitude of the Moone from the Sunne , because it is alwayes twice so much , as is the middle longitude of the Moone from the Sunne . 9. And it is called the center of the Moone , because it sheweth the distance of the center of the Moones Epicycle from the Apogaeum . 10. The equation , or Prosthaphaeresis of the center , is the arch of the Epicycle , betweene the middle and true Apogaeum of the Epicycle . This equation or Prosthaphaeresis is nothing at all , when the center of the Epicycle is in the Apogaeum , or Perigaeum of the Eccentrick . But the Epicycle being in any other part of the Eccentricke there is alwaies some equation of the center ; yea in some parts thereof , where it groweth greatest , it is 13. degr . 9. minutes : and so long as the center of the Epicycle , is in the halfe of the Eccentrick descending from the Apogaeum to the Perigaeum , that equation is to be added to the motion of the Epicycle ; but in the other halle of the Eccentricke ascending ; , it must be subtracted ; that so the true Argument 〈…〉 the Epicycle may be had . 11. The Argument , or Anamalie of the Moone is nothing els , but the motion of the Moones Epicycle . 12. The true or middle argument , 〈…〉 is the arch of the Epicycle from the true or middle Apogaeum of the Epicycle , vnto the center of the body of the Moone , reckoned that way , which the epicycle moueth . 13. The equation of the argument , or Prosthaphaeresis of the epicycle , is the arch of the Zodiack , 〈…〉 the middle , and 〈◊〉 place of the Moone . This equation is 〈◊〉 , when the Moone is in the true Apogaeum , or Perigaeum of her epicycle . But it is greatest , when the center of the Moone commeth 〈…〉 of the world , and touching the epicycle , when it is in the Perigaeum of the eccentrick . And the Moone being in the first , that is in the 〈…〉 of the Epicycle , 〈…〉 from the true Apogaeum thereof , the middle place of the Moone goe 〈◊〉 before the true place , and the equation of the argument must therefore be subtracted : but when the Moone is 〈…〉 semicircle of the epicycle , 〈…〉 before the middle place , and to that equation must be added to the Moones 〈◊〉 middle motion , that the true motion and place of the 〈…〉 may be found . CHAP. XV. The reason of the variety of the Moones equation , &c. THis equation becommeth lesser or greater , according as the epicycle 〈…〉 or nearer to the center of the world . The least equations are , when the epicycle is in the Apogaeum of the eccentrick , and contrarywise , the greatest must happen , the epicycle being in the Perigaeum of the eccentrick . The difference between these greatest , and least Equations , Ptolemee and Copernicus call the excesse : but 〈◊〉 , and the Alphonsines call it the diuersitie of the Diameter ; because that difference of the equations ariseth by reason of the diuerse apparent hignesse of the diameter of the Epicycle , according as it is nearer to vs , or further from vs. Therefore in the Astronomicall tables , they vse to set downe those equations onely , which happen when the Epicycle is in the Apogaeum of the eccentrick , which are the least equations , whereto they also adioyne the excesse , or diuersity of diameter , shewing how much those equations , which happen when the Epicycle is in the Perigaeum of the Eccentrick , exceed those which happen , the epicycle being in the Apogaeum of the eccentrick . Moreouer , there are annexed certaine min. which they call Scrupula , or minuta proportion●alia : that is , proportionall minutes : whereby is found , how much of the sayd excesse , is to be added to the foresayd equations , when the epicycle is in any other part of the eccentrick , then in the Apogaeum : that so the true equation of the argument , for the same part of the eccentrick might at any time be found . For then onely is that whole excesse to be added , when the epicycle is in the Perigaeum of the eccentrick . But if the epicycle be in any other part of the eccentrick ; then looke what proportion 60. hath to the whole excesse , the same proportion haue the proportionall minutes , answerable to that part of the eccentrick , wherein the epicycle is , vnto the part proportional of the excesse , which ( part proportionall ) being added to the equation before found , shall giue you the true equation . CHAP. XVI . The reason 〈◊〉 Moones proportionall minutes , &c. THe reason of those proportionall minutes , may in some sort be shewed , by those concentricall arches of circles , which you see drawne vppon the Moones eccentricall Orbe , in this Sphaere : but indeed all those arches must bee vnderstood , to haue alwayes the same center with the world , and not to be moued about togither with the Eccentrick . The vppermost of them is to be drawne by the center of the Epicycle being in the Apogaeum of the Eccentrick , and the nethermost is drawne by the same center when it is in the Perigaeum of the Eccentrick : so as the distance of these two arches , or Peripheryes , is iust twise so much as the eccentricitie ; that is the distance of the center of the Eccentrick , from the center of the world , shewed by the distance of the short lines NO , or FF , vppon the Orbe carying the Apogaeum ; or of PQ , or GH , vpon the caryer of the Perigaeum of the Moone . The whole distance , between these two peripheries , from the vttermost to the innermost , is vnderstood to be deuided into 60. equall parts , imagining euery one of these to contayne 10. as may appeare by the figures set to euery one of them , from the vppermost to the nethermost , in this order : 10. 20. 30. 40. 50. 60. Now the intersections of these Peripheries with the Eccentrick ( that is ) with the vppermost of the two deuided Peripheries , which are drawne round about through the midst of the Moones eccentricall Orbe ) do shew what proportionable min. answer to any part of the eccentrick , after this manner : In the vppermost of the two foresaid graduated Peripheries , looke that distance of the center of the moones Epicycle from the Apogaeum of the Eccentrick , ( that is to say ) that doubled longitude of the Moone as the Alphonsines call it ) which you desire : Then looke which of the consentricall arches before mentioned passeth by the the terme , or end of that distance or doubled longitude : And thirdly , looke about in the same arch , what number is set thereuppon , for that sheweth you the number of the proportionall minut . answerable to the scituation of the Epicycle , at that distance from the Apogaeum of the Eccentrick . These proportionall min. therefore may be defined to be nothing else , but the sixtieth parts of the diuersity of diameter , or of the excesse wherwith the equations of the argument , or Prostaphaeresis , of the Epicycle are to be augmented when the Epicycle is any other part of the Eccentrick , then in the Apogaeum . Otherwise also , these proportionall min. may be defined , to be sixtieth parts of the excesse , wherewith the line drawne from the center of the earth , to the Apogaeum of the Moones Eccentrick , exceedeth the line drawne from the same center to the Perigaeum of the Eccentrick : For these sixtieth parts also may not vnfitly be called proportionall min. because that alwaies looke how many of these parts there are left without the circumference of the Eccentrick , or beyond the center of the Epicycle ; so many of the former sixtieth parts of the diuersity of diameter , or of the excesse of the Prostaphaerses of the Epicycle , must be added to the Equation of the argument , that the true equation of the argument may bee had , for that position , or scituation of the Epicycle , in the Eccentrick . CHAP. XVII . The reason of the Eclipses of the Sunne and Moone , &c. NOw by this Sphere , it may easily be conceiued , why there is not an Eclipse , in euery coniunction or opposition of the Sunne and Moone . For seeing that the Moone hath for the most part a greater apparent latitude , then the visible or apparent conioyned semediameters of the Sunne and Moone in the coniunction : and because the true latitude of the Moone , is also for the most part greater then the apparent semediameters of the Moone and shadow of the earth ( at that place where the Moone should passe through that shadow ) in the oppossition , to make an Eclipse : it commeth to passe , that in most coniunctions and oppositions of the Sunne and Moone , there is no Eclipse . And the reason hereof is this , because that the Moone commeth vnder the way of the Sunne ( which wee call the Ecliptick line ) onely twise in a moneth , and those 2. points ( wherin the wayes of the Sunne and Moone crosse each other ) onely twise in a synodicall moneth , which two points wee called the Dragons head and taile ; whereof wee haue also spoken before , ) Wherfore , seeing the Sunne ( going but once only through the compasse of the Ecliptick in a yeare ) can come but once in a yeare to eyther of those points ; the Moone for the most part , when she cōmeth to bee in opposition , or coniunction with the Sun , must needs be fo farre wide from the Ecliptick line , or way of the Sunne , either towards the North or South : that she can neither come betwixt vs and the Sun in the coniunction , nor yet within the compasse of the shadow of the earth in the opposition . But when the Sunne commeth neare eyther of those points ( which hapneth once in six moneths ( there must needs for the most part be some Eclipse , eyther of the Sunne or Moone , or both . CHAP. XVIII . Of the diuersity of the bounds or spaces , within which an Eclipse may happen : and the reason of that diuersity . THe bounds or distances from the Dragons head or taile , within which there may happen an Eclipse of the Moone , are sometimes greater and sometimes lesse , by reason of the diuers distances of the Sunne , or Moone , or both of them , from the earth . For seeing the body of the Sunne is greater then the globe of the whole earth ( as it is manifestly demonstrated by Ptolemee and Copernicus ) it must needs be , that the greater distance the Sun hath from the earth , the greater shadow must the earth haue ; and the nearer the Sunne is to the earth , the lesse shadow shall the earth haue , at the place of the Moons passage through the shadow , at equall distances from the earth . Contrariwise , the further that the Moone is from the earth , the lesse shall the shadow of the earth be , and the nearer the Moone is to the earth , the greater shall the shadow be , at the place where the Moone is to passe through the shadow . The greatest distance therefore from the Dragons head or taile , wherein there can at any time happen any Eclipse of the Moone , is about 13. degrees . And the least distance at which it is possible for the Moone to auoid an Eclipse , is about 10. degr . and one third part of a degree ; which hapneth when the Moone is in the Apogaeum of her Epicycle , in her greatest distance from the earth , and the Sunne in his Perigaeum , in the time of his greatest eccentricity , for then the Sunne commeth nearest to the earth and maketh the least shadow : as contrarywise at the same time of his greatest eccentricity , beeing in his Apogaeum , he hath his greatest distance from the earth , and so maketh the earth cast forth her greatest shadow . At which time , if the Moone also chance to be in the Perigaeum of her Epicycle , and so in her nearest distance from the earth , she may be something Eclipsed , although she be full 13. degrees or something more from the Dragons head or taile . CHAP. XIX . How to find the place of the Dragons head and taile for any time . NOw the place , and time of the full Moone , being easily knowne by some Almanack , or Prognostication ; it shall not be hard , to giue a reasonable neare estimate , and to foretell both the time , and quantity of the Eclipse of the Moone , the place of the Dragons head and taile , being first knowne after this manner . The place of the Dragans head , being first giuen for any time , for euery yeare before the same time , adde to the same place : and for euery yeare after the same time subtract 19. degrees and one third part of a degree and for euery moneth a degree and an halfe and a tenth part of a degree and for euery day 3. minutes and the remainder shall shew you the place of the Dragons head after the same time : or the summe before that time without any great errour . As for example , The 30. of Iune this present yeare 1600. suppose you would know the place of the Dragons head : The place therefore of the Dragons head being first giuen , for the beginning of the same yeare , in 0. degree 45. minutes , of Aquarius : and six moneths onely of that yeare being passed , I take for those six moneths 6. degrees and 6. halfe degrees that is 9. degrees and sixteenth parts of a degree that is 36. min. the summe of all which is 9. degrees and 36. minutes . Which being subtracted out of 0. degree , 45. minutes of Aquarius , there remaine 21. degrees 9. min. of Capricorne , for the place of the Dragons head at that time . CHAP. XX. A table for finding the place of the Dragons head and taile more exactly and the declaration thereof . BVt if you would haue the place of the Dragons head more exactly , you may find the same most easily , by meanes of the table following , for any time within the space of these 20. yeares , yet to come . This table conteyneth three principall parts or columnes , the first part sheweth you in what signe , degr . and min. the Dragons head is , at the beginning of any yeare ; from this present yeare 1600. till the yere 1620. The second part sheweth how much the Dragons head moueth , in any number of moneths of the yeare : the third part giueth you the motion of the Dragons head , in any number of dayes of the moneth . The place of the Dragons head .   Yeare Sign . Deg. Mt. Moneths Complete . De. Mi. Da. De. Mi. 1600 Aquarius 0 45 Ianuary 1 38 1 0 3 1601 Capricorn 11 21 February 3 8 2 0 6 1602 Sagittar . 22 2 March 4 46 3 0 10 1603 Sagittar . 2 42 Aprill 6 22 4 0 13 1604 Scorpio 13 22 May 8 0 5 0 16 1605 Libra 23 59 Iune 9 36 6 0 19 1606 Libra 4 39 Iuly 11 14 7 0 22 1607 Virgo 15 19 August 12 53 8 0 25 1608 Leo 25 59 Septemb. 14 28 9 0 29 1609 Leo 6 35 October 16 7 10 0 32 1610 Cancer 17 15 Nouemb. 17 42 11 0 35 1611 Gemini 27 55 Decemb. 19 21 12 0 38 1612 Gemini 8 35     13 0 41 1613 Taurus 19 12     14 0 44 1614 Aries 29 52     15 0 48 1615 Aries 10 32     16 0 51 1616 Pisces 21 12     17 0 54 1617 Pisces 1 49     18 0 57 1618 Aquarius 12 29     19 1 0 1619 Capricorn 23 9     20 1 4 1620 Capricorn 3 49     21 1 7             22 1 10             23 1 13             24 1 16             25 1 19             26 1 13             27 1 26             28 1 29             29 1 32             30 1 35 CHAP. XXI . To finde the place of the Dragons head or tayle , by the former table . FInde out in the former table , the moneth next going before the moneth giuen ; finde out also the day of the moneth , Adde together the numbers of degrees and minutes answerable to that moneth and day of the moneth , and subtract the same out of the place of the Dragons head at the beginning of the yeare , adding thereto 30. degr . ( ●●at is the whole signe next going before resolued in to degr . ) if the Sunne aforesayd be greater then the number of degr . shewing the place of the Dragons head at the beginning of the yeare : so shall you haue the place of the Dragons head for the time giuen . And the point of the Zodiack opposite to this , is the place of the Dragons taile . Take for example , The 29. of Nouember 1601. I find therefore against October ( the moneth going next before Nouember ) 16. degrees 7. minutes and against the 29. day 1. degree 32. minutes , the summe of both these added together is 17. degrees 39. min. the place of the Dragons head for the beginning of the yeare 1601. is 11. deg . 21. min. of Capricorne , which because they be lesse then 17. deg . 39. min. I adde vnto them 30. deg . that is the whole signe of Sagittarie , and the summe of both is 41. deg . 12. min. out of which subtract 17. deg . 39. min. and there shall remaine 23. deg . 42. minutes of Sagittarie ; the place of the Dragons head at that time . And the point of the Zodiacke which is opposite hereto ( that is the 2● 〈◊〉 42. minutes of Gemini ) is the place of the 〈◊〉 tayle . CHAP. XXII . To know at what time there shall be an Eclipse of the Moone . THe place of the Dragons head being thus knowne , finde out the same place vpon the horizon of the Sphaere , and see what day and moneth answereth thereto finde out also the place of the full Moone , which hapneth next before or after that day , which place if it chance to bee within 11. or 12. deg . eyther before or after that point of the Zodiack which is opposite to the Dragons head , there must needs be for the most part in Eclipse of the Moone . Likewise if you finde what day and moneth is answerable to the place of the Dragons taile vpon the horizon of the Sphaere if the place of the full Moone which hapneth next before or after that day chance to be within 11. or 12. degrees of the Dragons head , for the most part there shall bee an Eclipse of the Moone . As for example , The 20. of Ianuarie last this present yeare 1600. the place of the Dragons head was found ( by the former Chapter ) to haue beene in 29. deg . 41. min. of Capricorne ; whereto there answereth in the horizon the 10. day of Ianuarie the place of the full Moone hapning next after , vpon the 20. of the same moneth in the morning must needs be in the place opposite to the place of the Sunne the same 20. 〈◊〉 Therefore because 〈◊〉 Sun that day is in 9. deg . 〈◊〉 one halfe of Aquarius , therefore the place Notes, typically marginal, from the original text Notes for div A15751-e720 Why this Circle is called the Equinoctiall or Equator . Notes for div A15751-e5910 The scituation of the Orbe carying the Dragons head and tayle . The scituation of the rest of the Orbes . Why the Moone seemeth sometimes to moue swifter , sometimes slower . To finde the Moones proportionall minutes . What the proportionall minutes of the Moone are . ●t the begining of the 〈◊〉 of our ●●rd . 
A39865	----	A discovery of new worlds from the French, made English by A. Behn. Fontenelle, M. de (Bernard Le Bovier), 1657-1757. 1688 Approx. 226 KB of XML-encoded text transcribed from 103 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2003-03 (EEBO-TCP Phase 1). A39865 Wing F1412 ESTC R27986 10285760 ocm 10285760 44838 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A39865) Transcribed from: (Early English Books Online ; image set 44838) Images scanned from microfilm: (Early English books, 1641-1700 ; 1383:34) A discovery of new worlds from the French, made English by A. Behn. Fontenelle, M. de (Bernard Le Bovier), 1657-1757. Behn, Aphra, 1640-1689. [44], 158 p. Printed for William Canning, London : 1688. "To which is prefixed a preface, by way of essay, on translated prose, wherein the arguments of Father Tacquet, and others, against the system of Copernicus (as to the motion of the earth) are likewise considered and answered. Wholly new." Reproduction of original in the University of Illinois (Urbana-Champaign Campus). Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. 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Understanding these processes should make clear that, while the overall quality of TCP data is very good, some errors will remain and some readable characters will be marked as illegible. Users should bear in mind that in all likelihood such instances will never have been looked at by a TCP editor. The texts were encoded and linked to page images in accordance with level 4 of the TEI in Libraries guidelines. Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Plurality of worlds. Astronomy -- Early works to 1800. 2002-10 TCP Assigned for keying and markup 2002-11 SPi Global Keyed and coded from ProQuest page images 2002-12 Olivia Bottum Sampled and proofread 2002-12 Olivia Bottum Text and markup reviewed and edited 2003-02 pfs Batch review (QC) and XML conversion A DISCOVERY OF New Worlds . From the FRENCH . Made ENGLISH By Mrs. A. BEHN . To which is prefixed a PREFACE , by way of ESSAY on Translated PROSE ; wherein the Arguments of Father Tacquet , and others , against the System of Copernicus ( as to the Motion of the Earth ) are likewise considered , and answered : Wholly new . LONDON , Printed for William Canning , at his Shop in the Temple-Cloysters , 1688. To the Right Honourable , William , Earl of Drumlangrig , Eldest Son to his Grace , William , Duke of Queensberry ; and one of his Majesty's most Honourable Privy-Council in the Kingdom of Scotland . My Lord , THe Esteem I have for your Nation in general , and the great Veneration I am obliged to have for some particular Persons of Quality of it , has made me ambitious of being known to all those of Wit and fine Parts . Amongst that Number , none has a greater Character than your Lordship , whose early Knowledge of all that is excellent in Learning , and of all the Graces of the Mind , promised the World that accomplished Great Man , it now with so much Pride and Satisfaction beholds ; and which , even without the addition of your illustrious Birth , were sufficient , to gain you the Esteem of all Mankind ; and you are never mentioned , but with such vast Accumulations of Praise , as are given only to uncommon Men , and such , as something extraordinary alone can merit . To all your advantages of Nature , elevated Birth , Virtue , Knowledge , Wit , Youth , and Honours , to compleat your Happiness , Fortune has added her part too ; and has ally'd your Lordship by Marriage to the Great and Noble Family of Burlington , which has at once been honour'd with more Earls than any great Family cou'd ever boast , and whose Vertues , and Loyalty , deserve particular and lasting Trophies to celebrate them to Posterity . My Lord , I presume to dedicate this little Book to your Lordship , which I ventured to translate , because it pleased me in the French ; and tho but a trifle , has something in it out of the way of ordinary Wit , which renders it more worthy to be laid at your Lordships Feet . If it is not done with that exactness it merits , I hope your Lordship will pardon it in a Woman , who is not supposed to be well versed in the Terms of Philosophy , being but a new beginner in that Science ; but where I have failed , your Lordship's Judgment can supply ; and if it finds acceptance with your Lordship , I am already so much a Philosopher , as to despise what the World says of it , and will pride my self only in being , My Lord , Your Lordship 's most humble and most obedient Servant , A. Behn . The Translator's PREFACE . THE General Applause this little Book of the Plurality of Worlds has met with , both in France and England in the Original , made me attempt to translate it into English. The Reputation of the Author , ( who is the same , who writ the Dialogues of the Dead ) the Novelty of the Subject in vulgar Languages , and the Authors introducing a Woman as one of the speakers in these five Discourses , were further Motives for me to undertake this little work ; for I thought an English Woman might adventure to translate any thing , a French Woman may be supposed to have spoken : But when I had made a Tryal , I found the Task not so easie as I believed at first . Therefore , before I say any thing , either of the Design of the Author , or of the Book it self , give me leave to say someting of Translation of Prose in general : As for Translation of Verse , nothing can be added to that Incomparable Essay of the late Earl of Roscommon , the nearer the Idioms or turn of the Phrase of two Languages agree , 't is the easier to translate one into the other . The Italian , Spanish and French , are all three at best Corruptions of the Latin , with the mixture of Gothick , Arabick and Gaulish Words . The Italian , as it is nearest the Latin , is also nearest the English : For its mixture being composed of Latin , and the Language of the Goths , Vandals , and other Northern Nations , who over-ran the Roman Empire , and conquer'd its Language with its Provinces , most of these Northern Nations spoke the Teutonick or Dialects of it , of which the English is one also ; and that 's the Reason , that the English and Italian learn the Language of one another sooner than any other ; because not only the Phrase , but the Accent of both do very much agree , the Spanish is next of kin to the English , for almost the same Reason : Because the Goths and Vandals having over-run Africk , and kept Possession of it for some hundred of Years , where mixing with the Moors , no doubt , gave them a great Tincture of their Tongue . These Moors afterwards invaded and conquered Spain ; besides Spain was before that also invaded and conquered by the Goths , who possessed it long after the time of the two Sons of Theodosius the Great , Arcadus and Honorius . The French , as it is most remote from the Latin , so the Phrase and Accent differ most from the English : It may be , it is more agreeable with the Welsh , which is near a-kin to the Basbritton and Biscagne Languages , which is derived from the old Celtick Tongue , the first that was spoken amongst the Ancient Gauls , who descended from the Celts . The French therefore is of all the hardest to translate into English. For Proof of this , there are other Reasons also . And first , the nearer the Genious and Humour of two Nations agree , the Idioms of their Speech are the nearer ; and every Body knows there is more Affinity between the English and Italian People , than the English and the French , as to their Humours ; and for that Reason , and for what I have said before , it is very difficult to translate Spanish into French ; and I believe hardly possible to translate French into Dutch. The second Reason is , the Italian Language is the same now it was some hundred of Years ago , so is the Spanish , not only as to the Phrase , but even as to the Words and Orthography ; whereas the French Language has suffered more Changes this hundred Years past , since Francis the first , than the Fashions of their Cloths and Ribbons , in Phrase , Words and Orthography . So that I am confident a French Man a hundred Years hence will no more understand an old Edition of Froisard's History , than he will understand Arabick . I confess the French Arms , Money and Intrigues have made their Language very universal of late , for this they are to be commended : It is an Accident , which they owe to the greatness of their King and their own Industry ; and it may fall out hereafter to be otherwise . A third Reason is as I said before , that the French being a Corruption of the Latin , French Authors take a liberty to borrow whatever Word they want from the Latin , without farther Ceremony , especially when they treat of Sciences . This the English do not do , but at second hand from the French. It is Modish to Ape the French in every thing : Therefore , we not only naturalize their words , but words they steal from other Languages . I wish in this and several other things , we had a little more of the Italian and Spanish Humour , and did not chop and change our Language , as we do our Cloths , at the Pleasure of every French Tailor . In translating French into English , most People are very cautious and unwilling to print a French Word at first out of a new Book , till Use has rendered it more familiar to us ; and therefore it runs a little rough in English , to express one French Word , by two or three of ours ; and thus much , as to the Ease and Difficulty of translating these Languages in general : But , as to the French in particular , it has as many Advantages of the English , as to the Sound , as ours has of the French , as to the Signification ; which is another Argument of the different Genius of the two Nations . Almost all the Relatives , Articles , and Pronouns in the French Language , end in Vowels , and are written with two or three Letters . Many of their words begin with Vowels ; so , that when a word after a Relative , Pronoun or Article , ends with a Vowel , and begins with another , they admit of their beloved Figure Apostrophe , and cut off the first Vowel . This they do to shun an ill sound ; and they are so musical as to that , that they will go against all the Rules of Sense and Grammar , rather than fail ; as for Example , speaking of a Man's Wife they say , son Epouse ; whereas in Grammar , it ought to be sa Epouse ; but this would throw a French-Man into a Fit of a Fever , to hear one say , by way of Apostrophe S' Epouse , as this makes their Language to run smoother , so by this they express several Words very shortly , as qu'entend je , in English , what do I hear ? In this Example , three words have the Sound but of one , for Sound prevails with them in the beginning , middle and end . Secondly , their words generally end in Vowels , or if they do not , they do not pronounce the Consonant , for the most part , unless there be two together , or that the next word begins with a Vowel Thirdly , by the help of their Relatives , they can shortly , and with ease resume a long Preceeding Sentence , in two or three short words ; these are the Advantages of the French Tongue , all which they borrow from the Latin. But as the French do not value a plain Suit without a Garniture , they are not satisfied with the Advantages they have , but confound their own Language with needless Repetitions and Tautologies ; and by a certain Rhetorical Figure , peculiar to themselves , imply twenty Lines , to express what an English Man would say , with more Ease and Sense in five ; and this is the great Misfortune of translating French into English : If one endeavours to make it English Standard , it is no Translation . If one follows their Flourishes and Embroideries , it is worse than French Tinsel . But these defects are only comparatively , in respect of English : And I do not say this so much , to condemn the French , as to praise our own Mother-Tongue , for what we think a Deformity , they may think a Perfection ; as the Negroes of Guinney think us as ugly , as we think them : But to return to my present Translation . I have endeavoured to give you the true meaning of the Author , and have kept as near his Words as was possible ; I was necessitated to add a little in some places , otherwise the Book could not have been understood . I have used all along the Latin Word Axis , which is Axle-tree in English , which I did not think so proper a Word in a Treatise of this nature ; but 't is what is generally understood by every Body . There is another Word in the two last Nights , which was very uneasie to me , and the more so for that it was so often repeated , which is Tourbillion , which signifies commonly a Whirl-wind ; but Monsieur Des Chartes understands it in a more general sense , and I call it a Whirling ; the Author hath given a very good Definition of it , and I need say no more , but that I retain the Word unwillingly , in regard of what I have said in the beginning of this Preface . I know a Character of the Book will be expected from me , and I am obliged to give it to satisfie my self for being at the pains to translate it , but I wish with all my heart I could forbear it ; for I have that Value for the ingenious French Author , that I am sorry I must write what some may understand to be a Satyr against him . The Design of the Author is to treat of this part of Natural Philosophy in a more familiar Way than any other hath done , and to make every body understand him : For this End , he introduceth a Woman of Quality as one of the Speakers in these five Discourses , whom he feigns never to have heard of any such thing as Philosophy before . How well he hath performed his Vndertaking you will best judge when you have perused the Book : But if you would know before-hand my Thoughts , I must tell you freely , he hath failed in his Design ; for endeavouring to render this part of Natural Philosophy familiar , he hath turned it into Ridicule ; he hath pushed his wild Notion of the Plurality of Worlds to that heighth of Extravagancy , that he most certainly will confound those Readers , who have not Iudgment and Wit to distinguish between what is truly solid ( or , at least , probable ) and what is trifling and airy : and there is no less Skill and Vnderstanding required in this , than in comprehending the whole Subject he treats of . And for his Lady Marquiese , he makes her say a great many very silly things , tho' sometimes she makes Observations so learned , that the greatest Philosophers in Europe could make no better . His way of Arguing is extreamly fine , and his Examples and Comparisons are for the most part extraordinary , just , natural , and lofty , if he had not concluded with that of a Rose , which is very irregular . The whole Book is very unequal ; the first , fourth , and the beginning of the fifth Discourses are incomparably the best . He ascribes all to Nature , and says not a Word of God Almighty , from the Beginning to the End ; so that one would almost take him to be a Pagan . He endeavours chiefly two things ; one is , that there are thousands of Worlds inhabited by Animals , besides our Earth , and hath urged this Fancy too far : I shall not presume to defend his Opinion , but one may make a very good use of many things he hath expressed very finely , in endeavouring to assist his wild Fancy ; for he gives a magnificent Idea of the vastness of the Vniverse , and of the almighty and infinite Power of the Creator , to be comprehended by the meanest Capacity . This he proves judiciously , by the Appearances and Distances of the Planets and fixed Stars ; and if he had let alone his learned Men , Philosophical Transactions , and Telescopes in the Planet Jupiter , and his Inhabitants not only there , but in all the fixed Stars , and even in the Milky-Way , and only stuck to the greatness of the Vniverse , he had deserved much more Praise . The other thing he endeavours to defend and assert , is , the System of Copernicus . As to this , I cannot but take his part as far as a Woman 's Reasoning can go . I shall not venture upon the Astronomical part , but leave that to the Mathematicians ; but because I know , that when this Opinion of Copernicus ( as to the Motion of the Earth , and the Sun 's being fixed in the Centre of the Vniverse , without any other Motion , but upon his own Axis ) was first heard of in the World , those who neither understood the old System of Ptolemy , nor the new one of Copernicus , said , That this new Opinion was expresly contrary to the holy Scriptures , and therefore not to be embraced ; nay , it was condemned as Heretical upon the same Account : After it had been examined by the best Mathematicians in Europe , and that they found it answered all the Phaenomena's and Motions of the Spheres and Stars better than the System of Ptolemy ; that it was plainer , and not so perplexing and confused as the old Opinion ; several of these learned Men therefore embraced this ; but those that held out , when they saw all Arguments against Copernicus would not do , they had recourse to what I said before , that this System was expresly against the holy Scriptures . Amongst this Number is the learned Father Tacquit , a Iesuite ; who , I am told , has writ a large Course of Mathematicks , and particularly , of Astronomy , which is deservedly much esteemed . In the end of this Treatise , he cites several Texts of Scripture ; and particularly , the 19th . Psalm , And the Sun standing still at the Command of Ioshua . If I can make it appear , that this Text of Scripture is , at least , as much for Copernicus as Ptolemy , I hope it will not be unacceptable to my Readers : Therefore , with all due Reverence and Respect to the Word of God , I hope I may be allowed to say , that the design of the Bible was not to instruct Mankind in Astronomy , Geometry , or Chronology , but in the Law of God , to lead us to Eternal Life ; and the Spirit of God has been so condescending to our Weakness , that through the whole Bible , when any thing of that kind is mentioned , the Expressions are always turned to fit our Capacities , and to fit the common Acceptance , or Appearances of things to the Vulgar . As to Astronomy , I shall reserve that to the last , and shall begin with Geometry ; and though I could give many Instances of all three , yet I shall give but one or two at most . The Measure and Dimensions of Solomon's Molten Brass Sea in 1 King. 7.23 . the Words are these , And he made a molten Sea , ten Cubits from one brim to the other , it was round all about , and his heighth was five Cubits , and a Line of thirty Cubits did compass it round about : That is to say , the Diameter of this Vessel was a Third of its Circumference : This is indeed commonly understood to be so , but is far from a Geometrical Exactness , and will not hold to a Mathematical Demonstration , as to the just Proportion between the Diameter and Circumference of a Circle . In the next place , as to Chronology , I could give many Instances out of the Bible , but shall only name two that are very apparent , and easie to be understood by the meanest Capacity . See 1 King. 6.1 . the Words are these , And it came to pass , in the four hundred and fourscorth Year after the Children of Israel were come out of the Land of Egypt , in the fourth Year of Solomon's Reign over Israel , in the Month Zif , which is the second Month , he began to build the House of the Lord. Compare this Text , and number of Years with Act. 13.17 , 18 , 19 , 20 , 21 , 22. which is the beginning of St. Paul's Sermon to the Jews of Antioch , and the number of Years therein contained : The Words are these , Ver. 17. The God of this People of Israel chose our Fathers , and exalted the People when they dwelt as Strangers in the Land of Egypt , and with an high Hand brought he them out of it . Ver. 18. And about the time of forty Years suffered he their Manners in the Wilderness . Ver. 19. And when he had destroyed seven Nations in the Land of Canaan , he divided their Land to them by Lot. Ver. 20. And after that , he gave unto them Judges , about the space of four hundred and fifty Years , until Samuel the Prophet . Ver. 21. And afterwards they desired a King , and God gave them Saul , the Son of Kish , a Man of the Tribe of Benjamin , for the space of forty Years . Ver. 22. And when he had removed him , he raised up unto them David to be their King. King David the Prophet reigned seven Years in Hebron , and thirty three Years i Jerusalem ; and for this see 1 King. 2.11 . To this you must add the first three Years of his Son Solomon , according to the Text I have cited , in 1 King. 6.1 . Put all these Numbers together , which are contained in St. Paul's Sermon at Antioch , with the Reign of King David , the first three Years of Solomon , and seven Years of Joshua's Government , before the Land was divided by Lot , which is expresly set down in Act. 13.19 . the number of the Years will run thus : Forty Years in the Wilderness , the seven Years of Joshua , before the dividing the Land by Lot ; from thence , till Samuel , four hundred and fifty Years ; forty Years for the Reign of Saul , forty Years for the Reign of David , and the first three Years of Solomon ; all these Numbers added together , make five hundred and eighty Years ; which Computation differs an hundred Years from that in 1 King. 6.1 . which is but four hundred and eighty . It is not my present Business to reconcile this difference ; but I can easily do it ; if any Body think it worth their Pains to quarrel with my Boldness , I am able to defend my self . The second Instance is , as to the Reign of King Solomon ; for this , see 1 King. 11.42 . where it is said , he reigned but forty Years over Israel . Josephus says expresly , in the third Chapter of his eighth Book of Antiquities , that King Solomon reigned eighty Years , and died at the Age of ninety four . I would not presume to name this famous Historian in contradiction to the Holy Scriptures , if it were not easie to prove by the Scriptures , that Solomon reigned almost twice forty Years . The Greek Version of the Bible , called commonly the Septuagint or seventy two Interpreters has it most expresly in 3 King. 2. But the first Book of Kings according to our Translation in English , says , that Solomon sat upon the Throne of his Father David , when he was twelve Years of Age. But for Confirmation , be pleas'd to see 1 Chr. 22.5 . and 29.1 . where it is said , that Solomon was but young and tender for so great a work , as the building of the Temple . Rehoboam the Son of Solomon was forty one Years old , when he began to reign , see 1 King. 14.21 . How was it possible then that Solomon could beget a Son , when he was but a Child himself , or of eleven Years of Age according to the Septuagint ? This Difficulty did strangely surprise a Primitive Bishop , by Name , Vitalis , who proposed this Doubt to St. Jerome , who was strangely put to it to return an Answer ; and the Learned Holy Father is forc'd at last to say , that the Letter of the Scripture does often kill , but the Spirit enlivens . The Difficulty is still greater than what Vitalis proposed to St. Jerome in his Epistle . Rehoboam was the Son of Naamah an Ammonitish , stranger Woman , as you may see in 1 King. 14.31 . Now it is clear , that Solomon did not abandon the Law of God , nor give himself to strange Women till the end of his Reign , see 1 King. 9. where he had so many strange Wives and Concubines , besides his lawful Queen , the King of Aegypt's Daughter ; and I hope this will convince any rational Man , that the Scripture names only the first forty Years of the Reign of King Solomon , which was the time , wherein he did what was Right in the Sight of the Lord ; which I think is Demonstration , that the Holy Scripture was not designed , to teach Mankind Geometry , or instruct them in Chronology . The Learned Anthony Godean , Lord and Bishop of Venice , seems to have been sensible of this great Difficulty ; for in his Learned Church-History , his Epitome from Adam to Iesus Christ , writing the Life of Solomon , he says , he was twenty three Years old when he began his Reign . Vpon what Grounds , or from what Authority I know not ; but this agrees better with the Age of Solomon's Son Rehoboam ; but it doth not remove the Difficulty , so well as what I have said . I come now in the last place to perform what I undertook , which is to prove , that the Scripture was not designed to teach us Astronomy , no more than Geometry or Chronology . And to make it appear that the two Texts cited by Father Tacquet , viz. that of Psal. 19.4 , 5 , 6. and Iosh. 10.12 , &c. are at least as much for Copernicus his System , as they are for Ptolemy's . The Words of the 19th Psalm are , In them hath he set a Tabernacle for the Sun , which is as a Bridegroom coming out of his Chamber ; and rejoices as a strong Man to run his Race , &c. That these words are Allegorical is most plain . Does not the Word Set import Stability , Fix'dness and Rest , as much as the Words run his Race , and come forth of his Chamber , do signifie motion or turning round ? Do not the Words Tabernacle and Chamber express Places of Rest and Stability ? And why may not I safely believe , that this makes for the Opinion of Copernicus , as well as for that of Ptolemy ? For the Words of the Scriptures favour one Opinion as much as the other . The Texts of the Suns standing still at the Command of Joshua , are yet plainer for Copernicus , in Josh. 10. and the latter part of v. 12. the Words are these . Sun stand thou still on Gibeon , and thou Moon on the Valley of Ajalon , &c. The best Edition of the English Bible , which is printed in a small Folio by Buck , in Cambridge , has an Asterism at the Word stand , and renders it in the Margent , from the Hebrew , Be thou silent : If it be so in the Hebrew , be thou silent makes as much for the Motion of the Earth , according to Copernicus , as for the Motion of the Sun according to Ptolemy , but not to criticize upon Words , consider this miraculous Passage , not only the Sun is commāded to stand still , but the Moon also , And thou Moon on the Valley of Ajalon . The Reason the Sun was commanded to stand still , was to the end the Children of Israel might have Light to guide them , to destroy their Enemies . Now when by this Miracle they had the Light of the Sun , of what Advantage could the Moon be to them ? Why was she commanded to stand still upon the Valley of Ajalon ? Besides , be pleased to consider , the Holy Land is but a very little Country or Province : The Valley of Ajalon is very near Gibeon , where Joshua spoke to both Sun and Moon together to stand still above , in Places so near each other , it is Demonstration , that the Moon was at that time very near the Sun ; and by Consequence was at that time either a day or two before her change , or a day or two at most after new Moon ; and then she is nearer to the Body of the Sun , as to appearance , so could not assist the Children of Israel with Light , having so little of her own : It was then for some other Reason that the Moon stood still ; and for some other Reason that it is taken notice of in Holy Scripture . Both Systems agree that the Moon is the nearest Planets to the Earth , and subservient to it , to enlighten it , during the Night , in Absence of the Sun. Besides this , the Moon has other strange Effects , not only on the Earth it self , but upon all the living Creatures that inhabit it ; many of them are invisible , and as yet unknown to Mankind ; some of them are most apparent ; and above all , her wonderful Influence over the ebbing and flowing of the Sea , at such regular Times and Seasons , if not interrupted by the Accident of some Storm , or great Wind. We know of no Relation or Corresponding between the Sun and the Moon , unless it be what is common with all the rest of the Planets , that the Moon receives her Light from the Sun , which she restores again by Reflection . If the Sun did move , according to the System of Ptolemy , where was the necessity of the Moon 's standing still ? For if the Moon had gone on her Course , where was the Loss or Disorder in Nature ? She having , as I demonstrated before , so little Light , being so very near her Change , would have recovered her Loss at the next Appearance of the Sun , and the Earth could have suffered nothing by the Accident ; whereas the Earth moving at the same time , in an Annual and Diurnal Course , according to the System of Copernicus , would have occasioned such a Disorder and Confusion in Nature , that nothing less than two or three new Miracles , all as great as the first , could have set the World in Order again : The regular Ebbings and Flowings of the Sea must have been interrupted , as also the Appearing of the Sun in the Horizon , besides many other Inconveniences in Nature ; as , the Eclipses of the Sun and Moon , which are now so regular , that an Astronomer could tell you to a Minute , what Eclipses will be for thousands of Years to come , both of Sun and Moon ; when , and in what Climates they will be visible , and how long they will last , how many Degrees and Digits of those two great Luminaries will be obscured . So that I doubt not but when this stupendious Miracle was performed by the Almighty and Infinite Power of God , his omnipotent Arm did in an Instant stop the Course of Nature , and the whole Frame of the Vniverse was at a stand , though the Sun and Moon be only named , being , to vulgar Appearance , the two great Luminaries that govern the Vniverse . This was the space of a Day in Time , yet can be called no part of Time , since Time and Nature are always in motion , and this Day was a stop of that Course . What is there in all this wonderful stop of Time , that is not as strong for the System of Copernicus , as for that of Ptolemy ? And why does my Belief of the Motion of the Earth , and the Rest of the Sun contradict the holy Scriptures ? Am not I as much obliged to believe that the Sun lodges in a Tabernacle ? ( as in Psal. 19. ) Are not all these Allegorical Sayings ? In the above-named Edition of the English Bible of Buck's at Cambridge , see Isa. 8.38 . where the Shadow returned ten Degrees backwards , as a Sign of King Hezekiah's Recovery , and there follow these Words , And the Sun returned ten Degrees ; but on the Margin you will find it from the Hebrew , The Shadow returned ten Degrees by the Sun ; and this is yet as much for Copernicus as Ptolemy . Whether God Almighty added ten Degrees or Hours to that Day , or by another kind of Miracle , made the Shadow to return upon the Dial of Ahaz , I will not presume to determine ; but still you see the Hebrew is most agreeable to the new System of Copernicus . Thus I hope I have performed my Vndertaking , in making it appear , that the holy Scriptures , in things that are not material to the Salvation of Mankind , do altogether condescend to the vulgar Capacity ; and that these two Texts of Psal. 19. and Josh. 10. are as much for Copernicus as against him . I hope none will think my Vndertaking too bold , in making so much use of the Scripture , on such an Occasion . I have a Precedent , much esteemed by all ingenious Men ; that is , Mr. Burnet's Book of Paradise , and Antedeluvian World , which incroaches as much , if not more , on the holy Scriptures . But I have another Reason for saying so much of the Scriptures at this time : We live in an Age , wherein many believe nothing contained in that holy Book , others turn it into Ridicule : Some use it only for Mischief , and as a Foundation and Ground for Rebellion : Some keep close to the Literal Sense , and others give the Word of God only that Meaning and Sense that pleases their own Humours , or suits best their present Purpose and Interest . As I quoted an Epistle of St. Jerome to Vitalis before , where that great Father says , that the Letter kills , but the Spirit enlivens ; I think it is the Duty of all good Christians to acquiesce in the Opinion and Decrees of the Church of Christ , in whom dwells the Spirit of God , which enlightens us to Matters of Religion and Faith ; and as to other things contained in the Holy Scriptures relating to Astronomy , Geometry , Chronology , or other liberal Sciences , we leave those Points to the Opinion of the Learned , who by comparing the several Copies , Translations , Versions , and Editions of the Bible , are best able to reconcile any apparent Differences ; and this with all Submission to the Canons of General Councils , and Decrees of the Church . For the School-men agitate and delate many things of a higher Nature , than the standing still , or the Motion of the Sun or the Earth . And therefore , I hope my Readers will be so just as to think , I intend no Reflection on Religion by this Essay ; which being no Matter of Faith , is free for every one to believe , or not believe , as they please . I have adventur'd to say nothing , but from good Authority : And as this is approved of by the World , I may hereafter venture to publish somewhat may be more useful to the Publick . I shall conclude therefore with some few Lines , as to my present Translation . I have laid the Scene at Paris , where the Original was writ ; and have translated the Book near the Words of the Author . I have made bold to correct a Fault of the French Copy , as to the heighth of our Air or Sphere of Activity of the Earth , which the French Copy makes twenty or thirty Leagues , I call it two or three , because sure this was a Fault of the Printer , and not a mistake of the Author . For Monsieur Des Cartes , and Monsieur Rohalt , both assert it to be but two or three Leagues . I thought Paris and St. Denis fitter to be made use of as Examples , to compare the Earth and the Moon to , than London and Greenwich ; because St. Denis having several Steeples and Walls , is more like Paris , than Greenwich is to London . Greenwich has no Walls , and but one very low Steeple , not to be seen from the Monument without a Prospective Glass . And I resolv'd either to give you the French Book into English , or to give you the subject quite changed and made my own ; but having neither health nor leisure for the last I offer you the first such as it is . The Author's PREFACE . I Find my self reduced almost to the same Condition in which Cicero was , when he undertook to put Matters of Philosophy into Latin ; which , till that time , had never been treated of , but in Greek . He tells us , it would be said , his Works would be unprofitable , since those who loved Philosophy , having already taken the pains to find it in the Greek , would neglect , after that , to read it again in Latin ( that not being the Original ; ) and that those who did not care for Philosophy , would not seek it , either in the Latin , or the Greek . But to this Cicero himself answers ; and says , That those who were not Philosophers would be tempted to the Reading of it , by the Facility they Would find in its being in the Latin Tongue ; and that those who were Philosophers would be curious enough to see how well it had been turned from the Greek to the Latin. Cicero had reason to answer in this manner ; the Excellency of his Genius , and the great Reputation he had already acquired sufficiently defend this new Undertaking of his , which he had dedicated to the benefit of the Publick . For my part , I am far from offering at any Defence for this of mine , though the Enterprize be the same ; for I would treat of Philosophy in a manner altogether unphilosophical , and have endeavoured to bring it to a Point not too rough and harsh for the Capacity of the Numbers , nor too light and trivial for the Learned . But if they should say to me as they did to Cicero , that this Work is not at all proper for the Learned , nor would it instruct the rest of the World , who are careless of Knowledge ; far be it from me to answer as Cicero did , who , perhaps , in searching for a middle way to Philosophy , such as would improve every Understanding , I have taken that which possibly will be advantageous to none : It is very hard to keep to a Medium , and I believe I shall scarce take the pains to search a second Method to please . And if it happen that this Book should be read , I advertise those that have some Knowledge in Philosophy , that I have not pretended to instruct , but to divert them , in presenting to them in a more agreeable manner , that which they already know solidly : And I also advertise those to whom this Subject is new , that I believe it will at once instruct and please them : The Knowing will act , contrary to my Intentions , if they seek only Profit ; and the rest , if they seek only Pleasure . I will not amuse my self in telling you , that I have taken out of Philosophy the matter the most capable of inspiring a Curiosity ; for in my Opinion , we ought to seek no greater Interest , than to know how this World which we inhabit , is made , and that there are other Worlds that resemble it , and that are inhabited as well as this : After all , let those that please , give themselves the trouble of finding out this Truth , but I am sure they will not do it in Complaisance to my Book : Those that have any Thoughts to lose , may cast them away here ; but all People are not in a Condition , you will say , to make such an unprofitable Expence of Time. In this Discourse I have introduced a fair Lady to be instructed in Philosophy , which , till now , never heard any speak of it ; imagining , by this Fiction , I shall render my Work more agreeable , and to encourage the fair Sex ( who lose so much time at their Toylets in a less charming Study ) by the Example of a Lady who had no supernatural Character , and who never goes beyond the Bounds of a Person who has no Tincture of Learning , and yet understands all that is told her , and retains all the Notions of Tourbillions and Worlds , without Confusion : And why should this imaginary Lady have the Precedency of all the rest of her delicate Sex ? Or do they believe they are not as capable of conceiving that which she learned with so much Facility ? The truth is , Madam the Marquiese applies her self to this Knowledge ; but what is this Application ? It is not to penetrate by force of Meditation , into a thing that is obscure in it self , or any thing that is obscurely explained ; 't is only to read , and to represent to your selves at the same time what you read , and to form some Image of it that may be clear and free from perplexing Difficulties . I ask of the Ladies ( for this System ) but the same Attention that they must give the Princess of Cleve , if they would follow the Intrigue , and find out the Beauties of it ; though the truth is , that the Idea's of this Book are not so familiar to the most part of Ladies , as those of the Princess of Cleve ; but they are not more obscure , than those of that Novel , and yet they need not think above twice at most , and they will be capable of taking a true Measure , and having a just Sense of the whole . I do not pretend to take a System in the Air , without a Foundation , but I have made use of true Philosophical Reasons ; and of those , employed as many as are necessary ; and , as it happily falls out , the Notions of Philosophy upon this Subject are pleasant ; and at the same time that they satisfie the Reason , they content the Imagination with a Prospect as agreeable , as if they had been made on purpose to entertain it . Where I found some pieces not altogether so diverting as I wish'd , I gave them Foreign Ornaments : Virgil made use of the same Method in his Georgicks , where he adorned his Subject ( of it self altogether dull ) with several Disgressions , and very often agreeably . Ovid himself has done as much in his Art of Loving , though the Foundation of his Theme was infinitely more agreeable than any thing that could be mixed with it ; therefore it is to be supposed , he imagined it would be tiresome , always to treat of one and the same thing , though it was of Gallantry : But for my part , I , who have much more need of the Assistance of Disgression , have , notwithstanding , made use of them very frugally : I have authorized them by the Liberty of natural Conversation , and have put them but in those places where I thought every body would be glad to find them ; I have put the greatest part of them in the beginning of my Work , because the Mind will not be then so well accustomed to the principal Idea's that I present . In fine , I have taken them from the Subject it self , or , at least , approaching to it . I would not have any Imagination of the Inhabitants of the Worlds that are entirely fabulous , but have endeavoured to relate only that which might be thought most reasonable ; and the Visions themselves that I have added , have something of a real Foundation in them ; the True and the False are here mixed , but they always are very easie to be distinguished ; yet I do not undertake to justifie a Composure so fantastical : This is the most important Point of this Work , and 't is this only that I cannot give a Reason for ; but the publick Censure will inform me , what I ought to think of this Design . There remains no more for me to say in this Preface , but to speak to one sort of People , who , perhaps , will be the most difficult to content ( and yet I have very good Reasons to give them , but , possibly , such as they will not take for current Pay , unless they appear to them to be good ; ) and these are the scrupulous Persons , who may imagine , that in regard of Religion , there may be danger in placing Inhabitants any where , but on this Earth ; but I have had a Respect , even to the most delicate Niceties of Religion , and would not be guilty of any thing that should shock it in a publick Work , though that Care were contrary to my Opinion . But that which will surprize you is , that Religion is not at all concerned in this System , where I fill an infinite number of Worlds with Inhabitants ; and you need only reform and clear one Error of the Imagination : But when I shall tell you the Moon is inhabited , you presently represent to your Fancy Men made as we are ; and if you are a little of the Theologician , you will then be presently full of Difficulties : The Posterity of Adam could not possibly extend to the Moon , nor send Colonies into that Country ; then they are not the Sons of Adam : And that would be a great perplexing Point in Theology , to imagine there should be Men , and those not to descend from Adam ; there is no need of saying any more , all the Difficulties are reduced to that , and the Arguments we ought to employ in a tedious Explanation , are too worthy of Gravity to be put into this Book , though perhaps I could answer solidly enough to their Objections , if I undertook it ; but 't is certain , I have no need of answering them ; let the Men in the Moon do it , who are only concern'd ; for 't is they that put the Men there , I only put Inhabitants , which , perhaps , are not Men. What are they then ? 'T is not that I have seen them , that I speak of them ; yet do not imagine that I design , ( by saying there are no Men in the Moon ) to evade your Objections , but you shall see , that 't is impossible ( according to the Idea's that I have of the infinite Diversity that Nature ought to use in her Works ) that there can be none . This Idea governs all the Book , and it cannot be confuted by any Philosopher ; therefore I believe I shall meet with no Objection from any , but those who speak of these Entertainments , without having read them . But is this Reason enough for me to depend on ? No , 't is rather a sufficient Reason for me to fear , that this Objection will be often urged in several places . TO Monsieur de L — SIR , YOV expect I shou'd give you an exact Account in what manner I pass'd my Time in the Country , at the Castle of Madam the Marquiese of — but I am afraid this Account will enlarge it self to a Volume , and that which is worse , to a Volume of Philosophy , while you , perhaps , expect to hear of Feasting , Parties at play , and Hunting-matches . No , Sir ; you will hear of nothing but Planets , Worlds and Tourbillions , nor has there been any other things discours'd on . Perhaps you are a Philosopher , and will not believe my Discourse , so ridiculous as it may appear to the less Learned ; and possibly , you will be glad to hear that I have drawn Madam the Marquiese into our Party : We cou'd not have made an Advantage more considerable , since I always esteem'd Youth and Beauty as things of great value . If Wisdom her self wou'd appear to Mankind , with a Design to be well received , she wou'd not do ill to assume the Form and Resemblance of Madam the Marquiese ; and cou'd she be so agreeable in her Conversation , I assure you , all the World wou'd run after her Precepts . You must not expect to hear Wonders , when I shall make you a Relation of the Discourse I had with this beautiful Lady ; and I ought to have as much Wit as her self , to repeat all she said in the same graceful manner she express'd it ; however , I hope to make you sensible of the Readiness of her Genius , in comprehending all things ; for my part , I esteem her perfectly witty , since she is so with the most Facility in the World. Perhaps you will be apt to say , that her Sex must needs be wanting in those Perfections which adorn ours , because they do not read so much . But what signifies the reading of so many vast Volumes over , since there are a great many Men who have made that the Business of their whole Lives , to whom , if I durst , I wou'd scarce allow the Knowledge of any thing ? As for the rest , you will be oblig'd to me . I know , before I begin to open the Conversation I had with Madam the Marquiese , I ought , of Course , to describe to you the Castle , whither she was retir'd , to pass the Autumn . People are apt , on such Occasions , to make very large Descriptions , but I 'll be more favourable to you . Let it suffice , that when I arriv'd there , I found no Company , which I was very glad of : The two first Days there pass'd nothing remarkable , but our Time was spent in discoursing of the News of Paris , from whence I came : After this , pass'd those Entertainments which , in the Sequel , I will impart to you . I will divide our Discourse therefore into Nights , because , indeed , we had none , but in the Nights . THE First Night . WE went one Evening after Supper to walk in the Park , the Air was cool and refreshing , which made us sufficient amends for the excessive heat of the Day , and of which I find I shall be obliged to make you a Description , which I cannot well avoid , the fineness of it leading me so necessarily to it . The Moon was about an hour high , which shining through the Boughs of the Trees , made a most agreeable Mixture , and checker'd the Paths beneath with a most resplendent white upon the green , which appeared to be black by that Light ; there was no Cloud to be seen that could hide from us , or obscure the smallest of the Stars , which lookt all like pure polisht Gold , whose Luster was extreamly heightened by the deep Azure Field on which they were placed : These pleasant Objects set me a thinking , and had it not been for Madam la Marquiese , I might have continued longer in that silent Contemplation ; but the Presence of a Person of her Wit and Beauty hindered me from giving up my Thoughts intirely to the Moon and Stars . Do not you believe , Madam , said I , that the clearness of this Night exceeds the Glory of the brightest day ? I confess , said she , the Day must yield to such a Night ; the day which resembles a fair Beauty , which though more sparkling , is not so charming as one of a brown Complexion , who is a true Emblem of the Night . You are very generous , Madam , said I , to give the advantage to the brown , you who are so admirably fair your self : Yet without dispute , day is the most beautiful thing in Nature ; and most of the Heroines in Romances , which are modelled after the most perfect Idea fancy can represent by the most ingenious of mankind , are generally described to be fair . But , said she , Beauty is insipid , if it want the pleasure and power of charming ; and you must acknowledge that the brightest day that ever you saw could never have engaged you in so agreeable an Ecstasie , as you were just now like to have faln into by the powerful attractions of this Night . I agree to what you say , Madam , said I , but I must own at the same time , that a Beauty of your complexion would give me another sort of transport than the finest Night with all the advantages obscurity can give it . Though that were true , said she , I should not be satisfied ; since those fair Beauties that so resemble the day , produce not those soft Effects of the other . How comes it , that Lovers who are the best Judges of what is pleasing and touching , do always address themselves to the Night , in all their Songs and Elegies ? I told her , that they most certainly paid their acknowledgments to the Night ; for she was ever most favourable to all their Designs . But , Sir , replied the Marquiese , she receives also all their Complaints , as a true Confident of all their Entrigues ; from whence proceeds that ? The silence and gloom of the Night , said I , inspires the restless Sigher with thoughts very passionate and languishing , which the busier day diverts a thousand little ways ( though one would think the Night should charm all things to repose ) and though the day affords Solitudes , dark Recesses , Groves and Grottoes , equally obscure and silent as the Night it self ; yet we fansy that the Stars move with a more silent motion than the Sun , and that all the Objects which the Heavens represent to our view , are softer , and stay our sight more easily ; and flattering our selves that we are the only Persons at that time awake , we are vain enough to give a loose to a thousand thoughts extravagant and easing . Besides , the Scene of the Universe by day-light appears too Uniform , we beholding but one Great Luminary in an Arched Vault of Azure , of a Vast Extent , while all the Stars appear confusedly dispersed , and disposed as it were by chance in a thousand different Figures , which assists our roving Fancies to fall agreeably into silent thoughts . Sir , replied Madam la Marqueise , I have always felt those effects of Night you tell me of , I love the Stars , and could be heartily angry with the Sun for taking them from my sight . Ah , cry'd I , I cannot forgive his taking from me the sight of all those Worlds that are there . Worlds , said she , what Worlds ? And looking earnestly upon me , asked me again , what I meant ? I ask your Pardon , Madam , said I , I was insensibly led to this fond discovery of my weakness . What weakness , said she , more earnestly than before ? Alass , said I , I am sorry that I must confess I have imagined to my self , that every Star may perchance be another World , yet I would not swear that it is so ; but I will believe it to be true , because that Opinion is so pleasant to me , and gives me very diverting Idea's , which have fixed themselves delightfully in my Imaginations , and 't is necessary that even solid Truth should have its agreeableness . Well , said she , since your Folly is so pleasing to you , give me a share of it ; I will believe whatever you please concerning the Stars , if I find it pleasant . Ah , Madam , said I , hastily , it is not such a Pleasure as you find in one of Mullier's Plays ; it is a Pleasure that is — I know not where , in our Reason , and which only transports the Mind . What , replied she , do you think me then incapable of all those Pleasures which entertain our Reason , and only treat the Mind ? I will instantly shew you the contrary , at least as soon as you have told me what you know of your Stars . Ah , Madam , cry'd I , I shall never indure to be reproach'd with that neglect of my own happiness , that in a Grove at ten a Clock of the Night , I talk'd of nothing but Philosophy , to the greatest Beauty in the World ; no , Madam , search for Philosophy some where else . But 't was in vain to put her off by Excuses , from a Novelty she was already but too much prepossest with : There was a necessity of yielding , and all I could do was to prevail with her to be secret , for the saving my Honour ; but when I found my self engaged past retreat , and had a design to speak , I knew not where to begin my discourse , for to prove to her ( who understood nothing of Natural Philosophy ) that the Earth was a Planet , and all the other Planets so many Earths , and all the Stars Worlds , it was necessary for the explaining my self , to bring my Arguments a great way off ; and therefore I still endeavoured to perswade her that 't was much better to pass the time in another manner of Conversation , which the most reasonable People in our Circumstances would do ; but I pleaded to no Purpose , and at last to satisfie her , and give her a general Idea of Philosophy , I made use of this way of arguing . All Philosophy is grounded on two Principles , that of a passionate thirst of knowledge of the Mind , and the weakness of the Organs of the Body ; for if the Eye-sight were in perfection , you could as easily discern there were Worlds in the Stars , as that there are Stars : On the other hand , if you were less curious and desirous of knowledge , you would be indifferent , whether it were so or not , which indeed comes all to the same purpose ; but we would gladly know more than we see , and there 's the difficulty : for if we could see well and truly what we see , we should know enough ; but we see most Objects quite otherwise than they are ; so that the true Philosophers spend their time in not believing what they see , and in endeavouring to guess at the knowledge of what they see not ; and in my Opinion this kind of life is not much to be envied ; but I fansy still to my self that Nature is a great Scene , or Representation , much like one of our Opera's ; for , from the place where you sit to behold the Opera , you do not see the Stage , as really it is , Since every thing is disposed there for the representing agreeable Objects to your sight , from a large distance , while the wheels & weights , which move and counterpoise the Machines are all concealed from our view ; nor do we trouble our selves so much to find out how all those Motions that we see there , are performed ; and it may be among so vast a number of Spectators , there is not above one Enginier in the whole Pit , that troubles himself with the consideration how those flights are managed that seem so new and so extraordinary to him , and who resolves at any rate to find out the contrivance of them ; You cannot but guess , Madam , that this Enginier is not unlike a Philosopher ; but that which makes the difficulty incomparably greater to Philosophers , is , that the Ropes , Pullies , Wheels and Weights , which give motion to the different Scenes represented to us by Nature , are so well hid both from our sight and understanding , that it was a long time before mankind could so much as guess at the Causes that moved the vast Frame of the Universe . Pray , Madam , imagine to your self , the Ancient Philosophers beholding one of our Opera's , such an one as Pythagoras , Plato , Aristotle , and many more , whose Names and Reputations make so great a noise in the World ; and suppose they were to behold the flying of Phaeton , who is carried aloft by the Winds , and that they could not discern the Ropes and Pullies , but were altogether ignorant of the contrivance of the Machine behind the Scenes , one of them would be apt to say — It is a certain Secret Virtue that carries up Phaeton . Another , That Phaeton is composed of certain Numbers , which make him mount upwards . The third — That Phaeton has a certain kindness for the highest Part of the Theatre , and is uneasie when he is not there . And a fourth — That Phaeton was not made for flying , but that he had rather fly , than leave the upper part of the Stage void : Besides a hundred other Notions , which I wonder have not intirely ruined the Reputation of the Ancients . In our Age Des Cartes , and some other Moderns would say — That Phaetons 's flight upward is because he is hoisted by Ropes , and that while he ascends , a greater weight than he descends . And now men do not believe that any corporeal being moves it self , unless it be set on Motion , or pusht by another Body , or drawn by Ropes ; nor that any heavy thing ascends or descends , without a counter-poise equal with it in weight to balance it ; or that 't is guided by Springs . And could we see Nature as it is , we should see nothing but the hinder part of the Theatre at the Opera . By what you say , said Madam la Marquiese , Philosophy is become very Mechanical . So very Mechanical , said I , that I am afraid men will quickly be ashamed of it ; for some would have the Universe no other thing in Greeat , than a Watch is in Little ; and that all things in it are ordered by Regular Motion , which depends upon the just and equal disposal of its Parts ; Confess the Truth , Madam , have not you had heretofore a more sublime Idea of the Universe , and have not you honoured it with a better Opinion than it deserved ? I have known several esteem it less since they believed they knew it better ; and for my part , said she , I esteem it more since I knew it is so like a Watch : And 't is most surprising to me , that the course and order of Nature , how ever admirable it appears to be , moves upon Principles and Things that are so very easie and simple . I know not , replied I , who has given you so just Idea's of it , but 't is not ordinary to have such ; most People retain in their minds some false Principle or other of Admiration , wraped up in obscurity , which they adore : They admire Nature , only because they look on it as a kind of Miracle , which they do not understand ; and 't is certain that those sort of People never despise any thing , but from the moment they begin to understand it : But , Madam , I find you so well disposed to comprehend all I have to say to you , that without further Preface , I need only draw the Curtain , and shew you the World. From the Earth where we are , that which we see at the greatest distance from us , is that Azure Heaven , or that vast Vault , where the Stars are placed as so many Golden Nails , which are called fixt , because they seem to have no other motion , but that of their proper Sphere , which carries them along with it , from East to West ; between the Earth and the last , or lowest Heaven ▪ are hung at different heights , the Sun , the Moon , and five other Stars , which are called Planets , Mercury , Venus , Mars , Iupiter , and Saturn . These Planets not being fixt to any one Sphere , and having unequal Motions , they are in different Aspects , one to another , and according as they are in conjunction , or at distance , they make different Figures ; whereas the fixt Stars are always in the same Position , one towards another : As for Example , Charles's - Wain , or the Constellation of the Great Bear , which you see , and which consists of Seven Stars , has always been , and will still continue the same ; but the Moon is sometimes near the Sun , and sometimes at a great distance from it , and so through all the rest of the Planets : It was in this manner that the Celestial Bodies appeared to the Ancient Chaldean Shepherds , whose great leisure produced these first Observations , which have since been so well improved ; and upon which all Astronomy is founded : For Astronomy had its beginning in Chaldea , as Geometry , was invented in Egypt , where the inundations of the River Nile , having confounded and removed the Limits and the Land-marks of the several Possessions of the Inhabitants , did prompt them to find out sure and exact Measures , by which every one might know his own Field from that of his Neighbours : So that Astronomy is the Daughter of Idleness , Geometry is the Child of Interest ; and should we inquire into the Original of Poetry , we should in all appearance find , that it owes its beginning to Love. I am extreamly glad , said the Marquiese , that I have learned the Genealogy of the Sciences , and I find that I must content my self with Astronomy , Geometry , according to what you have said , requiring a Soul more interested in worldly Concerns , than I am , and for Poetry , 't is most proper for those of a more Amorous Inclination ; but I have all the leisure and time to spare that Astronomy requires : Besides that I live now happily retired in the Fields and Groves , and lead a sort of Pastoral Life , so very agreeable to Astronomy . Do not deceive your self , Madam , said I ; 't is not a true Pastoral Life , to talk of Planets and fix'd Stars : Be pleased to consider , that the Shepherds in the Story of Astroea did not pass their time in that kind of divertisement ; they had business of a softer , and more agreeable Nature . Oh , said she , the Life of the Pastorals of Astraea is too dangerous : I like that of the Chaldean Shepherds better , of whom you spoke but now : Go on with them , for I will hear nothing from you , but Chaldean : So soon as that Order , and these Motions of the Heavens were discovered , what was the next thing to be considered ? The next thing , said I , was , to guess how the several parts of the Universe were to be disposed and ranged in order ; and that is what the Learned call , The making a System : But before , Madam , I explain to you the first System , be pleased to observe , that we are all naturally made like a certain Athenian Fool , of whom you have heard ; who fansied that all the Ships that came into the Port of Piraa , belonged to him ; for we are so vain as to believe , that all this vast Frame of Nature was destined to our use : For if a Philosopher be asked , for what all this prodigious number of fixed Stars serve ( since a very few would supply the business of the whole ) he will tell you gravely , that they were made to please our sight . Upon this Principle , at first , Man believed , that the Earth was immoveably fixed in the Centre of the Universe , whilst all the Celestial Bodies ( made only for her ) were at the pains of turning continually round , to give Light to the Earth : And that it was therefore above the Earth , they placed the Moon ; above the Moon , Mercury ; then Venus , the Sun , Mars , Iupiter , Saturn ; and above all , the Sphere of the fixed Stars : The Earth , according to this Opinion , was just in the middle of the several Circles , described by the Planets ; and the greater these Circles were , the further they were distant from the Earth ; and by consequence , they took a longer time in compleating their round ; which is certainly true . I know not , said the Marquiese , why you should not approve of this Order of the Universe , which seems to be so clear and intelligible ; for my part , I am extreamly pleased and satisfied with it . Madam , said I , without Vanity , I have very much softned and explained this System : Should I expose it to you such as it was first invented by its Author Ptolemy , or by those that have followed his Principles , it would frighten you : The motion of the Planets being irregular , they move sometimes fast , sometimes slow ; sometimes towards one side , sometimes to another ; at one time near the Earth , at another far from it . The Ancients did imagine I know not how many Circles , differently interwoven one with another ; by which they fansy'd to themselves , they understood all the irregular Phaenomena's , or Appearances in Nature . And the Confusion of these Circles was so great , that at that time , when men knew no better , a King of Arragon , a great Mathematician ( not over devout ) said , That if God had call'd him to his Council when he form'd the Vniverse , he could have given him good Advice . The thought was impious , yet 't is odd to reflect , that the confusion of Ptolemy's System gave an occasion for the sin of that King : The good Advice he would have given , was , no doubt , for surpassing these different Circles , which had so embarrass'd the Celestial Motions ; and , it may be also , with regard to the two or three superfluous Spheres , which they had plac'd above the fixed Stars . The Philosophers , to explain one kind of motion of the heavenly Bodies , did fansie a Sphere of Christal above that Heaven which we see , which set the inferior Heaven on motion ; and if any one made a new discovery of any other Motion , they immediately made a new Sphere of Christal : in short , these Christalline Heavens cost them nothing . But why Spheres of Christal , said Madam la Marquiese ? Would no other Substance serve ? No , said I , Madam ; for there was a necessity of their being transparent , that the Light might penetrate ; as it was requisite for them to be solid Beams . Aristotle had found out , that Solidity was inherent in the Excellency of their Nature ; and because he said it , no body would adventure to question the truth of it . But there have appear'd Comets , which we know to have been vastly higher from the Earth , than was believed by the Ancients : These , in their course , wou'd have broke all those Christal Spheres ; and indeed , must have ruined the Universe : So that there was an absolute necessity to believe the Heavens to be made of a fluid substance ; at least , 't is not to be doubted , from the observation of this , and the last Age , that Venus and Mercury move round the Sun , and not round the Earth . So that the ancient System is not to be defended , as to this particular : But I will propose one to you , which solves all Objections , and which will put the King of Arragon out of a condition of advising ; and which is so surprisingly simple and easie , that that good quality alone ought to make it preferrable to all others . Methinks , said Madam la Marquiese , that your Philosophy is a kind of Sale ▪ or Farm , where those that offer to do the Affair at the smallest Expence , are preferr'd . 'T is very true , said I ; and 't is only by that , that we are able to guess at the Scheme , upon which Nature hath fram'd her Work : She is very saving , and will take the shortest and cheapest way : Yet notwithstanding , this Frugality is accompany'd with a most surprising Magnificence , which shines in all she has done ; but the Magnificence is in the Design , and the Oeconomy in the Execution : And indeed , there is nothing finer than a great Design , carried on with a little Expence . But we are very apt to overturn all these Operations of Nature , by contrary Idea's : We put Oeconomy in the Design , and Magnificence in the Execution : We give her a little Design , which we make her perform with ten times a greater Charge than is needful . I shall be very glad , said she , that this System , you are to speak of , will imitate Nature so exactly ; for this good Husbandry will turn to the advantage of my Understanding , since by it I shall have less trouble to comprehend what you have to say . There is in this System no more unnecessary difficulties . Know then , that a certain German , named Copernicus , does at one blow cut off all these different Circles , and Christalline Spheres , invented by the Ancients ; destroying the one , and breaks the other in pieces ; and being inspir'd with a Noble Astronomical Fury , takes the Earth , and hangs it at a vast distance from the Centre of the World , and sets the Sun in its place , to whom that Honour does more properly belong ; the Planets do no longer turn round the Earth , nor do they any longer contain it in the Circle they describe ; and if they enlighten us , it is by chance , and because they find us in their way : All things now turn round the Sun ; among which , the Globe it self , to punish it for the long Rest , so falsly attributed to it before ; and Copernicus has loaded the Earth with all those Motions , formerly attributed to the other Planets ; having left this little Globe none of all the Celestial Train , save only the Moon , whose natural Course it is , to turn round the Earth . Soft and fair , said Madam la Marquiese ; you are in so great a Rapture , and express your self with so much Pomp and Eloquence , I hardly understand what you mean : You place the Sun unmoveable in the Centre of the Universe ; Pray , what follows next ? Mercury , said I , who turns round the Sun ; so that the Sun is in the Centre of the Circle he describes : And above Mercury , Venus ; who turns also round the Sun : Next comes the Earth ; which being more elivated than Mercury , or Venus , describes a Circle of a greater Circumference that those two Planets : Last , come Mars , Iupiter and Saturn , in their order , as I have nam'd 'em : So that you see easily , that Saturn ought to make the greatest Circle round the Sun ; it is therefore that Saturn takes more time to make his Revolution , than any other Planet . Ah , but , said the Marquiese , interrupting me , you forget the Moon . Do not fear , said I , Madam ; I shall soon find her again . The Moon turns round the Earth , and never leaves it ; and as the Earth moves in the Circle it describes round the Sun , the Moon follows the Earth in turning round it ; and if the Moon do move round the Sun , it is only because she will not abandon the Earth . I understand you , said she : I love the Moon for staying with us , when all the other Planets have left us ; and you must confess , that your German Copernicus would have taken her from us too , had it been in his power ; for I perceive by his procedure , he had no great kindness for the Earth . I am extreamly pleas'd with him , said I , for having humbled the Vanity of mankind , who had usurp'd the first and best Situation in the Universe ; and I am glad to see the Earth under the same Circumstances with the other Planets . That 's very fine , said the Marquiese : Do you believe that the Vanity of Man places it self in Astronomy ; or that I am any way humbled , because you tell me the Earth turns round the Sun ? I 'll swear , I do not esteem my self one whit the less . Good Lord , Madam , said I , Do you think I can imagine you can be as zealous for a Precedency in the Universe , as you would be for that in a Chamber ? No , Madam ; the Rank of Place between two Planets will never make such a bustle in the World , as that of two Ambassadors : Nevertheless , the same inclination that makes us endeavour to have the first place in a Ceremony , prevails with a Philosopher in composing his System , to place himself in the Centre of the World , if he can : He is proud to fansie all things made for himself ; and without reflexion , flatters his Senses with this Opinion , which consists purely in Speculation . Oh , said the Marquiese , this is a Calumny of your own invention against mankind , which ought never to have received Copernicus his Opinion , since so easie , and so humble . Copernicus , said I , Madam , himself was the most diffident of his own System ; so that it was a long time before he would venture to publish it , and at last resolv'd to do it at the earnest intreaty of People of the first Quality . But do you know what he did , the Day they brought him the first printed Copy of his Book ? That he might not be troubled to answer all the Objections and Contradictions he was sure to meet with , he wisely left the World , and died . Hold , said the Marquiese , we ought to do Justice to all the World ; and 't is most certain , 't is very hard to believe we turn round , since we do not change places , and that we find our selves in the Morning , where we lay down the Night before . I see very well by your Looks , what 't is you are going to say ; That since the Earth moves all together — Most certainly , said I : 'T is the same thing as if you were asleep in a Boat , sailing on a River , you would find your self in the same place in the Morning , and in the same Situation as to the several parts of the Boat. True , said she , but with this difference ; I shou'd at my waking , find another Shoar ; and that would convince me , my Boat had chang'd its Situation : But 't is not the same with the Earth ; for there I find every thing as I left it the Night before . Not at all , Madam , said I ; the Earth changes the Shoar , as well as your Boat. You know , Madam , that above and beyond all the Circles , described by the Planets , is the Sphere of the fixed Stars ; that 's our Shoar : I am on the Earth , which makes a great Circle round the Sun ; I look towards the Centre of this Circle , there I see the Sun ; if the brightness of his Rays did not remove the Stars from my sight , by looking in a streight Line , I shoud easily perceive the Sun corresponding to some fixed Star beyond him ; but in the Night-time , I see clearly the Stars , to which the Sun did answer , or was opposite to , the Day before ; which is , indeed , the same thing . If the Earth were immoveable , and did not alter its Situation in its own Circle , I shou'd always see the Sun opposite to the same fixed Stars ; but I see the Sun in different Opposition to the Stars , every Day of the Year : It most necessarily follows then , the Circle changes its Situation , that is , the Shoar , round which we go daily : And as the Earth performs its Revolution in a Year , I see the Sun , in that space of time , answer in direct Opposition to a whole Circle of fixed Stars ; this Circle is called the Zodiack : Will you please , Madam , that I trace the Figure of it on the Sand ? By no means , said she ; I can satisfie my self , without that Demonstration : Besides that , it would give a certain Mathematical Air to my Park , which I do not like . Have not I heard of a certain Philosopher , who being shipwreck'd , and cast upon an unknown Island ; who seeing some Mathematical Propositions drawn on the Sea-sands , called to one of those with him , and cry'd , Courage , my Friend , here are the Foot-steps of Men ; this Country is inhabited ? You know , it is not decent in me to make such Foot-steps , nor must they be seen in this place . 'T is fit , continued I , Madam , that nothing be seen here , but Steps of Lovers ; that is to say , your Name and Cypher engraven on the Bark of Trees by the hand of your Adorers . Pray , Sir , said she , let Adorers alone , and let us speak of the Sun. I understand very well , how we imagine he describes that Circle , which , indeed , we our selves describe ; but this requires a whole Year's time , when one wou'd think the Sun passes over our heads every day : How comes that to pass ? Have you not observ'd , said I , that a Bowl thrown on the Earth , has two different Motions ; it runs toward the Jack , to which it is thrown ; and at the same time it turns over and over several times , before it comes that Length ; so that you will see the Mark that is on the Bowl , sometimes above , and sometimes below : 'T is just so with the Earth ; in the time it advances on the Circle it makes round the Sun , in its yearly Course , it turns over once every four and twenty Hours , upon its own Axis ; so that in that space of time , which is one natural Day , every point of the Earth ( which is not near the South or North-Poles ) loses and recovers the sight of the Sun : And as we turn towards the Sun , we imagine the Sun is rising upon us ; so when we turn from it , we believe she is setting . This is very pleasant , said the Marquiese : You make the Circle to do all , and the Sun to stand idle ; and when we see the Moon , Planets and fixed Stars turn round us in four and twenty Hours , all is but bare Imagination . Nothing else , said I , but pure Fancy , which proceeds from the same Cause ; only the Planets make their Circle round the Sun , not in the same space of time , but according to their unequal distance from it ; and that Planet which we see to day , look to a certain Point of the Zodiack , or Sphere of fixed Stars , we shall see it answer to every other Point to Morrow ; y as well because that Planet moves on its Course , as that we proceed in ours : We move , and so do the other Planets : By this means we vary both Situation and Opposition , as to them , and we think we discover Irregularities in their Revolutions , which I will not now trouble you with ; 't is sufficient for you to know , that any thing that may appear to us to be irregular , in the Course of the Planets , is occasion'd by our own Motion meeting theirs in such different manners ; but upon the whole the Course of the Planets , is most regular . I agree with all my heart , said the Marquiese ; yet I wish with all my heart , that that Regularity were not so laborious to the Earth : I fansie Copernicus has not been very careful of its Concerns , in making so weighty and solid a Mass run about so nimbly . But , Madam , said I , wou'd you rather , that the Sun , and the Stars ( which are generally far greater Bodies ) shou'd make a vast Circumference round the Earth in a Day , and run an infinite number of Leagues in twenty four Hours time ? Which they must of necessity do , if the Earth have not that Diurnal Motion on its own Axis . Oh! answered she , the Sun and Stars are all Fire , swiftness of Motion is easie to them ; but for the Earth , that does not seem to be very portable . And wou'd you believe it , said I , Madam , if you had never seen the Experiment , that a First-Rate Ship , of a hundred and twenty Guns , with fifteen hundred Men , and proportionable Provision , with all her Ammunition and Tackle a-board , were a very portable thing ? Notwithstanding , a gentle Breeze will move this Ship on the Sea , because the Water is liquid , and yielding easily , makes no resistance to the motion of the Vessel : So the Earth , notwithstanding of as vast bulk and weight , is easily mov'd in the Celestial Matter , which is a thousand times more fluid than the Water of the Sea ; and which fills all that vast Extent , where the Planets swim , as it were : And to what wou'd you fix or grapple the Earth , to hinder it from being carry'd along with the Current of this Celestial Matter or Substance ? It wou'd be just as if a little wooden Ball shou'd not follow the Current of a rapid River . But , said she , how does the Earth support its vast weight , on your Heavenly Substance , which ought to be very light , since it is so fluid ? That does not follow , answered I , Madam , that a thing must be light , because it is fluid : What say you to the First-Rate Ship , I spoke of , with all its Lading ? Yet 't is lighter than the Water , because it swims upon it . As long as you command your First-Rate Frigat , said she , angrily , I will not argue with you ; but can you assure me , that I am in no danger , by inhabiting such a little Humming-Top , as you have made the World to be ? Well , Madam , said I , the Earth shall be supported by four Elephants , as the Indians fansie it is . Here 's a new System indeed , cry'd Madam la Marquiese ; yet I love those Men , for providing for their own security , by resting upon a solid Foundation ; whereas we that follow Copernicus , are so inconsiderate , as to swim at a venture upon your Celestial Matter : And I dare say , if these Indians thought the Earth in any danger of falling , they wou'd quickly double the number of their Elephants . They wou'd have all the reason in the World to do so , said I , Madam ; ( laughing at her fancy ; ) and wou'd not spare Elephants to sleep in quiet , without fear of falling : And , Madam , we will add as many as you please to our System for this Night , and take them away by degrees , as you get more Assurance . Really , said she , I do not think they are needful at present ; for I feel I have Courage sufficient to turn round . You must go a step further , said I , and you shall turn round with delight ; upon this System you will form to your self very pleasant and agreeable Idea's : As for Example ; Sometimes I fansie I am hanging in the Air , and that I stay there without moving , while the Earth turns round under me in four and twenty Hours time , and that I see beneath me all those different Faces ; some white , some black , some tawny , others of an Olive-colour ; first I see Hats , then Turbants , there Hands cover'd with Wool , there shav'd Heads ; sometimes Towns with Steeples , some with their long small-pointed Pyramids , and Half-moons on their tops ; sometimes Towns with Porcelane Towers ; after them , spacious Fields , without Towns , only Tents and Huts ; here vast Seas , frightful Desarts ; in short , all the Variety that is to be seen upon the Face of the Earth . Indeed , said she , such a sight wou'd be very well worth twenty four Hours of ones Time : So that by this System , through the same place where we now are ( I do not mean this Park , but that space of Air which our Bodies fill ) several other Nations must successively pass , and we return hither , in twenty four hours , to our own place again . Copernicus himself , said I , Madam , did not understand it better . At first will be here the English , discoursing , it may be , upon some politick Design , with more Gravity , but less Pleasure , than we talk of our Philosophy : Next will come a vast Ocean , in which there will be sailing some Ships , perhaps not so much at their Ease as we are : Then will appear the Canibals , eating some Prisoners of War alive , they seeming very unconcern'd at what they suffer : After them , the Women of the Country of Iesso , who spend all their time in preparing their Husbands Meals , and in painting their Lips and Eye-brows with Blew , to please the ugliest Fellows in the World : Next will succeed the Tartars , who go , with great Devotion , on Pilgrimage to that great Priest , who never comes out of an obscure place , where he has no other Light but Lamps , by which they adore him : After them , the beautiful Circassian Women , who make no difficulty of granting any Favour to the first Comer , except what they essential know does belong to their Husbands : Then the Crim , or Little Tartars , who live by stealing of Wives for the Turks and Persians : And at last , our selves again , perhaps talking as we do now . I am mightily taken , said the Marquiese , with the Fancy of what you say ; but if I cou'd see all these things from above , I wou'd wish to have the power to hasten and stop the Motion of the Earth , according as I lik'd or dis-lik'd the several Objects that pass under me ; I wou'd make the Polititians , and those that eat their Enemies , to move very fast : But there are others that I shou'd be very curious to observe ; and particularly , the fine Cercassian Women , who have one so peculiar a Custom . That is , said I , their Husbands , who finding so many Charms in their Embraces , as more than satisfie them , do freely abandon their fair Wives to Strangers . The Women of our Country , said the Marquiese , must be very ugly , if compar'd to the Circassians ; for our Husbands will part with nothing . That is the reason , said I , that the more is taken from 'em ; whereas — No more of these Fooleries , said the Marquiese , interrupting me ; there 's a serious Difficulty come into my head : If the Earth turn round , then we change Air every Moment , and must breath still that of another Country . By no means , Madam , said I ; the Air which encompasses the Earth extends it self to a certain heighth , it may be , about twenty Leagues , and turns round with us . You have , no doubt , seen a thousand times the business of the Silk-worm , where the Balls which these little Creatures do work with so much Art , for their own Imprisonment , are compact , and wrought together with Silk , which is very closely join'd ; but they are cover'd with a kind of Down , that is very light and soft : Thus it is , that the Earth , which is very solid , is wrapp'd in a Covering of soft Down of twenty Leagues thickness , which is the Air that is carried round at the same time with it : Above the Air is that Celestial Matter I spoke of , incomparably more pure , more subtile , and more agitated than the Air. You represent the Earth to me , said the Marquiese , as a very contemptible thing , by the despicable Idea's you give me of it : 'T is , nevertheless , upon this Silk-Worm-Ball , there are perform'd such mighty Works ; and where there are such terrible Wars , and such strange Commotions as reign every where . 'T is certainly true , said I , Madam ; while at the same time , Nature , who is not at the pains to consider these Troubles and Commotions , carries us all along together , by a general Motion , and does , as it were , play with this little Globe . It seems to me , said she , that 't is very ridiculous to inhabit any thing that turns so often , and is so much agitated ; and the worst of all is , that we are not assur'd whether we turn round , or not ; for , to be plain with you , and that I may keep none of my Doubts from you , I do extreamly suspect , that all the Pre-cautions you can take , will not convince me of the Motion of the Earth : For is it possible , but Nature wou'd have taken care to have given us some sensible Sign , by which we might discover the turning round of so vast a Body ? The Motions ( answer'd I ) which are most natural to remove , are the least perceptible ; and which holds true , even in Morality ; for the Motion of Self-love is so natural to us , that for the most part we do not feel it , while we believe we act by other Principles . Ah , said she , do you begin to speak of Moral Philosophy , when the Question is of that which is altogether natural ? But I perceive you are sleepy , and begin to yawn ; let us therefore retire , for there 's enough said for the first Night , to morrow we shall return hither again ; you with your Systems , and I with my Ignorance . In returning to the Castle , to make an end of what might be said to Systems , I told her , there was a third Opinion invented by Ticho-brahe , who wou'd have the Earth absolutely immoveable , and plac'd in the Centre of the Universe , and made the Sun to turn round it , as he did the other Planets to turn round the Sun ; because , since the new Discoveries , it cou'd not be imagin'd that the other Planets turn'd round the Earth . But my Lady Marquiese , whose Judgment and Understanding is solid and penetrating , found , there was too much Affectation in endeavouring to free the Earth from turning round the Sun , since several other great Bodies cou'd not be exempt from that Labour ; and that the Sun was not so proper and fit to turn round the Earth , since the other Planets turn round the Sun ; and that this new System was only good to maintain the standing still of the Earth , if one had a mind to undertake that Argument ; but 't is not proper to perswade another to believe it . At last , we resolv'd to hold our selves to the Opinion of Copernicus , which is more uniform , and more agreeable , without the least mixture of Prejudice ; and , indeed , its Simplicity and Easiness perswades as much as its Boldness pleases . The Second Night . AS soon as one could get into my Lady Marquiese's Apartment , I sent to know how she did , and how she had slept that Night in turning round . She sent me word , that now she was pretty well accustom'd to the Motion of the Earth , and that Copernicus himself cou'd not have rested better that Night than she did . A little after this , there came Company to visit my Lady , which , according to the nauseous Country-fashion , stay'd till the Evening , and yet we thought our selves happy that we were so easily rid of 'em then , since , according to the custom of the Country , they might have prolong'd their Visit till the next Day ; but they were so civil , as not to do it ; so that Madam the Marquiese and I found our selves at liberty . In the Evening we went again to the Park , and the Conversation began as it ended before , of our System : My Lady Marquiese had comprehended 'em so well , that she wou'd not be at the pains to re-assume any thing of what had pass'd , but press'd me to lead her to something that was new . Well , said I , since the Sun , which is now immoveable , and no longer a Planet ; and that the Earth , that moves round the Sun , is now one , be not surpriz'd if I tell you , the Moon is another Earth , and is , by all appearance , inhabited . Said she , I never heard of the Moon 's being inhabited , but as a Fable . So it may be still , said I ; I concern my self no further in these Matters , than Men use to do in Civil Wars ; where the Uncertainty of what may be , makes People still entertain a Correspondence with the adverse Party : As for me , tho' I see the Moon inhabited , I live very civilly with those that do not believe it ; and I carry my self so trimmingly , that I may , upon occasion , with Honour go over to their side who have the better ; but still they gain some considerable Advantage over us . I 'll tell you my Reasons that make me take part with the Inhabitants of the Moon : Suppose then , there had never been any Commerce between Paris and St. Denis , and that a Citizen of Paris , who had never been out of that City , shou'd go up to the top of the Steeple of our Lady , and shou'd view St. Denis at a distance , and one shou'd ask him if he believ'd St. Denis to be inhabited ; he wou'd answer boldly , Not at all ; for ( he wou'd say ) I see the Inhabitants of Paris , but I do not see those of St. Denis , nor ever heard of ' em . It may be , some body standing by , wou'd represent to him , That it was true , one cou'd not see the Inhabitants of St. Denis from our Lady's Church , but that the distance was the cause of it ; yet that all we cou'd see of St. Denis , was very like to Paris ; for St. Denis had Steeples , Houses and Walls ; and that it might resemble Paris in every thing else , and be inhabited as well as it . All these Arguments wou'd not prevail upon my Citizen ; who wou'd continue still obstinate in maintaining , that St. Denis was not inhabited , because he saw none of the People . The Moon is our St. Denis , and we the Citizens of Paris , that never went out of our own Town . Ah , interrupted the Marquiese , you do us wrong ; we are not so foolish as your Citizens of Paris : Since he sees that St. Denis is so like to Paris in every thing , he must have lost his Reason , if he did not think it was inhabited : But for the Moon , that 's nothing like the Earth . Have a care , Madam , said I , what you say ; for if I make it appear , that the Moon is in every thing like the Earth , you are oblig'd to believe that the Moon is inhabited . I acknowledge , said she , if you do that , I must yield ; and your Looks are so assur'd , that you frighten me already : The two different Motions of the Earth , which wou'd never have enter'd into my Thoughts , make me very apprehensive of all you say . But is it possible that the Earth can be an enlighten'd Body , as the Moon is ? For , to resemble it , it must be so . Alas , Madam , said I , to be enlightned , is not so great a matter as you imagine , and the Sun only is remarkable for that Quality : 't is he alone that is enlightned of himself , by virtue of his particular Essence ; but the other Planets shine only , as being enlightned by the Sun : The Sun communicates his Light to the Moon , which reflects it upon the Earth ; as the Earth , without doubt , reflects it back again to the Moon , since the distance from the Moon to the Earth is the same as from the Earth to the Moon . But , said the Marquiese , is the Earth as proper for reflecting the Light of the Sun , as the Moon ? You are always for the Moon , said I , and you cannot rid your self of those Remains of Kindness you have for her . Light is compos'd for little Balls , which rebound upon any solid Body , which is opaque , or obscure , and are sent back another way ; whereas they pass through any thing that offers them an Opening , or Passage , in a streight Line ; which is Diaplanus , or clear ; such as Air and Glass : So that the Moon enlightens us , because she is an Opaque , solid Body , which retorts these little Balls upon us ; and I believe you will not dispute the same Solidity to the Earth . Admire then , Madam , how advantageous it is , to be well posted ; so that the Moon being at a great distance from us , we see it as an enlightned Body only , but are ignorant that 't is a gross , solid Mass , very much like the Earth : On the other hand , the Earth having the ill luck to be seen by us too near , we consider it only as a great massy Body , fit only for the producing of Food for living Creatures . 'T is just , said the Marquiese , as when we are struck and surpriz'd with the Splendour of Quality above our own ; we do not perceive , that in the main , there 's no difference between them and us . 'T is just so , said I ; and we will needs be judging of every thing ; but we have the mis-fortune , still to be plac'd in a false Light : Wou'd we judge of our selves , we are too near ; if of others , we are too far off : Cou'd one be plac'd between the Moon and the Earth , that wou'd be a true Station to consider both well : To this End , we ought only to be Spectators of the World , and not Inhabitants . I shall never be satisfy'd , said the Marquiese , with the Injury we do the Earth , in being too favourably engag'd for the Inhabitants of the Moon , unless you can assure me , that they are as ignorant of their Advantages , as we are of ours ; and that they take our Earth for a Star , without knowing that the Globe they inhabit is one also . Be assur'd of that , Madam , said I , that the Earth appears to them to perform all the Functions of a Star : 'T is true , they do not see the Earth describe a Circle round 'em , but that 's all one ; I 'll explain to you what it is : That side of the Moon which was turn'd towards the Earth at the beginning of the World , has continu'd towards the Earth ever since ; which still represents to us these same Eyes , Nose and Mouth , which our Imaginations fansie we see compos'd of these Spots , Lights and Shadows , which are the Surface of the Moon : Cou'd we see the other half of the Moon , 't is possible our Fancy wou'd represent to us some other Figure . This does not argue , but the Moon turns however upon her own Axis , and takes as much time to perform that Revolution , as she does to go round the Earth in a Month. But then , when the Moon performs a part of her Revolutions on her own Axis , and that she ought to hide from us ( for Example ) one Cheek of this imaginary Face , and appear to us in another Position , she does at the same time perform as much of the Circle she describes in turning round the Earth ; and tho' she is in a new Point of Sight or Opposition as to us , yet she represents to us still the same Cheek : So that the Moon , in regard to the Sun , and the other Planets , turns upon her own Axis ; but does not so as to the Earth . The Inhabitants of the Moon see all the other Planets rise and set in the space of fifteen Days , but they see our Earth always hanging in the same Point of the Heavens . This seeming Immovability does not very well agree with a Body that ought to pass for a Planet ; but the truth is , the Earth is not in such perfection : Besides , the Moon has a certain trembling Quality , which does sometimes hide a little of her imaginary Face , and at other times shews a little of her opposite Side ; and no doubt but the Inhabitants of the Moon attribute this shaking to the Earth , and believe we make a certain swinging in the Heavens , like the Pendulum of a Clock . All these Planets , said the Marquiese , are like us Mortals , who always cast our own Faults upon others : Says the Earth , It is not I that turn round , 't is the Sun : Says the Moon , It is not I that tremble , 't is the Earth : There are Errors and Mistakes every where . I wou'd not advise you , said I , to undertake to reform any of 'em ; 't is better that I make an end in convincing you , that the Moon is in all things like the Earth . Represent to your self these two great Globes , hanging in the Heavens ; you know that the Sun does always enlighten one half of any Globe , and the other half is in the Shadow ; there is therefore always one half of both Moon and Earth that is enlightned , or half Day , and the other half is still in the Darkness of Night . Be pleas'd , besides , to consider that a Ball has less force and swiftness after it re-bounds from a Wall , against which it was thrown , than it had before it touch'd the Wall , which sends it another way ; so Light is not so strong , after 't is reflected by any solid Body : This pale Light which comes to us from the Moon , is the Light of the Sun it self , but we have it only by Reflection from the Moon , and has lost a great deal of that Strength and Vivacity which it had when 't was receiv'd by the Moon , directly from the Sun ; and that bright and dazling Light which we receive from the Sun , must in the same manner appear to the Inhabitants of the Moon , after 't is reflected by the Earth , on the Moon : So that the Surface of the Moon , which we see enlightned , and which shines upon us in the Night , is that half of the Moon that enjoys the Day , as that half of the Globe of the Earth which is enlightned by the Sun , when 't is turn'd towards the darkned half of the Globe of the Moon , does give Light to the Inhabitants there , during their Nights . All depends upon the different Opposition and Aspects between the Moon and the Earth : The first and second Day of the Moon , we do not see her , because she is betwixt the Sun and us , and moves with the Sun by our Day ; it necessarily follows , that the half of the Moon which is enlightned , is turn'd towards the Sun , and the obscure part towards the Earth ; 't is no wonder then , that we cannot see that half which is dark ; but that same half of the Moon which is in Darkness , being turn'd towards the enlightned half of the Earth , the Inhabitants see us , without being seen , and the Earth appears to them , as their Full-Moon does to us ; and so , if one may use the Expression , 't is with them Full-Earth . After this , the Moon going on in her Monthly Circle , dis-engages her self from the Sun , and begins to turn towards us a part of her enlightned half , which is the Crescent ; at the very same time , the darkned half of the Moon loses some share of the enlightned part of the Earth , and then the Earth is in the Wain , as to its Inhabitants . Say no more , said the Marquiese , briskly , I shall know all the rest when I please ; I need only think a little , and follow the Moon in her Monthly Circle : I see in general , that the Inhabitants of the Moon have their Month , the exact Reverse of ours ; and I am perswaded , when 't is Full-Moon , the enlightned half of it is turn'd towards the obscure part of the Earth , and then they do not see us , but a certain new Earth . I wou'd not have any Body reproach me with the want of so much Sence , as that you need explain so easie a thing to me . But as to the Eclipses , What is the Cause of them ? If you do not understand that , said I , 't is your own fault . When 't is New Moon , and that she is between the Sun and the Earth , and that all her obscure half is turn'd towards us , who then enjoy the Day , you may see easily , that the Shadow of this darkned half is cast upon the Earth ; if the Moon be directly under the Sun , this Shadow hides the Sun from us , and at the same time darkens a part of the enlightned half of the Earth , which was seen by the Inhabitants of the obscure half of the Moon : And this is an Eclipse of the Sun to us , in our Day ; and an Eclipse of the Earth to those in the Moon , in their Night . When the Moon is at the Full , the Earth is betwixt her and the Sun , and all the obscure part of the Earth is turn'd towards the enlightned half of the Moon , the Shadow of the Earth is then cast upon the Moon ; and if it falls directly on her Surface , it obscures the enlightned half which we see , and hides the Sun from that enlightned part of the Moon that enjoy'd the Day : This is an Eclipse of the Moon to us , during our Night ; and an Eclipse of the Sun to them , during their Day . By this Reason , it falls out , that there are not always Eclipses when the Moon interposes between the Sun and the Earth , or the Earth is interjected between the Sun and the Moon ; because these three Bodies are not opposite one to another , in a streight Line ; and by consequence , that of the three , which ought to make the Eclipse , casts its shadow a little to one side of that which shou'd be eclips'd . I am extreamly surpriz'd , said the Marquiese , that ( since there is so little of Mystery or Difficulty in Eclipses ) every body does not find out the Cause of ' em . Do not wonder at that , said I , Madam ; there are many Nations in the World , that , as they go to work , will not find it out for Ages to come ; for all over the East-India's , the Inhabitants believe , that when the Sun or Moon is eclips'd , certain Demons , or Spirits , who have very black Claws , do stretch them forth upon these two Luminaries , which he endeavours to sieze : and during the time of the Eclipse , you may see all the Rivers cover'd with Heads of Indians ; for they go into the Water , up to the Neck , thinking that most devout posture for obtaining from the Sun and Moon , a defence against that Demon. In America , the People were perswaded , that the Sun and Moon were angry with 'em when they were eclips'd ; and God knows what pains they are at , to make their Peace with ' em . But the Grecians , who were so polite a People , Did not they believe for a long time , that the Moon was bewitch'd , and that the Magicians made her come down , to throw a certain poisonous Scum or Dew upon the Herbs and Grass ? And even we our selves , Were we not frightned out of our Wits at an Eclipse of the Sun , that happen'd about thirty Years since ? Did not a great many People shut themselves up in Vaults and Cellars ? And did not the learned Men write in vain , to assure us , there was no danger ? Certainly , said the Marquiese , that 's very disgraceful to Mankind ; and I think there ought to be a Law made by universal Consent , never to speak of Eclipses hereafter , lest the memory of such Folly shou'd be preserv'd to Posterity . Pray , Madam , said I , let there be another Law made , for abolishing the Memory of all things past ; for I know of nothing , that is not a Monument of the Folly of Mankind . Pray , tell me , said the Marquiese ; Are the Inhabitants of the Moon as much afraid of Eclipses as we are ? It seems to me very ridiculous , that some of 'em shou'd run into the Water up to the Neck ; that others shou'd think our Earth angry with 'em ; some , that our Earth shou'd be bewitch'd , and that we are coming to spoil their Grass . Without all doubt , said I , Madam : Why shou'd the Inhabitants of the Moon have more Sense than we ? And what Right have they to frighten us , more than we have to frighten them ? Nay , more ; I am apt to believe , that as there has been , and still are , many Inhabitants in our Globe , who are such Fools to adore the Moon ; there are also Inhabitants in the Moon , foolish enough to adore our Earth . At that rate , said the Marquiese , we may very well pretend to send Influences to the Moon , and to give a Judgment on their Distempers . But since there is only requisite , a little more Wit and Ingenuity in the Inhabitants of that Country , to blast the Honour we flatter our selves with , I confess , I am still apprehensive , they may have some Advantage over us . Do not fear , said I ; there is no likelihood that we are the only Fools of the Universe . Ignorance is naturally a very general Talent ; and though I do but guess at that of the Inhabitants of the Moon , yet I no more doubt of it , than I do of the most certain News we have from thence . And what , pray , are these certain News you have from thence , interrupted she ? They are , said I , Madam , such as are brought us every Day by the Learned , who travel daily thither by the help of long Telescopes : They tell us , they have discover'd vast Countries , Seas , Lakes , high Mountains , and deep Valleys . You surprize me , said the Marquiese : I know very well , that Mountains and Valleys may be discover'd in the Moon , by the remarkable Inequality we see in its Surface ; But how do they distinguish Countries and Seas ? Very easily , said I ; because the Water permits a part of the Light to pass through it , and reflects less , and appears , at a great distance , to be obscure Spots ; and that the Earth , which is solid , reflects the whole Light , and therefore must appear the brightest part of the Globe of the Moon . These different parts are all so well known , that they have given them all Names of learned Men : One place is call'd Copernicus ; another , Archimedes ; and a third , Galileus : There are too a Caspian-Sea , Porphory-Hills , and the Black Lake . In short , they have fram'd so exact a Description of the Moon , that a learned Man , if he were there , wou'd be in no more danger of losing his Way , than I wou'd be , if I were at Paris . But , reply'd the Marquiese , I shou'd be very well pleas'd to have a farther Account of this Country . 'T is impossible , reply'd I , that the nicest Observators shou'd inform you so well as Astolpho , of whom you ought to enquire ; and who was conducted to the Moon by St. Iohn . What I shall tell you now , is one of the most pleasant Fooleries in all Ariosto ; and I am satisfy'd , 't will not displease you to know it . I own , I ought not to meddle with St. Iohn , whose Name is so worthy of Respect : But since there is a Poetical Licence , and Liberty of Conscience , it ought to pass as a Gayety . The whole Poem is dedicated to a great Church-man , and another great Church-man has honour'd it with a signal Approbation ; which one may perceive by the several Editions . See what he treats of . Orlando Nephew to Charlemain , became mad , because the fair Angelica had proffer'd Medora to him ; one day Astolpho the brave Paladine , found himself in a terrestrial Paradise , which was on the brink of a very high Mountain whither his flying Horse had carry'd him ; there he met Saint — who told him that to cure the Madness of Orlando , 't was necessary they shou'd take a Voyage to the Moon ; Astolpho who desir'd nothing more than to see that Country , wanted no intreaties , and behold on a sudden a Chariot of Fire carry'd the Saint , and the Paladine through the Air. As Astolpho was no great Philosopher , he was much surpriz'd to see the Moon so vastly bigger than it had appeared to him upon the Earth , and was much more amaz'd to see Rivers , Lakes , Mountains , Plains , Groves , Towns , and Forests , ( and that which wou'd have surpriz'd me also ) beautiful Nymphs that hunted in those Forests . But that which he beheld yet more rare , was a Valley where he found all things that were lost on Earth , of what kind soever , Crowns , Riches , Renown , and Grandure , Infinity of hopes , time lost in waiting and depending on promising States-men , or thrown away at Play ; the Alms that one causes to be given after ones Death ; The Verses and Dedications one presents to Princes and the sighs of Lovers . As for the Sighs of Lovers , reply'd the Marquiese , interrupting me , I know not whether in the time of Ariosto they were lost or not , but in ours , I know of none that go into the Moon . Were there none but you Madam reply'd I , smiling , you have caus'd so many to sigh in vain , that you have made a considerable Treasure in the Moon : in short the Moon is exact in collecting all that is lost here below , and which are all to be found there , even to the Donation of Constantine . ( But Astolpho told me this only in my Ear. ) Besides all the Folly that was ever committed upon the Earth is well preserv'd there ; these are so many Vials full of a subtil and penetrating Liquor , which easily evaporates as soon as opened , and upon every one of these Vials is writ the name of those to whom it belongs . I believe that Ariosto put 'em all in one Cup , but I had rather fansie to my self that they were orderly plac'd in one Gallery . Astolpho was very much astonisht to see the Vials of so many Persons whom he believed to be very wise , and yet notwithstanding their Vials were so very full ; and for my part , I am perswaded that mine is as full as any since I entertain you with Visions , both Philophick and poetical . That which comforts me is , that 't is possible by what I am perswading you to believe , I shall very suddenly make you have a Vial in the Moon as well as my self . The good Paladine did not fail to find his own among the Number , and by the Permission of the Saint , he took it and snuff'd up the Spirit as if it had been the Queen of Hungary's Water : But Ariosto said he wou'd not carry it far , and that it wou'd return to the Moon again by a Folly that he committed seven Years after : But he did not forget the Vial of Orlando which was the occasion of his Voyage ; he had a great deal of difficulty to carry it , for the Spirit of this Hero was in its own Nature very heavy , and did not want a drop of being full . But here Ariosto according to the laudable Custom of speaking what he pleas'd , addressing himself to his Mistriss , speaks to her thus in good Verse . That I ought to cause one to mount the Heavens , my fair one , to make me recover the Senses your Charms have made me lose , yet I will not complain of this Loss , provided it does not go too far , but if there be a Necessity that your Cruelties must continue , as they have begun , I have no more to do but to expect just such a Fate as Orlando's ; however I do not believe , that to recover my Senses 't is requisite I go through the Air to the Moon ; my Soul does not lodge so high ; it wanders about your fair Eyes , and Mouth ; and if you will be pleas'd to give me leave to take it , permit me to recover it with my Lips. Is not this witty for me to reason like Ariosto ? I am of opinion that a Man never loses his Wits but for Love ; and you see they do not travel far , while their Lips only know so well how to recover ' em . But when one loses 'em by other means ( as we lose 'em by Philosophizing ) they go directly to the Moon , and one cannot retrieve 'em when one pleases . In recompence of this , said the Marquiese , our Vials shall be Honourable among the Ranks of the Philosophers : For our Spirits will go on in wandring and erring on something that is worthy of 'em ; but to accomplish this , and rid me of mine . But pray tell me seriously , said the Marquiese , do you believe that there are Men in the Moon ? For hitherto , you have said nothing to me positively as to that . I do not believe there are Men there , Madam , but some other odd sort of Creatures : Pray , Madam , consider but how much the Face of Nature is chang'd betwixt this and China ; other Faces , other Shapes , other Manners , and almost quite different Principles of reasoning , from this to the Moon the difference ought to be more considerable . When one travels towards the new discovered World of America , &c. and finds the Inhabitants there to be hardly Men , but rather a kind of Brutes in humane shape , and that not perfect neither , so that could we travel to the Orb of the Moon , I do not think we should find Men and Women there . What kind of Creatures should we find then said the Marquiese , with a very impatient look ? I swear I cannot tell , said I Madam , were it possible for us to be rational Creatures and yet not Men , and that we inhabited the Moon , cou'd it ever enter into our Imagination , that there dwelt here below so extravagant an Animal as that of Mankind ? Could we fansie to our selves any living Creatures with such foolish Passions , and so wise Reflections ; of so small Duration , and yet can see so vast a Prospect beyond it ; of so much knowledge in Trifles , and so much Ignorance of important things ; so earnest for liberty , yet so enclin'd to servitude and Slavery ; so very desirous of Happiness , and yet so uncapable of attaining it ; it wou'd require a great deal of Wit and Judgment in the Inhabitants of the Moon , to find the Reason and Mystery of such an odd composition ; for we that see one another daily , have not as yet found out how we are made . It was said of old amongst the Heathens , that the Gods when they made Man were drunk with Nectar , whom when they had consider'd when sober , they cou'd not forbear laughing at the ridiculousness of their handy Work. We are then secure enough , said the Marquiese , that the Inhabitants of the Moon will never guess what we are ; but I wish we could attain to the knowledge of them ; for I must confess it makes me uneasie to think there are Inhabitants in the Moon , and yet I cannot so much as fansie what kind of Creatures they are . And why are you not as uneasie , said I , upon the account of the Inhabitants under and near the South-Pole , which is altogether unknown to us ? They and we are carried as it were in the same Ship , they in the Stern , and we in the Head ; and yet you see there is no communication between the Stern and the Head , and that those at the one end of the Ship do not know what kind of People they are on the other , nor what they are doing , and yet you would know what passes in the Moon , in that other great Ship sailing in the Heavens at a vast distance from us . Ah , said the Marquiese , I look upon the Inhabitants under the South-Pole , as a People known to us , because they are most certainly very like us ; and that we may see them if we please to give our selves the trouble ; they will continue still where they are , and cannot run away from our knowledge ; but we shall never know what these Inhabitants of the Moon are ; 't is that that vexes me . If I shou'd answer you seriously , said I , that we may one day know 'em , wou'd not you laugh at me ? Nay and I shou'd deserve it : Yet I cou'd defend my self very well if I shou'd say so ; there is a certain ridiculous thought in my Head , which has some shadow of likelihood , which satisfies me , tho I do not know on what it is founded , it being so impertinent as it is ; yet I will lay you what you will , that I will oblige you to believe against all Reason , that there may one day be a correspondence between the Earth and the Moon . Reflect a little , Madam , upon the State and Condition of America , before it was discovered by Christopher Columbus ; it's Inhabitants liv'd in a most profound Ignorance , so far from the knowledge of Sciences , that they were ignorant of the most simple and useful Art : They went stark naked and cou'd not imagine that Men cou'd be cover'd by Skins of Beasts ; had no other Arms but Bows , and who look upon the Sea as a vast space forbidden to mankind , joining , as they thought , to the Sky ; beyond which they saw nothing . 'T is true after having spent several years with hollowing the root of a great Tree with sharp Flints , they after ventur'd to go in this kind of Boat , which was driven along the Shore by the Winds and the Waves ; but as this kind of Vessel was very subject to be over-set very often , they were necessitated to swim to catch their Boat again ; and indeed , they did swim for the most part , except when they were weary . If any Body had told them there was a Navigation much more perfect than that they knew ; and that by it , it was easie to cross that vast extent of Water to any side , and in what manner we pleas'd , and that it was possible to stop and lie still in the midst of the Waves , while the Vessel is in Motion ; that Men cou'd move fast or slow as they pleas'd ; and that the Sea , notwithstanding the vastness of its extent , was no hindrance to the commerce of distant Nations , provided that there were People on the other shoar ; surely the Indians wou'd never have believ'd that Man that should have told 'em this , to them impossibility : nevertheless , the day came , that the strangest and least expected Sight that ever they saw , presented it self to their view , huge great Bodies , which seem'd to have white wings with which they flew upon the Sea belching Fire from all parts , and at last landed upon their shoar a Race of unknown Men , all crusted over with pollish'd Steel , ordering and disposing at their Pleasure the Monsters that brought 'em thither , carrying Thunder in their Hands which destroy'd all that made any resistance , while the wondring Indians cried , from whence came they ? who brought them over the Seas ? who has given 'em the Power of Fire and Thunder ? are they Gods or the Children of the Sun ? for certainly , they are not Men. I know not , Madam , whether you conceive as I do , the extraordinary surprize of these Americans , but certainly there was never any equal to it ; and after that , I will not swear , but there may be one day , a commerce betwixt the Earth and the Moon : Had the Americans , any Reason to hope for a correspondence betwixt America and Europe , ( which they did not know ? ) It is true , there will be a Necessity to cross the vast Extent of Air and Heaven that is betwixt the Earth and the Moon . But did these Americans think the Ocean more proper to be crossed , and pass'd through ? Sure , said the Marquiese , you are mad ; and looking earnestly on me ; I do not deny it , answer'd I ; nay , said she , it is not sufficient to confess it , I will prove you to be mad . The Americans were so ignorant , that the Possibility of making a way or passage through the vast Ocean , cou'd never enter into their Thoughts ; but we that know so much , we easily find out that it wou'd be no hard matter to pass through the Air if we cou'd support our selves . There are those Men , said I , who have found out more than a possibility of it ; for they actually begin to fly a little , and several have made and fitted wings to themselves , and invented a way to give themselves Motion , for supporting the Body in the Air , for crossing of Rivers , and flying from one steeple to another . 'T is true , these were not flights of an Eagle ; and it has cost some of these new Birds a Leg or an Arm : But this Essay is like the first Planks that were carry'd on the Water , which yet gave beginnings to shipping ; and there was a very great difference between these Planks and Ships of mighty burden ; yet you see that time by degrees has produc'd great Ships . The Art of flying is but in its Infancy , time must bring it to Maturity , and one day Men will be able to fly to the Moon . Do you pretend to have discover'd all things , said she , or to have brought them to that perfection that nothing can be added ? Pray , Madam , said I , by consent , let us save something for the Age to come . I will never yield , said she , that Men will ever be able to fly without breaking their Necks . Well , said I , Madam , since you will needs have Men always to fly so ill , it may be the Inhabitants of the Moon will fly better , and will be fitter for that Trade ; for 't is all one , if we go to them or they to us . And we shall be like the Americans , who did not believe Navigation possible , when at the same time , sailing was so well understood on the other half of the Globe . Sure , said she , in anger , the Inhabitants of the Moon wou'd have been with us before now , if that were likely . Pardon me , said I , Madam , the Europaeans did not sail to America , till after six thousand years , all that time was requisite for performing Navigation . The Inhabitants of the Moon , it may be , at that time , knew how to make little Journeys in the Air , and are now practising ; and it may be when they have more skill , we shall see ' em . And God knows what a strange Surprise 't will be to us . This is insupportable , said the Marquiese , to banter me on thus with such frivolous Arguments . If you anger me , said I , I know what I have to say to enforce 'em , and make all good . Observe , Madam , how the World is daily more and more unfolded . The Ancients believed the torrid and the frozen Zones uninhabituable for extremity of cold or heat : And the Romans confin'd the general Map of the World to their own Empire , which carry'd as much of Grandure as Ignorance . But we know that there are Inhabitants both in these extreme hot , and extreme cold Countries ; by this the World is much augmented . Then it was believed , that the Ocean cover'd all the Earth , except what was inhabited : And that there was no Antipodes ; for the Ancients never heard of them : Besides they cou'd not believe Men cou'd have their Feet opposite to ours , with their Heads hanging down ; and yet after all this the Antipodes are discover'd , the Map of the World is corrected , and a new half added to the World. You understand my meaning , said I , Madam ; these Antipodes which have been discover'd contrary to all Expectation , ought to make us more circumspect in judging by appearances : The World , and secrets of Nature will be daily more and more discover'd ; and at last we may come to know somewhat more of the Moon . Certainly , said the Marquiese , looking earnestly on me , I see you so charmed with this Opinion , that I doubt not but you believe all you say . I shou'd be very sorry to find my self so , said I ; my endeavour is only to show , that chimerical Opinion may be so far defended by strength of Argument , as to amuse a Person of your Understanding and Sense , but not to perswade : Nothing but truth it self has that Influence ; even without the Ornaments of all its convincing Proofs ; it penetrates so naturally into the Soul , that one seems but to call it to mind ; tho it be the first time that ever one heard of it . Now you ease me , said she , for your false way of arguing did confound and incommode me , but now I can go sleep soundly ; so , if you please , let us retire . The Third Night . MY Lady Marquiese wou'd needs engage me to pursue and continue our Discourse by Day-light ; but I told her , 't was more proper to reserve our Fancies and Notions till the Night ; and since the Moon and Stars were the Subjects of our Conversation , to trust it only to them . We did not fail to go that Evening into the Park , which was now become a place consecrated to our Philosophical Entertainment . I have a great deal of News to tell you , said I : The Moon , which I told you last Night ( by all appearance ) was inhabited , now I begin to think , may be otherwise ; for I have been reflecting upon a thing , which puts its Inhabitants in great danger . I shall never suffer that , said the Marquiese ; for you having prepar'd me last Night , put me in hopes to see these People arrive one Day upon our Earth ; and to day , you will not allow them a being in the Universe : You shall not impose upon me at this rate . You made me believe there were Inhabitants in the Moon ; I have overcome all the Difficulties my Reason suggested to me against that Opinion , and now I am resolv'd I will believe it . You go too fast , said I , Madam ; one ought to give but one half of ones Thoughts and Belief to Opinions of this nature , reserving the other half free for receiving the contrary Opinion , if there be occasion . I am not to be deluded , reply'd the Marquiese , with fair Words ; let us come to the subject matter in debate : Must not we reason the same way of the Inhabitants of the Moon , as we did of your St. Denis ? Not at all , Madam , answer'd I ; the Moon does not so much resemble the Earth , as St. Denis does Paris . The Sun draws from the Earth , Waters , Exhalations and Vapours ; which ascending into the Air , to a certain heighth , are gather'd together , and form Clouds ; these Clouds , hanging in the Air , move regularly round our Globe , and over shadows sometimes one Country , sometimes another : And if it were possible for any one to see and consider the Earth at a great distance , he wou'd perceive great Changes as to the appearance of its Surface ; for a great Country , cover'd with Clouds , wou'd appear to be a very obscure part of the Globe , and will become clear and enlightned as soon as these Clouds dis-appear ; and one wou'd see these obscure places change their Situation , meeting together in different Figures , or disappearing all together . We shou'd see therefore the same Changes upon the Surface of the Moon , were it encompass'd with Clouds , as the Earth is ; but on the contrary , all the Obscurities , or dark places , as also those parts that are enlightned , are still the same , fix'd to the same Situation , without Variation or Change ; there lies the difficulty : And for this reason , the Sun draws no Vapours or Exhalation from the Globe of the Moon ; and by consequence , 't is a Body infinitely harder , and more solid than our Earth , whose subtile parts are easily separated from the rest , and mount upward , being once set in motion by the heat of the Sun : So that the Moon must needs be nothing else but a vast heap of Rocks and Marble , from which no Vapour can be exhal'd ; which Vapours are so essential and natural to Waters , that 't is impossible the one can be without the other . Who can then be the Inhabitants of those Rocks that produce nothing ? Or what living Creatures can subsist in a Country without Water ? How ! cry'd my Lady Marquiese ; Have you forgot that you assur'd me , there were Seas in the Moon , which we cou'd distinguish from hence ? That 's only a Conjecture , said I ; and I am very sorry that these obscure places , that may be taken for Seas , are , possibly , nothing else but deep Caverns , and vast Cavities ; and guessing is pardonable , at the great distance we are at from the Moon . But , said she , is that sufficient to make us reject the Inhabitants of the Moon ? Not altogether , Madam , said I ; nor must we absolutely declare either for 'em , or against ' em . I confess my weakness , said she ; I am not capable of such Indifference , and I must be positive in my Belief ; therefore let us free our selves of one Opinion ; let us either preserve the Inhabitants of the Moon , or annihilate 'em for ever , never to be heard of again ; but , if possible , let us preserve 'em , for I have an Inclination and a Kindness for 'em , I wou'd not willingly lose . I shall not unpeople the Moon then , Madam , said I , but for your sake shall restore to it its Inhabitants : And the truth is , that by the Appearance of the obscure and enlightned places of the Moon , which are still the same , without change , we have no reason to believe that there are any Clouds surrounding it , which might obscure sometimes one place , sometimes another ; but yet that does not argue , but she may emit Vapours and Exhalations : Our Clouds which we see carry'd in the Air , are nothing but Exhalations and Vapours , which are separate in Particles , too small to be seen ; which meeting with cold Airs , as they ascend , by it are condensed , and render'd visible to us , by the Re-union of their Parts ; after which , they become thick and black Clouds , which float in the Air , as Stranger-Bodies , till at last they fall upon the Earth in Rain : But sometimes it falls out , that the same Vapours and Exhalations are extended , and kept from joining together , and so are imperceptible , and are only gather'd together so far as to form a kind of small Dew , so very subtile , that it cannot be seen as 't is a-falling . It may be , in like manner , that the Vapours which proceed from the Moon ( for certainly it emits Vapours ; ) and 't is impossible to believe , that the Moon can be such a Body , as that all its parts shou'd be of an equal Solidity , and so equal a temper , one with the other , that they are incapable of receiving any Change , by the attracting and moving Influence of the Sun upon 'em : We know no Body of this nature , the hardest Marbles are not of this kind ; and there is no Body , how hard and solid soever , but is subject to Change and Alteration , either by secret and invisible Motion in it self , or by some exterior Impulse it receives from another . It may be therefore , as I said , that Vapours which arise from the Moon are not gather'd together , as a rounded Surface , into Clouds , but fall gently upon it again in insensible Dews , and not in Rain : And 't is sufficient to demonstrate this , to conjecture only , that the Air which environs the Moon , is as different from the Air that environs the Earth , as the Vapours of the Air from the Exhalations of the other ; which is more than likely to be true ; and it must follow , that Matter being otherwise dispos'd of in the Moon , than in the Earth , its effects shou'd also be different ; and imports nothing , whether it be an interior Motion of the parts of the Moon , or the Production of external Causes , which furnish it with Inhabitants , and them with a sufficient Food for their Subsistence ; so that , in our Imagination , we may furnish 'em with Fruits and Grain of several sorts , Waters , and what else we please ; for Fruit , Grain and Water , I understand , are agreeable to the nature of the Moon , of whose Nature I know nothing ; and all these proportion'd and fitted to the Necessities of the Inhabitants , of whom I know as little . That is to say , said the Marquiese , that you only know , that all is very well there , without knowing in what manner ; that is a great deal of Ignorance , with a little Knowledge ; but we must have patience : However , I think my self very happy , you have restor'd the Moon its Inhabitants again ; and I am very much pleas'd , you have surrounded it with Air of its own ; for without that , I shou'd think a Planet too naked . These different Airs , answer'd I , hinder the Communication and Commerce of these two Planets : If flying wou'd do the business , what do I know , but we might come to perfection in that Art I discours'd of last Night . I confess , Madam , there seems but little likelihood of what I say , since the great distance between the Moon and the Earth makes the difficulty so hard to overcome , which is very considerable ; but tho' it were not , and that the Earth and the Moon were plac'd near one another , yet it wou'd not be possible to pass from the Air of the Earth , to the Air of the Moon . The Water is the Air and Element of Fish , who never pass into the Air and Element of Birds ; 't is not the distance that hinders 'em , but 't is because every one of 'em are confin'd to the Air which they breath . We find that our Air is mix'd with Vapours , that are thicker and grosser than those of the Moon ; and by consequence , any Inhabitants of the Moon , who shou'd arrive upon the Confines of our World , wou'd be drown'd and suffocated as soon as they enter'd into our Air , and we shou'd see 'em fall dead upon the Earth . Oh , but I shou'd be glad , cry'd the Marquiese , that some great Ship-wreck , occasion'd by a mighty Tempest , wou'd throw a good many of these People upon our World , that we might at leisure consider their extraordinary Shape and Figure . But , answer'd I , if they had Skill enough to sail upon the external Surface of our Air , and that from thence they shou'd catch us , like Fish , out of a Curiosity of seeing us ; wou'd that please you , Madam ? Why not , said she , laughing ? I wou'd go of my self into their Nets , to have the satisfaction of seeing those that had caught me . Consider , said I , that you wou'd be very weak and feeble , before you come to the Surface of our Air ; for we cannot breath it in all its Extent , and we can hardly live on the Tops of high Mountains ; and I wonder that those who are so foolish as to believe , that Corporeal Geniuses inhabit the purest Air , do not tell us why these Geniuses visit us so seldom , and stay so short a while : I do believe , 't is because few amongst 'em know how to dive ; and that even those who are skilful in that Art , have great difficulty to penetrate the grosness of the Air which we breath . You see therefore , that Nature has set many Bars and Fences , to hinder us from going out of our World , into that of the Moon . However , for our Satisfaction , let us conjecture and guess as much as we can of that world : For Example ; I fansie that the Inhabitants of the Moon must see the Heavens , the Sun , and the Stars , of a different Colour than what they appear to us . All these Objects we see through a kind of natural Perspective-Glass , which changes them to us ; this Perspective-glass of ours is mix'd with Vapours and Exhalations , which do not ascend very high . Some of late pretend , that the Air of it self is blew , as well as the Water of the Sea ; and that that Colour is not apparent in the one , nor the other , but at a great depth : The Heavens , say they , in which are plac'd the fixed Stars , has of it self no Light ; and by consequence , ought to appear black : But we see it through our Air , which is blew ; and therefore the Heavens appear of that Colour . If it be so , the Beams of the Sun and Stars cannot pass through the Air , without taking a little of its Tincture , and at the same time lose as much of their own natural Colour : But supposing the Air had no Colour of it self , 't is certain , that a Flambeau , seen at a distance , through a thick Fog , appears of a reddish Colour , tho' that be not natural to it ; so all our Air , which is nothing else but a thick Fog , must certainly alter the true natural Colour of the Heavens , Sun and Stars to us ; for nothing but the pure heavenly Substance is capable to convey to us Light and Colours , in their Purity and Perfection , as they are : So that the Air of the Moon is of another nature than our Air , or is , of it self , of an indifferent Colour ; or , at least , is another Fog , changing , in appearance , the Colours of the Celestial Bodies . In short , if there be Inhabitants in the Moon , they see all things chang'd , through their Perspective-glasses , which is their Air. That makes me prefer our place of Habitation , said the Marquiese , to that of the Moon ; for I cannot believe , that the mixture of the Heavenly Colours is so fine there , as it is here . Let us suppose , if you will , the Heavens of a reddish Colour , and the Stars of a greenish , the Effect wou'd not be half so agreeable as Stars of Gold , upon a deep Blue . To hear you speak , said I , one wou'd think you were fitting of Furniture for a Room , or chusing a Garniture for a Suit of Cloths : Believe me , Nature is very ingenious , therefore let us leave to her Care the finding out a Mixture of Colours agreeable to the Inhabitants of the Moon ; and I assure you , 't will be perfectly well understood ; she certainly has not fail'd of changing the Scene of the Universe , according to the different Situation and Position of the Beholders , and still in a new and agreeable way . I know the Skill of Nature perfectly well , said Madam the Marquiese ; and she has spar'd her self the pains of changing her Objects , as to the several Points from whence they may be seen , and has only chang'd the Perspective-glasses , through which they are seen ; and has the Honour of this great Variety , without the Expence : She has bestow'd on us a blue Heaven , with a blue Air ; and it may be , she has bestow'd upon the Inhabitants of the Moon , a Heaven of Scarlet , with an Air of the same Colour , and yet their Heaven and ours is one and the same : And it seems to me , that Nature has given every one of us a Perspective-glass , or Tube , through which we behold Objects in a very different manner , one from the other . Alexander the Great saw the Earth as a fine place , fit for him to form a great Empire upon : Celadon only look'd upon it , as the Dwelling-place of Astraea : A Philosopher considers it as a great Planet , all cover'd over with Fools , moving through the Heavens : And I do not see that the Object changes more from the Earth to the Moon , than it does here from one Man to another . The Change of Sights is more surprizing to our Imagination , said I ; for they are still the same Objects we see at different Views ; and it may be , in the Moon they see other Objects than we see ; at least , they do not see a part of those we see : Perhaps in that Country they know nothing of the Dawning of the Day , of the Twi-light before Sun-rising , and after Sun-setting ; for the Beams of the Sun , at these two times , being oblique and faint , have not strength to penetrate the grosness and thickness of the Air , with which we are environ'd ; but are receiv'd and intercepted by the Air , before they can fall upon the Earth , and are reflected upon us by the Air ; so that Day-break and Twi-light are Favours of Nature which we enjoy by the by , or , as it were , by chance , they not having been destin'd for us ; but 't is likely that the Air of the Moon , being purer than ours , is not so proper and fit for reflecting the faint Beams of the Sun before its Rising , and after its Setting ; therefore I suppose , the Inhabitants of the Moon do not enjoy the favourable light of the Aurora , or Dawning ; which growing stronger and stronger , does prepare us for the glorious Appearance of the Sun at Noon ; nor the Twi-light , which becoming more faint by degrees , we are insensibly accustom'd to the Absence of the Sun : So that the Inhabitants of the Moon are in profound Darkness , when on a suddain a Curtain is drawn , as it were , and their Eyes are dazl'd with the Rays of the Sun , and they enjoy a bright resplendent Light ; when by a suddain motion , as quick as the former , down falls the Curtain , and instantly they are reduc'd to their former Darkness : They want those Mediums , or Interstices , which join Day and Night together ( and which participates of both ) which we enjoy . Besides , these People have no Rain-bow ; for as the Dawning is an Effect of the thickness of our Air , so the Rain-bow is form'd upon Exhalations and Vapours , condens'd into black Clouds , which pour down Rain upon us , by divers Reflections and Refections of the Sun-beams upon these Clouds : So that we owe the Obligation of the most agreeable and pleasant Effects , to the ugliest and most dis-agreeable Causes in Nature : And since the Purity of the Air of the Moon deprives it of Clouds , Vapours and Rain , adieu to Rain-bow and Aurora : To what then can the Lovers in the Moon compare their Mistresses , without these two things ? I do much regret that loss , said the Marquiese , for in my Opinion , the Inhabitants of the Moon are fully recompens'd for the want of the Rain-bow , day-break and twi-light , since for the same Reason , they have neither Thunder nor Lightning , both which are produc'd by Clouds and Exhalations ; they enjoy bright serene Days , and never lose the Sun by Day , nor the Stars by Night . They know nothing of Storms and Tempest ; which seem to us the effects of the wrath of Heaven . And can you think their condition is so much to be lamented ? You , said I , Madam , represent the Moon as a most charming abode . Now methinks it should not be so desirous and agreeable to have a burning Sun always over ones Head , without the interposition of any Clouds to moderate its heat : And it may be for this Reason , Nature has sunk these Caverns in the Moon , which are big enough to be seen by our Telescopes : Who knows but the Inhabitants of the Moon , retire into these Cavities , when they are incommoded with the Excessive heat of the Sun , and it may be they live no where else , but build their Towns and Villages in these hollow places ? And do not we know that Rome , which is built under ground , is almost as great as the City above ground ? So that if we shou'd suppose , that the City of Rome above ground shou'd be ras'd , and quite remov'd , Rome under ground wou'd then be just such a Town , as those I have imagin'd to be in the Moon . Whole Nations live in these vast Caverns ; and I doubt not but there may be Passages under ground , for the communication and commerce of one People and Nation with another . You are pleas'd to laugh , Madam , at my Fancy , do so with all my Heart , I agree you shou'd ; and yet you may be more mistaken than I : For you believe , that the Inhabitants of the Moon dwell upon the Surface of their Globe , as we do on that of the Earth ; it is very likely that 't is just the contrary ; for there is most certain , a vast difference between their way of living and ours . No matter , said the Marquiese , I cannot resolve to suffer the Inhabitants of the Moon to live in perpetual Darkness . You wou'd be harder put to it , Madam , said I , if you knew that a great Philosopher of old , believ'd the Moon to be the abode and dwelling of the Souls who had merited Happiness by their good Life in this World ; and that theit Felicity consisted in hearing the Harmony of the Spheres as they turn'd round , and that they were depriv'd of this heavenly Musick , as often as the Moon was obscur'd by the Shadow of the Earth ; and that then these Souls roar'd and cry'd out as in despair , and that the Moon made haste to recover her Light again , to bring the Souls out of that Affliction . At that rate , said she , we shou'd see the bless'd Souls come from the Moon to us ; for why shou'd not the Earth be to the Moon , as the Moon is to the Earth , since according to the opinion of your Philosopher , there was no other Felicity for the Souls of the blessed , than to be transported from one World to the other ? Seriously , said I , Madam , 't would be a great Pleasure and Satisfaction to see several different Worlds ; and I am often glad , to make these Journeys in Imagination ; what joy then it wou'd be to do it in reality ; that wou'd be far better than to travel from hence to Iapan , crawling as it were with difficulty from one point of this Globe to another , and still to see nothing but Men and Women over and over again . Well , said she , what hinders , but we shou'd make a Journey through the Planets as well as we can ? Let us by imagination place our selves in several Positions , and situations , fit for considering the Universe . Have we no more to see in the Moon ? No , said I , at least , I have shown you all I know . Going out of the Moon towards the Sun , the first Planet you meet with is Venus ; and here I must again make use of my former Simile of Paris and St. Denis . Venus turns round the Sun on her own Axis , as the Moon does round the Earth ; and by the means of Telescopes , we discover that Venus waxes and wanes , being sometimes altogether enlightned , and sometimes darkened according to her different Positions in respect to the Earth . By all appearance the Moon is inhabited , why shou'd not Venus be so , as well as she ? Ay , but interrupted the Marquiese by your why nots , you will people all the Planets . Do not doubt of it , Madam , answer'd I ; why has not Nature sufficient to give Inhabitants to 'em all ? We see that all the Planets are of the same Nature , that they are all Opaque solid Bodies , having no Light but what they receive from the Sun ; which they send one to another by Reflection , and that they have all the same kind of motion ; thus far equal , and after all this must we conceive that all these vast Bodies were made not to be inhabited ? And that Nature has made only an exception in Favour of the Earth , he that will believe this , may , but for my part I cannot . I find you , said the Marquiese , very resolute and settled in your opinion of a sudden : A little while ago , you wou'd scarce allow the Moon to be inhabited ; and seem'd to be very indifferent , whether it were so or not ; whereas now , I am confident , you wou'd be very angry with any body that shou'd tell you that all the Planets were not inhabited . It is true , Madam , in the minute wherein you have surpriz'd me , had you contradicted me , as to the Inhabitants of all the Planets , I wou'd not only have defended my opinion , but have proceeded , to have given you an exact description of all the several Inhabitants of the Planets . There are certain Moments of believing things ; and I never so firmly believ'd the Planets to be inhabited , as in that Moment I spoke of 'em ; but now , after cooler Thoughts , I shou'd think it very strange , that the Earth shou'd be inhabited as it is ; and the other Planets shou'd be so entirely desolate and desarted : For you must not think , that we see all the living Creatures that inhabit the Earth . For there are as many several species and kinds of Animals invisible , as there are visible . We see distinctly from the Elephant to the Mite ; there our sight is bounded , and there are infinite numbers of living Creatures lesser than a Mite , to whom , a Mite is as big in proportion , as an Elephant is to it . The late invention of Glasses call'd Microscopes , have discover'd thousands of small living Creatures , in certain Liquors , which we cou'd never have imagin'd to have been there . And it may be the different tastes of these Liquors , proceed from these little Animals , who bite , and sting our Tongues and Palates . If you mix certain ingredients in these Liquors , ( as Pepper in Water , ) and expose 'em to the heat of the Sun , or let 'em putrefie , you shall see other new species or living Creatures . Several Bodies , which appear to be solid , are nothing else but Collections or little heaps of these imperceptible Animals ; who find there as much room , as is requisite for them to move in . The leaf of a Tree , is a little World inhabited , by such invisible little Worms : To them this leaf seems of a vast Extent , they find Hills and Valleys upon it : And there is no more Communication between the living Creatures on the one side , and those on the other , than between us and the Antipodes . And I think there is more reason , to believe a Planet ( which is so vast a Body ) to be inhabited . There has been found in several sorts of very hard Stones , infinite multitudes of little Worms , lodg'd all over them in insensible varieties ; and who are nourish'd upon the Substance of these Stones which they eat . Consider the vast Numbers of these little Animals , and how long a tract of Years they have liv'd upon a grain of Sand. And by this Argument , tho my Moon were nothing but a confus'd heap of Marble Rocks , I wou'd rather make it be devour'd and consum'd by its Inhabitants , than to place none at all in it . To conclude , every thing lives , and every thing is animated ; that is to say , if you comprehend the Animals , that are generally known ; the living Creatures lately discover'd , and those that will be discover'd herafter , you will find that the Earth is very well Peopl'd ; and that Nature has been so liberal in bestowing them , that she has not been at the pains to discover half of ' em . After this , can you believe , that Nature , who has been fruitful to Excess as to the Earth , is barren to all the rest of the Planets ? My Reason is convinc'd , said the Marquiese , but my Fancy in confounded with the infinite Number of living Creatures , that are in the Planets ; and my thoughts are strangely embarass'd with the variety that one must of Necessity imagine to be amongst 'em ; because I know Nature does not love Repetitions ; and therefore they must all be different . But how is it possible for one to represent all these to our Fancy ? Our Imaginations can never comprehend this variety , said I , let us be satisfied with our Eyes , or we may easily conceive by an universal view , Nature has form'd variety in the several Worlds . All the Faces of Mankind are in general near the same Form. Yet the two great Nations of our Globe , the Europaeans and Africans , seem to have been made after different Models . Nay , there is a certain resemblance and Air of the Countenance peculiar to every Family or Race of Men. Yet it is wonderful to observe how many Millions of Times , Nature has varied so simple a thing as the Face of a Man. We , the Inhabitants of the Earth , are but one little Family of the Universe , we resemble one another . The Inhabitants of another Planet , are another Family , whose Faces have another Air peculiar to themselves ; by all appearance , the difference increases with the distance , for cou'd one see an Inhabitant of the Earth , and one of the Moon together , he wou'd perceive less difference between them , than between an Inhabitant of the Earth , and an Inhabitant of Saturn . Here ( for Example ) we have the use of the Tongue and Voice , and in another Planet , it may be , they only speak by Signs . In another the Inhabitants speaks not at all . Here our Reason is form'd and made perfect by Experience . In another Place , Experience adds little or nothing to Reason . Further off , the old know no more than the young . Here we trouble our selves more to know what 's to come , than to know what 's past . In another Planet , they neither afflict themselves with the one nor the other ; and 't is likely they are not the less happy for that . Some say we want a sixth Sense by which we shou'd know a great many things we are now ignorant of . It may be the Inhabitants of some other Planet have this advantage ; but want some of those other five we enjoy ; it may be also that there are a great many more natural Senses in other Worlds ; but we are satisfi'd with the five that are fal'n to our Share , because we know no better . Our Knowledge is bounded to certain limits , which the Wit of Man cou'd never yet exceed . There is a certain point where our Ingenuity is at a stand ; that which is beyond it is for some other World , where it may be some things , that are familiar to us , are altogether unknown . Our Globe enjoys the Pleasure of Love ; but is destroyed in several places by the fury of War. Another Planet enjoys constant Peace , without the delights of Love , which must render their Lives very irksom . In fine , Nature has done to the several Worlds in great , as she has done to us Mortals in little by making some happy , others miserable . Yet she has never forgot her admirable Art in varying all things , tho she has made some equal in some respects , by compensating the want of any one thing , with another of equal value . Are you satisfi'd , said I , Madam , very gravely ; have not I told you Chimeras in abundance ? Truly , I find not so much difficulty to comprehend these differences of Worlds ; my Imagination is working upon the Model you have given me And I am representing to my own Mind odd Characters and Customs for these Inhabitants of the other Planets . Nay more , I am forming extravagant shapes and figures for 'em : I can describe 'em to you ; for I fansie I see 'em here . I leave these shapes , said I , Madam , to entertain you in Dreams this Night , to morrow , we shall know , if they have assisted you , to describe the Inhabitants of some other Planet . The Fourth Night . THe Dreams of my Lady Marquiese were not lucky , they still represented to her something like what we see on Earth ; so that I had as much reason to reproach her , as certain People have to blame us when they see some of our Pictures ; for they being ignorant of drawing , and designing , and pleasing themselves with their extravagant and grotesque Figures , tell us , our Pictures are nothing but Men and Women , and that there is no Fancy in 'em ; there was therefore a necessity of laying aside all sorts of the Forms and Figures of those Animals that inhabit several Planets , and to rest satisfy'd by guessing as well as we can , in pursuing our Journey , which we had begun , through the several Worlds of the Universe . We were at Venus : And there is no doubt , said I to my Lady Marquiese , but Venus turns upon her own Axis , but 't is not known in what time , and by consequence , we know not the length of her Days , but her Years must consist but of eight Months , since Venus turns round the Sun in that space of time . As Venus is forty times less than the Earth , the Earth must necessarily appear to the Inhabitants of Venus , to be forty times bigger than Venus appears to us ; and as the Moon is also forty times less than the Earth , by consequence , it must appear to the Inhabitants of Venus , about the same bigness that Venus appears to us . You afflict me , said the Marquiese , extreamly ; I see very well , that our Earth is not that happy Planet to the Inhabitants of Venus , as she is to us ; for our Globe of the Earth must appear too big to the Inhabitants of Venus , to be the Fountain of Love , but the Moon , which appears to the World of Venus , of the same size that Venus appears to us , is exactly cut out to be the Source of their Amours , and the lucky Star of their Intrigues ; which Titles are most agreeable to the pretty , clear , twinkling Planets , which have in 'em a certain Air of Gallantry . 'T is certainly a happy Fate for our Moon to give Laws to the Loves of the Inhabitants of Venus : No doubt , but these People are very soft , and have the Art to please extreamly well . Without dispute , Madam , said I ; the very Mobile of Venus are all made up of Celladons and Silvanders , and their most ordinary Conversations excel the finest in Clelia ; the Climate being more savourable to Love : Venus being nearer the Sun than we , receives from its Influence a brighter Light , and a more enlivening Heat . I perceive very well , interrupted the Marquiese , what kind of People the Inhabitants of Venus are ; they are , like our Moors of Granada , a sort of little Sun-burnt Gentlemen , always in Love , full of Life and Fire , given to making Verses , and great Lovers of Musick , and every Day inventing Feasts , Balls and Masquerades , to entertain their Mistresses . Pray , Madam , said I , you are very ill acquainted with the Inhabitants of Venus ; for our Moors of Granada are , in respect to them , as the Inhabitants of Lapland , or Greenland , for Coldness and Stupidity . But what then must the Inhabitants of Mercury be , for they are yet more near to the Sun ? They must certainly be mad , by having too much Light and Fire ; and I believe they have no more Memory , than the most part of our Negroes ; they never think , and are void of all Reflection , and they only act by Chance , and by suddain Impulses . In short , the Planet Mercury must certainly be the Bethlem of the Universe ; they see the Sun a great deal bigger than we do , because they are so much nearer to it ; he darts upon 'em so strong a Light , that if the Inhabitants of Venus were here , they wou'd take our finest Days for the Remains of a saint Twi-light ; and it may be , the Light we enjoy , wou'd not serve them to distinguish one Object from another ; and the Heat they are accustom'd to is so excessive , that the greatest warmth enjoy'd by the Inhabitants of the middle of Africk , wou'd frieze them to death . Their Year casts but three Months ; the length of their Day is yet unknown , Mercury being so little a Planet , and so near the Sun , in whose Rays he is so continually lost , that he is hitherto scarce discoverable by the Art and Skill of Astronomers , who cou'd never yet get so much hold of Mercury , as to observe the Time in which he performs his Revolution upon his own Axis or Centre ; but the smallness of his Planet perswades me 't is in a very short time , and then , by consequence , his Days are very short , and his Inhabitants must see the Sun as a very great flaming Brasier , very near their Heads , which , to their Apprehension , moves with wonderful Rapidity ; this makes them so earnestly wish for the coming Night , which , no doubt , must be much more grateful to 'em than the Day ; and during those cooler Hours , they are enlightned by Venus , and by the Earth ; which two Planets must appear to them of considerable bigness . As for the other Planets , since they are remov'd further than Mercury , towards the Firmament , his Inhabitants must see them less than they appear to us , and receive but little Light from 'em , it may be , none at all ; the fixed Stars must appear less to 'em also , and they lose the sight of some of 'em entirely , which , in my Opinion , is a very great Loss ; for I shou'd be very sorry to see the vast arch'd Roof of the Heavens adorn'd with fewer Stars , or those I do see , appear less , and not so bright . I am not so much concern'd for that Loss , said the Marquiese , as for their being so extreamly incommoded with excessive Heat ; and I wish with all my heart , we cou'd ease 'em of that Trouble . Let us therefore allow 'em long and continued Rain , to refresh 'em ; such as are in some of the hot Countries of our Earth , which fall for four Months together , during the hottest Seasons . That may be done , said I ; but we may find out another Remedy , to relieve the Inhabitants of Mercury ; for there are Countries in China , which , by their Situation , must be very hot ; yet notwithstanding , the Cold is so excessive during the Months of Iuly and August , that the Rivers are frozen : The Reason is , These Climates abound with Salt-Petre ( whose Exhalations being very cold ) the force of the Heat draws out of the Earth in great abundance . Let us therefore suppose Mercury to be a little Planet , made of Salt-Petre ; and let the Sun extract out of himself a Remedy to his Disease which he gives to the Inhabitants . This is certain , that Nature produces no Animal , but in places where they may live ; and Custom and Use , joined with Ignorance of what is better , supplieth all Defects , and makes Life agreeable ; for ought we know , the Inhabitants of Mercury want neither Rain , nor Exhalations of Salt-Petre . After Mercury , you know , the next Planet we find in our Journey , is the Sun ; and if we judge by the Earth ( which is inhabited ) that other Bodies of the same kind may be so too , we are mistaken , and the Why not will fail us here ; for the Sun is a Body of a quite different Nature from the Earth , and other Planets : He is the Source and Fountain of all that Light , which the other Planets do only reflect from one to another , after having receiv'd it from him ; and so they can exchange Light one with another , but are incapable of producing it : The Sun alone draws from it self this precious Substance , which he darts a-round him with great Force and Violence , and which is intercepted by every Body that is solid ; so that there is reflected from one Planet to another long streams and streaks of Light , which crossing and traversing each other in the Air , are interwoven a thousand different Ways , and so form a Mixture of the richest substance in Nature : For this end the Sun is plac'd in the Centre , which is the Situation most proper and commode ; from whence he may equally dispence and distribute his Light and Heat , for the livening and enlightning all things round him . The Sun is therefore a Body of a particular Substance ; but what kind of Body , or what kind of Substance , is all the difficulty : Heretofore 't was believ'd , that the Sun was a pure Fire ; but the Error of this Opinion was found out in the Beginning of this Age , by Spots which were discover'd upon the Surface of the Sun ; as a little after that time , there were new Planets discover'd , of which I shall speak hereafter : The learned part of the World were full of nothing else but these new Planets ; and Discourses of 'em were so much in fashion , that they believ'd the Spots in the Sun were nothing else but these new Planets , moving round 'em , which necessarily hid a part of his Body from our sight , when their obscure Side was turn'd towards us . The learned Men of the World made their Court to most Kings and Princes , with these new discover'd Planets ; giving the Name of one Prince to one , and of another Prince to another ; so that they were like to quarrel , to whom they shou'd belong . I am not pleas'd with that at all , said the Marquiese : You told me the other Night , that the Philosophers and learned Men had given Names of Philosophers , Astronomers and Mathematicians to the several Countries of the Moon , and I was very well satisfy'd , and think it but just , that since the Kings and Princes possess the Earth , that they ought to suffer Philosophers and Astronomers to rule in the Moon and the Stars , without incroaching upon ' em . What , said I , Madam , Will not you allow Kings and Princes some Corner of the Moon , or some Star , to take their part in time of need ? As to the Spots in the Sun , they can be of no manner of use to 'em ; for it has been found , they are not Planets , but Clouds of Smoak and Vapours , and , as it were , a Scum arising from the Surface of the Sun ; for sometimes they appear in great Quantities , sometimes in less , and at other times they dis-appear ; sometimes they join in one , and other times they are dispers'd and dissipated ; so that it shou'd seem , the Sun is a liquid Substance ; some say , 't is of melted Gold , which boils incessantly , and produces those Impurities ; and by the force of its Motion , throws upon the Surface its Scum and Dross ; and as those consume , new ones are produc'd . Pray , Madam , fansie to your self what strange Bodies these Spots of the Sun must be ; there are some of 'em full as big as the Globe of the Earth ; judge then what a great quantity there must be of this melted Gold , and of the Extent of this vast Ocean of Light and Fire , which we call the Sun. They say , the Sun appears , through Telescopes , to be full of great Mountains which vomit Flames , and that it is , as it were , a Million of Mount Aetna's , join'd together ; but at the same time they acknowledge that these Mountains may be altogether visionary , and that they are nothing else but the Effects of the Glasses of the Telescopes . To whom shall we trust then , when these very Glasses , to which we owe so many new Discoveries , deceive us ? In fine , Let the Sun be what it will , it does not at all seem proper to be inhabited ; and yet 't is pity , for the Situation wou'd be extreamly fine ; its Inhabitants wou'd be plac'd in the Centre of the Universe , and wou'd see all the other Planets turn regularly round 'em , whereas we observe infinite Irregularities in their Course ; and 't is only because we are not in a proper Situation to consider 'em , as not being in the Centre of their Motion . Is it not hard , that there is but one place in the Universe , where the Study of the Stars wou'd be easie , and that that place alone shou'd be uninhabitable ? You do not think , whilst you speak , said the Marquiese , were any living Creature in the Sun , he wou'd see neither Planets , nor fixed Stars ; nor , indeed , any thing ; the brightness of the Sun wou'd render all things else invisible ; and if there were Inhabitants in the Sun , they wou'd be apt to believe themselves the only People in Nature . I confess , said I , I am mistaken , I consider'd only the Situation of the Sun , without the Effects of its Light. But , pray , Madam , allow me to tell you , that you who have corrected me so justly , may also be mistaken your self : The Inhabitants of the Sun wou'd not so much as see it self ; for they wou'd be incapable to support the dazling of his Light , or unable to receive it , by being too near ; and all things well consider'd , the Sun wou'd be a Country of blind Men only . So that , once for all , I conclude , the Sun cannot be inhabited ; and if you please , Madam , we will continue our Journey to the other Worlds : We are now come to the Centre , which is the lowest Point in all Circular Figures ; and therefore must return back again , and go upwards . In the Way , we shall find Mercury , Venus , the Earth , and the Moon ; all which Planets we have visited . The next that presents it self to our Observation is Mars , who contains nothing rare or curious that I know of : His Days are not a full Hour longer than ours , but his Years are double the length of ours . Mars is less than the Earth , and his Inhabitants see the Sun neither so big , nor so bright as we do . In short , Mars is not worthy the pains of a longer Discourse ; but 't is very curious to observe Iupiter , and his four Moons , or Guards : they are four little Planets , which turn round Iupiter , as our Moon turns round us . But , says the Marquiese , interrupting me , why are there some Planets attending upon others , who , it may be , are no better than themselves ? In my Opinion , it wou'd be more regular and uniform if all the Planets , great and small , had but one Motion round the Sun. Ah , Madam ! said I ; if you understood the Tourbillions , or Whistlings of Monsieur Des Cartes , whose Name is so terrible , and Idea's so agreeable , you wou'd not talk at that rate . Let my Brains turn round , said she , laughing , if they will ; I long to know what these Tourbillions are ; make haste therefore to satisfie me , I 'll manage my self no longer , but henceforth abandon all my Thoughts to Philosophy , without Reserve , let the World talk what they please ; but let me understand these Whirlings . I did not think you capable of such Transports , said I , Madam ; and I am sorry they have not a fitter Object : But to satisfie you , a Tourbillion is a heap of Matter , whose parts are disjoin'd one from another , yet moving round all one way ; each little part being allow'd a particular Motion of its own , provided always they do not obstruct the general Circular Motion . As for Example ; A Tourbillion of Air , call'd a Whirl-wind , or a Hurricain , is an infinite quantity of little Particles of Air , turning all round together , carrying along every thing they meet with in their way : You know that the Planets are carry'd round in the Celestial Matter , which is incredibly subtile and swift ; all that vast Ocean , and Mass of Celestial Substance , which is between the Sun , and the Sphere of the fixed Stars , turns round , and carries with it the Planets one way , from East to West , round the Sun , which is plac'd in the Centre ; but in shorter or longer time , as they are distant or nearer the Centre , all things turn round , even the Sun it self ; but he turns round upon his own Axis : And you are to observe thus ; if the Earth were in the middle of the Celestial Matter , as the Sun is , she wou'd also turn round upon her own Axis , like that : This is that great Tourbillion , of which the Sun is , as it were , Governor ; but at the same time , all the Planets have little Whirlings peculiar to themselves , in imitation of that great one , the Sun ; notwithstanding , they are all carry'd round the Sun , yet every one of them turns round upon his own Axis , and sweeps along with him a share of the Celestial Substance , which yields easily to any Impulse of Motion it receives , provided that does not obstruct its general Motion round the Sun ; and this is call'd the particular Whirling , or Tourbillion of a Planet , which extends as far as the Sphere of its Activity can reach ; and if it falls so out , that any lesser Planet than that which governs the Tourbillion comes in its way , 't is carry'd with it , and indispensably forc'd round it ; but yet that does not hinder both the greater Planet , and the lesser , with their Whirlings , to turn round with the great Tourbillion of the Sun. 'T was thus that , after the Creation of the Universe , the Earth carry'd the Moon round it self , because the Moon fell within the Extent or Sphere of Activity , and forc'd its Obedience . Iupiter , of whom I have said somewhat already , was happier or stronger than we ; there fell four little Planets in his Neighbourhood , and he subdu'd 'em all four : Our Earth , which is now a chief Planet , had it fallen within the Tourbillion of Iupiter , you may easily believe he wou'd have forc'd us to have turn'd round him also , Iupiter being ninety times bigger than our Earth ; and then we had been nothing but a Moon depending upon Iupiter , whereas now the Earth has a Moon of her own turning round her : So true it is , that Chance of Situation has decided our Fortune . Pray , what Assurance have we , said the Marquiese , that our Earth shall always remain in the same Situation ? I am afraid we may make a Trip one Day or other , towards some Planet as dangerous as Iupiter , who may sweep us round with it self ; or that some other stronger Planet may approach nearer to us ; for I fansie , that the violent Motions of the heavenly Matter you speak of , may agitate and shake the Planets so irregularly , that it might sometimes bring 'em nearer together , and at other times remove 'em farther from one another . We might gain rather than lose by that Bargain , said I ; for it may be , our Earth wou'd be carry'd near Venus and Mercury , which are little Planets , and cou'd not resist ours : But we have nothing either to hope or fear from such an Accident ; the Planets must remain where they are , new Conquests are forbid them , as they were heretofore to the Kings of China . You know very well , when one mixes Oil and Water together in a Vessel , the Oil will swim above ; and if you throw any very light thing into the Vessel , the Oil will support it , and it will not penetrate into the Water : Throw in any other thing , somewhat heavier , of a proportionable weight to penetrate the Oil , which is too weak to stop it ; 't will fall upon the Water , and swim , the Water being sufficiently strong to bear it up . So that this Vessel , full of two Liquors , which does not mingle together two Bodies of an unequal weight , rests naturally in two different Positions , the one above the other ; so as the lightest can never descend , the heaviest can never ascend . If you add other Liquors that will not mingle together , and throw as many Bodies into 'em of proportionable weight , 't will still be the same thing . Imagine to your self , that the Celestial Substance which fills the vast Tourbillion , or Whirling of the Sun , is compos'd of different Coats , wrapp'd within one another , like an Onion ; these Coats are of different weights and force , as Oil and Water , and other Liquors . The Planets also are of different weights ; and by consequence , every one of the Planets must stop upon that Coat proportionable to its weight , and which has necessary strength for supporting it , and keeping it in an equal Balance ; and you will perceive it is not possible in Nature they can remove from thence . I understand very well , said the Marquiese , how these different Weights are regulated , according to their several degrees : Wou'd to God , there were some such Order amongst us Mortals , to confine every Man to the Station that is fit for him . I am now no longer in fear of Iupiter ; I am satisfy'd that he will leave us at ease in our own little Whirling , or Tourbillion ; I am easily pleas'd , and do not envy Iupiter his four Moons . You wou'd be to blame if you shou'd , said I ; for he has no more than what is necessary for him ; considering the great distance he is from the Sun , his Moons receive and reflect but a very faint Light. 'T is true , that Iupiter turns upon his own Axis in the space of ten Hours , his Nights are but four Hours long ; and being so short , one wou'd think he had no great need of four Moons : But you must consider , in our Earth , under the North and South Poles , there are six Months of Day , and six Months of Night ; because the two Poles being the two Points of the Earth , remotest from those Countries and Places , upon which the Sun darts his beams directly , and over which , to our Apprehensions , he seems to perform his Course : The Moon holds , or appears to us to hold the same Road with the Sun : So that if the Inhabitants near the South and North Poles see the Sun during one half of his yearly Course , and then lose his Light during the other half , it must follow , that they see the Moon during one half of her monthly Revolution , and lose her during the other half ; that is , for the space of fifteen Days . One of Iupiter's Years is twelve of ours , and there must be two opposite Poles in that Planet where there are Days and Nights of six Years long apiece . A Night of six Years long is very long , and I believe these four Moons were chiefly created for that reason : The highest of the four , as to Iupiter , performs its Course round him in seventeen Days , the second in seven Days , the third in three Days and an half , and the fourth in forty two Hours . These Revolutions being thus divided by equal halves in these unhappy Climates , where there are six Years of continued Night , one and twenty Hours cannot pass without their seeing appear , at least , the last of the four Moons ; which is a very great satisfaction , during so long and irksome a Darkness : But upon whatever place of Iupiter you shou'd inhabit , these four Moons wou'd represent to your view one of the most agreeable Sights in Nature : Sometimes they rise all four together , then they separate according to the inequality of their Motions ; sometimes they see 'em over their Heads , directly above one another ; at other times they see 'em appear above their Horzion , at equal distances ; at another time , two of the four are rising , when the other two are setting ; but above all , I shou'd be pleas'd to see their constant Eclipsing one another , or the Sun ; for there passes no Day , without one of the two ; and since Eclipses are so familiar to that World , they must certainly be a Divertisement to them , whereas they frighten the Inhabitants of our Earth . And you will not fail , I hope , says the Marquiese , to bestow Inhabitants upon these four Moons , though they be little , inferior Planets , and only made to enlighten the Inhabitants of a greater , during their long Nights . You need not doubt of it , said I , Madam ; these four Planets are no less deserving of Inhabitants , because they are so unhappy as to be subject to , and turn round a more important Planet . I wou'd , says the Marquiese , have the Inhabitants of these four Moons to be Colonies of Iupiter , and receive their Laws and Manners from thence , and pay Homage and Respect to Iupiter , and not to look upon that great Planet , but with Veneration . And wou'd you not also , said I , have these four Moons to send Ambassadors , from time to time , to the Inhabitants of Iupiter , and swear Fealty to him ? For my part , we having no Authority over the Inhabitants of our Moon , makes me think that Iupiter has no more over the Inhabitants of his four ; and I believe , one of the Advantages he has most reason to brag of , is , that he frightens ' em . For Example ; The Inhabitants of that Moon next to Iupiter , see him three hundred and sixty times bigger than our one Moon appeareth to us : And as I believe that little Moon to be much nearer to Iupiter than Ours is ; so his greatness must be by that considerably augmented ; and they must constantly see that monstrous Planet hanging over their Heads , at a very small distance . And if it be true , that the Gauls of old , apprehended the falling of the Heavens : The Inhabitants of that Moon have more Reason to fear the falling of Iupiter . It may be , said she , they have that fright , instead of that of the Eclipses , which you told me , they are free from ; and which must be supply'd by some other piece of Folly. It must be so infallibly , said I , Madam , for the great inventer of the third System , of which I spoke to you the other Day , the Ticho-Brahe one of the greatest Astronomers that ever liv'd , was far from fearing Eclipses as the Vulgar do ; but instead of that , he fear'd , if the first he met ( as he went out of his House in the Morning ) were old , or if a Hare happen'd to cross his way , he instantly return'd home , shut himself up , and did believe that day to be unlucky ; nor wou'd he dare to attempt Business of the smallest Consequence . It is not just , said the Marquiese , that since that great Man was not free from the Fear of Eclipses for nothing , that the Inhabitants of that little Moon , shou'd come off at an easier rate : Let us give 'em no Quarter , but force 'em to submit to the common Law of Nature , and oblige 'em to yield to some other Folly. But since I will not trouble my self to guess at this time , what that may be , pray solve me one difficulty , which my Fancy has just now suggested ; if the Earth be so little , in respect of Iupiter ; does the Inhabitants of Iupiter see our Earth ? I am afraid we are altogether unknown to ' em . Really , I believe it to be so , said I , for the Inhabitants of Iupiter must see the Earth ninety times less than Iupiter appears to us ; which is too small to be perceiv'd by them ; and all we can imagine for our advantage , is , to suppose that there are Astronomers in Iupiter , who after having taken a great deal of Pains , and fitting excellent Telescopes ; and having chosen a very clear Night for making the Observation , they at last discover in the Heavens a little Planet , they had never seen before ; and streight they set it down in the Philosophical Transactions of that Country . The rest of the Inhabitants of Iupiter , either never hear of it , or laugh at it if they do ; the Philosophers themselves whose Opinion that discovery destroys , resolve not to believe it ; and there are but some very rational People , that will trouble themselves with the thoughts of it . These Astronomers make new Observations ; they again look upon this little Planet , and they begin to be assur'd that it is no Fancy but a real thing ; then they begin to conclude , this little Planet has a Motion round the Sun ; and after a thousand Observations , they at last find out that this Motion or Revolution , is performed in a Years time . So that , thanks to these learned Men , the Inhabitants of Iupiter know our Earth is a Planet and a World : The Curious are earnest to look on it through a Telescope ; tho 't is so little , 't is hardly discoverable . If it were not , said the Marquiese , very disagreeable for me to believe , that our Earth is not to be perceiv'd by the Inhabitants of Iupiter , but by the help of a Telescope , I shou'd find an Infinite Pleasure in imagining , I shou'd see those Telescopes pointing towards us ; and ours from a mutual Curiosity are levell'd at them , whil'st those two Planets gravely considering one another , the Inhabitants of both ask at one and the same time , What World is that ? What People are those ? Don't go so fast , Madam , said I ; suppose , the Inhabitants of Iupiter , cou'd see our Earth ; yet , they cou'd never see us , or so much as suspect our Earth to be inhabited ; or if any Body were Fool enough to imagine it , God knows , how he wou'd be laugh'd at and ridicul'd by the rest of the Inhabitants . And it may be , we are the Cause , that some Philosophers in that World have been sued and persecuted for this Opinion : However , I believe , that the Inhabitants of Iupiter are employed enough in the discovery of their own Planet , without troubling themselves with the thoughts of us . And had Christopher Columbus been of that Country , and understanding Navigation so well , he cou'd not have wanted employment . And the People of that World know not the hundredth part of its own Inhabitants ; whereas , in Mercury ( which is a very little Planet ) they are all Neighbours one to another , and converse familiarly together ; and they esteem it , as but a Walk to go round their little World ; and if the Inhabitants of Iupiter do not see us , you may easily judge , they can far less perceive Venus and Mercury , both which are more diminutive Worlds , and further distant from it than we : But in lieu of this , they see Mars , and there are four Moons , and Saturn with the five that belong to him . There are Planets enough , to perplex all the Astronomers there : And Nature has had the goodness to hide from 'em what remains of the Universe . What , said the Lady Marquiese , do you look upon that as a Favour ? Without doubt , said I , Madam , there is in this great Tourbillion or whirling of the Sun , Sixteen Planets . And Nature , who is willing to save us the labour of studying all their Motions , has discover'd to us only seven of them ; and is not that a great Favour . But we who are not sensible of this Grace , have so ordered the matter that by our Endeavours we have found out the other nine , which Nature had conceal'd from us , and we are sufficiently punish'd for it , by the great Pains and Labour , which is at present requisite for the Study of Astronomy . I see , answer'd she , by the number of sixteen Planets , that Saturn must have five Moons . He has so , said I , Madam , and two of the five are discover'd very lately , but there is yet something more remarkable in that Planet ; for his Year is as long as thirty of ours ; and consequently there are Climates in that World , where one Night lasts for fifteen Years together . Can you guess what Nature has intended for the enlightning of Nights so long and dreadful ? She was not satisfied to bestow on Saturn five Moons ; but has also given him a great Circle or Ring , which environs him entirely , and which is elevated sufficiently high enough to be out of the shadow of this Planet . It reflects the Light of the Sun perpetually upon the Inhabitants of Saturn , who have the Misfortune to live in that Climate , that is , so long a time depriv'd of the influence of his Beams . Well , said the Marquiese , ( with the Air of a Person return'd to herself from some great astonishment ) all that you say is contriv'd with wonderful Order , and sure Nature has seen and provided for the necessity of some animate Beings ; and that the distribution of these Moons , was not a work of Chance , since they are bestowed only upon these Planets , that are at a great distance from the Sun , the Earth , Iupiter and Saturn ; for Venus and Mercury have no need on 'em ; they enjoy but too much Light already ; and their Nights are very short ; and it may be the Inhabitants of this Planet esteem Night a greater benefit of Nature , than the Day it self . But hold , said Madam the Marquiese , it seems to me , that Mars , who is farther distant from the Sun than the Earth , ought to have a Moon too . I must confess , said I , Madam , he has none ; but certainly , the Inhabitants of that Planet enjoy some other advantage , which supplies that defect . You have seen several bodies , both liquid and dry , which draw in the Light of the Sun ; and afterwards shine and cast a light in the dark . It may be , that there are great Rocks very high ; which are naturally of such a kind of Substance , as to receive great Provision of Light in the Day time from the Sun , which they restore in the Night ; and if it be so , you cannot deny , but it must be a very pleasant Scene or Representation , to see all those Rocks from all Quarters begin to shine , as soon as the Sun is down , and make Magnificent Illuminations without Art or Expence . You know also that in America , there are certain Birds , which shine so in the dark ; that one may read by their Light , as well as by that of a Candle ; and who knows , but there are many of these Birds in the Planet Mars , which fly about and enlighten that World as soon as the Sun is set ? Your Rocks , and your flying Birds , said the Marquiese , do not at all satisfie me . I confess such objects wou'd be very pretty ; but since Nature has given so many Moons to Saturn and Iupiter ; 't is a sign , that they are absolutely necessary as well to Mars . I shou'd have been glad that all the Worlds distant from the Sun , cou'd have had their Moons ; and that Mars might not have been so disagreeably excepted . Oh! Madam , said I , if you think it worth your pains to make any further Progress in Philosophy , you must accustom your self to such Exceptions ; in the best Systems , there are always some things that agree exactly ; but there are other things , that one must adjust as well as one can , or leave them as they are , if there be no hopes to overcome the difficulty : Let us do so if you please with Mars ; and since he is not favourable to us , say no more of him . And tell me if it wou'd not be strangely surprizing , if we were in the World of Saturn , to see above our Heads in the Night that great Ring in the form of a Semi-Circle , going from opposite Points of the Horizon ; and which reflecting the Light of the Sun upon us , wou'd have the effect of a continu'd Moon . And shall we place no Inhabitants upon that great Ring , said the Marquiese , laughing ? I answer'd her , that ( tho in the Humour I was in , I was enclin'd to put Inhabitants every where ) I confess , I dare not set any upon so irregular a Habitation ; but for the five little Moons , there is no dispensing with them , for they must have Inhabitants . But some do imagine , that this Ring or great Circle is compos'd of Moons join'd very near together , having all an equal Motion , and turning one way , and that the five little Moons I spoke of , had only escaped out of this great Ring ; what an Infinity of Worlds are there then in the Tourbillion or whirlings of Saturn ? and yet whatever is the Cause , the Inhabitants of Saturn are miserable enough , notwithstanding the Assistance of this great Ring . 'T is true , it gives them Light , but what kind of Light ? Sure a very feeble one at that great distance from the Sun , where she her self appears to 'em , but as a little pale Star , a very faint heat and Light , so that if you wou'd carry some of the Inhabitants of Saturn to our coldest Countries , as Green-Land , or Lap-Land , you wou'd see 'em all of a sweat , and melt away with heat . You give me an Idea of Saturn , said the Marquiese ; that makes me shiver with cold ; whereas before you warm'd me as much with the descriptions you gave me of Mercury . There is a Necessity , said I , that the two Worlds that are at the extremity of this great Tourbillion , must be contrary one to another in every thing . At that rate , said she , the Inhabitants of Saturn must be very wise ; for you told me the Inhabitants of Mercury were down-right mad . If the People of Saturn , said I , be not wise , they are at least in all Appearance so , and are very flegmatick , they know not what it is to laugh ; and who take a whole days time at least , to answer the most trifling Question : They wou'd have look'd upon the grave Cato the Censor , as too wild and youthful for their Conversation . There is a thought come into my Head , said the Marquiese ; all the Inhabitants of Mercury are verly lively , and the Inhabitants of Saturn extremely dull : Now upon our Earth , we have a mixture of both , some are very airy , and some as insipid : Does not that proceed from our being situate in the middle , between these two Worlds , that we participate so of the Qualities of both these Extremes ; and there is no fixt settled Character of Mankind ; some resemble the Inhabitants of Mercury , others of Saturn ; and we are a mixture of all the several kinds of People , that inhabit all the other Planets ? I like that Idea well enough , said I , we are of such an extravagant Composition , that one wou'd really believe , that we were collected and drawn together from all the other Worlds . And at this rate , 't is very convenient to live in ours , since here we see an abridgement of all that can be seen in the other Worlds . At least , said the Marquiese , Our World has one real advantage and conveniency , that it is neither so hot as Mercury or Venus , nor so cold as Iupiter and Saturn : And we have the good luck over and above , to be born in a Climate of this Earth , that has neither excess of heat nor cold . And if a certain Philosopher thank'd Nature for being a Man and not a Beast , a Grecian , and not a Barbarian ; for my Part , I thank her , that I inhabit the most temperate Planet of the Universe , and the most temperate Climate of that Planet . If you will trust me , said I , Madam , you ought to thank her for being young , and not old , young and handsome , and not young and ugly , young , handsome , and a French Woman , and not a young and handsome Italian . You have abundance of other Reasons of Gratitude , than those of the Situation of your Tourbillion , or the temperate Qualities of your Country . Good God , said she , suffer me to be grateful for every thing ; even to the very Tourbillion where I was born : The measure of the Happiness bestow'd upon us , is too little to lose any part of it ; and it is good to have such a Sense and Taste of the commonest and most inconsiderable things , as to turn all to our Advantage and Profit . If we shou'd look after no other Pleasure or Satisfaction , than this World afforded , we shou'd enjoy but very few , expect 'em long , and pay dear for ' em . If Philosophy be the Pleasure , you propose , said I , Madam , I have the Boldness to wish , that when you remember the Tourbillions , you wou'd be pleas'd to think of me . Yes , answer'd she , provided you take care your Philosophy furnishes me always with new Pleasures . At least , for to Morrow , answer'd I , I hope you shall not want ; for I have the fixed Stars prepared for you , which surpass all you have hitherto heard . The Fifth Night . MY Lady Marquiese was very impatient to know what shou'd become of the fix'd Stars . Can they be inhabited as the Planets are , said she to me ? or are they not inhabited ? what shall we make of ' em ? If you wou'd take the Pains , you cou'd not fail to guess , said I , Madam , the fixt Stars cannot be less distant from the Earth , than fifty Millions of Leagues ; nay , some Astronomers make the distance yet greater ; that between the Sun and the remotest Planet is nothing if compared to the distance between the Sun or Earth , and the fix'd Stars ; we do not trouble our selves to number 'em , their Lustre as you see is both clear and bright . If the fix'd Stars , receive their Light from the Sun , it must certainly be very weak and faint before it comes to 'em , having passed through a hundred and fifty Millions of Miles of the Celestial Substance , I spoke of before : Then consider , the fix'd Stars are oblig'd , to reflect this borrow'd Light upon us at the same distance , which in reason must make that Light yet paler and more faint , it is impossible that this Light if it were borrow'd from the Sun , and not only suffer'd a Reflection , but pass'd through twice the distance of a hundred and fifty Millions of Miles , cou'd have that Force and Vivacity , that we observe in the fix'd Stars : Therefore I conclude they are enlightned of themselves ; and are by consequence so many Suns . Do not I deceive my self , cry'd out the Marquiese , do I see whither you are going to lead me ? Are you not about to tell me the fix'd Stars , are so many Suns , and that our Sun is the Center of a great Tourbillion which turns round him ; what hinders but a fix'd Star may be the Center of a Tourbillion , whirling or turning round it ? Our Sun has Planets , which he enlightens , why may not every fix'd Star have Planets also ? I have nothing to answer , but what Phoedra said to Oenone , 't is you that have hit it . But said she , I see the Universe to be so vast , that I lose my self , I know not where I am , and have conceived nothing all this while . What is the Universe thus divided into Tourbillions , confusedly cast together ? Is every fixt Star the Center of a Tourbillion ; and it may be full as big as our Sun ? Is it possible , that all this Immense space , wherein our Sun and Planets have their Revolution , is nothing but an inconsiderable part of the Universe ? And that every fix'd Star must comprehend and govern an equal space with our Sun ? This confounds , afflicts , and frightens me . And for my part , said I , it pleases and rejoices me ; when I believ'd the Universe to be nothing , but this great Azure Vault of the Heavens , wherein the Stars were placed , as it were so many golden Nails or Studs , the Universe seem'd to me too little and strait ; I fansied my self to be confin'd and oppress'd : But now when I am perswaded , that this Azure Vault has a greater depth and a vaster Extent , and that 't is divided into a thousand and a thousand different Tourbillions or Whirlings , I imagine I am at more Liberty , and breath a freer Air ; and the Universe appears to me to be infinitely more Magnificent . Nature has spared nothing in her Production , and hath profusely bestow'd her Treasures upon a glorious Work worthy of her : You can represent nothing so august to your self , as this prodigious Number of Tourbillions , whose Center is possess'd by a Sun , that makes the Planets turn round him . The Inhabitants of the Planets of any of these infinite Tourbillions , see from all sides the enlightned Center of the Tourbillion with which they are inviron'd ; but cannot discover the Planets of another , who enjoy but a faint Light , borrow'd from their own Sun , which it does not dart further than its own Sphere or Activity . You show me , said the Marquiese , so vast a Prospect , that my sight cannot reach to the end of it : I see clearly the Inhabitants of our World ; and you have plainly presented to my Reason the Inhabitants of the Moon , and other Planets of our Tourbillion or Whirling : After this you tell me of the Inhabitants of the Planets of all the other Tourbillions . I confess , they seem to me to be sunk into so boundless a depth , that whatever force I put upon my Fancy , I cannot comprehend 'em ; and indeed you have annihilated 'em by the Expressions you made use of in speaking of 'em and their Inhabitants . You must certainly call 'em the Inhabitants of one of the Planets , of one of these infinite Tourbillions ; and what shall become of us in the middle of so many Worlds ; since the Title you give to the rest agrees to this of ours ? And for my Part , I see the Earth so dreadfully little , that hereafter I shall scorn to be concern'd for any part of it . And I admire why Mankind are so very fond of Power , so earnest after Grandure , laying design upon design , circumventing , betraying , flattering , and poorly lying , and are at all this mighty Pains to grasp a part of a World they neither know nor understand , nor any thing of these mighty Tourbillions : For me , I 'll lazily contemn it , and my carelesness shall have this Advantage by my Knowledge , that when any Body shall reproach me with my Poverty , I will with vanity reply , Oh! you do not know what the fix'd Stars are . I do believe , said I , Madam , that Alexander the Great himself did not know : For a certain Author who holds that the Moon is inhabited , says very gravely , that it was impossible , but Aristotle must be of so reasonable an Opinion ( for how cou'd such a truth escape so great a Man as Aristotle ? ) but that he wou'd never say any thing of it for fear of displeasing Alexander ; for had he known there had been a World which he cou'd not have conquer'd , it wou'd have reduc'd him to certain Despair . There was yet more Reason to conceal the Tourbillions of the fix'd Stars from him ; if they had been known in those Days , he wou'd have made his Court very ill to that great Prince , who shou'd but have mention'd ' em . As for me who know 'em , I am very sorry I can draw no advantage from that Knowledge , which can cure nothing but Ambition and Disquiet , and none of these Diseases trouble me . I confess a kind of Weakness in Love , a kind of frailty for what is delicate and handsom , this is my Distemper , wherein the Tourbillions are not concern'd at all . The infinite Multitude of other Worlds may render this little in your Esteem , but they do not spoil fine Eyes , a pretty Mouth , or make the Charms of Wit ever the less : These will still have their true Value , still bear a price in spight of all the Worlds in the Universe . It is a strange thing , said the Marquiese laughing , that Love saves himself from all Dangers , and there is no Systeme or Opinion can hurt him : But tell me frankly , are your Systemes certainly true ? Do not dissemble , for I promise to keep it secret : I fansie 't is founded upon a very small bottom , a fix'd Star enlightned of it self , as the Sun is , and therefore it must be a Sun , the Soul and Center of the World having Planets turning round it as that also has . Is this absolutely necessary , says she ? I fear , Madam , said I : Since we are always in the humour of mixing some little Gallantries with our most serious Discourses , give me leave to tell you , that Mathematical reasoning is in some things near a-kin to Love ; and you cannot allow the smallest Favour to a Lover , but he will soon perswade you to yield another , and after that a little more , and in the end prevails entirely ; so if you grant the least Principle to a Mathematician , he will instantly draw a consequence from it , which you must yield also , and from that another , and then a third , and maugre all your Resistance , in a short time , he will lead you so far , that you cannot retreat . These two sorts of Men , The Lover and Philosopher always take more than is given ' em . You must acknowledge that when I see two Objects alike in every thing that I do see , I have Reason to believe them to be also alike in what I see not ; for where is the hindrance or difficulty ? From thence I have argu'd that the Moon is inhabited because it is like the Earth ; that the other Planets are inhabited because they are like the Moon . I find that the fix'd Stars are like our Sun as to what I see ; and therefore , I conclude they are Suns , and have Planets turning round about 'em ; and every thing else we attribute to our Suns . Now , Madam , you are too far engag'd to retire ; and therefore you must generously yield . By this rule of resemblance , said she , which you make betwixt our Sun and the fix'd Stars , the Inhabitants of another Tourbillion , must only see our Sun as a small fix'd Star , which only appears to them , during their Night . Without doubt , said I , Madam , our Sun is so near us , in respect of the Suns of the other Tourbillions , that his Light must have infinitely greater force upon our Sight than the Light of the other Suns ; when we see our Sun , we see nothing else , his brightness makes all other things disappear : In another great Tourbillion , where another Sun governs , he in his turn removes and darkens our Sun , which does not appear , but in the Night as a fix'd Star amongst the other strange Suns ( that is ) fix'd Stars , and our Sun appears to the Inhabitants of that Tourbillion in the great Vault of the Heavens , as a Star of some Constellation , such as the Bear or the Bull : As to the Planets which turn round about him ( as our Earth for example ) since they cannot see it at so great a distance , they do not so much as think of it , so that all these Suns are Suns by day for the Tourbillion which they govern , and fix'd Stars by Night ; for all the other , every one of them is the only one of his kind in his own World ; but serve only to make up the Number of fix'd Stars for all the other Worlds . Notwithstanding , said she , of this Equality of Resemblance of the Worlds , yet I cannot believe , but they differ in a thousand things , for likeness upon the main does not hinder infinite little differences . Most certainly , said I ; but the difficulty will be , to find out those Differences . What do I know but in one Tourbillion , there are more Planets turning round it than in another ? In one there are Inferior Planets turning round the greater , in another there are none at all : In one Tourbillion the Planets are gather'd together , as it were a little Party , round their Sun , and beyond them a vast Vacuity , extending to the next Tourbillion ; in another , the Planets take their Course towards the Extremity of their Tourbillion , and leave a Void in the middle , and I do not doubt but there are Tourbillions destitute of Planets ; and others , where their Sun is not plac'd in the middle , and yet has a free Motion , and carries his Planets round with him ; others , where the Planets rise and fall in respect of their Sun , according to the Changes of the Counterpoise which balances ' em . What wou'd you have , Madam ? Have not I said enough for a Man that was never out of his own Tourbillion ? No , said she , not for the quantity of Worlds which you say there is : What you have describ'd will suffice but for five or six , and I see thousands . What wou'd you say , Madam , said I , if I shou'd tell you that there are infinitely more fixed Stars than those you see , that by the help of Telescopes an unaccountable number are discover'd , which we cannot see with our Eyes alone ; and that in one Constellation , where we counted but twelve or fifteen fixed Stars , there have been discover'd more than we see with our Eyes in the whole Heavens ? I ask your Pardon , said she ; I yield and confess , you have over-charg'd me with Worlds and Tourbillions . Madam , said I , I have still a Reserve for you : You see that Whiteness in the Hemisphere , call'd The Milky Way ; Can you imagine what it is ? 'T is nothing but an Infinity of little fixed Stars , which cannot be seen by our Eyes , because they are so very small , and are plac'd so near to one another , that they appear to be but one continued Whiteness : I wish you cou'd see this Ant-hill or Stars , and these Seeds of Worlds ; they look like the Maldevia-Islands , or those twelve thousand little Isles , or Banks of Sand , separate only by small Canals of the Sea , which one may over-leap with as much Ease as a Ditch . So that these little Tourbillions of the Milky Way , being so near one to another , may converse and shake hands with those of their Neighbouring World ; at least , the Birds of one World may fly into another ; and they may teach Pidgeons to carry Letters , as they do in the Levant . By which , the Sun , in his own Tourbillion , as soon as he begins to spread his Light , he faceth that of all other Stranger-Suns ; for if you were in one of these little Tourbillions of the Milky Way , your Sun wou'd not be so near to you ; and by consequence , wou'd have but little more power , force , or influence upon your Eyes , than a hundred thousand other Suns of the neighbouring Tourbillions ; you wou'd then see your Heaven shining with an infinite number of Fires , very near to one another , and not far distant from you ; and tho' you shou'd lose the sight of your own Sun , you wou'd still have Light enough , and your Nights wou'd be no less bright than your Days ; at least , you wou'd not be sensible of the difference ; or , to speak more properly , you wou'd have no Night at all : The Inhabitants of this World , accustom'd to perpetual Day , wou'd be strangely surpriz'd if one shou'd tell 'em , that there are several People in the Universe , who are under the Tribulation of dismal , real Nights , and who fall into long and profound Darknesses , and who , when the Light returns , behold one and the same Sun : They wou'd look upon such People as the Out-casts of Nature , and the very Thoughts of our sad Condition wou'd sieze them with Horrour . I do not ask you , said the Marquiese , whether there be any Moons in the World of the Milky Way ; I see very well , that they wou'd be of no use to these Planets that have no Night ; and who besides , move in too little Room to be troubled with an Equipage of inferior Planets . But do you know that by your multiplying upon me such a multitude of Worlds , you have started a great Difficulty to my Fancy , which , I doubt , you will hardly satisfie : The Tourbillions , whose Suns we see touch the Tourbillions where we are , and all the Tourbillions are round , how is it possible that so many different Globes can touch one single one ? This I wou'd willingly understand , but find I cannot . There 's a great deal of Sense , said I , Madam , in your proposing of this Difficulty , and no less in your not knowing how to salve it ; for 't is very judicious in it self , and unanswerable , as you understand it ; and 't is an Argument of very little Wit , to answer an Objection that is unanswerable . If our Tourbillion were in the shape of a Dy , it wou'd have six plain Superficies , and wou'd be very far from being round ; yet upon every one of these six Superficies , or flat Sides , a Tourbillion might be plac'd , being of the same Figure : But instead of six flat sides , suppose it had twenty , fifty , or a thousand ; then it were possible to place a thousand Tourbillions upon it , every Side bearing one ; and you easily understand , that the more Superficies , or flat Sides any Body has , the nearer it approaches to a Globe : So a Diamond cut in Fossets on all sides , if those Fossets were very small , that Diamond wou'd be as round almost as a Pearl of the same bigness ; the Tourbillions are only round in this sense , they are compos'd of an infinite number of flat Sides , and every one of 'em carries another Tourbillion : The flat Superficies are very unequal ; here they are big , there they are little ; the smallest Superficies of our Tourbillion , for Example , answer to the Milky Way , and support all those little Worlds ; but if two Tourbillions , that rest upon two neighbouring Sides or Faces , have any void space below between 'em ( as that must fall out very often ) Nature , who will lose nothing , and turns all her work to the best advantage , instantly fills up that Vacuity with one , two , or it may be a thousand little Tourbillions , which does not at all trouble or incommode the rest , and yet every one of these may have a World in it ; so that there may be more Worlds , than our Tourbillion has flat Sides to support : And I dare say , that although these little Worlds were only made to fill up Chinks of the Universe , which otherwise wou'd have been useless , and that they are altogether unknown to the other Worlds which touch them ; yet I doubt not but they are very well contented with their own Condition , and 't is they whose little Suns we discover by the helps of Telescopes , whose number is so prodigious . In fine , all these Tourbillions are so rightly adjusted , and join'd to one another in so delicate a Form , that every one turns round his own Sun , without changing his Situation ; every one takes that way of turning , which is most proper and commode to its place : They are fixed to one another like the Wheels of a Watch , assisting one another in their Motions , and yet moving contrary to one another . And 't is said , that every World is like a Balloon , or Foot-ball , which swells and fills of it self , and which wou'd extend farther , if it were not hinder'd by neighbouring Worlds , who press it , and then it shrinks to its first form ; after that , it swells a-new , and is again depress'd . And the Philosophers pretend , that the fixed Stars transmit to us a trembling Light , and an unequal Sparkling , because their Tourbillions push against ours , and ours against theirs . I am extreamly in love , said the Marquiese , with these Idea's you give me of the Balloons , which swell and fall every Moment ; and those Worlds , which are always justling together : But , above all , I am pleas'd to consider , that this Strife amongst 'em produces a Commerce of Light , which is the only Traffick they can have . No , no , said I , Madam ; that is not the only Traffick ; the neighbouring Worlds send Envoys sometimes to us , and that with a great deal of Splendor : We have Comets from thence too , who are always adorn'd with shining Hair , a venerable Beard , and a Royal Train . Good God! said the Marquiese , laughing ; What Ambassadors are these ? We cou'd easily dispence with their Visits , for they do nothing but fright us . They fright only Fools and Children , Madam , said I ; but of those Ignorants , I confess , there are a great number : The Comets are nothing but Planets which belong to some neighbouring Tourbillion , who make their Course toward the Extremity , or Out-side of it : But this Tourbillion being press'd by others that encompass it , 't is rounder above than it is below , and it is from below that they appear to us . These Planets , which have begun to move in a Circle above , and not fore-seeing that their Tourbillion will sail 'em below , because it is , as it were , braz'd or squeez'd in that part ; these Planets , which we call Comets , are necessitated , for the Continuance of their Circular Motion , to come into another Tourbillion , which happens sometimes to be ours , making their passage through the Extremity of it : They all appear to us highly elevated , their Course being constantly above Saturn . 'T is very necessary for the Defence of our System ( for Reasons that do not at all relate to our present Subject ) that there shou'd be a great vast space betwixt Saturn , and the Extremities of our Tourbillion , free from Planets . Our Adversaries do constantly reproach us with the unusefulness of this great Void ; but let 'em not trouble their Heads with that , for we have found an Use for it ; and it is the Appartment , or Chambers of State , where we receive the Stranger Planetary Ambassadors . I understand you , said she , and am pleas'd with your Chamber of State ; for we do not permit 'em to come directly in the middle of our Tourbillion , but receive 'em as the Grand Seignior does his Foreign Ministers ; he does 'em not the Honour to lodge 'em in Constantinople , but sends 'em to the Suburbs . Madam , reply'd I , we agree with the Turks also in one thing more ; that is ( as they ) so we receive Ambassadors , but send none ; for none of our Planets ever go to visit other Worlds . At this rate , said the Marquiese , we are very proud , yet I know not what to think of the matter ; these Stranger-Planets , with their long Tails and Beards , have usually but a scurvy threatning Look , and it may be they are sent to terrifie us ; whereas ours , not being made of that terrible Form , wou'd not be so proper to frighten People , were they sent into another World. These Tails and Beards , said I , are not real , but only Appearances , and these Stranger-Planets differ in nothing from ours ; but entring into our Tourbillion , they take a Tail , or a Beard from a certain kind of Illumination which they receive from the Sun ; which , as yet , is not fully explain'd amongst us . But let this be found out when it can , we now are sure it is nothing but a kind of Illumination , or false Light. I wish then , said the Marquiese , that our Saturn wou'd take a Tail , or a Beard , and go into some other Tourbillion , to frighten its Inhabitants ; and that afterwards , laying aside this terrible Equipage , he wou'd return , with the rest of our Planets , to his own place . 'T will be better for him , said I , not to go out of our Tourbillion : I have told you already of the Encounter between two Tourbillions pushing against one another ; and I believe , upon that occasion , a poor Planet is strangely shaken , and that his Inhabitants are not the better for it . We believe our selves very miserable when we see a Comet appear , but it is the Comet it self that is most unhappy . I do not believe that , said the Marquiese , for it brings its Inhabitants to us in good health ; and you know , nothing is wholsomer than Change of Air : As for us that never go out of our own , Life languishes but dully on . If the Inhabitants of a Comet had but the Skill to fore-see their Passage into our World , those who have already made that Voyage will tell these new Adventurers what they will see in their way : A Planet , say they , which has a great Ring round him , meaning Saturn ; and then you will see another that has four little ones following him , and it may be that amongst them there are People set a-part , on purpose for observing the very Minute when they shou'd enter into our World , and who are instantly to cry out , A new Sun ! A new Sun ! as our Mariners do , Land ! Land ! after a long Sea-Voyage . I hope you will no longer pity the Inhabitants of a Comet ; but , no doubt , you will commiserate those who live in a Tourbillion where the Sun comes to be extinct , and leaves them in Eternal Night . What! cry'd out Madam the Marquiese , Can Suns be extinguish'd ? Yes , said I , without dispute . The Ancients have seen fixed Stars in the Firmament , which we see no more ; these Suns have lost their Light : A great Desolation certainly for that Tourbillion , and a great Mortality for all the Inhabitants of its Planets ; for there is no living without a Sun. That Idea , said she , is too mournful ; Is there no way to pass it by ? If you please , said I , Madam , I 'll tell you what very learned Men say ; that the fixed Stars which have disappeared are not however extinguished , but that they are Half-Suns ; that is to say , they have one side obscure , and the other englightned ; and as they turn upon their own Axis , sometimes they present their enlightned half , and then we see 'em ; and sometimes their obscure half , and then we lose ' em . To oblige you , Madam , I shall follow this Opinion , because 't is more favourable than the other ; but it must only be for certain Stars , who have regular Seasons of appearing and disappearing , as hath been discover'd ; otherwise these Half-Suns cannot subsist . But what shall we say of Stars that disappear , and do not shew themselves again after the time in which they ought certainly to have perform'd the Revolution upon their own Axis ? You are too just , Madam , to oblige me to believe that these Stars are Half-Suns : However , for your Satisfaction , I will endeavour to solve this Objection another way : Those Suns shall not be extinguish'd then , but shall only be sunk into the depth of the vast Heavens , which removes 'em from our sight ; and in that Case , these Suns are follow'd by their Tourbillions , and all is well . 'T is true , that the greatest part of the fixed Stars have no such Motion as carry them from us ; if they had , they might as well approach more near us , and we shou'd see 'em sometimes bigger , sometimes less ; which can never fall out : Let us therefore suppose that there are some little Tourbillions of less Light and Activity , which slide in among the others , and make certain Turnings ; after which , they come back again , whilst in the mean time the great Tourbillions remain where they did before ; and 't is a strange Misfortune that there shou'd be certain fixed Stars which appear to us , and after a great deal of time of appearing and dis-appearing , entirely vanish , and are lost . In that time the Half-Suns , I spoke of , wou'd appear again , and Suns that were sunk into the Heavens wou'd dis-appear once , and not to appear again for a long time . Resolve well what to think , Madam , and take Courage ; there is a necessity that these Stars must be Suns , which grown obscure enough to be invisible to our sight , are afterwards enlightned , and in the end must lie extinguished . How ! said the Marquiese ; Can a Sun be obscur'd , or entirely extinguish'd , who is himself the Fountain of Light ? The most easily in the World , said I , Madam : According to the Opinion of Des Cartes , our Sun has Spots ; let 'em be Scum or Vapours , or what else you will , these Spots may condense , and many of 'em may come together , and form a kind of Crust , which may afterwards augment , and then farewel the Sun and all its Light. 'T is said , we escap'd once very hardly , for the Sun was grown extreamly pale for several Years together ; and particularly the Year after the Death of Iulius Caesar , it was that Crust that began to gather , and the Face of the Sun brake and dissipated it ; but had it continu'd , we had been all undone . You make me tremble , said the Marquiese ; and now that I understand the Consequences of the paleness of the Sun , I shall henceforth every Morning , instead of going to my Looking-Glass to consult my own Face , go and look up to the Heavens to consider that of the Sun. Madam , said I , be assur'd there goes a great deal of time to ruin a World. Then , said she , there is nothing requisite but Time. I acknowledge it , Madam , said I ; all this vast Mass of Matter which composes the Universe , is in perpetual Motion , from which no part of it is entirely exempt ; and therefore Changes must come sooner or later , but always in Time proportionable to the Effect . The Ancients were foolish to imagine , that the Celestial Bodies were of an unchangeable Nature , because they never saw any Change in 'em ; but they had neither Leisure nor Life long enough to undeceive themselves by Experience ; but the Ancients were young in respect of us . Suppose now , Madam , that the Roses , which last but for a Day , shou'd write Histories , and leave Memorials from one to another ; the first wou'd have describ'd the Picture of their Gardener of a certain manner ; and after fifteen thousand Ages of Roses , the others that had follow'd 'em wou'd have alter'd nothing in that Description of the Gardener , but wou'd have said , We have always seen the same Gardener , since the Memory of Roses we have seen but him , he has always been as he is , he dies not as we do ; nay , he changes not , and certainly will never be other than what he is : Wou'd this way of arguing of the Roses be good ? Yet it wou'd be better grounded than that of the Ancients , concerning Celestial Bodies ; and tho' there had never happen'd any Change in the Heavens to this Day , and tho' they shou'd seem to last for ever , yet I wou'd not believe it , but wou'd wait for a longer Experience ; nor ought we to measure the Duration of any thing by that of our own scanty Life . Suppose a thing had a Being a hundred thousand times longer than ours , shou'd we therefore conclude it shou'd last for ever ? Eternity is not so easie a matter ; and some things must have pass'd many Ages of Men , one after another , before any sign of Decay had appear'd in ' em . I am not so unreasonable , said the Marquiese , as to consider the Worlds as things eternal , nor will I do them the honour to compare 'em to your Gardener , who liv'd so many Ages longer than the Roses : They are themselves but as a Rose , which are produc'd but in a Garden , that bud one Day , and fall the next ; and as those Roses die , new ones succeed ; so for some ancient Stars that dis-appear , other new ones are born in their places , and that Defect in Nature must be so repair'd , and no Species can totally perish . Some will tell you , they are Suns , which draw near to us after having been long lost in the depth of Heavens : Others will say , they are Suns that have cast off the Crust which began to cover them . If I cou'd easily believe all this , yet I shou'd believe also that the Universe was made in such a manner , that new Suns have been , and may be form'd in it from time to time ; and what shou'd hinder the Substance proper to make Suns from gathering together , and producing new Worlds ? And I am the more inclin'd to believe these new Productions , since they are more correspondent to the great Idea I have of the glorious Works of Nature : And why shou'd not she who knows the Secret to bring forth and destroy Herbs , Plants and Flowers , in a continu'd Succession , practise also the same Secret on the Worlds , since one costs her no more Pains and Expence than the other . Indeed , says the Marquiese , I find the Worlds , the Heavens and the Celestial Bodies so subject to change , that I am altogether returned to my self . Let us return yet more , said I , and if you please , make this subject no longer , that of our Discourse ; besides you are arriv'd at the utmost bounds of Heaven ; and to tell you , that there are any Stars beyond that , were to make my self a wiser Man than I am , place Worlds there , or place none there , it depends upon your Will. These vast invisible Regions , are properly the Empires of Philosophers , which it may be are or are not , as they themselves shall fansie . 'T is sufficient for me to have carried your Understanding as far as your sight can penetrate . What , cry'd out the Marquiese , have I the Systemes of all the Universe in my Head , am I become so learned ? Yes , Madam , you know enough ; and with this Advantage , that you may believe all or nothing of what I have said , as you please . I only beg this as a Recompence for my pains , that you will never look on the Heavens , Sun , Moon or Stars , without thinking of me . FINIS . Books lately Printed for W. Canning . LA Montre ; or , The Lover's Watch : by Mrs. Behn . The Lucky Chance ; or , An Alderman's Bargain : A Comedy . By Mrs. Behn . The Island-Princess ; or , Generous Portuguese : A Comedy . Altered by Mr. Tate . An Historical and Geographical Account of the Morea , Negropont , and the Maritime Places , as far as Thessalonica : Illustrated with forty two Maps of the Countries , Plains and Draughts of the Cities , Towns and Fortifications . Written in Italian by P. M. Coronelli , Geographer to the Republick of Venice . Englished by R. W. Gent. Gesta Grayorum ; or , The History of the high and mighty Prince , Henry Prince of Purpoole , Arch-Duke of Stapulia and Bernardia , Duke of High and Nether Holborn , Marquis of St. Giles and Tottenham , Count Palatine of Bloomsbury and Clerkenwell , Great Lord of the Cantons of Islington , Kentish-Town , Paddington and Knights-bridge , Knight of the most Heroical Order of the Helmet , and Sovereign of the same : Who reigned and died , A. D. 1594. Together with a Masque , as it was presented ( by His Highness's Command ) for the Entertainment of Q. Elizabeth ; who , with the Nobles of both Courts , was present thereat . Hearing a Translation of the Plurality of Worlds , was doing by another Hand , the Translator had not the opportunity to supervise and correct the Sheets before they were wrought off ; so that several Errata have escaped . The most material ones are under-written . PAge 17. line 26. read Piraeum . p. 20. l. 21. for Beams , r. Bodies . p. 21. l. 6. f. least , r. last . p. 28. l. 1. f. Circle , r. Earth . p. 29. l. ult . f. Circle , r. Earth . p. 30. l. 13. f. every , r. any . p. 32. l. 1. f. as , r. it s . p. 34. l. 6. f. hands , r. heads . p. 36. l. 28. for twenty , r. two or three . p. 37. l. 11. for twenty , r. two or three . p. 38. l. 17. del . to remove . p. 44. l. 20. r. Diaphanous . p. 48. l. 13. r. hath day . p. 50. l. 21. f. certain , r. say it is . p. 65. l. 17. f. Waves , r. Sea. l. 18. f. vessel is , r. waves were . p. 72. l. ult . r. irregularly . p. 76. l. 25. f. as a rounded , r. around her . p. 77. l. 2. f. Air , r. one . p. 85. l. 13. for Refections , r. Refractions . ibid. l. 25. after I do , add not . p. 92. l. 16. f. varieties ; r. vacuities . p. 100. l. 20. f. easts , r. lasts . p. 106. l. 23. f. effects , r. defects . p. 109. l. 8. r. or Whirlings . p. 125. l. 19. f. flying , r. shining . p. 147. l. 26. f. braz'd , r. embarass'd . p. 154. l. 8. f. face , r. force or heat . 
A60283	----	The principles of astronomy and navigation, or, A clear, short, yet full explanation of all circles of the celestial and terrestrial globes and of their uses : being the whole doctrine of the sphere and hypotheses to the phenomena of the primum mobile : to which is added a discovery of the secrets of nature which are found in the mercurial-weather-glass &c. : as also a new proposal for buoying of a ship of any burden from the bottom of the sea / by George Sinclair. Sinclair, George, d. 1696. 1688 Approx. 146 KB of XML-encoded text transcribed from 82 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2003-11 (EEBO-TCP Phase 1). A60283 Wing S3857 ESTC R26242 09398782 ocm 09398782 42972 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A60283) Transcribed from: (Early English Books Online ; image set 42972) Images scanned from microfilm: (Early English books, 1641-1700 ; 1315:23) The principles of astronomy and navigation, or, A clear, short, yet full explanation of all circles of the celestial and terrestrial globes and of their uses : being the whole doctrine of the sphere and hypotheses to the phenomena of the primum mobile : to which is added a discovery of the secrets of nature which are found in the mercurial-weather-glass &c. : as also a new proposal for buoying of a ship of any burden from the bottom of the sea / by George Sinclair. Sinclair, George, d. 1696. Sinclair, George, d. 1696. Proteus bound with chains, or, A discovery of the secrets of nature which are found in the mercurial-weather-glass. [6], 85, 49, 14 p. Printed by the heir of Andrew Anderson, Edinburgh : 1688. "Proteus bound with chains, or, A discovery of the secrets of nature which are found in the mercurial-weather-glass" has special t.p. and separate pagination. Reproduction of original in the Cambridge University Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. 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Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Astronomy -- Early works to 1800. Navigation -- Early works to 1800. 2003-07 TCP Assigned for keying and markup 2003-07 Apex CoVantage Keyed and coded from ProQuest page images 2003-09 Mona Logarbo Sampled and proofread 2003-09 Mona Logarbo Text and markup reviewed and edited 2003-10 pfs Batch review (QC) and XML conversion THE PRINCIPLES OF Astronomy and Navigation : OR , A Clear , Short , yet Full Explanation , of all Circles of the Celestial , and Terrestrial Globes , and of their Uses , being the whole Doctrine of the Sphere , and Hypotheses to the Phenomena of the Primum Mobile . To which is Added A Discovery of the Secrets of Nature , which are found in the Mercurial-Weather-Glass , &c. AS ALSO A New Proposal for Buoying up a Ship of any Burden from the Bottom of the Sea. By GEORGE SINCLAR , sometime Professor of Philosophy in the Colledge of GLASGOW . Edinburgh , Printed by the Heir of Andrew Anderson , Printer to His most Sccred Majesty , Anno d 〈…〉 Academiae Cantabrigiensis Liber . To the Right Honourable MAGNUS PRINCE , Lord Provost ; Alexander Brand , Alexander Simpson , Iohn Morray , and William Montgomery , Baillies ; Iames Nicolson Dean of Gild , Edward Marjorebanks Thesaurer ; and remanent Members of the Honourable Senate , of the Antient City of Edinburgh . May it please your Lordship , and the Honourable Senate , IT is neither Ambition , nor Ignorance of your Worth and Merit , which have inclin'd me , to prefix your Names to the Frontispiece of this mean Pamphlet , but the sure experience I have of your encouraging all vertuous Actions and Learning . What I have now in Equity and Reason presented , I humbly desire the Honourable Senate , may accept favourably . I owe all I have , and my Self too , to your Devotion and Service . I chuse rather to be doing somewhat Amiss , than doing Nothing . 'T is the Widows Mite , which I have shelter'd under the Wings of your Protection . If I should endeavour , but to recapitulat , what Sentiments of your Kindness I have found , both Time , and my Memory would fail me . None can think , that there is any Deserving in me , which can be proportionable to those unvaluable Acts of your Bounty . If there be any , I am confident , it is too too scanty to Oblige . When I was able to do more , none were found more willing . I endeavoured indeed , according to my Capacity , to contribute my Assistance for promoving that great and noble Design , which was accomplish'd ; for which the Generations to come , shall call you Happy , whom you have Enriched , with Refreshing-Streams of Cooling-Waters , more Advantagious and Useful to the City , than the Fruit of the Vine . I cannot satisfie all the Obligations to Duty , which ly upon me . The more I was inclin'd to offer this Trifle , the more I was overcome with Reasons perswading to the contrary . But the uprightness of my Intention , to beautify this trivial Subject , with the Splendor , and Glory of your Names , will excuse the faillings of my Understanding . I cannot remunerat the Kindness of the Honourable Senate , better , than by Hearty Prayer , that the LORD may give you , the Spirit of Wisdom , and Government , to Manage the Weighty Affairs of the City , and His Conduct , not only to Guide each one of you , in his particular Calling , but all of you , to the endless Fruition of Immortal Life . This I fervently wish , while I am Your Lordships and the Councils , much Obliged Servant , GEORGE SINCLAR . TO THE READER . I Iudge it altogether needless to Preface any thing by way of Commendation to the following Tracts . They will ( I hope ) commend themselves , to the intelligent Reader . There is first , The Doctrine of the Sphere , so compendiously set down , that nothing can either be Added , or Subtracted . It is the very Rudiments of Astronomy and Navigation , and of many other Mathematical Sciences . By the use of the Globes , the whole Doctrine of the Sphere may be easily comprehended , even by the meanest Capacity . The second Tract , is not so evident , because more Physical , and less Mathematical , but perhaps as sure . I have set down my own Thoughts only , If any Man shall offer to salve the Phenomena better , I shall be glad . The third Tract is , a new Invention for Buoying up of Ships from the Ground of the Sea. This Proposal was made some few Years ago , to try the Invention and Wit of some Notional Men , but though they have plowed with my Heifer , yet were they not able , to find out my Riddle : Nay some of them were so confident to aver , that when this Proposal was made to them , How to make a Vessel Sail below the Water ; they Replyed , it might be easily resolved by their Analyticks . ERRATA . IN the second Tract , Page 28. line 13. for earthly read earthy . pag. 33. lin . ult . for Idaea read Idea . THE PRINCIPLES OF Astronomy and Navigation . CHAP. I. Of the Circles of the Sphere in general . THE material Sphere , is an Instrument , whereby all the Phenomena of the Primum Mobile , are most easily known . It is composed of Ten Circles chiefly , which are , the Equinoctial , the Zodiack , the two Colures , the Horizon , the Meridian , the two Tropicks , and the two Polars . Those Circles , are three manner of ways distinguished among themselves . First , Some of them are called Circuli Maximi , the Greatest Circles ; others are called Circuli Minores , the lesser Circles . The Greatest are , the Equinoctial , the Zodiak , the two Colures , the Horizon , and the Meridian ; because there cannot be greater Circles in the Sphere , than they are . The lesser Circles are , the two Tropicks , and the two Polars . They are so called , because there are found in the Sphere greater ones . Secondly , The Circles of the Material Sphere , while the Primum Mobile is turning about , are either Parallel one to another , Right , or Oblique , that is , to ly crosly . The Parallel Circles , are the two Polars , the two Tropicks , and the Equinoctial , which ly middle between them , together with their Equinoctial , who live under the Poles . The Oblique Circles are , the Zodiack , and the Oblique Horizon . For this cutteth the Equinoctial , at Oblique Angles ; the other by reason of its Situation doth the same to the rest of the Circles . The Circles called Right Circles , are the two Colures , the Meridian , and the Right Horizon , because they cut the Equinoctial at Right Angles . Thirdly , The Circles of the Sphere , are either Moveable , or Immoveable . The Moveable Circles , are these which are turned about with the Sphere , being eight in number , to wit , the Equinoctial , the Zodiack , the Equinoctial Colure , the Solstice Colure , the Tropick of Cancer , the Tropick of Capricorn , the Polar Artick , and the Polar Antartick . The Circles Immoveable , are the Meridian , and the Horizon ; so called , because while the Sphere is carried about , they stand stedfast , and unmoveable . CHAP. II. Of the Equinoctial . THe Equinoctial , is one of the greatest Circles , of the Sphere Moveable , and equally distant from the Poles of the World. It is called one of the greatest , that it may be distinguished from the lesser , as well from those , which are fixed in the Sphere , as from others , which we must imagine to be in it . It is called Movable , that it may be distinguished , from the Horizon of those , who live under the Poles , which coinciding with the Equinoctial , must differ from it in this , that the one is Movable , the other Immovable . Lastly , by reason of the third difference ( equally distant from the Poles of the Sphere ) it is distinguished from the Oblique , and Right Circles of the Sphere . It is called by divers Names . For sometimes it is called the Equator , sometimes the Equinoctial , and sometimes the Middle , and greatest of the Parallels . The Uses and Offices of the Equinoctial are these . 1. It measureth the first Motion . For this Circle , of all the Circles of the Sphere , under any Position whatsoever , moveth equally ; and therefore , it ought to be also the Measure of Time , it being most fit for determining the quantity of the Artificial , and Natural Days . For this cause , it is , that the Degrees of the Equinoctial , are called by some , Tempora , Times . 2. It pointeth forth to us in the Ecliptick , the two Equinoctial Points ; those Points , in which the Equinoctial , and Ecliptick cut one another , in the beginning of Aries and Libra . For when the Sun cometh to these Points , the Day and the Night are of equal length over all the Earth , which falleth out on the 10 or 11 of March , and on the 13 or 14 of September . 3. That which is Anomolous , and Irregular in the Oblique Motion of the Zodiack , is reduced to a sure Rule , by the help of the Equinoctial . 4. It divideth the Sphere into two equal parts ; the one called the North part , in which is the Pole , named Polus Septentrionalis , Boreus , or Articus : the other called the South part , in which is the Pole , named Polus Australis , Meridionalis , or Antarticus . 5. By this means , it divideth the Zodiack into six Signs , called Northern Signs , and into other six called Southern Signs . 6. From the Equinoctial are numbred the Declinations of all , and whatsoever Points in Heaven , as well South as North. The Declination of any Point , or Star , is an Arch of a Circle of Declination , measured between the Equinoctial , and the said Point , or Center of the said Star. Circles of Declinations , are of the Greatest Circles in the Sphere Movable , passing thorow the Poles of the World , and any point given . 7. Upon the Equinoctial , we reckon the Right Ascension of any , or whatsoever Point in Heaven . Right Ascension , is nothing else , but an Arch of the Equinoctial , measured between the first Point of Aries , and that Circle of Declination , which passes thorow the point given . 8. Upon the same Equinoctial , we measure the Oblique Ascension , and Descension of any point in Heaven whatsoever . Oblique Ascension , is an Arch of the Equinoctial , measured between the first Point of Aries , and that Point of the Equinoctial , which riseth in the same Moment of Time , with the Point given . Oblique Descension , is an Arch of the Equinoctial measured between the Point foresaid , and that Point of the Equinoctial , which sets in the same Moment of Time , with the Point given . 9. Upon the Equinoctial , we count and reckon the Ascensional Difference , which is nothing else , but an Arch of the Equinoctial , by which Right Ascension differs from Oblique . 10. Upon the Equinoctial , we measure the Rising and Setting Amplitude . This Rising and Setting Amplitude , is nothing else , but an Arch of the Horizon , measured between the Rising , or Setting of the Equinoctial , and the Rising or Setting of any Star , or Point given . 11. Upon the Equinoctial , we number the Longitudes of Places , and upon the same , we reckon the Latitudes of Places . The Longitude of a place , is an Arch of the Equinoctial , measured between the first Meridian , and the Meridian of the Place . The Latitude of a Place , is an Arch of the Meridian measured between the Equinoctial , and Zenith of the Place . 12. The Equinoctial is most useful for making of Sun-Dials : for there must be as many Hours upon the Plain , as there are 15 Degrees in the Equinoctial , four and twenty times numbred . CHAP. III. Of the Zodiack . THe Zodiack , is one of the Greatest Circles of the Sphere , Movable , under which the Planets perpetually haunt . The first and second Difference are added , as in the Definition of the Equinoctial . The third , which is in these words ( under which the Planets perpetually haunt ) do distinguish the Zodiack from all other Circles . For it may come to pass , that , this or that Planet , by his proper motion , may be under the Meridian , may be under some Horary Circle , may touch lightly the Horizon , but that is not always , nor do they always abide in the same Situation : but their stay is perpetual under the Zodiack . And because the Planets wander in the Heavens , viâ obliquâ , therefore this Circle is made oblique , and seing in this obliquity , they make digression , from this side , to that side , and from that to this , therefore Astronomers have granted to this Circle Latitude , whereby also it may be differenced from all other Circles , none of which ever claimed Latitude . The Zodiack is divided , first in relation to its Latitude , into North Latitude , and South Latitude . North Latitude , is that half part of the Zodiack , which from the Ecliptick ( the middle Line of it ) declines toward the North. South Latitude is opposite to this . Each one of them contains Eight Degrees , whereof the Equinoctial contains 360. The Ecliptick , or middle Line of the Zodiack , is one of the Greatest Circles of the Sphere , Moveable , under which , the Sun from West to East moves perpetually . This Line , as likewise the Zodiack , is divided according to Longitude into twelve Parts , which are called in Greek 〈◊〉 . Every one of these twelve , are subdivided into 30 parts , so that the whole Zodiack contains 360 Degrees . These twelve Divisions are called Aries , Taurus , Gemini , Cancer , Leo , Virgo , Libra , Scorpius , Sagittarius , Cap●…s , Aquarius , Pisces . But seing there are four Cardinal Points , two of the Equinoctial , and two Solstice Points , it hath pleased Astronome●… , to make the beginning of their reckoning , from the Vernal Equinoctial Point ; because the Sun being there , he not only begins the Spring , but openeth the Earth , and giveth life to all Vegetables , and things which grow ; which cannot be done , either in any of the Solstices , or when he is in the Autumnal Equinoctial Point . Next , the distinction of the Signs is manifold . For some of them are called Northern Signs , and others are called Southern . The Northern , decline from the Equinoctial towards the North , which are Aries , Taurus , Gemini , Cancer , Leo , Virgo . The Southern decline from the Equinoctial towards the South , which are Libra , Scorpius , Sagittarius , Capricornus , Aquarius , Pisces . Secondly , Some of them are called , Signs Ascending , others are called Signs Descending . The first sort , are these , wherein the Sun , and the rest of the Planets do ascend from the South towards our Zenith , which are Capricornus , Aquarius , Pisces , Aries , Taurus , Gemini . The Descending are these , wherein the Sun , and the rest of the Planets , do move from our Zenith towards the South , which are Cancer , Leo , Virgo , Libra , Scorpius , Sagittarius . Thirdly , The Signs of the Zodiack , are either Vernal , Estival , Autumnal , or Hybernal . The Vernal , are Aries , Taurus , Gemini . The Estival , are Cancer , Leo , Virgo . Autumnal , are Libra , Scorpius , Sagittarius . And the Hibernal , are Capricornus , Aquarius , Pisces . Fourthly , The Signs are either Cardinal , Middle , or Fixed , or Common , or Two-bodied . The Cardinal Signs , are Aries , Cancer , Libra , Capricornus : so called , because their beginnings are the very Cardinal Points . The Middle or Fixed Signs , are Taurus , Leo , Scorpius , Aquarius . They are called Middle or Fixed , because they keep the Middle place between the Cardinal and Common Signs . They are Fixed , because when the Sun is in them , we have a perfect temperament of the Air , agreeing to the given Quadrant of the Heavens . As when the Sun is in Taurus , we have a perfect Spring ; in Leo , a perfect Summer ; in Scorpius , a perfect Harvest ; and in Aquarius , we have a perfect Winter . They are called Common , or Two ▪ bodied , as Gemini , Virgo , Sagittarius , and Pisces ; because each one of them , hath two Bodies indeed . For Gemini are two Twins . Virgo hath an Ear of Corn in her Hand . Sagittarius is made up of a Man , and a Horse . And lastly , The Fishes are double . They are called Common , because Astrologers find , that they participate of the Nature , both of the Fixed Signs , and the Cardinal which follow . Fifthly , The Signs are divided into four Triplicities , which are called by Astrologers Trigons . The first is called the Fiery Trigon , which contains Aries , Leo , and Sagittarius . The second is the Earthy , which contains , Taurus , Virgo , and Capricorn . The third is the Aerial , which contains , Gemini , Libra , and Aquarius . The fourth is the Watery , which contains , Cancer , Scorpius , and Pisces . If it happen , that Saturn , and Iupiter be in Conjunction this year in Leo , their next Conjunction will happen 20 years after , or truly 19 years , 315 days , and 19 hours , after in Sagittarius . From Sagittarius to Aries , from Aries to Leo , and so in round till 198 years and 236 days passing , they make a Transit into a new Trigon ; so that the Revolution of one Trigon , consumes almost 200 year . The uses of the Zodiack and Ecliptick are these . 1. As the Equinoctial , is the Measure of the Pri●… Mobile , so is the Zodiack and Ecliptick , the Square and Rule of the second Movables . For as the Sun is always , in or under the Ecliptick ; so are the rest of the Planets always , in or under the Zodiack . Therefore as in the Celestial Globe , the Zodiack hath the chief place , so in the Terrestrial Globe the Equinoctial . 2. Upon the Ecliptick we reckon the Longitude of Stars , and from the same Ecliptick , we count their Latitude . The Longitude of a Star , is an Arch of the Ecliptick , measured between ●●e true Equinoctial Point , or begin●ing of Aries , and the Circle of Lati●●de passing thorow the Center of that ●tar . Circles of Latitude , are great Movable Circles , passing thorow the Poles of the Ecliptick , and the Center ●f the Star given . They are of that ●umber of Circles , which cannot be ●●aced Artificially in the Sphere . Ne●ertheless , of that same Number , is the ●olurus Solstitiorum fixed in the Sphere . The Latitude of a Star , is an Arch of a Circle of Latitude , measured between ●he Ecliptick , and the Center of the ●tar . 3. According to the Degrees , and ●arts of the Zodiack and Ecliptick , the whole Heavens , and the whole Universe 〈◊〉 divided into twelve Signs ; nay eve●y Point contain'd in the Sphere of the Fixed Stars , is said to be in this or that Sign ; tho , to be in a Sign , is said many ways . For first , To be in a Sign , is nothing else , but to be under any ●welfth part of the Zodiack . In this ●ense , the Sun is said to ●e in a Sign , because he is always under the Ecliptick . Then the Stars are said to be in a Sign , which are indeed out of the Ecliptick , nevertheless are under the Zodiack . In this sense , the Planets , which wander from the Ecliptick , are said to be in the Sign of Aries , and Taurus , &c. Thirdly , Any thing is said to be in a Sign , which is included , in any of the twelve parts , which arise from the division of the whole Heavens , passing thorow the beginnings of the Dodekatemoria , or the Poles of the Ecliptick ; they being six great Circles , which mutually cut one another , in the same Poles . In this sense , any Star , as well fixed , as wandring , or new appearing , as a Comet , are said to be in the Sign of Aries , Taurus , &c. 4. The obliquity of the Ecliptick , is the cause of the inequality of days : for seing it moves unequally , and not evenly , the Sun , which is the true Parent of Time , must of necessity make the days unequal . 5. The Year , the Month , and the four Seasons of the Year , are determined by the Ecliptick . 6. When the Sun and Moon , are both of them in the Ecliptick , of necessity there must be Eclipses ; and for this cause , it is called the Ecliptick . 7. How much is the obliquity of the Ecliptick , so much is the distance , between the Poles of the World , and the Poles of the Ecliptick : so much also is the distance , between the Equinoctial , and either of the Tropicks . CHAP. IV. Of the Colures . THe Colures are nothing else , but Circles of Declination , defined above , in the second Chapter of the Equinoctial . They are called Colures from two Greek words , Kolos , or Kolobos , Mancus , maimed or defective , and Oura , Cauda , a Tail , because in an oblique Sphere , they have some part unseen , as if they were maimed , or wantting . But all the rest of the Circles of the Sphere , while it is going about , may be seen : but the Colures , have always some of their parts towards either of the two Poles , lying hid , and unseen . There are only two of them , which use to be placed in the Sphere , one whereof is called the Solstice Colure , the other the Equinoctial Colure . The Equinoctial Colure , is one of the greatest Circles of the Sphere , Movable , passing thorow the Poles of the Sphere , and the Equinoctial Points , the first of Aries , and the first of Libra , which are called Cardinal . By the word movable , the Colures are differenced ; First , From the Meridian ; Secondly , From the Right Horizon ; And thirdly , From the Horary Circles , with all which , by one turning about of the Sphere , they are twice united . But in this they differ , that those do not move , but these follow the motion of the Primum Mobile . The Solstice Colure , is one of the greatest Circles of the Sphere , movable , drawn thorow the Poles of the Sphere , and the two Solstice Points , by which difference , they are distinguished from other Colures . The uses of all the Colures in common are these . First , We reckon upon them , the Declinations of all the Points of the Heavens whatsoever . 2. They terminate and bound the Right Ascensions . 3. They are like unto a Right Horizon , and a Meridian in any Sphere , whether Right , Oblique , or Parallel . The Uses of the Colures , which are set down in the Sphere , are these in common , 1. Without them , the Parallel Circles in the Material Sphere cannot stand , 2. By their mutual cutting one another , they shew the Poles of the Sphere . 3. They divide the Ecliptick into four Quadrants . The peculiar Uses of the Equinoctial Colure are these . 1. It demonstrats to us the Equinoctial Points , by its mutual Section , with the Ecliptick ; in which Points when the Sun is existing , there is an Universal Equinox over the whole Earth . 2. It is divides the Ecliptick into two halfs , the one called the North part , the other the South part . 3. It distinguishes the Signs , in which when the Sun is existing , the Days are longer than the Nights , from those Signs , in which when the Sun is existing , the Nights are longer than the Days . The proper Uses of the Solstice Colure are , 1. It demonstrats to us the two Solstice Points , in which when the Sun is existing , he is either nearest to our Zenith , or furthest removed from it . 2. Upon this Colure , we reckon the Suns greatest Declination , or the greatest Obliquity of the Ecliptick , which is found to be this day twenty three Degrees , and thirty Minuts . 3. It divides the Zodiack into two halfs ; the one called Ascending , the other Descending . 4. It distinguisheth the Signs , in which when the Sun is existing , the Days become longer , and the Nights become shorter , from those Signs , in which when the Sun is existing , the Nights become longer , and the Days become shorter . 5. In this Circle , are the two Poles of the Ecliptick , as many Degrees , distant from the Poles of the World , as the greatest obliquity of the Ecliptick contains . 6. Upon this Colure , the Latitudes of the Zones are determined . For between the Tropicks , is contained the breadth of the Torrid Zone , between the Tropicks , and the nearest Polar Circles , are contained the two Temperate Zones , and the other two remaining Arches of this Circle , contain the breadth of the two Frigid , or Cold Zones . CHAP. V. Of the Horizon . THe Horizon , is one of the greatest Circles of the Sphere , Immovable , and equally distant from the Vertical Point . It is called Immovable , that it may be differenced from the rest of the Movable Circles ; but especially , First , From their Equinoctial , who live under the Poles . Secondly , From their Ecliptick , whose Zenith is placed in the Polar Circles : for their Ecliptick every day is twice united with their Horizon , but without delay . Thirdly , From their Circles of Declination , or their Colures , who live under the Line : for there , the forementioned Circles , and the Horizon , are twice , by every Revolution of the Sphere , united : but the Circles of Declination follow the Motion of the Primum Mobile , but the Horizon stands Immovable . The Horizon is said indeed to be Immovable , but not Unchangable , for there are as many Horizons , as there are Vertical Points ; and while we change our Vertical Point , of necessity we change our Horizon also . Two ways is the Horizon divided . First , In relation to the Equinoctial , which is called a Right Horizon , an Oblique Horizon , and a Parallel Horizon . The Right Horizon , is so called , because it cuts the Equinoctial at Right Angles . It is called Oblique , because it cuts the Equinoctial at Oblique Angles . And it is called a Parallel Horizon , when it lies Parallel to the Plain of the Equinoctial , or rather when it is united , with the Equinoctial . And according to this Relation , it hath to the Equinoctial , the Sphere it self , hath obtained the same Division . Secondly , The Horizon is either Rational , or Sensible . The Rational Horizon , is defi●…ed above , and is understood to divide the whole World , or Sphere of the World into two equal parts , the first whereof is called the uppermost Hemisphere , the second the nethermost Hemisphere . It is called Rational , because tho we cannot see the whole World , or the exact half of it , yet Reason tell us , by the Rising and Setting of the Sun , Moon , and Stars , that the inferior part of the World , is equal to the superior part . The Sensible Horizon , is nothing else , but so much of the Earth , as a man , by turning his eye once , doth behold round about him . The Uses of the Horizon are these . First , it divides that part of the Heavens , which is seen , from the other which is not seen , the Superior part from the Inferior part . 2. Thorow the Poles of the Horizon the Meridian ought to pass : therefore the Description of the Meridians depend from the Horizon . 3. By the Situation of the Horizon , we know whether it be a Right Sphere ▪ Oblique Sphere , or a Parallel Sphere . 4. In the Horizon , the Rising or Setting of the Stars are observed 5. The Horizon sheweth , what Degree of the Ecliptick , what part also of the Equinoctial , or what Degree , with any given point of the Heaven riseth or setteth . 6. It boundeth and terminats the Ascensional Difference . 7. Upon the Horizon is numbred , the Rising or Setting Amplitude , of any point in the Heaven . 8. It demonstrats , and sheweth the Cause and Reason of the equality of Days and Nights in a Right Sphere , and of the unequality of the same in an Oblique Sphere . For the Horizon in a Right Sphere cutteth all the Circles of the Natural Day equally , but unequally in an Oblique Sphere . 9. From the Horizon we number the Morning-Twilight : for when the Sun ●…s distant , in some Vertical Circle 18 or 19 Degreees from the Horizon , so that ●…rom that Moment , he approach nearer ●…nd nearer unto it , then begins the Morning-Twilight . But the Evening-Twilight ends , when the Sun after his Set●…ing comes to that 18 or 19 Degree ●…oresaid ; for then doth the Light turn ●…nto Darkness . 10. From the Horizon , we number the Elevation of the Pole , ●…nd Equinoctial . 11. From the Hori●…on are numbred various and divers ●…inds of Hours , as the Italick , and Iewish Nocturnal Hours from the West part of the Horizon : but the Babylonish Hours , ●…nd the Iewish unequal Diurnal Hours , ●…rom the East part . CHAP. VI. Of the Meridian . THe Meridian is one of the greatest Circles in the Sphere , passing thorow the Poles of the World , and the Poles of the Horizon . By the words , thorow the Poles of the Horizon , it is distinguished from the Horary Circles , of which none but it self , passes thorow the Poles of the Horizon . It has acquired divers and sundry Names , by reason of its manifold uses , by Astrologers , which are not fit to repeat now . What was said above concerning the Colures , and Circles of Declination , to wit , that they are in number equal to the Vertical Points , the same may be said of the Meridian , for as many of them may be imagined , as there are Vertical Points , which are infinite , providing a man travel from East to West : for if a man go from North to South , or from South to North , he travels round about the World , without variation of his Meridian . The Brasen Meridian in the Celestial , or Terrestrial Globe , supplyes the office of them all , which are innumerable . But in Geographical Tables , and Mapps , Geographers use to extend one Meridian , thorow two , and two opposite Degrees of the Equinoctial , for finding out , the more easily the Latitudes of Places . Of all these Meridians there is a common beginning se●…led in the Fortunate , or Canary Islands , because the Antient Geographers deemed those Islands to be the Westmost part of the World , and therefore they fixed their first March-stone there , whence they begin to reckon . But the later Geographers , have removed this March-stone 10 Degrees more Westerly , and have made the common beginning of the Meridian to pass thorow one of the Islands called Osores , whence they begin to reckon from West to East , imita●…ing the order of the 12 Signs . The uses of the Meridian are these , 1. It distinguisheth the Eastern part , of the World , from the Western part , the Anterior part , from the Posterior part . 2. It lets us know the South part of the World , and the North part . For when the Sun is in the Meridian , ●…en is Mid-day , and when the Sun is in the Northern part , of the Meridian , then is Mid-night . 3. It divides the Nocturnal and Diurnal Time into two halfs : that is , when the Sun is come to the Meridian in our Hemisphere , as much of the day is past , as what is to come : and when the Sun is come to the Northern part of the Meridian , as much of the Night is past , as what is to come . 4. The Meridian supplies in every Oblique Sphere the place of the Right Horizon : therefore , as the Stars do ascend above the Right Horizon , so they pass over the Meridian , and those ●…ransitions are called the Right Ascensions of the Middle Heaven . 5. From the Meridian , Astronomers begin their Time. 6. In the Meridian , we find out the Zenith ; therefore when the Stars come to it , they are either highest above the Horizon , and are said by Astrologers to culminate , or they are in the lowest , and opposite part of it , which is the Nadir . 7. In the Meridian , we find out the distances between the Tropicks , and the whole Obliquity of the Ecliptick . 8. Upon the Meridian , we number the Latitude of Places upon the Earth , and likewise the Elevation of the Pole , and Equinoctial . The Elevation of the Pole , is defined , an Arch of the Meridian , measured between the Horizon , and the apparent Pole of the World , which may be found out , after the following manner . Observe the greatest and least Altitude of any of the Stars , which do not set . Subtract the least Altitude from the greatest , and divide the difference . This difference being subtracted from the greatest Elevation , or added to the least , gives the true height of the Pole. December 17. 1669 , I observed with a large Quadrant , half 9 a Clock at night , the foremost Guard-star , when it was in the Meridian , and lowest , to have 41 Degrees , 22 Minuts of Altitude . And on Ianuary 7. 1670 , at 7 a Clock in the Morning , I found it , when it was in the Meridian , and heighest , to have 70 Degrees , 27 Minuts . I subtract 41 Degrees , 22 Minuts , from 70 Degrees , 27 Minuts , and the difference is 29 Degrees , 5 Minuts . Divide this , and you have 14 Degrees , 32 Minuts , and 30 Seconds . This being added to 41 Degrees , 22 Minuts , gives you 55 Degrees , 54 Minuts , 30 Seconds . Or subtract 14 Degrees , 32 Minuts , and 30 Seconds , from 70 Degrees , 27 Minuts , and there remains 55 Degrees , 54 Minuts , and 30 Seconds , for our height of the Pole at Edinburgh . 9. The Meridians do terminate , and bound the Longitudes of Places , as well in the Terrestrial Globe , as in the Mapps , and Cards projected in Plano . 10. The Meridians do terminate , and bound the Breadths and Latitudes of the Zones , and also of the Climats . 11. We find out in the Meridian , the Antipodes , the Anteci , and Perieci . CHAP. VII . Of the Tropicks . THe Tropicks are lesser Movable Circles of the Sphere , described from the Solsticial Points , by the mo●…ion of the Primum Mobile . They are called Lesser , because there are in the Sphere Greater Circles , than they are . They are called Movable , that they may be distinguished chiefly , from the Paral●…els of their Horizon ( called Almican●…ars ) , who live under the Poles ; and ●…rom the antient Polars of those , who ●…ive under the Polars , with whom the Tropicks are equal to those Circles , which comprehend the Stars , which never come above the Horizon , nor ever go under it . They are two in number , to wit , the Tropick of Cancer , and the Tropick of Capricorn . The Tropick of Cancer , is a lesser movable Circle , described from the Summer-Solstitial-Point of the Ecliptick , by the motion of the Primum Mobile . The Tropick of Capricorn , is lesser movable Circle , described fro●… the Winter-Solstitial-Point of the Ecliptick , by the motion of the Primum Mobile . The uses of the Tropicks are these 1. They demonstrate to us , in the Ecliptick , the two Tropical or Solstic Points , to wit , the beginning of Cancer , and the beginning of Capricorn 2. They terminate and bound , the Sun greatest Declination , and consequently the greatest Obliquity of the Ecliptick 3. When the Sun comes to either of th●… two Tropicks , he is either nearest t●… our Vertical-Point , or furthest removed from it . 4. In an Oblique Sphere , they ly Parallel to the longest , and shortes●… Day . 5. Between the Tropicks , i●… comprehended the Torrid Zone , as well in the Heavens , as in the Earth : and by the same Tropicks , the Torrid Zone is divided from the Temperate Zones . CHAP. VIII . Of the Polars . THe Polars are lesser Circles of the Sphere , movable , described from the Poles of the Ecliptick , by the motion of the Primum Mobile . For this cause , they are called the Polar Circles . They are two in number , the Polar Artick , and the Polar Antartick . The Polar Artick is a lesser Circle of the Sphere , movable , described from the North Pole of the Ecliptick , by the Motion of the Primum Mobile . The Polar Antartick , is a lesser Circle of the Sphere , movable , described from the South Pole of the Ecliptick , by the motion of the Primum Mobile . They let us see first , the Poles of the Zodiack , and they measure their distance from the Poles of the World. 2. They bound the Temperat Zones , and separats them from the Cold Zones , which are bounded and inclosed by their circumferences . It is to be observed , that the antient Astronomers , Proclus , Cleomedes , and the rest , had not the same description of the Polars , which we have . For the Antients , did not describe them , as passing thorow the Poles of the Ecliptick , but thorow the common Sections of the Meridian , and Horizon , equidistant to the Equinoctial ▪ and therefore , so much was their distance from the Poles of the World , a●… the height of the Pole was above the Horizon . And by this means , where there is no Elevation of the Pole , as in a Right Sphere , there are no Polars . But from thence , they are more , and more gradually augmented , and enlarged , according to the increment of the Poles Elevation . The uses of the Polars , according to the Antients , are these , 1. They comprehend the Arch of the Elevation of the Pole. 2. Of all the Parallels of the Equinoctial , which are always seen above the Horizon , they are the greatest and of all the Parallels of the Equinoctial , which ly hid under the Horizon , they are the greatest also . But contra●…iwise , of all the Parallels of the Equinoctial , which arise and set in twenty four Hours , they are the least . Therefore ( 3. ) the foresaid Polars , comprehend within their Compass , and Circle , ●…he whole Stars and Points of Heaven , which are always in sight , and do not ●…et . Hence , there ariseth a threefold ●…istinction of the Stars . 1. There are ●…ome , which have a perpetual Day , and ●…ever set , or fall under the Horizon , to ●…it , those which are comprehended within the Circle of the Polar Artick . 2. There are others , which have a perpetual Night , which never rise , or come ●…p above the Horizon , to wit all those , which are included within the Circle of ●…he Polar Antartick . There are ( 3. ) others which both rise and set in four ●…nd twenty Hours , to wit those , which ●…ither on this side , or that side of the Equinoctial , tend towards and come nearest to the foresaid Polars . CHAP. IX . Concerning other Circles of the Sphere , both greater and lesser , which cannot be conveniently drawn upon it . BEside the Circles of the Sphere hitherto explained , there are yet innumerable more , both of the greatest and lesser sort , which Astronomers have excogitated for attaining a more perfec● knowledge of the Heavenly Motions ▪ 1. There are of the greatest sort Verticals , which pass thorow every point o● the Horizon , cutting one another there which by the Arabians are called Azimuths . 2. There are the Horary Circles , which divide the Heavens , into four and twenty parts , which are o● three sorts . For either they have the beginning in the Meridian , and pa●● thorow the Poles of the World , or the have their beginning in the East , o● West-part of the Horizon , by whic● means they touch lightly , the two Circles lying parallel to the Equinoctial , of which one is the greatest of all , which are always seen above the Horizon , the other the greatest of all , which are not seen above the Horizon : or lastly , they have their beginning in the Horizon , but neither go thorow the Poles , of the World , nor go near to the foresaid Parallels , but divide all the Segments of the Parallels , which are above or below the Horizon , into twelve equal parts . 3. There are Circles of Declination , which pass thorow the Poles of the World , and every point of the Equinoctial . There are 4. Circles of Latitude , which pass thorow the Poles of the Ecliptick , and every one of his Degrees . The lesser Circles are infinite also ; for there is no great Circle , which hath not his own Parallels . As first the Horizon , which hath Circles of Altitude , called by the Arabians Almicanthars . The Equinoctial , hath its own Parallels , to wit , described by the Primum Mobile , from all , and whatsoever Points are in the Heavens . So hath the Zodiack his Parallels , described about the Poles of the Ecliptick , which Parallels every Star , or point of the Heavens , according to the proper motion of the eight Sphere , do describe , and many more are there invented by Astronomers for Astronomical uses . CHAP. X. Of the Zones . TO the Doctrine of the Sphere , is commonly annexed the Geographical Tractat of the Zones . The Zones therefore are nothing else , but as much bounds , of the Heaven , or of the Earth , as is comprehended between both the Tropicks , or between either of the two Tropicks , and the next Polar , or between either of the two Polars , and the neighbouring Pole. Therefore the Zones , are either Celestial , or Terrestrial . The Celestial Zones , are bounded by themselves , and their own Circles in the Heavens . The Terrestrial Zones , ly directly under the same places of the Heavens . They are five in number , one Torrid , two Temperate , and two Frigid . The Torrid Zone , is that space of the Heavens , or the Earth , comprehended between the two Tropicks . This is divided into two parts , of which one is called the Northern , the other the Southern part . It is called Torrid , because here , the Rays of the Sun are more perpendicular , and so hotter , that the Inhabitants are in a manner scorched , and burnt up with Heat . The Temperate Zones , are that space of the Heavens , or of the Earth , comprehended between either of the two Tropicks , and the neighbouring Polars : and that which is included , between the Tropick of Cancer , and the Polar Artick , is called the Temperate Northern Zone , wherein are contained , all Europe almost , and a great part of Asia , and also a part of America . But that which is included between the Tropick of Capricorn , and the Antartick Polar , is called the Southern Temperate Zone . This contains more Sea , and less Land. They are called Temperate , because the Rays of the Sun , being more oblique , there is not such a reflection of Heat , but offer a most commodious Dwelling to the Inhabitants . The Frigid Zones , are that space of the Heavens , and of the Earth , comprehended between either of the Polars , and the neighbouring Pole of the World. And that bounds , which is included between the Polar Artick , and the North Pole , is called the Northern Frigid Zone : and that bounds which is included , between the Polar Antartick , and the South Pole , is called , the Southern Frigid Zone . They are called Frigid , because the Rays of the Sun are most Oblique , and are absent almost half a Year ; so that all things become rigid and stiff , with Frost , Yce , and Snow . In this Zone , lyes Island and Greenland , but in the Southern cold Zone , the parts are unknown to us . The Inhabitants of the five Zones , have obtained divers names . For those , who inhabite the Torrid Zone , are called Amphiscii , as having a shadow on both sides . I say on both sides , in respect of the Vertical Point . For the Sun with them , is sometimes on this side , and sometimes on that side of their Vertical Point : sometimes the shadow of their Dials is projected from South to North , and sometimes from North to South , when he is in the Meridian . The Inhabitants of the Temperate Zones , are called Heteroscii , as having but one shadow . For at 12 a Clock in the Day , the shadow is either casten towards the North , as with us , or towards the South , as with those , who dwell in the Southern Temperate Zone . But those , who live in the Frigid Zones , are called Periscii , as having a shadow , which goes round about them ; because they have the Sun for several Months of the Year , above their Horizon , and the Heavens there , like a Milstone , is whirled about , so that the Sun and Stars describe Parallels to the Horizon , and therefore in four and twenty Hours , he runs about without rising and setting , and projects his shadow into an Orb , or Circle . There are likewise , the Antipodes , Anteci , and Perieci . Antipodes , are those , who have the same Meridian , but dwell in points of it , diametraliter opposite , and are under opposite Parallels , ( to wit in an oblique Sphere , ) of which the one is Southern , the other Northern . These following Phenomena , are proper to them . 1. Though they have the same Rational Horizon , yet beholding the opposite Faces , all things fall out to them contrariwise . For when we have Day and Mid-day , our Antipodes have Night and Mid-night . When we have Summer , they have Winter . When the Sun rises to us , he sets to them . We have North Latitude , they have South Latitude . The Anteci are those , who dwell under opposite Parallels , equally distant from the Equator , towards both the Poles , under the same Meridian , but not in Points diametraliter opposed , but in a Semi circle of the Meridian intercepted between the Poles . They have these Phenomena proper to them . First , They agree in the same Longitude , and Latitude ; for how much is the South Pole elevated to those , so much is the North Pole elevated to these . 2. In the same Moment of Time , both of them have the Sun in their Meridian . But in this they differ ; while the Sun is coming to the Tropick of Cancer , those have Summer and longer Days , but these have Winter , and shorter Days . Again , when the Sun is returning , those have Harvest , the Days Decreasing , but these have the Spring , the Days Increasing . Hence it is , that the Sun doth not rise , and set to both , at the same time . The Perieci are those , who dwell under the same Parallel and Meridian , but in Points of the same Parallel diametraliter opposite ; so that both of them behold the same Pole , with equal height above the Horizon . First , They dwell in the same Zone . Secondly , They have the same Elevation of the same Pole. They have the same Winter , the same Summer , the same longest Day , and the same increment , and decrement of the Natural Days . But here they differ ; those having the Sun rising , these have it setting ; those having the Sun in the Meridian , these have it at our Mid-night : and contrariwise , when to those the Sun is setting , to these he is rising , when to those it is Mid-night , to these it is the Meridian . CHAP. XI . Of the Rising and Setting of the Stars according to the Poets . HItherto we have treated of the Hypotheses , to wit , the Circles of the Sphere , which so much conduce for explaining the Phenomena of the Primum Mobile . It now remaineth , that we speak and treat of the thing it self , to wit , the Phenomena themselves . And in the entry , we ought to have spoken of the rising and setting of the Stars , called Ortus & occasus stellarum Astronomicus ; but the knowledge of those things , cannot be taught here compendiously , nor without the Science of Spherical Trigonometry ; therefore passing this , we come to explain the rising and setting of the Stars , called Ortus & occasus Poeticus , which is the second Phenomenon of the Primum Mobile . This rising and setting of the Stars according to the Poets , is nothing else , but the rising of a Star above the Horizon , and the setting of a Star under it , in relation to the various Position of it , with the Sun. It is called Poetical , not because it doth not belong to Astronomers ; for it is a part of their Science to determine those Risings and Settings , but because the Poets in describing certain Seasons of the Year , use this method , as will be seen afterward . Of this Poetical Rising and Setting , there are three forms . First , That which is called the Rising and Setting of a Star Cosmice . Secondly , That which is called the Rising and Setting of a Star , Acronyce . Thirdly , That which is called the Rising and Setting of a Star Heliace . Each one of those hath a double signification ; one general , the other special . The Rising of a Star Cosmice generally taken , is the Rising of a Star above the Horizon , falling out from the Rising of the Sun to his Setting . The Setting of a Star Cosmice , generally taken , is the Setting of a Star , falling out from his Rising to his Setting . The Rising of a Star Acronyce , generally taken , is the Rising of a Star above the Horizon , falling out the whole time , the Sun is under the Horizon . The Setting of a Star Acronyce generally taken , is the Setting of a Star under the Horizon , falling out all the time the Sun is under the Horizon . The Rising of a Star Heliace generally taken , is the appearing of a Star after the Sun is Risen . The Setting of a Star Heliace generally taken , is the disappearing of a Star , after the Sun is set . But their special signification denotes , and determines , a certain , and definite time . Therefore , the Rising of a Star Cosmice , is the ascending of a Star above the Horizon , in the same moment , wherein the Sun Rises . The Setting of a Star Cosmice , is when a Star goes down , while the Sun is Rising . The Rising of a Star Acronyce , is when a Star comes above the Horizon , the Sun going down under the Horizon that same moment . The Setting of a Star Acronyce , is when a Star Sets with the Sun , that same moment . The Rising of a Star Heliace , is when a Star , which could not be seen , by reason of its nearness to the Sun , is now seen in the night time . The Setting of a Star Heliace , is when a Star , by reason of the Suns great distance from it , might have been seen in the night time , but the Sun coming nearer to it , it disappears out of our sight . We have an Example of the Rising of a Star Cosmice , in the first Book of the Georgicks . Vere fabis satio : tunc te quoque Medica putres Accipiunt sulci , & Milio venit annua cura Candidus auratis aperit , cum Cornibus annum Taurus , & adverso cedens Canis occidit Astro. When Taurus with his gilded Horns , Begins the Year , then Sowe your Corns Sowe Millet-seed , an yearly toil , Sowe Claver-grass , in putrid soil , Sowe yearly Pulse , and what you please Sowe in the Spring , both Beans and Pease . Virgil doth express here the Spring time , when the Millet-seed is to be sown●… which is in the beginning of April : An●… seing the Sun at that time , is about th●… end of Aries , it must be understood of the Rising of Taurus , which at that time riseth with the Sun Cosmice . At this time the Romans used to sowe their Beans , their Claver-grass , and their Millet , which every year must be renewed ; whereas the Claver-grass is to be sown but once in ten years . We have likewise an Example of the Setting of a Star Cosmice , from that same place in Virgil. Ante tibi Eoae Atlantides abseondantur Gnosiaque ardentis decedat stella Coronae Debita quam sulcis committas semina . When Pleiades , the Maidens seven , Are set into the Western-Heaven , When Ariadnes Crown full bright Before the Sun comes in our sight , Then sowe your Ground with Wheat and Rye 'T is of October eighteen day . Before you sowe your Ground ( says he ) let the Pleiades , or Seven-stars be set , which about October 18 , go down in the West , in the same Moment of Time , while the Sun is Rising in the East , which is called Occasus Cosmicus . We have an Example of the Rising of a Star Acronyce , from Ovid , in his first Book de Ponto . Quatuor autumnos Pleias orta facit . Four Harvests surely there have been , For Pleias four times have been seen . Ovid is here speaking of the Harvest time , when the Sun is in Scorpio , therefore when the Sun is Setting , Taurus or the Bull , and the Pleiades are Rising Acronyce . We have also an Example of the Setting of a Star Acronyce , from the same Ovid , in his second Book of his Fasts . Illa nocte aliquis tollens ad sidera vultus Dicet ubi est hodie , quae Lyra fulsit heri . Last Night when I surveyed the Sky , saw the Harp , 't is gone away This Night . This time , is the second day of Fe●…uary , at which time the Constellation ●…lled the Harp , sets Acronyce , with the ●…u . We have likewise an Example of the Rising of a Star Heliace , from the first Book of the Georgicks . Gnosiaque ardentis decedat stella Coronae . When Ariadnes Crown full bright Before the Sun comes in our sight . 'T is eviden●… that Virgil speaks here of the Rising of this Constellation Heliace , called Aridnes Crown , when the Sun is in the beginning of Scorpio . For seing this Constellation rises at Rome , where Virgil lived , with the 27 Degree of Virgo , it is needful to conceive this Crown to be seen in the Morning , the Sun being yet under the Horizon . Note , That there is a Figure called Hypallage in the word Decedat : for the Crown doth not recede from the Sun , but the Sun from it . And lastly , We have an Example of the Setting of a Star Heliace , from the same place of Virgil. Taurus , & adverso cedens Canis occidit Astro. And when the Dog shall disappear , By Phebus Beams him coming near . The Poet is here speaking of the Suns ingress into Taurus , which fell out in Virgils time on the 1●… of April . But seing the Dog-star sets at Rome with the 22 Degree of Taurus , therefore , the Sun setting in the Evening , the Dog-star setteth Heliace , or disappears out of our sight , by reason of the Suns Rays , which now are nearer him . Observe , That what Stars do arise Cosmice , which is also called Ortus Matutinus , they set Acronyce , which is called Occasus Vespertinus : and what Stars do arise Acronyce , which is called Ortus Vespertinus , they set Cosmice , which is called Occasus Matutinus , according to the following Rhyme . Cosmice descendit signum , quod Chronice surgit , Chronice descendit signum , quod Cosmice surgit . Aliter . Mane vehit supra terram tibi Cosmicus ortus Sidera , sed Phoebi lumine tecta latent . Mane dat Heliacus quaedam subvecta videre Astra , sed Achronycus nocte videnda trahit . Note secondly , That the word Cosmicus , comes from Kosmos , the World. That the word Chronicus , comes from the Greek word Chronos , Time. But Acronycus comes from Acra & Nux , which is the first part of the Night , or the Evening ▪ Twilight . That Heliacus comes from Helios , the Sun. Lastly , That Chronice , and Acronyce have the same signification . CHAP. XII . Concerning the Natural , and Artificial Days . NOw follows another Phenomenon of the Primum Mobile , to wit , the Doctrine of Days Natural and Artificial . Days are twofold , Astronomical , and Civil . Astronomical Days , are such as are measured , by the Revolutions of the Equinoctial , and determined by a certain quantity . Days Civil , are such as every Nation , according to their own Custom make use of . The Astronomical Day , is either Natural , or Artificial . The Natural Astronomical Day , is a space of time , wherein the Sun , by the Motion of the Primum Mobile , being carried about , from whatsoever immovable point of the Heavens , returns to that same point again . These Astronomical Days have their beginning in the Meridian , as was insinuate before . The Artificial Astronomical Day , is a Space of Time , wherein the Center of the Sun remains above the Horizon . And the Artificial Night , is as much Time , as the Center of the Sun remains under the Horizon . The Doctrine of the Artificial Days and Nights , is contained in the following Theorems . 1. The Artificial Days and Nights , with the Amphiscii , Heteroscii , and partly with the Periscii , are parts of the Natural Day : but with the Periscii , in those parts of the Earth , wherein the Sun , by the going about of the Primum Mobile , perfects some Circumgyrations , either above the Horizon , without setting , or under the Horizon , without rising , one Artificial Day , or one Artificial Night , doth excresce into many Natural Days ; so that indeed under the Poles , the Artificial Day contains half a Year , and the Artificial Night as much ; and so to speak properly , the whole Year consists but of one Day , men looking to the Analogy of the Natural Day . 2. Under a Right Sphere , the Artificial Day , is equal to the Night : for the Horizon , in this Position of the Sphere , cuts the Circuli Dierum , the Day-Circles , into two equal parts . The Day-Circles , are called those Parallels of the Equator which the Sun doth dayly describe , by the Motion of the Primum Mobile . 3. In an Oblique Sphere , there are only twice a Year , two Equinoxes , when the Sun is in the beginning of Aries and Libra . The Reason of this appears , from the mutual Section of the Horizon , with the Circuli Dierum , or Day-Circles , which is indeed unequal , except when the Sun is in the Equinoctial . 4. In an Oblique Sphere , which hath the vicissitude of the Artificial , and Natural Day , by one Revolution of the Equator , the Sun being in the. Tropick of Cancer ( we are now speaking of this uppermost part of the Sphere ) we have the longest Day in all the Year , and the shortest Night : but the Sun being in the Winter Solstice , the Day is shortest , and the Night longest . 5. In the same Position of the Sphere , thorow the whole half of the Ecliptick descending , the Sun maketh the following Days shorter , than the Days going before , but the Nights longer . But in the half of the Ecliptick ascending , the Sun maketh the Days following longer , than the Days going before , but the Nights shorter . 6. When the Sun is existing , in places of the Ecliptick , equally distant , from the same Solstitial Point , Days are equal to Days , and Nights to Nights . 7. When the Sun is existing in places of the Ecliptick equally distant , from the same Equinoctial Point , the Day of one Place , is equal to the Night of another . 8. In an Oblique Position of the Sphere , the greater the Elevation of the Pole is , the greater are the increments of the longest Day , and shortest Night , until coming under the Polars , the longest Day contains twenty and four Hours . 9. In an Oblique Sphere , of such as dwell between the Polar , and next Pole , the longest Day excresceth into many Natural Days , as also the longest Night . But there are certain intermediat Horary Circles , a part of which is above the Horizon , and a part under , in which , when the Sun is existing , the Artificial Days , as also the Nights , are ▪ parts of the Natural Day . 10. In a Parallel Sphere , such as they have , who live under the Poles , the whole Year , is divided into one Artificial Day , and one Artificial Night . The length of every Artificial Day , is known by the Diurnal , and Nocturnal Arch. First , find the Oblique Ascension or Point of the Equinoctial , which riseth with the Sun , and Oblique Descension , or Point of the Equinoctial , which setteth with the Sun. Subtract the lesser from the greater , and half the difference , is the Ascensional difference , which added to six Hours in the Summer half Year , but subtracted therefrom in the Winter half Year , gives half the Diurnal Arch , whose double is the whole Diurnal Arch , and the Complement of the Diurnal Arch to 24 Hours , is the Nocturnal Arch. For Example , The tenth day of April 1687 , the Oblique Ascension of the Sun ( being in the first Degree of Taurus ) is 10 deg . 21. m. the Oblique Descension is 45 deg . 27 m. whose difference is 35 deg . 6. m. whose half is 17 deg . 33 m. the Ascensional difference , which being added to 90 deg . or 6 Hours , is 107 deg . 33 m. which make 7 hours , 10 m. fere , for the time of the Suns setting , which is always half the Diurnal Arch. Therefore the Diurnal Arch is 14 hours , 20 m. Which taken from 24 hours , there remains 9 hours , 40 m. for the Nocturnal Arch required . Note , That the Ascensional difference added to the Oblique Ascension in the Summer half Year , but subtracted from it , in the Winter half Year , gives the right Ascension of the Sun , or any of the Stars . What is said of the Day in respect of the Sun , may be most commodiously applyed to the Stars . For the Day of a Star , is rightly called the space of Time , wherein it is above the Horizon : and the Night of a Star , the space of Time , wherein it is below the Horizon . Concerning the days of the fixed Stars , let the following Theorems be observed . 1. In a Right Sphere , the Stars have a perpetual Equinox . 2. But in an Oblique Sphere , the fixed Stars , whose North Declination , is greater than the Complement of the Altitude of the Pole , are said to have an Eternal Day : but those Stars , whose South Declination , exceeds the Complement of the Altitude of the Pole , are said to have an Eternal Night . The intermediate Stars , have the course of rising and setting . 3. In a Parallel Sphere , the fixed Stars are said to have Eternal Days , and Eternal Nights . Days Civil , are called the space of Time , of one Revolution of the Equinoctial , which according to every Nation , or Countrey , is divers ways begun , and made use of . For as there are various and divers Nations in the World , so each one hath a different way of beginning their Hours . For the Iews , by Divine Institution , began their Day , from the setting of the Sun , which custom the Italians do observe . The Babylonians began their Day from Sun rising , whose practice , the Norinbergers , the People called the Umbri , and the Egyptians do imitate . The Arabians as the Astronomers , begin their Day from the Meridian . The Romans from Midnight . The Germans , the Frenches , and Spainards begin their Day from the Meridian , and Mid-night . For their Clocks , and Watches are so contrived , that they return from one a Clock in the Night-time , to twelve a Clock in the Day-time , and from one a Clock in the Day-time , to twelve a Clock at Night-time . Their Days are divided , as the Astronomical Days , into one Artificial Day , and likewise into Forenoon , and Afternoon . And because Hours are parts of the Days , therefore we must speak a little of them . The Hour is the twentieth and fourth part of the Natural Day , or the space of Time , wherein the twentieth and fourth part of the Equinoctial , or 15 Degrees thereof , riseth above the Horizon . But this Definition is not sufficient , because it doth not agree to all Hours : for every twelfth part of every Day , and every Night whatsoever , was called by the Iews , and the Antients an Hour . But 15 Degrees of the Equinoctial , do not always ascend above the Horizon , every one of these Hours ; but sometimes more , and sometimes fewer , as will appear afterward . Therefore , an Hour may rather be defined thus , a certain part of the Artificial Day , and Night , made use of by divers Nations , after a divers manner , that it may be known generally , what the Hour is . For in effect , that definition agrees only to to those Hours , which are called Hor●… Aequales , equal Hours . The Hours then , which are called unequal , ought to be defined thus . The twelfth part of every Artificial Day and Night : therefore according to the divers Seasons of the Year , the Hours are sometimes shorter , and sometimes longer : in Summer longer , and in Winter shorter , as are th●… Iewish Hours : for they divide both the Day , and the Night into twelve parts , both in Summer and in Winter , calling the rising of the Sun , the beginning of the first Hour , and consequently nine their third Hour ; twelve their sixth Hour , three a Clock in the Afternoon their ninth Hour , and the setting of the Sun , the end of their twelfth Hour , by which means , their Hours must be far longer in Summer , than in Winter . The equal Hours are of three sorts : for some take their beginning from the setting of the Sun , as the Italian Hours . Others take their beginning from the rising of the Sun , as are the Babylonish Hours , and the Hours of the City of Norimberg , who from the rising of the Sun begin the number of the Hours of the Day ; the Circles of which Hours do lightly touch the greatest Parallels , of all , which do appear above the Horizon , and of all which do not appear . Lastly , Others do take their beginning from the Meridian , which Astronomers make use of , and these Nations , which either take their beginning of Hours from the superior part of the same Circle , or from the inferior part . CHAP. XIII . Concerning Years . AS Hours make up Days , so Days make up Years , therefore we must speak somewhat of Years . The Year then is twofold , Astronomical , and Political . The Astronomical Year , is the space of Time , wherein the Sun returns , either to the same Point of the Ecliptick , or to the same fixed Star. And this is twofold , the Tropical Year , called Annus Vertens , or the Syderial Year . Annus Vertens , is a space of Time , wherein the Sun leaving some Point of the Ecliptick , returns again to the same Point . The quantity of this Year is changeable ; for sometimes it is more , and sometimes it is less . Between these two extreams , the middle Year contains 365 days , hours 5 , m. 49 , sec. 15. thirds 46. But the true or apparent Year is sometimes 365 days ▪ hours 5 , min. 56. sec. 53 , thirds 1. Sometime it is 365 days , hours 5 , min. 42 , sec. 28 , thirds 27. The Syderial Year , is a space of Time , wherein the Sun under the Starry Sky , returns to the same fixed Star. The quantity of this Year is 365 days , hours 6 , min. 6 , sec. 39. It is always equal to it self , and therefore the measure of the Year called Annus Vertens . The beginning of this Annus Vertens , is taken from the Vernal Equinox , but the beginning of the Syderial Year , from the first Star of Aries . The Political Year , is an Annual space of Time , which is either accommodated to the course of the Sun , or the Moon , or to both , according to the common reckoning of several Countries and Nations . This Political Year is manifold ; for it is either Iulian , which contains 365 days , hours 6 , which six Hours , if they were reckoned every Year , would make confusion : therefore the Masters of Astronomy have appointed , they should be omitted , till the fourth Year , and then four times six , make 24 , which make up a full and compleat Day , which being inter caled , that is , interlaced , or put between , as in Leap Year there is a Day put between the 28 of February , and the first of March , the Year is called Annus Intercalaris , or Bissextile Year . It is to be adverted , that the cause of correcting the Iulian Calendar , by Pope Gregory the 13 , in the year 1582 , was the unjust quantity of it . For by this , it came to pass , that after some Ages , the four Cardinal Points did anticipate and prevent their Seats ; and so at length the four Seasons of the Year , might be interchanged . From this it is evident this Day , that according to these times , the Equinoctial , and the Ingress of the Sun into the 12 Signs have anticipated almost 13 Degrees . That is , the entering of the Sun , into Aries , Taurus , &c. falleth out sooner by 13 Degrees , than to the Romans : which comes to pass , because more , than what is just , is given to the space of the Year . For there were given to the Year , by the correction of Iulius Cesar , 365 days , and six hours : for which hours , every fourth year , one day is added , and so the common Iulian year contains 365 days , but the Bissextile 366. But seing the Solar year , in which the Sun runs thorow the whole Ecliptick , is less than this space , by almost eleven Minuts of Time every Year ; it comes to pass , that in 50 year , and a half , one hour remains , and in the space of 130 years , a whole day remains . I said the Political Year , was manifold , either Iulian , of which hitherto , or Egyptian , or Iudaical . The Egyptian year contains always 365 days . This Year was esteemed most useful by the antient Astronomers , for the Art of reckoning the Celestial Motions . The Iudaical Year is accommodated and fitted to the Motion of the Moon , and contains , for the greatest part , twelve , and sometimes thirteen Lunations . This Year did the Astronomers use , before the reformation of the Calendar , instituted by Iulius Cesar , by the help of one Sosigenes , a famous and learned Mathematician . The beginning of these Years is divers also . For the antient Romans , began their Year from March : the later Romans from the midst of Winter , called Bruma . The Iews , by Divine Institution , began their Year from the New Moon , which was next after to the Vernal Equinox . That we this day begin our Year from the first of Ianuary , it is for this , because we following the custom of the late Romans , beginning their Year from the midst of Winter , which was nearest to the first of Ianuary , by little and little the Winter Solstice did prevent , and anticipat its Seat , and Place . The Egyptian year , hath not a sure beginning , by reason that six hours are omitted . Hence is it , that every fourth Year it anticipats one Day : and therefore within 365 Years , four times numbered , or 1460 Iulian Years , the beginning of the Egyptian Year , wanders over all the Days of the Iulian Year . CHAP. XIV . Concerning the divers Phenomena , which are to be seen in the various Positions of the Sphere . THe last part of this little Tractat , shall be in examining the Phenomena , which are proper to the various Situations , and Positions of the Sphere . The Sphere may have seven different Positions , 1. When both the Poles of the World do rest in the Horizon , which is called a Right Sphere . The second Position is Oblique , when our Vertical Point , is terminated between the Equinoctial , and either of the Tropicks . The third Position is , when our Zenith is under either of the Tropicks . The fourth is , when our Zenith is between either of the Tropicks , and the neighbouring Polar . The fifth is , when our Zenith is in the very Polar itself . The sixth is , when our Zenith is between either of the Polars , and the neighbouring Pole of the World. And lastly , when the Poles of the World , do fall in with the Poles of the Horizon , which is called a Parallel Sphere . CHAP. XV. Concerning the Phenomena of the first Position . 1. EVery Star in the Heavens riseth and setteth , neither is there one of them , without this property : and therefore in this Position , there is neither Polar Artick , nor Antartick , according to the Antients . 2. There is here a perpetual Equinox . 3. The Sun every Year passing twice over their Heads , is to them twice Vertical , to wit , when he is in the Equinoctial Points . 4. As much , as the Sun declines from their Vertical Point , towards the North , as much also doth he decline from their Vertical Point , towards the South . 5. They have four Solstices , two when the Sun is highest in their Vertical Point , and two , when he is lowest , in Cancer , and Capricorn . 6. They have two Summers and two Winters , but only Analogically : for even in Winter , their Bodies are scorched with heat . 7. There are here in this Position , five different Shadows , the Meridional , or South Shadow , the North Shadow , a Shadow from the East , a Shadow from the West , and a perpendicular Shadow , which falls out only , when the Sun is in the Equinoctial Points . 8. The end or extremity of their Gnomons , upon their Horizontal Dialls , which are our Polar Dialls , describe the whole Year , the Figure called Hyperbole , except when the Sun , is in the beginning of Aries and Libra , where he describes a straight and right Line . CHAP. XVI . Of the Phenomena of the second Position ▪ 1. SOme Northern Stars tarrying always above our Horizon , have Eternal Days ; and contrariwise , there are some about the South Pole , which never come above the Horizon , but have Eternal Nights . 2. The Artick , and Antartick Circles , according to the Antients , are not as yet equal to our Polars . 3. The Artificial Day is not equal to its own Night , two Days only excepted , when the Sun is in the Equinoctial Points , at which time , there is thorow the whole World an Equinox . 4. The longest Day there , doth not exceed thirteen Hours and a half . 5. The Sun is to them , twice Vertical every Year , to wit , when he comes to those Degrees of the Ecliptick , whose Declination , is equal to the Latitude of the Place ; for he describes then , a Parallel thorow the Zenith . 6. The Sun in the Meridian , goeth further towards the South , than towards the North. Note , That we are now speaking , and in the following Discourse , of those seven Positions , which are in the Northern Sphere . 7. There are here , four Solstices , two high , and two low . The two highest fall out , when the Sun is in that Parallel , which passeth thorow the Zenith . The two lowest are , when the Sun is in the Tropicks . Yet that which falls out in the Tropick of Capricorn , is lower , than that which falls out in the Tropick of Cancer . 8. They have two Summers , and two Winters , but unequal , as appears from the various Situation of the Parallels . 9. The longest Day is not , when the Sun is in the highest Solstices , but in the Tropick of Cancer . 10. There are five different Shadows , as we observed in the first Position . 11. The end or extremity of the Gnomon , by its Shadow , when the Sun is out of the Equinoctial , describes ( as in the first Position ) the Figure called Hyperbole , but the opposite sides are not equal as there , but unequal . 12. In any part of this Position , where the Elevation of the Pole , is less , than the Declination of the Sun , the Shadow of a Style perpendicularly erected upon a Plain , may have a natural , visible , Retrocession . In the matter of Ahaz his Dial , the Retrogradation of the Shadow was miraculous , because it was done without , and not within the Tropicks , neither is it possible in nature , it can happen , but where the Elevation of the Pole , is less than the Suns Declination , which is only within the Tropicks . But the foresaid Dial was placed far without , to wit , under the Latitude of 35 Degrees . CHAP. XVII . Of the Phenomena of the third Position . 1. ALL the Stars , which are comprehended within the North Polar , remain always above the Horizon , neither do they ever set , unless it be , by a general setting Heliace : and contrariwise , all the Stars , which are comprehended within the South Polar , have a perpetual Night ▪ therefore the Polars , according to the Antients , are now equal to our Polars . 2. The longest Artificial Day is , when the Sun passeth over our Zenith ; the shortest , when the Sun is farthest in the Meridian removed from it . 3. Once a Year only is the Sun Vertical , to wit , when he is in the beginning of Cancer . 4. The Sun in the Meridian , never descendeth from the Zenith towards the North , but returning from the Tropick of Cancer , he is alway in the South . 5. There are here , but two Solstices , one high , another low . The highest , when the Sun is in the Tropick of Cancer ; the lowest when the Sun is in the Tropick of Capricorn . 6. The Day is longest , when the Sun is in the Tropick of Cancer , it is shortest when the Sun is in the Tropick of Capricorn . 7. There is one Summer , when the Sun is in the Zenith , and one Winter , when he is in the Winter Solstice . 8. They have four different Shadows , one Perpendicular , one Oriental , one Occidental , and one Meridional . Here begin the Heteroscii , for the Meridional Shadows begin there to decay , that is , the Shadows projected towards the South . 9. The extremity or end of their Gnomon , upon their Dials , describe also the Figure called Hyperbole , the sides opposite being unequal . CHAP. XVIII . Of the Phenomena of the fourth Position . AS the Artick and Antartick of the Antients , are greater than our Polars , so there are more Stars in this Position of the Sphere , seen perpetually , and more perpetually lurking under the Horizon , than in the last Position . 2. The unequality of Days and Nights , are also augmented . The Artificial Day is at the longest , when the Sun comes nearest to our Zenith , and at the shortest , when he is furthest removed from it : and as the shortest Artificial Day cannot be less , than 13 Hours and a half , so the longest Day cannot be 24 Hours . This least Artificial Day , is truly the longest Day , our Vertical Point coming nearest to the Tropick . It is called the least Artificial Day , because it is the shortest of all the longest Days , which can arise from the variation of the Vertical Point , between the Tropick and the Polar : and therefore , itis not called Minima the least , in respect of the rest of the days of the same Elevation of the Pole , but in respect of the rest of the longest Days , which may be found between the Tropick and Polar . The longest Day in this fourth Position of the Sphere , the Zenith coming nearest to our Tropick , cannot be less , than 13 Hours and a half , as the longest Day cannot contain 24 Hours . For this comes to pass , when the Zenith is in the Polar : therefore we must read , as the shortest Artificial longest Day , cannot be less , than 13 Hours and a half , &c. 3. The Sun can never come to their Zenith , neither can he ever touch lightly ( stringere ) their Horizon , when he is in the Meridian . 4. There are two Solstices , one when the Sun is in Cancer , and highest , another lowest , when he is in the Tropick of Capricorn . 5. There is one Summer , and one Winter . 6. There are only three different Shadows , one Oriental , the second Occidental , and the third Northern . 7. The extremity or end of their Gnomons , fixed upon the Ground perpendicularly , describe as yet Hyperboles . CHAP. XIX . Of the Phenomena of the fifth Position . ALL the Stars , whose distance from the Equinoctial , is greater than the Obliquity of the Ecliptick , either do not set under the Horizon , if they be Northern Stars , and do not rise above the Horizon , if they be Southern Stars : Therefore the Artick , and Antartick of the Antients are equal to the Tropicks . 2. The longest Day contains 24 Hours , and then there is no Night : and contrariwise , the longest Night consists of twenty and four Hours , and the Artificial shortest Day is nothing . 3. The Sun every year toucheth lightly the border of the Horizon twice , without rising and setting , namely when he is in the Tropicks . 4. The Sun at twelve a Clock in the Day , is alway South , nevertheless , when he is in the Tropick of Cancer , the half of his Body may be seen in the North , at 12 a Clock at Night . 5. There are here two Solstices , one high in Cancer , the other low in Capricorn . But according to the similitude of Solstices , which are in other Zones , we may say there are three Solstices there , one high in Cancer , when the Sun is high in the Meridian , to wit , 47 Degrees above the Horizon , which is the distance of the Tropicks ; there are two lower , of which one is in the same Tropick of Cancer towards the North , when he toucheth lightly the border of the Horizon , the other in the Tropick of Capricorn , where he also lightly toucheth the border of the Horizon . 6. There is one Summer , and one Winter . 7. There are four different Shadows ; one Eastern , one Western , one Northern , and one Southern ; tho this happens but once a Year , the Sun shineing with the half only of his Rays , which makes the light more obscure and dark , than when he shines with his full Rays . Here begin the Heteroscii . 8. The extremity or ends of the Gnomons , describe the Figure called Parabola , upon the Horizontal Dials , but an Hyperbole , so soon , as the Sun is gone from the Equinoctial , whereas on all other Plains , he describes always straight and right Lines . CHAP. XX. Of the Phenomena of the sixth Position . THere are very few Stars , which can rise or set , to wit , those only , whose Declination is less than the distance of the Tropicks ; because the Artick , and Antartick Circles , comprehending within them , the Stars which do set , and do not set , are greater than the Tropicks . 2. They have an Equinoctial , as other parts of the Earth . But when the Sun is in that Parallel whose Declination from the Equinoctial , is equal to the distance of the Poles of the World from the Zenith , the Day is twenty and four Hours , and the Artificial Day excresceth , and shoots out , into many Natural Days . 3. The Sun being in the same Parallel , he lightly toucheth , the border of the Horizon , and coming to it , she shines only with an half Orb. 4. They have but only one Solstice , in the Tropick of Cancer ; for the other in the Tropick of Capricorn cannot be seen . But Analogically , and ●…n similitude there are six Solstices . Two high , when the Sun is in the Tropick of Cancer : for there , as well to the ●…outh , as to the North , the hight of ●…he Sun in the Meridian is highest , al●…eit the Northern be greater than the ●…outhern : and four lowest , when the ●…he Sun toucheth lightly the Horizon . ●… . They have one Summer , and one ●…inter , but their Summer may be so ●…alled only Analogically : for these ●…laces of the Earth , are perpetually stiff ●…ith Snow and Yce . 6. They have four different Shadows , one from the East , one from the West , one from the South , and one from the North. Here are the Periscii . 7. The Gnomons , and stiles of their Dials , describes with their Points , Elliptical Figures . CHAP. XXI . Of the Phenomena of the seventh and last Position . 1. THere are here no Stars , which either rise or set , but all of them are whirled about , equally distant from the Horizon . The Artick and Antartick Circles , are one and the same with the Horizon , and Equinoctial , which are now united . Understand this of the fixed Stars only ; for the Planets absolving their course , rise and set , in their appointed times . 2. The Artificial Day is extended to half a Year ; so is the Artificial Night , and therefore the quantity of the Natural Day , and the whole Year is one and the same . 3. When the Sun is in the Equinoctial , he shines only with half his Orb , and toucheth lightly the Horizon , and there he riseth and setteth only at those times . 4. No point of the Heavens , can be called , either West , East , South or North , seing the Pole of the World doth not incline to any part of the Horizon , by which Inclination the four Points of the Universe , have their distinction . 5. They have only one Solstice , to wit , in Cancer , but Analogically two other may be added , to wit , when the Sun is in the beginning of Aries , and Libra . 6. There is one Summer and one Winter : but their Summer is rather to be called a slender slaking of the Cold. They have one Winter , because the Sun is under their Horizon a whole half Year together . 7. The Gnomons of their Dials , describe with the extremity of the Shadow , upon an Horizontal Plain , perfect Circles . FINIS . Proteus Bound with Chains : OR , A Discovery of the Secrets of Nature , which are found in the Mercurial-Weather-Glass , unfolding the Reasons , and Causes , why before Fair Weather the Quicksilver Ascends , and before Foul Weather , it falls down , and Descends . A Subject not hitherto Treated of . TOGETHER With some brief Observes upon the Parisian Weather-Glass , and an Explanation of the Sealed Weather-Glass , and common Weather-Glass . To all which is Added The Theory of the Weather , according to the Perpendicular Weather-Glass . By GEORGE SINCLAR , sometime Professor of Philosophy in the Colledge of GLASGOW . Felix qui potuit rerum cognoscere causas . Edinburgh , Printed by the Heir of Andrew Anderson , Printer to His most Sacred Majesty , Anno Dom. 1688. Proteus bound with Chains : OR , A Discovery of the Secrets of Nature , which are found in the Mercurial Weather-Glass , &c. THere are many excellent Questions to be Refolved , and Causes of the various Phenomena of Nature to be rendred , before a man can have knowledge to mount the Mercurial-Weather-Glass . Yet there are many , who rashly adventure , and bring upon that unerring and infallible Master-piece of Nature , the scandalous and odious Character of Falibility , either by raising the Mercury too high , or fixing it too low in the Cylindrical-Glass , both which Extreams must be cautiously shunned . For if it be not ordered according to the Authentick Observations of the Weather for many Years past , it cannot but err . And herein its infallibility and perfection consists , to give the Theory of the Weather a just and determinate hight , according to long Observation , and by consequence the top of the Cylinder the same hight , none of which no ignorant person can do . The Questions to be resolved , are such as follow , 1. What sustains the Mercury in the Glass-Tube , whilst the Orifice is always downward , and open ? 2. Why the Glass must exceed in length , one and thirty Inch ? 3. Why the Mercury falls not down , if it be shorter than twenty and eight ? 4. Why the Mercury is carried up with violence to the top of the Glass-Tube , whilst the Orifice is raised above the surface of the stagnant Mercury ? 5. Why as much Mercury in hight , is sustained in the wide Glass , as in the narrow ? 6. Why , tho the Glass were in hight many Foot , yet the whole Mercury falls down to twenty and nine , or thirty Inch above the Cistern ? 7. What fills up the space left empty behind ? 8. Why the Mercury subsides by degrees , as the Weather-Glass is carried up some high Mountain , and why it rises again , as it is carried down ? 9. Why a Glass of thirty six Foot high is required to make a Weather Glass with Water in it ? 10. What 's the reason , I do not find the weight of the Mercury within the Glass , whilst I poise it between my Fingers , and yet I find another weight exactly the weight of it ? 11. What that other weight is ? All these and many more are fully and clearly resolved in my Philosophical Experiments twenty years ago . But there is a late Question , which troubleth all the Learned to resolve , which now I intend shortly to explain , viz. What 's the reason , why the Quicksilver in the Weather-Glass creeps up before Fair Weather , and falls down before Foul Weather ? For an answer to this considerable Question , it is to be observed , that in the foulest Weather , I have found the Quicksilver fall down to twenty and eight , and in the dryest , and fairest Weather , I have found it up at thirty and one Inch. From this excellent Phenomenon only , it is called the Weather-Glass , Kat'exohen , by way of excellency : because before this alteration was found in it , it was called by the most part of Philosophers , the Torricellian Experiment . For clearing the Question in hand , I suppose that in the Beginning , there went up a Damp from the Earth to water the whole face of the Ground . Moses ( Gen. 2. ) relates now the ordinary means appointed by God in Nature , for bringing forth of Herbs , Bushes , and Trees out of the Ground , viz. the Damp , which causeth the Rain , and moistneth the Earth , which Damp being by the heat of the Sun rarified , ascendeth to the middle Region of the Air , where by means of the coldness thereof , these Vapors are condensat , and thickned , and tur●…d into a Cloud , and afterward are turned into Rain , and so fall down . That there are such Damps and Vapors , which ascend from the Earth , and Waters , cannot rationally be denyed ; nay many Thousands and Millions of them ascend , which we do not see nor observe . I have seen in Frosty Mornings the mouths of Coal-sinks , and empty passages from waste Ground , where Coals have been digged out , Fumes and Vapors coming out so plentifully , as Fumes from a Salt-pan . Some do fitly compare this Earth to a Bag-pudding , taken out of a Boiling-pot , which sends forth Vapors in abundance . Likewise from the surfaces of standing and running Water , what numbers may be seen in a warm Summers Evening . Nay from the Bodies of Men and Beasts , there is a perpetual Perspiration . But the finest and purest of all , are those which are exhaled from the Earth , and Waters . We see , that when the Sun is hot in Summer , the whole face of the Ground after Rain , covered over with Unduls , or little curled Waves , a small Gale of Wind being stirring , like unto the curled Waves of the Sea , Analogically . And so slender and pure are they , that whilst a man is among them , he cannot see them , but at a distance he may , looking alongs the face of the Ground . Likewise what multitudes of them may be seen alongs the surface of the Sea , a man standing at a considerable distance from the Coast. And so thick are they , that they have wonderfully lifted up , and magnified , much of the Land , and have made it appear , far otherwise than it was ; nay , eclipsed whole Villages and Towns , and metamorphosed them into various shapes and forms , all which have come to pass , by reason of their multiplicity and thickness . Now these Vapors , flowing from the Earth and Waters , are carried up to the middle Region of the Air , where by process of time , they are condensat , and thickned , by the coldness thereof , and fall down in Rain . But here it may be inquired , By what cause , ●…r power , are these Vapors carried up , seing they are Material things , and endued with weight ? For answer , I must premit some few things , which do not ordinarly occur . First , That in all heavy Bodies , there is a twofold weight , one Specifical , the other Individual . The Specifical weight is found in Bodies , which differ by Nature , as Wood , and Stone , ballanced one with another , equal quantity with equal quantity . ●… Individual weight , is likewise found in the same Bodies , but after a different way and manner . For example , Stone is naturally , or specifically heavier than Wood , putting equal quantity against equal quantity ; for a Cubical-foot of Stone , is heavier , than a Cubical-foot of Water . Bodies of the same Individual weight , or such as are weighed in a pair of Scales , as a Pound of Lead , and a Pound of Wool , are individually of the same weight , but of different weight Specifically . Secondly , There are two sorts of Ballances , the one Natural , the other Artificial . The Natural Ballance , is the Mercurial Weather-Glass , wherein the Mercury counterpoiseth the Air , and the Air the Mercury , both of them observing an equal Altitude , according to their natural weights : for since the Mercury is reckoned 14000 times heavier than the Air , the pillar of the one must be 14000 times lower than the other ; and so both are of the same hight , according to their Specifical weights . The Artificial Ballance , is that Mechanical Power , called the Libra . Thirdly , That one Body naturally lighter than another , may become of equal weight , or heavier , than that other . For example , the Vapors , which ascend are far lighter specifically , than the Air , yet they become heavier specifically , when contracted , and reduced by a Cold , to a thicker habit , or consistency , and most of all when they are converted to Rain . But how shall it be known , that the Vapors are naturally lighter , than the Air ? I answer , If it were possible to take an equal quantity of Vapors , with an equal quantity of Air , and weigh them in a Ballance , the Air would be heavier . We know that Oil is lighter than Water , for being put under Water , it riseth to the Surface : so the Vapors go up thorow the Air , as Oil goeth up thorow the Water . Now I come to the Question in hand , and I affirm , that the Vapors are carried upward , not by the heat of the Sun , which is an vulgar error , but they being specifically , and naturally lighter , than the Air , are prest up by it , as Smoak , till they come so far up , as the pressure of the Air , is able to carry them . I shall make this evident , by the following Experiment . Let a Diver go down to the bottom of the Sea , with a Bottle of Oil in his Hand , and pour it out there , he shall find , that such is the pressure of the Water , it shall drive it all up to the Surface above . For as the Oil is naturally lighter than the Water , so these Vapors are naturally lighter than the Air. Now these Vapors , which are infinite in number , ascending from all the parts of the Earth , to the Atmosphere many Miles above the Clouds , causeth the Air here below press with greater weight , upon the stagnant Mercury , and so raiseth the Quicksilver in the Weather Glass , one Inch or two , and sometimes three : for it is not possible , that the Air above , can be prest down , and burdened , with that new weight , and addition of Vapors ascending , but the stagnant Mercury below must find the said pressure . But how are these Vapors condensat and thickned together , and fall down in Rain ▪ I shall do this , by a most evident , and clear example . We cannot more fitly compare these Vapors , ascending and descending again in Rain , than to an Alembick , or Distillater . For these Fumes being carried upward within the Pot , and meeting with a cold Receptacle ( for the Pipe descending goeth ordinarly thorow a Vessel full of cold Water ) they are presently reduced , to their first condition , and fall down in Liquor . So are the Vapors , which ascend from the Stomach to the cold Brain received and distilled . But why should the falling down of the Rain cause the Quicksilver fall down , and why should the rising of the Vapors , cause the Quicksilver to rise ? For clearing of this , it is to be adverted , that whilst the Mercury is up at one and thirty Inch , there is an equal ballance or weight between the weight of the Atmosphere and the weight of the Quicksilver , so that there cannot be the least weight subtracted from the pressure of the Atmosphere , but as much must be subtracted , from the hight of the Quicksilver : as by taking away one Ounce from this Scale of a Ballance , the other presently goeth down , or by adding one Ounce to this Scale of a Ballance , the other Scale presently goeth up . Hence is it , that the pressure of the Atmosphere becomes less , by the falling down of the Vapors , and consequently the hight of the Quicksilver , must decresce also . And contrariwise ( which clears the second part of the Question ) whilst the Vapors are ascending , and going up , the Atmosphere is more burdened , and by consequence the Quicksilver riseth , sometimes less , and sometimes more , sometimes one Inch , sometimes two or three . But how comes it to pass , that the whole Air , or that great and vast bulk of it , can be in equal weight , with so small a portion of Quicksilver , granting the Air to be so heavy , as is commonly reported ? I answer , It is not the Air according to its thickness , or bulk , which makes any counterballance with the Quicksilver , but it is the Air reckoned according to hight , because Fluid Bodies do not counterpoise one another , according to all their dimensions , but only according to Altitude ; this is only proper to Solid Bodies . For let never so much weight be added to the Air in thickness , itshall never make the least alteration in the Mercury . But if there be but the least addition made in hight , the Quicksilver presently knows it , by rising and falling accordingly . For by how many thousand times the Air is specifically lighter than Quicksilver , by so many thousand times is the pillar of Air , higher than the pillar of Quicksilver . And contrariwise , by how many thousand times the Quicksilver is naturally heavier than the Air , by so many thousand times must the Cylinder of Quicksilver , be shorter than the Cylinder of Air , which sustains it . The proportion is ordinarly reckoned as 1 to 14000. That is to say , one Cubick-Inch of Quicksilver counterpoiseth 14000 Cubick-Inches of Air , both being put into a Ballance . It is evident from this , and many other things , that there is a proportion observed in all the Works of Nature , as here between the hight of the Atmospere , and the hight of the Quicksilver : for all the Lords Works , are made in Weight , Measure , and Number . This truth is so evident in the Mathematical part of Learning , that there is no need of proof . And if this proportion be not observed in things Artificial , viz. by Architects and Builders of Houses , the whole Fabrick looks pitifully , and wants that face , and delicate aspect , it ought to have . And as the most wise Artist of the World , hath created all things in proportion one to another , so all the parts of his Holy Word , are in such a proportion one to another . For this we have Scripture , and Divine Authority : for it is said , Whether we prophesie , let us prophesie according to the proportion of Faith. The Original word is , Analogia Pisteos , well rendered in our Vulgar Language , the proportion of Faith , or Analogy of Faith , not as some , the Measure of Faith. GOD is not tied to Numbers , yet nevertheless , he doth and disposeth his Works , by Number , Weight , and Measure . It is observed , that after the going up out of Egypt , GOD caused to be numbred all the Israelites , from the Age of twenty years and upward , ( Exod. 38. 26. ) and there were found six hundred three thousand five hundred and fifty men . The year following , GOD commanded to make a second Review of the People , ( Numb . 1. 46. ) but without comprising the Levites , which had been numbred the first time with the other Tribes . Notwithstanding this Subtraction , and the Casualities , which might have changed the number of the People , since the year foregoing , it is found that their number was yet justly and precisely six hundred three thousand five hundred and fifty men . In which is seen a proportion which GOD held in the multiplication of that People . There is also observed a Mystery in the exact number of the two and twenty thousand Levites , which were then reckoned ( Numb . 3. 39. ) For the rest , I contend not against the common opinion , touching the hundred fourty and four thousand of the seventh of the Revelation , that they ought to be taken for an indefinite number , as well as the seven thousand which had not bowed the Knee to Baal . But it ought to be considered , why the Holy Ghost , who speaketh nothing superfluous , is not contented to have named the total sum of them , that were sealed in Israel , but also divideth it , in twelve times twelve thousand , distributed by equal portions among the twelve Tribes , every one of which is mentioned , the one after the other , with the expression of its particular number : for this sheweth , that the number of the Elect , and the multitude of Believers , are measured by certain proportions , which are known to him , who is the Author . Certainly , the resemblance of the seventy Disciples of Christ , to the seventy Judges , which were substituted to Moses , and to the seventy Children , which Iacob had when he went down into Egypt , is a line of this admirable Symmetry , with the which God hath limited , and proportioned the Body of the Church . Now this fortifieth that Maxime , that the number of the Elect cannot suffer addition , nor diminution : and that Election proceedeth not , from the Will of the Elect , but that of God , which prevented them . For it cannot be said , that all the Elect , from the beginning of the World to the end , have agreed together to make a Company composed precisely of a number certain and regular . But I return . It may be here inquired , Whether those Vapors , and Exhalations go perpetually up from the Earth , or not ? 'T is probable , that they are alway ascending , tho insensibly to us , and as many of them in the Night , as in the Day-time . Nay , more ( it seems ) in extream Frost and Cold Weather , than at any other time ; as we see in Greenland , where the greatest extremity of Cold is , there are infinite Treasures of Snow , which Snow could not fall down so plentifully , if there were not Vapors perpetually ascending . Next , after Rain , and the falling down of the Mercury to 28 , or 29 Inch , I have found the ascent of it , in that same Night eight or ten Degrees , which could not happen , unless there had been an addition of new weight to the Atmosphere . And this is observed , to be rather in the Winter , than in the Summer Season , especially in calm Nights . I have observed , that the next Morning after Frost all the Night , the standing Waters in Furrows , which have remained many Days entire , dry up , and nothing remaining , but emptiness below a surface of thin white Y●…e . This Water could not sink into the Ground , more that Night , than many others before ; but the Frost coming on , and the Air becoming dry have turned all the Waters into Vapors , and so have been exhaled . I would have it made more evident , how the greater pressure of the Atmospere by the weight of these Vapors make the Quicksilver rise in the Weather-Glass ? I answer , Take the Weather-Glass , and place it within a dry Harbour , before the Water begin to flow . Then suppose the hight of the Mercury to be eight and twenty Inch. I say , when once the Water hath flowed , but three Foot and a half in hight , above the stagnant Mercury in the Cistern you will find the Mercury in the Weather-Glass three Inch higher . For as the growing of the Tide above the stagnant Mercury raiseth it higher , and higher in the Glass , so the ascending of the Vapors loadneth the Atmosphere , more and more , and consequently it presseth with more weight upon the Mercury in the Cistern . And as the Vapors are turned into Rain , and the Mercury falls down ; so by the ebbing of the Water , the three Inch of Mercury , falls down within the Weather-Glass . It may be inquired , How far do these Vapors ascend ? I answer , That Philosphers distinguish the Air into three Regions , the first , second , and third . But both Philosphers and Astronomers do vary exceedingly in determining the hight of any of them . I shall not curiously inquire , but shall speak a little to what concerns the present purpose . 'T is probable , that these thin and light Vapors , which flow out of the Earth and Waters , go many Miles above the Clouds , where there is neither Wind nor Rain : for the pressure of the Air being powerful many Miles up , must carry the Vapors , so far up . But to determine particularly , it is not possible , only in general they ascend very far . Now it is evident , that the Atmosphere , is composed , and consists of such Vapors being called Sphaera halituum , which no doubt , is of a considerable thickness , and hight . These Vapors , when they are once past the inferior Region of the Air , which will not exceed an English Mile , and a half , go up quickly , and are received by the Atmosphere , where they accresce to a considerable hight , perhaps 40 or 50 Mile above the Clouds , where by some extrinsick cause , as extremity of Cold , they fall down from the Atmosphere , first as Mist or Dew , till they come to the lowest Region , where in a very short time , they cover the whole Heavens , tho never so clear before . How many times before Rain , will this be seen . Besides , there is above the Atmosphere , that which Astronomers call the Diluculum and the Crepusculum , that is , both the Dawning of the Day , and the Twilight in the Evening , the one beginning about two Hours before the Sun rise , and the other ending about two Hours after the Sun is gone down . For if that Crepusculum were not there , we should have no Light , until the Body of the Sun were above the Horizon , and should have no Light after the Body of the Sun is set . This Sphere is unalterable , and without accresce or decrease , but the Atmosphere is not so , by reason of the Vapors coming to it , and decreasing again . Next , the Refraction , which makes the Sun or Star to appear above the Horizon higher , than really it is , is caused by the Atmosphere . 'T is observed by Shepherds , that if the Sun appear sooner above the Horizon , than ordinary , the Day following shall be Rainy . They see indeed the Image of the Sun , a little before he rise , which is caused by the Refraction , or thick Medium of the Vapors , which ly about the Horizon . For example , Let a man so fix his Eye , upon a wide Vessel , with an open mouth , with a piece of Money in the bottom , he shall not see it , till the Vessel be fill'd with Water . For Water being a thick Medium raiseth the Image of the Money , and brings it to the Eye by a broken and crooked Line , which is Radium refrangere , or rather refringere . It may be further inquired , Why the Clouds are sustained , or what keeps them up from falling down ? This is a considerable Question , and well worthy of a Divine Answer . The Lord says to Iob , Dost thou know the ballancing of the Clouds , the wondrous works of him who is perfect in Knowledge ? The Clouds then are suspended , not miraculously , yet wonderfully by Natural Causes ; for as a Ship is sustained from sinking by an even Ballance with the Water , so are the Clouds keeped up , by an even and equal Ballance with the pressure of the Air , which really sustains them . If they be light and thin , they go further up , but if they be heavy and black , they come nearer to the Earth , but are still in an equal Ballance , with the pressure of the Air. And as the Loadned Ship goeth further down in the Water , than the Ship , that 's not burdened ; so do the black and heavy Clouds swim lower , than the light and white Clouds . But when there is a great convocation of Clouds together in one place , each one presseth upon another , and so like Honey-Combs they distil their Drops upon the Earth . Note , That the greatest Ship in Europe , with all her Furniture for War , is but the just and exact weight of the Water , thrust out of its place by the Ships Water-draught . It may be yet inquired , How far are these Clouds from the Earth , which send down the Rain ? I answer , The surest way to know , is by the Thunder . Observe then , how many Seconds of Time , do pass , between the first seeing of the Glance , and the hearing of the Crack . If the Noise be straight up , five or six will pass , which make an English Mile . In Mountainous Ground , which lyeth higher , three at the most will interveen , about five hundred pass . To know exactly a Second of Time , whereof 3600 make an Hour , follow this method . Take a small Chord of thirty and seven Inch and a half exactly . To which append a Lead-bullet of seven or eight Ounce . Hang it so , that it may swing to and fro of its own accord . Each one of these Swings are a Second of Time. But may it not be affirmed , that the greater pressure of the Air , which raiseth the Quicksilver , is caused by the weight of the Clouds , which swim above us : and that the falling down of the Quicksilver is caused by the dissolution of these Clouds into Rain ? I answer , This cannot be : for when the Heavens are most serene and clear , the Mercury is furthest up ; and when the Heavens , are nubilous , and covered with Clouds , the Mercury many a time is furthest down . It may be inquired , Whether the cracking of Thunder , maketh any alteration upon the Weather-Glass ? I answer , There are three things to be considered in Thunder , First , The Lightning . Secondly , The Crack . Thirdly , The Thunder-bolt : which three are lively represented to us by the shooting of a Cannon ; for the Fire coming out of the Muzzle , represents the Lightning ; the Report , represents the Crack ; and the Bullet , the Thunder-bolt . But there is a more lively representation of Thunder , in Aurum fulminans , which like the Thunder-bolt carrieth its stroak downward , three Grains of which , tho never so little made hot , takes Fire , and gives a greater Report , than two Ounces of Gun-powder , so stupendious is it . But there is nothing here , which can make any alteration upon the Weather ▪ Glass . It may be inquired , If the Winds make any alteration upon it ? I answer , Winds are nothing but Air agitated ; nor Tempests , but Air-floods , or violent Agitations of the Air. These do really influence the Weather-Glass , not only in causing the Quicksilver subside , and fall down , but in causing the top of the Mercury tremble , and make some visible reciprocations up and down , especially , when the Wind blows very high . Next , Winds which come from the South and South-west , by reason of much moistness , which they bring alongs with them , influenceth the Quicksilver much indeed . But Northerly Winds , which are more drying , have less influence . Nay Easterly and North ▪ east Winds even with Rain , keep up the Mercury , and suffers it not to fall down so far , as other Winds . Because such Winds come from the Great Continent , bringing with them many Earthly Particles , and Atoms , which being dry , have not that influence upon it , as moist Winds from the South and West . It may be inquired , If the Weather-Glass doth foretell Winds , as it doth Rain ? I answer , It doth not so much foretell Winds , as it is actually influenced by them . Yet , if a man were a diligent Observer of the Winds , before they blow , and took narrow inspection of the Weather-Glass , he would surely foresee them approaching , by some alteration or other in it . It may be inquired , Whether Mist or Fog , doth affect the Weather-Glass ? I Answer , Yes , for I have observed , when the Mercury has been up at Fair , the falling down of a Fog , hath brought it down three or four Degrees . It may be inquired , When the Mercury i●… at the highest Station , in the fairest Weather , as above Long Fair , how many Days doth it prognostick Rain , before it come ▪ I Answer , When it first begins to alter , it must fall down to Long Fair , half an Inch ; next to Fair , another half Inch. Thirdly , To Changeable , as much : And lastly , To Rain . This Motion is slow , and therefore it foretells , sometimes three Days , sometimes four , sometimes less ▪ But this is sure , it cannot fall down in one Day so much bounds , nor in two , neither in three . I have seen it fall down from Long Fair to Fair , and then halt , by reason of some stirring Winds , or by reason , of some small change of Weather , in some County near hand . When it 's far up , as at Long Fair , or above it , it is next to impossible , that either Wind or Rain can be . Some , who are not acquaint with the Weather-Glass judge it erring , when they see the Mercury at Rain , and yet no Rain . I confess it may be so , if it be not rightly adjusted , at the first setting up ; but if it be set , according to Art , the Mercury cannot be at Rain , but there must be Rain , either here , or some place near hand . It may be inquired , If Snow and Hail have the same effects upon the Weather-Glass , which Rain have ? I answer , Yes ; for they are both from the same cause , namely moist Vapors . I have 〈◊〉 s the next adjacent Hills covered with Snow , when there was neither Rain nor Snow in the Valley Countrey , and the Mercury down at Rain , tho it had been always up before the Snow fell . And many times it is found , that Rain falling in the next Shires , or Counties , tho none here , have made the Quicksilver fall down to Rain . The last year 1687 , in November , I have seen the Quicksilver , below Much Rain , and yet the Days going before , or following , have been pretty fair . But the Weather , was under a strong disposition , and inclination to be Tempestuous and Stormy , which soon followed . 'T is observable , that the Quicksilver , is never so high in the Weather-Glass , as about the hinder end of the Month of October , or rather in the Winter Season . In Rainy Years , I have not seen the Mercury further up than Fair , and that seldom . Might the Weather-Glass be useful in Ships ? I answer , Yes ; but the commotion of the Ship , ( you say ) renders it useless . I answer , it might be so suspended , that it might hang always perpendicular . And tho this were not , yet the Nature of it is such , that it can recline without hurt , as much as the Ship can●…ly , either to Starboord , or Larboord , and fall right again , when the Helm is righted . In a word , whatever advantage a man might have by it , in his Chamber , he may have as much , by having it in his Cabin . There is a person of Honour , and great Learning , who hath written lately in Natural Philosophy , and among other things , hath not omitted to shew the reason of this marvellous Phenomenon , whereof I have been Treating . He toucheth it briefly in 9 or 10 Lines , and says , Id autem mirum satis videtur , &c. 'T is a strange thing ( says he ) that in Rainy and Windy Weather , when the Air seems to be heaviest , yet the Mercury is furthest down . The reason ( says he ) is taken from the temperament of the Air , where the Clouds are ; for when the Clouds are grosser , tho much elevated , they intercept the Rays of the Sun , and are thereby melted , and turned into Rain . And the Air being eased of the burden of these Clouds , and being rarified above , by the Sun-beams , is becomes lighter , and so bears less down the surface of the stagnant Mercury in the Cistern . But when the Air is nubilous and Cloudy , the weight of the Air , is augmented , by the weight of the Clouds , which make it press with greater weight upon the stagnant Mercury in the Cistern . I dare not oppose any thing to the Opinion , of such an eminent man , tho I might , he being a hundred Stages beyond many . Yet there are not some wanting , who male-apartly set at nought his Philosophical System , as insufficient both for Matter , and Form ; whereas among all the Learned Abroad , his Writings are held in great Estimation . There is one of the Professors of Philosophy at Aberdeen , whose publick Theses the last Year , came to my view : yet I shall adventure to say something anent them . The Author , ( whom I have not the favour to know ) seems to be well acquaint with the new Philosophy , and a good Schollar . He confutes rationally Malebranch , and Spinosa , two wild Philosophers . He seems to be a Cartesian in his Philosophy , yet affirms that the Demonstration ( as he calls it ) of God's Existence , by the Idaea , being abstract and Metaphysical , goeth far beyond the capacity of the Vulgar , and therefore being compell'd by Reason , he averreth , that the Apostle Paul reasons far better in the first to the Romans . He speaks honourably of the late Lord President in confuting some of his Doctrine , for which he deserveth more thanks for his good Estimation of him , than for the strength of his Reasonings against him . He hopes the Lord Stair , will hold him excused , if he do not acquiesce to his Decisions . This seems to be jeastingly spoken . Casting my Eye further thorow , I found somewhat anent the Causes of Winds , Tempests , and Rain , and the reason why the Atmosphere , is sometimes lighter , and sometimes heavier . But he hath not touched the Nail upon the Head. Some Notes upon the Parisian Weather-Glass . THere is a New Invention of a Weather-Glass , which cometh from Paris ( facile est inventis addere , ) set in a curious gilded Frame , more specious to behold , than profitable and useful . It is lyable to several Abatements . The first makes it a dumb Weather-Glass , wanting the whole Theory of the Weather , so that when a man looks to it , he knows not whether it shall be Fair or Foul. A man seeth indeed the sides of the Frame , divided by French Measure into Inches and half Inches ; but these Measures have no signification of the Weather . When a man looks upon it in the Morning , he sees the Tinctured Liquor at such a hight ; and in the Afternoon , he observes again , and finds it higher or lower . This is all it signifieth . And if perhaps he be informed that in Fair Weather , the Liquor descends , and in Foul Weather it ascends , then he may conclude , observing it further down than it was , that it is probable to be Fair. The second Abatement is , that there are two Oval-Glasses , which rather ought to be Cylindrical . Now unless there be a just and exact measure in hight , between the top of the one Oval-Glass , and the bottom of the other , it cannot be un-erring , or between the middle of the one , and the middle of the other . Because the Mercury cannot raise the Liquor in the right side , by equal portions , since the rising of it depends essentially upon the falling down of the Mercury from the left Oval-Glass . For the Glass being in form of a Pullets Egg , more Mercury falls down , whilst it is terminate about the middle , being there wider , than whilst the Mercury , is near either of the extreams , which are narrower . And I believe the Contriver hath foreseen this . The third Abatement is , that the Tinctured Liquor is subject to Corruption , the Orifice of the Glass being open , suffering Evaporation , by which means , the whole Contrivance is rendred useless . The fourth Abatement is , that the Orifice of the Glass , upon the left Hand , must be Hermetically Sealed , which few or none can do . The fifth Abatement is , if it be once Mounted , and set a going , it cannot be well Dismounted , for the end which is Hermetically Sealed , must be opened , and cannot be well Sealed again . Lastly , The Glass is brought Home from Abroad , not without hazard of breaking , the Glasses being very small and slender . But there are none of these Difficulties found in the Perpendicular Glass . For it may be set up , and dismounted , as oft as you please , and transported from one place to another . And the excellency of it is , that it sets it self ; for whatever weight of Mercury it once takes , the same will suffice it for ever . And which is marvellous , the Mercury falls down alway according to the Nature of the Weather , and there halts , whether it be Fair , or Foul. There is a second sort of Weather-Glass much in use , called the Sealed Weather-Glass , whose use is only to shew the Heat and Coldness of the Air. It hath a round Glass below , about two Inch in Diameter , and a Stem going up from it , about a Foot and a half in length , but slender and narrow within . This Glass is filled with the finest Spirit of Wine , three or four times distilled , so in effect , being full of fiery Spirits , the least Heat or Warmness in the Air , rarifieth it , and the least Coldness contracteth it . When the Ball is once full , and the Stem too , the open Orifice above is Hermetically Sealed , and coming to the cold Air , from the warm place it was in , the Liquor creeps down towards the Ball , and by this means , it demonstrats by its creeping up , the warmness of the Air , and by creeping down it shews the Degrees of Cold. It is Hermetically Sealed , that the outward ▪ Air , may have no influence upon it . It is set in a curious gilded Frame , with the several Degrees of Heat and Cold affixed to it . They come from Paris , and London , not without hazard of breaking by the way . There is a third sort , specially different from the rest , called the Water Weather-Glass . It hath a round Head above , with a long Stem going down from it , and the Mouth below remaining open , is drown'd among Tinctured Water . To set it a going , they use to warm the Head , and Body of it , at the Fire , and then to thrust the open end among the Liquor in the Cistern . When the heat begins to abate in the top , the Air within , begins to contra●… it self , and so the Water follows up , and hangs about the middle of the Stem . This in cold Weather creeps up , and in warm Weather creeps down . It creeps up for fear of Vacuity , as was maintained long since , before the pressure of the Air was known by the Torricellian Experiment . This Weather-Glass was esteemed infallible ; but now it is known to be most fallacious , and uncertain . The reason is , because it is acted and moved , not only with Heat and Cold , but with the greater and lesser pressure of the Air. If it be demanded , how shall I know , whether it be the coldness of the Air , or the greater pressure of the Air , which causeth the Water to ascend : and whether it be , the warmness of the Air , or the Iesser pressure of the Air which causeth the Water to descend ? I answer , It is difficult to know ; for both do sometime concur , that is , the weight and greater pressure of the Air , and the coldness too . And sometime the lesser pressure of the Air with warmness , make the Water fall down . And sometime the greater pressure of the Air raiseth the Water , without any addition of Cold : And sometimes the addition of Cold , without any alteration in the Air , as to more weight , will raise it . And tho by this means it be fallacious , yet many notable Phenomena do appear from it . By the help of this , and the Mercurial-Weather-Glass , and the Sealed one , and by the help of the Hygroscope , which marvellously shews the least alteration in the Air , as to Moisture and Dryness , and by contemplating the Heavens , the Sky and the Clouds , and considering the Winds , how they blow , and the various Aspects of the Planets one to another , ( as Star-gazers do affirm ) men might come to foretell the Weather particularly . The Theory of the Weather , according to the Mercurial-Weather-Glass . THE Theory of the Weather , is either Ingraven upon Brass-Plates tichtly polished , or upon a piece of Lombard-paper , wrought in the Taliduse-press . The Brass , or the Paper , is divided into Six half Inches ; and every half Inch into Five Degrees ; or every whole Inch into Ten equal parts . I call the upmost Station , Long Fair ; the second half an Inch under it , Fair : the third , Changeable : the fourth , Rain : the fifth , Much Rain : the sixth , Storm●… ; and if you please to add the seventh , call it Tempests . These six or seven , contain the whole Alterations , which use to be in the Weather . When the top of the Quicksilver is at Long Fair , it toucheth exactly the Line under it . If it fall down , it is said to be one Degree under Long Fair , or two or three , accordingly as it falls down , till the top be at the Line under Fair , and then it is Fair Weather , and so of the rest of the Stations . It may be asked , At what hight , must Long Fair be affixed ? I answer , The Situation of the place must be considered , and the Climat under which we live : for a Glass appropriated to this Parallel , will not serve in the Braes of Athol , or Annandale . And if there be not a just , and exact hight , to a Hairs breadth , of all the Stations from below , it cannot be un-erring . The several Stations are found out , not by Algebra , or any Mathematical Demonstration , but by many years Observations . Whosoever taketh upon him to mount a Weather-Glass , without the knowledge of these Praecognita , he plays but the Fool. There are many other things necessary to be known , which every Fallow , which hath no more in his Scull , but a Bag-pudding in stead of Brains , is not capable to understand . I shall briefly run thorow the several Stations , with some Observes upon each one of them . In the first and upmost , is Long Fair , or most pleasant Weather . I have seen the Quicksilver sometimes above it , yet seldom doth this fall out , but in extraordinary Seasons . The Mercury being at this hight , it is next to impossible , either to be Wind or Rain . Nothing for several Days , but settled calm Weather . Sometime the Heavens are covered with dry and gray Clouds , but not the least appearance of Rain . The second ●…tation , half an Inch lower , is Fair. The Mercury being here , I have observed a small Showre of Rain to fall , from the lowest Region of the Air , as a th●…ck Dew or Mist , but immediatly after , the Day became Clear and Fair. The whole year 1686 almost , it was a rare thing to see the Mercury up at Fair , but frequently below Rain , and Changeable , because of the frequent Rains , which fell out that year . And which is observable , all that Summer , the Hygroscope went not once about , whereas in dry Summers , it goeth twice about , sometimes more and sometimes less . The third Station half an Inch lower , is Changeable . That is , sometimes Fair , sometimes Foul , sometimes Frost , sometimes Thaw , sometimes Sleet , and sometimes Snow , sometimes Wind , and sometimes Calm . The fourth Station is Rain , not actually Rain , but a stormy inclination in the Air to be Rain , and sometimes Rain . Nay , sometimes the whole Day will be Fair. But still the Rain is approaching , or hath been Rain , either here , or some place about . The fifth Station is Much Rain , the worst of Weather almost , as in the Summer , or Winter Season , when Rain is accompanied with stormy South-west Winds , or westerly Winds . This last October , or November , I have seen the Mercury below this Station , and yet no Rain in the mean time , nor all the Day , but the Sky black , and tempestuous , thick Clouds lying about the Horizon . Above Fife , great Heaps of them : some like Castles and Towers , others like ragged Rocks , hanging over each one another . All of them fore-runners of Rain . The sixth Station , Stormy , extraordinary Foul Weather . In the last place , I have subjoyned Tempests , or Hirricano's , which do not fall out in this Countrey . If it be asked , Why doth not the Mercury fall down to Tempests ? And why doth it not go half an Inch above Long Fair ? I answer , There are here two Tropicks , namely Storms , the nethermost , and Long Fair the upmost . Above this , the Air is not able to press , except some few Degrees . And at Storms the pressure is least . The length of the Tropicks then , are about three Inch. General Rules . The further the Mercury goeth up , the Weather inclines to be the Fairer , and the further it falls down , it inclines to be the Fouler . Secondly , When the Mercury is highest , Fair Weather seems to be universal ; when it is lowest , Foul Weather seems to be universal . Thirdly , It is not so much Foul Weather actually , which influenceth the Mercury , as it is the Disposition and Inclination of the Weather to be Foul : so that the Mercury will be many times at Rain , when it is not actually Raining , which is wanting when the Quicksilver , is at Fair , or Long Fair. Fourthly , Not only Foul Weather in this County or Shire , maketh the Mercury fall down , but Foul Weather , in the next adjacent County , tho there be none here : as the Weather-Glass at Edinburgh , will be altered , with Rain in Tweeddale , or in Lammer-moor . And as it shews the Nature of the Weather , so it predicts and foretells , sometimes a Day , sometimes two or three , if so be the Mercury hath been far up . But if it hath been only at Changeable , or below Fair , it predicts some few Hours , before it be Rain , by falling down a Degree , two or three , or four . When it is a falling down , the top of the Mercury is flat and level , but when it is a rising , it is somewhat round . 'T is said , that the Ladies , and Gentlewomen at London do Apparel themselves in the Morning by the Weather-Glass . Whatever be in this , 't is certain , that when a man riseth in the Morning , he may know infallibly , what sort of Weather will fall out ere Night . It is most useful for the Husband-man , both in Seed-time , and Harvest , and for winning of Hay . It is useful for taking a Journey , for when I see the Mercury up at Fair , or Long Fair , I may be confident , there shall be no Rain for eight or ten Days , chiefly when it 's up at Long Fair. There are many other uses , for which it is profitable , which are needless here to repeat . It is always infallible , because guided by God in Nature , tho to our apprehension it seems to err . There are so many Changes , and Alterations in the Air , that a particular Rule cannot be assigned for each one of them . But the general Observations which are affixed , are sure . If any man would find out all these Intricacies , he must diligently observe , the Changes , and Quarters of the Moon , and the several Aspects of the Planets , and the Winds how they blow , comparing them with the Changes and Alterations of the Weather-Glass . Neither can it be subject to Corruption , tho it stand an hundred year . The Glass cannot fail , neither the Quicksilver , which are incorruptible by Nature . Neither can the Frame decay , for many years , being made of Oak . FINIS . Postscript . To Buoy up a Ship , of any Burden , from the Ground of the Sea. THE Art of Diving hath not been much known , but of late ; for it depends essentially upon the knowledge of the pressure of Fluid Bodies , which knowledge hath not been further known to the generality of Learned Men , than by name : tho some ignorantly have averred , that the Hydrostaticks , is a Science long ago perfected . Among the first , who have essayed in this Nation , was the late Marquess of Argile , who having obtained a Patent from the King , of one of the Spanish Armado , which was sunk in the Isle of Mull , anno 1588 , employed Iames Colquhoun of Glasgow , a man of singular knowledge , and skill , in all Mechanical Arts and Sciences . This man , not knowing the Diving Bell , went down several times , the Air from above , being communicated to his Lungs , by a long Pipe of Leather . He only viewed , and surveyed the Ship , but I suppose buoy'd nothing up . About the year 1664 , when this Art became more perfected , and was advanced , by the Practice , and Invention , of Learned Men. The late Lord Argile did employ a most ingenious Gentleman , the Laird of Melgim , who went down with a Diving Bell , and made a further inquiry . After some pains , and labour , he buoy'd up three Guns , one of Iron , judging it to be of some other Mettal , one of Copper , and one of Brass , about eight Foot long apeice , and eight Inches of Diameter . The third Essay was made by the late Earl of Argile himself , several years after , who did more . There was one Captain Smith , who undertook after that , yet more , who thought himself so sure of the Spanish Gold , that he would not suffer a Carpenter with himself : but this Interprize turned to nought . To effectuate the Proposal , I shall offer these six Propositions , which with small pains may be made evident , from Hydrostatical Principles ; and next infer some Conclusions , needful for the design in hand . First , The whole Ship , with all its Loadning , is the just and precise weight , of as much Water , as the lower part of the Hull expells , or is expelled by the Ships Water-draught . Secondly , When the Ship becomes heavier than the said quantity of Water , it sinks . Thirdly , Water doth not weigh in Water . This is evident , for when a man pulls a Bucket full of Water from the bottom of a Well , he finds no weight thereof , till it come to the Surface . Fourthly , Nothing lighter in specie than Water , or of the same weight with Water , can sink . Hence , neither Timber , Wine , Bear , nor Oil , can tarry at the Sea Ground , but must be buoyed up of necessity . Fifthly , By how much , the whole Timber of the Ship , is lighter in specie , than as much Water equal to it in bulk , by so much is it the more able to buoy up . Imagine , the whole Timber of the Ship , reduced to a Cube of so many Foot , and a Cube of Water given of the same quantity . Now I say , as many Pounds , as this Cube of Water , is heavier , than that of Timber , so many Pounds of Iron , Lead or Stone , will the Ship buoy up , or support , even tho full of Water . Sixthly , A heavy Body , as Iron , Lead or Stone , weighs as much less in Water , than in Air , as the quantity of Water it expells . A Square Foot of Lead , which I suppose weighs in the Air 728 Pound , weighs but 672 Pound in the Water , less by 56 , the weight of a Square Foot of Water . From these Propositions , I infer , that when a Ship is to be buoy'd up from the Ground of the Sea , nothing of her weighs , save her Ballast . By Ballast , I understand , taking the word largely , every thing in the Ship , heavier in specie , than Water , as Guns , Ankers , Bullets of Iron , and Lead , Iron-bolts , Nails , and all manner of Iron-work . Next , That the whole weight of the Ballast , doth not preponderate or weigh down . Lastly , That the Timber of the Ship , and all things in it , lighter in specie , than Water , concur for buoying up the Ballast . The best expedient for raising of Ships entirely , are Arks of Wood , applyed either to the sides of the Ship without , or just above the Orlop . These Arks must be so close , on all sides , that neither Air , nor Water , can pass . The Ark , to describe it more particularly , must have four Sides , and a Cover above , but open compleatly below . At every Corner , next to the Mouth , must be fixed , a strong Iron-Ring . Four likewise above , that is , one in each Corner , answering to the four below , which are for fixing a second Ark above the first , if need be . If the Ship , which is to be raised , be twenty Foot over , make your Ark twenty Foot wide , and as much in hight . Bring it just over the place , where the Ship lyeth , and filling it with Water , that it may sink without difficulty , thrust it down , till it come just above the Orlop , and fasten it within five or six Foot of the same , with Ropes passing thorow the four Rings , and the Beams or Balks of the Ship. The Arks being thus fastned to the Ship , by a Diver , the next work is to beget a power , or force within it , which shall be able to buoy up the Ship from the Ground of the Sea. This may be done , either by sending down Buckets full of Air , with their Mouth foremost , one after another , from the Surface of the Water , and then cause a Diver receive them , and thrusting them somewhat within the Mouth of the Ark , turn up the Orifice , by which means , the whole Air in it , shall ascend up thorow the Water of the Ark , and rest above , next to the top . This Device being often repeated , will at last expell , the whole VVater of the Ark , and fill it compleatly with Air. This is so sure an Experiment , that none needs to call it in question . Or by communicating Air to the Ark from above , by the help of a pair of large Bellows , and long Pipes of Leather , going down within the Mouth of the Ark. Or thirdly , By the multiplication of Bladders full of VVind , filling the Ark within , which may be done more easily . The Ark being oncefull of Air , will have a considerable pull with it , which is more , and less , according to the dimensions thereof . For knowing this , you must consider , that whatever t●…e dimensions of the Ark are , it will buoy up , as much weight as the VVater weighs , which fills it . I●… then , the Ark be twenty Foot wide , and as much in hight , it must contain eight thousand Square Foot of Water ; and since every Square Foot of Water thereof weighs fifty six pound Trois , the whole must be 448000. An Ark then of twenty Foot Square , will buoy up , four hundred and fourty eight thousand pound weight , the weight of 58 Cannons Royal , each one whereof , I suppose weighs 8000 pound . Or the weight of 74 Demi-cannons , or the weight of 97 Culverings : or of 149 Demi-culverings : or of 298 Sakers , each one of this sort weighing 1500 pound . Or lastly , the weight of 250 Tun of Wine , reckoning four Hogsheads to a Tun , and each one of these weighing 448 pound . If you fasten a second Ark above the first , by the help of the Rings upon the top , which I mentioned , both will buoy up together 896000 pound , the weight of 112 Cannons Royal. But if your Ark be 30 Foot in all its dimensions , it must contain twenty and seven thousand Square Foot of Water , which will weigh , one million , five hundred and twelve thousand pound weight of the weight of 189 Cannons Royal , or the burden of 252 Demi-cannons , which is the weight of 844 Tun of Wine . But supposing the Ark to be more in quantity , the one way than the other , that is 40 Footlong , it shall be able to buoy up , two million and sixteen thousand pound , the weight of 252 Cannons Royal , or the weight of 1125 Tun of Wine , or Water . If the Arks be applyed to the sides of the Ship , you must fix , as many upon the one side , as upon the other , which need not be so large , as those which are fastned upon the Orlop . I shall suppose , that upon each side , there are four Arks , each one 10 Foot Square . If this be , every single Ark , must contain 1000 Square Foot of Water , which will weigh fifty six thousand pound . All of them together , therefore must buoy up 448000 pound weight , the burden of 56 Cannons Royal. To know , how to proportion the quantity of your Ark , to the burden of the Ship , which is the great secret , follow this Method . Consider first , that neither the Timber of the Ship , nor the Water which is in her , nor any other thing , which is lighter in specie than Water , ( that is , any thing which floats upon the Surface ) or of the same weight , with it , preponderats , or weighs down , but only what is heavier in specie , than Water , as Guns , Ankers , Iron-bolts , Iron-nails , and such like , the just quantity , or very near , may be found . Calculate then , as near as you can , and supposing the weight of all this Ballast , to be about 448000 pound ; you must next consider , what the dimensions of the Ark , must be , which is able to buoy up so much weight , which may be found out thus . Divide the just account of your Ballast by 56 , and the Cubique Root of the Product , gives you the just dimensions of the Ark. For example , Divide 448000 by 56 , and you will find 8000 , the Cubique Root whereof is 20 , the quantity of your Ark within . If you judge ▪ it more convenient to apply lesser Arks , namely to the sides of the Ship , ye may have eight , by dividing this into so many parts , four for each side , and every single Ark 10 Foot Square , which are equivalent . Remember , that tho the whole Ballast , weigh 448000 pound , yet this whole weight is not to be buoy'd up by the Ark , seing heavy Bodies weigh less in Water , than in Air , according to the sixth Proposition . As for fastening the Arks , either to the sides of the Ship , or just above the Orlop , several ways may be thought upon , which I leave to the Invention of others , who are skilful in building of Ships . Let it suffice , that I have made it probable , if not evident with Reason , that the greatest Ship may be buoy'd entirely up from the ground of the Sea , which was the thing to be demonstrated . If it be Objected , That the strong pressure of the Water , will put the Ark in hazard of bursting , when its full of Air. I answer , There is here not so much hazard , as every one may believe . The Reason is , because the pressure within the Ark , is very near equal , to the pressure from without . This I add , because the top of the Ark within , is more prest up by the Air within , than it is prest down with the Water without . The pressure upon the sides , is more uniform , and so there is the less hazard there . In a word , if the Ark be able to support , as much VVater , as fills it , without bursting , it shall go down thorow the deepest VVater imaginable without trouble . That is , hang it by Ropes in the Air , full of VVater . If the bottom be able to support this weight , there shall be no hazard of bursting , when it 's full of Air within the deepest VVater . From this unequal pressure , which the top of the Ark suffers , it follows of necessity , that if there be any Rift , or Leck in it , the whole Air will go out by degrees , and so render the Ark useless . I answer , this endeavour , which the Air within , hath to be out , is just the same , with that , which the VVater within , hath to be out , when the Ark is full , and hung in the Air with Ropes . If Art can cure the one , it may find a remedy for the other also . But I leave this to such as are skilful in Calking of Ships . Tho I seem to insinuate , that the Arks must be Cubical or Foursquare in their form , yet there is no necessity for that ; for they may be made under what fashion or form you please , provided they contain , as much Air as will be sufficient to raise the Vessel . And though I mention Arks of 20 or 30 Foot Square , which will go near to buoy up the greatest Ships , as Men of VVar ; yet for ordinary Vessels , Arks of far less size will suffice . Some may imagine , that a Ship sunk ( for example ) with Coal , is as difficult to buoy up , as to raise her out of a dry Harbor . But this cannot be , since a pound of Coal , will not weigh three or four Ounce in the VVater . A Ship loadned with VVine or Oyl , weighs nothing at all in the VVater , but may be very easily buoy'd up , if the Ballast be considered , as I said . Many Ships have been buoy'd up entirely , by thrusting down empty Hogsheads , and putting them below the Deck . But here occurs a difficulty , if the Water exceed eight or nine Fathom , the strong pressure of it crusheth the sides of the Hogshead together . But here is a soveraign cure against that trouble . Bore a small Hole in any part of the Vessel , where you please : for the Water entering , brings the Air within , to press equally with the Water without . Tho this Invention , may seem difficult to some , to be made practicable , yet to such who are intelligent , and know well the Principles of the Hydrostaticks , it appears plain and easie . But the very Speculation of it wants not its own pleasure , being founded upon infallible and sure Conclusions , drawn from the surest grounds in Nature . Labor improbus omnia vincit . 
A40528	----	Meteors, or, A plain description of all kind of meteors as well fiery and ayrie, as watry and earthy, briefly manifesting the causes of all blazing-stars, shooting stars, flames in the aire, thunder, lightning, earthquakes, rain, dew, snow, clouds, sprigs, stones, and metalls / by W.F. Fulke, William, 1538-1589. 1655 Approx. 199 KB of XML-encoded text transcribed from 93 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2004-11 (EEBO-TCP Phase 1). A40528 Wing F2260A ESTC R28245 10456179 ocm 10456179 45121 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A40528) Transcribed from: (Early English Books Online ; image set 45121) Images scanned from microfilm: (Early English books, 1641-1700 ; 1384:49) Meteors, or, A plain description of all kind of meteors as well fiery and ayrie, as watry and earthy, briefly manifesting the causes of all blazing-stars, shooting stars, flames in the aire, thunder, lightning, earthquakes, rain, dew, snow, clouds, sprigs, stones, and metalls / by W.F. Fulke, William, 1538-1589. F. W. Observations on Dr. F. his booke of meteors. [8], 174, [1] p. Printed for William Leake, London : 1655. "Observations on Dr. F. his booke of meteors, by F.W." p. 157-174, has special t.p. Reproduction of original in the Harvard University Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. 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Metallurgy -- Early works to 1800. 2004-02 TCP Assigned for keying and markup 2004-03 Aptara Keyed and coded from ProQuest page images 2004-07 Melanie Sanders Sampled and proofread 2004-07 Melanie Sanders Text and markup reviewed and edited 2004-10 pfs Batch review (QC) and XML conversion Meteors : OR , A plain Description of all kind of Meteors , as well Fiery and Ayrie , as Watry and Earthy : BRIEFLY Manifesting the Causes of all Blazing-Stars , Shooting-Stars , Flames in the Aire , Thunder , Lightning , Earthquakes , Rain , Dew , Snow , Clouds , Springs , Stones , and Metalls . By W. F. Doctor in Divinitie . LONDON , Printed for William Leake at the Crown in Fleet-street , between the two Temple Gates , 1655. To the Reader . I Shall not beg your pardon for publishing this Book ; for as 't is none of mine ( being written by a famous and learned Divine ) so I doe not set it forth relying on my own judgement , but had the opinions ●nd approbation of divers persons of known abilities , who knew best what is most usefull for publique Benefit . And I may ( without breach of Modesty ) affirm , that there is not in our Language any Booke of so small a bulke , containes so much of the Doctrine of the Meteors . We daily behold and view divers Meteors , but very few are skill'd in their Causes ; but those that are not , may be informed . And I must tell you also , that this Book on perusall hath been found so advantagious , that a person of quality hath lately taken paines to make divers worthy Observations upon it , which here I have subjoyned , because you should not pay for two Books instead of one . These Observations were never published till now , and I trust thou wilt find the Author did thee a Courtesie . Farewel . The Table . The first Booke . WHy Meteors be called Unperfectly mixed . 3. Why they be called perfectly mixed . 3. The generall cause of all Meteors , and first of the materiall cause . 4. The places in which they are generated . 10. The Second Book , of fiery Meteors . 13. The generation of the Impression , called Burned Stubble , or Sparkles of fire . 14 Torches . 15 Dancing or leaping Goates , ibid. Shooting and falling Stars . 16 Burning Candles . 18 Burning beams and round pillars , ibid. Burning Spares , ibid. Shields , Globes , or Bowles , 20. L●mps . ibid. Flying Dragons , or fire Drakes , ibid. The Pyramidal pillar , like a Spire or broched steeple . 23 Fire scattered in the Aire , ibid. Lights that goe before men , and follow them abroad in the fields in the night season . 24 Helena , Castor and Pollux . 27. Flames that appeare upon the haires of men and beasts 29. Comets , or blazing Stars . 30 Apparitions . 35 Colours , wide gapings , and deep holes which appear in the clouds . 36. Wide gaping . ibid. Round openi●g Hiatus . 37. The third Book , of Airy Impressions . 37. Of Winds . 38. Earthquakes . 41. Divers kinds of Earthquakes . 43 How so great winds come to be under the earth . 46 The signs and tokens that go before an Earthquake most commonly . 47 Thunder . 50 Lightning , 55 Fulgetrum . ibid. Coruscation . 57 Fulgur . 58 The fourth kind , called Fulmen . 59. The first kind . 60 The second k●nd . 62 The third kind . ibid. The marvailes of Lightning , and their causes . ibid. Storme Winds . 67 Whirle winds . 70 The fired Whirlewind , 72 Circles . 73 The Rainbow . 77 The Milk way , called of some the way to S. James and Watling-street . 81 Beames or streames of light appearing through a cloud . 86 Of Many Suns . 89 Many Moons . 92 Wonderfull apparitions . 94 The fourth Booke , Of watry Impressions . 100 Of Clouds . 101 Mists . 103 Empty clouds . 104 Raine . 106 The signes of Raine . 109 Monstrous or prodigious Raine . 111 Dew . 115 Hoare frost . 117 Haile , Snow . 118 , 120. Springs and Rivers . 121 Fountaines , Brooks , Rivers . 123 Lakes . 125 Hot Baths , ibid. The divers tasts that are perceived in wells , 126 A recitall of such Rivers and Springs , as have marvelous effects , whereof no natural caus can be assigned by most men , although some reason in a few may be found . 127 Of the Sea. 132 The saltnesse of the Sea , 133 The ebbing and flowing thereof . 134 The fifth Booke , Of earthly Meteors , or bodies perfectly mixed . 135 Of Earth● . 136 Liquors concrete 139 Metals 142 Gold. 143 Silver . 145 Copper . 146 Tynne . 148 Lead . ibid. Iron . 149 Quicksilver . 150 Stones . 151 The divers kinds of stones 153 The vertue of stones . 154 FINIS . THE FIRST BOOK . FOr as much as wee intend in this Treatise , to declare the causes of all those bodies that are generated in the earth called Fossilia , as well as those other Impressions named of their height Meteors ( which no writer hitherto hath done , that we have seen ) the common definition given by the most Writers , in no wise will serve us ; and whether we may borrow the name of Meteoron , to comprehend the whole subiect of our worke , we are not altogether out of doubt ; although the Philosopher deriving it from doubtfulnes , giveth●us some colour so to take it ; and peradventure we might be as well excused to apply it to Minerals , as other authors are to use it for earthquakes : yet to avoid all occasions of cavilling at words , we shall both define and also describe the subject of our matter on this manner : It is a body compound without life natural : and yet to stop one hole , because here wanteth the name of the thing to be defined ; it is no new thing to them that have read Aristotles workes , to find a definition of that whereof there is no name . But what need you be so precise ( will some man say ) ? meane you so to proceed in all your discourse ? no verily , but because many of quick iudgement , not considering the stile to bee attempered to the capacitie of the readers , will impute the plainesse to the ignorance of the Author , wee thought good in the beginning to pluck the opinion out of their minds that ( as the common saying is ) they may know , wee have skill of good manners though we little use them . The Meteors are divided after three manner of wayes : First , into bodies perfectly and imperfectly mixed : Secondly , into moist impressions and drie : Thirdly , into fiery , airy , watry , and earthly . According to this last division ▪ we shall speake of them in foure bookes following : but first we must be occupied a little in the generall description of the same , that afterward shall be particularly treated of . Why they be called imperfectly mixed . THey are called imperfectly mixed , because they are very soon changed into another thing , and resolved into their proper elements of which they do most consist , as do all impressions , fierie , airie , watry : as snow into water , clouds into waters &c. Why they be called perfectly mixed . THe last sort , namely earthly Meteors , are called perfectly mixed , because they will not easily be changed and resolved from that form which they are in , as be stones , metalls , and other mineralls . According to the qualitie of the matter , they are divided into moist and drie impressions , consisting either of Vapors or Exhalations . Vapors are called moist , and exhalations drie , which termes must be well noted , because they must be much used . Of the general causes of all Meteors ; and first of the material cause . THe matter whereof the most part of Meteors doth consist , is either water or earth : for out of the water , proceed vapors , and out of the earth come exhalations . Vapor , as the Philosopher saith , is a certain watry thing , and yet is not water ; so Exhalation hath a certain earthly nature in it , but yet it is not earth . For the better understanding of Vapors , understand that they be as it were fumes or smokes warme and moist , which will easily bee resolved into water , much like to the breath that proceedeth out of a mans mouth , or out of a pot of water standing on the fire . These vapours are drawn up from the waters and watery places by the heat of the Sun , even unto the middle region of the aire , and there after divers manner of meeting with coldnesse , many kind of moist Meteors are generated , as sometimes clouds and raine , sometime snow and hail ; and that such Vapours are so drawn up by the Sunne , it is plaine by experience : for if there be a plash of water on a smooth and hard stone , standing in the heat of the Sun , it will soon be drie ; which is none otherwise but that the Sun draweth up the water in thinne Vapors : for no man is so fond to say , that it can sink into stone or mettal ; and it is as great folly to think it is consumed to nothing : for it is a general rule , That that which is once a thing , cannot by changing become nothing : wherefore it followeth , that the water on the stone , as also on the earth , is for the most part drawn up , when the stone or earth is dryed . Exhalations are as smokes that be hot and dry , which because they be thinne , and lighter then Vapors , passe the lowest and middle Region of the aire , and are carryed up even to the highest Region , where for the excessive heat , by neerness of the fire , they are kindled , and cause many kind of impressions . They are also sometimes viscose , that is to say , clammy , by reason whereof , they cleaving together and not being dispersed , are after divers sorts set on fire , and appear sometimes like Dragons , sometimes like Goats , sometimes like candles , sometimes like spears . By that which is spoken of Vapours and Exhalations , it is evident , that out of the fire and aire , no matter whereof Meteors should consist , can be drawn , because of their subtilty and thinnesse . For all Exhalation is by making a grosser body more thinne : but the fire ( we mean the elemental fire , and not the fire of the Kitchin chimney ) is so subtil and thinne , that it cannot be made thinner ; likewise the aire is so thinne , that if it be made thinner , it is changed into fire ; and as the fire , if it were made thicker , would become aire ; so the aire being made grosser , would be turned into water . Wherefore to conclude this part , the great quantity of matter , that causeth these Meteors , is taken out of the earth and the water . As for the aire and the fire , they are mixed with this matte● as with all other things , but not so abundantly , that they may be said th● material cause of any Meteor , thoug● without them none can be generated . The efficient cause of all Meteors , is tha● caus which maketh them ; even as the Carpenter is the efficient cause of an house . This cause is either first or second . The first and efficient cause is God the worker of all wonders , according to that testimonie of the Psalmist , which saith , Fire , haile snow , ice , wind and storme , doe his will and commandment ; he sendeth snow like wooll , &c. Almightie God therefore being the first , principall and universall cause efficient of all natural works and effects , is also the first cause of these effects , whose profit is great , and operation marvellous . The second cause efficient , is double , either remote , that is to say , farre off or next of all . The farther cause of them as of all other naturall effects , is the same ; the Sun with the other Planets and Stars , and the very heaven it self in which they are moved ; But chiefly the Sunne , by whose heat all or at least wise the most part of the vapors and Exhalations are drawn up . The next cause efficient as the first qualities , are heat and cold , which cause divers effects in Vapors & Exhalations . But to return to the heat of the Sun , which is a very neere cause , it is for this purpose two wayes considered . One way , as it is meane and temperate ; Otherwise , as it is vehement and burning . The meane , is by which he draweth vapors out of the water , and exhalations out of the earth , and not onely draweth them out , but also lifteth them up very high from the earth into the aire , where they are turned into divers kinds of Meteors . The burning heat of the Sunne is , by which he burneth , dissipateth and consumeth the vapors and exhalations before he draweth them up , so that of them no Meteors can be generated . These two heats proceed from the Sun , either in respect of the place , or the time ; but most properly according to the casting of his beames either directly or undirectly . In place where the Sunnes beames strike directly against the earth and the water , the heat is so great , that it burneth up the Exhalations and Vapours , so that there are no fiery Meteors , much lesse watery : as it is in the South parts of the world , under and neere to the Equinoctiall line . But in places where the beames are cast indirectly and obliquely , and that where they are not too nigh to the direct beams , nor too far off from them ; there is a moderate heat , drawing out great abundance of matter , so that in those Countries , many Meteors of many sorts are generated , as in the far North parts are few but watry impressions . Also in Autumn and Spring are oftner Meteors seene , then in Summer and Winter , except it be in such places where the Summer and Winter are of the temper of the Spring and Autumne . Let this be sufficient for the Efficient causes of impressions , as well first and principall , as second and particular . Concerning the formal and finall cause , we have little to say , because the one is so secret , that it is known of no man : the other so evident , that it is plaine , to all men . The essentiall Form of all substances , Gods wisedome comprehendeth ; the universall chiefe and last End of all things , is the glory of God. Middle Ends ( if they may be so called ) of these impressions are manifold profits to Gods creatures , to make the earth fruitfull , to purge the aire , to set forth his power , to threaten his vengeance , to punish the world , to move to repentance ; all which are referred to one end of Gods eternall glory , ever to be prased , Amen . Of the places , in which they are generated . THe places in which Meteors are caused , be either the aire or the earth : in the air be generated rain , hail , snow , dew , blazing stars , thunder , lightning , &c. In the earth be welles , springs ▪ earthquakes , metals , minerals , &c. made , and as it were , in their mothers belly begotten and fashioned . But for the better understanding hereof , such as have not tasted the principles of Philosophy , must consider that there be foure elements , Earth , Water , Aire , and Fire , one compassing another round about , saving that the waters by Gods commandement are gathered into one place , that the land might appear . The highest is the spheare of the Fire , which toucheth the hollownesse of the moons heaven : the next is the aire , which is in the hollownesse of the fire : the aire within his hollownesse comprehendeth the water and the earth , which both make but one spheare or Globe , or as the common sort may understand it , one ball . So each element is within another , as scales of a perch are one above anothes : or ( to use a grosse similitude ) as the peeles of an Onion are one within another : after the same sort from the highest heaven to the earth that is lowest , one part that is greater compasseth round about another that is lesser . But for this present purpose it is to be knowne , that the aire is divided into three regions , the highest the middle and the lowest . The highest because it is next to the region of the fire , is exceeding hot : the lowest being next the earth and waters , is temperate , and by repercussion or striking backe of the Sunne beames waxeth hot , and by absence of them is made cold , being subject to winter and summer . The middle region of the aire , is alwaies exceeding cold , partly because the sunne beames cannot be cast back so high , and partly because the cold that is there , betweene the heat above , and the heat beneath it , is so kept in , that it can not get out , so that it must needs be excessively cold : for the water and the earth , being both cold Elements , after the Sunne setting in the night season , doe coole the aire , even to the middle region . But in the morning the Sunne rising warmeth the aire , so farre as his beames which are beaten backe from the earth and the water , can extend and reach ; which is not so high as the middle region , and by heat on both sides is inclosed and kept , saving that a little thereof falleth downe in the night , which the next day with much more is driven back againe . Wherefore this region being so cold , is dark and cloudy , in so much that some doting Divines have imagined purgatory to be there in the middle region of the aire . In the highest region be generated Comets or blazing stars and such like of divers sorts . In the middle region clouds , rain , stormes , winds &c. In the lowest region , dew , frost , hoar-frost , mists , bright rods , candles , burning about graves , and gallowses , where there is store of clamy , fattie or oily substance , also lights and flaming fires seen in fields , &c. And thus much for the general causes of all Meteors . THE SECOND BOOKE Of Fiery Meteors . A Fiery impression , is an Exhalation set on fire in the highest or lowest region of the aire , or else appearing as though it were set on fire and burning . They are therefore divided into flames and Apparitions . Flames are they which burn indeed , and are kindled with fire . These are discerned by four ways ; by the fashion of them , by their place , by the abundance of their matter , and by the want of their matter . Their placing is after the abundance and scarcity of the matter whereof they consist : for if it be great , heavy and grosse , it cannot be carried so far as the middle region of the ayre , and therefore is set on fire in the lowest region : if it be not so great , light , and full of heat , it passeth the middle region , and ascendeth to the highest , where it is easily kindled and set on fire . According to their divers fashions , they have divers names : for they are called burning stubble , torches , dauncing or leaping Goates , shooting or falling starres , or candles , burning beames , round pillars , spears , shields , Globes or bowles , firebrands , lampes , flying Dragons or fire drakes , painted pillars , or broched steeples , or blazing starres , called Comets . The time when these impressions doe most appeare , is the night-season : for if they were caused in the day time , they could not be seen , no more then the stars be seen , because the light of the Sunne which is much greater , dimmeth the brightness of them being lesser . Of the generation of the impression called burning stubble or sparkles of fire . The generation of this Meteor is this ; when the matter of the Exhalation is in all parts alike thin , but not compacted or knit together , then some part of it being caryed up into the highest Region , by the fiery heat is set on fire before another part that cometh up after it , and so being kindled by little and little , flieth abroad like sparkles out of a chimney , insomuch that the common people suppose , that an infinite number of stars fall down , whereas it is nothing else but the Exhalation that is thin , kindled in many parts , sparkling as when sawdust or cole-dust is cast into the fire . Of Torches TOrches or firebrands are thus generated : when the matter of the exhalation is long and not broad , being kindled at one end thereof in the highest region of the aire , it burneth like a torch or firebrand , and so continueth till all the matter be burnt up , and then goeth out ; none otherwise then a Torch when all the stuffe is spent , must needs burne no longer . Of dancing or leaping Goates DAncing Goates are caused when the exhalation is divided into two parts , as when two torches be seen together , and the flame appeareth to leap or dance from one part to the other , much like as bals of wild fire dance up and down in the water . Of shooting and falling stars . A Flying , shooting , or falling star , is when the exhalation being gathered as it were on a round heape , and yet not throughly compacted in the highest part of the lowest region of the ayre , being kindled by the sodaine cold of the middle region , is beaten backe , and so appeareth as though a starre should fall , or slide from place to place . Sometime it is generated after another sort ; for there is an exhalation long and narrow , which being kindled at one end burneth swiftly , the fire running from end to end , as when a silk thred is set on fire at the one end . Some say it is not so much set on fire , as that it is direct under some Star in the firmament , and so receiving light of that star , seemeth to our eies to be a Star. Indeed sometimes it may be so ; but that i● is not so alwayes , nor yet most commonly , it may be easily demonstrated . The Epicureans , as they are very grosse in determining the chiefe goodness : so they are very fond in assigning the cause of this Meteor . For they say , that the stars fall out of the firmament , & that by the fall of them , both thunder and lightning are caused : for the lightning ( say they ) is nothing else but the shining of that Starre that falleth , which falling into a waterie cloud , and being quenched in it , causeth that great thunder , even as hot Iron maketh a noise if it be cast into cold water . But it is evident , that the starres of the firmament cannot fall , for GOD hath set them fast for ever ; he hath given them a Commandement which they shall not passe . And though they should fall into the clouds , yet could they not rest there , but with their weight being driven down , would cover the whole earth . For the least starre that is seen in the firmament , is greater then all the earth . Here will step forth some merrie fellow which of his conscience thinketh them not to be above three yards about , and say it is a loud lie ; for he can see within the compasse of a bushell , more then 20 stars . But if his bushell were on fir● 20 mile of , I demand how bigge it would seeme unto him ? He that hath any wit will easily perceive , that starres being by all mens confession , so many thousand miles distant from the earth , must needs be very great , that so far off should be seen in any quantity . Thus much for the shooting or falling starres Of burning Candles . WHen the Exhalation carried up into the highest part of the ayre , is in all parts thereof of equall and like thinness , and also long , but not broad , it is set on fire and blazeth like a candle , until the Exhalation be quite consumed . Of burning Beames and round Pillars . THese are caused , when the Exhalation being long and not very broad , is set on fire all at once , and so burneth like a great beame or logge . The difference of Beames and Pillars is this ; for beams are when they seeme to lie in length in the ayre , but they are called Pillars , when they stand right up , the one end neerer to the earth then the other Of Burning Speares . BUrning speares are generated , when a great quantity of exhalations , which may be called a dry cloud , is set on fire in the middest , and because the cloud is not so compact , that it should suddenly rend , as when thunder is caused , the fire breaketh out at the edges of the cloud , kindling the thin Exhalations , which shoot out in great number like fiery speares , or darts , long and very small ; wherefore they continue not long : but when they fayle , within a short while after , more fire breaking out , they shoot as many more in their place : and likewise , when they are gone , others succeed , if the quantity of the matter will suffice , more then a douzen courses . This impression was seene in London , Anno Dom. 1560. the thirty day of Ianuary , at eight of the clock at night , the ayre in all other places being very darke ; but in the North-east where this cloud burned , it was as light as when the day breaketh toward the Sunne rising , in so much that plaine shaddow of things opposite was seene . The edge of this cloud was in the fashion like the Raynebow , but in colour very bright , and oftentimes casting forth almost innumerable darts of wonderfull length , like squibs that are cast into the ayre , saving that they move more swiftly then any squibs . Of Shields , Globes or Bowles . THese Meteors also have their name of their fashion , because they are broad , and appeare to be round ; otherwise their generation differeth not from the cause of the like impressions before mentioned . Of Lampes . THe Lampe consisteth of an Exhalation that is broad and thick , but not equally extended ; namely , smaller at one end then at another , which being kindled about the middest thereof , burneth like a lampe . The cause why , as well this impression , as many other , appeareth round , is not for that alwaies they are round indeed , but because the great distance causeth them to seem so . For even the square formes far off seem to be round . 〈◊〉 is written , that a Lamp fell down at Rome , when Germanicus Caesar set forth forth the fight of sword players . Of flying Dragons or fire Drakes . Flying Dragons , or as Englishmen call them , fire-Drakes , be caused on this manner . When a certaine quantity of ●apors are gathered together on a heap , ●eing very neere compact , and as it were ●ard tempered together , this lump of ●apors ascending to the region of cold , ●forcibly beaten back ; which violence ●f moving is sufficient to kindle it ; ●lthough some men will have it to be ●used between 2 clouds , a hot and a ●●ld ; then the highest part , which was ●iming upward , being by reason more ●btill and thin , appeareth as the Dra●ns neck , smoking , for that is was ●ely in the repulse bowed or made ●●oked , to represent the Dragons belly . ●e last part by the same repulse turned ●ward , maketh the tayle , appearing ●aller for that it is both further off , ● also for that the cold bindeth it ▪ ●is dragon thus being caused , flyeth ●ng in the ayre , and sometime turneth ●nd fro , if it meet with a cold cloud eat it back , to the great terrour of 〈◊〉 that behold it : of whom some 〈◊〉 it a fire Drake : some say it is the ●ill himselfe , and so make report ●thers . More then 47 yeeres ago● , on May day , when many young folk went abroad early in the morning , remember by six of the clocke in th● forenoone , there was newes come to London , that the Devill , the same morning , was seen flying over the Thames ▪ afterward came word , that he lighte● at Stratford , and there was taken an● set in the Stockes , and that though h● would fane have dissembled the matte● by turning him selfe into the likenes● of a man , yet was he known well enoug● by his cloven foot . I knew some the● living , that went to see him , and returning , affirmed , that he was seen flying in the ayre , but was not take● prisoner . I remember also , that som● wished he had been shot at with Gun● or shafts , as he flew over the Thame● Thus do ignorant men iudge of the things that they know not . As for th● Devill , I suppose , it was a flying Dr●gin , whereof we speake , very fearefu● to looke upon , as though he had 〈◊〉 because he moveth , whereas it is n●thing else but clouds and smoake : 〈◊〉 mighty is God , that he can feare 〈◊〉 enemies with these and such like op●rations , whereof some examples may be found in holy Scripture . Of the Pyramidall Pillar like a spire or broached Steeppe THis sharpe poynted pillar , is generated in the highest region of the ayre , and after this sort : When the Exhalation hath much earthly matter in it , the lighter parts and thinner ( as their nature is ) ascending upward , the grosser , heavier , and thicker , abide together in the bottome , and so is it of fashion great beneath , and small poynted above , and beeing set on fire it is so seene , and thereof hath his name . Of fire scattered in the ayre . FIre scattered in the ayre , or illuminations , are generated in the lowest region of the ayre , when very drie and hot Exhalations are drawne up , and meeting with cold clouds , are sent back again , which motions doe set them a fire ; whose parts being not equally thick or ioyned together , seeme as though fire were scattered in the ayre : Yea sometimes , the whole ayre seemeth to burne , as though it would rayne fire from Heaven , and so it hath come to passe , burning both Cities and Townes . Then iudge how easy it was for God to raine fire upon Sodom and Gomorra , for their sins and wickedness . Of lights that goe before men , and follow them abroad in the fields , by the night season . THere is also a kind of light that is seen in the night season & seemeth to goe before men , or to follow them , leading them out of their way into waters , and other dangerous places . It is also very often seene in the night , of them that saile on the Sea , and sometime will cleave to the mast of the Shippe , or other high parts , sometime slide round about the Shippe , and either rest in one part till it goe out , or else be quenched in the water . This impression seene on the land , is called in Latine Ignis fatuus , foolish fire , that hurteth not , but onely feareth fooles . That which is seene on the Sea , if it be but one , is named Helena ; if it be two , it is called Castor and Pollux . The foolish fire is an Exhalation kindled by meanes of violent moving , when by cold of the night , in the lowest region of the ayre , it is beaten downe ; and then commonly , if it be light , seeketh to ascend upward , and is sent down againe ; so it danceth up and downe . Else if it move not up and downe , it is a great lumpe of glewish or oyly matter that by moving of the heat in it selfe , is enflamed of it selfe , as moyst hay will bek indled of it selfe . In hot and fennie Countries , these lights are often seene , and where is abundance of such unctuous and fat matter , as about Church-yards , where through the corruption of the bodies there buried , the earth is full of such substance : wherefore in Church-yards , or places of common buriall , oftentimes are such lights seene , which ignorant and superstitious fooles have thought to be soules tormented in the fire of Purgatory . Indeed the Devill hath used these lights ( although they be naturally caused ) as strong delusions to captive the minds of men with feare of the Popes Purgatory , whereby he did open injury to the blood of Christ , which onely purgeth us from all our sins , and delivereth us from all torments both temporall and eternall , according to the saying of the wise-man , The soules of the righteous are in the Hands of God , and no torment toucheth them . But to returne to the lights , in which there are yet two things to be considered . First , why they lead men out of their way . And secondly , why they seeme to follow men and goe before them . The cause why they lead men out of the way , is , that men , while they take heed to such lights , and are also sore afraid , they forget their way , & then being once but a little out of their way , they wander they wot not whither , to waters , pits and other very dangerous places . Which , when at length they hap the way home , will tell a great tale , how they have beene led about by a spirit in the likenesse of Fire . Now the cause why they seeme to goe before men , or to follow them , some men have said to be the moving of the ayre , by the going of the man , which ayre moved , should drive them forward if they were before , and draw them after if they were behind . But this is no reason at all that the Fire , which is oftentimes three or foure miles distant from the man that walketh , should be moved to and fro by that ayre which is moved through his walking , but rather the moving of the ayre and the mans eyes , causeth the fire to seeme as though it moved , as the Moone to children seemeth , if they are before it , to run after them : if she be before them , to run before them , that they cannot overtake her , though she seeme to be very neere them . Wherefore these lights rather seeme to move , then that they be moved indeed . Of Helena , Castor and Pollux WHen the like substance in the lowest region of the ayr , over the Sea , by the like occasion is set on fire , if be one only , it is called Helena ; if their be two , they are called Castor , and Pollux . These impressions will oftentimes cleave to the mast , and other parts of Ships , by reason of the claminesse and fatnesse of matter . Helena was of the Heathen men taken as a Goddesse , the daughter of Jupiter and Leda . Castor and Pollux were her brethren . Helena was the occasion that Troy was destroyed ; therefore the Mariners by experience trying , that one flame of fire appearing along , signified tempest at hand , supposed the same flame to be the goddesse Helena , of whom they look'd for nothing but destruction . But when two lights are seen together , they are a token of fair weather , and good luck : the Mariners therefore beleeved that they were Castor and Pollux , which sayling to seek their sister Helena being carried to Troy by Paris , were never seen after and thought to be translated into the number of the Gods that gave good successe to them that sayl , as we read in the last Chapter of the Acts of the Apostles , that the Ship wherein S. Paul sayled , had a badge of Castor and Pollux . A naturall cause why they may thus foreshew either tempest or calmnesse , is this ; One flame alone may give warning of a tempest , because that as the matter thereof is compact , and not dissolved ; so it is like , that the matter of the tempest ( which never wanteth ) as wind and clouds , is still together , and not dissipated , then is it like not long after to arise . By two flames together may be gathered , that as this Exhalation which is very thick , is divided : so the thick matter of tempests is dissolved and scattered abroad by the same cause that this is divided . Therefore not without a reason , the Mariner to his mates may promise a prosprous course . Of flames that appeare upon the haires of men or beasts . THere is another kind of fiery impression , which is flames of fire upon the haires of men and beasts , especially horses . These are sometime clammy Exhalations , scatered abroad in the air in small parts , which in the night , by resistance of the cold , are kindled , cleaving on horses eares , on mens heads and shoulders that ride or walke . In that they cleave upon hayres , it is by the same reason that the dew will be seen also upon haires or garments , whose wooll is high , as frize mantels and such like . Another sort of these flames are caused , when mens or beasts bodies being chafed , send forth a ●at and clammy sweat , which is in like manner kindled as the sparks of fire that are seene when a black horse is curried . Livius reporteth of Servius Tullius , that as he lay asleep , being a child , his hair seemed to be all on a flame , which for all that did not burn his hair or hurt him . The like history he reciteth of one Marius a Knight of Rome , that as he made an Oration to his Soldiers in Spain , they saw his head burning on a light fire , and himself not ware of it . Thus much concerning these Flames . Of Comets or Blazing Stars . A Comet is an exhalation hot and dry , of great quantity , fat and clammy , hard-compact like a great lump of pitch , which by the heat of the Sun is drawn out of the Earth into the highest region of the Air , and there by the excessive heat of the place is set on fire , appearing like a star with a blazing tayl ; and somtime is moved after the motion of the Air which is circular , but it never goeth down out of the compass of sight , though it be not seen in the day-time for the brightness of the Sun , but still burneth until all the matter be consumed . An argument of the greatness is this , that there was never any Comet yet perceived but at the least it endured 7 days ; but much longer they have been seen ; namely forty days long , yea fourscore days ; and some , six months together . Wherefore it must needs be a wonderfull deal of matter that can give so much nourishment for so great and fervent fire , aud for so long a time . There are considered in a Comet specially the Colour and Fashion , which both arise of the disposition of the matter . Their Colours be either white , ruddy , or blew . If the matter be thin , the colour is white ; if it be meanly thick , then is the Comet ruddy , after the colour of our fire ; but when the matter is very thick , it is blew , like the burning of brimstone . And as the matter is more or less after this disposition , so is the Comet of colour more or less like to these three principal colours : some yellowish , some duskish , some greenish , some watchet , &c. In Fashion are noted three differences ; for either they seem to be round , with beams round about , or with a beard hanging downward , or else with a tayl stretched out sidelong in length . The first fashion is when the matter is thickest in the midst , and thin round about the edges ; the second is when the Exhalation is upward thick , and in length downward also meanly thick ; the third form is like the second , saving that the tayl hangeth not down but lyeth aside and is commonly longer then the beard . The time of their generation is oftnest in Autumn or Harvest : for in the Spring there is too much moisture , and too little heat to gather a Comet ; in Summer is too much heat which will disperse and consume the matter that it cannot be joined together ; as for Winter , it is clean contrary to the nature of a Comet which is hot and dry , Winter being cold and moyst : therefore no time so meet as Autumn . Now for so much as many Learned men have gone about to declare the signification of Blazing stars , we will omitt nothing that hath any shadow of Reason , but declare what is written of them . Such things as are set forth of the betokening of Comets are of two sorts : The first is of natural ; The second of Civil or Politick Effects . They are said to betoken Drought , Barrenness of the Earth and Pestilence . Drought , because a Comet cannot be generated without great heat ; and much moysture is consumed in the burning of it . Barrenness , because the fatness of the Earth is drawn up whereof the Comet consisteth . Pestilence , for so much as this kinde of Exhalation corrupteth the Air , which infecteth the bodies of men and beasts . The Second sort might well be omitted , saving that Aristotle himself disdaineth not to seek out Causes for some of them . Generally it is noted of all Historiographers , that after the appearing of Comets most commonly follow great and notable Calamities . Beside this , they betoken ( say some ) Wars , Seditions , Changes of Commonwealths , and the Death of Princes and Noble men . For what time Comets do shine , there be many hot and dry Exhalations in the Ayr , which in dry men kindle heat whereby they are provoked to Anger : of Anger commeth brawling : of brawling , fighting and war : of war , victory : of victory , change of Commonwealths : then also Princes living more delicately then other men , are more subject to infection ; and therefore dye sooner then other men . If it were lawfull to reason of this sort , we might enduce them to betoken not only these few things , but all other things that chance in the world . Yet these predictions have a shew of Reason : though it be nothing necessary ; but it is a wonder to see how the Astrologians dote in such devices ; they are not ashamed to an earthly substance to ascribe an heavenly influence , and in order of judgment to use them as very stars . Surely , by as good reason as to the Celestial stars they attribute Divine influences and effects . But this their folly hath been sufficiently detected by divers godly and learned men , and this place requireth no long discourse thereof . Wherefore this shall suffice , both for the natural Causes of Blazing stars , and also for all Flames in general . It followeth therefore that with like brevity we declare the Causes of Fiery Apparitions . Of Apparitions . AN Apparition is an Exhalation in the lowest or highest Region of the Air , not verily burning , but by refraction of light either of the Sun or of the Moon seeemeth as though it burned : which appearance of colour riseth not of the mixtion of the four qualities , as it doth in bodies perfectly mixed , as Herbs , Stones , &c. but only the falling of light upon shadow : the light is instead of white , and the shadow of darkness instead of black . These diversly mixed according to the divers dispositions of the Exhalation , which ministreth variety by thickness or thinness , cause divers Colours . There be commonly recited three kindes of Fiery Apparitions ; Colours , Wide-gapings , and Deep holes which appear in the Clouds . Of Colours . Colours are here meant when there is nothing else to be noted but the Colours of the clouds : and they are caused ( as it is said ) by casting the light into the shadowy Cloud , according as it exceedeth more or less in thickness ; whereof some be very bright-white , and that is when the Exhalation is very thin ; some yellowish , when the Exhalation is thicker ; some ruddy , when it is meanly thick ; and very black , when it is very thick . The red and ruddy Colours are seen in the morning and evening , when the light of the Sun is not in his full force : for at other times of the day his light is too vehement , clear , strong and peircing . Thus much of Colours . Of Wide-gaping . Wide-gaping is caused when an Exhalation is thick in the midst , and thin on the edges , then the light being received into it , causeth it to appear as though the sky did rend , and fi●e break out of it . Of round opening Hiatus . These holes called Hiatus , differ from Wide-gapings in nothing but that they be less , and therefore seem as though they were deep pits or holes , and not rending or gaping ; And these be those Apparitions that appear Fiery , and yet be not so indeed . Therefore let this be sufficient to have shewed the natural Causes of all Fiery Meteors . THE THIRD BOOK . Of Airy Impressions . UNder the name of Airy Impressions , be comprehended such Meteors , whose matter is most of the Air. Of this sort be Winds , Earthquakes , Thunder , Lightnings , Storme-Winds , Whirlwinds , Circles , Rainbowes , The White Circle , called of some WATLING street , many Suns , many Moons . Of Winds . THe Wind is an Exhalation hot and dry , drawn up into the Air by the power of the Sun , and by reason of the weight thereof being driven down , is laterally or sidelong carried about the Earth . And this Definition is not to be understood of general Winds that blow over all the Earth , or else some great Regions ; but besides these there be particular Winds which are known but only in some Countries , and them not very large . These Winds oftentimes have another manner of generation , and that is on this manner ; It must needs be confessed , that within the globe of the Earth be wonderfull great holes , caves or dungeons , in which when Air aboundeth ( as it may by divers Causes ) this Air that cannot abide to be penned in , findeth a little hole in or about those Countries as it were a mouth to break out of , and by this meanes bloweth vehemently : yet that force and vehemency extendeth not far ; but as the wind that commeth forth of bellows , neer the comming forth is strong , but far off is not perceived : so this Particular Wind , in that particular Country where it breaketh forth , is very violent and strong , in so much that it overthroweth both trees and houses , yet in other Countries not very far distant , no part of that boysterous blast is felt . Wherefore this Wind differeth from the general Winds both in Qualities and Substance or Matter : for the Matter of them is an Exhalation , and the Qualities such as the nature of the Exhalation is , very Airy , but not Air indeed : but of this particular Wind the Matter and Substance is most commonly Air. There is yet a third kinde of Wind , which is but a soft , gentle and cool moving of the Air , and commeth from no certain place ( as the general Wind doth ) yea it is felt in the shadow under trees , when in the hot light and shining of the Sun it is not perceived . It commeth whisking suddenly , very pleasant in the heat of Summer , and ceaseth by and by ; this properly is no Wind , but a moving of the Air by some occasion . As for the general Winds , they blow out of divers Quarters of the Air now East , now West , now South , now North , or else inclining to one of the same Quarters : Among which the East-wind following the nature of the Fire is hot and dry ; the South-wind expressing the quality of the Air is hot and moyst ; the Western blast agreeing with the Waters property , is cold and moyst ; the North that never was warmed with the heat of the Sun , being cold and dry partaketh the condition of the Earth . The middle Winds have middle and mixed qualities , after the nature of those Four principal Winds , more or less , as they incline toward them more or less . Generally the profit of all Winds , by the wonderfull wisdom of the Eternal God , is very great unto his Creatures . For besides that these Winds alter the Weather . some of them bringing rain , some driness , some frost and snow , which all are necessary ; there is yet an universal Commodity that riseth by the only moving of the Air , which were it not continually stirred as it is , would soon putrify , and being putrified would be a deadly infection to all that hath breath upon the Earth . Wherefore this wind whose sound we hear , and know not from whence it commeth nor whither it goeth ( for who can affirm from whence it was raised , or where it is laid down ? ) as all other Creatures beside , does teach us the wonderfull and wise providence of God , that we may worthily cry out with the Psalmist and say , O Lord , how manifold are thy works ! in wisdome hast thou made them all &c. Let this be sufficient to have shewed the generation of the Winds . Of Earthquakes , AN Earthquake , is a shaking of the Earth which is caused by meanes of wind and Exhalations , that be enclosed within the caves of the Earth , and can find ●o passage to break forth , or else so narrow a way that it cannot soon enough be dilivered . Wherefore , with great force and violence it breaketh out : and one while shaketh the Earth , another while rendeth and cleaveth the same : somtime it casteth up the Earth a great hight into the Air , and somtime it causeth the same to sink a great depth down , swallowing both Cities and Townes , yea and also mighty great Mountaines , leaving in the place where they stood , nothing but great holes of an unknown depth , or else great lakes of Waters . Of divers kinds of Earthquakes . DIvers Authors write diversly of the kinds of Earthquakes , some making more and some less , but we shall be content at this time to comprehend them in four sorts . The first kind is when the Earth is shaken laterally , to one side , which is when the whole force of the wind driveth to one place , and there is no other contrary motion to let it . This wind , if it be not great , shaketh the Earth , that it trembleth as a man that hath a fit of an ague , and doth no more harme : but if it be great and violent , it looseth the foundations of all buildings , be they never so strong , and overthroweth whole Cities , but especially the great buildings , and not only such buildings , but somtimes also casteth down great Hilles , that cover and overwhelm all the valleys under them . Many noble and great Cities have been overthrown by this kind of Earthquake . It is written , that twelve of the most beautifull Cities , and most sumptuous buildings in all Asia , were overthrown and utterly destroyed with an Earthquake . How often Antiochia , yea within short time was destroyed , they which have read the Histories , can testifie . How terrible was the Earthquake that shook Constantinople a whole year together , that the Emperour and all the people , were fain to dwell abroad in the fields under tents and pavilions , for fear their houses would fall on their heads , it is recorded in the Chronicles , and worthy to be remembered . The second kind is , when the Earth with great violence is lifted up , so that the buildings are like to fall , and by and by sinketh down again : this is , when all the force of the winds striveth to get upward , after the nature of gunpowder , and finding some way to be delivered out of bondage , the Earth that was hoysied up , returneth to his old place . The third kind is a gaping , rending , or cleaving of the Earth , when the Earth sinketh down , and swalloweth up Cities , and Townes , with Castles , and Towers , Hilles and Rocks , Rivers , and Floods , so that they be never seen again . Yea the Sea in some places hath been drunk up , so that men might have gone over on foot , untill the time of tide or flood returning covered the place with Waters again . But in the land , where this Earthquake swalloweth up any City , or Country , there appeareth nothing in the place thereof , but a marvellous wide and deep gulfe , or hole . Aristotle maketh mention of divers places , and regions that were overthrown with this kind of Earthquake . The fourth kind , is when great mountaines are cast up out of the Earth , or else when some part of the land sinketh down , and in stead thereof arise Rivers , Lakes , or Fires breaking out with smoake and Ashes . It causeth also overflowings of the Sea , when the Sea bottome is lifted up , and by this means arise many Islands in the Sea , that never were seen before . These and other such miracles , are often found In the Writers of Histories , also in the Philosophers , as Aristotle , Seneca , and Plinius . Nevertheless , the effects of some as most notable , it shall not be unprofitable to recite . Plato in his Dialogue intituled Timeus , maketh mention by the way of a wonderfull Earthquake , whereby not only Africa was rent asunder from Europe and Asia ( as it is indeed at this day , except a little neck by the red Sea ) the Sea entring between them that now is called Mare Mediterraneum : but also a wonderfull great Island , which he affirmeth , was greater then Africa and Asia both , called Atlantis , was swallowed up , and covered by the Waters , in so much , that on the Sea called Atlanticum , for a great while after , no Ship could sayl , by reason that the same huge Sea , by resolution of the Earth of that mighty Iland , was all turned into mudde . The famous I le of Sicilia was also somtime a part of Italy , and by Earthquake rent asunder from it● Seneca maketh mention of two Ilands , Theron and Therea , that in his time first appeared . It should seeme both by Aristotle , and also by Herodotus , that Egypt , in ancient time , was a gulph of the Sea , and by Earthquake made a drie land . During the reign● of Tiberius the Emperor , twelve notable Cities of Asia were overthrown in one night , &c. How so great VVinds come to be under the Earth . THe great Caves and Dennes of the Earth , must needs be full of Ayr continually : but when by the heat of the Sunne , the moysture of the Earth is resolved , many Exhalations are generated as well within the Earth as without ; and whereas the places were full before so that they could receive no more , except part of that which was in them , were let out in such countries where the Earth hath few pores , or else where they are stopped with moysture , it must needs follow , that these Exhalations striving to get out , must needs rend the Earth in some place , or lift it up , so that either they may have free passage , or else room enough to abide in . Of signes and tokens that go before an Earthquake most commonly . THe first , is the raging of the Sea , when there are no tempestuous Winds to stirre it , yea , when the Ayr is most calme without Wind. The caus why the Sea then rageth , is , that the wind beginneth to labour for passage that way , and finding none , is sent back , and soon after shaketh the land . The second signe is calmness of the Ayr , and cold , which commeth to pass by reason that the Exhalation that should be abroad , is within the Earth . The third signe , is said to be a long thinne strake of cloud seen , when the skie is clear ; after the setting of the Sun. This ( say they ) is caused , by reason that the Exhalation or Vapor , which is the matter of clouds , is gone into the Earth . Others affirm , that it is the Exhalation that breaketh out of some narrow hole of the Earth , out of which the rest of the wind cannot issue , neither will it waite the time : wherefore within a while after , it seeketh and maketh it self by sudden eruption a broader way to be delivered out of prison . Also the Sunne , certaine daies before it appeareth dimme , because the Winds that should have purged and dissolved the grosse Ayr , that causeth this dimness to our eyes , is enclosed within the bowels of the Earth . The Water in the bottome of deepe wells is troubled , and the savour thereof infected , because the pestilent Exhalations that have been long inclosed within the Earth , doe then beginne a little to be sent abroad . For thereof cometh it , that in many places where Earthquakes have been , great abundance of smoak , flame , and ashes is cast out , when the abundance of brimstone that is under the ground , through violent motion is set on fire and breaketh forth . Finally , who knoweth not , what stinking Minerals and other poysonous stuff doe grow under the Earth ? wherefore it is no wonder , if Well-water , before an Earthquake , be infected : but rather it is to be marvelled , if after an Earthquake there follow not a grievous Pestilence , when the whole mass of infection is blown abroad . Last of all , there is heard before it in the time of it , and after it , a great noise and sound under the Earth , a terrible groaning , and a very Thundring , yea , somtimes when there followeth no Earthquake at all , when as the wind , without shaking of the Earth , findeth a way to passe out at . And these for the most part , or at least some of them , are forewarnings , that the most fearfull Earthquake will follow , then the which there is no naturall thing that bringeth men into a greater feare . Cato was very curious to confesse himselfe , that he repented that ever he went by water , when as he might have gone by land . But what land can be sure , if it be the Lords will by this work of his to shake it ? what building so strong , that can defend us , when the more strong , the more danger , the higher , the greater fall ? Of Thunder . THunder is a sound caused in the clouds by the breaking out of a hot and dry Exhalation beating against the edges of the cloud . It is often heard in Spring and Summer by reason that the heat of the Sun then draweth up many Exhalations , which meeting in the middle region of the Air with moyst and cold Vapors , are together with them inclosed in a hollow cloud : but when the hot Exhalation cannot agree with the coldness of the place ; by this strife being driven together made stronger and kindled , it will straight break out , which sudden and violent eruption causeth the noyse which we call Thunder . A Similitude is put by great Authors , of moist wood that cracketh in the fire : we may adde hereunto the breaking of an egge in the fire , of an apple or any like thing ; for whatsover holdeth and withholdeth inclosed any hot wind , so that it can have no vent , it will seek it self a way by breaking the skin , shell or case . It were no ill comparison to liken Thunder to the sound of a gun , which be both caused of the same or very like causes . The sound of Thunder is divers ; after which men have divided the Thunder into divers kinds , making first two sorts , that is , smal Thunder and great . But as for the diversity of sounds , generally it comes of the divers disposition of the clouds , one while having more holes then at another ; somtime thicker in one place then in another . The smal or little Thunder is when the Exhalation is driven from side to side of that cloud making a noise , and either for the smal quantity and less forcibleness , or else for the thickness of the clouds walls , is not able to break them , but rumbleth up and down within the cloud , whose sides be stronger then the force of the Exhalation is able to break , it runneth up and down within , and striking against the cloud and moist sides , maketh a noise not unlike the quenching of hot i●on in cold water . And if the Exhalation be meanly strong , and the cloud not in all places or like thickness , it breaketh out at those thin places with such a buzzing as wind maketh blowing out of narrow holes . But if the cloud be so thin that it cannot keep in the Exhalation , although it be not kindled , then it bloweth o●t with like puffing as wind commeth out of a pair of bellowes . A great Thunder is when the Exhalation is much in quantity , and very hot and dry in quality ; the clouds also very thick and strong , that easily will not give place to the wind to escape out . Wherefore if the Exhalation do vehemently shake the cloud , though it do not at the first disperse it , it maketh a long and fearfull rumbling against the sides of the cloud , untill at the last being made stronger by swifter motion , it dissolveth the cloud , and hath liberty to pass out into the open Air ; the cloud dissolved droppeth down , and then followeth a showre of Rain . Otherwhiles it shaketh the cloud not long , but straight way rendeth it a long space and time , whose sound is like the rending of a Broad-cloth , which noyse continueth a pretty while . And sometime it discusseth the cloud at once , making a vehement and terrible crack like a gun , sometime with great force casting out stones , but most commonly fire which setteth many high places on fire . As in the year of our Lord 1561. the Fourth day of June , the steeple of Saint Pauls Church in London was set on fire , as it hath been once or twice before , and burned . The noyse of Thunder though it be great in such places over which it is made , yet is not hard far off , especial-against the wind ; Whereof we had experience also in the Year of our Lord , 1561. on Saint Matthias day in February , at the evening , when there was a great flash of Lightning and a very ter●ible crack of Thunder following ; they that were but 15 Miles from London Westward heard no noise nor sound thereof ; the Wind that time was Western . The effect of Thunder is profitable to men , both for that the sweet showre doth follow it , and also for that it purgeth and purifieth the Air by the swift moving of the Exhalation that breaketh forth , as also by the sound which dividing and peircing the Air , causeth it to be much thinner : which may be verified by an History that Plutarch in the life of Quincius Flaminius reporteth , that there was such a noyse made by the Grecians , after their Liberty was restored , that the Birds of the Air that flew over them were seen fall down by reason that the Air divided by their Cry , was made so thin , tha● there was no firmity or strength in i● to bear them u● . And let this suffice for Thunder , which Lightning succeedeth in treaty , that seldom is from it in nature . Of Lightning . AMong the divers kinds of Lightnings which Writers in this knowledg do number , we shall treat only of four kinds ; yet so , that under these Four all the rest may be comprehended . The names we must borrow of the Latine Tongue ; the first is Fulgetrum , the second Coruscatio , the third Fulgur , the fourth Fulmen . Of Fulgetrum . FUlgetrum we call that kinde of Lightning which is seen on Summer nights and evenings after a hot day . The generation hereof is such ; when many thin , light and hot Exhalations by the immoderate heat have been drawn up from the Earth , and by the absence of the Sun be destitute of the force whereby they should have been drawn further upward ; yet something ascending by their own nature , in that they be light and hot , they meet with the cold either of the night in the lowest region , or else of the Air in the middle region ; and so by resistance of contraries ( as it hath been oft before rehearsed ) they are beaten back , and with vehement moving set on fire . This Lightning commonly goeth out in the Air terrible to behold , not hurtfull to anything , except sometime when the matter is earthy and gross , being stricken down to the earth , it blasteth corn and grass with other smal hurt . Sometime it setteth a barn or thatched house on fire . The Colour of this Lightning as of all other , is divers , partly according to the matter , and partly according to the light . If the matter be thin , it is white ; if the substance be gross , it is ruddy , like flames of fire . In great light as in the day , it appeareth white ; in the night , ruddy : yet sometime in the day time we may see it yellow , wich is a token that the matter is wonderfull thick and gross . Old Wives are wont to say that no night in the year except one , passeth without Lightning , but that is true as the rest of their Tales , whereof they have great store . Of Coruscation . Coruscation is a glistering of fire , rather then fire indeed ; and a glimering of Lightning , rather then Lightning itself : which is two manner of ways : One way , when clouds that be lower then the upper part of the Earth , without the compass of our fight are enflamed , and the reflection of that flame is cast up into our sight , appearing in all points like Lightning , saving that the Air where it appeareth , is so clear , that we are perswaded , no Lightning can be there caused . Another way is , when there be thick clouds over us , and commonly a double order of clouds , one above another : if Lightning or any other Inflammation be in the upper part of these clouds , the light of them peirceth thorow the lower parts as thorow a glass , and so appeareth as though it Lightned , when perhaps it did Lighten indeed , yet that which we saw , was but the shadow thereof : and this is often without Thunder . Of Fulgur . FUlgur is that kinde of Lightning which followeth Thunder , whereof we have spoken before . For when that violent Exhalation breaks forth , making a noyse as it beateth against the sides of the cloud , with the same violence it is set on fire , and casteth a great light , which is seen far and neer . And although the Lightning appear unto us a good pretty while before the Thunder-clap be heard , yet it is not caused before the noyse , if any Thunder at all follow , but either is after it or with it . Wherefore that we see it before we hear the Thunder , may be ascribed either to the quickness of our Sight that preventeth the Hearing , or else to the swift moving of the fire and the light thereof to our eyes , and the slow motion of the Sound unto our ears and Hearing . These three kindes of Lightnings are more fearfull then hurtfull , but the fourth seldom passeth without some dammage doing . Of the fourth kind , called Fulmen . THe most dangerous , violent and hurtfull kind of lightning is called Fulmen , whose generation is such as followeth : What time a hot Exhalation is enclosed in a cloud and breaking the same , bur●reth forth , it is set on fire and with wonderfull great force stricken down toward the Earth . The crack of thunder that is made when this Lightning breaketh out , is sudden , short , and great , like the sound of a Gunne . And oftentimes a great stone is blowne out with it , which they call the Thunder-bolt , which is made on this maner . In the Exhalation which is gathered out of the Earth , is much Earthly matter , which clortering together by moysture , being clammy by nature , consisting of brimstone , and other metalick substance by the excessive heat , is hardened as a brick is in the fire , and with the mighty force of the Exhalation strongly cast toward the Earth , and striketh down steeples , and high buildings of stone , and of wood , passeth thorow them , and setteth them on fire ; it cleaveth trees and setteth them on fire : and the stronger the thing is that resisteth it , the more harme it doth to it . It is sharp-poynted at one end , and thick at the other end , which is caused by reason that the moyster part , as heavier , goeth to the bottome of it ; so is the top small , and the bottome thick . Men write , that the thunder-bolt goeth never above five foot deep , when it falleth upon the Earth : which standeth with reason , both because the strength of it is weakned before it come so neer the ground , and also because the continual thicknesse of the Earth breaketh the force , were it never so great . Both Aristotle , Seneca , and Plinius divide this lightning into three kinds . Of the first . THe first is drie , which burneth not to be felt , but divideth and appeareth with wonderful swiftnesse : For being subtil and pure , it passeth thorow the pores of any thing , be they never so small ; and such thing● as give place unto it , it hurteth not ; but such things ●s resist , it divideth and peirceth . For ●t will melt money in mens purses , the purses being whole and unharmed . Yea , ●t will melt a sword in the scabberd , and not hurt the scabberd at all . A wine ●essell it will cleave , and yet the wine shall be so dull that by the space of three dayes , it will not runne out . It will hurt a mans hand , and not his glove . It will burne a mans bones within him ●o ashes , and yet his skinne and flesh shall appearefaire , as though nothing had come to him . Yet otherwise the whole man in the moment of an houre shall be burned to ashes , whereas his clothes shall not seeme to have been touched . It will also kill the childe in the mothers belly , and not hurt the mother : And all because the matter is very subtill , and thinne , burning , and passing thorow whatsoever it be , that will not give it free passage . Of the second kind . The Second kinde is moyst : and because it is very thin , it burneth not to ashes , but only it blasteth or scorcheth trees , corn and grass : and by reason of the moystness it maketh all things black that it commeth neer , as moyst wood burning is smoaky , and maketh things neer it to be black and smoaky . Of the Third kinde . THe Third kinde is most like our common fire that wee have here on the earth of gross and earthly substance ; wherefore it leaveth a print where it hath been , or else consumeth it into ashes , if it be such a body as will be burned with fire . Of the Marvels of Lightning , and their causes . BEside the wonderful effects of lightning , that have been already remembred , there be many other which hereafter ensue , with the reason and causes unto them belonging ; as thus : The nature of Lightning is , to poyson beasts that are stricken therewith , as though they had been bit by a Serpent . The cause of this is that the matter of Lightning is much infected with Brimstone & other poysonous metallike substance , because it is thin , and giveth them passage into every part of the body . It is notable that Seneca writeth how winevessels of wood being burned with lightning , the wine would stand still , and not run out : the reason hereof , is , the swift alteration and change , whereby also all the clamminesse of the wine is drawne to the outward most part , and so keepeth in the wine as in a skin , that by the space of three days it will not run . It will also poyson wine , insomuch that they which drink thereof shall either be mad or dye of it : the cause hereof was set● forth before . Lightning that striketh a poysonous beast , purgeth it from the poyson , in so much that it causeth a Serpent or Snake which it killeth , to breed worms , which otherwise it would not do : but being purged from the natural poyson by the swift peircing of the Lightning , nothing letteth but that it may breed wormes as all other corrupt flesh will doe . If Lightning strike one that sleepeth , it openeth his eyes ; and of one that waketh , it shutteth the eyes . The cause is this , that it waketh him that sleepeth , and killeth him , before he can close his eyes againe . And him that waketh it so amazeth , that he winketh , as he will doe at any sudden chance : so he dyeth , before he can open his eyes againe . All living things turne their face toward the stroke of the lightning , because it is their nature , to turne their head if any thing come suddenly behind them . The rest that have their face toward it when it commeth , never turn before they be killed . The Reason why it killeth the child in the mothers womb , not hurting the mother , is the tenderness of the one and the strength of the other , when the lightning is not vehement ; otherwise both should dye together . Sometime Lightning burneth onely the garments , shooes or hair of men , not hurting their bodies , and then the Exhalation is nothing vehement . Sometime it killeth a man , and there appeareth no wound without , neither any hurt within , no not so much as any sign of burning : for then the Exhalation which being kindled is called Lightning , is wonderfull subtil and thin , so swiftly passing thorow , that it leaveth no mark or token behind it . They that behold the Lightning , are either made blind , or their face swelleth , or they become Lepers ; for that Fiery Exhalation received into the pores of their face and eyes , maketh their face to swell and break out into a Leprosy , and also dryeth up the Chrystalline humour of their Eyes , so that consequently they must needs be blind . Eutropius sheweth that the same day in which Marcus Tullius Cicero was born , a certain Virgin of Rome riding into Apulia , was stricken with Lightning , so that all her garments being taken from her without any rending , she lay starke naked , the lasing of her breast being undone , and her hose-garters untyed , yea her bracelets , collars , and rings being all loosed from her : Likewise her horse lay dead , with his bridle and girts untyed . The places of them that are burnt with Lightning , are colder then the rest of their bodyes , either because the greater heat draweth away the lesser , or else because that by the great violence the vital heat is quite extinguished in that place . The Sea-Calf is never hurt with Lightning : wherefore the Emperours Tents were wont to be covered with their skins . The Bay Trees and Box Trees are never , or seldom stricken with Lightning ; The Cause of these may be , the Hardness of their Skinne , which hath so few Pore-holes , that the Exhalation cannot enter into them . The Eagle also among Fouls , is not stricken with Lightning ; Wherefore the Poets feigne , that the Eagle carrieth Jupiters Armour , which is Lightning . The Reason may be the thickness and dryness of her feathers , which will not be kindled with so swift a fire . Of Storme Winds . A Storme Wind is a thick Exhalation , violently moved out of a Cloud , without inflammation or burning . The Matter of this Storme is all one with the Matter of Lightning , that hath been spoken of : namely , it is an Exhalation very hot and dry , and also gross , and thick , so that it will easily be set on fire ; but then it hath another name and other Effects . The Form or Manner of the generation is such ; When abundance of that kinde of Exhalation is gathered together within a Cloud , which needs will have one way out or other , it breaketh the cloud and causeth Thunder , as it hath been taught before : but if the matter be very thick , and the Cloud somewhat thin , then doth it not rend the Cloud , but falling down , beateth the Cloud before it , and so is carried as an arrow out of a bowe . It doth always goe before a great sodain showre : For when the Cloud is broken , the water must needs fall down . Also it is so gross and so thick , that it darkneth the Air and maketh all the Lowest Region of the Air to be in a manner as a dark Smoaky Cloud . It causeth Tempests in the Sea , and Wonderfull great Danger to them that bear Sayle ; whom if it overtake , it bringeth to utter destruction . So sodain is this kinde , that it cannot be resisted with sodain helpe : so violent it is , that seeble force cannot withstand it . Finally , It is so Troublesome with Thunder , Lightning , Rayne , and Beasts : besides these , Darkness and Cold , that it would make men at so neer a Pinch , to be at their Wits End if they were not accustomed to such Tumultuous Tempests . Wherefore it were profitable to declare the Signes that goe before it , to the End Men might beware of it . But they are so common to other Tempests , that either they are known well enough , or else being never so well known , in a Seldom Calamity they would little be feared . The Sea-ships subject to more Danger , have more Helpe , if it be used in Time : But no Signes foreknowne can profit the Dweller of the Land to keep his House from Ruine , except it were to save his Life from the fall of his Mansion . The sudden violence of this Tempest to him is more seldome times , but more incurable when it commeth then to the Mariner who hath some Ayd to look for by his comming ▪ the other if he escape with his life , may comfort himself that he was neer a great danger , and cast with himself to build up his House again . Of Whirlwinds . A Whirlwind , is a Wind breaking out of a Cloud , Rouling or Winding round about , overthrowing that which standeth neer it , and that which commeth before it , carrying it with him aloft in the Air. It differeth from a Stormy Wind in three points . First , in the Matter which is less in Quantity , and of thinner Substance . Secondly , in the Moving , which is Circular , Winding about : whereas the Storme bloweth Aslope and Sidelongs . Also a Whirlwind , in the Moving divideth not it self abroad and bloweth Directly , as the Storme doth . And Thirdly , in the manner of the generation ; for a Storme doth always come out of one Cloud ; but a Whirlwind sometime is Caused by means of two Contrary Winds that meet toether . In like manner , as we see in the streets of Cities , where the wind is beaten back from two walles , meeting in the middest of the street , there is made a little whirle-wind , which whisking round about , taketh up the dust , or strawes , and bloweth it about , after the very similitude of the great and fearefull whirlewind . The reason of the going about is this , that when the walls beat back the wind from them , which aboundeth in that place , and those winds when they meet , by reason of equall force on both sides , can neither drive one the other back againe , nor yet passe thorrow one the other ; it must needs be , that they must both seek a way on the side at once , and consequently be carried round about , the one as it were pursuing the other , untill there be space enough in the aire , that they may be parted asunder . The matter of a whirlewind , is not much differing from the matter of storme and lightning , that is , an Exhalation hote and drie , breaking out of a cloud in divers partes of it , which causeth the blowing about . Also it is caused , as it hath been said , by two , or more windes , blowing from divers places , which may be of particular causes , that have been shewed before in the Chapter of windes ; this tempest is noysome to man and beast , Sea and Land , things living , and life lacking : For it will take up both men and beasts , stones and clods of earth : which when it hath borne a great way , will not be so curteous as to set them downe againe , but negligently letteth them fall from a great height , or else violently throweth them downe to the earth . It breaketh Trees , winding them about , and pulling them up by the roots . It turneth about a Ship , and bruiseth it in peeces with other mischiefes besides . Of fired Whrlewinds . SOmetime a whirlewind is set on fire within the cloud , and then breaking forth , flyeth round like a great cart-wheele , terriblie to behold , turning and over browing all drie things that it commeth neer , as Houses , Woods , Corn , Grasse , and what soever else standeth in the way . It differeth not from a whirlewind , saving that it is kindled and set on fire , so appearing , else the generation of both is called one . Of Circles . THe Circle called Halon is a garland of divers colours that is seen about the Sunne , the Moon , or any other Star , especially about Jupiter or Venus , for their great brightnesse . It is called of the Greeks a compassed plat , of the Latines , a Crown or Garland . The matter wherein it is made , is a cloud of equall thickness , or thinnesse , comming directly under the body of the Sunne , the Moone , or other Starres , into which the light of the heavenly body is received & so appeareth round , because the Starre is round : as a stone cast into the water , maketh many round circels , dilating in breadth , untill the violence of the moving is ended ; so is it in the aire ; the light beames peircing it , cause broad circles to be dilated , which appeare white , purple , black , red , green , blew , and other colours , according to the disposition of the clouds matter . The cause of such colours , is shewed before in the peculiar treaty of colours . This circle is oftner seene about the Moone , then about the Sunne , because the heate of the Sunne draweth the vapors too high , where it cannot be made . Also , because the night is a more quiet time then the day from wind , it is more often in the night , then in the day . Seldome , about other Starres , because their light beames , are too weake often to pierce a cloud : yet oftner about smal stars then the Sunne , because the light of the Sunne pierceth the cloud more forcibly , than that this Halon can many times be cause . Otherwhiles it is seen about a candle , which must be in a very thicke and grosse aire of such proportionate thickness , that it may receive the light as the cloud doth from the starres , as in the smoaky places , or hot houses . This kinde of circle is sometimes like a Rainebow , saving that it is a whole circle unlesse the starre under which it is caused , be not all risen , or else the cloud , in which it is seen , be not all come under the Star , or after it hath come under some part therof , be dissolved from the rest . These Circles be sings of tempests and windes , as witnesse both Virgil , and Aratus . The Wind shal blow from that quarter , where the Circle first beginneth to break . The cause whereof is this , that the Circle is broken by the Winde that is above which is not yet come down towards us , but by this effect above ; we may gather , both that it will come , and also from what quarter . A great Circle about the Moon , betokeneth great cold and frost to follow after . But if it vanish away and be dissolved altogether , it is a signe of faire weather . If it be broken in many parts , it signifieth tempest . If it wax altogether thicker and darker , it is a forewarning of raine . One alone , after Ptolomee , pure and white , vanishing away by little and little , is a token of faire weather . Two or three at once , portendeth tempest : if they be ●uddy , they shew wind to come ; and toward snow , they seem as it were broken and rocky . Being darke or dimme , they signifie all these foresaid events , with more force and abundance : it is oftner caused in Autumne and Spring , then in Winter or Summer : the cause is the temperatenesse of the time . The cause why it appeareth sometime greater , and sometime lesser , is in the quality of the matter , which as it is grosse or thinne , will more or lesse be dilated and stretched abroad , & also as some will have it , of the weakenesse of mans sight . Of which , Aristotle bringeth an example in one Antipho , which did alwayes see his owne image before him in the ayre , as in a glasse : which he affirmeth to have been for the weaknesse of his sight-beames that could not peirce the aire , so that they were reflected again to himself . And thus much for Halon , and the causes , signes , or toke●s of it . Of the Rainebow THe Rainebow , is the apparition of certaine colours in a cloud , opposite against the Sunne , in fashion of half a Circle . Possidonius said , it was the Sunnes looking glasse , wherein his image was represented , and that the blue colour was the proper colour of the cloud ; red of the Sunne ; all the other colours of commixtion . It differeth manifoldly from Halon : for the Raynebow is alwayes opposite against the Sunne : but Halon is directly under it . They differ not onely in place , but also in fashion : the Raynebow is but halfe a Circle : the Halon is a whole Circle . Likewise they vary in colour : for the Raynebow is more dimme , and of purple colour ; the Halon , whiter and brighter . Also , in continance ; for the Rainbow may continue longer then Halon . The image of the Rainebow may be seen on a wall , the Sunne striking thorow a fix poynted stone , called Iris , or any other Christall of the same fashon ; also thorow some glasse window . Halon is seen about Candles , in smokie places , as are baths and kitchings . The manner of the generation of the Rainebow is such : There is opposite against the Sunne , a thick watery cloud , which is already resolved into dewy drops of raine , is ( for a grosse similitude ) is seene on the potlid , when the Water in the Vessell hath sodden , or is very hot , the lid will be all full of small drops of water , which come from the water in the Vessell ; first , by heat resolved into smoake ; after , when it cannot goe at large , it is resolved again . Wherefore upon such a cloud , the Sunne beams striking , as upon a smooth glasse , do expresse the image of the Sun unperfectly , for the great distance . Or else the Sunne beames striking into a hollow cloud , where they are refracted or broken , and so come to the eyes of him that beholdeth the Rainbow . The similitude thereof is seen , when men sayle or row in Boats , the Sunne shineth upon the water , which casteth on the vessels side , the colours and image of the Rainbow . Lifewise , water in an urinall holden against the Sunne , receiveth the light , and sheweth colours on the wall . There be two kinds of Rainbows , one of the Sun , another of the Moon ; the one by day , the other by night : the Rainebow of the Sun often , but of the Moon very seldome , in so much that it can be but twice in fifty yeeres , and that when the Moon is in the East or West , full in perfect opposition . It hath not been many times seene since the writing of Histories , yet sometimes , and for the rarenesse , is taken for a great wonder . Yet is it in colour nothing so beautiful as the sunnes , but for the most part white as milke : other diversities of colours are scant perceived . When it appeareth , it is said to signifie tempest . The time of the Rainbow is often after the point of Autumne , both for the placing of the Sunne in competent lownesse , and also for abundance of matter , seldom or never is the Rainebow see about the midst of Summer . There may be many Rainebows at one time , yet commonly but one principall , of which the rest are but shaddows and images ; the second shaddow of the first , the third of the second , as appeares by placing of their colours . It remaineth to shew why it is but halfe a circle , or lesse , and never more ; and why the whole cloud receiveth not the same colours that the Raynebow hath . The cause of the first is , because the center or middle part of the Raynebow , that is Diametrally opposite to the center of the same , is alwayes either in the Horizon ( that is , the circle cutting off our fight of Heaven by the earth ) or under it . The cause why the whole cloud is not coloured , is , because that in the middest , the beames as strong , peirce thorow , but on the edges where they are weaker , they are reflected or refracted . Now for so much as GOD made the Raynebow a sign and Sacrament of the promise , some think it was never seene before the flood : their reason may be this , that the earth , after the first creation was then so fruitfull , that it needed hone or very little Raine , so that such dark clouds were not often gathered , the fruitfull ground not so easily remitted his moysture , that then was fat and clammy , hard to be drawne up : so it might be , that there was no Rainebow before , as we cannot find that ever , it rained before . But whether it were or not , it is certaine , that then it became a Sacrament , whereas it was none before which when we behold , it behoveth us to remember the truth of God in all his promises , to his glory and our comfort . The milke way , called of some the way to S. James , and Watling Streete . THe milke way is a white circle seen in a cleare night , as it were in the firmament , passing by the sings of Sagittarius and Gemini . The cause thereof is not agreed upon among Philosophers , whose opinons I thought best to report , before I come to the most probable causes . First of all , Pythagoras is charged with a Poeticall fable , as though it had been caused by reason that the Sun did once run out of his path way , and burned this part , whereof it looketh white . Others , as Anaxagoras and Democritus sayd , that it was the light of certaine Starres , shining by themselves , of their owne light , which in the absence of the Sun might be seene . But this opinion is also false ; for the Starres have no light of themselves , but of the Sun : also if it were so , it should appear about other Starres . Democritus is also reported to have said , that it was nothing else but innumerable little Starres , which with their confuse light , caused that whitenesse : to this opinion , Cardane seemeth to subscribe . The Poets have foure fables of it : one of Phaeton , which on a time guided the Chariot of the Sunne , and wandring out of the way , did burne that place , wherefore of Jupiter he was striken downe with lightning . The second , That it is the high street in Heaven , that goeth streight to Jupiters palace , and both sides of it the common sort of gods doe dwell . The third , that Hebe , one which was Jupiters Cupbearer , on a time stumbled at a straw , and shed the Wine or Milke that was in the Cup , which coloured that part of Heaven to this day : wherefore she was put out of her office . The fourth , That Apollo stood there to fight against the Giants , which Jupiter made to appear , for a perpetual memory . Theophrastus , a Philosopher , affirmed , That it was the joyning together , or came of the 2 half Globes , which made ●t appeare more light in that place then anothers . Others said , it was the reflexion of the shining light of fire or starre light , ●s it is seen in a glasse , but then it should ●e moveable . Diodorus affirmed , that it was Heavenly fire , condensed or made thick into a circle , and so became visible , whereas the rest , for the pureness , clearnesse , and thinnesse , could not be seen . Possidonious , whose mind to many seemeth very reasonable , said , it is the ●nfusion of she hea● of the Stars , which therefore is in a Circle , contrary to the Zodiake , ( out of which the Sun never wandereth ) because it might temp●● the whole compass with vital and livel●hea , Although in my mind he hath rather expressed the finall cause , then th● efficient . Aristotles opinion is , that it should be the beames of a great Circle which 〈◊〉 caused by a cloud or Exhalation draw● up by those Starres , which be calle● Sporades . This opinion of Aristotles 〈◊〉 misliked of most men that have travailed in this science ; and worthil● ▪ For if it were of the nature of elements as Exhalations are , it would be at length consumed . But this circl●● never corrupteth , therefore it is not 〈◊〉 Exhalations . Also it neither increase● nor diminisheth , which is a plain pro●● that it consisteth not of elemental matter , although Aristotle seem to make double circle , one celestiall , another elemental . The last opinion is , of them that 〈◊〉 it is the nature of heaven , thicker 〈◊〉 substance , then other parts of Heaven be , having some likenesse to the substance of the Moon , which being light ●●ed by the same as all the Starres b● appeareth white . And this opinion I take to be most probable , because that sentence of Starre light seemeth not so reasonably , to be only in that place , and not elsewhere . The finall cause of this Milke-white circle , hath beene already touched in the opinion of Possidonius , whereunto also Plinius in the 18. Book , and 29. Chapter of his natural History agreeth , affirming , that it is very profitable for the generation and fruitfull increase of things that grow on the ear●h . The Mathematitians that have measured the breadth thereof , affirme , that toward the north it passeth over the Ecliptical line of the ninth spheare , from the 18. degree of Gemini , unto 2 degrees of Cancer , which is 13. degrees and toward the South , from the 8 degree of Sagittarius , to the 13 degree of the same signe : and because it is there divided into two branches ( as may easily be seen in a cleare night ) it reacheth from 24 of Sagittarius , to the 2 degree of Capricorne . This circle , if it be of the nature of Heaven , is unproperly placed among Meteors or impressions : but because of Aristotles mind , who will have it to be an impression kindled , and their opinion which think it proceedeth of the light of Starres , it is not without good cause in this place treated of . Of beames , or streames of light , appearing thorow a Cloud . THere is yet another kind of impression caused by the beames of the Sunne , stricken through a watery cloud , being of unequall thinnesse , and is thinner in one part then in another , so that it cannot receive the beames in any other forme , then that they appeare direct or slope downeward of divers colours ; and the same that are the colours of the Rainebow , though not so evident , because the reflexion is not so strong . They vary in colours : some are more urple or ruddy , when the cloud is thicker ; some yellow and whitish , when the cloud is thinner , and so other colours are caused likewise , whereof you may read the proper cause in the colours of clouds and other like parts of this Treatise . The common people call it the descending of the holy Ghost , or our Ladies Assumption , because these things are painted after such a 〈◊〉 Others say that it is raine , striking down in another place , as though they 〈◊〉 see the drops falling . And they are 〈◊〉 altogether deceived , but in the time ; for soon after it will raine , because this impression appeareth out of a watry cloud . They are called by divers names , as Rods , Wands , Cords of Tents , unto which they are not touch unlike staves and little pillars , when they seeme greater and thicker , many being ioyned together . The Rainebow , the Circles , and these light Beams , are all of one manner of generation , in so much that if you divide the Circle , it shall be a Rainbow ; if you draw it streight in length , it maketh streames or beames . Herein they agree , namely , in forme and matter , but they differ in outward form , which we may call fashion , as the one is round , the other halfe round , and the third direct , straight or falling aslope . Also they differ in place about which they stand : for streames are onely about the Sunne ; Rainebowes about the Sunne often , and seldome about the Moon ; but circles both about the Sunne and the Moon , and also about any other of 〈◊〉 the Starres , yet rather and oftner about bright Starres . To make an end of these streams , they appear diversly , after the fashion and place wherin the cloud hangeth , in respect of the sunne ; for sometimes they are seen only in the edge of a cloud , all the breadth of that cloud : sometime thorow the midst of a cloud , being thinner 〈◊〉 then in other parts , and then they are spred round about like a tent or pavillion used in War. They are most commonly seen in such times as there 〈◊〉 abundancee of raine , which they by their apparition do signifie not yet to be ended . And thus much concerning direct light beames , called Roddes , &c. Of many Sunnes . IT is strange and marvelous to behold the likelyhood of that which Alexander the Great , sending word to Darius , said to be impossible , that Two Sunnes should rule the World. But oftentimes , men have seen , as they thought in the firmament , not only two Sunnes , but oftener three Sunnes , and many more in number thought not so often appearing . These , how wonderfull soever they appear , proceed of a natural cause , which we will endevour to expresse . They are nothing else but Idols or Images of the Sun , represented in an equall , smooth , and watery cloud placed on the side of the Sunne , and somtimes one both sides , into which the Sunne beams being received , as in a glasse , expresse the likenesse of fashion and light that is in the Sunne appearing as though there were many Sunnes ▪ whereas indeed there is but one , and all the rest are images . This thick and watery cloud , is not said to be under the Sunne ; for then it would make the Circles , called crowns or garlands : it is not opposite to the Sunne , for then would it make the Rainbow : but it is said to be on the side where the image may be best represented . Also it may not be too far off , for then the beams will be too feeble to be reflected : neither yet too neer ; for if it so be , the Sunne will disperse it : but in a competent and middle distance : for so representation of many Sunnes is caused . They are most often seene in the morning and evening , about the rising or going down of the Sunne , seldome at noone time , or about the midst of the day , because the heat will soone dissolve them : yet have there been some seen , which began in the morning , and continnued all the day long , unto the evening . Somtimes there appeare many little Suns , like unto little starres , which are caused after the same sort as we do see a mans face to be expressed in all the pieces of a broken glasse . So when the cloud hath many separations , there appeare many Sunnes , on one , side of the true Sun , somtimes great and somtimes little , as the parts of the cloud separated are in quantity . They do naturally betoken tempest and rayne to follow , because they cannot appeare but in a watery disposition of the Ayre . Also , if they appeare on the South-side of the Sunne , they signifie a greater tempest , then if they appeare on the North-side . The reason is alleadged , because the Southerne Vapor is sooner resolved into Water then is the Northerne . For a supernaturall signification , they have oftentimes been noted to have portended the contention of Princes of kingdomes : As not long before the Contention of Galba , Otho , and Vitellius for the Empire of Rome , there appeared three Sun. Also of late , toward the slaughter of Lewis King of Hungary , were seen three Suns , betokening three Princes that contended for the kingdome , namely Ferdinnando since Emperour , John Vayvode , and the great Turke . Of many Moones . AFter the treaty of many Suns , it were not hard for any man without farther instruction to know the natural Cause of many Moons ; For they are likewise Images of the Moon , represented in an equal Cloud , which is watry , smooth and polished , even like a glass . Some call them ( as Plinius saith ) night-Suns ; because they , joined with the light of the true Moon , give a great shining light , to drive away the shadow and darkness of the night . It were superfluous to write more of their Causes or Effects , which are all one with those that have been declared of the Suns . It may be doubted , why the other stars do not likewise expness their image in watry Clouds ; and so the number of them , as to our sight , should be multiplyed . It may be Answered that their light or beams are too feeble and weak to express any such Similitude or likeness in the watry Clouds . For although they have garlands or circles about them , that are caused in a Vapour that is under them , yet it is manifest that this Apparition hath not need of so strong a light as is required to print the images of them in the Clouds . Again , the Garlands are direct under , and therefore apter to receive such Apparition . It may be again Objected that the Stars have their Image perfectly and sufficiently expressed in glasses here on the Earth ; yea and at the day-time , when their light is either none , or most feeble and weak : as we see it is used at Midsummer to behold that great star called Syrius in a glass even at Noon-days . Also we see every night the image of the Stars in calm and quiet standing waters : then what should let but that their images might also be expressed in watry Clouds ? Hereto may be answered that the Let is in the Cloud , which is neither so hard as is the glass , nor yet so continual as is the water , but consisteth of innumerable smal drops : so that except the light of the stars were stronger , it can in them express no uniform images of them , as it doth in glasses and in the water . Notwithstanding , in Writers of Wonders we read some such likething sometime to have chanced . There hath been often seen many Suns in the day-time and after the Sun setting : at the rising of the full Moon there have appeared many Moons , which was by this means , that the same Cloud that received the Sun-beams in the morning , tarried in the same place , and at the Moons rising was ready also to receive her image . Of Wonderfull Apparitions . WE will close this Book with a brief declaration of the natural Causes of many things that are seen in the Air , very wonderfull and strange to behold , which in these latter Years have been often seen and beheld to the great admiration of all men , not without the singular providence of God , to forewarne us of many dangers that hang over us in these most Perillous Times . The apparitions of which , as it is most wonderfull , so the searching of the Cause to us is most difficult : a great deal the rather , because no man hath hitherto enterprised ( to my knowledge ) to seek out any cause of them , but all men have taken them as immediate miracles , without any natural meane or cause to procure them . And I truly do acknowledge that they are sent of God as wonderfull signs to declare his Power , and move us to amendment of life ; indeed miraculous , but not yet so that they want a natural cause ; for if they be well weighed and considered , it is not hard to find that they differ much from such Miracles as are recorded in the Scripture and admitted of Divines . So that as I abhorre the Opinion of Epicurus to think that such things come by Chance , but rather by the determined purpose of Gods providence : so I consent not with them that suppose when any thing is derived from any natural caus , God the chief and best Cause of all things is excluded . Some of these Wonderfull Apparitions consist of Circles and Rainbowes of divers fashions and placings , as one within another , the edge of one touching another , one dividing or going thorow another , with like placing of small Circles about great Circles or parts of small Circles , some with the ends upward , some downward ; some aside , and some across ; but all for the most part in uniform order constituted or placed for the order of them pleasant to behold , but for the strangness somwhat fearfull . Such a like Apparition is made with the Suns or Moons images joined unto these Circles set also in good and uniform order . The cause of all these is the meeting together of all those several Causes that make the Circles , Rainbowes , Streames and Images of the Sun or Moon , which joined all together , make the wonderfull sight of Rainbowes , positions of Circles , Crosses and divers Lights which pertain to the knowledg of Optice and Catoptrice that teach how by divers refractions and reflects , ons of beams such visions are caused . So that he which will know how they are generated , must return into the several Treatises of Rainbowes , Circles , Streams & Images of the Sun or Moons and if in them he find not knowledg sufficient to instruct him , I must send him to the Demonstrations of Perspective , where he shall want nothing . Another sort of them , no less often beheld within these few years then the former , but a great deal more strange and wonderfull to look upon , are the Sights of Armies fighting in the Air , of Castles , Cities and Towns , with whole Countries , having in them Hils , Vallies , Rivers , Woods , also Beasts , Men and Fouls , Monsters of which there are no such kindes on the Earth , and finally all manner of things and actions that are on the Earth , as Burials , Processions , Judgments , Combates , Men , Women , Children , Horses , Crowns , Armes of certain Noble men and Countries , Weapons of all sorts , somtimes Stars● , Angels as they are painted with the Image of Christ crucified , beseiging of Castles and Townes , many things and gestures done by men or beasts , thevery Similitude of Persons known to the Beholders ; as of late was seen the very Image of the Emperour Charles , insomuch that they which beheld it , put off their Caps , thinking verily it had been he : and of John Frederick Prince Elector of Saxony , who that time was Prisoner with the Emperour : Also the Image of smal Crosses , which hath been not only in the Air , but also on the Earth , on mens apparell , on dishes , platters , pots , and all other things , so that the Jewes have been full angry that they could neither wash nor rub them out of their apparell . In Germany also Fires and many such things as it were long stories seen in the Air. All these wonderfull Apparitions may be caused two manner of ways ; the one Artificially , the other Naturally . Artificially , by certain glasses and Instruments made according to a secret part of that knowledg which is called Catoptrice ; and so peradventure some of them have been caused ; but The most part ( doubtless ) Naturally , when the disposition of the Air hath been such , that it hath received the image of many things placed and done on Earth . And because it is apt to receive divers images , as well in one place as in another , these monstrous forms and strange actions or stories proceed of the joining of divers forms and actions : as if two Histories were confusedly painted in one , the whole Picture would be strange : or ( as the Poet saith ) if a Painter , to a mans head , should sett a horses neck , and after , divers feathers . Sometimes also one image is multiplyed in the Air into many or infinite , as are letters and crosses which fill the Air , even beneath : And the light of the Sun received into little parts , maketh to appear as it were many smal stars . Let this suffice concerning these wonderfull Apparitions : once again admonishing the Reader , though I have enterprised to declare these by natural Reason , yet verily believing that not so much as one Sparrow falleth to the ground without Gods providence . I do also ackowledg Gods providence bringeth these to pass , to such ends as before I have shewed , using these causes as meanes and instruments to do them . The Fourth Book . Of Watery Impressions . THose be Watery Impressions that consist most of Water . In the Treaty of them are wont to be handled these Impression ; namely , Clouds , Rain , Dew , hoar Frost , Hail , Snow , Springs , and the great Sea it self . Of Clouds . A Cloud is a Vapor cold and moist , drawn out of the Earth and Waters by the heat of the Sun into the middle region of the Air ; where by cold it is so knit together , that it hangeth untill either the weight or some resolution causeth it to fall down . The place wherein the Clouds do hang , is said to be in the middle region of the Air , because men see it is necessary that there should be a cold which should make those Vapors so gross and thick , which for the most part are drawn so thin from the Earth , that they are invisible as the Air is . And although they are known often times , as Aristotle witnesseth , to be in the lowest region of the Air , neer to the Earth , insomuch that sometimes they fall down to the Earth with great noise , to the great fear of men , and no less loss and danger : yet may it be reasonably thought that these Clouds were generated in the middle region of the Air far distant from the Earth , which by their heaviness do by little and little sink down lower into the lowest region , and sometimes also fall down to the Earth . The Common Opinion is , that they goe not higher then nine mile ; which because it leaneth to no reason , is uncertain . Albertus Magnus whose reason also is to be doubted of , affirmeth that the Clouds do scarce exceed Three miles in height when they are highest . And some let not to say that oftentimes they ascend not past the half of One mile in height . Again , Others pretending to finde out the truth by Geometrical Demonstrations , make it aboue Fifty mile to the place where the generation of Clouds is . How these men take the distance from the Earth , it is uncertain : whether that they assigne the least distance and meane it from the highest parts of the Earth as are hill tops , or from the common playn . Again , whether they that assign the highest distance to be from the lowest valleys of the Earth , or from the hill tops . The Reason before shewed , moveth me to think that the most usual and common generation , I mean the condensation or making thick of these thin Vapors into Clouds , is in the middle region of the Air : but for the distance of the Clouds when they be generated , I think they be sometime Nine mile , sometime Three mile , sometime Half a mile , and sometime less then a Quarter of a mile from the Earth . Of Mists . THere be Two kindes of Mists ; the one ascending , the other descending . That which ascendeth , goeth up cut of the Water or the Earth as Smoak , but doth not commonly spread over all other parts : it is seen in Rivers and moist places . The other Mist that goeth down toward the Earth , is when any Vapor is lifted up into the Air , by the heat of the Sun , which being not strong enough to draw it so high that the Cold may knit it , suffereth it after it is a little made thick , to fall down again , so it filleth all the Air with the gross Vapors , and is called Mists , being usually a Sign of fair Weather . Of empty Clouds . THere be certain Cloudes that are empty , and send no Rain ; they come of two sorts . One sort are the Remnants of a Cloud that hath rained , which cannot be converted into water for their dryness . Another sort is of them that are drawn up out of wett and dry places , and be rather Exhalations then Vapors ; that is , they be dry , hot and light , so that it were hard for them to be turned into Rain : they look white like flocks of wooll , when the light striketh into them . There be also empty Clouds , which when the Winds have dispersed abroad any Cloud , are scattered over all the sky : but these Clouds though for a time they be empty , yet because they consist of such a substance as is watry , they may be , and are oftentimes gathered together , and give plentifull Rain . Of the Colours of Clouds we have spoken in the Second Book of Fiery Meteors , where those Colours and the causes of them are described , which seem to be Fiery , or may be thought to be Inflammations or burnings , as to be Red , Fiery and Yellowish . But besides those there be White , Black , Blew and Green. White clouds be thin , and not very Watry : so that the light received in them , maketh them to appear White . Black clouds be full of thick , gross and earthly matter that makes them look so dark . Blew clouds be full of thick drose and earthly , as the Black : so the light received in them , maketh them to seem Blew . Green clouds are altogether watry , resolved into water , which receiving into them the night , appear Green as Water doth in a great vessel , or in the Sea and Rivers . Of Rayne . AFter the generation of clouds is well knowne , it shall not be hard to learne from whence the Rayne commeth . For after the matter of the cloud being drawne up , and by cold made thick ( as is said before ) heat following , which is most commonly of the Southerne wind , or any other wind of hot temper , doth resolve it againe into Water , and so it falleth in drops , to give increase of fruit to the Earth , and move men to give thankes to God. There be small showers of small drops , aud there be great stormes of great drops . The showres with small drops , proceed either of the small heat that resolveth the clouds : or else of the great distance of the clouds from the Earth . The streames with great drops contrariwise doe come of great heat , resolving or melting the cloud , or else of small distance from the Earth . Whereof we see a plaine experiment , when Water is powred forth from an high place the drops are smal , but if it be not from high , it will either have no droppes , or very great . The caus why raine falleth in round drops , is both for that the parts desire the same forme that the whole hath , which is round , and also that so it is best preserved against all contrary qualities : like as we see Water powred upon dry or greasy things to gather it selfe into roundels , to avoid the contrariety of heat and drynesse . It is not to be omitted , that raine Water , although a great part of it be drawne out of the Sea , yet most commonly it is sweet not salt . The caus is , becaus it is drawn up in such small Vapors , and that salt part is consumed by the heat of the Sunne . The raine water doutlesse doth more encrease and cherish things growing on the Earth , then any other Water wherewith they may be Watered , becaus the raine Water retaineth much of the Sunnes heat in it that is no small comfort to all growing plants . The Water that commeth from Heaven , in raine , will sooner come to putrifaction , or stinking , then any other , becaus it hath been made very subtill by heat and also for that it is mixed with so many Earthly and corruptible substances . Rain water , that falleth in the summer , by Avicens judgement , is more wholesome then other Water , becaus it is not so cold and moyst as other Waters be , but hotter and lighter . Sometime there is salt rayne , when some Exhalation which is hot and dry , is commixed with the Vapor whereof the rayne consisteth . Somtime it is bitter , when some burnt Earthly moysture is mixed with it . This rayne is both unwholesome , and also unfruitfull . In these countreys , there is great store and plenty of rayne , becaus the Sunne is of such temperate heate , that it gathereth many Vapors , and by immoderate heat doth not consume them . But in the East parts , in some ho● Countrys , it never or seldom is seen to rayne , as in Egypt and Syria , but in stead of rayne , Egypt hath the River Nilus , whose overflowings doe marvilously fatten the Earth . In Syria and other like Countries they have more plentifull dew then we have , which doth likewise make their Earth exceeding fruitful . Seneca testifieth that the Rain soaketh no deeper into the Earth then ten Foot deep . Of the Signes of Rain . FIrst , If the Skie be red in the morning , it is a token of Rain , because those Vapors which cause the Redness , will be shortly resolved into Rain . If a darke cloud be at the Sun rising , in which the Sunne soon after is hid , it will dessolve it , and rayne will follow . If then appeare a cloud , and after , Vapors are seen to ascend up to it , that betokeneth rayne . If the Sunne or Moone looke pale , looke for rayne . If the Sunne in the East seem greater then commonly he appeareth , it is a signe of many Vapours which will bring rayne . If the Sunne be seen very earely , or few Stars appeare in the night , it betokeneth rayne . The often changing of the Winds , also sheweth tempest . The most sure and certaine signe of raine is the Southerne wind , which with his warmenesse alwayes resolveth the clouds into raine . When there is no dew at such times as by nature of the time there should be , raine followeth : for the matter of the dew is turned into the matter of watry Clouds . If in the West , about the Sunne setting there appeare a black cloud , it will rayn that night , becaus that cloud shall want heat to disperse it . When much dust is raised up , and when the woods make a great noyse , some tempest is towards . Hard stones will be moyst , and sweate against rayne : lamps and candles by sparkling , frogs crying , Trees breaking , leaves falling , and dust clottering , forewarne us of tempest . Fleas , flyes and gnats , bite sore toward a tempest , Kin● feed greedily , birds seeke their victuals more busily : for in the grosse Ayre disposed to rayn , their stomacks are hotter , and they more hungry . But these kind of signes pertaine not so properly to Meteorologie , as to Mariners and Husbandry , which have a great many more then these . And Virgil in the first booke of Georgikes , hath a great number for them that list to learn. Wherefore let these hitherto suffice . Of monstrous or prodigious rayne . HItherto we have made mention onely of naturall rayne , and that which is common , which no man doth marvell at . But there is some time such rayne , that worthily may be wondred at : as when it raineth wormes , frogges , fishes , blood , milke , flesh , stones wheat , iron , wooll , bricke , and quicksilver . For historic maketh mention , that at divers times , it hath rayned such things whose naturall caus , for the most part , we will goe about to expresse , notwithstanding , accounting them among such wonders , as God sendeth to be considered for such ends , as we have before declared , Wormes and Frogges may thus be generated : The fat Exhalations are drawn up into the Ayr , by a temperature of hot and moyst , such vermine may be generated in the Air , as they are one the Earth , without copulation of male and female . Or else that with the Exhalations and Vapors , their Seed and Egges are drawn up , which being in the clouds brought to form , fall down among the rain . Likewise the spawn of fishes , being drawn up , maketh fishes to rain out of the clouds . The vehement heat of the Sunne in Summer , and specially in hot Countries , draweth milke out of the Paps of Beasts and Cattel , which being carryed up in Vapors , and dissolved againe into milke , falleth downe like rain . After the same manner , the Sun also from places where blood hath been spilt draweth up great quantity of blood , and so it raineth blood . It raineth flesh , when great quantity of blood being drawn up , it is clotted together , and seemeth to be flesh . Avicen saith , That a whole Calfe fell out of the Air ; and some would make it seem credible , that of Vapors and Exhalations , with the power of heavenly bodies concurring , a Calfe might be made in the Clouds . But I had rather thinke , that this Calfe was taken up in some storme of Whirlwinde , and so let fall again , then agree to so monstrous a generation . It is a great deale more reasonable , that stones of earthly matter gathered in clouds , should be generated as we said before of the Tunder-bolt . Yet some men think , that wind in Caves of the Earth breaking upward violently , carryeth before it , earth and stones into the aire , which cannot long abide , but fall down , and are counted among prodigious raine . Exhalations that be earthly and drawn out of clay , have much grosse substance in them , which gathered together , and by great heat burned in the clouds , make brick , which is no great marvell . He that hath seen an Eggs-shel full of dew drawn up by the Sun into the Air , in a May morning , will not think it incredible , that Wheat and other Graine should be drawne up in much hotter Countries then ours is , much rather the Meale or Flower which is lighter . A certaine mostinesse , like Wooll , as is upon Quinces , Willowes , and other young Fruits and Trees , is drawne up of the Sunne among the Vapors and Exhalations , which being clottered together , falleth downe like locks of Wooll . Quicksilver , all men know with small heat , will be resolved into most thin Vapors , whereof when quantity is drawne up , it falleth downe againe : As it is read , that once at Rome it rained Quicksilver , wherewith the Brazen Money being rubbed it looked like silver . Titus Livius maketh mention that it rained chalk , whereof the cause cannot be hid to them that read how stone and brick come in the Air. Iron hath also rained out of the clouds , and sundry times , as Histories witness , whereof this hath been the cause . The general matter of all mettals which is quicksilver and brimstone , with the special matter of mixtion that maketh Iron , were all drawu together and there concocted into the mettal : so came the strange Rain of Iron . Avicen saith he saw a piece of Iron that fell out of the clouds , that weighed about an hundred pound weight , whereof very good swords were afterwards made . Of Dew . DEw is that Vapour which in Spring and Autumn is drawn up by the Sun in the daytime , which because it is not carried into the middle region of the Air , abiding in the lower region , by cold of the night is condensed into water , and falleth down in very smal drops . There is common Dew , and sweet Dew . One kinde of sweet Dew is called Manna being white like Sugar , which is made of thick and clammy Vapors , which maketh it so to fall thick and white . It falleth only in the East parts . As for that Manna which God rained to the Israelites , it was altogether miraculous . In Arabia ( as Plinius writeth ) is a very precious kinde of Dew that is called Ladanum , which falling upon the herb Cusus , and mixed with the juice of that herb which Goats do eate , is gathered off Goats hairs and kept for a treasure . There is another kinde of sweet Dew that falieth in England , called the Meldews , which is as sweet as honey being of such substance as honey is : it is drawn out of sweet herbs and flowers . There is also a bitter kinde of Dew that falleth upon herbs , and lieth on them like branne or meal ; namely because it is of an Earthly Exhalation , and so remaineth when the moisture is drawn away : This Dew killeth herbs . The common Dew drunk of Cattle doth rott them , because the matter is full of viscosity , bringing them to a fluxion . There be Three things that hinder Dew from falling ; that is , great heat , great cold , and wind ; for Dew falleth in the most temperate calme time . Of Hoare-Frost . HOare frost , or white frost , is nothing else but dew congealed by overmuch cold . The South and East wind do cause dew , but the North and Northern winds do freeze the Vapors , and so it becommeth hoar frost ; which if that excessive cold had not beene , should have turned into dew . The dew and the hoare frost agree in three things , namely , in matter , in quality of time , and place of the generation . In matter they agree ; for they are both generated of a subtill and thin Vapor , and also small in quantity . In quality of time they consent , for both are made in a quiet and calm time : for if there were great wind , it would drive away the matter , and so could there be no generation . Thirdly , they are both generated in the lowest Region of the Air ; for ( as Aristotle affirmeth ) upon the high hills there is neither dew nor hoar frost . They differ also in three things . For the hoare frost is congealed before it be turned into water ; so is not the dew . Secondly , The dew is generated in temperate weather , the white frost in cold weather . Last of all , hot Winds , as the South and East , do cause dew ; but cold winds as the North and West , do cause hoare frost , Hoare frost doth often stinke , because of the stinking matter whereof it consisteth , which is drawn out of lakes and other muddy and stinking places . Of Hayle . HAyle is a hote Vapor in the middle Region of the Air , by the cold of that Region made thick into a cloud , which falling down to the sudden cold of the lowest Region , is congealed into Ice . There be so many kinds of Haile , as there be of raine : The fashion of haile is sometime round , which is a token that it was generated in the middle region of the Air , or very near it ; for falling from high , the corners are worn away . When the Haile stones are square , or three-cornered , the haile was generated neere the earth . Oftentimes there is heard a great sound in the Cloud as it were of Thunder before haile , or of an Army fighting , &c. The cause is , That Vapors of contrary qualities , being inclosed in the Cloud , do strive to break out , and make a noyse , even as cold water doth , being put into a seething pot . In Spring and Harvest-time is often haile , seldome in Summer and Winter . In winter there want hot Vapors , in Summer the lowest region is too hot to congeale the raine falling down . In Spring and Autumne , there want neither hot Vapors to resist the cold , nor sufficient cold to harden the drops of that hot shower of raine . The haile stones are sometimes greater , and sometimes lesser ; greater , with greater cold ; and lesser , with lesser cold . There is seldom haile in the night , for want of hot vapors to be drawn up . Sometime haile and rain fall together , when the latter end of the cloud , for want of cold in the lowest region , is not congealed . Haile-stones are not so cleare as Ice , because they are made of grosse and earthy vapours , Ice is congealed of clear water . Haile is sooner resolved into water , then Snow , because it is of a more sudden and swift generation . Of Snow . SNow is a cold congealed by great cold , before it be perfectly resolved from vapours into water . Snow is white , not of the proper colour , but by receiving the light into it , and so many small parts ; as in fome , or the white of an egge beaten . Snow is often upon high hills , & lyeth long there , because their tops are cold , as they be neer to the middle Region of the Air ; for oftentimes it raineth in the valley , when it showeth on the Hills . Snow melting on the high Hills , and after frozen again , becommeth 〈◊〉 hard , that it is a stone , and is called Christall . Other matter of Snow , because they are common with Rain , are needlesse to be spoken of . To be short , feet is generated even as Snow , but of lesse cold , or else beginneth to melt in the falling . Snow causeth things growing to be fruitfull , and encrease , because the cold driveth heat unto the roots , and so cherisheth the plants . Of Springs and Rivers . THe generation of Springs is in the bowels of the Earth , and therefore something must be said of the body of the earth . The earth , though it be solid and massie , yet hath it many hollow gutters and veines , in which is alwaies aire to avoid emptinesse : for the ignorant in Phylosophie must be admonished , that all things are full , nothing is empty ; for nature abhorreth emptinesse ; so that where nothing else is , there is Air and Vapors , which by cold , as it hath often been said , will be resolved into drops , as we see experience in marble Pillars and such like hard stones toward raine . This Air and Vapors therefore being turned into drops of water , these drops sweat out of the earth , and find some issue at the length , where many being gathered together , make great abundance of water , which is called a Fountaine or Spring . The cause why such Springs do run continually , is , because that Air can never want in those veines , which by cold will alwaies be turned into water , so that as fast as the water runneth forth , so fast is aire againe received into the place , whereby it commeth to passe , that so many Springs are perpetuall , and never dryed : but if any be dryed up , it is in a hot Summer , and such Springs also they be , whose generation is not deep in the earth , and therefore the Vapors may be made dry , and the earth warm , so the Spring may fail . There be foure kinds of springs ; fountaines , brookes , Rivers and lakes . Of Fouutaines . FOuntaines be small springs , which serve for wels and conduits , when there is but one place where the Water is generated ; and that is not very abundant , either because it is of small compasse , or small veines , and not many . Of Brookes . BRookes , boornes or fordes , be small streames of Water , that run in a channell like a river . They are caused when either the spring occupieth a great compasse , or else two or three small springs meet together in one channell . Of Rivers . RIvers are caused by the meeting together , not only of many springs but also of many brookes and fords , which being received in divers places as they passe , are at the length caried into the broad Sea for the most part . Howbeit some Rivers as swallowed up into the Earth , which perchance run into the Sea , by some secret and unknowne channels : some Rivers there be , that hide their heads under the Earth , and in another place , far off , breake out againe . They Write also , that some Rivers being swallowed up of the Earth , in one Island do run under the bottome of the Earth and Sea , and breake forth in another Island . There be also many great Rivers , that run under the Earth in great Caves , which never breake forth . Aristotle sheweth of ponds and lakes , that be under the Earth . And Seneca speaketh of a pond that was found by such as digged in the Earth , with fishes in it , and they that did eat of them , dyed . As Eeles that be found in darke places , as Wells that have beene dammed up , &c. are poyson , Of Lakes . LAkes are made by the meeting together of many Rivers , Brooks and Springs into one deep valley : whereof some are so great , that they have the name of the Seas , as the Lake called Hircane , or Caspian Sea. These Lakes sometimes unlade themselves into the Sea by small Rivers , sometimes by passages under the Earth . The cause of the swiftnesse of Rivers , is double ; for they are swift , either for the great abundance of waters , or else because they 〈◊〉 down from an hilly place , as the River Rhene falleth down from the top of wonderful high hills . Of hot Bathes . SOme waters that are generated and flow out of veines of Brimstone , are sensibly warm , and some very hot , because they run out of hot places . These waters being also drying by nature , are wholesome for many infirmities specially breaking forth of scabs , &c. Such are the Baths in the West Country , and S. Anne of Buck-stones well in the North part of England , and many other elsewhere . Of the divers tastes that are perceived in Wells . FOr a generall reason , the waters receive their taste of that kinde of earth thorow which they run as thorow a strayner . Some salt , that run thorow salt veines of the earth : some sweet , that be well strained , or run thorow such mineralls as be of sweet taste : some bitter , that flow out of such earth as is bitter by adustion or otherwise . Some sowre or sharpe , like vineger , which run thorow veines of Allome , coperas , or such minerals . Aristotle writeh of a Well in Sicilia , whose water the Inhabitants used for Vineger . In Bohemia neare to the City called Bilen , is a Well that the people used to drink of in the morning , in stead of bunrt wine . And in divers places of Germany , be Springs that taste of such sharpeness . Some have the taste of Wine ; as in Paphlagonia is a Well that maketh men drunk which drink thereof ; which is , because that water receiveth the ●●●osity of Brimstone and other Minerals thorow which it runneth , and so filleth the brain as wine doth . A recitall of such Rivers and Springs as have marvellous effects , whereof no naturall cause can be assigned by most men , although some reason in a few may be found . CLitumnus , which maketh Oxen that drink of it white , is a River or Spring in Italy , Propert , lib. 3. This may be the quality of the water , very flegmatick . In Boetia is a River called Melas , that maketh sheep black if they drink thereof . Seneca speaketh of a River that maketh red hairs : These two with the first may have some reason , that the quality of the reason may alter complexion , and so the colour of hairs may be changed , as we see in certain diseases . In Lybia is a Spring , that at the Sun rising and setting is warme , at mid-day cold , and at mid-night very hot . This may be , by the same reason that wel-water is colder in Summer then it is in Winter . Seneca writeth , that there be Rivers whose waters are poyson : this may be naturally the water running thorow poysonous Mineralls , taking much fume of them . Other Wells that make wood and all things else that can be cast into them , stones , such wells be in England , the cause is great cold . Another Well maketh men mad that drinke thereof . This also may have as good reason , as that which maketh men drinke : As also that Well which maketh men forgetfull by obstruction of the brain . The same Seneca speaketh of a Water , that being drunke , provoketh unto lust and lechery . And why may not that quality be in a Water which is mixed with divers Mineralls and kinds of earth , which is in herbs , roots , fruits and liquors ? S. Augustine speaketh of a Well in Egypt , in which burning Torches are quenched , and being before quenched , are lighted . Among the Garamants is a Well so cold in the day , that no man can abide to drink of it : in the night so hot , that none can abide to feel it . It is incredible that is written of a Well in Sicilia , whereof if Thieves did drink , they were made blind . In Idumea was a Well that one quarter of a year was troubled and muddy , the next quarter bloody , the third green and the fourth cleer . Seneca writeth of another Well that was six hours full and running over , and six hours decreasing and empty : perchance because it ebbed and flowed with the Sea or some great River that was neer it . In the Hill Anthracius is said to be a Well , which when it is full , signifieth a fruitfull Year : when it is scarce and empty , a barren and dear Year . The sufficiency of moisture maketh fertility , as the want causeth the contrary . Men say there is a River in Hungary , in which Iron is turned into Copper : which may well be , seeing Inke in which is but smal Coperas , and artificially mixed of Iron , doth counterfeit Copper in colour . In this stream may be much Copperas , and that is naturally mixed . Both Seneca and Theophrastus witness that waters there be , which within a certain space , being drunk of sheep , ( as Seneca saith ) or of birds ( as Theophrastus will have it ) changeth their colours from black to white , and from white to black . Vitruvius writeth , that in Arcadia is a Water called Nonacrinis , which no Vessel of Silver , Brasse , or Iron can hold , but it breaketh in peices , and nothing but a Mules hoof will hold it and contain it . In Illyria , Garments that are holden over a most cold Well , are kindled and set on fire . In the Isle of Andros , where the Temple of Bacchus stood , is a Well , that the fifth day of January flowed wine . Isidore saith , there is a Well in Italy , that healeth the wounds of the eyes . In the Isle of Chios is a Well that maketh men dull-witted that drink thereof . There is another , that causeth men to abhor lust . Lechnus , a Spring of Arcadia , is good against abortions . In Sicilia are two Springs , of which one maketh a woman fruitful , and the other barren . In Sardinia be hot Wells , that heale sore eyes . In an Isle of Pontus , the River Astares overfloweth the fields , in which whatsoever sheep be fed , doe alwaies give black milke . In Aethiopia is a Lake , whose water is like oyle . Also many Springs of Oyl have broken forth of the Earth , which commeth of the viscosity or fatnesse of the same earth . The Lake Clitory in Italy , maketh men that drink of it , to abhor wine . The Lake Pentasium ( as Solinus saith ) is deadly to Serpents , and wholsome to men . Seneca writeth of certain Lakes that will bear men which cannot swim . And that in Syria is a Lake , in which bricks do swim , and no heavy thing will sinke . It is said , that the River Rhene in Germany will drown bastard Children that be cast in it , but drive aland them that be lawfully begotten . The River in Hypanis in Sythia , every day brings forth little bladders , out of which flyes do come that die that same night . Matrona . the River of Germany , as the common people saie , never passeth day but he taketh some prey . Of the Sea. THe Sea , in this treatise hath place as a mixed substance : for else the element of Waters being simple , were not here to be spoken of . The Sea is the naturall place of the Waters , into which all Rivers and other Waters are received at the length . And here it is to be understood , that the very proper and naturall place of the water , were to cover all the Earth , for so be the elements placed : the Earth lowest , and round about the Earth the Water , about the Water , the Air , and about the Ayr , the fire . But God the most mighty and wise creator of all things , that the Earth might in some parts be inhabited of men and beasts , commanded the Waters to be gathered into one place , that the dry land might appeare , and called the dry land Earth , and the gathering of Waters he called Seas . In the Sea are these two things to be considered ; the saltnesse , and the ebbing and flowing . Of the saltnesse of the Sea. THe saltnesse of the Sea , according to Aristotles mind is caused by the Sun , that draweth from it all thin and sweet Vapors to make raine , leaving the rest as the setling or bottome , which is salt . But men of our time , peradventure more truely , doe not take this for the only and sufficent cause to make so great a quantity of water salt , but say , that the Sea , by Gods wisdom ; is gathered into such valleyes of the Earth , as were otherwise barren and unfruitfull ; such Earths are salt , the Sea Water then mixed with that Earth , must needs be Salt ; else Rivers by Aristotles mind , should be salt as well as the Sea. The Reader may choose which opinion is most probable . Of the ebbing and flowing . THe ebbing and flowing of the Sea , as Aristotle sermeth to teach , is by reason of Exhalations that be under the Water , which driveth it to and fro , according to contrary bounds and limits , as upward and downeward , wide and narrow , deepe and shallow . This opinion of Aristotle also , as more subtil then true , experience teacheth men to mislike , and to ascribe the cause of ebbing and flowing , to the course of the Moone , which ruleth over moysture as the Sunne doth over heat : for from the new Moone to the full , all humors do encrease ; and from the full to the new Moone decrease againe . Also , the very true time of the ebbing and flowing may be known by the course of the Moone , with whom , as the Lady of moysture , we will close up the fourth book of m●yst and watery impressions . The fifth Book . Of earthly Meteors , or bodies perfect●y mixed . THis last Treatise containeth such bodies whose chiefe matter is the earth , and are called perfectly mixed , because they are not easily resolved into the chief matter whereof they are generated . These are divided into four Kinds . The first be divers sorts of Earth : The second be Liquors concrete : The third be Metalls and Metallikes : The fourth be Stones . This division is not altogether perfect , both for that there be many of these Minerals which partake of two kinds , and also for that the names of these kinds may be said of others . Yet minding as plainly as can be , to declare the things themselves ; the controversie and cavillation of names , shall not greatly trouble us , especially seeing we pretend not to teach Philosophers , but such as need a ruder and plainer instruction . They may therefore be content with this division , which shall not serve them to dispute of these matters , but to understand the truth of these things that they desire . Of these foure therefore we will speak orderly and generally , not minding to treat of every particular kind ( for that were infinite ) but to open such universall causes , as they which have wit may learn ( if they list ) to apply unto all particulars . Of Earths . THe Earth is an element , one of the four , cold and dry , most gross and solid , most heavy and weighty , the lowest of all other in place . When I say an Element , I meane a simple body uncompounded . This Earth is no Meteor , but as it was shewed in the water , to the end there should be generation of things . There is no Element that we have which is pure and simple , but all are mixed and compound . Our fire is grosse and compound , so is our aire , our water , and our earth : but the earth notably and above the rest , is mixed . For the pure and naturall Earth is dry and cold ; but we see much to be moist , and much to be hot . The natural earth is black of colour : but we see many Earths white , many yellow , and many red . So that first , the greatest part of the Earth is mixed with water , that maketh it to cleave together , with aire and some fire , which make an oylie , fat or clammy earth , as is clay made , &c. Another great part is dried , not into the naturall drinesse of the first quality , but as a thing once mixed , and after dryed , either by cold , as sand , gravell , &c. or else by heat , as chalke , oaker , &c. And yet somewhat more plainly and particularly to discourse upon these causes , admitting the natural colour of the Earth to be black , of the water to be blue , of the aire to be white , and of the fire to be ruddy , it followeth , that upon the mixtion of these colours , or chiefe domination of them , all things have their colour . The grosse substance of the Earth therefore being diversly mixed with other Elements , and those mixtures again being eftsoones altered by divers and sometime contrary qualities , hath brought forth so many kinds of earth , as clay , marble , chalke , sand , gravell , &c. Clay is mixed with fat moysture , taking his Colour of the mixture with red from white ; but being cold , it is not so fruitful as Marble , which is not alwaies so moist as it . Chalke is an Earth by heat concocted , after divers mixtions , and dried up . Oker , both yellow and red , with such like , are of the same nature , with mixtion of red , more or lesse . Sand and gravell , are dryed Earths , as it were frozen by cold : gravell is grosse and apparent ; sand , though it be finer , is of the same generation , consisting of many small bodies , which are congealed into stones . Sand seemeth to be clay dryed by cold , and clotted together into small stones ; whereof some are thorow-shining , which were the moist parts ; the thick were of the grosse part : the same is gravell , but of greater stones consisting . The like judgment is to be given of all other kinds of Earth , whose generation by the similitude of these will not be very hard to find out . They that list to know the divers kindes of Earths , must have recourse to Plinius , Cardanus , and other Writers , that recite a great number of them : but these are the chiefe and most common kindes . Of Liquors concrete . WE take not liquors concrete so largely as the word doth signifie , for then should we comprehend both the other kinds following . But only those liquors , called in Lattine Succi , which are as it were middle betweene metalls and stone , of which , some being fat and oyly , doe burne as Brimstone , Sea-coles , Jet , bitumen , &c. and the kinds of all these . Othersome do not burne , as Salt , Allum , Copperas Saltpeeter , &c. and the kinds of these . Of the first sort , which are generated of Earthy and Airy Vapors , Fumes and Exhalations , the chief and most notable is Brimstone , which seemeth to be the matter of all dry and hot qualities that are in Earthly Meteors . The rest are generated of such like Vapors as Brimstone is , but then they be diversly mixed : as the coles have much Earth mixed with Brimstone ; Jet seemeth to be all one but better concocted then coles . Of Amber is great contention , whether it be a minerall , or the sperme of a Whale : for it is found in the Sea , cast upon the shore . Now the Whales seed being of the very same qualities , is taken more and lesse concrete of divers hardness ; some almost as hard as Amber : some softer , and some liquid : yet Cardan plainly defineth , that Amber is a Mineral . Whether he have reason or experience , contrary to the vulgar opinion , let them consider that list to contend . These Minerals that will resolve with fire , it is apparent , that they were concrete with cold : in that they burnt , it is manifest , they have a fat and clammy substance mixed with them , as the other kind hath not , which will not resolve so well with fire as with Water ; which be salt , copperas , saltpeeters , &c. These burne not , being watery , Earthy , and not fat , unctuous , nor clammy . These be of divers colours , black , as Coles , and Jett , because there is much Earthy substance mixed with their sulphurous matter . Some be sheere , as Salt , and Allome , having a substance Watery dryed , and concrete . Copperas is greene , because it hath much cold matter that is blue , mixed with it . Salt , the most common and necessary of all these liquors concrete , that be moist and not fatty , hath two manner of generations ; one natural , and the other artificial . The natural generation is when it is first generated in the Earth ; after commeth the water of the Sea , and is infected with it ; out of which the Salt is againe artificially gathered . Of these liquors concrete , be those strange wel● and springs infected , of which was spoken in the latter end of the fourth book . Most notably Brimstone causeth the hot Bathes , and burneth in Aetna of Sicilia , and Vesuvius of Italy , casting up the Pumice stones , of which is no place here to treat . Of Metals . MEtals be substances perfectly mixed , that will melt with heat and be brought into all manner of fashions that a man will. Of these the Alchymists say there be Seven kinds to answer to the Seven Planets ; Gold , Silver , Copper , Tinne , Lead , Iron , and Quick-silver that they call Mercury . But saving their Authority , Quick-silver is no more a Metal then Brimstone , which is as necessary to the generation of Metal as Quick-silver is . For they all agree , that all Metals are generated of Sulphur , that is Brimstone , which because it is hot they call the father ; and Mercury , that is Quick-silver , which because it is moist , they call the mother : so by as good reason may they call Brimstone a Metall as Mercury . Then there remaineth but Six perfect Metals ; Gold , Silver , Copper , Tinne , Lead and Iron . Of Gold. THat most unprofitable and hurtfull of all Metals , Gold which most men dispraise , and yet all men would have , is of all other Metals the rarest : it is only perfect , the rest are corruptible . Gold never corrupteth by rust , because it is pure from poysonous infection , and most solid , that it receiveth not the Air into it which causeth all things to corrupt . It is perfectly concocted with sufficient heat and mixture of Sulphur : all other Metals either are not so well concocted , or else they have not the due quantity of Brimstone . This opinion hath also place among the Alchymists , that because Nature in all her Works seeketh the best End , she intendeth of all Metals to make Gold ; but being lett , either for want of good mixture , or good concoction , she bringeth forth other Metals , indeed not so precious , but much more profitable ; and the less precious , the more profitable : for there is more use to the necessities of mans life in Iron and Lead , then in Gold and Silver ; but either the beauty or the perfection , or at least the rareness of Gold and Silver have obtained the estimation of all men , so that for them is sold all manner of things , holy and profane , bodily and spiritual . What paines do not men take to win Gold ? Every man hath one way or other to hunt after it : but the Alchymist despising all other ways as slow , unnatural and unprofitable , laboureth either to help Nature in her work , as of unperfect Metals to make perfect , or else to force Nature to his purpose by his Quintessences and Elixars , so that whatby purging , what by concocting , what by mixing of Sulphur and Quick-silver and much other like stuff , at length he turneth the wrong side of his gown outward , all the teeth out of his head , and his body from health to a Palsey , and then he is a Philosopher , and so he will be called . Of Silver . SIlver the most pure Metal next unto Gold , hath indifferent good concoction in the Earth , but it wanteth sufficient heat in the mixture that maketh it pale . It is found ( as they say ) running into divers veins , as all other Metals be , but this most specially , after the shape and fashion of a tree lieing along with a body or stock , of proportion like to the body of a tree , also with armes● , branches , leaves and fruits . This Metal Silver lacketh sufficient heat , and therefore commeth neither to the colour , solidity nor perfection of Gold , and is generated in cold countries , neer unto the North and South Poles , in so great quantity , that the Husbandmen when they plow their ground , turn up silver among he clods in their daily labours , which they do hide and conceal , least the greedy Princes for Coveteousness of the Mettal , should overturn and destroy their land . The Gold Mines are contrariwise most found in the hot Countries of India and Aethiopia , because in them is sufficient of heat for that unhappy generation . This Silver also the Alchymists would fain make by Ai● ; but Mercury the chief Master of the Work , is so subtile and so sly , that nothing can hold him , nothing can kill him : for if the glass be not very thick , he will soon break out of prison , and so there is nothing left . Of Copper . COpper in colour comming neerest to Gold , being not so solid nor massy ( for of all Metal Gold is the heavyest ) giveth way to Corruption , being infected with that green Mineral Copperas . Hereof be divers kindes , Brass , Latin and such like , which differ in digestion ; the Copper being purest , is of best digestion and neerest unto Gold : and so the rest in like degrees . Copper is most like Silver in the weight and in the hammering : wherefore the Alchymists have learned to make it white , that it deceiveth mens sight and handling : but the Gold miths do easily try it , and by the taste of counterfeit Silver make Copper again . Copper or Brass doth always grow neer to the Mine of Copperas , which running with it in the digestion or natural concoction , hindereth it of perfection , maketh it to stink , and to be eaten of a green rust . Much adoe the Alchymists have to tu●n it into Gold , if it might be : they dispute very reasonably and conclude almost necessarily in their Talk , that it may be converted into Gold as a body that wanteth little of perfection , which may be easily added unto it : but in conclusion of the work , it is an harder matter to bring to pass , then it was to purpose , before they had done it , to build an Abbey at every Miles end upon Salisbury Plain , as one was minded . Of Tinne . TInne whereof great plenty groweth in the West parts of England , in beauty and colour commeth neerest to Silver , and of Silver wanteth nothing but solidity and hardness : for Tinne is raw and undigested metall , also very porose and compact , which causeth it to crash when it is broken or bitten : so it faileth of heat in the commixtion , and also sufficient digestion in the Earth : otherwise it is a fair and profitable metall , to serve the use of them unto whom Silver and Gold are not so plentifull . Of Lead . LEad also found in great abundance within this Realm , is a raw and undigested metall as Tinne is , but yet of better digestion then commixtion : for it is mixed with a gross earthy substance , which maketh it to be in colour so black and so fowl to corrupt : so that of the same Fumes and Exhalations ( which if they had been pure and well digested , if the place and matter would have suffered should have ben concrete into Silver ) for lack of the same , Lead is generated , which comming plentifully , doth better service then Silver . Of Iron . IRon the most necessary and profitable of all other metals ( and yet as ill used of many as any other ) is generated of such substance as Silver is , but mixed with a red Mineral which ●ateth it with red rust , and also being of too extreame digestion , passing ●ll other metals in hardness . And as other metals to the perfection of Silver want sufficient concoction , whereby ●hey come not to the same hardness : ●o Iron passeth and exceedeth Silver in ●mmoderate digestion . But though it ●ome not to the perfection of Silver , God forbid that all Iron had been tur●ed into Silver : for then we should ●ore have missed it then silver or gold , ●e want of which would hinder us ●othing at all . Of Quick-silver . THough Quick-silver be no metal , yet because it is the mother of all metals , something is here to be spoken of it . There be divers and sundry opinions , both of the generation and also the qualities of it , which make the generation hard to find out . For if the quality were certainly agreed upon , there were an easier way found to try out the generation . Some affirm that it is exceeding hot , and that they would prove by the swift peircing thereof into other things that be porose . Others say it is exceeding cold , and that they prove by the exceeding weight of it . As for the peircing , they say it is caused of the exceeding moistness , of which quality both parts d● grant that it is . Concerning the generation , some have said that it is pur● and Elemental water : some again have thought that it droppeth out o● heaven , and is a part of the heavenl● stance . And others say that it is generated in the Clouds , and falleth down in the feilds in a Circle , on those round Circles which are seen in many feilds , that ignorant People affirm to be the rings of the Fairies dances . It is certain that Quick-silver hath divers times faln out of the Clouds , as we have declared in the Treatise of Wonderfull and Marvellous Raine : but whether it so fall in ●ircles it is doubtfull . The most probable opinion is , that it is generated of moyst Vapors of the Earth , coacted by cold , much like to Water , as Brimstone is of hot fumes , coacted by cold , much like to fire . And thus much of metals . Of Stones . STones , the fourth kind of Earthly mixed bodies have two manner of generations , by most contrary qualities for heat doth harden moist bodies into stones ; and we see that , clay , it maketh exceeding hard brick . Also the Thunderbolts in the clouds are generated by heat , as before hath been shewed . But cold doth by congealing , generate many more stones then heat doth ; for the most part of all the stones that are digged out of the Earth , are generated by cold , which is able to convert any other kind of mixed substance into stone , as hath beene partly shewed in the nature of wels and springs , of which , there be some in England , which by their cold , turne wood , or any like thing into stones . I have seene a peece of rotten wood , which to sight was very light , and like wood , but in handling , a very stone that was taken out of such a Wel. Also of other things taken out of the Earth , turned into stones , I have seene and found my selfe , fl●●s ; with head and wings , very hard stones ; also , I have seen a heart , a birds tongue , a beasts stone , a peare , a plumme , and divers other things turned into hard stones . Of divers kinds of stones . STones may first be divided into rude and beautifull : the rude containe those great Rocks , which are generated by many small parts ioyned together , and the common pibble stones that be found every where in the Earth , among gravell , and on the shore of the Sea , or bancks of the Rivers . These are generated of grosse and Earthly humours , congealed by cold : and because they be neither faire of colour , nor thorow shining , and also common , they are contemptible . The faire or beautifull stones , be either great or small . The great be as marble of divers kinds and colours , alablaster , and such like , which being hard and well concocted , may be polished and become beautifull . Their colour is as they are mixed , being uncongeled , so is their purenesse . The small are more precious , and they be either thick or pellucide . The thick be neither so faire nor so precious , as the Achates , the Tasper , Prassios , &c. These consisting of a pure matter , and not very watery , are congealed into such stones . The clear stones be liquore concrete , as the Diamond , the Saphir , the Emerald , &c. they are praised for their greatnesse , hardnesse , clearnesse , and faire colours , of which enough hath bin spoken , saving that some be of opinion , that these be generated by heat , becaus the best are found in hot countries , in the East , and in the South . Answer may be made , that the hotter the Air is , the colder is the Earth : so that reason is of small force . Of the vertue of Stones . SOme perchance , would looke that we should make a long discourse of the vertue of stones , and would be well content that we should treat of divers properties of gemmes and precious stones , which matter though it be out of our purpose ( which considereth only the generation ) yet seeing it is not out of their expectation , some thing briefly , and yet sufficiently shall be said of the vertue of stones . That vertue that is ascribed unto them , is either Natural or Magical . Naturall vertue , is either that which is known to have a natural cause , or a natural effect , as the Magnes or Loadstone to draw Iron , which is by a simitude of nature , & such an appetite as is between the Male and the Female . Also , the said Magnes moveth toward the North , and as some say , there is another kind found in the South , that draweth toward the South . They say , that there are great hils of this stone in the North and South , which maketh it look that way . Others bring a Mathematicall reason , which because it is more curious then can be understood of the common sort , not exercised in Geometry , I omit . The Jet and Amber draw hairs , chaffe , and like light matter , but being before chafed , for heat is attractive . Also the precious Stone called Astroites , moveth it self in Vinegar , the sharpnesse of the Vineger peircing it , and the aire excluded driving it forward . These vertues because I have seen , I have set for an example ; generally all other like naturall vertues , proceed of like naturall causes , which by their effect , the ingenious must seek to find out . As for Magical Vertues , they be they which are grounded on no reason , or natural cause ; which if they take effect , it is rather of the superstition and credulity of him that useth them , then of the vertue of the stones . As that an Emerald encreaseth love , a Saphir favour , a Diamond strength , and such like vertues , of which Alberius in his Age , surnamed the Great , took paines to write a Book , which I suppose to be Englished . To conclude with the cause why Stones melt not , as Metalls do , may be gathered by that which hath been said before , because they are congealed past that degree , and also because there is left in them no unctuous or clammy matter . Let this suffice for Stones ; and and so the whole purpose is at an end . OBSERVATIONS On Dr. F. his BOOKE OF Meteors . By F. W. LONDON , Printed for William Leake at the Crown in Fleet-street . CHAP. I. Of the Earth . IT is a great Question amongst Philosophers , Whether the External and Visible Riches and Plenty which groweth and springeth on the face of the Earth : or the Internal and Hidden Treasure be more precious and valuable ? Flowers and Fruits , Corn and Cattel , and all other external terrestrial Births are of most rare and exquisite use for mankind : but the Earth is an Element not only beautified without , but most richly stored within with great Varieties of admirable Creatures , both pleasant , rare and profitable for humane Content and Conservation . From this very Consideration the Philosophers of Old reckoned and esteemed the Earth as the first and most antient of all the Gods , and so stiled her * The Grandmother or Mother of all the Gods. And the Heashens did not only honor the Earth as a Mother , but did adore her as a Goddess , giving her the names of Ops , Cibele , Rhea , Proserpina , Vesta , Ceres , and other Appellations to signify the diversities and several effects and vertues which she produced . The Earth was called Ops , which signifyeth Aid , because she affordeth aid and comfort to all Creatures inhabitant on her : And Pausanias reports that neer the River Crasside in Greece , there stood a little Temple dedicated to the Earth , wherein she was adored Dea largi pectoris as the Goddess of the open and large brest , freely feeding all her Children which in numerous companies were ranged by her . Her Robe was rich aud glorious , embroidered with the most pleasant flowers of all colours : and she was adorn'd with a Mantle of Tissue whose ground was a beautifull Green , signifying her great Plenty of all things wherewith Man-kind might be affected , as most valuable and precious ; and such are her rich Mines of Gold , Silver , Copper , Brasse , and Iron : or yet more highly priz'd Commodities , as precious Stones , and rare rich Gems of all kinds . CHAP. 2. Of Metalls . THe visible beauty of the Earth is obvious to every eye , which is not the subject here in hand : Her abstruse and hidden riches , Preciosa periculaterrae , as Boetius calls them ; her precious Metalls and Mines , which force men to be so bold and ingenious , are the matter of this Discourse : These Aristotle calls Corpora perfectè mixta , inanimate bodies of compleat mixture , made up of Sulphur and Quick-silver , the veines of the Earth being composed of a fit temper for such production : Some Philosophers make the 〈◊〉 of Metallum , from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which signifies a change effected in the Subterranean Veines with long labour and much difficulty . Some Naturalists are more short , and seem more plain ; affirming , That Metalls is that which is plyable by the hammer , and hard : Stones are hard , but not plyable , and Wax and Mud are plyable , but not hard . CHAP. 3. Of the number of Metalls . MEtalls are seven in number , as the Planets are ; Gold , Silver , Amber , Iron , Lead , Brasse , Copper . Gold presenteth the Sun , Silver the Moon , Amber called Electrum Mercury , Iron Mars , Lead Saturn , Brasse Venus , and Copper Jupiter ; or else the seven may be distinguished thus : All Metall is perfect , soft and pure as Gold ; or it is pure and hard as Silver ; or it is hard and impure as Iron ; or it is soft and impure as Lead : And for Amber , it is compounded of Gold and Silver , as Cyprus Copper is made of Brasse and Iron , containing an equall substance of Brasse and Iron , which causeth that too much concocted , and high tincted is easily changed into Brass , and rechanged againe into Copper . CHAP , 4. Of Gold. GOld is Metallnm puriffimum , the purest Metall of all others ; and nature never took delight to make a more perfect elementary substance then Gold is ; and therefore in price and estimation , is far above all other riches . The Composition of Gold is proportioned in equall quality , fitly Correspondent in the symmetry of the elements which compound it ; it is even in the Originals so purified already , as are the simple & pure Elements , in such sort , that by their conjunction together in equall power , there is engendred so delicate and perfect a mixture of indissoluble union , composing an accord so faithfully , that there is made thereby an incorruptible Past , which is permanent to all eternity , in the excellency and goodnesse thereof ; wherefore Gold cannot be vanquished by injury of time and antiquity ; neither can contain in it felte , nor support any excre●●ncy and superfluity of Rust ; for though it be put into the water or fire , and there remain a long space ; yet it is never stained , nor accepteth it any other quality but what is Naturall . Nor yet doth Gold fail any whit , which is a sole priviledge belonging to this royall Metall , all other being subject to alteration and corruption , for though Gold be drawn into the smallest wire , and be extenuated as fine as the threds in the Spiders wed ; and though it be buried in the most piercing medicaments as are Sublimatum , Verdegrease , Salt , Venegar , and that it remain three thousand years therein , it will not for all that be corrupted , but rather the more refined , provided the Gold be perfect , and not sophisticated and false . CHAP. 5. Where Gold is found . GOld is found in divers manners , to wit , mixt with Sand as in Bohemia : on the shore-side amongst the water neer to Goldborough & Risegrond ; and amongst the stones in mountaines , as in Calecut , and in the Indies . The Generation of Gold is usually on the tops of Mountaines , because that there in the highest places the Sun doth more easily purifie that which retaineth too much earthiness in it : and when the Raine and Torrents do flow downe , they carry the Gold downe with them to the foot thereof , where it is gathered amongst the sand , or else in waters neer thereunto , whether it is driven by the violence of floods , except the Ground perhaps open with those inundations , and the Gold fall into the gaping jaws of the Earth , and so stick there . Now it is observable , that that which is found in the entrance of the Mine , is not the purest , but is as an earnest to invite to farther labour and pains . That which is found in Waters and Rivers is fished for , and is in form of little Grains : In Rocks and Mountains it is taken out by delving and digging . And there be three sorts of Mines , some are called Pendent , some Jacent , and some Oblique and turning : Pendent are those which are found in the superficies and tops of Mountains : Jacent are low , and lie in plain fields : Oblique have a cross Course , whether it be to that which is Pendent , or Jacent , all whereof is driven by Rivers into the next floods . CHAP. 6. Of Silver . THe most noble amongst Metalls next to Gold , is Silver ; for though Copper in colour , and Lead in waight do nearest approach unto Gold ; yet in Tenuity of substance , in pureness and fastnesse , Silver is so like unto it , that good silver may be rightly said to be imperfect Gold in substance ; sailing in colour , and that by succession of time , it is sometimes changed into Gold , as in many years space Lead turneth into Silver . The Mines of Silver are more ordinary then Mines of Gold ; and it is usually engendred in four manners , to wit , either in the Earth , or in Brass , or in Lead , or in Stones , which being purged and melted , yeeld some quantity of Silver . In the Mountain called Mons Regius , stones retain very much Silver , which being put in the fire , there is found in every pound of silver that runneth out of them , half an ounce of Gold at least . Silver is many times found to be mixed with Copper , as in Alsaria , near to the Rhine in the Mountains of S. Anne , and in Messein . When Silver is separated from Lead , it leaveth a scum which is called Lithargyrium , which is a kind of impure Lead . CHAP. 7. Of Quick-silver . QUick-silver is called Materia Metallaris , the matter of the Metalls ; and though it have the name of Silver , yet in nature it approacheth nearer to Gold ; for it is like unto it in Tenuity and weight , and to Silver onely in colour . And notwithstanding the opinions of many Chymists , Quick-silver is not a Metall , but a Water condensate , not by heat ( for it is not hardned ) nor by cold ( for then it would be a stone or metall ) but by some other terrestriall rare and pure portion , whereby it commeth to be weighty and cold , splendent and liquide , and is therefore ranked amongst those metalline substances which differ but little from water ; and it is common in experience , that the Mountains wherein Quick-silver is found , are very green and full of fountains . CHAP. 8. Of Electrum or Amber . MAny Authors , Philosophers , and Chymists , disagree in their opinions and discourse of Amber ; some reckon Amber amongst plyable and hard metalline substances ; others will not acknowledge it but to be but the gum of a Tree producing Rosin which is common in Arabia . Philemon writeth , that in two places of Scythia , Amber is digged out of the ground like a kind of stone , and in one place it is white , and in another it is yellow ; to omit this Argument , and to agree with those who allow Amber to be a Metall , is most consonant to reason : The nature and property of it is a mean betwixt Gold and Silver , and such is the true and naturall Amber : as for that which is used for Beads , it is but artificiall . Amber partaketh more of Gold then Silver , because it is more pure , & more apt to be wrought ; for if it consist more of Silver , it could not endure the forge and hammer . Vessels are made of Amber , some for beautie , some for profit : and if composed of true and good Amber , they will discover poysons by cracking , and making signs of an Arch within : for when the rare humidity thereof commeth to be consumed by the force of venome , it cracketh , and the colour changing in the Vessel , it seemeth in stead of the great splendor thereof , there doth a kind of stain represent it selfe like unto an Arch. Now that this Metall is more rare , is ignorance that knoweth not the vertue ; or avarice , that greedily thirsteth after Gold and gaine . CHAP. 9. Of Iron . IRon is taken out of the Earth , and to make it Malleable , the mass thereof is laid to drie in the Sun ; and that which is Earthy , doth soften and moulder with the Rain , as that which is moist doth melt with the Sun ; which as the venome of it is consumed in the Furnace by the fire , by how much more it is purged in the fire , by so much the more it is pure in its goodnesse , in such sort as that which is earthy , doth at last turn to schales and dross , and the most subtil part thereof doth convert into Steel . CHAP. 10. Of Steel . THe common Steel is artificiall extracted Iron , Iron more excellently purged , and a little Marble added thereunto ; but in many places there is Naturall Steel , namely in Persia very good , and in the Chaldean Isle , and neer Damascus , whereof the best Cemiters and Faulchions in the world are made , which cut so well , that there is no Rasor , be it never so well steeled and tempered , that hath a more keene and sharper edge ; for this cause some say , That there are some kinds of Steel and Iron so excellent , that weight for weight , they are esteemed of greater price then Gold. CHAP. 11. Of Lead . LEad is a gross dull Metall , Procreated and Consistent of more impure Quicksilver , and more feculent and crass Sulphur ; it least indures the fire of any Metall , and therefore soonest melteth . Galen saith , Lead buryed long in moist subterranean Caves and holes , increaseth in magnitude and weight , and therefore is a Cover ( if wel considered ) lesse proper for any buildings but where the Roofs are of infinite strength . There be divers kinds of Lead , some red , some white , some balck , and a fourth sort of a m●an quality betwixt white and black , found in the mountaines of Bohemia . The Ore of Lead is melted in furnaces , and is let runne through pipes out of the furnace , whether the Workmen will. Lead is an incongruent and malignant Metal to all others ; and if but one ounce be mixt incorporated with one hundered ounces of Silver or Gold , the mixture will reader the whole mass brittle and fragil ; and so it will be in all like proportions . CHAP. 12. Of Tinne . TIn is a white Metal somwhat like to Silver for i●s splendor & whiteness , and yet not much above Lead for its softnesse and porosity . And this is the difference betwixt Tinne and white Lead , that the one is ingendered where there is some Silver mine or veine , but the other is generated apart without the company of so rich a Neigbour . CHAP. 13. Of Brasse . BRass is a more impure Metal : which composed of much sulphurous matter , is more hot , light , and less pory , and so less subject to corruption and rust by reason of all moisture and humidity ( almost ) consumed in it . In times past , it was very usuall to make Shields and Bucklers , and Pike● , & Launces therof , as Homer reports how Menelaus pursued Paris with a brazen Launce . This Metal is proper for ●rumpets , because it maketh a great noise in Dorick musick , and inflameth men to Combat : That of Cyprus is harder , and therefore better then any other . CHAP. 14. Of Copper . COpper , or Orichalcum , is Latten , or as some call it as factitium , artificiall brass ; it represents with it a golden Complexion , but is somwhat more yellow then Gold ; some because of Copper , make two kinds of Brass , the one Natural , the other Artificial ; the best hath spots of shining Gold intermin gled ; and the Merchants tell us , that in Nova Hispania in America , a peice of it hath bin found of two hundered pound weight . The Artificial brass , commonly called Copper or Latten , is very ordinary ; and the most excellent is that which in foure pounds of brass , doth containe in it one pound of white Lead . Also when the white Lead is mixed to the eight part of brass , then is the Copper very good ; but it is base when mixed with black Lead : the use of Copper is chiefly for faire instruments , as Ordinance , Cauldrons , and such like , wherein it is more excellent then brass ; and it giveth no ill taste or smell to meat boyled in it . FINIS . The Table . OF the Earth in general , Chap. 1 page 159 Of Metalls , Chap. 2. p. 161 Of the number of Metalls , Chap. 3. p. 162 Of Gold , Chap. 4. p. 163 Where Gold is found , Ch. 5. p. 165 Of Silver , Ch. 6. p. 166 Of Quick-silver , Ch. 7. p. 167 Of Electrum or Amber , Ch. 8. p. 168 Of Iron , Ch. 9. p. 170 Of Steel , ibid. Of Lead , Ch. 11. p. 171 Of Tinne , Ch. 12. p. 172 Of Brasse , Ch. 13. p. 173 Of Copper , ibid. Printed or sold by William Leake , at the signe of the Crown in Fleetstreet between the two Temple Gates : These Bookes following . YOrk's Heraldry , Folio A Bible of a very faire large Roman letter , 4● Orlando Furioso , Folio Callis learned Readings on the Stat. 21. Hen. 8. Cap. 5. of Sewers . Perkins on the Laws of England . Wilkinsons Office of Sheriffs Persons Law. Mirrour of Justice . Topicks in the Laws of England Sken de significatione verbor● . Delaman's use of the Horizontal Quadrant . Wilby's 2 d set of Musick , 3 , 4 , , 5 , & 6 Parts . Corderius in English. Exercitatio Scholastica . Nyes Gunnery and Fire-works . Cato Major with Annotations . Mel Helliconium , by Alex. Ross. The History of Vienna and Paris . Lazarillo de Tormes two Parts . Posing of the Accidence . Man become guilty , by John Francis Senalt , and Englished by Henry Earl of Monmouth . The Ideot in 4 books . The life and Reign of Hen. the eighth , written by the L. Herbert . Aula , 〈◊〉 or the house of Light. The For● Royall of ● ly-Scriptures . by 1. H. ● A Tragedy of Christs Passion , written by the most learned Hugo Grotius , & Englished by Geo. Sands . Mathematical Recreations , with the generall Horologicall Ring , and the double Horizontall Dial , by William Outhtred . The Garden of Eden , or an Accurate description of all Flowers & Fruits now growing in England , with particular rules how to advance their Nature and Growth as well in Seeds and Herbs , as the secret ordering of Trees and Plants , by Sir Hugh Plat. Knight , the 2 d Edition enlarged . PLAYES . Hen. the Fourth . Philaster . The Wedding . The Hollander . Maids Tragedy . King and no King. The gratefull Servant . The strange Discovery . Othello the Moor of Venice ; The Merchant of Venice . Notes, typically marginal, from the original text Notes for div A40528-e1230 Aristot. The materiall cause . What be vapors , and what exhalations . What the middle region is , shall bee told afterward A generall rule . What Exhalations be . The efficient cause . What the regions of the aire be Notes for div A40528-e1890 Sparks of fire . Torches . Dancing Goats Shooting Starres . The Epicurians Opinion . Ps. 148 The greatnes of Starres A proofe of the Starres greatness Burning candles . Burning Beames and round pillars Burning Speares . Shields , Globes or Bowles . Lampes . Flying Dragons , or fire Drakes , Of Spires Fire scattered . Light that goeth before men , & followeth them in the night Helena , Castor , Pollux . Flames upon haires of men and beasts . Livius . Servius Tullius . Comets or blazing Starres ▪ The temper of the four quarters . The signification of Comets . Aristot. Apparitions . Colours in the Aire . Wide gaping of clouds in the Aire . Round opening in the Aire . Notes for div A40528-e3530 Winds . The second kind of winds . The third kind of Winde . The qualities of the winds and the four quarters of the world . The quality of middle wind . The profit of wind . Joh. 3. Psal. 104. Earthquakes . Divers kinds of Earthquakes . Twelve Cities overthrown with one Earthquake . Constantinople the chiefest City of Greece , now the Turks Palace . The second kind . The third kind . Earthquake on the Sea. Aristot. The fourth kind . New Islands in the Sea. Aristot. Seneca . Plinius . Plato . A wonderfull Earthquake . Africa , Europe , Asia , the three parts of the earth Maremediterraneum , because it goeth thorow the midst of the earth . Atlantis an Island . Senecca . Theron & Therea . Arist. Herodotus . Egypt sometime a gulph of the Sea. The signes of an earthquake . Thundering under the earth . Cato . Thunder . A similitude . Divers kinds of Thunders . Small Thunder , and the kinds thereof . Great thunder and the kinds whereof . How far thunder is heard . The profit of thunder Plutarchus T. Quincius Flaminius . Lightning . Fulgetrū . Coruscatio . Fulgur ▪ Fulmen . Fulgetrum . The colour of this Lightning . Coruscation . Fulgur . The lightning is not before the thunder , though it seeme so . Sight preventeth hearing . The thunder-bolt cast out of the clouds . Strongest things are most hurt of lightning . How deep a thunder-bolt goeth into the earth . Aristot. Seneca . Plinius . Day lightning . Money melted in mens Purses , and swords in Scabberds . Moyst lightning . Why it maketh black . Grosse lightning . The mmrvell of lightning . Lightning poysoneth . Seneca . Wine not running , the Vessels being broken . Lightning pur●eth a poysonous beast . A Snake breedeth no Worms Lightning openeth his eyes that sleepeth , and closeth his that waketh . Living things turn their face toward lightning . Garments burnt , the body unhurt . Lightning causeth blindnesse , swelling or Leprosie . Eutropius , Marcus Tullius Cicero . Apulia . The wounds of Lighting cold . Sea Calfe not hurt with lightning . Bayes and Box Trees seldome hurt with Lightning . The Eagle Jupiters harnesse-bearer . Storm winds . Whirlewinds . The troubles of whirlewinds . Fired whirlewinds . Circles about the Sunne , the Moone , and other Starres , Jupiter & Venus Planets . Circles in the water . The colours of circles . Circles at bout a candle . The fignes of these circles . Virgilius , Aratus , Poets . Signe of Frost . Signe of faite weather . Signe of tempest . Signe of raine . Ptolomeus Sign of faire weather . Signe of Snow . Aristotle . Antipho . Raynebow Possidonius A 〈◊〉 stone 〈…〉 A similitude . The similitude of the Rainebow . Rainbow of the Sun. Rainbow of the Moone . The white circle seed in the night pythagoras Anaxagoras Democri●●● Cardanus . Phaeton . Ovid. Me●a . Hebe . Apollo . Theophrastus . Diodorus . Possidonius . Zodiake . Aristotle . Sporades . Possidonius Plinius The breadth of this circles Beames or streames . Many Sunnes at once . Alexander the great . Darius . Many sm●l Sunnes like stars . Similitude . The signification of many Sunnes . Galba , Otho , and Vitellius . Many Moones . Plinius . Why other stars are not so represented . Objection . Syrius a great Star seen at noone in Summer . An answer . Wonderfull apparitions . Optice . Catoptrice Catoptrice . Horarius . Notes for div A40528-e8460 Clouds . Astristor . The height of the Clouds . Albertus Magnus . Mists . Empty oleuds . Of the colours of Clouds . Raine . Why rain water is not salt . Avicen . Salt raine . Bitter raine . The River Nilus . Seneca . Signes of Raine . Of Monstrous Raine . Worms & Frogs . Fishes . Milke . Blood. Flesh. Avicen . Stones . Brick . Wheat . Wooll . Quicksilver . Chalke . T. Livius . Iron . Avicen . Dew . Manna . Plinius . Arabia . Ladanum . Cusus . Bitter dew . Hoare frost . Aristot. Hayle . Snow . Original● of Christall . Nothing is empty . Fountaines . Brookes . Rivers . Astristot . Seneca . Lakes . Hot Baths . Tastes of waters . Aristotle . Well water used for Vineger . Bohemia . Paphlagonia . Marvelous waters . Clitumnus Propert. Boetia . Melas . Seneca . Libia Seneca . S. August . Garamants Sicilia . Idumea . Seneca . Anthracius Hungaria . Seneca . Theophrastus . Vitruvius . Arcadia . Nonacrinis . Illyria . Andros . Bacchus . Isidore . Chios . Lechnus . Sicilia . Sardinia . Pontus . Astares . Aethiopia . Clitory . Pentasium . Solinus . Syria . Rhene . Hypanis . Sythia . Matrona . The Sea. The naturall place of the water . Gen. 1. Aristot. Ebbing & flowing . Aristot. Notes for div A40528-e12270 Earthly bodies . Of Earths . Plinius . Cardanus . Aetna and Vesuvius . Metals Mercury . Gold. Why Gold rusteth not . The opinion of the Alcumists . Silver . Tinne . Lead . Iron . Quick-silver . Stones . Rockes . Pibble stones . Marble . Aehates . Jasper . Prassios . Diamond . Saphir . Emerald . The praise of precious Stones . The vertue of Stones . The vertue of Stones , either naturall or magicall , Magnes . Jet and Amber draweth chaffe . Astroites , a Stone moveth in vineger . Albertus Magnus , Notes for div A40528-e13640 * Ils l'appelloient lamere grand & la mere de dieux . Antoine du verdier En la Relligions de Pagens . Ops. 
A57666	----	The new planet no planet, or, The earth no wandring star, except in the wandring heads of Galileans here out of the principles of divinity, philosophy, astronomy, reason, and sense, the earth's immobility is asserted : the true sense of Scripture in this point, cleared : the fathers and philosophers vindicated : divers theologicall and philosophicall points handled, and Copernicus his opinion, as erroneous, ridiculous, and impious, fully refuted / by Alexander Rosse ; in answer to a discourse, that the earth may be a planet. Ross, Alexander, 1591-1654. 1646 Approx. 343 KB of XML-encoded text transcribed from 64 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2003-01 (EEBO-TCP Phase 1). A57666 Wing R1970 ESTC R3474 11790114 ocm 11790114 49171 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A57666) Transcribed from: (Early English Books Online ; image set 49171) Images scanned from microfilm: (Early English books, 1641-1700 ;547:9) The new planet no planet, or, The earth no wandring star, except in the wandring heads of Galileans here out of the principles of divinity, philosophy, astronomy, reason, and sense, the earth's immobility is asserted : the true sense of Scripture in this point, cleared : the fathers and philosophers vindicated : divers theologicall and philosophicall points handled, and Copernicus his opinion, as erroneous, ridiculous, and impious, fully refuted / by Alexander Rosse ; in answer to a discourse, that the earth may be a planet. Ross, Alexander, 1591-1654. [8], 118 p. Printed by J. Young and are to be sold by Mercy Meighen and Gabriel Bedell ..., London : 1646. Reproduction of original in Cambridge University Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. EEBO-TCP is a partnership between the Universities of Michigan and Oxford and the publisher ProQuest to create accurately transcribed and encoded texts based on the image sets published by ProQuest via their Early English Books Online (EEBO) database (http://eebo.chadwyck.com). The general aim of EEBO-TCP is to encode one copy (usually the first edition) of every monographic English-language title published between 1473 and 1700 available in EEBO. 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Keying and markup guidelines are available at the Text Creation Partnership web site . eng Astronomy -- England -- Early works to 1800. 2000-00 TCP Assigned for keying and markup 2001-06 SPi Global Keyed and coded from ProQuest page images 2002-08 Olivia Bottum Sampled and proofread 2002-08 Olivia Bottum Text and markup reviewed and edited 2002-10 pfs Batch review (QC) and XML conversion THE New PLANET no PLANET : OR , The EARTH no wandring STAR ; Except in the wandring heads of GALILEANS . HERE Out of the Principles of Divinity , Philosophy , Astronomy , Reason , and Sense , the Earth's immobility is asserted ; the true sense of Scripture in this point , cleared the Fathers and Philosophers vindicated ; divers Theologicall and Philosophicall points handled , AND COPERNICUS his Opinion , as erroneous , ridiculous , and impious , fully refuted . By ALEXANDER ROSSE . In answer to a Discourse , that the Earth may be a PLANET . LACTANT . do falsâ Sapientiâ lib. 3. cap. 24. Quid dicam de iis nescio , qui cum semel aberraverint , constanter in stultitia perseverant , & vanis vana defendunt , nisi quòd eos interdum puto , aut joci causâ philosophari , aut prudentes & scios mendacia defendenda suscipere , quasi ut ingenia sua in malis rebus exerceant vel ostentent . LONDON . Printed by I. Young , and are to be sold by Mercy Meighen , and Gabriel Bedell , next to the middle-Temple-gate . 1646. To the Right honourable GEORGE Lord BERKLEY , Baron of Berkley , &c. My Lord , THey who have been long at sea , when they come on shore , think that the Earth moveth as the Sea did , till their brains be settled ; even so these men who have been lately travelling in the new found world of the Moon , which swiftly moveth about the Earth , think when they come down hither , that it is the Earth which moveth : This false imagination I have endeavoured to remove in this Book , which now comes abroad under your Lordships Name ; the reason of my dedication is , because I understand by your Lordship , that the Gentleman , who came down a while agoe from the Moon , with newes of a late discovery there , is of this opinion ; and one who hath relation to your Lordship , which indeed I knew not till now , that the Book is almost printed : my other reason is , for that I am bound in a dutifull recognition of your Lordships respects to scholars in generall , and to me in particular ; which sheweth that not only are you noble by extraction , but by your affection also and disposition to learning , which is now so much slighted , yea vilified , by such as are either ignorant , or wicked ; the one slight learning , because they know it not , — ignoti nulla cupido ; and like the Fox in the Fable , disparage the grapes , because he could not reach them ; the other raile against learning , as the mad Africans do against the Sun ; and how can Owles and Bats love the light , which manifest their deformity ? Can theeves and cut-throats , whilst they are penetrating the works of darknesse , abide the light of a torch ? The infernall ghosts tremble to see any light , — trepdiant immisso lumine manes : But your Lordship , being de meliore luto , — knowes the worth of learning , and therefore loves it ; which that you may long know , love , and live , shall be the wish of Your Honours most humble servant to command , ALEXANDER ROSS . To the READER . GOod Reader , there is a namelesse man come down from the Moone , who brings us strange newes of a late discoverie ; to wit , of a world found there ; This man of the Moone goeth about to perswade us , in a booke which he hath set out , come lately to my hands ; that the world , ever since Adam , hath been in a dreame , in thinking that the heavens move , and the earth rests : He tells us another tale , to wit , that it is the earth that moveth , and the heavens stand still : He lieth in ambush , and from his darke lurking place , shoots abroad his arrowes ; so that we can no more see him , then if he were in the Moone still ; but it is a cowardly part to hide himselfe ; and from the cloud , in which he is wrapt , to let fly his darts against me , and that Book which a few yeares agoe I wrote in Latine , in confutation of this new phantasticall Chimaera . My case is like that of Volscus in the Poet , who knew not whence those darts came that killed Sulmo and Tagus , Saevit atrox Volscus , nec teli conspicit usquam Authorem , nec quo se ardens immittere possit . I might be thought , luctari cum larvis , to fight against shadowes , as AEneas did going down to hell . If I should make any reply to a namelesse disputer , but I am advised however to answer him , least he should sing ( iò triumphe ; ) and not to suffer by silence my reputation to be wounded , the truth prejudiced , and the Scriptures abused , with his idle glosses . Therefore here I present to thee the weaknesse and vanities of this mans conceits , as far as the shortnesse of time , and my other studies and affaires would permit me ; which I pray thee accept in good part , and so farewell . The PREFACE . THe title of this new book is a may be ( that the Earth may be a Planet ) but I say that may not be : For a Planet is a wandring starre , and the Earth is not a starre in its essence , nor a wanderer in its motion . And indeed you wrong our common mother , who so many thousand yeares hath been so quiet and stable , that now she should become a wonderer in her old age ; but if she may be a Planet , tell us whether she may be one of the seven Planets , who are called Errones in Latine , ( not for that they have an erroneous , but because they have a various motion ) or whether she may be an eighth Planet , that so wee may make up our week of eight dayes ; for why should not mother Earth have one day of the week , aswell as the other Planets , to carry her name ? And so let there be dies terrae , aswell as dies Solis , & Lunae , Earth day , aswell as Sunday , or Moonday ; and whereas the Planets are moved according to the motion of the spheares , you had done us a pleasure , if you had told us the spheare in which the Earth moveth : Againe , if the Earth be a Planet , and each Planet hath its period of time for finishing its course : Saturne 30. yeares , Iupiter 12. Mars 2 , &c. What is the time which you will allot to the Earth for the accomplishing of her annuall motion ? If it be true , that the lower the Planet is , the swifter it is in its annuall motion ; as the Moon in 27. dayes , and 8. houres , doth finish her course , which Saturne ends not but in 30. yeares space ; doubtlesse , this Earth-planet , being the lowest of all , must in a very short time expire its annuall race . Moreover , if the Earth be the eight Planet , Sol , who is the King of this planeticall Common-wealth , cannot have his throne in the midle , as Antiquity , and Truth too have placed hiw ; for hee shall have three on his one hand , and four on the other , and so cannot impart his light equally to all . And whereas every one of the Planets hath his office in this Reipublick ; to wit , Saturne the Counceller , Iupiter the Judge , Mars the Captaine , Venus the Steward , Mercury the Scribe or Chancellour , and the Moone the Messenger : Wee must needs finde out some office for the Earth , otherwise she will be counted idle , and none of the Planets . But that the Earth may be a Planet , is as true as that the Sun may be a burning stone , that there may be a man in the Moon , that there may be an infinite number of Suns and worlds , that the Stars and Planets may have had their first originall and being from the Earth , which have been the extravagant conceits of giddy headed Philosophers : But I remember what Aristotle saith of some may-bees or possibilities ; 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 that which may be , may not be , and never shall be , and so the Earth may be a Planet ; that is , it neither is , not ever shall be a Planet . But now let us leave your title , and examine the substance of your following Discourse . The CONTENTS of this Book . CHAPT . I. IN the Preface , and first Chapter , is shewed . 1. The vanity and falshood of this new opinion . 2. The Fathers concerning their judgement of the Antipodes cleared and vindicated , and the Philosophers condemned . 3. Job defended and explained . 4. Pythagoras deciphered , and his opinions condemned . 5. Some Pythgoreans touched and censured . Numa was not of this new opinion , nor Pythagorean . 6. This opinion hath few followers , and how condemned by the Colledge of Cardinals . 7. What is to be thought of those who have revolted from the truth of our opinion . 8. The Church , the Scripture , sense , and reason must be beleeved in this point of the earths stabilitie , &c. 9. This new opinion how and when an heresie . CHAP. II. 1. Wee must beleeve the Scripture , not our owne phansies . 2. The Scripture never patronizeth a lye or an errour , nor doth it apply it selfe to our capacity in naturall things , though it doth in supernaturall mysteries . 3. We must sticke to the literall sense , when the Scripture speaks of naturall things . 4. Some particular Scriptures vindicated from our adversaries false glosses , as namely , Psal. 19 of the Suns motion like a Gyant and Bride-groom , of the ends of heaven , and of his heat . Eccles. 1. of the Suns rising and setting . Jos. 12. of the Suns standing still , of the midst of heaven ; how over Gibeon , and how no day like that . Isa. 38. of the Suns returning ten degrees , of the greatnesse and meaning of this miracle ; neither known to the Gentiles . The testimony of Herodotus concerning this . CHAP. III. 1. The Scripture doth not speake according to vulgar opinion , when it calls the Moone a great light , for so it is . 2. Nor when it speakes of waters above the Heavens , for such there are . 3. Nor when it calls the Starres innumerable , for so they are . 4. Nor when it mentions the circumference of the b●as●n Sea to be thirty cubits , and the diameter tenne , for so it was . Why the lesser number is sometime omitted . 5. Nor in saying the earth is founded on the waters , which is true . 6. The right and left side of heaven how understood , and how the heaven is 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and of the Intelligences . 7. The Scripture speaketh properly in attributing understanding to the heart . The Galenists opinion discussed . 8. Of ova aspidum , and the Vipers egges , how understood . 9. The Aspe or Adder how hee stops his eare . 10. Of the North and South winde in Scripture . 11. The Sun shall be truely darkned , the Moon turned to blood , and the starres shall fall , &c. 12. Of the windes whence they come , &c. 13. The sea the onely cause of springs . 14. The thunder is truly Gods voice . 15. The 7. Stars . CHAP. IIII. 1. Many Philosophicall points are handled in Scripture . 2. The heavens how round in the opinion of the Fathers . 3. Wee must have a reverend esteem of the Fathers 4. How the seas not overflowing the land may be esteemed a miracle . 5. The works of Nature may be called miracles . CHAP. V. Divers Scriptures vindicated from false glosses : as , Eccles. 1. 4. by which is proved the earths immobility , and heavens motion . 2. How the earth is eternall and renewed . 3. The Scripture speaketh not plainly and ambiguously in the same place . 4. The Scripture useth Metaphors . 5 How the earth stands out of the water , 2 Pet. 3. 5. by which its immobilitie is proved 6. What is meant , 1 Chron. 16. 30. &c. by these words , The world is established , &c. 7. What is meant Psal. 90. 2. by the earth and the world . 8. How the heavens Prov. 3. 19. are established : and the Moon and Starres , Psal. 89. 37. &c. 9. How the heavens 2 Sam. 22. 8. bath foundations . 10. What are the pillars of heaven in Job 10. of the ends , sides , and corners of the earth in Scripture . 11. What is meant Isa. 51. 6. by the planting of the heavens . 12. How the earth is established . 13. What Job meanes by the earth moved out of its place . CHAP. VI. 1. The earth is in the middle and center of the world , and why . 2. Hell is in the center or middle of the earth . 3. The earth lowest and basest , how . 4. Every thing is made questionable by some . 5. Aristotle defended . 6. The earth is in the center , because in the midst of the equinoctiall Horizon , &c. 7. The imagination must be conformable to the things , not these to it ; the vanity of imagininary circles . 8. Astronomers reproved , and their vanity shewed , chiefly about the bignesse of the stars . 9. The earth is the least cirle : therefore the center , how understood . CHAP. VII . 1. The Starres have not their light because the Sun is in the center , nor hath the Sun lesse light being out of it . 2. Why the Earth in the center . 3. The Sun is not the center , because the Planets move about him . 4. The center is not the most excellent place , neither are the best things next it or in it . 5. There is an harmony amongst the Starres , though the Sun be not in the center . CHAP. VIII . 1. How the eye is deceived , and how not ; and that if the earth moved , we should see it . 2. Motion and rest how the objects of the eye , and of the common sense . 3. If the earth moved , the clouds would but seeme to move as well as the sunne . 4. How the eye can be deceived in the motion of a lucid body . 5. The naturall motion of the foundation cannot keep buildings from falling . 6. The heavens fitter for motion then the earth . 7. Rugged bodies not fittest for motion . 8. The sight hindred by the motion of the subject , medium , and object . 9. One simple body hath but one naturall motion , proved . 10. Essentiall properties more chiefly in the whole then in the parts , the earth is heavy in its owne place how , bignesse how a hinderance to motion , of the earths ineptitude to a swift motion . 11. The magneticall qualities of the earth , a fiction . 12. Similitudes no prooses ; the seas ebbing and flowing , what . 13. The whole earth moveth not , because the parts move not round . 14. Absurd phrases ; and the spots about the sunne , censured . 15. That the earth turnes about the moone is ridiculous . 16. Some observations to prove that the earth turnes about the clouds refuted . 17. Of a mixed motion , of the place , medium , and space . 18. Of the motion of comets . 19. My nine arguments defended . 1. That the earths motion would make it hot . 2. The aire purer . 3. A sound . 4. Heaven hath all things fit for motion . 5. Of similar parts and the whole . 6. The sunne is the heart of the world . 7. It workes by motion . 8. The earth is the firme foundation . 9. The authority of Divises ; the heaven called AEther ; the earth hath not two distinct motions . CHAP. IX . 1. The earth cannot be the cause of its owne motion . 2. The vastnesse and thicknesse of the heaven no hinderance to its motion . 3. The matter of the heavens and their smoothnesse no binderance to their motion . 4. Bignesse helps motion . 5. The heavens swistnesse illustrated by other motions . 6. The earth neither the finall nor efficient cause of its motion , the heaven sitter for motion , because greater , and more constant ; nature worketh not still the most compendious way , some idle similitudes refuted . 7. Bodies having the same properties have not alwayes the same motion ; motion belongs to the noblest creatures . 8. The smoothnesse , subtilty , and purity of bodies no hinderance to their motion ; the aire moves the water , the circular motion of the fire naturall how . 9. Of Intelligences how and why they move the heavens . 10. Magneticke vertue an idle conceit . CHAP. X. 1. The idle and uncertaine conceits of Astronomers concerning the celestiall bodies . 2. The appearances of the Sunne , and other Planets cannot be so well discerned by the earth if it did move . 3. The excellency of Divinity above Astronomy , and an exhorlation to the study of it . The new PLANET no PLANET . The CONTENTS . 1. The vanity and falshood of this new opinion . 2. The Fathers concerning their judgement of the Antipodes cleared and vindicated , and the Philosophers condemned . 4. Pythagoras deciphered , and his opinions condemned . 5. Some Pythagoreans touched and censured . Numa was not of this now opinion nor Pythagorean . 6. This opinion hath few followers , and how condemned by the Colledge of Cardinals . 7. What is to be thought of those who have revolted from the truth of our opinion . 8. The Church the Scripture , sense , and reason must be beleeved in this point of the earths stabilitie , &c. This new opinion how and when an heresie . CHAPT . I. I Had shewed how unreasonable it was , that an upstart novelty concerning the Earth's motion , should thrust out a truth of so long continuance and universality , as this of the Earth's immobility . You answer , That wee must not so doat upon antiquity , as to count that Canonicall , which is approved by the consent of the Ancients . To this I answer : 1. Make it appeare that your opinion of the Earth's motion is true , and ours false ; and we will prefer yours , though new . 2. If you can make it appeare that your opinion is any waies usefull or advantageous , wee will admit it . 3. Suppose that both your and our opinion were but conjecturall , and that there were but an equall probability in both ; yet you must not prefer , nor equall your opinion to ours , because we have antiquity and consent of all times , of all nations , of so many holy , wise , and learned men for us , which you want ; in this respect then , if both our opinions were put in the balance , yours will be found too light , though you should adde to the scale that heavie Prussian Copernicus . 4. Though there were no hurt in your opinion , yet wee may not entertaine it ; for the world is pestered with too many opinions already ; and a great many might be well spared . 5. But whereas your opinion is false , absurd , and dangerous , as we have partly shewed , and will shew afterwards , wee were mad to receive it ; having neither truth , reason , sense , consent , antiquity , or universality to countenance it . 6. That which you call the preserving of Philosophicall libertie , is indeed the loosing of the reines to exorbitant wits , to run headlong into every kinde of absurdity . 7. Wee doe not inslave our selves to the opinion of any one man , ( as you suppose we doe ) but we are of the opinion of all men , of all times , and nations . You inslave your selfe to one man , and is guilty of that which you accuse in us : Quis tulerit Gracchos ? 8. Wee condemne not your opinion because it is new , but because not true . A new falshood , a false novelty ; and such a new deformed brat is to be choaked in the infancy : Principiis obsta ; kill the Cockatrice in the egge . 9. You say it 's but a novelty in Philosophy , but I say it intrencheth upon Divinity : for Divinity tells us , that the standing of the sun , and moving of the earth are the miraculous workes of Gods supernaturall power : your new Philosophy tells us , that they are the ordinary workes of Nature ; and so this scope being granted , you may turn Divinity into naturall Philosophy , and confound the works of God , and of Nature . 10. You tell us , That Antiquity consists in the old age of the world , not in the youth of it . What Antiquity ? Of the world ? then you speak not properly , as you say you doe , but tautologically ; the worlds old age consists in its old age . If you mean that your opinion is not new , but old , because the world is old , you speak absurdly : for old opinions are so called , not because they were found out in the youth , or in the old age of the world , but because they have continued a long time in the world ; and so new opinions are new , though found out in the old age of the world . Opinions have no relation to the ages of the world , but to their owne continuance : Are you older then your great Grand-father , because the world is older now , than it was when hee lived ? 11. You are the fathers ( you say ) in such learning as may be increased by experiments and discoveries , and of more authority then former ages . Why doe you not tell us plainly , that you are fathers of learning , as well as in learning ? but indeed you are not the fathers of learning , you are onely fathers of your new discoveries and fresh experiments ; that is , of new , fond , and savourlesse phansies : and why you must be of more authority then former ages , I see no reason . Shall not Iuball , and Tuball-Cain , the inventors and fathers of their Arts , be of as great authority , as you that are the fathers of such mishapen monsters , though they lived in the infancy , and you in the old age of the world ? Why should I rather credit you in telling us of a world in the Moon , and of the Earth , that it is a planet , then those wise men of former ages , who never dreamt of such idle and ridiculous conceits ? You say , Truth is the daughter of time ; so say I , but errors , heresies , falshoods , are times daughters too . We see how fruitfull this later age of the world is of new and frivolous opinions . But how much are you beholding to old mother Time , who hath bestowed her eldest daughter , Truth , upon you , having past by so many worthy Suitors in all ages ? this is a transcendent favour , you are homo perpaucorum hominum , and have been wrapped in your mothers smock . 12. In leaving us to our liberty , to accept or reject your opinion ; I perceive you have no great confidence in your new married wife , Times daughter : you mistrust your cause , and the validity of your arguments ; and that you have imployed your pen more to shew your wit , then to evince our understanding . 2. You will not have this Philosophicall doubt decided by common people , for they judge by their senses , nor yet by the holy Fathers , for they were ignorant ( you say ) in this part of learning . Aristotle you have already disabled , for his works are not necessarily true ; and , I say , it is not fit that you should be Judges in your owne cause . Whom then will you name for Judges , seeing Scriptures , Fathers , senses , Peripateticks , are rejected ; reasons and arguments you have none : I think you must be faine to call for some of your people out of the Moon . Iuno Lucina . fer opem . But in calling of the Fathers ignorants in this part of learning , you doe them wrong ; for they were neither ignorant of Philosophy , nor of Astronomy ; they condemned the idle opinions of both ; amongst the rest , that of the Antipodes . For although I deny not the Antipodes , yet the * Philosophers opinions concerning them were vaine : as , That they inhabited that Region to which the sun riseth , when it sets with us . 2. In that they could not tell how these people came thither , seeing the vast ocean , beyond the straight of Gibraltar , was not navigable ; and they confessed that it could not be passed . 3. The reasons which they alledged to prove Antipodes were not demonstrative , nor experimentall , but meerly conjecturall ; so that the Fathers could receive no satisfaction from their reasons . 4. They held that those Antipodes were another race of men , then these of this hemisphere , and that they had been there perpetually ; and that they neither could , nor ever should know what kind of men they were . 5. They did waver in their opinion , sometimes saying that the westerne people were Antipodes to us ; sometimes the Southerne people ; sometime confounding Antipodes and Antichthones . 6. They would necessarily inferre from the roundnesse of the earth , that the lower hemisphere was dry earth , and inhabitated with people : the consequence of which S. Austine denies . 7. They held that the opposite earth to ours had an opposite motion . Of these , and other vaine opinions concerning Antipodes , you may see in Pliny , Austine , Macrobius , Lactantius , &c. It was not then out of ignorance , or peevishnesse , but upon good grounds and reasons , that they denyed Antipodes , as the Philosophers esteemed of them . Otherwise S. Austin knew and acknowledged there might be Antipodes . 2. What though the Fathers or Aristotle had been ignorant in this point , must therefore their authority in other points be slighted ? must their failing in one or two points of Philosophy , lessen their credit in all Philosophicall truths ? What if they had been ignorant in some one point of Divinity , must we therefore reject their authority in other points ? The Apostles were ignorant of the day of Judgement , and of some other points ; yet wee beleeve them never a whit the lesse in all other points . 3. There is odds between denying of Antipodes , and denying the motion of the Earth , and standing of the Sun : For the reasons which Philosophers brought to prove Antipodes , were neither experimentall , nor demonstrative , nor any waies satisfactory ; but for the stability of the earth , and motion of heaven , wee have both sense , reason , authority , divine and humane , consent , antiquity , and universality , as is said ; and what can be wanting to confirme a truth , which wee have not to confirme this ? 4. You say , That Solomon was strangely gifted with all kinde of knowledge : then would I faine know why hee did not plainly tell us , ( being so great a Philosopher ) that the Earth moved , and that the Sun stood still ; but quite contrary proves the transient vanity of humane affaires , from the earth's stability , and constant motion of the sun . 3. Iob , ( you say ) for all his humane learning , could not answer these naturall questions which God proposeth to him : as , Why the sea should be so bounded from overflowing the land . What is the breadth of the earth ? What is the reason of snow or haile , raine or dew , yee or frost ? which any ordinary Philosopher in these daies might have resolved . Answ. You would make Iob , who was both a King and a Priest , a very simple man , if wee would beleeve you . But how know you that Iob could not answer God ? Mary , because hee sayes of himselfe , That hee uttered that , he understood not : things too wonderfull for him which hee knew not . But , Good Sir , these words are spoken of the secret waies of Gods providence , and of his hid and unsearchable judgements , which are these wonderfull things that Iob knew not nor understood ; for his judgements are a bottomlesse depth , his waies are past finding out ; and they are not spoken of naturall causes of meteors . I pray , were there not haile and snow , raine and dew , yce and frost , in those daies , and did not hee know that these meteors were generated of vapours , as well as you ? or what should be the cause of his stupidity , and of your quicknesse of apprehension ? Alas ! how doe wee please our selves in the conceits of our supposed knowledge , whereas indeed wee have but a glimmering insight in Natures works , a bare superficiall and conjecturall knowledge of naturall causes ? Doubtlesse Iob was not ignorant but modest , in acknowledging the insufficiency of Philosophicall reasons , and therefore thought it better to be silent , then to shew his folly in superficiall and vaine answers : For both Astronomy , and naturall Philosophy , are arts of Diviners , rather then Disputers ; and Philosophy is but opinion , saith Lactantius ; and even in those things which Philosophers bragge that they found out , they are opinantes , potiùs quàm scientes ; carried with opinion , rather then knowledge , saith S. Austine ; which I have found by long experience . Iob knew that though humane and Philosophicall reasons would seem plausible enough to man , yet that God , to whom only truth is known , would check him , and account his wisedome but folly , to speak with Lactantius . If hee had answered God that the sea is bounded from overflowing the land , because the drienesse of the earth resisteth the moisture of the sea , which is the reason of Philosophers ; God would have shewed him the folly of his reason , by the daily flowing of the sea , on the dry lands ; and by the many inundations of the sea over whole couutries . I doubt not but if God had asked you the causes of clouds and raine , you would have answered him , that they were generated of moist vapours elevated into the aire , and there dissolved or squized by heat or cold ; but then why be there no clouds nor raine in Egypt , seeing the Sun elevates vapours out of Nilus ? So you will tell me that hail or snow are generated of moist vapours , condensate by cold into that form : but then why in the hottest countries , even under the line , are the greatest showres and biggest haile ? So might I reason with you of the other Meteors ; but that I will hasten to be rid of this taske , having other imployments . 4. I had said that there was no credit to be given to Pythagoras , whom you make a patron of your opinion ; because he was both a sorcerer , as Saint Austin sheweth , and the father of many monstrous absurdities , as I have shewed out of Theodoret. You would salve his credit by telling us , that all men are subject to errours ; and I deny it not : but it is one thing for a man to fall into an errour accidentally , and an other thing to broach a multitude of errours . A man may speake a lie by chance , and that shall not derogate from his credit ; but if he use to lie , I will scarce beleeve him when hee speakes truth . That Pythagoras was a witch , his name sheweth from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; either because hee spoke as Apollo Pythius did , falsly and obscurely ; or because he was possessed with the Pythian Spirit , or the Devill who deluded the Gentiles ; who appearing and deceiving them in the forme of the Serpent Python , which hee was said to kill , was called Pythius . His causing of an Eagle to flie to him by certaine conjuring words , and being at the same time in two severall places , at Thurii and Metapontii , with many other such like conjuring tricks , shew what he was . Pliny saith , that he went to Egypt , and many other places to learne Magicke : the Pythagoreans would kill no Serpents , so highly they honoured them . Saint Austin saith out of Varro , that Pythagoras was much addicted to Hydromancie and Necromancie , and to consult the infernall Spirits by bloud . And Tertullian deciphers him to be a notable impostor , who to make people beleeve his doctrine of transanimation , hid himselfe seaven yeares under ground ; macerating his body with hunger , thirst , nastinesse : hazarding his health and life with damps and filth , to confirme a grosse lie . Quomodo credam non mentiri Pythagoram , qui mentitur ut credam ? He that will with swearing , lying , and deceiving trickes , perswade us that he was in Hell , and that he had been Aethalides , Euphorbus , Pyrrhus , and Hermotimus , would make small bones to broach such monstrous opinions , as of the motion of the Earth , and immobilitie of the heavens , out of ambition to get him a name . And this is the goodly Patron of your opinion . Dignum patella operculum . The man of eminent note and learning as you call him ; highly esteemed for his divine wit and rare inventions . Againe when you say , that many of his absard sayings are to be understood in a mysticall sense : why will you in a literall sense understand his sayings of the Earths motion , and Heavens immobilitie ? 5. I had said that indeed Pythagoras was not the Author of this opinion , for no ancient writer ascribes it to him ; you reply , that many ancient Authors ascribe it to the Pythagorean Sect. For proofe whereof , in stead of many authors , you bring one , as if one were a multitude ; and that one is Aristotle . Answ. There is a difference betweene Pythagoras , and Pythagoreans ; betweene the Scholar and the Master : I spake of Pythagoras ; Aristotle , of the Pythagoreans . The Scholars oftentimes broach opinions which the Masters never knew ; it is ordinary in all Heretickes and Sectaries to father opinions on the first founders , and on other learned men , which they never knew nor dreamed of . That impure sect of the Nicolaitans , fathered their opinions on Nicolas the Deacon . The Arians would have made the world beleeve that Origen , Dionysius of Alexandria and Lucian the Martyr , had been the authors of their impieties . The Donatists alledge Saint Cyprian for the author of their separation from the Catholick Church : and the mad-headed Circumcellions called themselves Donatists . Therefore , when you say that it appeares by Aristotles testimony , that Pythagoras thought the Earth to be one of the Planets , you are deceived ; for he speakes not of Pythagoras , but of the Pythagoreans , of which number you are one ; not onely for affirming the Earth to be a Planet , but also in holding transanimation ; for you make no difference betweene Pythagoras and his disciples : thinking ( as it seemes ) that the soule of Pythagoras which had beene in so many bodies before , was now entred into the bodies of the Pythagoreans . 2. I said that Pythagoras held , that the heavens by their motions made a musicall harmonie , which could not consist with the earths motion ; you say it may consist , but you doe not prove how it may ; tell me , for what end doth the Heaven move ? Is it not for the benefit of the Earth ? But if the earth move to receive its benefit from the Heaven , surely the Heaven moveth to no end or purpose . Againe , you would faine escape by telling us , That Pythagoras meant by the musicall concent , i. the proportion and harmony that is in the bignesse and distance of the Orbes . You tell us so , but how shall we beleeve you ? This saying of his is not reckoned amongst his symbolicall speeches ; and if it be symbolicall , why not that saying of the Earths motion ? Is not that also mysticall ? 6. You set down seaven or eight men of speciall note ( as you say ) for their extraordinary learning , and for this opinion . Answ. If this opinion makes men to be of speciall note , then you must needs be a noted man , or shall be hereafter , when you are come downe from the Moone , or freed from the cloud that inwraps you , for you are of this opinion ; but you might have spared your labour , for these men were Pythagoreans ; and I told you before , that Pythagoreans were of this opinion ; but few of these were noted men for their extraordinary learning : they were obscure men , and very little spoken of in old Histories . Aristarchus the Tyrant , Aristarchus the Poet , and that rigid Aristarchus the Grammarian , and censurer of Homer , were noted men ; but not your Aristarchus the Mathematician . So Philolaus , Nicetas Syracusanus , Ecphantus and Lysippus have little said of them : as for Heraclides Ponticus , he was a man noted more for his ambition , then for his learning ; in that he affected to be a god , causing his friends to convey his dying body out of the way , and a dragon to be laid in his bed : that the world might thinke he was now a dragon ; and that he should be worshipped in that forme : and indeed he shewed himselfe to be that , which he desired to be ; to wit , a beast , and not a man. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , as Diogenes Laertius speakes of him . As for Plato it is not certaine if he were of your opinion , and if he had been , the matter is not great . And as for Numa Pompilius , he was not Pythagoras his scholar , for he lived about a hundred years before Pythagoras ; who live about the time that Brutus was Consul , who drove out the Kings , as Solinus witnesseth , and Tullie . Livie saith , that he flourished in the time of Servius Tullus . Neither doth Plutarch affirme that Numa was scholar to Pythagoras , but because their institutions were much alike , it was supposed by some ( saith he ) that Numa had familiarity with Pythagoras . It is true that Numa built a round Temple , not in reference to this opinion of the Earths motion , as you dreame ; for he was not of this opinion ; but in reference to the roundnesse of the world , as Plutarch saith : And he placed the Vestall fire in the middle , not to represent the Sunne in the center of the world , ( that is your glosse , ) but to represent the site of the elementary fire , which he conceived to be in the midst of the world . 7. Sure , Brag is a good dog with you ; for you tell us that there is scarce any of note or skill , who are not Copernicus his followers ; and more there are of his opinion , then all the rest put together ; and yet you tell us but of one Cardinall Cusanus , and sixe more , to avoide tediousnesse . But in this you speake by the figure Antiphrasis , by contraries : You name but one Cardinall on your side , and within three leaves after , you tell us of two Sessions of Cardinalls on our side who condemned this opinion : are not twelve more then one ? and shall not the judgement of so many be preferred to one ? How many more can you picke out of the whole Colledge of Cardinalls , that were of your opinion , beside Cusanus , who was knowne to be a man that affected singularitie ? But I think you looked through a multiplying glasse , when you concluded from the induction of five Copernicits , that there were more of his opinion , then all the rest put together . Are you not like him who thought that all the ships and goods that came into the Pyreum were his owne ? And yet of these five which you muster up for your defence , there was one , even the chiefest , and of longest experience , to wit , Galileus , who fell off from you ; being both ashamed , and sorry that he had been so long bewitched with so ridiculous an opinion ; which was proved to him both by Cardinall Bellarmine , and by other grave and learned men ; that it was contrary both to Scripture , Divinitie , and Philosophie : therefore Galilie on his knees did abjure , execrate , and detest , both by word and writ , his errour which you maintaine ; and promised with his hand on the holy Evangil , never to maintaine it againe : the other five , are men of no great note , except in your Bookes . 8. You advise us out of Aristotle and Ptolemy , to speake that which is most likely ; to entertaine that which is most agreeable to reason ; to frame such suppositions of Heaven as be most simple : and you tell us that Rheticus and Keplar wish that Aristotle were alive againe . But your advice is superfluous , and their wish is ridiculous : for we speake and intertain that which is most reasonable ; if we do not , prove it , that we may amend our errour . Our suppositions of Heaven are not so simple as could be wished ; but we were better content our selves with them , then move the earth with you : for that is , ex fumo in flammam , to leap out of the frying-pan into the fire . Now to wish Aristotle alive , or to thinke that he or Clavius would ever be of your opinion , are meere dreames and phancies . And though Clavius had found that Ptolomies Hypotheses had not beene so exact as should be ; yet he would not have beene so mad , as to beleeve the Earths motion , and the Suns rest . And though some have fallen off from Aristotles and Ptolomies opinion , to Copernicus , that will but little help your cause : for in all professions there have ever been some unconstant and giddy-headed men ; many have fallen off from Christianity to Mahumetisme ; from Calvinisme to Anabaptisme ; will you condemne therefore their former professions ? so some have revolted from Copernicus to Ptolomie . You challenge then too great a priviledge , when you say that none who having bin once setled with any strong assent on your side , that have afterwards revolted from it : besides that it is false , there was never any profession that could brag of such a priviledge : not Christianity the best of all professions . And though some men reject that opinion in which they were nursed , and have approved for truth , and now embrace your absurd Paradox , which is condemned in the Schooles ; yet it will not follow that yours is the righter side : for will you say that because many Christians become Turks and Jews ; many Orthodox men have become Arians , Nestorians , Eutychians , Macedonians ; that therefore these Heretickes were in the right ? There are too many wavering Spirits shaken like reeds , and carried about like clouds with every winde of doctrine , unsetled and instable in all their wayes . You tell us , that most of those opposers of your opinion , have been stirred thereunto , either by a partiall conceit of their owne inventions , for every one is affected to his owne brood : or by a servile feare , in derogating from the ancients authoritie ; or opposing of Scripture Phrases ; or by judging of things by sense rather then by reason . Answ. The first of these reasons will be retorted upon your selfe ; for the partiall conceit of your owne inventions , and the affection you carry to your own brood , have made you fall off from that ancient and universall truth , to embrace an errour : and this was it that moved Copernicus to oppose Ptolomie , Alphonsus , and the other famous Astronomers . Therefore , Tycho did not oppose Copernicus to make way for his owne Hypothesis as you say , but to maintaine that truth which had so long continued in the world . As for your second reason , I answer , that we should not without extraordinary and urgent cause , derogate from the authority of the ancients ; much lesse , from the meaning of Scripture phrase ; which the Church of God from the beginning hitherto hath delivered to us : neither doe we adhere to the meaning of Scripture phrase , out of a superstitious feare of the supposed infallible Church , as you say ; but out of a filiall feare to the true Church , our Mother , the ground and pillar of truth : If wee heare not the voice of this Mother , we cannot have God for our Father . A wise son honoureth his father , but he is a foole that will despise his mother . Why should we thinke that you or Copernicus can better understand the Scripture phrase , then the Church of God from time to time hath done ? this was the proud conceit of Nestorius , that he onely understood the Scripture phrase , as Vincentius complaines of him . That which you call the new Creed of Pius the Fourth , that no man should assent unto any interpretatione of Scripture , which is not approved by the ancient Fathers ; is indeed the old Creed of the Church , as Vincentius sheweth : let us no wayes no wayes ( saith he ) depart from that sense which our holy Fathers and predecessours have maintained . And againe , whatsoever ( saith he ) the Catholique Church hath of old retained , that onely shall a true Catholique maintaine and beleeve : therefore he shewes that it is the trick of Heretickes to delight in novelties ; and to reject and despise old doctrines . Us profanis novitat bus gaudeant , antiquitatis scit a fastidiant . If then the Jesuites , in reverence to the Churches authority , and to the ancient Fathers doe oppose this opinion they deserve commendation : and so did these Cardinals that called it in , and punished the defenders of it . Thirdly , you say that we judge of things by sense , rather then by reason ; but indeed you have no reason to say so : for although that sensitive things , such as the Earths stability , and Sunnes motion , are to be judged by sense ; yet we have many reasons for us , whereby we judge it must be so as I have shewed heretofore . But I confesse we judge not by your reasons , because they are but shadowes of reason , and no way satisfactory : neither doe we so tie the meaning of Scripture to the letter of it ( as you say , ) but that we give freedome to raise other senses , whether allegoricall , tropologicall , or anagogicall ; so they be not repugnant to faith and good manners . But in historicall things , Saint Austin tells us , that we must chiefly adhere to the literall sense ; and it is a Maxime in the Schooles , that we must not reject the literall sense , which is not contrary , agendis aut credendis , to the Creed or the Law : neither is it unlawfull to conclude Philosophicall points from the letter of Gods word , seeing there is but one truth in Divinitie and Philosophie . But to conclude Philosophicall points flat contrary to the letter of divine Scripture , as you doe , is too much boldnesse : therefore , I will speake to you in the words of Saint Austin , writing of the Philosophers of his time ; Quicquid de tuis voluminibus his nostris literis contrarium protuleris , an t aliqua facultate oftendamus , aut nulla dubitatione credamus esse falsissimum . Your assertion of the Earths motion , is contrary to the letter of the Scripture ; therefore we doubt not to say , is it most false . As for our ignorance of your Astronomicall grounds , it is excusable , seeing your owne ignorance is the cause of it : how can the Scholar know , if the Master be ignorant himselfe of these Principles which he undertakes to teach ; or knowes not which way to make them intelligible ? How can the blinde lead the blinde ? Non obtusa adeo gestamus pectora . We are not so dull but we can understand other Principles : but yours being Chimaera's , fictions , non entities ; having no other ground but your owne phansie , cannot informe our understandings which have entities for their objects . 9. No councell hitherto ( say you ) have censured this opinion for an Heresie . Answ. The Church by her councells doth not presently censure Heresies ; she knowes best her owne times and seasons , and reasons too . The Physician doth not alwayes in the beginning of a disease , prescribe purging physicke . 2. From the Churches forbearance to censure an Heresie , you must not conclude the nullitie of an Heresie : for the Heresies of Arius , Macedonius , Euryches , and Nestorius , were Heresies , before they were censured by the four generall Councells . And the Church , saith Saint Austin , suffers and beares with many Heretickes , so long as they doe not pertinaciously maintaine , nor maliciously ( to the disturbance of the Church ) spread abroad their falshoods ; Quod si fecerint , tune pollantur . Many are Heretickes in sore Coeli , which are not in foro Ecclesie : and he is not onely an Hereticke which denieth an Article of the Creed , but he also that gain-sayeth any plaine place of Scripture . The broacher or maintainer of any false and new opinion , is an Hereticke saith Saint Austin . 3. Either you have not read , or have not observed the censure of Galilies opinion by the councell of Cardinals ; who not onely call it a false opinion , erroneous in the faith , a doctrine contrary to the holy Scripture : but also in plaine tearmes they call it Heresie . 4. When you say that Fromundus calls it a rash opinion , bordering upon Heresie , that Paul the Third was not so much offended at Copernicus , when he dedicated his booke to him ; that the Fathers of Trent call Epycicles and Eccentrickes , but fictions : these are such weake helps to support your cause , that if you leane on them , they will prove no stronger then reeds or cob-webs : if I should insist on them , I should but discover your weaknesse , in alledging of them . And likewise , your instancing of Shonbergius , who importunately begged the Commentaries of Copernicus : was is not rather out of curiosity to see how he could defend such an absurd Paradox , then out of true affection to embrace it ? So Herod desired to see Christ ; I doubt not but many will desire to see your booke of this subject , which ( I dare presume ) will never be of your opinion . Lastly , where as you say , It is absurd not to assent to any thing in naturall questions , but what authority shall allow of . I say , it were both absurd and dangerous for mens soules , and the peace of the Church , if men were suffered to assent to any absurditie , against Scripture , sense , reason , and the Churches authority . CHAP. II. 1. Wee must beleeve the Scripture , not our own phansies . 2. The Scripture never patronizeth a lye or an error , nor doth it apply it self to our capacity in naturall things , though it doth in supernaturall mysteries . 3. Wee must stick to the literall sense , when the Scripture speaks of naturall things . 4. Some particular Scriptures vindicated from our adversaries false glosses : as namely , Psal. 19 of the Suns motion like a Gyant and Bridegroome , to the ends of heaven : And of his heat , Eccles. 1. Of the Suns rising and setting . Josh. 12. Of the Sunne standing still , of the midst of braven ; how over Gibeon , and how no day like that . Esay 38. Of the Sunnes returning tenne degrees ; of the greatnesse and meaning of this miracle : whether knowne to the Gentiles . The testimony of Herodotus concerning this : IT were happy for us ( say you ) if we could exempt Scripture from Phisophicall controversies . And I say , It were happy for us , if all Philosophicall controversies could be decided by Scripture ; or if men would be so modest , as to rest contented with Scripture phrases , and expressions of such Philosophicall points , as are mentioned there : But what hope is there to end controversies , when many are so wedded to their own phansies , that neither will they yeeld to Scripture , except they may have leave to interpret them ; nor to reasons , except they may have leave to forme them ; nor will they trust their own senses , but will captivate and enslave them also to their groundlesse imaginations ? The Scripture tells us in plaine tearmes , the Earth is immoveable : our senses doe assure us , and many reasons which I have heretofore alledged , induce us to beleeve the truth of this assertion : and yet you spurning at Scripture , sense , and reason , as if your phansie were instar omnium , would have our judgements , senses , Scripture , Church , and all regulated by your absurd dictates ; therefore it is an unreasonable thing in you , to desire that the holy Ghost should not be Judge of his owne assertions in naturall truths ; and that there should be more credit given to your conceits , ( which you call industry and experience ) then to Gods own words . Indeed this travell hath God left to the sonnes of men , to be exercised with , as a punishment for their sins ; to toile and labour all their dayes about shadowes , imaginations , and indeed meer nothing ; groping at the doore of knowledge ( like blinde Sodomites ) all their dayes , and cannot finde it ; so that they who have spent their whole life in Astronomie , may with Saint Peter , say on their death bed ; Master We have laboured all night , but have caught nothing . Thus with Martha , they are busie about many things , and neglect that one thing which is onely necessary . 2. It is but a conceit of yours to say , That the Scripture accommodates it selfe to the vulgars conceit , in saying , the Sunne riseth and falleth , &c. I warrant you , if the vulgar should conceive that the heavens were made of water , as the Gnostickes held ; or that the Sunne and Moone were two ships , with the Manichees ; or that the world was made of the sweat of the AEones , with the Valentinians : or whatsoever other absurd opinion they should hold , you would make the Scripture say so , and to accommodate it selfe to their conceits . The stability of the Earth , and motion of the Heaven , are absurd and false opinions in your conceit ; and yet the Scripture affirmes them . You are as unapt I know to beleeve that the Sunne moves , as others are that it stands still ; therefore it 's a wonder you do not begin to call the Scripture authority in question , that affirmes the Suns motion : seeing you say men would be apt to doe so , if the Scripture had said , the Sunne standeth , &c. How shall the Scripture please both parties ? if it say the Sun moveth , your side will except against it : if it say the Sun standeth , ours will be offended at it . Why should the Scripture be more loath to offend us then you , except it be because we are the stronger side ; and we have our senses to witnesse with us , which you have not ? I wish you would conceive a more reverend opinion of the Spirit of truth , who cannot lie ; nor will affirme a falshood upon any pretence whatsoever ; neither will he countenance a lie , to confirme a truth ; or speake false in one thing , that wee may conceive his meaning the better in another thing . He needs not such weake and wicked helps as falshoods , to make us understand his will ; his word is strong and mighty in operation ; it 's the power of God unto salvation ; a sharp two edged sword ; his hammer , his scepter , &c. As it stands not with his truth to affirme a lie , so doth it no wayes consist with the power of his Word and Spirit , to helpe our understanding by a lie . 3. You say , That if the Scripture had said , the Earth riseth and setteth , and the Sunne stands still ; the people being unacquainted with that secret , would not have understood the meaning of it . Answ. What matter is it whether they had understood it or not ? For you tell us that these things are not necessary in themselves ; and that it is besides the scope of these places , to instruct us in Philosophicall points . Will you have the holy Ghost then speake a falshood ? for feare lest we should not understand the meaning of a secret , which is not necessary for us to know : if it be not needfull for us to know whether the Earth stands or not ; so it was lesse needfull for the Scripture to say the Earth standeth , when it doth not stand . But you doe well to call the motion of the Earth a secret , for so it is a great secret , hid from the wise and prudent of this world , and revealed onely to such babes as your selfe . But why is this a secret ? If it be a naturall effect , it is no secret ; for though naturall causes doe not incurre into our senses , yet the effects doe ; and if this be a secret effect and not sensible , it cannot be an effect of nature ; but I thinke it be such another secret as the Philosophers stone , which never was , and never shall be . Though it be beside the chiefe scope of Scripture to instruct us in Philosophicall points : yet it will not follow , that these Philosophicall tearmes are to be otherwise understood , then as they are expressed . There be many Geographicall , Historicall , and Chronologicall passages in Scripture , mentioned incidently , and not chiefly to instruct us in such points : shall we therefore understand them otherwise then they are set downe , or rather the cleane contrary way ? But when you say the Earths motion is beyond our reach ; I grant it : because we cannot reach that which is not made manifest to us , either by sense or reason , or divine authority ; If you can either of these wayes make it appeare , I doubt not but our understanding will reach it : and if you cannot one of these wayes make it appear to us , we will account it a meere nothing . For idem est non esse , & non videri : and indeed you say well out of the Glosse , that God doth not teach curiosities which are not apprehended easily ; for your motion of the Earth is an incomprehensible curiosity . And it is well said by you againe , that the Scriptures authority might be questioned , if it did teach naturall things contrary to our senses ; and therefore if any booke of Scripture should affirme , as you doe ; that the earth moves naturally and circularly , I should verily beleeve that that booke had never been indicted by the holy Spirit , but rather by a Pythagorean spirit , or by the spirit of Dutch beer . You condemne Tertullians Heretickes for retching Scripture a wrong way , and forcing it to some other sense agreeable to their false imagination ; and rather then they would forgoe their tenents , yeelded the Scripture to be erroneous . De te fabula narretur . You retch the Scripture a wrong way , forcing it to your false imaginations ; you do not indeed call the Scripture erroneous , but you make it to speake one thing , and meane the cleane contrary ; therefore , you shall doe well to apply Saint Austins counsell to your selfe , and doe not settle your opinion rashly on that darke and obscure conceit of the Earths motion . It is true also what you alledge out of Saint Austin , that the holy Ghost being to deliver more necessary truths , left out to speake of the forme or figure of Heaven , &c. because hee would not have us spend too much time in these things , and neglect the meanes of salvation ; but you should have done well to have subjoined the following words of that same Father , to wit ; That is true which is affirmed by divine authority , rather then that which is guessed at by humane infirmity . For there he speakes of Philosophicall points , which seeme to be contrary to Scripture : but you are mistaken when you say , that God descends to our capacity in naturall things ; and conformes his expressions to the mistake of our judgements , as he doth apply himselfe to our apprehensions , by being represented like a man. There is infinite oddes betweene God and naturall things ; wee that are corporall cannot understand spirituall things , much lesse that infinite Spirit , but by familiar expressions ; yet such as doe in some sort represent his attributes to us : as he is said to have eyes , hands , &c. by which are signified his knowledge , operations , &c. But for naturall things there was no such necessity , because naturall men , by natures light are able to understand naturall things : so wee know what a circular motion is ; and if the Earth did truely move , we should as soon apprehend the motion of it , as we do the Suns motion : therefore , there was no need why God should descend to our capacity in affirming an untruth , because wee cannot understand the Earths motion . God then doth not conforme his expressions to the errour of our judgements ; for our judgements doe not erre in this ; but he speakes according to the truth of the thing , which wee judge and apprehend as it is . We apprehend the fire to be hot ; if you were of an opinion that it were cold , ( which you may as well maintaine as the Earths motion ) you would doubtlesse tell us , that the Scripture in saying the fire is hot , applies it selfe to the vulgar errour or mistake of our judgements ; thus you may make the Scripture to serve you for defence of any absurdity , by using such a subterfuge , and running into such a starting hole . 4. You examine those particular Scriptures which are urged to prove the Suns motion , and you tell us that they are spoken in reference to the appearance of things , and the false opinions of the vulgar ; and in the 75. pag. of your Booke , you say it is a frequent custome for the holy Ghost to speake of naturall things , rather according to appearance and common opinion , then the truth it selfe . I would 1. know if this consequence be Logicke ; the holy Ghost speakes of naturall things according to appearance , frequently , and of some , ergo continually , and of all ; or particularly of this ; to wit , the Earths immobility . The Scripture oftentimes speakes of God according to mens opinion and capacity ; as , that he is angry , that he repents , &c. Ergo , the Scripture speaks still of God thus : and so , when the Scripture sayes , that God is a Spirit , or just , or infinite , or eternall ; that may be understood ( if your Logicke be good ) according to opinion or appearance ; this will prove a dangerous kind of reasoning . 2. Why doth not the holy Ghost tell us in plaine tearmes , that the Earth moves , if it doth move ? what end hath hee to tell us that it is immoveable ? Is it because we are not capable to understand such a high mysterie ? that is ridiculous . For is it a greater mysterie then Christs Incarnation , Resurrection , Ascension , &c. which are set downe in plaine tearms ? but indeed it is no mysterie ; it 's easie to understand the Earths motion , if it did move . Or is it because the holy Ghost would not give offence to the world , in telling them plainly that the Earth moved , being an opinion so repugnant to sense and reason ? Then doubtlesse he would not have told us , that the Sun and Moone stood still at Ioshua's command ; or that the Sea was divided by Moses Rod ; and those other miracles of holy Writ , as much repugnant to sense and naturall reason , as the Earths motion is : the holy Ghost useth not to hide or mince the truth , for feare of offending men . 3. There is great oddes betweene asseverations and allusions ; betweene the affirmation of a truth , and an allusion to a fiction The Scripture speaking of perverse men that will not heare Gods word , alludes to the fiction ( as you call it , ) of the adder stopping his eare ; ergo , when the Scripture speakes of the Earths immobility , it speaks according to common opinion . A goodly consequence ; as if you would say , the Scripture speakes figuratively of Christ , when it calls him a Lamb , a Doore , a Vine : ergo , when the Scripture speakes of the beheading of Iohn Baptist , it speakes according to common opinion : if there be no better Logicke taught in the Universities of the Moone , we will never send our Sons thither . 3. It is a rule in Saint Austin , that we should expound Scripture as the Saints have expounded it before us ; Quomodo bac verba intellexerunt Sancti , sic utique intelligenda sunt : But name me that Saint that ever expounded these Scriptures , which speake of the Heavens motion and of the Earths immobilitie , according to appearance and common opinion . Of St. Austins minde was the sixth generall Councell , prohibiting any man to interpret Scripture , otherwise then the Lights and Doctors of the Church , have hitherto expounded them by their writings ; which Canon is confirmed in the eleventh Session of the third Lateran Councell . 5. The ancient Fathers warne us , that we doe not deviate or depart from the literall sense of Scripture , so long as no absurdity doth follow thereupon : now , no absurdity doth follow upon the literall sense of the Earths immobilitie ; but upon your sense and exposition many absurdities follow ; therefore we must not depart from the literall sense . 6. Where the holy Ghost speakes obscurely and figuratively in one place , hee doth in another place open himselfe in plaine tearmes , as Saint Hierome observes : but speaking of the Earths immobilitie , he useth still the same phrases ; neither doth he explaine himselfe otherwise in any one place ; which doubtlesse hee would have done , if he had meant otherwise then hee spoake . 7. I absolutely deny that the holy Ghost speakes of naturall things , otherwise then in truth and reality ; and not ( as you say , ) according to common opinions . As for your expositions of these Scriptures which are for us , and your instances against our opinion ; they are wrested , and false , and impertinent , and of no soliditie , as we will shew by our answer or reply to each of them severally . 1. It is usuall with you to cut your throate with your owne sword , and to bring passages against your selfe ; for you would prove that the Scripture speakes of the Heavens motion , in reference onely to the Vulgars false opinion ; because , The Sunne is in his glory like a Bridegroome ; and in his motion like a Gyant . I answer , if the Sunne be in his motion like a Gyant , then sure the Sunne hath motion ; for how can that which is not , be compared to that which is ? Similitudes cannot illustrate non entities . 2. If the Sun were not a glorious creature , David had not compared his glory to without motion , he had not compared his motion , to the motion of a Gyant : if there be no motion in the winde and thunder , it had been idle to give wings to the one , or arrowes to the other , as David doth . 3. Will you make the Scripture not onely ass●er● a falshood in positive tearmes , but also bring similitudes to illustrate it ? this is to make the holy Ghost a cherither , fomenter , and maintainer of untruths ; for so it must be , if the Sunne move not , the Scripture shewing it doth move , and declaring by similies how it doth move . 4. What consequence is this ? The Scripture compareth the Sun to a Bridegroome , and a Gyant ; ergo , the Scripture speaking of the Suns motion , speakes in reference to the false opinion of the Vulgar ? it is all one with this : The Gospel compares Christ to a Bridegroome ; ergo , the Gospel speaking of Christs humanity , speakes in reference to the false opinion of the Vulgar . 5. There is ods between positive speeches and comparisons ; the Sun is never called a Bridegroome in Scripture , but is said to be like a Bridegroome : Simile non est idem . But in Scripture still , the Sun is said to move , and the earth to be stable , in positive tearmes . 6. That David in this comparison did allude to the phansie of ignorant people , supposing the Sun by night to rest in a chamber , is but your groundlesse conceit : you might say rather that he alluded to the fiction of Poets , describing Aurora to go to bed every night with Tythonus ; Tythous croceum ●●● quens Aurora cubile : or to that golden bed which Vulcan made him ; in which he is carried through the Sea. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . But neither to this pleasant bed , nor to that of Tythonus , nor to the Vulgar conceit doth David allude ; but simply sets out Gods Majesty in the glory of the Sunne , by a familiar example , taken from the glory of a Bridegroome coming out of his chamber . 7. This former part of the Psalme is interpreted by the Fathers mystically of Christ , whose motion and alacrity to run his race from the wombe to the grave , from heaven to earth , and from earth to heaven ; I hope you will not say , are to be understood in reference to the false opinion of the Vulgar . 8. He is not compared to a Gyant , in respect of his bignesse in the morning , ( as you say ) no more then he is to a dwarfe , in respect of his littlenesse at noone ; but in respect of the indefatigable swiftnesse of his motion , he is compared to a mighty runner : for there is no mention made of a Gyant in the Hebrew text , neither was it fit to compare him to a Gyant . 9. Nor doth David allude to the Vulgar opinion , when he speakes of the ends of Heaven ; for in a round globe or circle there are no ends : but he speaks with relation to the Hemisphere , which you must needs yeeld hath ends ; for it terminates and ends in the Horizon , called therefore Finitor . Besides , in the Hebrew , Greeke , and Latine texts , it is not said , the ends ; but the remotest parts of Heaven : and so you cannot deny but some parts are remoter from us then other parts . 10. Neither hath the Scripture any reference to the common mistake , as if the Sun were actually hot , when it saith , ( nothing is hid from the heate thereof : ) these Philosophers who deny any actuall heat in the Sun , yet say the Sun is hot : and I doubt not but you have said so many a time , and yet you have no reference to any actuall heate in the Sun. Do not you use to call cinnamon-water , and such like distilled waters , hot waters ? and yet they are actually cold . Philosophers tell us that Saturne is cold , and yet they doe not thinke that he is the subject of cold , but the cause onely . The Scripture saith , That none can avoid the anger of God ; and yet you will not say that this passion is in God. The Sunne then is hot , not by any heate in him , but by calefaction from him . 2. When the Scripture saith , The Sunne riseth and goeth downe ; this is not spoken in relation to the circumference which is equally distant from the Center ; but in reference to the Horizon as you confesse , or rather to the scituation of Judea ; and so of other Countreys : and in this respect , the Sunne doth not onely seeme , but doth in very deed rise and fall to the Inhabitants . For doth not the Sunne truely ascend when he comes to your meridian , and truely descend , when he removes from it ? Doth he not truly ascend and descend , to those who have him for their Zenith in their meridian ? Astronomers tell us that there is a true and reall rising and falling of the Starres , as well as an apparent ; and then are they not truely said to rise and fall , when they doe truely ascend above , and descend beneath the Horizon ? If the Sunne doth not truely ascend and descend , then the shadowes doe not truly increase and decrease ; and so our Sun-dialls doe not truely shew us the hours of the day , but in shew onely , and in appearance ; but wee see that the shadow still decreaseth , as the luminous body ascendeth , and encreaseth as that descendeth . Virgils Tytirus can tell you so much : Majoresque cadunt altis de montibus umbrae , Et Sol discadens crescentes duplicat umbras . 3. Joshua saith , That the Sunne stood still in the midst of heaven : Now , Heaven ( you say ) hath no midst but the Center , and so this is also spoken in reference to the Vulgar opinion . Answ. By the Center , either you must understand the Earth , or the Sunne ; the Earth indeed is in the midst of the world , but not in the midst of Heaven ; for it is not there at all : if it were , Christ needed not to ascend to Heaven , being in the midst of it , when he was on the earth . Wicked men then would have the best of it ; for as they have the largest possessions on earth , so should they have the largest shares in heaven . If by the Center you meane the Sunne , then you speake in reference to the Vulgar opinion ; for the Center is in the midst of Heaven , the Sunne is the Center ; therefore the Sun is in the midst of Heaven , and so Joshua saith . 2. By the Heaven he doth not understand the whole celestiall Globe , but the Hemisphere ; and so this having its Horizon or outmost limits and extreames , must also have its middle : and what can that else be , but the Meridian passing through the Zenith ? Thus then it is demonstrable that whatsoever is equally distant from the extreames is in the midsts ; but the Sun being in the Zenith or Meridian , is equally distant from the extreames : therefore the Sun being in the Zenith , is in the midst of Heaven . 3. The Hebrew Doctors tell us , that when the Sun stood still , hee was then in the Summers solstice , being the Tropicke of Cancer ; from which Judea is not farre distant : and so in that regard also Joshua might truly say , that the Sunne was in the midst of Heaven , being then over their heads . 4. If it be a vulgar opinion to say , that the Sunne is in the midst of Heaven ; then all the chiefe learned both in Divinitie , Philosophie , and Poetrie , speake as the Vulgar doe ; for they use the same phrase : hence came the word Meridian , Meridies , Mid-day , Mid-night . If the Sunne were not every day in the midst of Heaven ; how should the Artificiall day be divided into equall parts ? Therefore Clavins tells us , that the Meridian is called by Astronomers , the midst of Heaven ; the line of the midst of Heaven , &c. And the Prince of Poets speakes both of the Sunne and Moone in the midst of Heaven : Iam medium Phoebus conscenderat igneus orbem . Phoebe — Noctivago curra medium pulsabat Olympum . 5. I would know of you if all Vulgar opinions be false . That ( I hope ) you will not say : If then the Vulgar speake sometime truth , why may not the Scripture speake truth with the Vulgar ? or why should truth be of lesse esteeme , because vulgar ? it should be otherwise , for , Bonum quo communius eo meliús . It is ridiculous to think with you , that the Sun was over Gibeon only in appearance and vulgar conceit : For indeed the Sun was truly over Gibeon , although he was no more over that then over other places . Suppose you were in Pauls Church , and divers others were there too ; is the roofe of that Church over your head only in appearance and vulgar conceit , because it is over other heads as well as yours ; or because it is much larger then your head ? Or must that phrase be thought improper , the roofe is over your head ? 2. The figure Eclipsis is frequent in Scripture , when there some words wanting in a phrase which are to be supplied : as , 2 Sam. 6. 6. Vzza put forth to the Arke , is understood , his hand . So 2 Chro. 10. 11. I with Scorpions , is understood , will chastise you . So here , Sun stand still in Gibeon , is understood , while we are fighting ? and so the words must be rendered : Stand still whilest we are fighting in Gibeon ; for not onely the city , but its territories where Ioshua's army was , are called by the same name . So , Moon in the valley of Ajalon , is understood , goe not downe . These words , ( There was no day like that before it , or after it ) you say , are not to be understood absolutely , but in respect of the vulgar opinion ; because there be longer dayes under the Pole. Answ. Ioshua spoke not this with any reference to vulgar opinions , but to the Climate in which he lived , and where the miracle was shewed ; it was the longest day that ever was in those parts ; and what reason had he to except the dayes under the Poles , being nothing to his purpose ? When Christ saith , There be twelve houres in the day , his words cannot be understood absolutely ; for there be more houres where the Horizon hath any obliquity ; and the higher the Pole is elevated above the Horizon , the more houres have the dayes in Summer ; yet his words are true , in sphera recta , and in those Countreys that are under and neere the Line . And what will you conclude from this ? that because these and such like phrases , are not to be understood absolutely ; therefore this phrase ( the Sun moves , ) is not to be understood absolutely ? But I will reply . These phrases are true in respect of the Climate they were spoken of ; ergo this phrase also , ( the Sun moves ) is true , in regard of the Climate it is spoken of . If then Judea be the place where the Earth is stable , and the Sun moves , your opinion is quite overthrown by the force of your own instance : for if the Earth be immoveable in any Climate , and the Sun moveable , we have that which we desire : it lieth on you to shew how , and why the Sun should move there , and not elsewhere ; why and how the earth moves here and not there . 2. These words of Ioshua's , perhaps have no reference to the length of the day , although the vulgar Translation read it so ; but rather to the greatnesse of the miracle , the Heavens hearkening to the voyce of a mortall man. Ioshua acknowledgeth , That never any such day was before or since ; that the Lord hearkned to the voyce of a man : For so the Hebrew and Greeke read it . 4. The Scripture saith , That the Sun returned ten degrees in the dyall of Achaz ; this you will have to be understood of the shadow only : So I perceive the Sun and the shadow , light and darknesse , is all one with you . Take heed of the woe denounced against them that call light darknesse , and darknesse light : Why may you not in other places , aswell as in this , by the Sun understand the shadow : as , At Ioshua's command the Sun stood still ; that is , the shadow stood . Wee shall shine as the Sun , that is , wee shall be dark as the shadow ? 2. You mince the miracle , and the power of God too much ; for , is it not as easie for him to make the Sun goe back , as to make the shadow returne ? Wherein is his absolute Soveraignty seen , and his transcendent puissance , but in the obedience of all creatures , even of the Sun , Moon , and Stars , to his commands ? St. Austin , disputing against the Gentiles , sheweth them , That Nature is not the supreme guider of all things ; and hee instanceth in the standing , and going back of the Sun. His Argument had bin of no force , had not the Sun moved at all , as you think . 3. If the shadow moved onely without the Sun , then either that shadow moved it self , which is ridiculous to think ; or it was moved by the motion of the dyall , or of the gnomon and index of the dyall : Now , if the dyall or gnomon was moved by God or an Angel , tell us where you read it . Why might it not as well be turned about with a mans hand , or by some engine , and so this would have bin a suspected miracle ; or else the shadow returned according to the motion of some other luminous body , & so this were to multiply miracles needlesly ; for 1. that light must be created for that purpose . 2. It must have a particular motion of its own . 3. It must be a greater light then that of the Sunne , otherwise the shadow had not beene discernible . 4. It must either be united to some other light , or else vanish ; all which was needlesse : is it not safer then to adhere to Gods word ? from which when we wander , we fall into many by-wayes . And whereas you tell us , That the miracle is proposed onely concerning the shadow : I answer , we are not to consider so much what is proposed , as what was effected . God useth to effect more , then he proposeth , and to performe more then he promiseth . 2. You say , There would have been some intimation of the extraordinary length of the day , as it is in that of Ioshua : I answer , there was no such reason , why the length of this day should be mentioned ; because this day was much shorter then Ioshua's , in respect it fell out in the winter solstice ; whereas that of Ioshua was in the summer solstice , as the Hebrew Doctors observe . 3. Had the Sunne returned , This had been ( you say ) a greater miracle then those which were done on more solemne occasions . Answ. God regards not the solemnity of occasions , in shewing of his miracles ; if he had , Christ had never wrought his miracles in obscure and remote places , as hills and deserts : He would rather have shewed his transfiguration in Jerusalem , to all the world , then upon Mount Tabor , onely to three Disciples . He useth his miracles , as he did the loaves ; he bestowed seaven loaves on foure thousand men , and but five loaves upon five thousand : on small occasions God sometimes produceth great miracles , and upon great occasions sometimes hee sheweth none . 2. We must looke rather to the fitnesse of the miracle , then to the solemnity of the occasion : the Sunne represented the King , who was the life and glory of his kingdome . God would let him and all men see , that as he onely hath power to rule , and alter the course of the Sunne ; so it is he onely , that rules and turnes the hearts of Kings : the Sunne was obedient to Gods command , so should the King be . As the Sun moves to and fro , so doth the shadow ; and as the King is affected , so is the people . The going down of the Sunne bringeth sadnesse on the earth , so doth the death of a King. 3. The occasion of this miracle was not so small as you take it ; the sicknesse , prayers and teares of a good King ; the prayers of a great Prophet , the affection that God would shew his people , in delivering them from the hand of Assyria ; and the love that hee carried to such a King , that rather then his faith shall faile , the Sunne shall change his course ; and the lesson that he would teach us , that wee should honour Kings , whom God doth so much honour ; as to make the King of Planets stand still at the request of one , to goe backe at the petition of another : these I say were the occasions of this miracle . 4. The going backe of the Sunne is not a greater miracle ( as you say ) then his standing still ; for the standing of the Red-sea , was as great a miracle , as the going backe of Jordan . 5. The shadow in the historie of the Kings is onely mentioned , because the shadowes moving was more visible then the Suns . 6. This signe ( you say ) appeared not in the Sunne , because the wonder was done in the land . Answ. The signe was in the Sunne , and that the Babylonians saw ; they sent to know the wonder , that is , what strange effect it had done in the land of Judea . There be oftentimes strange Prodigies in the Aire , which cause strange effects on the Earth . If I should send to Italie or Germanie , to know of some strange Prodigies seene there in the Aire ; and if I should enquire what wonder or effect these had wrought in the land , or in these countreys ; would you conclude that there was no prodigious signe at all in the Aire ? The Wisemen saw a new Starre , which shewed to them the miraculous birth of a new King ; because they came to Judea , to see the wonder done in the land : you will therehence conclude , that there was no signe at all in the Heaven , neither Starre , nor motion of a Starre . 7. You doubt of the truth of the Sunnes going backe , because no mention of it in ancient Writers : But if you will doubt or deny all passages and miracles of Scripture , which are not mentioned by the Heathen writers , our Bible will be reduced to a small handfull : they mention not the standing of the Sunne , will you deny that too ? But you reply , That they had some light of it , by alluding to it in the Fable of Phaeton , when the Sun was so irregular in his course , that he burned some part of the world : but indeed , this seems rather to allude to the Suns going backe , then to his standing ; for an irregular course is more like a retrograde motion , then a standing still . But it is most likely that this Fable alludes to the conflagration of Sodome , and the other cities of the plaine : but however the Gentiles were not ignorant of this miracle , as may be seen by that message sent to Ezechias by the Babylonians , who were then the onely Astronomers . And Saint Austin proves , that this miracle was knowne to the Heathen , by that Verse in Virgil : Sistere aquam fluviis , & vertere sidera retro : Ascribing both the standing of the Red-sea , and of Jordan ; and the going backe of the Sunne , to Art , Magicke , which the Scripture attributes to the power of God. But Ioseph's in his first booke against Apion , will tell you the reasons , why the Gentile writers made little mention of the Jewish affairs and miracles ; partly out of ignorance ; as knowing little or nothing of the Jewes ; because they were not a people given to travell , or merchandising , and dwelt not in maritime towns : and partly out of malice to that Nation , they concealed Gods love to them , and the wonders done amongst them ; and indeed most of the ancient Records by injury of time , fury of fire and waters , and neglect of those that should have kept them are lost ; both amongst the Gentiles and the Jewes , as those Bookes of the Kings of Judah and Israel , which are onely named in Scripture . You reject the testimony of Herodotus concerning the returning of the Sunne , ( which he calls the rising of the Sun in the West ; ) because he exceeds in the computation of years : but by this means you will wrong all Historians , if you question the substance of the story for an errour in the circumstance : an errour in the computation of time takes not away the truth of the thing it selfe . The China people reck on an incredible number of yeares from the Creation of the world ; yet you will not deny but that they had some knowledge of the Creation , and that their relation of it is true . The Chaldeans and Egyptians reckon 432. thousand yeares before the Floud ; will you therefore say , they had no knowledge of the Floud ? The Septuagints reckon from Adam to the Floud , 2262. yeares ; whereas the Hebrews number onely 1656. yeares ; and yet the Fathers reject not the Septuagints testimony concerning the Floud ; but most of them also follow their supputation . And how doe you know but that Herodotus number of yeares may agree well enough with ours ; seeing divers Countreys did reckon their years diversly . The Arcadian year consisted but of three moneths ; the Acarnanian of sixe : the Roman at first but of tenne . The Egyptian year was various ; for sometime it consisted of thirteen months , sometime but of foure , and sometime of three onely , and of two , and of one onely sometime . Therefore doubtlesse Herodotus years were either Arcadian , or Egyptian ; and so compare them with our yeares , you will finde that there is no such oddes as you make : and that in speaking of the Sunnes retrogradation , he hath not reference to the times that never were . And whereas you say that this miracle hapned when Hesiod flourished , you faile in your Chronologie ; for Hesiod was above a hundred yeares before this miracle was effected , if you will beleeve Gentbrard and the other Chronologers . You are a wise Philosopher to tell us , that the shadow ( as well as the heat and beames ) is the effect of the Sunne . Can darknesse be the effect of light ? a privation is a defect , not an effect : if the shadow were an effect at all , it should be the effect of the darke and condensate body , but not of the luminous . Take heed that the light which is in you be not darknesse , for then how great will that darknesse be ? CHAP. III. 1. The Scripture doth not speake according to vulgar opinion , when it calls the Moone a great light , for so it is . 2. Not when it speakes of waters above the Heavens , for such there are . 3. Nor when it calls the Starres innumerable , for so they are . 4. Nor when it mentions by circumference of the brasin Sea to be thirty cubits , and the diameter tenne , for so it was . Why the lesser number is sometime omitted . 5. Nor in saying the earth is founded on the waters , which is true . 6. The right and left side of heaven how understood , and how the heaven is 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and of the Intelligences . 7. The Scripture speaketh properly in attributing understanding to the heart . The Galenists opinion discussed . 8. Of ova aspidum , and the Vipers egges , how understood . 9. The Aspe or Adler how hee stops his eare . 10. Of the North and South winde in Scripture . 11. The Sun shall be truely darkned , the Moon turned to blood , and the starres shall fall , amp ; c. 12. Of the Windes whence they come , &c. 13. The sea the onely cause of springs . 14. The thunder is truly Gods voice . 15. The 7. Stars . IN this Proposition you goe about to shew us , That the Scripture in naturall things conformes it selfe to our conceived errours , and that it speakes of things not as they are in themselves , but as they appeare . And yet the testimony of Vallesius which you bring to help you , overthrowes you ; for , Whatsoever ( saith hee ) is in Scripture concerning Nature , is most true , as proceeding from the God of Nature , from whom nothing could be hid . If the Scripture expressions of naturall things be most true , then they cannot agree with our erroneous conceits ; for truth and errour agree like light and darknesse : and you confesse your selfe that all naturall points in Scripture are certain and infallible ; but in that sense ( say you ) wherein they were first intended , and that is the sense that you give ; for you only are acquainted with the first intended sense of the holy Ghost , and so wee must take it upon your bare word that that onely is the true sense which your side delivereth : and I pray you what heresie may not be maintained by Scripture this way ? for heretickes will also say , That all things in Scripture are true , certaine , and evident , in that sense which was at first intended ; but when it comes to the point , it is the sense which they themselves have invented obtruded . The first instance which you bring for proof of your assertion , is from the Moon , which is called in Scripture , One of the great lights ; and yet by infallible observation ( say you ) may be proved to be lesse then any visible starre . Answ. Other Astronomers will prove as strongly as you can , that Mercury is the least of all starres ; shall wee beleeve you , or them ? 2. Though I should yeeld that the Moon were a small starre in bulk , will it follow that therefore it is a lesser light ? Must the light be intended , as the body is extended ? I have seen a fire yeeld lesse light then a candle ; Mercury , which you say is bigger then the Moon , hath not the hundreth part of that light which is in the Moon : so that if Mercury and the Moon should change places , yet the light of the Moon would not appeare much lesser , nor the light of Mercury much bigger : the eie which is the light of the body , is not the clearer because the bigger ; there is not so much light in an Oxe eie , as in an Eagle's : Divines hold , That the light which was created the first day , was no other then the light of the Sun diffused over the hemispheare ; the whole hemispheare is much bigger , I hope , then the body of the Sun ; and yet the world , I think , was not more enlightened the first day , then the fourth , when that diffused light was contracted and compacted in a narrower compasse . 3. To what end should there be so much light in each starre exceeding the light of the Moone ? They received their light not for themselves , but for us ; ( except you will say there be innumerable worlds , which must be enlightened aswell as ours ) but wee receive by many degrees more light from one halfe of the Moon , then wee doe from all the starres together . Surely God made nothing in vaine ; but in vain hath the starres so much light , if man , for whom they were made , receive no sight nor benefit from this light . 4. Astronomicall positions concerning the magnitude and heighth of each starre , on which they ground their darke conjecture of light , are toyes and fictions of their owne heads : they make false Maximes , and on these they build confused Babels of their owne conceits : yeeld to them that they have the semidiameter of the earth , and then Graeculus esuriens ad Coelum jusseris ibit ; Every smatterer will exactly tell you the height and bignesse of each starre , Haud secus ac si oculo rubricam dirigat uno . 5. I will tell you what St. Austine saith of this Question , and of the Astronomers of his time : Let them ( saith hee ) talk of heaven , who have but small interest in heaven ; wee confidently beleeve that these lights are greater then others , which the Scripture commends to be such . Let them give us leave to trust our owne eyes ; it is manifest that they give more light to the earth then all the rest do , &c. The Scripture then , and our owne senses assure us that these are the great lights . If you say that each starre is a bigger light in it selfe then the Moon , I will beleeve it when I see it ; or have talked with one of your world in the Moon , who perhaps can informe us better , then any reason you can bring to evince us . 2. Wee grant that Moses tells us of waters above the firmament , but we deny that this is in reference to an erroneous conceit ( as you say ) but rather wee hold , That it is an erroneous conceit to forsake the true fountaines of knowledge , to digge crackt cisternes ; to preferre any opinion to the plaine text of Scripture . What a forced exposition is it , to call clouds and raine below in the aire , and which are oftentimes lower then the tops of hills , to call these I say , waters above the heaven , of which the Psalmist speaks ; whereas these waters are so farre below the heaven ? And how can any conceive , that the second day there was raine below in the aire , and that God by the Firmament did separate that raine from the waters of the sea ? And though I should yeeld that the aire is called heaven sometime Synecdochically ; and that raine or clouds being in the aire , may be said to be in heaven : yet I cannot yeeld , that therefore they are above the heaven , for to be above , and to be in , differ much : therefore I hold with the ancient Doctors of the Church , That there be waters above the heaven , which is no more incredible ( saith St. Austine ) that there may be waters in the upper part of the great world , then that there may be waters in a mans head , which is the upper part of the little world . If wee look ( saith St. Ambrose ) 1. On the greatnesse and omnipotency of God in creating the world . 2. On his ordinary power in preserving the world , sustaining all things by the word of his might , by which he holds up the sea that it may not drown the low land . 3. On his miraculous power in causing the waters of the Red-sea to stand upon an heap , and Iordan to goe back : which miracle he made visible , that thou mayst beleeve these things which are invisible ; then why should wee doubt of these waters which be above the heavens ? If any aske mee what is the nature , use , or end of those waters , and how they are there ; St. Austine shall answer for me : Quomodo , aut quales ibi aquae sint , &c. how , or what kind of waters these be , is uncertain ; but that there be waters there wee doubt not , because greater is the authority of this Scripture , then the capacity of all humane wit. 3. When the Scripture speaks of innumerable starres , you say , that is to be understood according to the vulgar opinion : but I say , that it is the opinion of the best Learned , that they cannot be mumbred , even Clavius , whom you cite for you , confesseth , That though Astronomers have reduced the most conspicuous starres to the number of 1022. yet that there are multitudes of starres , besides these , that cannot be told , Hoc nunquam negabo , ( saith hee ) I will never deny this : and hee saith also , That God so enlarged Abraham's sight , that hee made him see all the starres of heaven . If then you looke in a cleare winters night towards the North ; if you look on the milkie way , if you consider the Stars towards the South pole , not discernable by us ; you must confesse that the Scripture speakes properly , and not according to vulgar opinion , when it saith , That the Starres are innumerable : therefore saith Saint Austin , Whosoever brags that he hath comprehended and set down the whole number of the Starres , as Aratus and Eudoxus did ; Eos libri hujus contemnit authoritas ; the authority of Scripture contemnes them . But when you tell us , That the Israelites did farre execed the number of the Starres ; that is nothing to our purpose : besides wee can easily answer , that God did not compare Abrahams carnall seed to the Starres , but his spirituall seed . His carnall seed is compared to the sand and dust ; and so writes Saint Austin . Againe , when you have found out the true number of all the Starres , then tell us , whether they or Abrahams seed be greatest in number . 4. You prove that the holy Ghost speakes not exactly of naturall secrets ; for he sets not downe the exact measure or proportion of Solomons brasen sea . Answ. I had thought that a brasen vessel had been the worke of art , and not a secret of nature : that Geometricall proportions are secrets of nature , is a maxime onely in your Philosophie . 2. I had said that Iosephus held this sea not to be perfectly round ; You reply , That then the disproportion will be greater , and that Scripture which calls it round , is to be beleeved before Iosephus . I answer , that I alledged not Iosephus to preferre him in my beliefe to the Scripture , but to shew that there could not be an exact proportion , betweene the diameter and the circumference , in a vessell not exactly round ; and yet the Scripture doth not say , it was exactly round , but onely round . Every thing that is called round is not of an exact round figure ; an egge is called round ; The Rainbow is said to be round about the Throne . And the hills to be round about Ierusalem . And children to sit round about the table &c. Which you will not say are to be understood of an exact round figure . But indeed I know not how to please you ; if I alledge Scripture , you answer , that Scripture speakes not exactly of naturall secrets ; that it accomodates it selfe to the errours of our conceits ; that it speaks according to the opinion of the vulgar , &c. If I alledge Iosephus or any other Author , then you tell us , that Scripture is to be beleeved before Iosephus ; so that you are more slippery then any eele . 3. I had said , that the Scripture for brevities sake in numbering , used onely to mention the greater number , and to omit the letter ; as Iacobs family were seaventy soules , which indeede were seaventy five ; and many other such passages I alledged . You answer , that this confirmes your Argument ; For the Scripture is so farre from speaking exactly of Philosophicall secrets , that in ordinary numbering , it doth conform to common customs . Answ. 1. Shew us that this kinde of numbering , was the common custome . 2. Will it follow : The Scripture doth not exactly number , sometimes for brevities sake ; ergo , it never speakes exactly of Philosophicall points ? 3. If this consequence be good , then it will follow , that you never speake exactly of Philosophicall points : for you sometimes in mentioning of numbers , omit the lesser number ; as when you say seaventy Interpreters , whereas there were seaventy two . Lastly , I answer , that there is great oddes betweene an historicall narration of the measure of a vessell , as it was taken by the work-men , who are not still exact Geometricians : and a plaine and constant affirmation of a Philosophicall truth . He that wrote the Bookes of the Kings , sets down the circumference of the brasen sea to be thirty cubites , and the diameter to bee ten ; for so doubtlesse the measure was taken by the work-men : but when the Scripture saith , The earth is immoveable ; it records this as a Philosophicall or Theological maxime ; and not as an historicall passage . Concerning the ends and sides of the earth , and of heaven we will speake anon . 5. That the earth is founded on the waters , is not the opinion of common people , but rather the contrary ; for they are led by sense as you use to say : and their sense shewes them , that the seas are above the earth ; and reason will teach them , That a lighter body cannot be the foundation of a heavier . But you bring a ridiculous reason , why some thinke the earth to be upon the water : Because when they have travelled as farre as they can , they are stopped by the sea : By the same reason , if you were travelling and stopt by a river , or lake ; you will conclude that the earth is upon that river or lake . But your opinion is true in some sense ; for when we are stopt by the sea , lake or river , we get up into a boate or ship , and then indeed earth is above water : but I thinke you was asleep when this watrish reason dropt from your pen. I have already shewed how the earth is said to be upon the sea ; that is , ( by the Hebrew phrase which wants comparatives ) that it is higher then the sea ; and that it is in some parts of it above the seas , flouds , and rivers , that are in the concavities of the earth . 6. You speake much of the right and left side of Heaven , and dextro Mercurio ; you have conveyed a great part of your discourse out of Clavius , without acknowledgement : but quorsum perditio bac ? This waste of words might have been better spared , as being impertinent . For that place of Iob speakes indeed of the right and lest hand , but not a word of heaven : neither is there any right or lest sidein heaven , nor needs there to be . For the left side is more imperfect and weak then the right , which cannot be said of heaven , being an uniforme , and every way perfect body . And how can there be a right and left side , where there is neither sense nor life , nor distinction of organicall parts ? Therefore , in trees and plants , there is no right or left side , though they have life ; much lesse can this be in heaven . 2. Tell us what part of heaven doth the Scripture call right or left ? this I know you cannot tell . 3. Though the Scripture should speak after the vulgar phrase , in naming the right and left side of heaven : doth it therefore follow , that the Scripture speaketh so concerning the stability of the earth ? 4. Whereas you say , That Aristotles opinion in this point is delivered upon wrong grounds , supposing the Orbes to be living creatures , and assisted with Intelligences : I confesse that he calls the heaven 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , as having a soule or spirit , which he calls Intelligence , we Angel , by which the heaven is moved : but he doth not hereby suppose the heaven to be a living creature ; for the Angels are not informing sormes of their Orbes , but assisting . When the Angel was in the poole of Bethesda , and moved the water , you will not inferre upon this , that the poole was a living creature : whatsoever is 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , animatum , that is , hath a soule or spirit in it ; is not therefore a living creature : for so you may say a paire of bellowes , or winde instruments of musicke , are living creatures ; for winde , breath and aire , are called sometimes soules : 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or anima , or animus , is common to them all . Quicquid ignes , animaeque valent : Phrygias audire animas , are spoken of bellowes , and musicall instruments ; so , Phrygius cornus liquida canit anima : And yet I will not deny , but metonymically , heaven may be called a living creature ; as being that which giveth life to living creatures : or by Analogie , it may be said to live , in respect of the Angel which supplies the roome of a soule , not in giving life , but , motion to it . 5. It was no wrong ground in Aristotle to say , that the heavens were assisted with Intelligences , seeing they cannot move themselves being simple substances ; neither can naturall forme give such multiplicitie of motions , as are in the heavens ; neither are they moved by other bodies ; for these bodies at last must be moved by spirits ; neither doe naturall bodies move naturally in their place , but , to their place : now the heavens are in their place . Of this opinion were not onely the Philosophers , but also the Christian Doctors : heavenly bodies are moved by the ministery of Angels , saith Saint Austin . Origen saith , that the Angels have the charge of all things , of earth , and water , aire , and fire : and perhaps Saint Hierome mistooke his meaning , when he attributes to Origen this errour , of assisting reasonable soules to the heavens ; he meant the Angels . And Thomas , by that Spirit , that compasseth the world by its motion , Eccles. 1. 6. understandeth an Angel. It were strange to thinke that so many Angels should be assigned by God for the earth ; and for inferiour officers towards men , and none should have the moving of the heavens : but of the Angels moving their spheares , I have spoken already against Mr. Carpenter . 7. The Spirit ( you say ) applies himselfe to the common tenent generally received heretofore , in attributing wisdome and understanding to the heart ; whereas reason and discursive faculties , have the chiefe residence in the head . Answ. 1. How know you that this was the generall tenent in Solomons dayes ? From what stories of these times have you had this ? The word ( heretofore ) must signifie the time before Solomon : I doubt me , if you should be put to it , you could not prove that the opinion of the understandings residence in the heart , was the common tenent in the world before Solomon ; but I perceive you would have it to be so , because Solomon placeth understanding in the heart : as if the Scripture set downe no positive Doctrines , but what were common tenents , whether true or false . 2. The word ( heart ) here may signifie the soule or minde ; as it doth often in Scripture , and in humane writings too ; the soule is called heart , and the heart is called soule oftentimes . So in Homer , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , eating their soules , that is , their hearts with cares . And in Plutarch , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , is to be without reason or understanding : vecordes and excordes , are men whose minds are distempered . So in Saint Peter , By the hidden man of the heart , is meant , the renovation of the minde . If then by the heart is understood the mind or soule , you must needs grant , that it is a tenent no lesse true then common , that the understanding is in the heart , whether you take it for a part , or for a power , or for a facultie of the soule . 3. This was not a common tenent many yeares after Solomon ; for neither Empedocles , nor the Epicures , nor the Egyptian Philosophers , nor the Arabians , nor the Academicks , held the understanding to be in the heart ; but some in the head , some in the breast , some in all the body . Herodotus affirmed it to be in the ears ; Blemor in the eyes ; Strato in the eye-browes : onely the Peripatetickes and Stoicks , placed it in the heart . 4. The holy Ghost attributes understanding to the heart ; not because it was a common , but because a true tenent : for howsoever Galen and his Sectaries hold the contrary , yet it is certaine , that the heart is the true seat of the understanding . For 1. The will is in the heart , therefore the understanding is there also ; such is the dependency of these two faculties , the one from the other , that the will is never without the understanding ; and indeed these two are but one in essence ; for the will is nothing else , but the understanding dilated , extended , inlarged to the desire and fruition of that object which it apprehends . 2. The Apostle saith , That we beleeve with the heart , ( except you will have this also to be spoken according to opinion , and not according to truth ) but without understanding , we cannot beleeve ; For to beleeve ( saith Thomas ) is the act of understanding , moved by the will to assent . 3. The heart is the originall subject of sense and motion , and consequently of understanding ; which cannot be in us without sense and motion . 4. Understanding is in the soule , the soule in the spirits , the spirits in the blond , and the bloud is originally in the heart ; which though it be in the liver as in a cisterne , and in the veines as conduit-pipes , yet it is in the heart , as in the fountaine . 5. The animall spirits in the braine , in which they say the understanding is , are both generated of , and preserved by the vitall spirits of the heart , being conveyed thither by certaine arteries , small strings , or fibrae . 6. In a sudden feare , which is the passion of the heart , the understanding is much darkened and disturbed . 7. Hippocrates every way a better man then Galen affirmes this truth : 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 : Mens , minde or understanding is in the left ventricle of the heart . That Booke , De morbo sacro , which goeth under the name of Hippocrates , which contradicteth this truth , is justly affirmed by Galen to be none of his . 8. Though I should yeeld to the Galenists , that the understanding is in the braine ; yet I will yeeld that it is there onely instrumentally and secondarily , and in respect of its act or exercise ; for originally , principally , and in respect of its faculty , it is in the heart onely : neither would there be any exercise of understanding in the braine , if it were not from the influence which it receiveth from the heart . Neither is this strange , that the act should be in one part , and the faculty in another ; for the faculty of seeing is in the brain , and yet the act of seeing is in the eye : so that though the eye were lost , yet the faculty would remaine still in the braine . As for any thing that the Galenists can say against this , it is of no moment ; for although the braine be hurt , wounded , or inflamed , yet the faculty of understanding is not lost , though the act or exercise be hindered . Besides , there is a phrensie or alienation of the minde , upon a hurt or inflamation of the Diaphragma , as well as of the braine ; therefore , the ancient Physicians called this muscule , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , because it being hurt , the minde was hurt : the remedies applied to the head by which the braine is cured , doe not argue that the understanding is there ; but that there it doth exercise it selfe : and yet remedies are applied sometimes to those parts where the disease is not , but in some other place ; but this I leave to Physicians . I remember that Philo will have the understanding which he compares to a King , to be in the head ; because there be all the senses , as the Kings guard : but he is deceived , for the guard may be in the same house with the King , but not in his bed-chamber . The guard or outward senses are in the outward court , the inward senses are in the privy chamber , but the King himselfe is in the heart , as in his bed-chamber . If any reply that the head is uppermost , and therefore the worthiest part of the body , and fittest for the King to be there ; I answer no ; for the garret or upper part of the house is for the servants to lodge in ; the King ought to be in the most inward and safest part of his palace . It is evident then by what we have said , that the holy Ghost by placing the understanding in the heart , did speake according to truth , and not to common opinion ; and therefore to write that the spirit of truth who leadeth us into all truth , speaketh rather according to opinion then truth ; is a note blacker then your inke , unfit to fall from the pen of a Christian. For even allegories , tropes , figures and parables , are truths : but I impute this slip rather to negligence in you , then malice . 8. The vipers egges will not help you : Ova aspidum ruperunt , they have broken the vipers egges , as you translate it : but 1. The viper hath no egges ; for whereas other Serpents lay egges , the viper excludeth young vipers and not egges : therefore called vipera , quasi vivipara : Vipers egges are such chimera's , as your world in the Moone . 2. The aspis and the viper are of different kinds ; to say that aspis is a viper , is as true , as if you did say , a cat is a pig , or a crow is a goose . Read AElian , Pliny , and others who have written the stories of these creatures , and Physicians who make treakle of vipers , not of aspes ; if you will not beleeve me . It was a viper , not an aspe , that leaped upon Saint Pauls hand : they were aspes , not vipers , that Cleopatra applied to her breasts . 3. This Scripture doth not allude to that common fabulous story of the viper , as you say , breaking his passage through the females bowels : but it compares the counsels and plots of wicked men to the egs of the aspes , which being white and faire to the eye , are venomous within , and cannot be broken without the indangering and poysoning of him that breakes them : so wicked mens smooth counsels and plots , howsoever specious in their pretences , are notwithstanding venemous and deadly in their intentions and execution . 4. Though I should grant you that vipers have egges , yet it is one thing for men to breake vipers egges , and another thing for young vipers to breake through the bowels of the female ; the Scripture speaketh of the former breaking , and not of the latter ; neither hath it any relation at all in this place to that story of the vipers breaking through the belly of the female . 5. Nor is this story so fabulous as you take it , having the patrocinie of so many great and grave Authors for it ; namely , Aristotle , Theophrastus , Herodotus , AElian , Plutarch , Horapollus , Pliny , Saint Basil , Saint Hierome , Isiodor , and divers others . Scaliger indeed writes , that he saw a viper bring forth her young ones without hurt ; and perhaps Angelus , Brodaeus , and some others have seen the like : but what though we have seen some unhurt ? it is a hard skirmish where none scapes . To inferre that no vipers are killed by their young ones , because some are not , is as much as if you would say , no women are sicke or pained in their childe-birth , because some are not . Thus you see that you can make no treakle or antidote of your viper for the strengthening of your opinion ; the very names which are given by the Greekes and Latines to this creature , shew that this is no fiction ; for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 quasi 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , having much paine in bringing forth ; and vipera , quasi vi pari●ns . But we will shake off this viper from our pen , as Saint Paul did that viper in Malta from his hand ; and if your viper hath bit us , let us see if your aspe ( for so naturalists doe write ) will cure us . 9. The aspe ( which you translate the adder ) stops his eares , ( saith the Psalmist ) against the voyce of the charmer . This you say is fabulous , if we may beleeve many naturalists , yet the holy Ghost alludes to it because it was the generall opinion of those dayes . Answ. You are a great Antiquary , for you know the common opinions that were in Davids dayes , and you tell us not out of what records or manuscripts you have this ; but indeed I will not beleeve you , nor your many naturalists , whom you , should have named , and shewed us their reasons , why they think this to be fabulous . 2. You will not ( I think ) hold inchanting of Serpents to be fabulous , except you will ( as you use to doe ) contradict both sacred and profane , ancient and recent stories . 3. Nor will you deny that there is great cunning and prudence in Serpents to avoid dangers , and to preserve themselves ; our Saviour will have us to learne wisdome of them ; why then may not the aspe naturally have this piece of policie to stop his eare ? 4. Though there were no such naturall policie in the Serpent , yet may he not be taught by inchanters to do so ? You shal read in stories of stranger matters done by Serpents ; if you will reade Irenaeus , Austin and Epiphanius of heresies , you shall finde how that sect of the Valentinians or Gnostickes called ( from worshipping of the Serpents ) Ophits , did teame and teach their Serpents to come out of their holes or boxes where they were kept , to crawle on their altars ; eo licke their oblations , to wrap themselves about their eucharist , and so returne to their holes : the like is recorded by Virgil of a Serpent on the altar which AEntas erected on his fathers tombe : Tandem inter pateras & levia pocula Serpent , Libavitque dapes , &c. I will not speake of Olympias her Serpent , and of many others . 5. May not Satan who hath still abused the Serpent to superstition , cause the aspe stop his eares when he is inchanted ? Is it a more incredible thing for an aspe to stop his eare , then for a Serpent to speake and discourse , as he did to Eva. I could tell you strange stories of the Serpent Epidaurius at Rome ; of that Serpent that barked at the ejection of Tarquinius , and of others recorded by grave Historians , which I will not account fabulous , though you perhaps will ; because I know that Satan by permission can doe strange things . 6. It is manifest that beasts , birds , and fishes , are diversly affected , with joy , fear , courage , anger , &c. according to the qualitie of the sound which they heare : why then should the relation of the aspe stopping his care be accounted so incredible ? It may be as naturall for him to stop his eare at an ungratefull sound , as for other creatures to run away from it . 7. Though men have but small knowledge of this , yet ( as St. Austin saith ) the Spirit of God knowes better then all men do ; who had not recorded this had it not been true ; so that what is by men accounted an opinion , in Scripture it is truth , saith the same Father : by all this you may see that the holy Ghost speaketh not according to mens opinions , but according to truth ; and though you should erect your two Serpents over your dore , as the Gentiles used to doe over their temples , yet they will not priviledge your opinion . 10. The North winde which the Scripture calleth cold and drie , the Southwinde which is hot and moist , are phrases as you say which doe not containe any absolute generall truth : for though the North-winde to us on this side of the line be cold and dry , yet to those beyond the other tropicke it is hot and moist . Answ. There is no absolute generall truth in most of the sublunarie works of nature , for they are subject to much change ; and especially the windes which are the emblemes of unconstancy . So that even here in this Island I have known northern windes warme and moist , and southerne cold and dry ; and if you read Acosta he will tell you , that ordinarily beyond the line , the North-winde is cold and dry , as it is in this side ; and not hot and moist ( as you say ) though it blow from the line . The windes doe vary according to the climate they blow through , and yet they keep not the same tenure still in the same climate : the North-winde is ordinarily cold and dry in that climate , where these Scriptures of Iob and Proverbs were penned ; and the Scripture speaketh onely of that climate : and yet if you will beleeve Acosta's owne experience , these Scriptures are true also of the North-winde beyond the line . But what will you inferre upon this ? marry that this proposition , the earth is immoveable , containes not a generall truth , because the North-winde is not generally cold and drie ; as if you would say , this proposition , the sea ebbes and flowes , containes not a generall truth ; ergo , this proposition , man is a reasonable creature , is not generally true ; who will not laugh petulants splene , to heare such Logick ? But you give a reason why this phrase of the coldnesse and drinesse of the North-winde is not generally true , because in some places it is hot and moist : prove unto us that the earth in some places moves circularly , and then we will yeeld that this phrase of the earths immobility is not generally true . 2. These Scriptures which you alledge for the coldnesse of the North-wind may be diversly understood : for Iob 37.9 . there is mention made of dispersers or scatterers , but not of the North-wind : and this quality is in every wind to disperse the clouds , as well as to bring them . In the Pro. 25. 23. it is said , that the North-winde bringeth forth raine ; for so the Hebrew word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 signifieth , as well as to drive away ; and so Iunius and Tremelius translate it , gignit ; and instead of Aquilo , they have Caecias , which is the North-East-winde , though some think it to be the North-West : so the seaventy Translatours have 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 to excite and stirre up : so Iob 37. 21. where some translate , faire weather ; in Hebrew , Greeke , and in the old Latine Translation , it is , Gold cometh out of the North. Thus upon tottering and uncertaine foundations , you raise the structure of your wilde phantasies . 11. The darkning of the Sunne , the turning of the Moone into bloud , and the falling of the Stars will not help you ; for these are not naturall effects , but miraculous workes of God to be done afore Christ second coming : and to say that these things shall be but in shew or appearance , is to make us thinke that God will affright the world , as we doe little children with hobgoblins . How will the truth of his miracles , the terrour of his judgements , the greatnesse of his majestie be seene , if these things shall not truely and really be effected ? you may as well say , that all former miracles were but in shew or appearance : as Christs turning of water into wine ; his walking on the Sea ; his raising of the dead ; curing of diseases ; appeasing of the storme , &c. Is it a thing more incredible for the Sun to be miraculously darkened at Christs second coming , then it was at his passion , when the Sun lost his light , the Moone being at full ? Which miracle was acknowledged by that learned Areopagite , being then in Egypt . Or is it more incredible that the Moone shall be turned into bloud , then for clouds to raine bloud ? of which bloudy showers , you may read in the Roman and French stories , and in our owne Chronicles at home , of bloud that rained seaven dayes together in this Island , so that the milke was turned into bloud . What say you of all the waters of Egypt which were turned into bloud ? and if wee may beleeve the Church stories , when Felix the Martyr suffered , for not delivering up the Bible to be burned , about the yeare of Christ , 302. the Moone was turned into bloud : thus God is able to make your world in the Moone Aceldama . And why shall we not as well beleeve that the Starres shall fall , as that they sought against Sisera , or that a new Starre conducted the Wise-men to Christ ? God is as able to shake the Heavens , and the Stars from them , as a winde is to shake a fig-tree and spoile it of leaves : he that setled the Stars may remove them . And to tell us that these Meteors which wee call falling Stars , are meant ; is a childish conceit , seeing such doe fall almost every night , and are the meer works of nature , no wayes fit to expresse Gods judgements , and the terrour of that day . 12. Christ saith to Nicodemus , that he knew not whence the winde cometh , nor whether it goeth . You inferre that none knows this as the vulgar thinke ; and therefore this , and such like phrases are to be understood in relation to their ignorance ; and the Scripture ( you say ) speaks of some naturall effects , as if their causes were not to be found out , because they were generally so esteemed by the vulgar . I perceive you are none of the vulgar , but , de meliore luto ; for it seemes you know these causes which the vulgar know not : you are gallinae filius albae ; a happy man that knowes the hid cauises of things : Foelix qui poteris rerum cognoscere causas . I confesse my ignorance in the most of these naturall causes ; Philosophers reasons are not satisfactory to me : Obstat cui gelidus circum praecordia sanguis . But if the wiser sort know from whence the winde commeth , which the vulgar doe not ; so likewise must the wayes of the Spirit in our regeneration be known to them also , though not to the vulgar : but sure that is not Christs meaning ; for he meanes that the way and manner of our regeneration are as hid & secret to men without divine revelation , as the wayes of the winde are : and as none knows the one , so none the other . 2. If you know from whence the winde cometh , and whither it goeth , I pray tell us , and hide not your light under a bushell : perhaps you will say that it cometh from North , or South , East , or West ; if you can say no more , you were as good lay your finger on your lip with Harpocrates , and say nothing . For tell us , out of what part of the earth or sea doth the North-winde arise , when it blowes over our Island ; and how farre doth it goe , or where doth it end ? Whence came the great South-West-winde , which the 27. of December last sunke so many ships , overturned so many trees , overthrew so many barnes and dwelling houses ? and where did this winde end ? Can you tell us whence the Brises or trade-windes under the line which blow continually from East to West , doe proceed ? or doe you know whence the Aniversarie windes in Egypt , called Etesiae , doe come ? These begin to blow when the dog-starre ariseth , and continue forty dayes together ; such windes blow in Spaine and Asia , but from the East ; in Pontus from the North. I thinke that though you should aske of the Finlanders who used to sell windes , ( if you will beleeve Olaus ) they cannot informe you . 3. How can Philosophers tell us from whence the winde cometh , when they know not as yet what the winde is , whether an exhalation , or the aire moved , whether it ariseth out of the sea , as Homer thinks , or out of the bowells and caves of the earth , as others suppose . Pliny will tell you of Caves where the winde blowes continually ; and Neptune , in Virgil , will shew you , that AEolus hath no power in his kingdome , but in the hollow caves and rockes of the earth : — tenet ille immania saxa , — Illâ se jactet in aulâ AEolus & caeco , &c. — 4. St. Austine was no vulgar man , and yet hee confesseth his ignorance , that he knowes not out of what treasure God bringeth forth his windes , and his clouds ; indeed wee may all acknowledge with Seneca , that our knowledge is but ignorance ; and because of the uncertainty of humane conjectures , it is best to content our selves with the knowledge of that supreme cause of all naturall effects revealed to us in Scripture . 13. Solomon ( you say ) doth onely mention the sea being obvious , and easily apprehended by the vulgar , to be the cause of springs and rivers , though in nature there be many other causes of them . I answer , Solomon doth mention the sea onely , not because the vulgar apprehends it so , but because indeed and verily it is so ; to wit , the onely prime cause of springs and rivers : If you should tell mee that raine and vapours are other causes , you would say nothing , for these are subordinate to the sea ; hee that names the prime and superiour cause of any effect , doth not exclude , but include all subordinate and inferiour causes . If , I say , the sea is the cause of springs , I say inclusively , that raine and vapours ( which have their originall from the sea ) are the causes also . When the Jewes said they were the sons of Abraham , they excluded not Isaac and Iacob . When Saint Paul saith that God giveth to every seed its body , hee excludes not the Sun , Raine , Earth , and the formative power of the seed , which are subordinate causes to God. 2. Solomons drift was not to make a Philosophicall discourse about the causes of rivers , but to shew the vanity of things by the continuall issuing and returning of rivers from and to the sea , as hee had done before by the Sunnes motion . 14. For the thunder , which David calls the voice of God ; wee say that this phrase is not to be understood with relation to some mens ignorance , as you fondly conceit , but to Gods omnipotency and providence ; who by his thunder , as by a voice , speaks unto the world : and a powerfull voice it is to shake the hearts of the proudest Atheists , even of Caligula himselfe ; and to teach the most perverse Epicures , that there is a God in heaven who ruleth and judgeth the earth . No eloquence prevailed so much with Horace as this , when hee was parcus Deorum cultor , an Epicure : it made him renounce his errour , — & retro vela dare ; by which the Gentiles acknowledged there was a supreme God , whom they called Iupiter , and that hee had the power of thunder , — qui fulmine concutit orbem . — qui foedera fulmine sancit . So the same Virgil acknowledgeth that the thunder made the people to stand in awe of God : — an te Genitor cum fulmina torques , Nec quicquam horremus , &c. By this , God moved the hearts of the Romanes to use the Christians kindly , when by thunder hee overthrew the Marcomans ; and the Christian Legion from thence was called , The thundering Legion . It is his weapon with which hee fights against wicked men , and which hee flings 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , against perjurers , as Aristophanes saith : all the thundering disputations of Philosophers , and the small sparkes of light or knowledge which they have of naturall causes , are but toyes ; they are no better then glow-wormes . What is the croaking of frogs , to the cracking of thunder , or the light of rotten wood , to lightning in the aire ? Therefore , in spight of all Naturalists , let us acknowledge with David , that it is the Lord that maketh the thunder , that this voice of the Lord breaketh the Cedars , and divideth the flames of fire , and shaketh the wildernesse , &c. Besides , the thunder is called Gods voice , as the winde Gods breath , by an Hebraisme : as tall Cedars and high mountaines are called the Cedars and Mountaines of God : the voice of God is as much as if you would say , an excellent voice . Then whatsoever Naturalists affirme peremptorily of the thunder , I will with Iob and David , acknowledge God to be the onely cause ; and will aske with Iob , The thunder of his power who can understand ? Quis tonitrus sonum , aut quemadmedum oriatur explicandis rationibus assequi possit ? saith Symmachus , on these words of Iob. 15. The constellation called the 7. Starres , are found ( you say ) by later discoveries , to be but six : What if I should grant you this , and more too then you desire ; to wit , that of old they were accounted but six of some : So Ovid , Dicuntur septeno , sex tamen esse solent . So Aratus , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 And generally the Poets held , that though Atlas had seven daughters , called Atlantides from him ; yet one of them , to wit , Merope , or as others say , Electra , hides her face : but divers others hold there be seven to be seen . And S. Basil tells us in plain termes , that there are seven stars of these , and not six , as some think : but let there be seven , or but six , what is this to your purpose ? Mary , that the Scripture , Amos 5.8 . speakes of seven starres , according to common opinion , being but six in Galilies glasse ; but indeed the Scripture speaks neither of six nor seven , but of a certaine constellation , which the Seventy Interpreters leave out , as a thing unknown to them . Symmacbru , and Theodotion interprete 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the old Latine hath it Arcturus , which is a starre in Bootes behinde the taile of the great Beare ; in English we call them Seven starres , and to mine eyes they seem to be so many : But if in Galilies glasse there be but six ; it 's no wonder , for you tell us elsewhere , That the better the glasse is , the lesse will the starres appeare . It is not like then , that so small a starre can be seen through it : Let therefore the number of 7. remaine , it is a sacred nnmber ; — numero Deus impare gaudet . CHAPT . IIII. 1. Many Philosophicall points are handled in Scripture . 2. The heavens how round in the opinion of the Fathers . 3. Wre must have a reverend esteem of the Fathers . 4. How the seas not overflowing the land may be esteemed a miracle . 5. The works of Nature may be called miracles . HEre you tell us of Learned men which have fallen into great absurdities , whilst they have looked for the grounds of Philosophy out of Scripture , which you shew by the Iewish Rabbines , and some Christian Doctors . Ans. As it is vanity to seek for all Philosophicall grounds in the Scripture , so it is stupidity to say there be no Philosophicall grounds or truths to be found in Scripture : whereas Moses , Iob , David , Solomon , and other Penmen of the holy Ghost , have divers passages of Philosophy in their writings , as I have shewed heretofore of divers constellations out of Iob : and why may not Philosophicall truths be sought for out of Scripture , seeing Philosophy is the contemplation or knowledge of divine and naturall things ; both which are handled in Scripture , divine things principally , naturall things in the second place ; that by naturall things we may come to the knowledge of Divinity , and by this to the attainment of eternall felicity . Therefore in Scripture is recorded the creation , the cause , qualities , and effects of the creature , that by these we may come to the knowledge of the Creator . If the Gentile Philosophers had not found much Philosophy in Scripture , they had never conveighed so much out of it , ( as they did ) into their Philosophicall books , as Theodore sheweth . The idle opinions of many Philosophers , which are grounded neither on sense , nor reason , ( as yours of the Earth's motion ) are not to be sought for in Scripture , but Philosophicall truths which are grounded on either , or both , may be sought and found there : and whatsoever idle conceits the Jewes have had of Scripture , or their idle fables which they have grounded on it , concerne us not : they were a giddy headed people , given over to a reprobate sense , groping at noone day ; having their hearts fat , and their eyes blinded , that they may not see : their seeking for Philosophicall truths in Scripture was not the cause of their foolishnesse , ( for few or none of them were addicted to the study of Philosophy ) but their owne voluntary blindnesse , pride , stubbornnesse , and contempt of Christ the internall and essentiall Word of God , are the causes of their ignorance in the externall Word ; so that they ( having forsaken the truth ) follow lyes . But as for the Christian Doctors , they have not exposed themselves to errours , by adhering to the words of Scripture , but you are fallen into grosse errors by rejecting the words of Scripture : These which you count errours , are truths ; as , That the Sun and Moon are the greatest lights , That there are waters above the firmament , That the starres are innumerable , as wee have already shewed . As for the roundnesse of the heaven , though the Fathers doubt of it , yet they doe not absolutely deny it . Iustine Martyr doth but aske the question , Whether their opinion may not be true , which hold the roundnesse of the heaven . St. Ambrose saith , that it is sufficient for us to know that God hath placed the heaven over us like a vault , and stretched it out like a curtaine or skin . St. Chrysostome ( whom Theodoret and Theophylact doe follow ) deny the roundnesse of heaven , as it hath relation to our climate or habitation ; for so the heaven is indeed , as the Scripture saith , a vault or skin ; so that albeit the whole heaven being considered with the whole earth , be round , yet being considered with reference to parts or climates of the earth , it is not round : Or wee may with St. Austine so understand the word [ vaults ] or [ curtaine ] or [ skin ] that these tearms may stand well enough with the roundnesse of heaven ; si sphaera est , undique camera est : if it be sphericall , it is a round vault ; pellis in rotundum sinum extenditur , a skin may be made round or sphericall : for a round bladder ( saith hee ) is a skin ; so then neither the word vault , skin , canopy , or tabernacle , are words repugnant to the roundnesse of heaven , neither have you such reason to insult over the Fathers , as if absolutely and peremptorily they had denyed the roundnes thereof : For S. Austine sheweth , that the stretching out of heaven like a skin , is mentioned onely to shew the power of God , and with what facility hee made the heavens , with more ease then wee should extend a skin : and St. Hierome saith , that the opinion of the earths roundnesse is the most common opinion , agreeing with Ecclesiastes . So when the Fathers say that the earth is founded on the seas , &c. they doe but follow the Scripture phrase , which how to be understood wee have already shewed , and will touch it againe anon . 3. Suppose these were errours ; yet you must not take advantage from some errours in the Fathers , to lessen their credit in other things ; they were but men , and had not the perfection of knowledge which is in Angels , called therefore Daemones and Intelligentiae . St. Bernard saw not all things ; we should be sparing in raking into their errours , in uncovering of their shame ; and like flies , delighting in their soares . But yet you cannot obtain your purpose in ripping up of their errours ; for it will not follow : the Fathers erred in denying the sphericall figure of the heaven , &c. therefore they erred in denying the motion of the earth : must it follow , that because S. Cyprian erred in the point of rebaptization , therefore no credit must be given to him in affirming Christs incarnation ? and , I pray , what great error was this in them , to conclude from manifest places of Scripture , that the seas not overflowing the land is a miracle , and that they are restrained by the speciall power of God ? I grant that all seas are not higher , nor so high as some lands ; but it is manifest , that the sea in some places is much higher then the land , as the Hollanders and Zelanders know ; and that their lands are not overwhelmed with the sea in a storme , is a miracle ; and the finger of God is to be seen in restraining of them : which seas , when hee is angry with the inhabitants , hee lets loose sometimes , to the overthrow of townes and villages : — Camposque per omnes , Cum stabulis armenta trahunt — In the dayes of Sesostris King of Egypt , it was by measure and observation knowne , that the Red-sea was much higher then the land ; but we need not goe so farre , the coast of our owne Island in divers places being lower then the sea , will prove this to be true ; where we may daily see Gods power , in curbing the violence of that furious creature : — For the Eternall knowing The Seas commotive , and unconstant flowing , Thus curbed her , and 'gainst her envious rage , For ever fenc'd our flowry mantled stage : So that we often see those rowling hills , With roaring noise , threatning the neighbours fields ; Through their owne spite to split upon the shoare , Foaming for fury that they dare no more . 5. Why then may not this be called a miracle , whereas many strange , yea ordinary effects of nature are called miracles ? Plato called man the miracle of miracles : and David saith , that fearfully and miraculously he was made . Doe not you know that Diana's Temple , the Egyptian Pyramides , and the rest of those stupendious buildings , were called the seven miracles of the world ? not only Gods extraordinary works above nature , but also his ordinary works in nature , are miracles , though they be not so accounted ( saith Saint Austin ) because we are so used to them . For as it was a miracle to turn water into wine in Cana of Galilee , so ( he saith ) that miracle is seene daily : for who drawes the moisture or water from the earth by the root into the grape , and makes wine , but God ? That Gods finger is to be seen in every worke of nature , the Poet doth acknowledge : — Deum namque ire per omnes Terrasque tractusque maris , coelumque profundum . A miracle is so called because it excites admiration ; and doe we not admire Gods power in earth-quakes , prodigious births , thunders , lightnings , and in the Eclipses of the great Luminaries ? therefore Saint Austin checks the vanity of Philosophers who went no higher in the contemplation of these naturall effects , then to naturall causes ; not looking unto God the supreme cause of all . Hence then it appeares that the Fathers are not mistaken , in attributing the not over-flowing of the sea to a miracle : howsoever ( as your figure sheweth ) the sea may seem to be , and yet is not higher then some lands . Neither is there any contradiction in Scripture , though sometime it make the sea higher then the land , and sometime lower ; for so it is according to the diversity of coasts ; and because of much moisture and water found in the bowels of the earth , and in that it is encompassed with the sea , it may be said , that the earth is founded on the waters : therefore no man can be deceived in concluding points of Philosophie from expressions of Scriptures ( as you say ) but from the misunderstanding of Scripture ; for what is true in Philosophie cannot be false in Divinitie ; for in subalternall sciences there can be no repugnancy . CHAP. V. Divers Scriptures vindicated from false glosses ; as , Eccles. 1. 4. by which is proved the earths immobility , and heavens motion . 2. How the earth is eternall and renewed . 3. The Scripture speaketh not plainly and ambiguously in the same place . 4. The Scripture useth Metaphors . 5. How the earth stands out of the water , 2 Pet. 3. 5. by which its immobilitie is proved . 6. What is meant , 1 Chron. 16. 30. &c. by these words , The world is established , &c. 7. What is meant Psal. 90. 2. by the earth and the world . 8. How the heavens Prov. 3. 19. are established : and the Moon and Starres , Psal. 89. 37. &c. 9. How the heavens 2 Sam. 22. 8. hath foundations . 10. What are the pillars of heaven in Job 10. of the ends , sides , and corners of the earth in Scripture . 11. What is meant Isa. 51. 6. by the planting of the heavens . 12. How the earth is established . 13. What Job meanes by the earth moved out of its place . YOu would faine here overthrow those Scriptures which shew the immobilitie of the earth . 1. That place of Ecclesiastes , ( one generation cometh , and another passeth , but the earth standeth for ever . ) You say , That it is not the purpose of this place to deny all kinde of motion to the whole earth ; but that of generation and corruption . But I say , that it is neither the purpose of this place to deny the motition of the earth , nor to affirme the motion of the sunne : for why should he either deny the one , or affirme the other , which no man doubted of , or called in question ? his drift is to prove the vanity of mankinde , from the stability of the earth , and motion of the sun , windes and waters ; thus man is inferiour to the earth , because the earth is firme , stable , and immoveable ; whereas man abideth not in one stay , but cometh forth like a flower , and is cut downe , he flyeth like a shadow , and continueth not . Or ( as it is here ) he cometh and goeth ; so that coming & going are motions , to which man is subject , and are opposite to the immobilitie of the earth . The Antithesis then or opposition here is not between the substance of man and of the earth ; for man in respect of his substance is permanent as well as the earth , if either we consider his soule , or his body , according to the first matter ; but the opposition is between the qualities , outward estate , and life of man , and the immobilitie of the earth , so that the standing of the earth must be meant either of its permanency , or immutabilitie , or immobilitie : not the first , for man ( as I said ) is not inferiour to the earth in permancie ; not the second , for the earth is subject ( as all sublunary things are ) to mutability and changes ; therefore the third , which is the earths immobility , must needs be understood . And if Solomon had thought otherwise , to wit , that the earth moved , and the sun stood still ; he would have said , The sunne standeth for ever , the earth ariseth , and the earth goeth downe , &c. But , for all his knowledge , he was ignorant of this quaint piece of Philosophie . Againe , he proves mans vanity from the motion of the sunne , windes , and waters , though they move and are gone for a while , yet they returne againe ; but man being gone returnes no more : so that man hath neither the stability of the earth , but passeth away , and being past , hath not the power to returne againe , as the sunne , winde , and waters doe . It is plaine then , that the standing of the earth is opposed to its locall motion , and to the motion of men coming and going ; but it were ridiculous , as you say , to inferre that the earth is immoveable , because permanent ; for the mill and ship may be permanent , and yet move ; this illation is none of ours , we say it is immoveable because Solomon here sayes so ; for he saith it standeth ; and if standing be motion , then the earth moves . It is more safe for us to say , That the earth is immoveable , because Solomon saith it stands ; then to say it is moveable , because the word standing may signifie permanency , or abiding . As for the motions ( as you cal them ) of generation and corruption , from which you free the earth , they are not indeed motions , but mutations : Metus est à termino positivo , ad terminum poserivum . You checke the Jewes for collecting the earths eternity from the word ( Legnolam : ) albeit I know that this word doth not alway signifie eternity , but a long continuance of time ; yet that the earth is eternall , à posteriori , I thinke you will not deny , except you will tread in some new way of your owne different from that both of ancient and modern Divines , who affirme with the Scripture , That there shall be a new earth ; but new in qualities , not in substance ; a change of the figure , not of the nature ; of the forme , not of the substance ; a renovation of that beauty which is lost by man , but no creation of a new Essence ; so that the Jewes might justly inferre from Solomons words , that the earth is eternall , or stablished for ever . You snap at Mr Fuller for urging that these words of Solomon must be all understood literally , and not some of them in reference to appearance , but without cause ; for can the same Scripture with one breath blow hot and cold ? At the same time speake plainly and ambiguously ; in the same sentence have a double meaning ? The Scripture which is plaine and simple , is farre from double dealing . Will any thinke that when Solomon saith , There be three moveable bodies , the Sun , Windes , and Rivers that there are indeed but two ; and that the Sun moves not but in appearance , that is , moves not at all ? This is to make the Scripture indeed a nose of wax ; for what may I not interpret this way ? Christ fed the people with five barley loaves , that is , with foure loaves , for one was a loafe but in appearance . Three Wise-men came from Persia to worship Christ , that is , two came indeed , but the third came onely in appearance . You would laugh at me , if I should tell you , that of any three ships or mills , which move really , one did move apparently ; whereas both you & I see them move really . Now , if the Sun doth not move , why doth the Scripture say it doth ? What danger would arise if it spoke plaine in this point ? You say , That the Scripture speaks of some naturall things , as they are esteemed by mans false conceipt : But this is a false conceit of yours ; the Scripture doth not cherish or patronise the falshood of our conceits ; the end of it is to rectifie our erroneous conceits . It is true that in high and obscure points of Divinitie , the Scripture condescending to our capacity , useth the tearms of familiar and earthly things ; that by them we may by degrees ascend to the love and knowledge of spirituall things ; for the naturall man understandeth not the things of God : but in naturall things which are obvious to our senses , we need no such helps . If the Sunne stood still , it were as easie for us to understand his standing , as his moving . What you talke of the ends of a staffe , and of the ends of the earth , is impertinent and frivolous ; for the Scripture for want of proper words useth metaphoricall : and because there is no other word to expresse the remote bounds of the earth , then the word End , therefore the Scripture useth it . But you inferre that because the ends of a staffe , and the ends of the earth cannot be taken in the same sense ; that therefore the motion of the sun , and of the winds must be understood in divers senses : make an Enthymeme and see the consequence ; the Scripture saith , That a staffe hath ends , and that the earth hath ends , which cannot be understood properly , and in the same sense ; ergo , when the Scripture saith , The sunne moveth , and the winde moveth , both cannot be understood properly and in the same sense : as if you would say , The Scripture affirms that Angels are the sons of God , and that Judges are the sons of God , but not in the same sense : ergo , when the Scripture saith , That the raven flew out of the Arke , and the dove flew out of the Arke : both must not be understood in the same sense , but the one properly , the other in appearance . Our second proofe out of Scripture which you goe about to undermine , is that of Saint Peter : The heavens were of old , and the earth standing out of the water , and in the water . You say , That the word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , is equivalent to ( fuit , ) but I say , that this were to confound two predicaments , to make the essence and accident all one : the site or immobility of the earth , and the essence or existence thereof cannot be one or equivalent . 2. This were to commit a plaine tantology , for so the words must run ; The earth was , was out of the water ; if these two words ( was ) and ( standing ) be equivalent . 3. The Apostles scope is not only to shew that God made all the earth , ( as you say ) but that he made it thus ; that is , standing or immoveable : that he is the authour not onely of its being and essence , but also of that inseparable accident of immobilitie . 4. We collect not the rest and immobilitie of the earth from the bare expression of its being or creation , but from its being thus made ; for so we may reason ; What God hath made to stand fast out of , and in the water , is immoveable ; but God hath made the earth thus : ergo , it is immoveable . 5. It were ridiculous to conclude the immobility of a ship or a mill-wheele , because a part of them was made to stand above , and another part under the water for they were not made for that end to stand , but to move : But if you had brought your Simile from the rockes of the sea , you had done well ; for God made these rockes to stand partly above , and partly under the water ; and hee made them not to fleete with the Isles of the lake Lommond , therefore they are not moveable , for God hath made them immoveable ; and so hee hath made the earth : therefore , both the old and new Latine translations , doe use the word consistere , which signifieth constanter stare . Our third Argument is taken from these words , The world is established that it cannot be moved ; which words you will have to be spoken of the world in generall , or the whole fabricke of heaven and earth ; but you are widely mistaken ; for in the Hebrew text , the word [ holam ] which signifieth the whole universe of heaven and earth , is not used in any of these places ; but the word [ Tebel ] which signifieth the round globe of the earth , or the habitable world , as Pagnine hath it . So the Greek Interpreters in all these places use the word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and not 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which signifieth the whole bulk of the world , so called from its beauty : Now 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 is alwaies used for the habitable earth , so that 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , is a Synod of men dwelling upon earth , and not of Angels or stars : And when the Patriarch of Constantinople assumed the title of Oecumenicus Episcopus , he did not purpose ( for all his pride ) to bring the Angels and starres within the verge of his Diocesse or Episcopacy . So the old Latine translation never useth the word mundus , but orbis , and orbis terrae ; and Iunius with Tremelius , use the words orbis habitabilis , that is , the earth ; so that orbis is not used for mundus in any classick Author in prose , but for the earth , or regions and dominions of the earth : as , Orbis Asiae , Europae , orbis Romanus , &c. Besides , in the 96. Psalme , the heavens and the world ( as wee translate it ) are distiuguished in the 5. ver . God made the heavens : in the 10. ver . hee established the world , or earth . We need not then to have recourse to a Synecdoche iu the three originall Tongues . But you tell us , That David ( you would have said Moses ) seems to make a difference between the earth and the world , when hee saith , Before thou hadst formed the earth and the world : hee doth but seeme to make a difference , but indeed hee makes none ; for the copulative [ and ] is put exepeticè , for the disjunctive [ or ] here , and elsewhere in Scripture : as in Exodus , Hee that smiteth his Father ; in the Hebrew it is Abiu ve Immo , his father and his mother : and in the 17. ver . of the same Chapter , Hee that curseth his father and his mother , which the Evangelist St. Matthew rendereth , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , father or mother : so among profane Authors the same kind of speech is used : as , Natus annos 60. & senex . Here then God made the earth and the world , that is , hee made the earth , or the habitable world . 2. Wee may explain Moses his words here thus : God made the earth the first day , and then it was 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , earth ; but it was not made habitable till the third day , and then it became 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , a habitable world ; and so in this respect there is some difference between the earth and the world , that is , between the earth mingled with the water , and separated from it . Because Solomon saith , That God hath founded the earth , and established the heavens , you inferre , That the places of Scripture can no more prove an immebility in the earth , then in the heavens . But here also your speak at randome ; for the Hebrew word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Conen here , which Arias Montanus and the old Latine translate , stabilivit , doth properly signifie , to dispose , or order ; and so we translate the word Conenu , Ps. 37.23 . a good mans steps are ordered by the Lord. This word also signifieth to prepare : as , David prepared a place for the Ark. Therefore the LXX . Interpreters explain this word here by 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , hee hath prepared the heavens ; and Iunius , with Tremelius , by [ statuit ] hee hath appointed , [ or disposed ] the heavens . But what though wee should yeeld that the word may signifie to establish , will it therefore follow that the heavens are immoveable , because established ? No : for there is the stability of nature , and naturall qualites , which is opposite to mutability , and so the heavens are established ; and there is the stability of rest , and so it is opposite to mobility : thus the earth is established . But , you will say , seeing the same word [ establish ] is spoken of both the heaven , and of the earth , how shall you know that it implyeth immobility in the earth , and not in the heaven ? I answer , well enough ; because the Scripture , speaking of the earth , saith , It is established that it cannot be moved : but the Scripture never speakes so of the heavens , but onely that they are established ; not a word to shew any rest or immobility in them . Now you urge us with those places that speak of establishing of the Moon , Ps. 89.37 . of the stars , Psa. 8.3 . of the heavens , Pro. 8.27 . Why ( say you ) should these be counted sufficient expressions to take away motion from the earth ? I answer , we do not count this word [ establish ] of it self a sufficient expression ; for the originall word is ambiguous , and diversly interpreted , both by the Greek and Latine ; and moveable things may be established ; the moving Tabernacle , as well as the immoveable Temple . But if I should tell you , that though the Tabernacle be fastened or established , yet it is moveable , and the Temple is so stablished that it cannot be moved : You cannot but say , that my expression is sufficient to shew the difference of stability in the one , in and the other . So speaks the Scripture in plain tearms of the Earth's stability , Thou hast founded , [ or established ] the earth , and it shall stand : Thou hast laid the foundations of the earth , that it shall not be moved for ever ; so it is in the Hebrew . When a thing then is said to be so established , as that it standeth fast on a sure foundation , and cannot be moved , wee must needs acknowledge , that this is a full expression of its immobility ; which phrases are never spoken of the heaven , or any starre ; wee reade that the Sun stood once , but that was by miracle : of any other standing in Scripture we never read . So we read of the moving of the earth by earthquakes , but not else , Isa. 13.13 . and of removing of Islands , Rev. 6.14 . but never of a circular motion of the earth : for in that respect he hath made the earth that it shall not be moved . And to tell us , as you do , that the earth is established so onely that it shall not be removed , is both to mince the Scripture , and the power of God ; for as it is more easie to move an heavy body then to remove it , so is the power of God so much the greater , in that hee hath made a body of such solidity , weight , and bignesse , that it cannot be so much as moved , farre lesse removed : and if the Scripture be so carefull and punctuall in setting forth Gods greatnesse and power on so small a matter , as is the moving of a little part of the earth by earthquakes ; doubtlesse it would not have been silent in a matter of such admiration and power , as is the moving of the whole body of the earth , if ever hee had moved it , either by himselfe , or by his Angels , or by Nature his handmaid . Whereas you say , That fundavit cannot be taken properly , as if the earth , like other artificiall buildings , did need any bottoms to uphold it . I answer , that fundare terram is not to settle the earth upon a foundation or bottome , but to make it the foundation of all heavy bodies ; and therefore it is called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , fundum , the bottome , and fundus , the foundation ; so that nothing hath any foundation but on and by the earth . Ships floating on the water , have not any foundation , till they be tyed by anchors to the earth ; which the Poet knew , when he said , Anchora fundabat naves : therefore not metaphorically , but properly , doth the Scripture speak , in saying , God hath founded the earth ; but whereas the heavens are said to have foundations , 2 Sam. 22.8 . by heavens there are understood the mountaines , and so the vulgar Latine reads it : and so in Psal. 18.8 the text hath mountaines , and not heavens . Mountaines are called heavens metonymically , because they are in that part of heaven which we call the aire ; therefore by the Poets they are called , Aërel montes ; and so all the space from the superficies of the earth upward , is called heaven both in sacred and profane writings ; even this upper part of the earth wherein wee live is called heaven by the Poet : Sed falsa ad Coelum mittunt insomnia Manes ; and the Inhabitants of the earth are called Superi by the same Poet , Quae quis apud Superos surto laetat us inani . And as hills are called heaven , so heaven is called hills by David , when hee saith , I will look unto the bills , from whence cometh my salvation . By the foundation of the heavens then , is meant nothing else but the foundation of the hills . Now why you should call the earth an artificiall building , I know not : it was neither built by an artificer , nor by the rules and tooles of Art ; your earth in the Moon may rather be called artificiall , as being the work , not of God , nor Nature , but of Copernicus the master carpenter , and his workmen , of which number you are one ; but you should doe better , if with that wise master builder St. Paul , you would build upon the corner stone , and the foundation Christ Jesus , according to the grace of God which is given to you . You say well , That the pillars of heaven mentioned by Job will not prove them to be immoveable ; for wee know that heavenly pillars are moveable as the heavens are : so were these two pillars that conducted Israel through the desart , and those night meteors , called fierie pillars . 2. By heaven may be meant the Church called oftentimes heaven in Scripture , and by pillars the eminent Doctors of it : So Peter , and Paul , were called pillars , and every good man shall be made a pillar in Gods Temple . 3. By the pillars of heaven may be understood the Angels , called also the powers of heaven , in the Gospell . 4. High hills may be called pillars of heaven , not because they uphold heaven , as the Poets write of Atlas , but because they are high in the aire , which is called heaven , — caput inter nubila coxdunt . 5. The onely true pillar by which both heaven and earth is sustained , is the power of God ; which power cannot be shaken in it selfe , but in its effects . 6. Which way soever you take the pillars of heaven they are moveable ; but now it will not follow that the pillars of earth are moveable also : though the pillars of the Tabernacle were moveable , the pillars of the Temple were not so . Such as the earth is , such be its pillars ; its selfe is immoveable , and so are its pillars ; except when that great Sampson shakes them being grieved for the many wrongs that hee suffers by our sins ; then hills , rocks , houses , and cities tumble down , and multitudes are buried before they be dead . If then we should prove the immobility of the earth , from the stability of its pillars , wee should have reason for it ; but to inferre that the heavens were immoveable , because they have pillars , were ridiculous . We read ( say you ) of ends , sides , and corners of the earth , and yet these will not prove it to be of a long or square forme . Answ. Yes it will : for the Scripture doth not describe the earth to us as a smooth and uniforme globe , but as a great body consisting of divers unequall parts ; as hills and vallies , and as a body broken by the irruption of many seas , as the Mediterran , &c. Consisting also of lakes and rivers , not to speake of Isles and Isthmus : hath not then the earth in this respect many ends , corners , and sides ? If you did saile along the coasts of the earth , you should finde it so . 2. The earth of it selfe is not round , for without the water it doth not make a globe . 3. Though it were perfectly round , yet it must have its longitude and latitude . 4. By the earth the Scripture oftentimes meanes the land of Judea , with the neighbouring countreys : as , his dominion shall be from the river to the ends of the earth ; which words were spoken of Solomon literally . All the ends of the earth have seene the salvation of God ; which was not seen by the Americans in Davids dayes . So all the world was taxed under Augustus , that is , the Roman world . 5. Whatsoever is finite hath bounds and ends , but such is the earth ; ergo , it hath ends . Therefore as the Scripture by the ends , sides , and corners of the earth , doth shew that it is not round ; so doth it also by the stable foundations thereof , shew , that it doth not move . Isaiah speaketh of the planting of the heavens , which you say , May as well prove them to be immoveable , as that which followes in that Verse concerning the foundation of the earth . Answ. I perceive your case is desperate , for like a man that is sinking in the water , you catch hold of every thing that is next you , though it be weeds and such as cannot help you . For 1. by heavens here may be meant the Church , which is that Vine , that God hath planted with his owne right hand . 2. Though this word heaven were taken in its proper signification , yet the planting of heaven is a metaphor , out of which you can conclude nothing , but must spoile your Syllogisme with quatuor termini . 3. Nothing is properly planted but what hath motion in it , as trees , hearbs , and such like vegetables . This word then may intimate , that there is motion in the heavens , as the word ( foundation ) sheweth , that there is no motion in the earth ; for it is very improper and dangerous for a foundation to move . When the Scripture saith , The earth is established : by this word you answer ) is means onely the keeping of it up in the aire , without falling to any other place . Answ. If the earth be established onely so , that it may not fall or be removed to any other place ; what singular thing hath the earth , that is not in other bodies ? for so are the heavens established , and every starre , that they shall not be removed out of that place or station which is appointed for them ; so is the sea confined within its bounds , which it cannot passe . But there is something else in the earth whereby it differs from other bodies , and wherein Gods power is the more admired ; to wit , That it is so established , that it cannot be removed : Nay , more then so , it cannot be stirred or wagged at all . Thus as Gods glory is admired in the perpetuall motion of other bodies , so is it in the perpetuall immobilitie of this . 2. The earth ( you say ) is kept up from falling . I pray you whither would the earth fall , being in its owne place , and sowest of all the Elements ? if it fall any where , it must fall upward , and that is as proper a phrase , as if I should tell you , the heaven must mount downeward : therefore , Mute hauc de poctore euram ; never feare the falling of the earth . The Gentiles were afraid that the heavens might fall being held up by the shoulders of Hercules ; therefore Artemon it seemes was afraid of this , who never durst venture abroad , but under a brasen target , carried over his head . And one Phaenaces in Plutarch was sore afraid , that the moon would fall downe , and therefore pitied the Ethiopians and others that were under the moone ; but if he had knowne what you know , That there is a world in the moone , his feare had been just . It may be the great shower of stones that fell heretofore in agro Piceno , were the stones of some buildings that had fallen downe in the moone . We need not feare the falling of our earth , which God hath so established , that it cannot be moved . You see no reason , but that we may prove the naturall motion of the earth from that place in Iob , Who moveth or shaketh the earth out of her place ; that is to say , We may prove a naturall motion out of a violent , or one contrary out of another ; we may prove the fire to be cold , because it is hot ; or that the earth may move naturally , becanse it moves violently . The motion that Iob speakes of , is an earth-quake extraordinary , which is a violent and temporary motion , and of some part only ; and a concussion rather then a motion ; the motion that you would inferre from thence , is a naturall , perpetuall , totall , regular , and a circular motion . Will you inferre that because the mill-wheele is turned about violently , that therefore the whole mill is turned about naturally . I have seen a Church-tower shake when the bells have been rung ; but if I should inferre that the whole Church therefore may move circularly , I should feare , Nè manus auriculas imitetur mobilis albas : lest I should be thought a creature of Arcadia . And I hope you are not so simple as to thinke that God did ever shake the whole earth out of its place , or if he had , that therefore it may move naturally and circularly . CHAP. VI. 1. The earth is in the middle and center of the world , and why . 2. Hell is in the center or middle of the earth . 3. The earth lowest and basest , how . 4. Every thing is made questionable by some . 5. Aristotle defended . 6. The earth is in the center , because in the midst of the equinoctiall Horizon , &c. 7. The imagination must be conformable to the things , not these to it ; the vanity of imagining circles . 8. Astronomers reproved , and their vanity shewed , chiefly about the bignesse of the stars . 9. The earth is the least circle : therefore the center , how understood . HEre you will not upon any tearmes admit , that the earth is the center of the Vniverse , because our arguments ( you say ) are insufficient . Answ. Our arguments may be insufficient to you , who hath an overweening conceit of your selfe , and a prejudiciall opinion of other men . But our arguments have been hitherto accounted sufficient , by moderate , wise , and learned men ; but to your sublimated understanding they give no satisfaction ; there are some men that are never content , and nothing to them is sufficient , no not Gods owne word : but what though our arguments were insufficient ? will you therefore reject them ? You may by this meanes reject all humane learning , for it hath not that sufficiency which perhaps you require . We know here but in part , the sufficiency of knowledge is reserved for a better life . — Si quid tamen aptius exit : But if you have more sufficient arguments for your opinion , impart them to us , and we will imbrace them ; if you have not , his utere mecum ; content your selfe with these till you know better . But you promise that you will cleerly manifest the insufficiency of our arguments in this Chapter . Let us see if you will be as good as your word , which we have not yet found in you ; only , large promises without performance . Larga quidena semper Drance tibi copia fandi . 1. We say that the earth is the center , not the sun ; because the earth is lowermost , and under the sunne . To this you answer , That since the sun is so remote from the center of our earth , it may be properly affirmed that we are under it , though that be in the center of the world . Answ. That the sunne cannot be the center of the world , and that the earth must needs be the center ; we have proved against Lansbergius , for neither could there be Eclipses of the Moone , nor could we discerne the medietie of heaven , nor of the Zodiac , if the earth were not the center . And whereas the center is the middle of the globe equally distant from all the parts of the circumference ; the wise God placed the earth in the midst of this great systeme of the world , not onely for mans sake , who being the Lord of this universe , and the most honourable of all the creatures , deserved to have the most honourable place , which is the middle : but chiefly that man with all other animall and vegetable creatures , might by an equall distance from all parts of heaven have an equall comfort and influence . For imagine there were two earths , this which is in the center , and another out of the center ; the influence and powers of heaven must needs more equally concurre and be united in this , then in that : and if the place be it which conserves the creatures , what place more fit for conservation , then that which is in the midst of the world ? Having an equall relation to all parts of heaven , and all the powers of the universe uniting themselves together in the earth , as in a small epitome . Therefore nature which is the hand-maid and imitatour of God , layes up the seed in the middle of the fruits , as being not onely the safest part , but also because in the middle as in the center , all the powers of the plant meet together in the forming of the seed , wherein it doth perpetuate it self . How unconvenient and unhealthy were mans habitation , if it were neerer the heaven then it is ? for the aire would be too pure and unproportionable to our grosse bodies , for they that travell overhigh hils find their bodies much distempered . Acosta witnesseth , that they who travel over the high hils of Peru , fall into vomiting , & become desperately sick , and many lose their lives , by reason of the subtilty & purenes of the air . But your words would be a little corrected ; For since the sun ( you say ) is so remote from the center of the earth , we are under it . Indeed we are under it , in that it is above us ; but not for that it is remote from us or from the earth . Under and above are relative tearms , so are neerenes & remotenes . 2. You slight the constant and perpetuall doctrine of the Church from the beginning , concerning the site of hell , which is in the center or bowels of the earth ; and you call it an uncertainty ; but so you may call any doctrine in Scripture , for where will you have hell to be , but either in heaven or in the earth ? These are the two integrall parts of this universe ; in heaven I hope you will not place it , except you will have it to be in the moone . But if there be any hell there , it is for the wicked of that world : as for the wicked of this world , they are not said to ascend to hell in the moone , but to descend to hell in the earth , as Core and his fellowes . Therefore it is called a lake , burning with fire and brimstone ; Abyssus , a deepe gulfe ; Gehenna , the valley of Hinnon . By Tertullian , Thesaurus subterraneus ignis arcant , The treasure of hid fire under ground . The Apostle speakes of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 of those that bow to Christ under the earth . Horrende voragines , fearfull gulfes they are , saith Lactantius . And that which you call uncertainty , is called certa fides , a sure faith , an undeniable truth by Prudentius : Certa fides rabidos sub terra nocte caminos , &c. And as this hath been the constant opinion of the Church , as may be seen both in the Greeke and Latine Fathers , so hath it been beleeved by the Gentiles , as I could instance out of Greeke and Latine Poets of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Tartarus , Phlegerbon , Cocytus , Styx , Acheron : which they shew to be in the center or bowels of the earth ; therefore I hope you are none of those that Iuvenal speaks of , who would not beleeve there was any hell under ground : Esse aliquos manes , & subterranea regna , &c. Nec pueri credunt . — For whosoever denied hell to be below , denied that there was any such place at all : as , Pythagoras , Epicurus , Lucretius , Tully , Seneca , Lucian , Pliny , and some others ; to whom I may adde the Gnostickes , who held there was no other hell , but this world , whom Irenaeus resutes . 2. As hell must needs be in the earth below , so must heaven the place of the blessed , be above all these visible heavens ; which is called , The third heaven , and the heaven of heavens . Therefore , it is no uncertainty ( as you say ) that it is concentricall to the stars : for if it be not , tell us where you will have it ? in the moone , or in the Elysian fields , or in Mahomets paradise ? I wish you would thinke the dictates of Gods word to be more certaine then your groundlesse phansies , and that the Scripture is a more stable foundation to build upon , then the Moone . 3. It is not an uncertainty that places must be as farre distant in scituation as in use : Therefore Abraham saith , That there 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , a great gulfe , or gap between Lazarus and Dives . So David distinguished between the height of heaven , and the deepe of hell ; so doth Amos , and Esay : and it 's fitting that heaven and hell , the saints and the wicked , the joyes of the one , and torments of the other , be as remote as may be ; which the Poet knew : — Tartarus ipse , Bis patet in praeceps tantum , tenditque sub umbras , Quantus ad aethereum coeli suspectus Olympum . 3. These things also you will have to be uncertaine . 1. That bodies must be as farre distant in place as in nobility . 2. That the earth is of a baser matter than other Planets . 3. That the center is the worst place . Answ. These are not uncertainties to men that have sense and reason ; for sense tells us , that the grosser simple bodies are , the lower place have they in this Universe : the heaven being a quintessence and of the purest matter , is uppermost ; next is the fire , then the aire , then the water , and lowest of all , the earth , as being the grossest ; and reason tells us , that God is the God of order ; and what a disordered world should we have , if grosse and heavy bodies were uppermost , the light and purest bodies beneath ? We see in our owne bodies , that the grosser the spirits are , the lower they are : the animall having their residence in the head , the vitall in the heart , the naturall in the liver . 2. Nor is it uncertaine that the earth is of a baser matter then the Planets ; the obscurity and dulnesse of the one ; the beauty , light , and swiftnesse of the other , doe shew what oddes there is in the matter . How are all Divines deceived who put men in minde of the base materialls of their body ; and teach that God made men of the basest element to humble him ? Animalium superbissimi origo vilissima ; and I thinke you are Planet-struck , or have a planeticall head , who thinke the earth to be a Planet . 3. That the center is the worst place , is not held by us ; for though we say the earth to be the ignoblest and basest element , in respect of its matter , and therefore the lowest ; yet as it is the center and habitation of the noblest creature , it is placed in the middle , as being the noblest place . 4. Our second argument is grounded ( you say ) upon two foolish foundations . 1. That the whole frame of nature moves round , excepting onely the earth . 2. That the whole earth is heavy , and more unfit for motion then the Planets : These you reject , because they are ( you say ) the thing in question . Answ. You are doubtlesse that third Cato that fell from heaven ; or octavus Sapientum . Our foundations of the earths stability , and gravity , are foolishnesse with you ; so was the Gospell foolishnesse to the Gentiles ; but you doe well to observe Solomons rule : Answer not a foole according to his folly ; which is the reason that you answer not at all to these foolish foundations of ours ; but onely with this ; they are the thing in question . But if you question the stability and gravity of the earth , is not your question as foolish as our foundation ? but seeing you may question every thing , every thing may be a foolish answer , or position to you . And what doe you thinke of the Scripture when it saith ; The earth standeth fast , and the stars move ? doth the Scripture in this speake foolishly ? Surely we are content to preferre the foolishnesse of Scripture to the wisdome of your scribling ; because such conceited wisdome is but foolishnesse with God. What foundation either in Divinity or Philosophy , what Article of the Creed hath not been questioned ? shall they be counted foolish foundations , or unfit to discusse controversies , because they have been questioned by pernicious Heretickes ? If you were as wise a man as you pretend your selfe to be , you should have with solid arguments refelled our foundations , which are so fully demonstrated by so many Philosophers , and then you should have shot your fooles bolt . The truth of these foundations I have shewed already , to which you answer nothing , therefore here I will not actum agere . 5. Our third Argument is , That our earth , must be in the center , because it is in the lowest place , or middest of the world ; this Aristotle proves by the descending of all heavy to the center , and the ascending of light bodies from it : But you reject Aristotle as being a master of Syllogismes , and being deceived whilst be supposeth that , which he pretends to prove . But indeed you are much deceived your selfe , whilst you reject this master of Syllogismes , who doth not suppose what he pretends to prove , but substantially proves , what you thinke hee supposeth . Hee saith the earth is the center , and thus syllogistically out of him it is proved ; To what place heavy bodies descend , that place is the center ; But to the earth , heavy bodies descend ; ergo , the earth is the center . You see now that this master of Syllogismes doth not suppose that which he brings unto the conclusion , but proves the earth to be the center by a medium , which you cannot answer : so that being put to your shifts , you know not how to elude the force of this and other arguments ; but by falling to your art of multiplying centers and circumferences , which is not difficult to you , that can multiply worlds . And because cause you cannot be so impudent as to deny the ascending of light bodies ; you say , That they ascend to some circumference which we cannot reasonably affirme to be concentricall with that of the world . But I would know of you , how you can reasonably affirme that circle to be eccentricall , which we sensibly perceive to be concentricall to the world ? If neither you nor we can perceive that circumference to which light bodies ascend eccentricall to the world , what reason have you to affirme it ? or how doe you prove what you affirme ? May you not as well tell us , that there are more suns then this one which we see ? For you will say that we cannot reasonably affirme there is but one sun . But you say , We cannot prove the descent of heavy bodies to the center , nor the ascent of light bodies to the circumference of the world ; because all our experience in this kind , extends but to things that are on earth , or in the aire above it . I pray you good Sir , how farre doth your experience reach beyond ours , that you should deny this our assertion ? Have you beene in the moone , and observed that which we cannot finde here below ? We see quantum acie possunt oculi servare , as farre as our eyes will give us leave ; to wit , light bodies mounting from the center towards the circumference ; doe you see otherwise ? I know you doe not , and cannot though you had as many eyes as Argus : therefore keep your wilde opinions to your selfe , for so long as you can neither by sense nor reason perswade us , your bare word will be too weake an argument to worke upon our beliefe . You conclude , That it were a senslesse thing , from our experience of so little a part , to pronounce any thing infallibly concerning the scituation of the whole . I grant our experience to be little , but yours is lesse , or none at all : a little is better then none , and we may more boldly inferre , that there is but one center , and one circumference ; ( because all light things ascend to one circumference , and all heavy things descend to one center ) then you can inferre two centers , and two circumferences ; whereas you never knew any light thing ascend , or heavy thing descend to any other circumference and center , then to these which we maintaine : are not you therefore much more senslesse then we ? for we follow the direction both of our sense and reason ; so doe not you . 6. Our Astonomicall reasons you refell as wisely as you have done the rest : for you grant us , That the earth is in the midst of the equinoctiall , horizon , and other circles ; but you deny that from hence can be concluded that it is in the center of the world . It seemes then that the equinoctiall , &c. are not concentricall to the world , and that the earth may be in the midst of the horizon and equator , though never so much distant from the center ; and what is this but to make another world ? consisting of another heaven and earth ? For if this earth be under any other equinoctiall besides that of the primum mobile , or any other horizon , it cannot have the heaven equally on all sides of it , and so cannot be in the lowest place which is the center , though it be the heaviest body ; and so against its nature must be higher then that body which is in the center . This is to take away that order which God hath placed in the creatures , to multiply worlds , and to bring in a strange confusion . And what a wise reason doe you give us why the earth would remaine in the midst of these circles , that is , the equinoctiall , &c. though distant from the center ; because it is the eye that imagins them to be described about it ? So then the earth doth not goe out of the midst of these circles , because the eye imagines them , &c. You have a strange fascinating eye , that can keepe the earth within its circles ; if you should winke ; or if you lose your eyes with your great patron ` Democritus , would not the earth give you the slip and fall out of your circles into the center of the world ? Besides , I had thought that the action of the eye had been to see , not to imagine . As you have made a confused Chaos in the great world , so you doe in the little world too , confounding the inward and outward senses , the sight and the imagination : I thinke you were begot of Chaos and caligo . Againe , what a reaching eye have you , that can describe circles about the earth ? If you had spoken of an artificiall Globe , you had said something ; but if your eye were as big as that of Polyphemus , Argolici clypei , aut Phoebaeae lampadis instar , yet you could not describe with your eye a circle about the earth : your imagination may describe it , but not your eye : your imagination cannot be the cause why the earth remaines within its circles ; your imagination must be conformable to the reality of things , and not they to your imagination : for though you imagine that there is a world in the moone , that the earth moves , &c. yet there is no such thing , because the earth is in the center : wee imagine it to be so , and beleeve it also ; but our imagination or beliefe do not make it to be so ; therefore , our collection is not weak when we inferre that the earth is in the center , because it is in the midst of these circles which are concentricall to the world ; or because the parts and degrees of the earth doe answer in proportion to the parts and degrees of heaven , which they could not well doe if the earth were eccentricall . 7. Now I thinke you go about to conjure us with your figures , circles , and characters , and to hem us in with a circle made by your pen , as Popilius the Roman Legate did inclose King Antiochius within a circle made with his rod : you remove the earth from one center to another , with more facility , then Archimedes could have done with his engine : you transferre the starres from one circle to another at your pleasure ; you can doe I thinke as she in the Poet , Sistere aquam fluviis & vertere sidera ritro ; and all this stirre is to informe us , that though the earth be never so farre distant from the center of the world ; yet the parts and degrees of your imaginary spheare about it will be alwayes proportionable to the parts and degrees of the earth . And what of all this ? You may imagine what spheares you will , and in your imagination place the earth as you will , yet the earth standeth fast for ever in this great fabricke of the world as the center , though in your head it move to and fro . You may place the earth upon the top of the primum mobile , and imagine a spheare about it , with proportionable degrees , and parts to those of the earth ; wee may retort these words upon the sunne your center , that though it be never so farre distant from the center of the world , yet the parts of an imaginary spheare about it will be proportionable to the parts of the sun : but though in your imaginary circle there be a proportion of parts and degrees to the earth removed from the center , I would know if the earth therefore is removed from the center : Or if you should remove the earth ten or twenty degrees neerer the pole Articke , or to the Zenith of the Meridian from the center ; is there , or can there be any proportion between the two hemispheares ? Will not the one be so much the lesse , by how much the other is inlarged ? Or can the true spheare of heaven be divided equally into twelve parts , or signes , so that sixe be alwayes above the earth , and sixe below ? Or can the stars in both hemispheares appeare of the same bignesse ? Doubtlesse though you make a proportion in your imaginary spheare , to your imaginary earth , in your imaginary center ; yet there can be no proportion between the reall spheare of heaven , and the reall earth , which is the reall center of the world : if it should be removed from its place where it is , your imaginations then are but the images , phansies , and toyes of your head , without ground or solidity ; therefore they are neither so strong , nor we so weake , as that they should make any impression upon our beliefe , as the mothers imagination doth upon the tender Embryo in her wombe . When you are pressed with the manifest absurdities and inconveniences which arise from removing of the earth from the center of the universe , you have no other way to escape , but like a hedgehog , to shrinke back into your imaginary globe or circle : for you grant that the earth must needs be placed both in the axis and aequator , but that must be in the center of the spheare which you imagine about it , and not in the midst of this universe . But why must the earth be removed from being the center of the universe , which by sense , reason , daily experience , and continuall observation of Astronomers , is knowne to be the center ? Why I say must it be removed from its owne reall circle , to your imaginary circle ? What inconvenience will follow in the world , if it remaine the center of the universe ? Or wherein shall the world be bettered , if it be removed to your supposed circle ? Nay , what absurdities will not follow upon this removall , which you will never be able to avoid for all your starting hole ? for whereas you say , That though the earth were as far distant from the center , as we conceive the sunne to be , yet it may be still scituated in the very concourse of the axis and aequator . Truly , though we should conceive it to be so farre distant , yet it would not be still in the concourse of these two lines ; for if either the sunne or the earth were there still , there would be a perpetuall equinox through the world , neither would there ever be any increase or decrease of dayes and nights . Now you present unto us a Scenography or plat-forme of your imaginarie world , in which , like another Joshua , you make the sunne to stand still , so that here is a perpetuall solstice ; if that American ( who would not acknowledge the sunne for a god , because it never rested ) had seen your sun , or had known of him what you know , he would have recanted his opinion . What fooles were the Poets to bestow so rich a chariot , and foure prancing horses on the sunne , who could make no use of them ? they should have bestowed this gift upon the earth , for she it is that undertakes all the toile , and rejoyceth as a Gyant to run her course . Ovid's second booke of Metamorphosis must be mended , and Phaeton must preferre his petition to the Earth his mother , and not to the Sun his father ; except perhaps in those dayes the Sun did travell about the Earth , but now being wearie to go about so often , and to take such paines for her thanklesse inhabitants , hath given over this toile , and hath left the earth to shift for her selfe and children . The reason why you present this figure to us , is to let us see , That though the sunne be in the center , and the earth in the suns orbe , yet that there can be no Eclipse , but when the sunne and moone are diametrically opposite . But here your opinion is diametrically opposite to the truth , for the line from the center to the circumference , is but a semidiameter ; and indeed the sunne is distant from the moone in your figure , nothing neere a semidiameter , and yet your moone is eclipsed . But what a mishapen world have you made us ? in which you have placed the sunne lowermost , and the earth above the sunne , and hath made such a vast circuit for the earth , and such a little circle for the moone . You told us afore , that the earth drawes about the moon , but in your figure it cannot be so ; for you have made the earth to compasse the sunne round ; but the moone to fetch a compasse of her owne aside off from the sunne : so that whereas you have placed the earth in Aries , she is between the sunne and the moone , but when she comes about to Libra the opposite signe , then the sunne will be between the moon and her . This is indeed a strange world , and doubtlesse none of Gods making ; I wish I were out of it , for I am wearie and sorrie to spend time in refuting of such toyes . You doe well to confesse the uncertainty of finding out the exact distance of the firmament , which is but conjecturall according to mens fancies , and so indeed are the motions , and magnitudes , and number , and order of the spheares , and starres ; about which Astronomers have so many digladiations and oppositions , which were tedious but to name . From their conjectures and uncertainties have proceeded such a number of conjuring words : as , Trepidations , Retrogradations , Excentricities , concentricities , Epicyles , Accessions , Recessions , and I cannot tell what ; so that as Cato said of Sooth-sayers , I may say of Astronomers , It is a wonder that they do not laugh at one another . The best of them all are but Cu va in terris animae , & coelestium inanes : They gaze and stare on the stars , and dispute , and assever with great boldnesse , that each star is of such and such a bignesse and altitude , and that they move thus and thus ; and that there be so many of each magnitude : and so expert they are , and quick-sighted in these things that are so remote , and yet cannot perceive the things that be hard at hand : therefore Anaximines gazing on the stars , fell in the ditch , and was checked by his maid for his curiosity in things beyond his reach , and neglecting that which most concerned him . Saint Ambrose complained of the Astronomers of his time , that they were busie in measuring of the heaven , in numbering of the stars , but carelesse of their salvation ; that was indeed , Relinquers causans salutis , error is quaerere . Even like the Pharisees whom Christ reproves , That they could discerne the face of the skie , and of the earth , but could not discerne the time . Saint Austin preferres that man who is conscious of his owne infirmities , to him that is curious in the speculation and serutiny of the stars : Laudabilior est animus cui nota est infirmitas sua , &c. Even in the opinion of Socrates , it 's 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , to be mad , to inquire curiously into these celestiall things , which are 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , not to be found outby us ; Furiosi dementesque sunt judicandi , they are furious and mad men , &c. saith Lactantius . I will not condemne the good uses that may be made of Astronomy in calculation of times , observation of seasons , prediction of eclipses , and such things as have their immediate dependence from the opposition and conjunction of starres ; and the uses that may be made of it in physicke , and in the campe : but that which I reprove , is the vaine curiosity of men , who cannot be content to know with sobriety things revealed , must needs with Phaeton and Icarns meddle with these heavenly bodies , in vaine and curious speculations ; the knowledge whereof in this life is denyed us , as being a part of Adams punishment for his affected knowledge , and being a meanes for us to have recourse to Christ , in whom are hid all the treasures of wisdome and knowledge . Therefore , for their needlesse paines , and presumptuous curiosity , God doth punish them with multitudes of contradictory opinions . Who can sufficiently laugh to heare their jars and dissentions , saith Theodoret ? for their difference is not about the measuring of an acre of ground , but of the whole world . Now ( saith the same Father ) who can measure the whole earth ! 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 God himselfe asketh Iob , Who is it that hath laid the measures of the earth , and who hath stretched the line upon it ? and he asketh him , whether he hath perceived the breadth of the earth , Ver. 18. intimating hereby , the impossibility thereof , and shewing what difference there is between Gods knowledge and mans : saith Saint Chrysostome on that place ; 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . For God ( saith the same Father ) will let Iob see how much man is inferiour to him , in that not onely hee cannot doe the workes that God hath done , but also that he hath not the knowledge of them . As it was Gods proper worke to make the earth , so it is proper to him alone to know the measure of it : if then we know not the earths measure which is but a point in comparison of heaven , what madnesse is it to measure the heavens , or to define the motions , scituations , altitude , densitie , or other accidents of them unknowne to us ? This is , coelum ipsum petere stulritia . Knowest thou the ordinances , ( or as some translations have it ) the conversions of heaven ? saith God to Iob. The Psalmist tels us , that it is onely he that numbereth the stars , and calleth them all by their names . He bids Abraham tell the starres if hee could , shewing that indeed he could not . 8. From hence appeares the vanity of your side , who thinke , That the stars would seeme no bigger to us then they now are , though our earth were neerer to them by 2000000. Germane miles , which is granted to be the diameter of that or be wherein the earth is supposed to move . I pray how come you to know this ? by relation , or revelation , or reason , or experience ? or have you dreamed it ? Qui amant ipsi sibi somnia singunt . Or doe you know it by the help of a perspective ? You tell us , that the better the perspective is , the lesser it makes the stars to appeare ; if my spectacles were of that quality , I could fling them away , and trust to my owne eyes : I wish you could tell us , how many Germane miles would suffice to finde out the true bignesse of the stars ; or in how many yeares will the bodies of the Saints be in ascending to heaven ; you must pardon us if we beleeve not what you say , such an infinite disproportion doe you make both betweene the bignesse and distance of our earth and the fixed stars . And though we will not thinke elephants and whales to be fictions and chimaera's , because they are bigger then mice ; yet if you should tell us of a whale that were as big as the I le of Saint Laurence , or of great Britaine ; and of an elephant that were able to overturne the Alpes with his trunke ; or of a Camell that had a bunch on his backe as high as the cape or top of Tenarisf , we would laugh sooner then beleeve such monstrous absurdities . And yet the disproportion of these supposed creatures to mice is nothing , to that of the earth and fixed stars . And the like credit doe we give to that incredible celerity of the eighth spheare , of which Astronomers write , and to the rest of their conceits concerning the reaching of the suns orbe to the pole starre ; and that the circle of the pole star is above foure times bigger then the orbe of the sunne ; and that the semidiameter of the earth , makes little or no difference in the appearance of the sunne ; as if the observations from the center and surface , were of the same exactnesse . Whereas , never any man hath been in the center to know this , neither doe the Astronomers agree amongst themselves about the compasse and diameter of the Earth ; Aristotle , Hipparchus , Eratosthenes , Ptolomy , Alphragan , Fernelius , and the later Professors of that faculty , being all of different opinions ; so that many Astronomicall principles are grounded upon meere uncertainties . 2. Wee doe not ground our argument ( as you say ) upon this supposition , That every body must necessarily be of an equall extension to that distance from whence there doth not appeare any sensible difference in its quantity , as you instance in a Bird , and a Tree : as that the Tree should be accounted by us forty paces thick because wee approaching neerer to it by forty paces , doe not finde any sensible difference . This is a crotchet hammered in your own head , but never supposed by us . 3. Wee grant with you , That it is presumption to conclude that to be superfluous , whose use wee understand not ; but yet wee must needs say , That what is not usefull at all , is superfluous ; as that immense and stupendious bignesse , and incredible distance of some starres , seeing they were made for the use of man onely ; ( for to what other end should they be made ? ) whereas if they had been neerer and lesser , they might have been more effectuall : Therefore wee cannot beleeve you that they are of that bignesse and distance you speak of . And as for other inhabitants , beside those that are upon this earth , by whom ( as you say ) these lesser stars may be discerned , I have nothing now to say to them ; I think you mean your men in the Moon , of whom perhaps I will speak hereafter : and as for these small stars , which you say are lately discovered ; I grant that they were made for mans use , though they be scarce discernable ; for their influence may be great though their light be small : and we have by them occasion to see how one star differeth from another star in glory , and we may admire Gods greatness in the least , aswell as in the biggest ; therefore he hath made Flies aswell as Eagles , and Mice aswell as Elephants . 9. You chase as if you had been slung with nettles at an argument of mine against Lansbergius , who held , as you doe , that the Sun was the center : my argument is this ; That which is least in a circle ought to be the center of it ; but the earth is farre lesse then the Sun , and the terrestriall Equinoctiall ( secundum te ) according to your owne words , is the least of all the circles , &c. This ( you say ) is so simple , that every fresh man would laugh at it , and it would make one suspect , that hee who should urge such an argument , did scarce understand any thing in Astronomy . Answ. 1. For any great skill that either you or I have in Astronomy , wee may shake hands : Astronomy is not my profession , yet so much I have as is convenient for a Divine , and enough to discover your vaine and ridiculous conceits ; and I have not the lesse because of your suspicion : I understand so much as that I dare say there be many absurd and foolish fancies taught by Astronomers , though the science it selfe be usefull in many things . 2. If you , or your fresh men laugh at this argument , you will shew that you have little salt in you , especially that salt whereof the Apostle speaks . 3. You shewed more malice then knowledge , more ill-will then skill , in repeating my argument ; for you left out ( secundum te ) that is , according to your owne words ; which sheweth that these were the words of Lansbergius , not mine ; to wit , The terrestriall Equinoctiall is the least of all circles : So that you cunningly would derive the ignorance and simplicity of your Champion upon mee , whereas I spake in his owne tearmes . 4. I did not speak of the earth , as it had relation to the Moon , or Mercury , but in reference to the Sun ; for I say that the earth is lesser then the Sun , and therefore fitter to be the center then the Sun , as Lansbergius would have it . 5. There is no certainty amongst Astronomers , whether the Earth , Moone , or Mercury , be the least spheare . 6. I said , minimum in circulo , not circuli ; that which is least within the circle , not that which is the least part of the circle . The Moon , and the rest of the Planets , are the thicker parts of the spheares , so is not the Earth , it is no part at all of any sphear , but it is within the sphears ; therefore the Earth , not the Moon , is fittest to be the center . Thus you have made mee say more now , then I did before . You had no reason then to put so much vinegar in your ink ; but you are a namelesse Moon-man wrapt in a cloud : Cernere ne quis te , ne quis contingere possit . But be not so high conceited of your selfe ; though your habitation be in the Moon , yet learn humility ; Tecum habita , & noris quàm sit tibi curta supellex . As for the other Objections , which you say are not worth the eiting , are indeed such as you know not how to answer them ; therefore you slight them , as the Fox did the grapes , which he could not reach . CHAP. VII . 1. The Starres have not their fight because the Sun is in the center , nor hath the Sun lesse light being out of it . 2. Why the Earth is in the center . 3. The Sun is not the center , because the Planets move about him . 4. The center is not the most excellent place , neither are the best things next it or in it . 5. There is an harmony amongst the Starres , though the Sun be not in the center . IN this Proposition you say , That the Sun may be the center ; and you tell us of deformities , wheeles , and screws , as if Nature in framing of the world had been put to such hard shifts by Ptolomie's and Tycho's Hypothesis : But indeed the wheeles , and screwes you speak of , are the whirle-gigs of your own head ; and I hope your Creed is , that not Nature , but the God of Nature , framed the world : but let us consider the weight of your arguments , by which you would prove Copernicus his Assertion . 1. You say , That the light which is diffused in the starres , is contracted in the center , which can onely be by placing the Sun there : so then it seemes by you , that if the Sun were not in the center , the light of the starres could not be so eminently contained and contracted in the Sun : either you must mean that the starres could not receive so much light as they doe from the Sun , or else that the Sun could not have in himselfe so much light as hee hath , if hee were not in the center : But both these are frivolous whimsies ; for neither hath any starre its light , because the Sun is in the center , ( as you would have ) nor would the Sun lose any of his light , if he were out of the center , no more then a candle can lose its light , though it be not placed in the midst of the roome . Now , whether the light of the starres be all one with that of the Sun , or any parcell of it , is not yet fully resolved . In your next Edition tell us more plainly what you meane by the light in the starres contracted in the center , and wee will give you a more satisfactory answer . 2. Because Clavius and others say , That the Sun was placed in the midst of the Planets , that hee might the more conveniently distribute his beat and light amongst them ; the force of this reason ( you say ) may more properly prove him to be in the center . I answer , that it will rather prove the Earth to be in the center thus : The Sun is in the midst of the Planets , that they may the more participate of his light ; so is the Earth placed in the midst and center of the world , that the Sun might the more conveniently distribute his light and heat to it : for the Sun was made chiefly for the Earth's sake , and the inhabitants thereof ; neither doe the stars so much need his light and heat as we , without which we can neither live , nor procreate : and as it is questionable whether the stars receive their light from the Sun , ( though the Moon doth ) so is it much to be doubted that they receive no heat from the Sun , seeing Saturne is cold ; and the Suns heat comes by reflexion , which cannot be in the starres . 3. You say , That the Planets move about the center of the world , and that I grant you ; but Saturne , Jupiter , Mars , Venus , Mercury , move about the body of the Sun ; ergo , the Sun is in the midst of the world . Answ. If you had been better acquainted with the master of Syllogismes , you had not framed such a lame Syllogisme as this ; for thus it runnes in briefer tearmes ; some Planets move about the center of the world , some Planets move about the Sun ; ergo , the Sun is the center of the world . Besides , that it consists all of particulars , the conclusion is falsly inferred against the lawes of the third figure ; for it should be formed in the first figure thus : What moves about the Sun , moves about the center of the world : the Planets move about the Sun , ergo , they move about the center of the world ; and all this I grant you , that the Planets move about the earth which is the center : now then I hope you will not say that the Sun is the center of the world , because the Planets move about him ; no more then Iericho was the center of Canaan , because the Priests went about it . 4. When you tell us that the revolution of Venus and Mercury is about the Sun , because they are never at any great distance from him , you alledge a cause fit to be laughed at ; for is the vicinity of one starre to another , the cause of its revolution about that starre ? because the mill-wheele is not farre distant from the miller , doth it therefore goe about the miller ? 5. The reason which you alledge from Pythagoras is also weak , for though the sunne in respect of his light were the most excellent body , and the center the most excellent place , yet it will not follow that he is there ; for we see that the most excellent creatures are not placed still next the center or in it , but farthest from it : as man is placed in the superficies or circumference of the earth , and not in the center of it the heart is not in the midst of the body ; if the middle or center were alwayes the sittest place for a luminous body , God would have commanded Moses to set the candlesticke with the lamps in the midst of the tabernacle , and not in the side of it : our eyes had beene placed in our navels , not in our heads . And albeit Plato say , that the soule of the world resides in the innermost place of it , yet I hope you doe not by this understand the sunne ; and you did well to alledge Macrobius against your selfe , in comparing the sunne in the world , to the heart in a living creature ; for as the heart is not in the center of the body , neither is the sun in the center of the world . But you give us a profound reason why in living creatures the chiefest part is not alwayes placed in the midst , because they are not of an orbicular forme as the world is ; then it seems that the outward figure is the cause why the best part is not placed in the midst . What thinke you of a Hedge hog when he wraps himselfe up in his prickles as round as a bowle , is the best part then more in the middle of his body then it was before ? Or hath the earth which is of a round forme better things in the center then in the superficies ? What difference is there betweene the middle and out-side of a round stone ? Againe , you say , the center is not the worst place , although Aristotle proves it from the dignity of the thing containing over that which is contained ; and your reason is , That though the center be contained , yet it is one of the termini or limits of a round body , as well as the circumference : but I reply , that though it be one of the limits , yet it is contained , and therefore more ignoble then that which containeth it ; so you have but offered to answer this argument , and indeed you know not how to answer it . 6. If we suppose the sunne to be in the center ( say you ) we may conceive an excellent harmony , both in the number and distance of the Planets . For my part I give you leave to conceive what you will , so that you doe not obtrude your conceits on us as oracles , but will keep them to your selfe ; if you continue to divulge them , we will conceit that your conceits are but idle phansies , if you cannot set them forth with better proofes then as yet you have done . We are confident the earth is in the center , and doe conceive that there is an excellent harmony in the Planets , though the sunne be not in the center ; and therefore to say that the harmony would be disturbed if the sunne were amongst the planets , you wrong both Pythagoras your master , whose conceit of the musicall harmony in heaven was grounded on the motion of the Planets ; and injurious to Apollo himselfe the author of musicall harmony , and the continuall companion of the Muses , without whom there can be no consort . CHAP. VIII . 1. How the eye is deceived , and how not ; and that if the earth moved , we should see it . 2. Motion and rest how the objects of the eye , and of the common sense . 3. If the earth moved , the clouds would but sceme to move as well as the sunne . 4. How the eye can be deceived in the motion of a lucid body . 5. The naturall motion of the foundation cannot keep buildings from falling . 6. The heavens sitter for motion then the earth . 7. Rugged bodies not fittest for motion . 8. The sight hindred by the motion of the subject , medium , and object . 9. One simple body hath but one naturall motion , proved . 10. Essentiall properties more chiefly in the whole then in the parts , the earth is heavy in its owne place how , bignesse how a hinderance to motion , of the earths ineptitude to a swist motion . 11. The magneticall qualities of the earth , a fiction . 12. Similitudes no prooses ; the seas ebbing and flowing , what . 13. The whole earth moveth not , because the parts move not round . 14. Absurd phrases ; and the spots about the sunne , censured . 15. That the earth turnes about the moone is ridiculous . 16. Some observations to prove that the earth turnes about the clouds , refused . 17. Of a mixed motion , of the place , medium , and space . 18. Of the motion of comets . 19. My nine arguments desended . 1. That the earths motion would make it hot . 2. The aire purer . 3. A sound . 4. Heaven hath all things sit for motion . 5. Of similar parts and the whole . 6. The sunne is the heart of the world . 7. It workes by motion . 8. The earth is the firme foundation . 9. The authority of Divines ; the heaven called AEther ; the earth hath not two distinct motions . THe chiefe businesse of this Chapter ( you say ) is to desend the earths diurnall motion . Indeed you are too busie ; Non amo nimium diligentes : neither is this businesse of yours anything else then idlenesse , otiosi negotium . And because you cannot answer our objections , you are as busie here as you can be to illude them , and to delude the world with your great brags & Rhodomontado's ; but let us see with what dexterity you dissipate the strength of our arguments ; you doe as Cacus did to Hercules , Cacus being too weake to resist that invincible champion , laboured to escape his hands by darkning the cave , and Hercules his eyes with smoake and ashes which hee belched out against him : the like stratagem you use with intricate words and smoakie phrases to darken the understanding of the Reader . 1. We objected , that if the earth did move we should perceive it ; you answer ( but in many intricate and ambiguous tearms which were tedious to relate ) That the sight judges of motion deceitfully ; your reason is , because motion is not the proper object of the sight , nor belonging to any other peculiar sense : and that the common sense apprehends the eye it selfe to rest immoveable , as when a man is carried in a ship . Ans The sight is oftentimes deceived , either in respect of the distance of the object , so the stars appeare lesse then they are ; or in respect of the agitation of the object , so a square thing seemes round being swiftly turned about . 2. In respect of the indisposition of the medium , and so the Planets rising and falling seeme biggest , the aire being thickned . 3. In respect of the organ , when the eye , optick nerves , or visive spirits are disturbed , vitiated , indisposed , or agitated , and so things that rest seeme to move , because the eye moveth ; for that apparent motion is not the object of the eye , as a true motion is , but as it were the effect of the eye moved . So then , tell us the cause why we cannot perceive the earth move , seeing it moves with such a stupendious swiftnesse ? You cannot say that the distance of it , nor the indisposition of the medium are the causes ; the eye then must be the cause . But are all mens eyes from the creation till now so disturbed , or agitate with an insensible motion , that they cannot perceive the earth nor any part of it to move , and yet doe perceive the sunne to move ? What ? will you make God so defective in his work of mans body , as to give him such eyes which shal continually delude him ; neither shall they ever apprehend their object , though never so neere ; or the medium , though never so well disposed ? Or will you make him so envious , as to give us such eyes , by which we should receive the knowledge of visible objects , and yet cannot see them when they are so neere us ? This is the curse of the Sodomites , who could not see Lot's dore though they were close by it . Your simile of the ship will not hold ; for though it be true that the shore apparently moves when the ship removes , yet we see and feele the true motion of the ship , as well as we see , or rather seeme to see the apparent motion of the shore . When I have beene in a ship , I have observed by looking on the mast how swiftly it is moved from the shore ; but being on the shore , and looking upon trees , I see no other motion in them then what is caused by the winde . When I am in a ship , I perceive the motion of the other ship that saileth by me , though the motion of both be equall and uniforme : but when I am in an Island , I can neither perceive the motion of it , nor the motion of the other Island that is by it . And although the motion of the eye makes a thing seeme to move which doth not move , yet it doth not make the thing seeme to move which doth really move , if it be within distance : for being in a ship I have discerned the running of horses and carts upon the shore really , though the shore it selfe moved apparently ; therefore , though I should yeeld that the earth did move , yet that motion could not make me thinke that the sun did not move really , no more then the motion of the ship can hinder me from discerning the true motion of a horse or wheele on the shore ; and albeit , motion be not the proper object of the eye , yet it is an object ; neither is the eye more deceived in apprehending or receiving the species of motion , then it is in receiving the species of colours , caeteris paribus : the action of the eye , or passion which you will , being no other towards the motion of a coloured object , then towards the colour of a moving object . Againe , it would be considered , whether the naturall motion of the earth ( as you call it ) and the violent motion of a ship produce the same effect in our eye ; as because the moving of a ship makes the shore seeme to move , therefore the moving of the earth makes the sunne seeme to move . 2. Your words seeme to be contradictory when you say , That motion is not the proper object of the sight , nor belonging to any other peculiar sense . We say that colours are the proper object of the sight , because they belong not to any other peculiar sense , and that motion is not the proper object of the eye , because it doth belong to other peculiar senses : but your other words are false , when you say , That the common sense apprehends the eye it selfe to rest immoveable . For when the eye is moved , the common sense apprehends it to be moved ; and so when it rests , the common sense apprehends it to rest ; otherwise , it and the imagination should be still deceived . But when you say , That the eye is an ill judge of naturall secrets , you should have said , That it is no judge of naturall secrets ; for the visible workes of nature are no secrets ; natures secrets are invisible , and therefore are judged by reason , not by sense . Now , though this be a good consequence , the earth doth not move , because it doth not appeare so to us , yet this consequence will not hold , the earth doth move , because it appeares to move : for an object that is immoveable may seeme to move , because the eye is moved ; but when we see a great body neere us , ( to stand still , wee justly inferre that it moveth not , because we see it not . For the apparent motion of the shore , there is a manifest cause , but for the apparent rest of the earth there can be no cause ; for if it did move it would not seem to rest , being there is no cause , not so much as imaginable of this supposed rest , but rather the contrary ; for if it did move , it and all things else would seeme to move : as for the apparent bignesse of the sunne and moone , I have already told you a reason , but you have not , nor can you tell mee a reason for the apparent rest of the earth . 2. I objected , That if the motions of the heavens be onely apparent , that then the motion of the clouds would be so too : your answer is , That I might as well inferre , that the sense is mistaken in every thing , because it is so in one thing . Answ. You should have rather inferred , that as the sense is mistaken in one thing , so it might be in any other thing ; but I will stand to your illation , the sense is mistaken sometimes in every thing , when it is mistaken in one thing of the same kinde : the eye is mistaken in the bignesse of one star , and so it is in the bignesse of every star , because the reason or cause of the mistake is alike in all , to wit , the distance . The eye is mistaken in the motion of one tree or house upon the shore , and so it is in all the trees and houses it seeth on the shore ; for the reason of this mistake is alike in all , to wit , the agitation of the eye : even so if the heavens move apparently , the clouds also move apparently ; Nam in horum motu potest decipi visus , non minus quam in motu coelorum : these are my words which you cunningly left out . The eye is deceivable in the one as well as in the other , therefore , my eye being alike disposed ( in respect of its agitation , by the supposed motion of the earth ) to the heavens , and to the clouds , it will follow , that as it is mistaken in the one , so it is in the other ; and consequently wee must no more trust our eyes in the motion of the clouds , then in the motion of the heavens , if the earth did move . Therefore , what you speake of Anaxagoras his opinion concerning the blacknesse of the snow , is fit for your selfe : for to hold the snow to be blacke , and the earth to move , are both alike absurd and ridiculous ; but this opinion is more dangerous then that . As for your conceit of the common sense , conceiving the eye to be immoveable , I have said already that it is false , and indeed the opinion of one that seems to want common sense ; and as boldly without proofe doe you affirme , that the clouds , though they seeme not to move , are carried about with our earth by a swift revolution ; for so you make the inferiour bodies against that order that God hath placed in the world , to move the superiour : as if you should say , The foot originally moves the head , and not the head the foot . But this is no hinderance ( you say ) why we may not judge aright of the other particular motions . It is true , I judge aright of the particular motions of the clouds , when I see them carried to and fro by the winde , and so I judge aright of the motion of the sunne ; but when I see the sun and a cloud moving from East to West , and you should tell me that the sunne doth not move , though the cloud doth move , I would know the reason why my eye should be more deluded in the one then in the other ; seeing the motion of the earth , and so of my eye , is alike disposed to both . It is as much as if you would tel me , when I see a horse and a man run both on the shore , that the man runs , but not the horse , whereas my eye is alike disposed to both . As for your similies of a man walking in the ship , and of the moving of the oares , they will not hold : for it is true , that though the banks seeme to move , yet it will not follow that my friend doth but seem to walke , or the oares seeme to move , when as they move truely ; the reason is , because the motion of the ship is no hinderance to the sight of that motion of my friend , or of the oares , being so neer to my eye ; although that same motion of the ship is a hinderance both to the sight of the earths stability , as also of the motion of such things as be afar off : for a horse a great way off on the shore running , will seeme to me a bush moving with the trees and bankes ; even so the motion of the earth may as well delude my eye in the moving of the clouds , as of the sunne . 3. I said that the eye could not be still deceived in its sight or judgement of a lucid body , which is its prime and proper object ; Your answer is , That the deceipt is not concerning the light or colour of these bodies , but concerning their motion , which is neither the primary nor proper object of the eye . Answ. The motion of the sunne as you take it , is no wayes the object of the eye ; for it is non ens in your opinion : What is apparent , is not , quod videtur non est ; a seeming motion is no motion , and therefore no object . 2. I said that a lucid body was the eyes object , the light it selfe , objectum quo , or the cause that bodies are discernable by the eye : now what probability is there , that the eyes which were made to looke upon these lucid bodies , should be still deluded , or can be , seeing their motion is rather the object of the eye , then their light , as is said ? albeit motion be a common object , I see their motion , I see their lucid bodies , but their light I see not properly : their light is the cause or meanes by which , but not the objectum quod , or thing that I see . 4. We say that our high buildings would be hurled down if the earth did move : You answer , That this motion is naturall , and therefore regular , and tending to conservation . Answ. Earth-quakes are naturall motions , which neither are regular , nor tend to conservation : the motion of windes , haile , raine , thunder , &c. are naturall , and yet doe much hurt ; therefore , the naturality of the earths motion cannot preserve our buildings from falling . But you say , If a glasse of beere may stand firmely in a ship , moving swiftly , much lesse will the naturall and equall motion of the earth cause any danger in our buildings . Answ. There is no proportion betweene a glasse of beer and a high building , nor is there between the motion of a ship and of the earth ; for the ship moves upon the plaine superficies of the water , being carried by the winde or tide : the earth moves circularly and with an incredible celerity , as your side say . You should compare the earths motion , to the motion of a wheele or great globe , and then set your glasse of beer upon it whilst it is whirling about : but you need not feare the fall of your high buildings though the heaven whirle about , except you meane to build castles in the aire , or to raise your house as high as the tower of Babell ; I thinke your buildings in the moone cannot stand upon such a whirling foundation . 5. I perceive by your Interjection ha , ha , he , that you are a merry gentleman , indeed you cannot answer for laughing ; but , Per resum multum , &c. I doubt me you are troubled with a hypochondriacke melancholy , or with the spirit of blinde Democritus : take heed of risus Sardonius . But let us see what it is that tickles you . I had said , that though this circular motion of the earth were naturall to it , yet it was not naturall to townes and buildings , for these are artificiall : To this you answer not but by your interjection of laughter , which is a very easie way to solve arguments , and so fooles will prove the best disputants . I hope you doe not thinke that townes and buildings are naturall bodies , or that the motion of the earth is naturall to them ; and if you thinke that artificiall things are priviledged from falling , by the naturall motion of a naturall foundation , you speake against reason and experience ; for a ship is not priviledged from sinking , because the foundation on which it is carried moves naturally ; and high buildings must needs be weakned by motion , let it be never so equall and regular ; hee that thinkes otherwise deserves to be laughed at . I have read of moving Islands , but without buildings , you were best goe build there . 6. I said , that the aire could never be quiet about us , but that there would be a continuall and forcible motion of it from East to West , if the earth did move with that celerity you speak of ; to this you answer , That the aire is carried along with the same motion of the earth : But this will not help you , for the carrying of the aire about with the earth , cannot hinder the forcible motion of it , nor can we be so senselesse as not to feele it . Doth not the whirling about of a great wheele move the aire about it ? and if you stood by , you should feele it . But you are very witty in your words following , If the motion of the heaven ( say you ) which is a smooth body be able to carry with it a great part of the three elements , &c. much more may our earth which is a rugged body be able to turne the aire next to it . You should rather say , If the earth which is but a small , dull , low , and heavy body , can carry the aire about with it , much more may the heavens doe this , which are vast , agil , active , and high bodies : for we finde that the superiour bodies are more apt to work upon , and to move the inferiour , then to be moved by the inferiour : as the inferiour parts of the little world of mans body are moved by the head , so it is in the great world . Againe , the heavens in respect of their agility , activity , subtlety , come neerer to the nature of spirits , then the earth , which is a dull , heavy , lumpish body , not apt to be moved , much lesse to move . Is it the earth that moves the aire , or the aire that moves the earth in earth-quakes ? Is it the earthy and heavy part of mans body that moves these aereall substances in the nerves , which we call animall spirits ? Or are not these rather the movers of our grosse bodies ? Your argument is just such another as this ; if the winde or aire be able to move about the weather-cocke , much more may the tower or steeple which is a rugged body move it : But that rugged bodies are more apt to move , or to be moved , then smooth bodies , I never heard before . I have observed that the smoother the bowle is , the swifter it runneth ; why did David choose five smooth stones to sling , if rugged ones were apter for motion ? When you would have your maid make you some mustard , give her a rugged dish , and a rugged bullet , and tell her that these are apter for motion ; she will presently entertain this new Philosophie with your interjection , ha ha he : so when you say that a rugged body carrieth more aire with it then a smooth ; you meant perhaps the bodies of Satyrs , or of the wilde Irish in their rugges . But now distrusting your rugged conceit , you flie to the earths magneticall vertue , whereby it can make all things neer unto it , to observe the same revolution : this is a farre fetched shift , and a strange property of the magnes ; did you ever know a loadstone move any thing except iron or steele , or to move it selfe circularly , and to make all things neere to it , to observe the same revolution ; that these conceits are , Non sani hominis , non sanus juret Orestes . 7. I said , That when the man or subject , the medium , and the object were all moved , the sight was hindered that the eye could not exactly judge of any thing . You answer , That it 's true where be seveverall motions , but when the subject , medium , and object , are all carried with the same equall motion , there is no impediment in the act of sieing . But this is a meere shift of yours ; for though the motion be equall in all , yet the sight will be hindered . Sit downe in a turning chaire , or on a turning table , take a booke in your hand , and spectacles on your nose , and let me turne you about , the motion shall be equall in all three , but I doubt me you will read ill-favouredly your instance of reading in a ship is nothing ; for the ship moves sometimes so slowly that it is scarce discernable : but let a ship or coach move swiftly , and you shall not read distinctly . If a ship should move foure miles in a minute as you say the earth doth , you should scarce see the booke in which you read , much lesse the letters . 8. I said out of Aristotle , That one simple body had but one naturall motion , as the earth to descend , the aire to ascend , and therefore could not have a circular motion . You answer , That these right motions belong onely to parts of the elements , and that too when they are out of their proper places . Indeed you shew your selfe a weake Philosopher , for from whence have the parts of the earth their motion of descent , but from the whole ? Doe you not know that old and triviall maxime : Propter quod unumquodque est tale , illud ipsum est magis tale ? If your hand be heavy , much more heavy is your whole body ; if a part of the sea be salt , much more salt is the whole . 2. When you say that the elements have these motions , onely when they are out of their owne places ; if you meane of the act of ascending and descending , you say true ; but if you meane of the power or naturall possibility , you are deceived : for though they bee in their proper places , yet this naturall power of these motions is not taken from them . 3. When you say that a load-stone , in respect of its matter and condensity naturally tends downward ; you doe againe bewray your ignorance in Philosophy , for gravity is the cause of descent , not matter and condensity ; for the stars have matter and condensity , and yet they neither can , nor do descend . 4. When you say , that the load-stone which is a heavy body , and naturally tends downward , may naturally move upward , you shew your selfe more and more absurd ; for besides that it is repugnant to the Maxime above said , for a simple body to have two contrary motions , so it overturns the naturall properties of the elements : for if heavy bodies may naturally ascend , then light bodies may naturally descend ; and so we shall not know how one element differs essentially from another ; and consequently the descending of fire of old upon the sacrifices , and the ascending of Elias his body into heaven , were not miracles , but naturall motions . 5. That desire of union and coition which one load-stone hath with another , by which it breaks the laws of Nature , is but your conceit : if one load-stone draw another , or if it draw yron upward , that ascent is no naturall motion , but in some sort is a violent attraction : therefore Aristotle's Maxime remaines firme , that one simple body hath but one naturall motion , and consequently the earth doth not naturally moved round . 9. We hold , that the gravity and magnitude of the Earth makes it unfit for so swift a motion . Your answer is , That heavinesse can onely be applied to those bodies which are out of their proper places , or to such parts as are severed from the whole . To this wee have partly answered already , that the essentiall properties of simple bodies are in the whole principally , and in the parts by reason of the whole . 2. It is false that heavy bodies are not heavy in their proper places ; for they lose not their essentiall qualities by being in their places . Is a mill-stone lesse heavy when it is on or in the ground , then when it is raised from the ground ? Put to your hand , and trie if you can with more ease wagge it upon the ground , then when it is raised some paces above it . 3. When you say , That the globe of the Earth in its right place cannot truly be called heavy : I say the contrary , that it can never be more truly called heavy , then when it is there ; for if it were not heavy there , it would not be there : it is in its owne place because it is heavy , if it were possible to remove it from its place , it would never rest till it returned thither , because its heavinesse would not suffer it to rest in any other place but in its owne , which is the lowest place fit for so heavy a body . 4. When you say , That in it , and in the rest of the Planets there is an ineptitude to motion by reason of the matter , and condensity of their bodies ; you know not what you say : For if there be no naturall aptitude to motion in the Planets , and in the earth , that motion must be violent or preternaturall . Why is the motion of the fire downward , and of the earth upward , violent motions , but because these elements have no aptitude to such motions ? 5. When you make the matter the cause of this ineptitude , you know not the grounds of naturall Philosophy ; for it is the matter that gives the aptitude , as the forme gives the act . 6. You say , That Nature may endow the earth with a motive faculty , proportionable to its greatnesse , as shee bestowes spirits upon other creatures ( for instance , an Eagle and a Flie , ) proportionable to their severall bodies . Sic parvis componere magna selebas : There is indeed so me proportion between an Eagle and a Flie ; but between an Eagle , and the vast body of the earth , there is none at all . If you had compared the motion of the Eagle , to the motion of the great bird Ruc , you had spake within compasse : If one should say that a little wheele , and a great mill-stone may be moved according to the proportion of their bodies : so likewise may the hill Athos or Atlas be turned about , he would be counted ridiculous : and yet there is a farre greater proportion between a mill-stone and those hills , then between an Eagle and the Earth . 7. Though the magnitude of the earth make it incapable of so swift a motion , yet this doth not make the heaven much more incapable , as you say : For it is the magnitude joyned with the heavinesse of the earth , that makes it incapable of such a motion : but the heavens are not heavy , though great . A cloud which may be a mile or two about , hath a greater magnitude then a pebble small stone ; and yet you see with what facility the cloud is carried , whereas the stone is not moved , ( though it were high in the air ) but with the motion of descent . 8. As for the swiftnesse of the earth's course , which exceeds not ( you say ) the celerity of clouds driven by a tempestuous winde ; of a cannon bullet which in a minute flies foure miles , &c. These ( I say ) are the phansies of a crasie braine in a dream : you are the onely darling and favourite of Nature , who both knowes the Earth's motion , and how much it can runne in a minute . It seemes this incredible swiftnesse of the earth hath made your head giddy , that you know not what you write : and how can it be otherwise ? for if you be carried 240. miles in an houre , and your pen whilst it is forming almost every letter foure miles in a minute , your braines flie as fast as the bullet out of the cannon : If this be true , I doe not think that either you know what you write , or where you are , nay you could not write at all ; nor were it possible for you to live , or for your lungs and heart to move , or draw breath . Your subsequent discourse of the Earths magneticall property is grounded ( as indeed all your Book ) upon ridiculous suppositions ; and on such grounds do you raise the structure of your Babel or bables . 1. You suppose that the lower parts of the Earth do not consist of such a soft fructifying soyl as in the surface , because there is no use for it . But what if I should suppose the contrary , that it doth consist of a fructifying soyle , and that there be people there , aswell as in your Moone ? I doubt not but I could prove it with as good reasons as you do your world in the Moon . 2. You suppose it consists of a hard rock is substance , because these lower parts are pressed close together by the weight of the heavy bodies above them . What if I should suppose the contrary , that the softest ground is in the lowest parts , as being farthest from the Sun which hardneth the earth ; therefore they that dig deep into to the bowells of the earth , finde it still softer and softer the deeper they goe : And wee know that many fruits and heavy bodies are hard and stonie without , but soft within ; the earth then is not like a cheese that by pressing groweth hard . 3. You suppose that this rockie substance is a load-stone . But what if I should suppose it to be a diamond , which is more likely ; both because it is the more precious stone , and Nature commonly layeth up the most precious things within her most inward parts ; and because it is harder , for according to your doctrine , the pressing close of heavy bodies is the cause of hardnesse . 4. It 's probable ( you say ) that this rockie substance is a load-stone , because the earth and load-stone agree in so many properties . What if I should say that they disagree in many more properties , and that therefore this cannot be the load-stone ? But what an Argument is this ? the earth and loadstone agree in many properties , therefore the lower part of the earth consists of load-stones : as if you would say , A man and an horse agree in many properties , therefore the lower part of a man consists , or is made up of a horse : or thus , The elementary and our culinary fire agree in many properties , therefore the inmost or lower part of the one consists of the other . 5. You say well that what hath all the properties of the load-stone , must needs be of that nature ; but because you are not well read in the Master of syllogismes you inferre that the inward parts of the earth consist of a magneticall substance , which is the conclusion without an assumption , which should have been this : but the lower parts of the earth have all the properties of the load-stone , which wee deny . Now let us heare how you prove it ; The difference ( you say ) of declination and variation in the mariners needle cannot proceed from it selfe , being the same every where ; nor from the heavens , for then the variation would not be still alike in the same place , but divers according to the severall parts of heaven , which at severall times happen to be over it ; therefore it proceeds from the earth , which being endowed with magneticall affections , diversly disposeth the motions of the needle . I answer , the Earth may have a disponent vertue to alter the needle , and yet not be a load-stone ; so the heavens are the causes of generation , corruption , alterations , &c. in the world , and yet they are not capable of these qualities : the Moon causeth the sea to ebbe and flow , doth shee therefore partake of the like affections ? or hath shee the properties of the sea ? The load-stone disposeth the motions of the yron , will you therefore inferre that the load-stone hath the properties of yron ? 2. If the variation , as you say , of the needle be divers , according to the severall parts of heaven passing over it ; it must follow , that the needle must vary every minute and scruple of an houre , even here where we live ; seeing every scruple or minute divers parts of the heaven are still passing over it . 3. If the Inclination or motion of the needle towards the North , is caused by the heaven , not by the earth ; why should not the variation and declination of it be caused by the heaven likewise ? You are driven to hard shifts , when you are forced to flie to similitudes for want of proofs , to strengthen your weak and absurd assertions ; for similitudes may illustrate , they cannot prove . 2. Because you cannot shew any similitude of the earth's motion with such things as you are acquainted , you are forced to borrow similitudes from those things with which you are not acquainted , rather then you will seeme to say nothing . You flie beyond the Moon , Saturne and Iupiter must serve you at a dead life , but I know not upon what acquaintance . This is your conceit : A bullet , or any part of the earth , being severed from the whole , observes no lesse the same motions , then if they were united to the whole : whereas Jupiter , Saturne , &c. doe constantly and regularly move on in their courses , hanging in the etheriall aire . But first tell us if Iupiter and the rest are separated from the whole ; if they be , what is it that moves them with contrarie motions ? If they be not , then your simile hath never a foot . Againe , doth this follow : Iupiter , Saturne , &c. have such and such motions ; therefore bullets and parts of the earth being separated , observe the motion of the whole ? You had been better to have brought your simile from the sea , which is neerer to the earth in place and nature then the heavens are ; thus : The sea ebbs and flowes , therefore parts of the earth being separated , may observe the motion of the whole . Doth not this hang well together like a rope of sand ? If you had told us that parts of the sea being separated , observe the motion of the whole in ebbing and flowing ; therefore parts of the earth separated , observe also the motion of the whole , you had said something ; but you know the contrary of the Antecedent to be true ; for you tell us that a bucket of sea water doth not ebbe and flow , though this motion be ( as you said ) naturall to the sea : But here you are deceived ; for if this motion were a naturall property flowing from the essence of the sea , the whole sea , and every part of it should ebbe and flow ; but it is not so , for the Adriatick sea hath this motion ; the Tyrrhene , Baltick , and some other seas have it not ; so some parts of the sea ebbe and flow more and longer then others ; but essentiall properties are not capable of more and lesse ; some thinke that this is no pure motion , but an alteration rather in the sea : but be it what it will be , it proceedeth not from the nature of the sea , but from externall causes ; partly from the force and motion of the stars , chiefly of the moon ; and partly from vapours and exhalations in the sea . 12. You say , The whole earth may moveround , though the severall parts thereof have no such revolution particular of their stone ; for there be many things agreeing to the whole frame , which are not discernable in the divers parts of it , which you instance in the sea water , and in the bloud and humours of our body , which ascend in the body , but descend , being separated from it . Answ. There is nothing proper and essentiall to the whole , but is also proper and essentiall to the parts separated or not separated ; thus if circular motions were naturall to the whole earth as you say , the parts of it would retaine their nature still though separated : therefore every part of the earth descends , because the whole doth , but no part thereof moves circularly , because the whole doth not . As for the parts of the sea water in a bucket , there is not ebbing and flowing as in the whole ; because that motion is not naturall to it , nor doth it proceed from the active forme , but from its passive , whereby it is apt to receive such a motion from externall agents : that motion which is essentiall and naturall to it , is not lost in the parts , being separated ; for every bucket , yea , every drop of sea water descends , because that motion is naturall , therefore not separable . As for the bloud and humours in our body , which you say ascend naturally to the head , I say , they ascend not naturally , for naturally they descend , because heavy ; but they are carried upward by the spirits in them , and drawne up by the attractive faculty , for each part drawes its aliment : now this bloud and humours being separated from the body , lose their heate and spirits , and so descend . Your instances then will not evert our maxime , to wit , that if the whole earth move circularly , the separated parts would retaine the same motion : but you say that this motion is not discernable in the parts ; I grant it , neither is it discernable in the whole ; and seeing it is neither discernable by the sense , nor demonstrable by reason , how come you to know it ? if you can perceive in the swift violent course of a bullet , the magneticall revolution of the whole earth , you are more quick-sighted then Lynx . You have certaine phrases like riddles , which stand in need of some Oedipus to explaine them . 1. You call the earth a great magnet ; What 's that ? A great load-stone ? If there be great store of iron in your moone world , this great magnet in time may draw down the moone upon us . 2. You say , That parts of the earth may according to their matter be severed from the whole : perhaps you meane they may be severed in respect of place , not of matter ; for if they have not the same matter with the whole , they cannot be parts , nor can they be the subject of these common magneticall qualities you speak of . 3. You say , That Iupiter and Saturn hang in the etheriall aire : you love to confound what our wise fore-fathers have distinguished , because you have an etheriall earth in the moon , you would fain have an etheriall aire to : God hath separated the heaven or etheriall region from this aereall , so must we . I have read once of aura aetherea in Virgil , but there the Poet divinely meanes our breath which wee have originally from heaven ; I know no other etheriall aire but this . 4. You say , That the flesh , bones , &c. tend downeward as being of a condensate matter : but gravity is the proper cause of descent , and not density ; for the fire and aire may be condensate , and yet tend upward . 5. You say , That Saturne , Iupiter , and the Sunne , are magneticall bodies : If you meane that these stars have the essentiall properties of the magnes to draw iron , then you wil make the earth and Planets to be of the same kind and species : if Mahomeis iron chest were hanged between the sun and the earth , it 's a question whether it should be drawne more forcibly upward or downeward . 6. You aske a reason , Why the earth should not move about its center as the Planets doe : I may rather aske you why it should , seeing it was made for rest , and they for motion ; neither is there any thing wherein they agree , but that they are corporeall substances , in all things else they differ : why then should wee inferre the earths motion from their motion ? 7. You that prove nothing , but boldly sayes any thing , as if men were bound to receive your dictates though never so unreasonable and ridiculous , as if they were oracles ; you I say tell us , Of spots about the sun , thought to be clouds or evaporations from his body : If your eagle eyes can see spots about the sun , then the heavens are not pure in your sight ; but who hath spotted them which God hath made cleare and pure without spot or wrinkle ? are not the spots in your glasse , or in your eye rather ? I have heard of one who with his spectacles , reading in a booke , beat the booke three or foure times , thinking he had seen a flye on the paper , when it was a spot in his glasse . If you had read the absurd opinion of the Manichees , who held with as great confidence as you doe your conceits , That the sunne was a great ship sailing about the world : perhaps you would have told us , that these spots are great whales playing about the sides of the ship ; and we should as soone beleeve you in this as in the other : but now you cannot certainly tell us , Whether these spots may not be clouds or evaporations from the body of the sunne . But I would know what use is there for clouds there ; except it be to shadow now and then , and to refresh with raine your world in the moon : and if there be any such watry meteors about the sun , they must needs be extracted out of the sea , lakes , and rivers , that are in your upper world . And seeing these vapours cannot be condensate into clouds without cold , it confirmes my opinion , that the sun is not hot formally ; and that the heaven was nick-named when it was called aether , ab ardore : but I much muse what these evaporations should be from the body of the sun ? What , doth the sun pant and sweat with his daily labour ? Evaporations are hot and moist exhalations , is there any moisture in the sunne ? Doe not these clouds and evaporations proceed rather from his horses nostrils ? But the prince of Poets tels us that they blow light out of their nostrils ; — Lucem que elatis naribus efflaus . thus you afford us matter of sport . But you goe on in your absurdities ; for having once plunged your selfe in this mire , the more you strive and struggle to get out , the faster you sticke , and the deeper you sinke in . You tell us , That the moone is turned about by our earth : why doe you not tell us also that the sunne is turned about by the moone , and the firmament by the sunne , and the primum mobile by the firmament , and the first mover by the primum mobile ? and so the world shall be turned topsie turvie . For is not any of these turnings as probable as the moon to be turned about by the earth ? perswade me this , and then you shall easily assure me that the cart drawes the horse , the crab courses the hare , and the ship turns about the wind ? You would make the common-wealth of heaven like many disordered common-wealths here on earth , where the inferiour and meaner sort of people will take upon them to rule and guide their superiors , Princes and Magistrates , and then all comes to confusion ; the horses run away with the coach and coach-man : — Frustra retinacula tendens , Fortur equis auriga , neque audit currus habenas . Is it not reasonable that the inferiour bodies should receive their motion from the superiour , as they have from them their beauty , perfection , and conservation ? But you give the moone many turners ; The earth by her magneticall motion ; Iupiter ( who turnes the foure lesser Planets ) by his body ; the Sun by his revolution . So here be three severall wayes of turning ; motion , body , and revolution : but is not revolution , motion ? And when Iupiter turnes by his body , is there no revolution ? Or when the Sunne turnes by his revolution , doth he not turne by his body ? It seemes that he that turneth by his body , toucheth , and so Iupiter toucheth the lesser Planets . He touched indeed Venus in the Poet when he kissed her : Oscula libavit natae : — But how he toucheth and turneth these Planets by his body , you doe not instruct us ; but your drift in all this , is to shew that if the Sunne carry about his spots or clouds ; the earth carry about the Moone , &c. much more may the earth carrie about an arrow or bullet : as if you would say , If the water carrie about the mill-wheel , and the wheele carrie about the mill-stones , much more may the mill carrie about the miller and his horse . Concerning other mens observations of the flame of a candle carried equally in a ship ; of an equall force , casting an heavy body but at an equall distance with & against the motion of the ship ; of a heavy body in a ship falling down in a straight line ; of a man leaping up in a ship , and abiding in the aire , one second scruple of an houre , and yet the ship not withdraw it selfe fifteene foot : Of these I will say but little , because I have already said something of them elsewhere ; yet I must tell you , that though the smoake and flame of a candle within the ship are carried with the ship , it will not follow that the clouds which are without the earth are turned about by the earth . If you could thrust the clouds within the bowels of the earth , they should be carried about with the earth if it did move ; but take the same candle which you talke , and place it in a calme night on the top of the mast , when the ship is carried with the tyde , then you shall see that though the candle is carried along with the ship , yet the smoake being separated from the candle doth not follow the ship , but remaines mounting upward in the aire . If the ship then carrie not along with it the smoak of the candle which is in it , how shall we thinke that the earth can carrie about the clouds which are so farre above it ? Now to salve this , you tell us , That the aire is as well limited in bounds , as that which is included in a roome . But then I answer , that it is one thing to be included , and another thing to be limited ; every thing that is included in a roome is limited , but not every thing limited is included ; what is included must needs partake of the motion of that which includes it : the aire within the ship is moved by and with the ship , because it is included ; but the aire without the ship though it be limited , yet moves not by or with the ship because it is not included . You ask where the bounds of the air are terminated , and you answer your selfe by the spheare of vaporous aire ; or which is all one , by the orbe of magneticall vigour ; so you distinguish between the aire , and vaporous aire : but you tell us not how farre this spheare of vaporous aire , or this orbe of magneticall vigour reacheth ; so that wee are not satisfied with your answer , except you meane that it reacheth to the moon ; for you told us before that the moon is turned about by the earth , but then you contradict your selfe , for you say here , that these bounds are not terminated by the concavity of the moone's orbe ; so where to finde you , and the bounds of your spheare of vaporous aire , I cannot tell ; neither doe I understand how vaporous aire being a substance , can be all one with magneticall vigour which is an accident : and how this accident can have its orbe , this is a new piece of Philosophie which would be illustrated , and so doe the words following ; That all earthly bodies are contained within these limits , as things are in a close roome , and as parts in that whole to which they belong . Though a heavy by equall force be cast at an equall distance , whether it move with or against the motion of the ship , yet will it not follow that a bullet being shot towards East or West shall passe the same distance ; for though you cast your bullet against the motion of the ship , it is not hindered nor furthered by its motion : so if the earth did move , that motion were no more to the bullets motion then if it stood still ; but it is the motion of the aire that furthers or hinders the bullets motion , whether in the ship , or out of it . The earth then turning about the aire with great violence from East to West , must hinder the motion of the bullet or arrow flying to the East , and further that which cometh from the East ; but it is not so in a ship , for the ship doth not carry the aire before it , but divides the aire whilst it moves , so that the aire gives place , as the water also doth to the ship , that there may not be penetration of dimensions . How then can the bullets motion be hindered or furthered by the motion of the ship , seeing the aire in which it moveth , is neither with it , nor against it ? Of the winde here I doe not speake . You grant that in a ship under saile , a stone being let fall from the mast will not descend to the same point , as if the ship stood still ; but you say , the motion of a ship is accidentall , and it is otherwise in these motions that are supposed to be naturall . I have shewed against Lansbergius , that there is no naturall motion in the earth , but though there were , what 's that to the furtherance or hinderance of the stones motion to the same point ; suppose that not nature but an Angel turned about the earth , the motion notwithstanding is circular , be the mover what it will be , externall or internall , Nature or Angel : therefore , it is true still , that as the stone falling from the mast will not descend to the same point when the ship saileth , as if it stood still ; so likewise a stone falling from an high tower , will not descend perpendicularly to the same point , the earth moving , as it would doe , if it stood still . Now , how farre the ship will withdraw it selfe in its greatest swiftnesse , from him that leaps up and stayes in the aire a second scruple of an houre : and how far the earth in that space will goe from him in that certaine , neither is it materiall ; it is sufficient that it will remove a certaine space , and that he shall not fall upon the same place from which he leaped up . What you granted but now you recall , and tell us of Galilaus , That the stone would still descend unto the very same place , whether the ship moved or not . So farre I yeeld , that if a heavy stone be let fall from a short mast whilest the ship moveth slowly , it is scarce discernable that the stone hath fallen or varied any thing from the perpendicular line : but if a small stone be let fall from a high mast whilest the ship moveth swiftly , then it is plaine to any man that hath sense , that the stone doth not fall upon the same point on which it would have fallen , if the ship had stood still . Now to say that the motion of the ship is impressed in the stone , is a toy ; for how can one body impresse a motion in the other whilest they are separated , as the stone and ship are before it fall ? of magneticall bodies I speake not . Being weary a ship-board you come on shore , and so having taken horse , you put spurs to his sides , and in your full cariere , you let a bullet drop out of your hand , which you say , Hath a transverse motion , besides the motion of the descent . But how should it have the transverse motion of the horse , seeing the hand doth but unfold it selfe to let it fall ; the arme indeed is carried by the swiftnesse of the horse , and so is the bullet whilest it is in the hand , but being let fall , how can it have a transverse motion , seeing the hand did not expresse any such motion in it ? for to let fall is not to give a transverse motion : and though you would make it all one to cast a thing from us , and to let drop a thing when we are on horseback , yet the contrary of this is so cleare , that any man may see it without the help of spectacles . And sure if there were any transverse motion in the descent of the bullet , it is rather to be ascribed to the motion of the aire , then to the opening of the hand ; therefore this is but a crotchet , as likewise your conceit of a bullet shot out of a cannon set on end ; you spend your powder , and bullets , and paper too , to no purpose ; for you shall never perswade me ( for all your two printed canons ) that the bullet shot out and being in the aire can partake of the earths circular motion , till first you prove that the earth doth move , and then bring me better reasons then as yet you have done , for the circular motion of the bullet in the aire ; it is not the picture ( which is the expression of your conceit and idea only ) that can evince my understanding , when sense and reason are on my fide ; for what may not men set forth in pictures ; Chimaera's , Centaures , Gorgons , &c. and what not ? Pictoribus atque Poetis , — you know what followes . Now you goe a birding ; for what is a gentleman but his pleasure ? and you discharge your peece with that dexterity that you hit the poore bird flying , as surely as if he were sitting upon a tree : and what followes upon this ? Namely , That the motion of the piece as in aiming it is made to follow the bird in its flight , is communicated to the bullet in the aire . But I see that though you have killed the bird , yet you are no good birder ; for at the instant whilst the peece is discharged , it is held steadie , so there is no motion of the peece imparted to the bullet in the aire ; but though the peece did move , will it follow therefore that the earth turnes about bullets in the aire ? if your powder and shot be not better then your arguments , you 'l never kill birds . But what a monstrous absurdity doe you tell us , That if a violent winde be able to drive ships , throw downe towers , turne up trees , much more may the diurnall motion of the aire ( which doth so farre exceed in swiftnesse the most tempestuous winde ) be able to carry with it the bodies of birds ? If the diurnall motion of the aire exceed the windes in impetuositie , how comes it , that it doth not the same effects that the winde doth ? why doe we not feele its force ? surely , if the aire did move with that violence from East to West , that a tempestuous winde doth , we should never have any ships come from the West Eastward ; nor ships bound Westward should stay for a winde , seeing the motion of the aire at all times would carrie them with a witnesse . If we should have occasion to saile to New England , wee should be there quickly , but no hopes ever to returne thence ; how should we be able to walke or sit on horsebacke , travelling against the motion of the aire , if it did move with that violence you speak of ? much lesse could birds in their flight resist such a force ; not the great bird Ruck ( that I may fit you with a bird somewhat proportionable to your conceits ) whose wings are twelve paces long , and snatches up elephants ( as if they were but mice ) in his talons a great way in the aire : sometimes you play the Painter , as in your circles and other figures ; and sometimes the Poet , as here : Admiranda sanis , sed non credenda . — As for your distinction of the motion of heavie and light bodies , to wit , That they being considered according to the space wherein they move , their motions are not simple but mixed of a direct and circular ; but according to the medium wherein they move , they have properly right motions . This I say is such a riddle , that Oedipus could scarce have solved it ; for why should not the motion be mixed as well in the medium as in the space ? Is the aire or medium a hinderance to circular motions , so that these bodies can onely move there in a straight line ? if so , you contradict your selfe , for you tell us still that bodies are moved round by the aire , and this by the earth . And how shall we understand that a stone falling downeward hath a mixed motion of a direct and circular according to the space wherein it moves , but a simple straight motion according to the aire wherein it moves ? What mean you by this word ( space ? ) you cannot meane the ubi of these bodies moving , for that is their rest in the place to which they move : ultima perfectio corpor is mobilis . You doe not understand I thinke the intervall of the ancients which Aristotle hath refuted , as being neither a substance nor an accident ; not a substance , because there would be penetration ; not an accident , for so an accident should be better then the substance ; for Locus est prior & nobilior locato . And if by space you understand the aire , then how will your distinction stand , the aire or medium , and the space being all one ? the place it cannot signifie , for the stone descendeth not in its place , but to it ; therefore what your space is , and how distinguished from the medium , I thinke you doe not know . If wee should aske you with what motion Christs body ascended into heaven , you will answer that according to the space wherein it moved , it ascended by a mixed motion of a direct and circular , but according to the medium , it ascended by a simple straight motion ; and so wee shall depart from you as wise as we came , like those that consulted with Sibylla ; Inconsultì ab●unt — You say , That Aristotle would not deny but that fire may ascend , and yet participate of a circular motion , so likewise must it be for the descent of any thing . Aristotle is beholding to you , for if you will beleeve him that heavie bodies must have a double motion , because he would not deny but that the fire may have a double motion ; then if he would not deny but that the heavens may move round , and that the earth may stand still , you will beleeve him ; much more I hope you will credit him when by irrefragable reasons hee proves the motion of the one , and immobilitie of the other : but how ever , it is bad reasoning from the possibilitie of one thing to the necessity of another ; great oddes between may be , and must be ; between fire and earth ; because Croesus may be poore , must therefore Irus be rich ? Because Aristotle saith the fire may descend , must the earth therefore ascend ? there is no consequence à posse ad esse ; much lesse à posse ad necesse . I will suppose with you , That whilst the ship is in her swistest motion , a ball of wax being let fall into a vessell full of water , may be slow in sinking , and that the motion of the ship will not be discernable in it . But that the wax should seem to the eye to descend in a straight line I wil not suppose , because I have found it otherwise ; the wax will seeme to have a transverse motion in the water though it descend in a straight line : so an oare seemes to be broken in the water , which element is not a true medium for the sight ; now the reason why the motion of the ship in the way is not discernable , is because the great disproportion betweene the bignesse of the ship , and smallnesse of the wax : and because that motion is not the waxes owne , but the ships : these two reasons concurring , make this motion in the wax indiscernable ; but suppose what you say were true in preternaturall motions , it will not therefore follow , that is also true in motions naturall . If the aire did move round with the earth , it is most certaine that the comets would seem alwayes to stand still , being carried about by the revolution of this aire ; but experience sheweth that they rise and set ; to this you answer , That most comets are above the spheare of the aire which is turned round with our earth . Answ. You told us before that the earth turneth about the moone , therefore it must follow that the comets are above the moone , if they be above that aire which is turned about with our earth . 2. We have already shewed that the aire sometimes moveth the earth , but that the earth moveth the aire is false and preposterous . 3. You tell us , That those comets which are within the orbe of our aire seeme to stand still , you instance that comet mentioned by Josephus , which hung over Ierusalem . Answ. That was no ordinary comet or the worke of nature , but a miracle or worke of supernaturall power , as the rest of those prodigies which happened about the same time ; to wit , the sudden light which appeared halfe an houre about the altar ; the Cow that brought forth a Lambe in the Temple ; the flying open of the brasen gate of its owne accord ; the chariots and armed men that were seene in theaire , &c. Now when you say , That this comet being within the orbe of our aire , seemed to stand still ; you are deceived , for it was Gods worke that it stood still over that place : and it did not seeme , but did truly stand still , by which it is plaine that the earth moveth not ; for if it did move , then the comets which are neerest to it would move swiftest ; but the contrary of this is true , for the higher the comet is , the swister it moveth , the lower , the slower ; yea scarce at all ; because it is the heaven that moveth the comets , and not the earth : so you falsifie Seneca , for he doth not say that these low comets seeme to move , but the clean contrary , that they are altogether immovable , undique immota . You say , That you might justly passe over my nine arguments which I urged in one Chapter , against your opinion ; but because I proceed ( say you ) with such scorne and triumph , you will examine my boastings . You doe wisely , like the Romans , who that their Generals might not be puffed up with the glory of their triumphs , caused some to walke along by their chariots , using upbraiding words ; the like doe you , calling my arguments cavills not worth the naming ; yet you are pleased to name them , to shew doubtlesse their weaknesse , and your wit. My first cavill ( as you call it ) is this ; If the earth move , it will be hotter then the water , because motion is the cause of heat : but that the earth should be hotter then water , is repugnant to that principall in naturall Philosophie which affirmes the earth to be colder ; besides , the water would never freeze if it were moved as swiftly as the earth . This argument because you cannot answer , you picke ( as you thinke ) a contradiction out of it , which is this ; The earth by motion is hotter then the water , and yet the water moves along with it , which water is made warme also by motion , that it is not capable of congelation . Answ. Is this a contradiction thinke you : the earth is hotter then the water , and yet the water is hot too ; the fire is hotter then the aire , and yet the aire is hot too ? who ever heard that the degrees of comparison make a contradiction ? I should not contradict my selfe , if I should say , Keplar was a cold disputant , but you are a colder . 2. Though I say that the water moveth along with the earth , yet the earth may be hotter then the water without any contradiction ; for of two bodies moving together , one may be hotter then the other , especially , if they be of different natures ; who knowes not that drie and solid bodies ( such as the earth is ) are more capable intensively of heate , then thin and moist bodies , such as the water is ? 3. Though the earth , water , and aire next to it , be not severed one from another , yet they are made hot by such a violent motion : when you runne , your cloathes , skin , flesh , bloud , &c. are not severed one from the other , and yet your motion makes them all hot . 4. If motion in fluid bodies were the cause of coldnesse ( as you say some do think ) then it would follow , that the more you move , your bloud should be the colder . Scaliger shewes , that they who water their horses being hot , use to stirre the water violently , that it may be brought to a warme temper , that the horses may drinke without danger . 5. I deny that all running waters are the coldest , neither are they the colder because they run , but because the meet still with fresh aire : so shall you in a cold day ( if you rise to walke ) be colder for a while , then when you sit still ; not because you walke ( for that in time will warme you ) but because you meet with fresh aire , vvhich you did not vvhilest you sate ; neither is there yet so much heat in you as to abate the sense of the cold aire , till your motion have caused it . 6. I deny that the strongest windes are still the coldest , though they blow from the same coast at the same time of the year , for I have observed that in one February , a gentle easterly vvind hath brought snovv , and the next February a strong East vvinde hath brought raine . 7. If rest be the cause that in cold vveather vvater doth freeze , then all vvaters that rest vvould freeze , and no running vvaters vvould freeze ; but this is false , for some vvaters resting doe not freeze , and sometimes running vvaters doe freeze , vvhen the motion is not so strong as to stirre up the heat ; therefore , it remaines that the heat caused by the motion , and not the motion it selfe , is the hinderance of the waters freezing . 8. If this motion were true that the earth runnes foure miles in a minute , the heat of the aire would be more then moderate ; even in winter you could not indure the heat of it ; we should need no fire to warme us ; wood would be cheap enough . 2. My second argument was this : If the earth did move the aire , then the aire which is next to the earth would be purer , as being more rarified ; but the contrary is true , for the higher the aire is , the purer it is . You answer never a word to this argument , which shewes you assent ; Qui tacet consentire videiur . 3. My third argument : If the earth did move the aire , it would cause a sound , but this is no more audible then the Pythagoricall harmony of heaven . You answer , That there is no reason why this motion should cause a sound , more then the supposed motion of the heavens . But I say , there is a great deale of reason , for if any solid body , be it never so small though an arrow , bullet , or wand , moving the air , cause a sound ; will not the vast body of the earth turning the aire with that violence cause a hideous noise , which would make us all deafe ? now , there is no reason why the motion of the heavens should make any sound , for neither are they solid bodies themselves , nor doe they move or encounter any solid body , nor is there any aire in heaven ; which things are required to make a sound . 4. I argued , that nature had in vaine endowed the heavens with all conditions requisite for motion , if they were not to move ; for they have a round figure , they have neither gravity nor levity , they are incorruptible , and they have no contrary . This you say will prove the earth to move as well as the heavens ; For that hath a round figure , it is not heavy in its proper place , and being considered as whole , the other two conditions you reject as being untrue , and not conducing to motion . Answ. Though I should grant you that the earth were round , yet it is not so exactly round and smooth as the heaven ; for it hath many mountaines and vallies , and some hills higher , some lower : is a globe or boule that hath knobs and dents in it so fit for motion as that which is smooth , and equally round ? 2. I have shewed already the folly of that conceit , which holdeth the whole earth not to be heavy in , it s own place ; as if the elements must loose their essentiall properties being in their own places , whereas it is the place that preserveth the propertiese and essenc of things . Have the fire and aire lost their levity because they are in their own places ? and is it not absurd to say ( as I have already shewed ) that there should be weight in a part of any thing , and not in the whole ? as if a piece of an yron bullet were heavie , but not the whole bullet : you were as good say , that totum non est majus suâ parte . 3. Whereas you say that the heavens are corruptible , you may say also that they are generable ; and so being subject to generation and corruption , they are of the same nature with sublunary bodies , and must have the same matter ; so that as there is a transmutation of the elements into each other , even so the heavens may be changed into the elements , and these into them : heaven may become earth , and earth heaven ; this is your admirable learning which passeth all understanding . 4. Heaven ( it seemes by you ) hath a contrary , but you tell us not what that is ; they are not contrary to one another , as fire and water ; nor are they contrary to sublunary things , for they cherish and preserve them ; neither have they the same common matter . 5. Any sensible man may easily conceive , that contrariety and corruption are hinderances to a perpetuall circular motion ; and because ( as is said ) the heaven is not capable of them , but the earth is , it will follow that I argued upon good grounds , that the heavens onely are endowed with all things requisit for motion , and not the earth : and therefore God will have nothing idle , as hee made nothing in vaine : hee hath made the heavens , and the three superiour elements to be exercised with motion , and the lowest element with generation and corruption ; but it were strange if the earth should be subject to all three , and the heavens to none , but should stand still , and be perpetually idle ; this is not sutable to the wisdome of the Maker . 5. I reasoned that all similary parts are of the same nature with the whole , but each part of the earth doth rest in its place , therefore doth the whole also . You say this Argument would prove , That the sea doth not ebbe and flow , because every drop of water hath not this motion ; or that the whole earth is not sphericall , because each part hath not the same forme . Answ. I have shewed already that the ebbing and flowing of the sea are not essentiall to the sea , for in many places the sea doth not ebbe and flow ; therefore it is no wonder , that parts of the sea , being severed from the whole , lose that motion , seeing many parts being joyned with the whole have it not . This motion then is caused by externall agents ; but those qualities which are essentiall to the whole , are not lost in the parts : Every drop of water is heavy , and moves downward , because the whole doth ; every drop of sea water is salt , because the whole is . 2. I have said already that the earth is not exactly sphearicall , and though it were , your conceit is nothing : for roundnesse belongs not to the earth , quà talis , as it is earth , sed quà tota , as it is whole . When a thing ceaseth to be whole , it loseth the figure of the whole , neither are external figures or outward qualities essential to things , but common accidents onely : Now , the qualitie of resting in the lowest place is essentiall to the whole earth , therefore to the parts also . 6. I said that the Sun in the world is as the heart in mans body , but the motion of the heart ceasing , , none of the members stirre ; so neither would there be motion in the world if the Sun stood still : This ( you say ) is rather an illusturation , then a proof . I grant it ; for I used it as an illustration to discover with its light the weaknesse , and to dispell the darknesse of your opinion . And were it not an absurd thing to think that the arteries move , but the heart standeth still ? So no lesse absurd is it to say , that the Earth moveth , but the Sunne standeth still . 2. Illustrations oftentimes are forcible proofs , and used they are both by Divines and Philosophers . 7. I said that the Sun and heavens work upon these inferiour bodies by their light and motion . You say , That the Sun and Planets working upon the earth by their owne reall , daily motion , is the thing in question , therefore must not be taken for a common ground . Answ. If nothing shall be taken for a common ground which is or hath been in question , then there are no common grounds in Divinity and Philosophy ; for I know no fundamentall doctrine in the one , or principall in the other , which hath not been questioned by wanton and unsettled spirits . 2. I said that the heavens work by motion ; you inferre , as if I had said , of a reall daily motion : I spake neither of daily nor annuall motion ; if hee doth not work by his daily , doth hee work by his annuall revolution ? 3. Tell mee if you can , from whence proceed the many motions and mutations that are in sublunary things ? from themselves they cannot ; from a superior cause then they must , and what is that but the heavens ? and what other media or meanes are in heaven by which they work , but light and motion ? If you can tell us any other besides these , wee will be beholding to you . 8. I proved that the earth must be firme and stable , because it is the foundation of buildings . You say , That it is firme from all jogging , and uncertaine motions . Answ. This is a jogging conceit of yours , and an uncertain answer , as I have shewed already ; for motion , as it is motion , is an enemy to buildings , be it never so uniforme ; and a moving foundation can be no settled foundation : If a foundation be stable , how can it move ? if it move , how can it be stable ? 9. My ninth Argument was taken from the authority of Divines , grounded on Scripture ; Thy Sun shall no more goe downe , &c. In the Revelations the Angel sweares there shall be no more time ; therefore the heavens must rest , whose motion is the measurer of time ; so S. Paul saith , The creature is subject to vanity ; this is the vanity of motion of which Solomon speaks : The Sun riseth , and the Sun goeth downe , &c. This ( you say ) is but a weake Argument ; for it is granted that this opinion is a Paradoxe . Answ. As it deviates from the opinion of other men , it is a Paradoxe , but as it is repugnant to Scripture , it is a Cacodoxe . 2. When you say that Isaiah speaketh of that light which shall be in stead of the Sun and Moon , doe you answer any thing at all to his testimony ? Thy Sun shall no more goe downe , &c. for hee distinguisheth between that light which God shall give to his Saints , and the light of the Sun which shall no more goe downe ; so that hee doth not confound these two lights which are in God and in the Sun , as you would have it . A part of the Churches happinesse shall be , that shee shall both enjoy the light of the Sun without intermission , and also that new inaccessible light of divine vision . If then the Sun shall goe downe no more , it argues that the Sun useth to goe downe : Now , if you will have these words understood mystically , yet the thing to which they doe allude must be understood properly ; to wit , the going down of the Sun. 3. You will have time to be measured by the motion of the earth , not of the heaven ; and this you prove out of Pererius , who saith , That time depends upon the motion and succession of any duration : But Pererius explaines himselfe in another place : that that is only time properly and principally , which is measured by the motion of the primum mobile : because the motion of the heaven is the first , and the cause of all other motions ; and because it is the least , as being the swiftest ; and it is most certaine , and uniforme , universall , and known to all : so that if the earth did move ( which as yet you have not proved ) yet these conditions cannot agree with the earths motion : time which is measured by other motions , is not properly and formally , but materially and improperly so called , ; so it is false that the earths motion is the cause of time , which Pererius never affirmed or dreamed of . 4. You will have the heavens subject to other vanities besides that of motion ; as first unto many changes , witnesse the comets seen amongst them ; and then to that generall corruption in the last day , when they shall passe away with a noise , &c. Answ. If changes be vanity , to how much vanity is your world in the Moon subject , which so often changeth ? 2. Though the heavenly bodies were subject to other vanities , as you say , yet these will not exempt them from the vanity of motion . 3. How comets , which are Gods extraordinary workes , and denouncers of his judgements , are vanities , I understand not . 4. That the Apostle speaks of comets in that place , is your part to prove either by reason or authority . 5. That comets which are seen onely by us in the aire , are discerned by you amongst the heavenly bodies , is no wonder , seeing you can discern a world in the Moon . 6. St. Ambrose on that place sheweth , that the vanity to which the heaven is subject , is the continuall toile of their motion , and that it expects rest , that it may be delivered from servile work . 7. If the heavens be subject to the vanity of corruption , as you say , tell us whether you speak properly and philosophically , or metaphorically ? If philosophically , you are absurd ; for every fresh-man can tell you that heaven is not capable of generation and corruption ; if metaphorically , you speak impertinently ; for by the passing away of heaven , is meant onely the abolition of imperfect qualities , and a perfecting of it to a more glorious estate . 8. The heavens ( you say ) are subject to that generall corruption in which all creatures shall be involved in the last day . But you cannot tell us what that corruption shall be , and so you speak at randome : you doe not mean ( I hope ) that the heavens shall be involved in the same corruption with snakes , rats , toads , and other such kinde of creatures . You say that there is not such invincible strength in my arguments , as might cause me triumph before hand . But I say there is so much vincible weaknesse in your answers , that makes me think that the refutation of them deserves neither triumph nor ovation ; so that my strife with you is but — pugna nullos habitura triumphos : neither did I purpose to make you any reply , had not some friends solicited me to vindicate the truth and my owne credit , which seemed to be somewhat eclipsed by the unwholsome fogs , and misty discourses of your Book . I said that the heaven was called AEthera , ab 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , from its continuall motion ; and the earth Vesta , quòd vi suâ stat , from its immobility . You say they were so called because it was then the common opinion , that the heaven moved , and the earth stood . But now because you are of another opinion , it 's fit that the names be changed aswell as the nature ; let the heaven now be called Vesta , and the earth AEtherae ; or let heaven be called Terra , quòd perenni cursu omnia terat , and the earth should be called coelum , à caelando ; so let all things and arts be confounded : Grammar , aswell as your Logick , Philosophy , and Astronomy . 2. If heaven and earth have their Etymology from what they seeme to be , not from what they are ; then the like may be said of other things . Fire is called focus , à fovendo , from cherishing ; the sea is called mare , quasi amarum , because it is salt or bitter ; not that these things are so , but because they seem to be so : the like may be said of other Etymologies . 3. For your conceit of the Hebrew word Erets from Ruts , because it runs , is but a running motion of your head . The Hebrews who were better skilled in their owne language , then you are , derive Erets from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , because it continually desires to beare fruit , as Munster sheweth in Genes . c. 1. You object to your selfe , How are two distinct motions conceiveable in the earth at the same time ? and you answer you selfe , that it is easily apprehended , considering how both these motions tend from West to East , as you instance in a bowle . Answ. How the earth should have two distinct circular motions , is not conceiveable by us , nor demostrable by you . Your similie of the bowle is a poor demonstrastration , and indeed , false ; for it running on the superficies of the ground , hath not two circular motions , as you should have shewed , but onely one such motion or rowling ; the other as it moves from your hand to the mark , is the motion of projection ; or rather the bowles motion , is indeed but one , being a mixed or compounded motion ; neither doth it move with two distinct circular motions in the same place the same time , as you will have the earth to doe : but it runs from one place to another ; neither is it naturall , but violent : and though it were true that the bowle had two distinct circular motions in the same place at the same time , yet it will not prove that the earth is either capable , or we conceiveable of these two motions , considering the disproportion that is between the vast and heavy earth , and a small light bowle . You conclude this Chapter , singing the triumph before the victory ; for you say that we may gather some satisfaction out of it , but indeed we can gather none : neither are we a whit the wiser for it , but leave it with as great discontents , and as little satisfaction , as they did Sibylla's cave , who came to consult with her intricate Oracles ; . Inconsulti abeunt , sedemque odêre Sibyllae . Chap. IX . 1. The earth cannot be the cause of its owne motion . 2. The vasinesse and thicknesse of the heavin no hinderance to its motion . 3. The matter of the heavens and their smoothnesse no hinderance to their motion . 4. Bignesse helps motion . 5. The heavens swistnesse illustrated by other motions . 6. The earth neither the finall nor efficient cause of its motion , the heaven fitter for motion , because greater , and more constant ; nature worketh not still the most compendious way , some idle similitudes refuted . 7. Bodies having the same properties have not alwayes the same motion ; motion belongs to the noblest creatures . 8. The smoothnesse , subtilty , and purity of bodies no hinderance to their motion ; the aire moves the water , the circular motion of the fire naturall how . 9. Of Intelligences how and why they move the heavens . 10. Magneticke vertue an idle conceit . IN this Chapter , ampullas loqueris & sesquipedalia verba ; you talk not like a man of this world , but like one who hath dwelt long in the Moone ; or as if you were Iupiters secretary with Minos , and had the honour with AEolus . — Epulis accumbere divûm . You dispute of the magnitudes and distances of the orbs , and of the swiftnesse of their motion with that exactnesse , as if you had measured them with a line : but I wonder how you could stand steady to take their measure , seeing the foundation on which you stand whirles you about foure miles every minute of an houre . I should thinke that your head was giddy when you wrote this , and that indeed you can no more dispute of these things , then a blinde man can doe of colours ; neither can we give you any credit untill first you goe thither , and bring us a certificate signed with the hands of these Angels which turne about the orbes ; otherwise you will but loose your labour : — Nec quidquam tibi prodest Aereas tentasse domos , anintóque rotundum , Percurrisse polum — . 1. You will have us suppose that the earth is the cause of this motion ; but this wee may not suppose , for if there be any motion in the earth , the earth is the subject of that motion , but not the cause ; for nothing can move it selfe ; movens & mobile are distinct things : but what if we should suppose what you desire , what will be gained thereby ? to wit this , That the heavens shall be freed from their inconceivable swiftnesse : and is not this a goodly reason . We cannot conceive how the heavens move so swiftly as they say , ergo we must suppose the earth to move ? Shall we suppose the fire to be cold , because we cannot tell how the sunne is hot ? If one cannot tell how the eye seeth , will you bid him suppose that the foot seeth ? This is , homines ex stultis insanos facere : let the swiftnesse of heaven be never so great , we cannot suppose the earth to move . For that they may be swifter then our thoughts , is not impossible , if either we look on Gods power , or on the aptitude in these bodies for such a motion : But you will not have us flye to Gods power what he can doe : I pray you then whither shall we flie ? If we goe up into heaven he is there , if we goe downe to hell he is there also . &c. Whatsoever is done in heaven , and in the earth , &c. he doth it himselfe , saith David . Hee sustaineth all things by the word of his power ; In him we live , move , and have our being : therefore the Philosophers said well , that he was the first mover , and that the outmost heaven was the first moveable . But if you will have us looke unto the usuall way of providence what is most likely to be done , then we say that it is most likely , that the heavens move , and the earth stands still , as is already proved . 2. You say , the heavens being vast , materiall , condensate substances , are not capable of such a motion : I heare words but to no purpose , for you should tell us , whether the matter of heaven , and the condensation thereof be like this of the earth ; and whether the mover be so weake as that he cannot turne about that vast body . I had told you heretofore that bodies move swifter or slower , not because they are greater or lesser , but because they are heavier or lighter Motion which you call a Geometricall thing ( but you are in this decived ) depends not from quantitie , lesser bodies move oftentimes flower then the greater ; a snaile then an elephant , a pebble stone then a great cloud : it is not then beyond the phansie of a Poet , or mad-man , ( as you madly speake ) for the heaven to move very swiftly ; but if any man will take upon him to tell exactly how swiftly the heaven moveth , or that the earth moveth at all ; I must needs tell him that he needs hellebor . 3. When we say that the heavens are bodies without gravitie , you answer us with your recocted coleworts , or idle evasion of yours so often repeated , That the whole earth in its owne place is not heavy : which shift we have divers times already refuted : but when you say , That the heavens being of a materiall substance , it 's impossible but that there should be in them some ineptitude to motion : you speake like one who is a stranger to Philosophie , for if it were not for the matter , there would be no motion in the world . As the forme moveth , so it is by reason of the matter that all things are moved , so that where there is matter , there can be no ineptitude to motion in respect of the matter . But it is a rugged conceit in you when you say , That it 's not conceiveable how the upper spheare should move the lower , unlesse their superficies were full of rugged parts , or else they must leane one upon the other . Answ. What rugged parts are there in the superficies of winds and clouds , when the windes move the clouds ? or what ruggednesse is there in smooth waters , when in rivers the formost waters are moved forward by the hindermost ? Or in the smoake when it carrieth upward a piece of paper ? But when you say , That the farther any spheare is distant from the primum mobile , the lesse it is hindered by it , in its proper course : It is true , and yet not repugnant to Ptolomies opinion , who saith , That in heaven there is no reluctancie ; for his meaning is , that there is no inferiour spheare that hindereth the swiftnesse of the primum mobile , and that is the reason why it is so swift : because it hath no resistance either from the forme , or from the matters ; or thicknesse of the medium . Novv , In nova fert animus , — you vvould faine play the Poet , and build castles in the aire , but indeed you have already played the Poet too much ; for your vvhole booke is nothing else but a heap of fictions ; your vvorld in the Moone , your moving earth , your standing heavens , your figures and characters , what are they else but pleasant dreames , and idle phansies , fit enough to be inserted into Ovids Metamorphosis , if you could digest them into good verses ? And you doe not onely play the Poet , but the Painter also in your figures , for a fictitious Picture is a visible Poem , and a Poem is an audible Picture , Painters and Poets have authority you knovv . But you wonder much why Poets have not feigned a castle to be made of the same materials with the solid orbes . Answ. I thinke the reason is , because they did not knovv that there vvere people in the Moone ; if they had knovvn this , doubtlesse they vvould have fitted them vvith inchanted castles , and other buildings ; novv vvhat they have omitted , doe you , that posterity vvhen you are dead may say ; — Nunc non cinis ille Poetae Faelix ? now levior cippus nunc imprimit ossa ? But I vvill not novv spend time in vievving the parts and materials of your Poeticall castle , till you have brought it to perfection ; and then I vvill take a survey of every particular . 4. I had said that a bigger body , as a mill-stone , vvill naturally descent svvifter then a lesse , as a pebble stone ; the cause of this , You will not have to be ascribed to the bodies bignesse , but to the strength of naturall desire which that big body hath to such a motion . Answ. You make a shevv as if you did ansvver our argument , but in effect you ansvver nothing : for if I should aske you vvhy a mill-stone falls faster then a pebble , you will answer , because it hath a stronger desire to fall ; but if I aske againe why it hath a stronger desire , you answer , because the bigger a thing is , the stronger is its desire , &c. and is not your opinion now all one with mine in effect ? that it is the bignesse that is the cause of this swiftnesse ? now the same reason is appliable to bodies moving circularly : for though they were in their proper scituations , yet there is in them as great a desire to move about the center , as there is in elementary bodies to move to and from the center ; therefore , the greater the body is , the greater desire it hath to move according to your opinion . Againe , I said that the winde will sooner move a great ship then a little stone , you answer , This is not because a ship is more easily moveable then a little stone , but because a little stone is not so liable to the violence from whence its motion proceeds . This answer is as wise as the former , for why is not the stone as liable to the violent cause of its motion as the ship , but because it is not so big , therefore the ship is more easily moveable then the stone ; because by reason of its bignesse it 's more liable to the violent cause of its motion . And when you say , That I cannot throw a ship as farre as a stone ; I grant it , but this will onely argue want of strength in me , but not want of aptitude for a swifter motion in the ship then in the stone , if I had strength to sling the one as well as the other . A bigger bullet out of the same peece will flie farther and swifter then a lesser . 5. I brought some instances to illustrate the possibility of the heavens swiftnesse , as the sound of a cannon twenty miles off ; of the sight of a starre in a moment , of the light passing suddenly from East to West ; of the swiftnesse of a bullet carried by the powder ; to these you answer , That the passage of a sound is but slow , compared to the heavens motion ; that the species of sound or sight are accidents , and so is the light ; that the disproportion is great betwixt the heavens motion and the swiftnesse of a bullet . Answ. Let the sound , and light , and species be what they will be , they are moved ; and if they be accidents they cannot be moved alone , but with the subject in which they are inherent : therefore , if there be such swiftnesse in the motion of these , what need we doubt of the swiftnesse of the heavens ? and if accidents can be so swiftly moved with and in their subjects , much swifter must be these heavenly substances having no resistance , whose matter is so pure , that it is a great furtherance to their motion : and though there be great disproportion betwixt the bullets motion and the heavens swiftnesse , yet the motion of the one serves to illustrate the swiftnesse of the other . And yet I take not upon me as you doe , peremptorily to tell how swift the heavens are ; and though I said that the light was an accident , yet I said also that it was corpori simillimum , that it comes very neere to the nature of a body : neither did Aristotle prove the light to be no body , because of its swiftnesse , as if no body were capable of that swiftnesse , for then he should contradict himselfe as you use to doe ; but he meanes that no sublunarie body had so swift a motion . It had been folly to illustrate the swiftnesse of the bullets motion by the motion of the hand in the watch ; for there by many other motions far swifter then this to expresse the bullets motion : but of sublunary motions there be none swifter then those I alledged to illustrate the motion of heaven . 6. You would have the earth to be both the efficient and finall cause of its motion : But indeed it is neither the one nor the other , for if it move at all , it must be moved by another mover then it selfe : and God made the heavens not for the earth , but for man ; so the diurnall and annuall motions have man for their finall cause , and heavenly movers for their efficient . 2. You say , That nature is never tedious in that which may be done an easier way : This I will not grant you , for nature doth not still worke the easiest , but the most convenient way ; but I deny that the earths motion is either more easie or more convenient then that of heaven ; for a light body , such as heaven is , is more easily moved then a heavy ; and it is more convenient that the foundation of our houses should remain firme and stable , then moveable , as I said . I could tell you how laborious and tedious nature is in the perfecting of mans body , and of many other things , therefore she doth not take still the most compendious way . 3. You say , It is not likely that the heaven should undergoe so great and constant a worke which might be saved by the circumvolution of the earths body . How tender hearted are you ? are you afraid that the heavens will grow wearie ? and I pray you , is not heaven sitter to undergoe a great and constant worke then the earth , so small , so dull , so heavy , so subject to change ? a great worke is fit for a great body , and a constant work fit for that body that knoweth no unconstancy . 4. You are deceived when you say , That the heaven receiveth no perfection by its motion , but is made serviceable to this little ball of earth . The perfection of heaven consisteth in its motion , as the earths perfection in its rest ; neither was heaven made to serve this ball , but to serve him who was made Lord of this ball . 5. Your Similies of a mother warming her childe , of a Cooke rosting his meat , of a man on a tower , of a Watch maker , are all frivolous . For a mother turneth her childe , and a Cook his meat to the fire , because the fire cannot turne it selfe to them ; the motion is in them , not in the fire : so he that is on a tower , turnes himselfe round to see the countrey , because the countrey cannot turne it selfe about him . If you had proved to us that the heaven cannot move , but that it is the earth that moveth , then we should yeeld that the earth did foolishly to expect the celestiall fire to turne about her ; but this you have not as yet proved , neither will you be ever able to prove . The earth indeed is a mother , but as senslesse and stupid as Niobe , who would suffer her children to starve with cold , if that heavenly fire did not move about her . As for your instance of a Watch-maker , I will use it in your owne words , but to our purpose : If a wise Watch-maker will not put any superfluous motion in his instrument , shall we not thinke that nature is as provident as any ordinary mechanicke ? Therefore doubtlesse it had been superfluous for the earth to move . And whereas you say , That the motion of the starres is full of confusion and uncertainties : That is true in respect of your ignorance ; there is an heavenly order , and harmony amongst them , the confusion is in your head , and the uncertainty in your knowledge . 7. You say , That motion is most agreeable to that which in kinde and properties is neerest to the bodies that are moved . But this I say is false , for an immoveable body is not made capable of motion , because it is neere in some properties to the body that is moved . A rocke and a mill-stone which perhaps was taken out of the same rocke , agree in kinde and properties , will it therefore follow , that because the mill-stone moves round , the rocke also moves round ? The sea-water and well-water agree in kinde and properties , doth the well-water therefore ebbe and flow ? But your drift is to shew , That the earth moveth with the six Planets , because both Earth and Planets have a borrowed light , whereas the Sunne and fixed Stars have it of their own . Answ. A goodly reason , the earth must move as well as the sixe Planets , because it hath a borrowed light as well as they ; as if you would say , Saturne and the Moone have a borrowed light , therefore they have the same motion and bignesse : or thus , the Planets have a borrowed light as well as the earth , therefore , they rest , or be as heavie as the earth ; but what if I should say , the Planets have some light of their owne , as may be seen by the Moone , which the earth hath not ; and therefore they agree not in this property of light , and consequently the earth moveth not as they doe . But when you say the fixed stars have light of their owne , you speake at randome , for you can shew no reason of this conceit , why the fixed starres should have light of their owne , and not the Planets ; or why the Planets borrow light , and not the fixed stars . Againe , you thinke , That the Sunne and Stars should rest , because they are of a more excellent nature : As if motion did belong to the ignoblest creatures ; we know the contrary , Man is a more noble creature then a rocke , yet man moveth , and the rocke is immoveable . The heart in our bodies is more noble then the guts , yet that moveth , they move not . Is the body of man lesse excellent when it is moved by the soule , then when it is at rest putrifying in the grave . When water rests from its motion it loseth its excellencie , and stinketh , therefore , motion in many things is more noble then rest : as for the rest which you say is ascribed to God , that is not to our purpose , for it is transcendent and hyperphysicall ; and as God is said to rest , so he is said to move , therefore called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . But why you should thinke the fixed Starres of a more excellent nature then the Planets , I know not , neither can you give any reason for it . 8. Aristotle you say tels us , that the time of the revolution of each orbe should be proportionable to its bignesse , which can only be you thinke , By making the earth a Planet . I answer , that of two evills the lesse is to be chosen , and better it is that there should be some disproportion between the bignesse of the orbes , and the time of their motion , then that the earth should move . 2. You cannot exactly tell what disproportion there is in their motions , till first you finde out the true knowledge of their magnitudes . That the Comets which move in the aire are not moved by the heavens , but by the earth , you prove ; Because the concave superficies of the Moone is thought to be smooth , so that the meere touch of it cannot turne about the fire with a motion not naturall to it ; nor can the subtle fire move the thicker aire , nor this the waters . Answ. How the upper spheares move the lower , is neither knowne to you nor me but by conjectures . 2. I have already shewed that one smooth body by its touch may move another , as the winde moves the clouds ; so in the Northerne seas , one mountaine of ice which is smooth , moves the other forward . 3. The subtiltie and puritie of the fire is no hinderance to its moving of the thicker aire , for doe not our animall spirits which are pure and subtle , and yet materiall , move our grosse bodies ? Doth not the winde move grosse substances ? 4. That the aire doth not move the water , is repugnant to experience , for within the Tropickes , the sea is continually moved from East to West by the aire ; and this by the heaven as I have shewed elsewhere . 5. That the circular motion of the fire is not naturall , is false ; for though this motion proceed not from an inward principle , as the straight motion doth , yet it is naturall , because the nature of the fire is preserved by it ; for the fire never gives off moving upward , till it begin to move circularly , and then is it in its chiefe perfection when it hath attained this motion . Lansbergius you say concludes that the earth is easily moveable , from the words of Archimedes , who said , that he could move the earth , if he knew where to stand and fasten his instrument ; it is a foolish conclusion , for so he might as well conclude , that armed men may arise out of the ground , because Pompey said , that if he did but stampe with his foot , the ground would yeeld him armed men . So because Medaea said : Ego inter auras aliti curru vebar ; That shee would flie in the aire in a chariot drawne by dragons , that therefore shee could doe as shee said ; this is to play the Poet. 9. The opinion of Intelligences , by which the heavens are moved ( you say ) hath its originall from Aristotle's mistake , who held the heavens to be eternall . I answer , that Aristotle was mistaken in holding the heavens to be eternall à priori ; but I deny that there is any errour in holding them to be eternall à posteriori , in respect of their substance . 2. Aristotle might have held the opinion of Intelligences , without holding the heavens to be eternall ; for the eternity of the mover doth not necessarily inferre the eternity of the thing moved : God is eternall , so is not the world , our soules are eternall , so are not our bodies . 3. You prove , That Intelligences are superfluous , because a naturall power intrinsecall to these bodies will serve the turne as well : So you might inferre that our soules are superfluous , because a naturall power resulting from the matter of our bodies , and intrinsecall to them will serve the turne as well . But indeed such excellent bodies as the heavens did require a more excellent forme then sublunary bodies doe ; for these are content with an informing form , but the heavens stood in need of an assisting forme : and how can we conceive that out of such pure and simple materials as the heavens are , there should result a naturall power to move them circularly , orderly , constantly , perpetually ? If our grosse and decaying bodies are moved with reasonable soules , which though they be internall formes , result not from the power of the matter ; much more should the heavens be regulated by Intelligent spirits , and not by any naturall power . 4. This naturall power of moving must be either the forme brought out of the matter , which is done by generation , but in heaven there is no generation , because there is no privation of an other forme , or any appetite in the matter to it ; or else this power must be a forme brought into the matter : but no forme is introduced into the matter , except the reasonable soule ; therefore , there is no informing forme in heaven , and consequently there can be no other movers but Angels . This Argument I urged against Carpenter , but you winked at it and said nothing . 5. You say , That Intelligences being immaterials cannot immediately worke upon a body . What is this to the purpose ? If they work upon bodies , it 's no matter how they worke ; wee know that our soules worke upon our grosse bodies , and so doe the Intelligences upon the heavens : we know that spirits work upon muteriall substances immediately , or else there would be no working at all ; and it is ridiculous in you to disable the Angels from working or moving , because they have no instruments or hands to take hold of the heavens . What hands hath your soule when it works on your body ? What hands hath the winde when it moves the clouds ? 6. You have no reason to insult so over the Schoole-men , who affirme , that the faculty whereby the Angels move their orbes , is their will ; for what faculty else can you imagine in them ? Doth not your soule worke upon your body by the will ? so , that albeit there be many instruments by which the soule moveth the body , yet the prime faculty by which it moveth is the will : so that if you suspend your act of willing a motion , you must needs stand still ; and on the contrary , your onely willing to move the hand or foot is sufficient as the chiefe medium or faculty to move them . And so it is with the heavens , saving onely that there are no subordinate organs by which the Angelicall will doth move the heavens : but when you say that there was no need of Angels , since this might be as well done by the will of God : You speake idlely , for so you may say that there is no need of our soules to move our bodies , since this might be as well done by the will of God : Angelicall and humane wills are subordinate and serviceable to the will of God , but not excluded by it ; For in him we live and move , and yet we live and move by our soules too . And as impertinent is your other question , How the orbes are capable of perceiving this will in the Intelligences , or what motive faculty have they of themselves to inable them to obey ? Answ. The orbes are as capable to perceive the will of the Angels , as your body is to perceive your will , or as those bodies were which the Angels of old assumed , and by them conversed with the Patriarchs : and as those bodies had a motive faculty to obey the Angels will , so have the heavens much more . Keplar's opinion that the Planets are moved round by the Sunne , and that this is done by sending forth a magneticke vertue , and that the Sun-beames are like the teeth of a wheele , taking hold of the Planets , are senselesse crotchets , fitter for a wheeler or miller , then a Philosopher : This magneticke vertue is a salve for all sores , a pin to stop every hole , for still when you are reduced to a non-plus , magneticke vertue is your onely subterfuge , like AEneas his target , Unum omniae contra tela Latinorum : If you had told us that the North starre had a magneticke vertue , because the needle touched with the magnes looketh towards it , some silly people perhaps would have beleeved you , and yet the magneticke vertue is in the needle , not in the star ; but that in the Sunne there should be a magneticke vertue , it hath no show of probability . This vertue ( you say ) may hold out to as great a distance as light or heat : But if this comparison hold , it will follow , that there is no such vertue in the Sunne , for that light which is in the aire is not in the Sunne , neither is that heate which wee feele caused by the Sunne , in the Sunne : but your following words are admirable ; That if the Moone may move the sea , why may not the Sunne move the earth ? As if you would say , If the North-winde shake the woods , why may not the South-winde shake the mountaines ? Or ( according to your doctrine ) if the earth can move the Moone , why may not Venus or Mercury move the Sunne ? or why may not the Sunne move the Firmament ? You conclude well , That your Quare's are but conjectures , and that no man can finde out the workes of God from the beginning to the end : and yet you have found out that which God never made , to wit , a rolling Earth , a standing Heaven , a world in the Moone ; which indeed are not the workes of God , but of your owne head : for his workes are incomprehensible , his wayes past finding out . Trouble not then your selfe too much in these things , which in this life you cannot understand ; learne to know your selfe that wee may know you too , and by the knowledge of your selfe , strive to know God , the knowledge of whom is life eternall . I will give you good counsell in the words of Hugo : Nosce teipsum ; melior es si te ipsum cognoscas , quaem si te neglecto cursus siderum , vires herbarum , &c. Coelestium omnium & terrestrium scientiam haberes ; multi multa sciunt , seipsos nesciunt , quum summa Philosophia sit cognitio sui . CHAP. X. 1. The idle and uncertaine concetes of Astronomers concerning the celestiall bodies . 2. The appearances of the Sunne , and other Planets cannot be so well discerned by the earth if it did move . 3. The excellency of Divinity above Astronomy , and an exhortation to the study of it . THis proposition is full of suppositions , fraughted with figures and characters , which more affect the eye then satisfie the minde ; neither doe they demonstrate the motions of the earth , but the motions of your head . The pictures in Ovids Metamorphosis adde not the more credit to his fictions , neither doe these figures to you phansies : wee will beleeve no more then you can demostrate by sense or reason ; demonstrations are of things true and reall , not of dreames and imaginations : therefore , neither your pictures , nor bare words , shall perswade us , that dayes , moneths , yeares , houres , weekes , &c. are or can be caused by the earths motion , till first you have proved that the earth moveth ; you that cannot abide Eccentrickes and Epicycles in the heavens , are forced now to make use of them , both for the motion of the Moone , and of the earth too ; so that you have not mended but marred the matter , rejecting Ptolomy because of Eccentrickes and Epicycles , aud yet you admit Copernicus with his new devised Moone Eccentricks , and Earth Eccentrickes , so that you thinke by these fictions to solve the divers illuminations , bignesse , eclipses , &c. of the Moone . A phantasticall Astronomer might devise other wayes besides these of Ptolomy and Copernicus , to shew the different appearances of the Planets ; for of things that are uncertaine and beyond our reach , divers men will have divers conceits and conjectures : many have held , and doe at this day yet maintaine , that the stars have soules and are living creatures , and why may not this be as true as your opinion , that there is a world of living creatures in the Moone ? What if I should hold that the eight spheare is a solid substance , therefore called firmamentum , full of holes , some great and some small ; so that these lights which wee call starres are but beames of that bright and cleare heaven above , called Empyreum , shining through these holes ? Or if I should say , that every starre had its Angel moving it about the earth , as wee use in darke nights to carry lanternes : divers Nations of Asia , Africke , and America , have divers opinions of the starres , and few or none true , all which do argue our ignorance and foolishnesse ; we are but Curvae in terris animae , & coelestium inanes . But any of these conjectures mentioned , is as probable as yours of the earths motion ; therefore , I was not without sense and reason when I concluded my Booke with this Argument , That if the Sunne stood still , there could be no variation of the shadow in the Sunne Diall : you will say that may be altered by the earths motion , but I say to you as I said to Mr. Carpenter , prove that , and what I profered to him , I also profer to you : — Phillida solus habeto . You will say this may be easily proved , if I will admit the earth to move : but so you may say , that you will easily prove an Asse to flye , if I should admit that hee hath wings ; but I will not admit that upon a false maxime of your devising , you shall inferre what you please . What if I should admit an absurd conceit of yours , that the Earth draweth the Moone about ? can you prove mee , that when the Moone shineth there is any variation of shadowes , when both the luminous and opace body are moved with the same motion ? 2. The difference ( you say ) betweene Summer and Winter , between the number and length of dayes , and of the Sunnes motion from Signe to Signe , and all other appearances of the Sunne concerning the annuall motion , may be seene by your Figures ; and easily solved by supposing the earth to move in an Eccentricall orbe about the Sunne . Answ. Not the Sunnes appearances but your phantasies are to be seene by your figures ; the earth doth not move because your figure represents it : it is also an easie matter to suppose things that never were , nor can be ; you suppose the earth to move about the Sunne , and not the Sunne about the earth : you may as well suppose the house to be carried about the candle , and not the candle about the house , and so all appearances may be solved as well this way as the other ; for if the house did move about the candle , the house shall be seene as well as if the candle did move about the house : and why may we not suppose the house to move sometimes neerer to , and sometimes farther from the candle , the neerer it moveth , the more it is illuminate , &c. But what Cato is so grave as to refraine from laughter at such absurd and foolish suppositions ? You spend much paper to shew how the Planets will appeare direct , stationary , retrograde , and yet still move regularly about their owne centers . This is , Magno conatu magnas nugas dicere ; and who but Iudaeus apella will beleeve , that one motion of the earth should cause so many different appearances in the severall Planets ? howsoever you talke of Ptolomie's Wheele-worke , I preferre his Wheele to your Whirlegig . It is more easie for many Planets to wheele about , then for one rocke or piece of earth to whirle about : but you are as exact in placing the Planets , as if you had been upon the top of Iacobs ladder . You place Mercury next to the Sunne , hiding himselfe under his rayes ; you say well , for theeves doe use to hide themselves ; but for one to hide himselfe in the open light is not usuall : darknesse ( one would thinke ) were more proper then that ; But how Mercury hath a more lively vigorous light then any of the other , I understand not : I should rather thinke that there were a more lively vigorous light in the Sun , Moone , and Venus . And whereas you say that Venus in her conjunction with the Sunne doth not appeare horned , is true ; but if her husband Vulcan had beene as neere the Sunne , his hornes doubtlesse had beene seene ; doe not you know how much ashamed Venus was , when the Sunne looked upon her , being in bed with Mars ? Now , that the orbe of Mars containeth our earth within it , I will not deny ; but I am sure our earth containeth Mars within it , who is oftentimes too exorbitant : — Toto saevit Mars impius orbe . And that the orbe of the Moone comprehends the earth in it , because shee is sometimes in opposition to the Sunne , is a feeble reason ; as , though the opposition of two round bodies should be the cause why that which is in the midst betwixt them , should be within the circumference of either of their circles or orbes . Other Planets have their oppositions , is therefore the earth within the orbe of either of them ? Or why is the earth more within the orb of the Moone then of the Sun , seeing the Moone is no more in opposition to the Sun , then the Sun is to the Moone ? 3. You conclude your Booke with a large digression upon the commendations of Astronomy , which hath for its object the whole world you say , And therefore farre exceeds the barren speculation of universale , and materia prima . Answ. It seemes you have left nothing for the objects of other sciences , if Astronomy must ingrosse the whole world for its object . 2. Vniversum , belike , exceeds Vniversale with you , and the extent of the one is not so large , nor the speculation so fruitfull , as of the other ; but surely your Vniversum or world in the Moone is as barren a notion , as that of Vniversale . 3. The knowledge of Philosophy and Logicke , is but cobweb learning in your conceit ; but we thinke that these cobwebs are strong enough to catch such flyes as you ; and indeed there is more substance in these cobwebs then in your Astronomicall dreames and phansies . 4. What you say of other knowledge , That is depends upon conjectures and uncertainty ; is most true of your Astronomicall Booke , wherein I have found nothing but suppositions , may-bee's , conjectures , and uncertainties . 5. Whereas you say , That man had os sublime , a face to looke upward , that he might be an Astronomer : You are deceived , it was that hee might be a Divine ; for the starres were made , not that he should doate upon them in idle speculations and niceties full of uncertainty , but that by their light and motion he might be brought to the knowledge of Divinity , which your self in your subsequent discourse is forced to acknowledge . But take heed you play not the Anatomist upon these celestiall bodies , ( whose inward parts are hid from you ) in the curious and needlesse search of them ; you may well lose your selfe , but this way you shall never finde God. 6. Whereas you say , That Astronomy serves to confirme the truth of the holy Scripture : you are very preposterous , for you will have the truth of Scripture confirmed by Astronomie , but you will not have the truth of Astronomie confirmed by Scripture : sure one would thinke that Astronomicall truths had more need of the Scripture confirmation , then the Scripture of them . And indeed , all Learning beside the Scripture , is but 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , as Theodoret saith ; that is , meere contention and strife of words not to be reconciled . Let us not then spend that time in vaine and needlesse speculations , which we should imploy in knowing God , and in working out our salvation with feare and trembling ; For it is life eternall to know God in Christ : in respect of which excellent knowledge , the Apostle accounted all things but drosse and losse . Moses was a great Astronomer , yet he reckoned the knowledge of this , and of all the Egyptian wisdome , but detrimentum & stultitiam , but losse and foolishnesse in respect of the knowledge of holy Scripture , saith Saint Ambrose . Astronomers with Martha , are busie about many things , but the Divine with Mary , hath chosen the better part which shall never betaken from him . How small was the store of gold and silver which the Hebrewes brought out of Egypt , in comparison of that wealth which under Solomon they had in Jerusalem ? so small and meane is all humane knowledge compared to the Scripture : for whatsoever learning is nought it is condemned here , whatsoever is profitable it is to be found here ; and more abundantly in the wonderfull height and depth of Scripture , then any where else , saith Saint Austin . Let it then be our delight , Nocturna versare manu , versare diurna : still to be meditating in this holy Law of God ; that like trees planted by the river side , wee may fructifie in due season . And as Alexander did carry about him Homers Iliads in the rich cabinet of Darius , even so let the holy Scripture be still our Vade mecum , and in the cabinet of our heart let us lay it up , as Mary did the words that were spoken of Christ. I may say of Scripture as the Apostle said of Christ , Whither shall we goe from thee ? thou hast the words of eternall life . Thus briefly and by snatches ( being with-drawne and distracted with many other businesses ) have I answered your Booke , which I undertooke partly out of the considence I have of the truth of our side ; partly to vindicate my owne credit ; partly to satisfie my friends ; and lastly , to excite others whose abilities exceed mine to maintaine and defend the truth of our opinion , and to explode the contrary as false , which in time may prove dangerous and pernicious to Divinitie . FINIS . Notes, typically marginal, from the original text Notes for div A57666-e410 l.g. Meta. 5.4 . Notes for div A57666-e2090 Cont. Lansbergium , l. tsect . 1. c. 20. * Plin. li. 2. cap. 65 . August . de civit . li. 16. cap. 9. Macrob. in som. Scipionis li. 2. c. 5. Lactanti . de falsá Sapien. li. 3. cap. 24. l. Categ . c. 10. Iob. 42.3 . Lactan. de fals . i Sapi. lib. 3. cap. 3. Aug. ad Lau. li. 1. cap. 10. Lact. li. 3. ca. 3. defal . Sap. Cont. Carpentar . Sect 2. c. 10. Aug. l. 7. de Civit. c. 35. Theod. ser. ad Grac. infid . Plin. l. 30. c. 1. Decivit . Dei , l. 7. c. 35. Tertul. l. de Anim. c . 28 , 29. Vide Laertum , l. 8. de viit . Phil. O. 5. Solin c. 16. Cic. 4. Tuscul. Litius Dec. 1. l. 1. Plutarch . in Numa . Mercure Francois An. 1633. Vincent . Lyr. adver . Hares . Vincent . ibid. Cont. Lansbergum . L. 8. De Genes . ad lit . c. 1 &c. 2. L. 1. De Genesi ad liter . c. 21. Lib. quast . E. vang . in Mat. 4. 12. Lib. de . utilit . s●edend . c. 1. Le Mercure Franc. an . 1633. In Gen. ad Fteram . De verbis Domini , Ser. 18. In Isai. c . 19. Psal. 19. Eccles. 1. Josh. 12. 14. In cap. 2. Spharajaero B●se . Geor. 4. AEn . 10. Esay 38. 8. 2 King. 20. 11. De Civit. lib. 21. c. 8. Vide in Iosuam Munster . Lyram , &c. 2 Chr. 32. 31 De civit . Dei l. 21. c. 8. L. 2. Chron. l. 1. Prooem . Philes sacr . De Genes . ad liter . l. 2. cap. 16. Psal. 148. De civitat . l. 11. cap. 34. Hexam . l. 2. cap. 3. De Genes . ad lit . l. 2. cap. 6. Gen. 15. 5. Psal. 147. 4. Ier. 35. 22. Inc. 1. sphae . De civit . Dei l. 16. c. 23. August . ibid. Rev. 4. Psal. 125. Cons. Lansberg . l. ● . sect . 1. 6. 9. Iob 23.8 , 9. De cognit . ver . vitae . c . 6. Hom. 8. in Ierem. Epist. 59. ad Aritum . Sect. 1. c. 6. Sect. 1. c. 1,4,5 . Prov. 8.5 . 10.8 . Eccles. 1.13 , 16 , 17. & 8. 5. Odyss . 1. 1 Pet. 3.4 . Secund. Sec. 9.4 . artic . 2. Oportet intelligentem speculari phantasmata . Arist. Lib. d corde . Esay 59. 5. Exercit. 201 Psa. 58.4,5 . AEn . 5. 7. In Psal. 57. & 67. Pinge duos angues . Histor. Indicar . l. 3. c. 3. Iob 37.9 . & 22.17 . Pro. 25.29 . Iohn 3. 8. In Psal. 134 Eccles. 1.7 . 1 Cor. 15. lib. 1. Od. 34. Act. 4. Psal. 29. Iob 26.14 . lib 4. Fast. in Apparen . In Caten . Comitoli in Iob 9. Cont. Lan the. l 1. sc. 1. c. 7. Rerum divinarum humanarumque , cognitio . Serm. 2. ad Grac. infid . Resp. ad Qu. 93. Hexamer . li. 1. cap. 6. Psal. 104.2 . Isa. 40.22 . De Genes . ad liter . l. 2. c. 9. August . In Psal. 104. Hier c. 3. ad Ephes. Iob 8.8 . Prov. 8.29 . Ier. 5.22 . Psal. 104. Du Eartas 3. Day . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Barbara Pyramidum sileat miracula Memphis Martial . Perseverantia consisetuimis amisit admirationem . De Trin l. 3. c. 2. c. 5. &c. 6. Virgil. l. 4. Geor. Eccles. 1.4 . 2 Pet. 3.5 . 1 Chr. 16.30 Psal. 93.1 . & 96.10 . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , habitor , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , habito . Psal. 90.2 . Prov. 3.19 . 2. Chro. 1.4 . Ps. 119.90 . Ps. 104.5 . Psal. 98.3 . Luke 2. 51.6 . Iob. 9.6 . c. 1. sec. 2. Apol. c. 47. Philip. 2. L. 7. Inslie . c. 7. De hamartigenia . Satyr . 2. Irenaeus l. 5. c. 31. Psal. 139. Amos 9. Esay . 14,13 , 14,15 . An. 6 . Pliny . Prov. 26. 4. Contra Lansberg . Luke 12.56 L. 4. De trin . In Prooem . in Xenoph. L. 3 . c.c . De fals . sapiens . Serns , 1. De side . Iob 38.5 . Verse 22. L. 1. sec. 1. c. 1. L. 1. sec. 1. c. 1. L. 1. Sec. 1. c. 5 AEn . 11. AEn . 1. De teros motu L. 1. c. 3. 4 , 5 , &c. De bello Iudaico . 7. c. 12 Natural . quaest . 1.7 . c. 6 L. 1. sec. 1. c. 6 . Isa. 60.20 . Rev. 10.6 . Rom. 8. Iovis arcanis Minos admissus . L. 2. sec. 1. c. 1. De Coelo . l. 2. c. 10. Lib. 1. de Anima . Serm. 1. De F. de . L. 1. De Officus . De Doctrina Christian. L. 2.6.41 . 
A31232	----	The English globe being a stabil and immobil one, performing what the ordinary globes do, and much more / invented and described by the Right Honorable, the Earl of Castlemaine ; and now publish't by Joseph Moxon ... Castlemaine, Roger Palmer, Earl of, 1634-1705. 1679 Approx. 442 KB of XML-encoded text transcribed from 96 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2007-01 (EEBO-TCP Phase 1). A31232 Wing C1242 ESTC R3787 12268677 ocm 12268677 58149 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A31232) Transcribed from: (Early English Books Online ; image set 58149) Images scanned from microfilm: (Early English books, 1641-1700 ; 624:1) The English globe being a stabil and immobil one, performing what the ordinary globes do, and much more / invented and described by the Right Honorable, the Earl of Castlemaine ; and now publish't by Joseph Moxon ... Castlemaine, Roger Palmer, Earl of, 1634-1705. Moxon, Joseph, 1627-1691. [9], 147 [i.e. 153], [6] p., 12 leaves of plates : ill. Printed for Joseph Moxon ..., London : 1679. Errata: prelim. p. [6]-[7]. Advertisement: p. [1]-[6] at end. Reproduction of original in Bodleian Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. 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Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Astronomy -- Early works to 1800. Globes -- Early works to 1800. 2006-07 TCP Assigned for keying and markup 2006-07 Apex CoVantage Keyed and coded from ProQuest page images 2006-08 Judith Siefring Sampled and proofread 2006-08 Judith Siefring Text and markup reviewed and edited 2006-09 pfs Batch review (QC) and XML conversion The ENGLISH GLOBE Sch. 1 The English GLOBE Being a STABIL and Immobil one performing what the Ordinary Globes do , and much more . Invented and described by the Right Honorable , the Earl of Castlemaine . And now publish't by Joseph Moxon , Member of the Royal Society , and Hydrographer to his most Excellent Majesty . Fundasti TERRAM super STABILITATE sua . Psal . 104. 5. LONDON . Printed for Joseph Moxon , at the Sign of Atlas on Ludgate 〈…〉 TO THE READER Concerning this Globe , and the occasion of the Inventing of it . NEW and profitable Inventions in Arts are like hidden Treasures found , which ought not to be reburied , and concealed again , but dispersed and made use of for the common good . This Globe then , and its Description ( which I have humbly obtained from the Right Honorable , the Earl of Castlemaine ) being both highly curious and useful , I thought I could not better serve ( as I have always endeavoured ) this , and future Ages , then by communicating it to them ; and because the occasion of the Invention is so accidental , and ( as it proves ) so happy , I shall give you a short account of it . Waiting upon my Lord in the beginning of Anno 1672 , at his then arrival into England , I brought his Lordship ( knowing that any thing new and ingenious would be acceptable to him ) one of my 3 Inch Terrestrial Globes , with the Stars described in the inside of its Case , which when his Lordship had considered , and bin inform'd by me , that its only Vse was to keep in memory the situation of Countries , and Order of the Constellations and particular Stars , He intimated , that certainly much more might be done by it , and so returning beyond Sea fell upon this excellent Work. When he came home again ( which happned above a year ago ) and was pleased to shew me what he had done , I was as much ravisht and suprised at the admirable Contrivance of his Globe , and the many unexpected Operations performed by it , as if I had bin a new Beginner in the Study of the Sphere ; Nor could my admiration be less , when I saw how ( without the usual assistance of a Meridian Line , Mariners Compass , or other such helps ) it composed it self to the true site and position of the World ; how that in an instant , the Suns Altitude was naturally and plainly found by it , and this in all places of the World at the same time ; Nor did it seem less strange to me , that so many curious Questions relating to Eclipses should be resolved by it , and what is more that Altimetry could possibly have any relation to a Globe . Besides , I saw that not only the Practical part of Dialling was now rendred easy to a wonder , but the Theorical also so plain , that every mean capacity might streight comprehend it ; Nay , all the forrain Requisites to this Art ( as the Declination of Planes , their Inclination , Reclination , &c. ) are here as artificially and exactly found , as by any Instrument invented for that intent alone . And this I can also say , that as to the Geographical part , it is ( considering its bigness ) not only the most useful , but also the best order'd and the best divided Globe extant ; and yet it would have bin not a little better , had not his Lordships late Troubles hinder'd him from finishing it , as he design'd ; for Directions are not always sufficient to express an Authors mind . But truly notwithstanding these and other prodigious Operations , that which surprised me with the most admiration was to find , that in a subject so trite as the Globe ( and so nicely Canvast by the greatest Mathematicians of all Ages ) any thing should be left to be added or invented to it ; which also shews that the Wit of Man has no bounds ; nor can any thing better demonstrate the noble Authors great Parts , who moreover ( because he would omit nothing that I had offered at in the Proto-type ) has here shew'd his excellent skill in relation to the Stars by a Projection on the Pedestal ; and doubtless this kind of Projection was never brought to that perfection before . But Gentle Reader , I shall injure you too much if I detain you longer from this rare present , and therefore after rendring again my thanks to his Honour for this favour and libertie , I subscribe my self His and Your Humble Servant , Joseph Moxon . June 24. 1679. A Postscript concerning the Erratas , and the Geographical part of this GLOBE . THE Erratas of the Press being many , I shall not set them down in a distinct Catalogue as usually , least the sight of them should more displease , than the particulars advantage , especially since they are not so material or intricate , but that any man may ( I hope ) easily mend them in the very reading . I confess I have bin in a manner the occasion of them , by taking from the Noble Author a very foul Copy , when he desir'd me to stay till a fair one were written over , so that truly 't is no wonder , if Workmen should in these cases not only sometimes leave out , but adde also , by taking one line for another , or not observing with exactness what words have bin wholly obliterated and dasht out . As to the Geographical part of the Globe be pleased to take notice that 1st , The Terms or Bounds betwixt EVROPE and ASIA , or between ASIA and AFRICA , are Strokes and Pricks — thus : between great Empires , single Strokes in this manner — ; and between Province and Province only Pricks . And by the way , the Author calls here an Empire , every great Tract of ground of one Appellation , as Barbary and Zara in Affric , Siam and Pegu in Asia , Italy and Germany in Europe , as well as France ; Spain , Persia , &c. that belong to one only Prince . These Empires are in little Capital Letters , but the Provinces or subdivided Kingdoms are in Round Roman , as Algiers and Tunis in BARBARY , Pomeren and Austria in GERMANY , &c. and for the Towns as London , Paris ; Venice , &c. they are generally in Italick , but when they happen to be in Round Roman , as Fez ; Morocco , Agra , &c. it shews that the Province gives the Name to the Capital City ; for the Name properly belongs to the Province , but to save trouble and room it is now by a Reference or Dash joyn'd to the Town . 2. The Old Name of any place is in Old Hand , and when it belongs to an Empire , 't is very big , as Sarmatia , Ethiopia , &c. when a Province , a great deal less , as Mesopotamia , Caldea , Assyria and the like , and when a Town very little , as Hippo , Cyrene , and so forth . 3. The Hills that are exprest have all before them the Letter M , and the Capes the Letter C , but the Rivers have eithe either an R or else sl . after them ; and whereas some Old names , as Thule , Ophir , &c. are repeated , it is to shew where One Author would have their situation to be , and where Another . But be pleas'd to remember , that whereas his Lordship did Direct in this * Treatise , that the Grand Meridian should pass throu ' St. Vincent , I have presum'd to draw it over St. Mary and St. Michael , 2 Isles of the Azores ; for truly thus it suits best ( according to my Tables ) with the 2 a Clock Circle , as his Lordship would have it do . An Advertisement . BEcause there are several who either want time , or Patience to go throu ' the whole Treatise , I here present the Reader with a Catalogue of the Operations , which are most pleasing and suitable to the fancy and humour of such , and which they may easily in a day or two learn , especially if they have a Master to help them . 1. TO set the Globe level . pag. 4. 2. To compose the Globe . p. 8. 3. To know the day of the Month. p. 9. 4. To take the Suns height above our Horizon , when he shines out clear ; and also when he shines dimly , and is overclouded , p. 5. and 6. 5. To find the Suns Azimuth and Bearing . p. 10 and 12. 6. To know the Hour several ways . p. 13. 7. To know at what hour the Sun rises or sets . p. 16. 8. To know what a Clock 't is all the World over . p. 31. 9. To find where 't is day and where 't is night all the World over . p. 33. 10. To find where ( at that moment ) they have nothing but Day , and where nothing but Night ; as also when this happens in any place subject to this Alteration . p. 33. 11. To find the Sun 's present Height and Depression all the World over , if he shines . p. 37. 12. To find where the Sun is rising and setting all the World over . p. 34. 13. To find what people have then the Sun Vertical , or over their heads . p. 35. 14. To know where they are rising , where they are going to Dinner , where to Supper , and where to Bed all the World over . p. 35. 15. To find how much any People ( if it be day with them ) are past Morning , or want of Evening ; and ( if it be Night with them ) how much they are past Evening and want of morning ; and consequently the Babilonish and Italian Hour all the World over . p. 36. 16. To know the Judaic Hour , p. 39. 17. To find in what Clime any Place lyes . p. 26. 18. To know in any Lunar Eclipse , what Countries see it wholly , what in part , and what not at all ; as also the true hour , which each people see her at , in her several Affections ; with her continual Height , Azimuth , and Bearing all the while . p. 59. 19. To represent the several Phases of the Moon . p. 61. 20. To find the Proportion between any Perpendicular and it's shade . p. 65. 21. To take the height of a Tower by the Globe . p. 66. 22. To do it seemingly without any Instrument . p. 66. 23. To know the Hour by your Stick . p. 67. 24. To learn presently how to make ( all the 5 Dials of a Cube , ( to wit , that on its * Horizontal , that on its direct † South , that on its direct * North , that on its direct † East , and that on its direct West Plane ) tho' a man be never so unacquainted with Mathematics . 25. To represent at any time the posture of the Heavens in relation to the appearing Fixt Stars ; and consequently to find the present Hour , with the Height , Azimuth and Bearing of any Star ; as also the time of its Rising , Setting and continuance both above and below the Horizon . p. 138. The General Heads . 1. THE Figure , or Delineation of this Globe , as also an account of it , and the occasion of its Invention , together with a Catalogue of the Operations fittest for those that cannot run over the whole Treatise , are contain'd in the unfigur'd or preceeding pages . 2. The Introduction begins pag. 1. 3. The first Section , solving the Questions which relate to the Sun in our Elevation . p. 4. 4. The second Section , resolving the Operations that concern Geography , and the Sun all the World over . p. 20. 5. The third Section , concerning the Moon , p. 48. 6. The Fourth Section relating to Perpendiculars and their Shades . p. 64. 7. The Fifth Section treating of Dialling . p. 70. The Figure of the Globe fitted for a Garden or open Portico . p. 121. Geometrical Problems , necessary for Dialling . p. 122. 8. The Vse of the Line of Lines , and Line of Sines on the Sector . p. 125. & 127. 9. The sixth Section , solving ( both by the Globe and Pedestal ) all the usual Questions which relate to the Stars . p. 129. & 135. The Explication of the Letters , &c. on Sch. 1. P. The North Pole of the World. N. The Northern Polar Circle . Z. The Zenith . E E. The Ecliptic . ♋ ♋ . The Tropic of Cancer . Jun. 1. The Parallel of that day . May 1. The Parallel of that day . Apr. 1. The Parallel of that day . AE AE . The Aequator . Mar. 1. The Parallel of that day . Feb. 1. The Parallel of that day . Jan. 1. The Parallel of that day . ♑ ♑ . The Tropic of Capricorn . H H. The Horizon . S. The Southern Polar Circle . P The South Pole. N. The Nadir . Z H. The Quadrant of Altitude : N. The Quadrant of Depression . Z H. The Quadrant of Proportion . P AE P. The Meridian of the Place or Solstitial Colure . LL The Meridian of the World. ♈ P. P. The Aequinoctial Colure . XII . I. II. &c. The Hour Circles , or particular Meridians . THE Introduction . THIS Globe whose several Operations we are here describing , neither hangs in a Frame , nor is moved about as the ordinary ones are , but stands stable and immobil on its Pedestal , which makes it not only to represent the Earth more naturally , according to the common Hypothesis , but renders it also more expedite and useful , as shall be fully shewn in the Conclusion or last Chapter ; for then ( after a view of the whole Treatise ) every body will the better comprehend all the new Operations it performs , and all the particular Advantages , it can any ways challenge to its self . But here my Reader must remember that though I endeavour all along ( even in the most ordinary things ) to be clear and easy , yet unless he has formerly read , Hewes , Bleau , or rather Moxons Book on the Globes , I cannot promise him I shall always be understood without the help of a Master ; for I have not time to descend to all the Definitions and minute Explanations , which those that are wholly unacquainted with Astronomical or Geographical Principles , may perchance expect . As for the Circles here describ'd , there are some common to all Globes ; as the Aequator , the Ecliptick , the Coluri , the ordinary Circles of Longitude , the Tropics , and the Polar Circles ; and some also particular to this Globe only , as the Horizon , the Meridian of the Place , and 16 Parallels to the Aequator , all within the said Tropics . Now that these Circles in general may be the sooner found and comprehended by any new Beginner , there are Capital Letters in the Great Figure , or Delineation of the Globe , in Scheme the first , which sufficiently distinguish them ; for the Aequator is markt with AE , the Ecliptic with E , the Polar Circles with N. and S. The Circles of Longitude with the Roman Figures , I. II. III. &c. as well where they fall upon the Polar Circles , as the Aequator ; and tho all the Circles , that thus cut the Aequator and Polar Circles at a Roman Figure be Circles of Longitude , yet they now serve for true Hour Circles also , since they are not here express'd , and drawn ( according to the usual manner of Terrestrial Globes ) at the distance of 10 Degrees , but of 15 asunder . And here be pleas'd to remember that since there is a difference between the Roman Figures which belong to the same Circle ( for if it cuts for example at IIII. on the Polar Circles , 't wil cut , you see at six hours difference , viz. at X in the Aequator , ) the reason of it will appear by and by very plainly when we come to the Operations , that concern these Circles ; of which the broadest ( passing through the Zenith and Nadir ) has two Quadrants gradually divided on one half of it , the first called the Quadrant of Altitude , reaching from the Pin Z or Zenith , to the Horizon H , the second ( called the Quadrant of Depression ) reaching from thence to the Nadir ; whereas on the other half , or back part of the said Circle , there is a single Quadrant only , viz. from the Zenith to the Horizon , which we shall for the future term the Quadrant of Proportion . This Circle is also markt on the Polar Circles with the Figure XII . representing thereby , not only the 12 a Clock hour Circle or Meridian of the place , for which the Globe is particularly design'd , but the Colurus Solstitiorum also ; so that the Colorus Aequinoctiorum must be the 6 a Clock Circle , whose half is ( as you see ) divided for several uses into Degrees from Pole to Pele . By these two Circles then , you have readily presented to you the 4 Cardinal Sections , or Points of the Globe ; for as the Graduated half of the said Meridian , shews the Globes Southern part or face , and the opposite its Northern , so the graduated half of the six a Clock Circle gives its Eastern , and the plain side of it its Western . Now for the Aequinoctial Parallels , or Sun 's Track for every 10th day , throughout the year , ( for to avoid Confusion of Circles , I describe no more ) they are distinguish'd by the Days of the Month , when the Sun comes to them , the uttermost of which are the two Tropics markt not only with the 11th . of June and 11th . of December , but with ♋ and ♑ , the usual Characters of Cancer and Capricorn . Lastly , for the Meridian of the World , or first Circle of Longitude , 't is markt with the Letter L , and prickt also ; and tho in the present Longitude ( i. e. that of London ) it stands for the 2 a Clock Hour-Circle , yet in its self 't is changeable , as shall be shewn hereafter , when we treat of its * Properties , and Divisions . These are then the Circles here describ'd , either common , ( as I said ) to all Globes , or particular to this , and being well observed and remembred will much facilitate the ensuing Operations , which are all naturally performed , either by the shadow of the Sun and Moon alone , or by the help of a small String , hanging sometimes from the Pin P , representing the North-Pole , sometimes from the Pin Z , representing ( as I said ) the Zenith , and garnisht with a little Bead and Plumet , according to its Figure in the Scheme aforesaid . And here you are to take notice that tho the one end of the String be absolutely fastned to the Pole , to prevent the loosing of it , yet 't will serve for the Zenith as commodiously as if it always hung from thence ; for there is made at a convenient distance from the said fastned end , a little Noose or Ring , which ( as occasion requires ) is now to be over this Pin , and now over that ; Nay if you give your String but half a turn about either of the Pins , you will ( with a little Allowance ) as exactly perform your Operation as if you used the said Noose it self . To conclude , the whole Treatise is divided into six Sections ; The first solving several Questions that relate to the Sun in our Elevation . The second , many Geographical ones , together with some that concern the Sun , not only where we live , but all the World over . The third is of the Moon ; The 4th . of the Proportion of Perpendiculars to their shades , with some useful Corollaries thence arising ; The 5th . of Dialling , and the 6th . of the Stars . SECT . I. Solving many questions , relating to the Sun in our Elevation . Operation I. To set the Globe level or parallel to the Horizon . I Begin here , because 't is what we first suppose done in most Operations , especially in the nice ones , nor is the performance difficult , for we have nothing to do , but to place the String and Plumet exactly upon the South side of the Meridian or 12 a Clock hour Circle , and if it hangs just over the little Star on the Pedestal , then the Plane where the Globe stands is Horizontal and Level ; otherwise 't is faulty as much as the Plummet varies from being Perpendicular to the said Star ; for the Star ( you must suppose ) is engraved by the Globe-maker there , where he found the Plumet to hang upon his Placing the Globe truly level . Let therefore the String and Plumet be always long enough to touch almost the Pedestal , for thereby you may better perceive any Error ; and remember also that in case the said Pedestal ( to be less cumbersom ) be not as big as the Diameter of the Globe , then there is to be under it a little wooden Ruler , which being drawn out , and markt with a Star will serve for this and several other uses as you will see anon . There is another way speculatively true , tho perchance not so exact in practice , which is thus perform'd . Place your Globe on your Plane with the String lying on the Meridian as before , and if the Extuberancy or swelling of the Globe just touches and bears up the String at the Horizontal Circle , then the Plane is Level , or Parallel to the Horizon , otherwise it differs as many degrees , as are between the point , where the said String touches the Globe , and its Horizon . The reason of this is , That seeing the greatest and most extuberant Circle on a Globe is that which lies 90 degrees from its Pole , the Horizon becomes here the greatest and most extuberant one that can be described from the Zenith , therefore the Globe being on a Level which makes its Zenith to correspond with the Zenith in the Heavens , the String cannot fall short of the Horizon , because it must rest on the most extuberant Circle that occurs ; nor can it touch below it , because the Plummet drawing the said String perpendicular from the greatest extuberancy , hinders its bending , and consequently its inclination to any part of the Globe beneath the Horizon . Now if the Plane be not level , then the Zenith of the Globe and Heavens not corresponding , another Circle or part of the Globe , instead of the Horizon must have the greatest extuberancy and this Circle , being 90 Degrees from the point of the Globe , ( which lies directly under our Zenith ) it must differ from the Horizon of the Globe , as many Degrees as its Zenith differs from that in the Heavens ; therefore the way prescribed is at least speculatively true . Operation II. To find the Suns Almucantar , or Height . THere are three distinct ways of performing this independent of the following Operations , and each of great use ; for the first gives you the Suns height in an instant if he shines . The second if you have the least glimps of him , or can guess at his place in a Cloud . The third , if you know the hour by any good Watch , Pendulum or the like , whether we see the Heavens or no. I. As for the first way , 't is this ; your Globe being level , move it 'till the shade of the Pin in the Zenith falls directly upon the Meridian , and then the shade of the Extuberancy ( i. e. that made by the swelling or bellying out of the Globe ) will touch the true degree in the Quadrant of Altitude reckoning from the Zenith to it . And thus you will find not only the Sun's height , sooner perchance than by any ordinary Quadrant , but will still have it before your eyes as long as you please , nothing being to be further done , but to move sometimes the Globe that the shade of the said Pin may still concur with the Meridian . But if your Globe be fix'd , ( or that for some particular reason , you have no mind to stir it at all , draw your string from the Zenith , through the shade of its Pin , i. e. lay the string in the Plane of the Sun , and then if you mount your Bead till it reaches the nearest part of the shade of Extuberancy , it will ( by bringing it to the Meridian or Quadrant of Altitude ) lye on the true Degree , reckoning ( as before ) from the Zenith to it . The Reason of the Operation is this ; The Sun when he rises brushes the Zenith and Nadir of the Globe with his Rayes , for he illuminates alwayes ( within some few Minutes ) just half of it , therefore when he gets ( v. g. ) a Degree higher , he must needs illuminate a Degree beyond the Zenith , and so proportionably from time to time , or else he would sensibly illuminate more or less of the Globe at one moment than at another , which is absurd . Now since the Sun in truth illuminates more than an Hemispere , the Reader must remember that Ptolomy reckons this excess ( take one time with another ) to be about 26 minutes , and Tycho something less , therefore substract 13 minutes ( or half the said Excess ) from what the shade of Extuberancy mark 's , and you have his Height with all ordinary Exactness : but should you chance at any time to doubt how far the said Shade of Extuberancy ( which is not so discernable as that made by a Gnomon ) just reaches , erect then a piece of stick , straw , quill , &c. or , if you please , rest your Finger on the Globe , between the Sun and the point in dispute , and where the shade of your Finger , straw , stick or quill is lost , that will be the true Term of the shade . As for the Second Way ( for both the former we reckon but one ) turn the Meridian of your Globe to the Sun as before , or because we suppose him not to shine out-right , direct by your Eye the said Meridian , so that it lye in the same Plain with him , and this you may do in a manner as well ( if you have the least glimps of him , or can by any accident guess whereabouts he is ) as if you had the fore-mentioned help of the Pin's shade in the Zenith . Having thus done , Take your String in both hands , and cross with it ( as exactly as you can at right Angles ) that part of the Meridian next your body , whether it happens to be the Quad. of Alt. or that of Proportion , then putting your Face close to it , and moving your Ey lower and lower , till by reason of the Extuberancy you can but just see the Sun , or his supposed place in Heaven , do but bring your String ( held as before ) to this point , viz. bring your String towards you till it just takes away the Sun or his supposed place from your Ey , and the degree in the Meridian on which it then lies will be ( counting from the Zenith ) the Height required ; for so far his raies would reach did he shine out-right . The third way is when we know the Hour by any Watch , Pendulum , &c. thus , Find among the Aequin . or Diurnal Parallels that belonging to the present Day , which we will suppose Apr. 10. and drawing your string from the Zenith over that Point in the said Parallel , where 't is cut by the Hour given , i. e. by the morning 9 a Clock Circle , move your Bead to the said Point , and the distance from the Bead to the Horizon will be the required Height , viz. about 36 degrees , as you 'l find if you bring the Bead to the Meridian and count the degrees between it and the Horizon . The Suns Height may be also known by its Azimuth , as by Operat . 5. Having therefore by any of the aforesaid waies his Height , 't will ( upon any doubt ) soon appear whether it be Fore or Afternoon , for as long as ever he increases in Degrees , i. e. mounts higher and higher above the Horizon , it wants of Noon , whereas if he falls or declines , 't is after Noon . OPERAT. III. To Compose the Globe , either by a Meridian Line , or without it , to the site of the World. IF you have a Merid. line drawn , viz. a Line lying exactly North and South , place the Globe * level with its Merid. directly over it , i. e. place so the little Notch in the Pedestal ( markt S ) that it cover the Southern extremity of the said line , and the Notch N the Northern , and then the Poles and Circles on the Globe will ( without sensible error ) correspond with those in Heaven , and each painted Region or Countrey on it , will be turn'd towards the real one which it represents . But if you have no line drawn , Know the day of the Moneth , and you have two quick waies to do this Operation without any forreign helps . The Globe having in it smal pin-holes , on the several intersections of the Merid. with the aforesaid Diurnal Parallels , or ( to be exacter ) on each point of the Merid. which an imaginary Parallel of each fifth day would cut ; for tho' we are to suppose Parallels for every day throughout the year , yet there being no sensible difference in the Sun from 5 daies to 5 days , such holes will be abundantly sufficient ; nay the aforesaid ones from ten Dayes to ten Days , may very well serve the turn in any ordinary Operation : I say , the Globe having holes in its Meridian at this distance , put the Zenith Pin , or , if you think better a Needle , in the Hole , which most agrees with the true day of the Month , and then exposing your Globe level to the Sun , do but move it till the shade of the said Needle or Pin falls directly along the Diurnal Parallel where 't is placed ; or , if it be not placed in any of the said Parallels , move the Globe till the shade falls parallel to the next Diurnal Parallel , and 't will be as truly Compos'd as before , supposing you know ( as we have already * taught you ) whether it be Forenoon or Afternoon when you operate ; for , as in the Morning the Stiles of Dials cast their shades Westward , and in the Afternoon Eastward , so must your Needle or Pin do when the Globe is Compos'd . But here the Reader must take notice , that in case the shade of the Needle or Pin will by no means fall sensibly parallel , but ( as you move the Globe ) draws nearer and nearer its being so , till at last it shortens to nothing , then the Sun is exactly South , and consequently your Globe is compos'd , as soon as the shade thus vanishes . Now , Because the shadow of the Pin is on the Globe an Arch of a Great Circle , this way of Composing the Globe cannot be accounted Mathematically true , For as the Sun approaches each Tropick and the Tropicks not Great Circles , it will happen Mornings and Evenings ( when the Pin projects long shadows ) that the shadow of the Pin will not ly exactly in the Parallel of the Day , but will ( more or less ) intersect it in the Center or Pin-hole . Therefore tho' the aforesaid way of Composing the Globe be true enough for ordinary uses , yet I shall give you two other waies without exception . Observe the Concentrics between the North Pole and its Polar Circle , and first you will find that they are equal in number to the Parallels , either from the Equator to the Tropick of Cancer , or to those from the said Aequator to Capricorn ; for to avoid the confusion of too many Parallels , there are usually but 8 Northern and 8 Southern described on the Globe . 2ly . That they are distant from the Pole as the said Parallels are from the Equator . And 3ly . That they are markt not only with the Daies of the Month of the Northern Parallels , but with those of the Southern also . The Day of the Month then being ( for example sake ) Apr. 10. Move but the Globe ( when level ) till the shade of Extuberancy touches the Concentric markt Apr. 10. and 't will be truly Composed ; supposing that the Eastern face of the Globe looks towards the Forenoon or Eastern parts of Heaven , and the Western face towards the Afternoon . In like manner , If the Day of the Month or Suns Parallel be an imaginary one between any two that are exprest ; for to avoid ( as I mention'd ) the confusion of too many Parallels there are usually but 8 Northern and 8 Southern described ; I say in like manner , If the Day of the Month , or Suns Parallel happens thus , let the said Shade but touch or fall proportionably between the correspondent Concentrics , and the Globe will be Compos'd , as before . The reason of the Operation is this ; The Sun illuminating ( as has been said ) half the Globe , the Shade of Extuberancy ( or in other terms the Confines between the Obscure and Illuminated parts ) will be still 90 degrees from the point or place where the Sun is vertical ; therefore if the Sun be ( v. g. ) in the Equator , the aforesaid Shade or Illumination must terminate in the Poles of the World ; and when he is in the Parallel of Ap. 10. the Illumination must fall short of the South Pole , and go beyond the North Pole as many degrees as the said Parallel declines from the Equator ; But the Concentric of Ap. 10. is by Construction just distant from the Pole those degrees ; Ergo when the said shade of Extuberancy or the Illumination touches this Concentric , the Globe must ( if its Eastern face looks towards the Fore-noon part of Heaven or the Western the Afternoon ) be illuminated as the Earth is , and consequently Compos'd ; for its corresponding with the Earth in its site and position is all we mean by Composing . As for the reason why I mark each Concentric with the 4 opposite Months , whereas the Parallels are markt only with 2 of them , 't is that the Globe may be Composed by the help of the Northern Concentrics , even when the Sun is in his Southern Declension , it being more convenient and ready for one to cast his Ey on the North Pole than to stoop to the South Pole ; about which otherwise there must have been the like number of Concentrics , and markt as the Southern Parallels are ; I say this is the reason of thus marking the Concentrics ; for since the Sun in its Northern declension illuminates beyond this Pole , he must in his Southern fall proportionably short of it ; therefore move the Globe as before ( let it be Summer or Winter or any other time of the Year ) till the said Illumination or Shade touch the Concentric markt with the day of the Month , and 't will be still Composed . The second way I shall defer to Operat . 10. because the intermediate ones conduce much to the facilitating it , as you 'l see . OPERATION IV. To find the Day of the Month. THis Operation is also perform'd two ways , as being the Converse of the former ; therefore since that requires the knowledge of the Day of the Month , this must require the Globe Compos'd . Having then Compos'd it by a Meridian line , or otherwise , Consider upon what Excentric , or between which of them the said Shade of Extuberancy or Illumination falls , and that will shew the Day of the Month. As for the second way , you shall have it when we come to Operat . X. which treats ( as we said ) of the Second way of Composing the Globe . OPERATION V. To find the Sun's Azimuth . THe Sun's Azimuth is an Arch of a great Circle , which passeth through the Zenith and Nadir over his body , so that his Mornings or Afternoons distance ( reckon'd by the Degrees of the Horizon ) from the Meridian or Southern Cardinal section of the Globe is the thing requir'd ; and for performing the Operation there are four several ways . * Compose your Globe ; Then standing on the illuminated side , or side next the Sun , and fixing your String by its nooze in the Zenith , hold it up by the Plummet-end , and move it along till its Shade falls on the middle of the Fulcrum or supporting Pillar , or ( to be more exact ) till it covers the Center of the Projection , being the point ( you see ) directly answering the Nadir ; for then the Degree in the Horizon , which the said Shade falls upon , gives from the above mentioned Meridian the requir'd Azimuth . Or else guide your String by winking ( or by any other convenient means , which practice will show you ) till it concur with the Shade of the Zenith-pin , that is to say , till they both ly in the same Plane ; for then the Shade of the String it self ( if it hangs strit along the Globe ) will cut the Horizon , as before . In case you have onely a glimpse , or faint sight of the Sun , then stand ( the Globe being Compos'd ) on the obumbrated , or other side of it , and letting your String hang down on that side also , aim or look along it with one by towards the Sun , and role the String gently with your finger backwards or forwards , till it lies exactly in the same Plane as the Sun does , or ( if the Clouds suffer you not clearly to see him ) till it lies in the Plane of its supposed Place , and the Degree under your String ( reckoning the contrary way , that is to say , from the Northern or back part of the Meridian ) is the requir'd Azimuth . Therefore ( by the by ) if the Sun shines out , 't is but drawing the String through the Shade of the Zenith-pin , and it will ( reckoning thus ) answer the Question . 3dly , Having taken the Sun's * Height , and having found it to be , suppose 36 deg . bring the String to the Merid. and by the help of the Degr. in the Quad. of Alt. Mount the Bead above the Horizon 36 deg . which Operation we shall frequently call hereafter , Rectifying your Bead to the Sun's height . I say having taken the Suns height , and Rectifi'd your Bead to it , put your Ring or Noose on the Zenith , and move your String , till your Bead lies exactly on the Parallel of the Day . Which we will alwayes in our Examples , or for the most part at least , suppose to be that of the 10th of April , and the said String will cut the Horizon at 58 Degrees Eastward ( or thereabouts ) for his then true Azimuth . And here you may remember , That as the Height gives the Azimuth , so the Azimuth once known , gives the Height ; for your string being on the true Azimuth , if you mount your Bead to the Parallel of the Day , it will show you in the Meridian the requir'd Height . Fourthly , Supposing that on the 10th of April , the hour given be 9 in the Morning , draw your String from the Zenith over the Point where the Parallel of the Day , and the 9 a Clock hour-Circle intersect , and it will fall on the 58 Degree in the Horizon Eastwardly of the Meridian for the then Azimuth . OPERATION VI. To find the Sun's Declension , Parallel , and Place on the Globe at all times . BY the Sun's Declension is meant , his Northerly and Southerly distance from the Aequator , therefore if you know the day of the Moneth to be the 10th of April , you have his Parallel , because 't is mark'd with the said day : Now since the Colurus Aequinoctiorum , or 6 a clock Hour Circle , is ( as we said ) gradually divided from the Aequator to the Poles , and that the said Parallel passes almost throu ' its 12th Degree , you have his Declension , as also his Place in his Parallel , if you have his Almucantar , or Azimuth as you will find by the second or following way . If now you know not the day of the Moneth , Take the Sun 's * Almucantar and † Azimuth by some of the foregoing wayes , and Rectifying your Bead to the Height , draw your String from the Zenith on the Horizon , according to the Azimuth found , and your Bead will lie on his true Place , and consequently show his Declension and Parallel ; for , as his Declension is ( as we said ) his Distance from the Aequator , so his Parallel is a Circle described from the Pole according to his Declination . And pray observe well this second Way ; for tho' it be not extremely necessary in Relation to the Sun , yet it is of singular use , when you come to the Moon and Stars , whose Declensions depend not on the day of the Moneth . OPERATION VII . To find the Sun 's Bearing , i. e. in what part of the Heavens he lies , according to the Points of the Compass . HAving found by the foregoing Operation ( on the 10th of April . ) the Sun 's true Place in his Parallel to be , suppose there where the 9 a Clock Hour Circle cuts it , say over this Point your String , from the Zenith , and 't will fall at the Horizon a little beyond the Character of SEbE for his Bearing according to the Points of the Compass . OPERATION VIII . To find when the Sun comes to true East or West , or any other Bearing . HAving found the Parallel of the Day ( viz. that of the 10th of April ) and put your String over the Zenith , bring it straight to the East point , that is to say , to the point of the Globe where the Horizon and 6 a clock Circle intersect , and you will find the said String to cut the said Parallel about 20 minutes before 7 in the Morning , which is the exact time of the Sun 's then coming to full East . Now if the String be laid on the Western Intersection , 't will cut the said Parallel at 20 minutes or thereabouts after 5 in the Evening , for the time of the Sun 's coming to full West . In like manner , if you would know , when he come's ( v. g. ) to S. W. you are only to draw your String ( as before ) over that Bearing , and you will find by the Intersection of your said string and Parallel , that at a quarter past 2 of the Clock in the Afternoon , or thereabouts he will have that Bearing . OPERATION IX . To find what Signs and Degrees of it the Sun is in , at any time . SEEK out the Parallel of the Day ( viz. that of the 10th of April ) and you will find it to cross the Ecliptic in two places , to wit at the first of Taurus , and the first of Leo ; Now because in April the Sun is still Ascending , that is to say , the Dayes encrease , you may conclude that the first of Taurus is his then true place in the Ecliptick ; for were he in Leo he would descend toward the Aequator , and consequently shorten the Dayes . OPERATION X. To find the hour of the Day by the Sun , together with a second way of composing the Globe , and finding the Globe , and finding the Day of the Moneth . MANY are the wayes to perform this Operation as to the Hour , But now wee 'l insist on four only , each of which has some peculiar Propriety belonging to it ; for the First gives us the Hour by the help of the Natural Stile ; the Second by an Artificial one ; the Third without any Stile at all ; and the Fourth ( together with the said hour ) the Contemplation of several pleasing Operations at a time , and among the rest this of Composing the Globe by the Shade . I. Having * Compos'd your Globe , ( and thus wee 'l suppose it in each of the following wayes ) look among the Hour Circles ( which are , as we said , distinguish'd near the Polar Circles , with little Roman Figures ) and the shade of the North-Pole , or Axis of the World ( which we may justly call the Natural Stile , ) will , during the Sun's Northern Latitude , as well as the shade of the South Pole in his Southern , shew you the Hour . And thus you may find it for a while by the Ordinary Globes , in Circulo Horario , when they are once set or Compos'd , which I wonder none , of those who writ of their Uses take notice of ; I say for a while , for it will only serve your Turn there from March to September . II. Your String hanging by one End on the North Pole , hold it straight by the other , some little distance from the Globe , and moving it on the Noose , till its shade touch , or cover , the Apex of the South-Pole , 't will show you ( among the aforesaid Polar Roman Figures ) the true Hour , even to a minute ; for the Shadow of the String ( which we call an Artificial Stile , because 't is Independent and Forrein to the Globe ) cutting at that Instant the Aequator , and Polar Circles , gives you in each place the Degrees of the hours , and consequently the minutes , since the 4th part of a Degree is an exact minute in time . III. Look where the shade of Extuberancy cut 's on the Aequator , and the great Roman Figures , ( which are there for that purpose ) will give you without a Stile or more adoe the exact hour , on what side soever of the Globe , you stand ; for you must remember that the Extuberancy casts on the Aequator two shades , the one still Preceding or going before the Sun , and the other Following him . Now if this shade be dubious , your Finger ( as I show'd you * before ) will help you , it being the constant Remedy on all Occasions of this Nature . IV. As now you find the Hour by your String hanging on the Pole , so this Fourth way is to show it you , in case it had hung on the Zenith ; nor have you more to do than to hold it by the end as before , and to move it on its Noose 'till its shade concurrs and agrees with that of the Pin in the Zenith , or for more Assurance till the Strings shade fall's so on the upper part of the Pillar or Fulcrum that it would cover the very Nadir , were it not hid , and then where the said String it self , or its shade cuts the Parallel of the Day , there will be the true hour , according to the Roman Figures of the Polar Circles . This way I would have you well observe for from hence I shall hereafter lead you to the Contemplation ( as I hinted before ) of several pleasing and useful * Operations at one glance or view ; and to give you a little Taste at present , I will here shew you the Second way of Composing the Globe by the shade . Having for Expedition's sake , turned the North-pole of the Globe , as near as you can guess to that of the World , Hold up your String with one hand to the Sun in the manner now prescribed ; That is to say , 'till the String hanging from the Zenith ) casts its shade on the Nadir , then move the Globe with your other hand , and making by a proportionable motion of the String its shade to pass still throu ' the said two points , observe when it cuts the Parallel of the day at the like hour with that , which the shade of the illuminated Pole indicates , and your Globe will be composed ; or , to express this in fewer words , Move thus the Globe , till the shade of the string and the shade of the illuminated Pole agree in the Hour . Nay fixing your String in the Zenith as before , and fastning a Thred on the North-pole , do but hold up both to the Sun till the shade of the String passes the Nadir , and that of the Thred the South Pole , if any body then moves your Globe about till the two shades ( passing still throu ' the foresaid Points ) intersect on the Parallel of the Day , you have your intent ; for the Sun being you see in the Planes of the Thred and String ▪ he must be in their Intersection . i. e. in the Parallel of the Day ; but 't is impossible for him ( as we * show'd you ) to be in the plane of that Parallel , on the true side of the Meridian , except the Globe be Compos'd , for the corresponding Circles of the Globe and Heavens can never else agree ; therefore the Operation is true ; and if so , let the Globe be but on a Meridian Line , or any way else Compos'd , and the Agreement of the hour in both places , or the Intersection of these two shades shews the Sun's Parallel and consequently the Day of the moneth . So much then for this second way of composing the Globe , and finding the Day of the Month , which first came into my thoughts by reflecting on the Projection of that great man Mr. Oughtred , who would have bin the Wonder of this Age , had he bin as ambitious and forward , as he was throughly learned . OPERATION XI . To find the Hour of the Day when the Sun shines not . TO perform this Operation , we must suppose you know either the Suns Almucantar , Azimuth or Bearing ; and by the way you may find these , tho he * shine's not ; I say you must suppose either his Almucantar , Azimuth , or Bearing , for they giving you his Place in his Parallel , the next Hour Circle to his said place shews you the time of the Day ; for if ( v. g. ) in the forenoon on the 10th of April . ) you know that the Sun is 36 degrees high , Rectify your Bead but to that height , and moving the String from the Zenith your said Bead will touch the Parallel of the Day at 9 of the Clock . In like manner if you know the morning Azimuth to be suppose , 58 degrees , draw your String from the Zenith over the said Degrees in the Horizon , and 't will also cut the Parallel of the day at 9. Or , if the Sun 's Bearing be ( for Example ) a little more than SEbE the laying of your String from the Zenith on that Character in the Horizon shows you on the Parallel of the day that 't is 9 as before . OPERATION XII . To know when the Sun rises and sets . FIND the Parallel of the Day ( to wit that of the 10th of April ) and where it cuts the Horizon on the East-side of the Globe , there the Suns place at his Rising will be so that the time of the day appears by the next Hour Circle to be a very little past 5 in the morning ; and if you cast your eye in the Intersection of the said Circle on the West , you 'l find the hour to be almost 7 in the Evening . This being so , here follow 's a very pleasant and useful Operation , as a Corallary , viz. How to find at what time of the year , and at what Declension the Sun rises or sets , an Hour , or any other space of time , either early or later , than it does at the proposing of the Question : for , if you observe but what Parallel intersects with the Horizon , on the 4 a Clock morning hour-circle which is an hour earlier than when it rises on the 10. of April , you will find it an Imaginary Parallel , which the next real or mark't one shews to be the Parallel , for the 14. of May and 12. of July , and consequently by the Devisions of the Aequinoctial Colure that the then Declension is about 21 Degrees . In like manner you must have look't on the West side of the Globe if you would have had the time of the Sun 's setting an hour later than 7 ; and thus you are still to operate when any other space of time is required . OPERATION XIII . To find the Sun's Amplitude , Ortive or Occasive . BY the Sun's Amplitude we mean his distance in the Horizon from the true East and West Points at his Rising or Setting ; so that this Operation is also a Corollary from the former ; for , knowing ( on the said 10. of April ) the point or place where he Rises , you will find the Ortive Amplitude to be Northward from East about 18 Degrees , and ( on the other side of the Globe ) the Occasive Amplitude , to be Northward as much from the West . OPERATION XIV . To find the length of the Day and Night . DOuble the hour of the Sun 's Setting , ( which on the 10. of April happens , as we said , about 7 at night ) and the Product ( to wit near 14 hours ) will be the length of the Day ; or double ( 5 ) the hour of his Rising , and the Product ( 10 hours ) gives the length of the Night . Nay , if you do but consider how the Parallel of the Day is cut by the Horizon , you have the whole business represented to the life at one view , even as it happens in the very Heavens themselves ; for that part of the said Parallel above the Horizon , being devided to your hand by the Hour-circles , into almost 14 hours , shews the Days length , and consequently that part under the Horizon ( shewing a little more than 10 hours , ) gives the length of the Night . OPERATION XV. To find the beginning and end of the Crepusculum . BY the Crepesculum is understood the Twilight which appears before the Sun 's Rising , and continues after his Setting ; for as soon as the Sun comes within 18 Degrees of the Horizon ( according to the Opinion of the antient Astronomers ) or within 16. Deg. according to that of Tycho , and some Modern ones ) his Rays are reflected from the Atmosphere or circumambient vapours , and consequently illuminates , so that this light still encreases , by how much the Sun approaches the said Horizon , and decreases as it recedes . Now to find it , you are to bring the String hanging on the Zenith to the Meridian , and making the Bead ( if you follow the latter Hypothesis ) to stand by the help of the Quadrant of Depression ) at 16 Degrees under the Horizon , move it on the East side of the Globe along the Parallel of the Day ( i. e. that of the 10. of April ) till it just touches the said Parallel , under the Horizon , and there will be the true point of the Morning Crepusculum , which the adjacent Hour-circle tells you begins about 3 in the morning ; In like manner if you move your Bead on the West or Eveningside of the Globe ▪ you will find it to end neer 9. OPERATION XVI . To find the Sun's Depression at any time of the Night . BY Depression we mean , how many Degrees the Sun is then under the Horizon , which is easily perform'd if you know the hour of the night , by the Moon , Stars , Clock , or the like ; for , finding ( as hath been * shown you ) what part or point of his Parallel the Sun is then in ; i.e. where the Hour-Circle ( corresponding to the time of the night ) and Parallel of the Day intersect , draw the String from the Zenith over it , and moving your Bead to it , bring the said Bead to the Merid. or Quadr. of Depression , and then by the help of the Degrees there ( reckoning from the Horizon to the Bead ) you have before you the required Depression . OPERATION XVII . To find the Sun 's Right Ascension . THE Right Ascension is that Point or Degree of the Aequator cut by the Meridian , or Hour Circle that runs through the Sun's place in the Ecliptic ; and this Degree is called the Right Ascension , because in the Position termed by Astronomers and Geographers the Right Sphere , ( which together with the Oblique and Parallel Spheres , shall be farther explained in the * Geographical Section ) it rises or Ascends with the Sun. To find then the Sun 's Right Ascension ( a thing often of great Use ) you are only to take the String ( hanging from the Pole ) and lay it on the Degree of the Ecliptic possest then by the Sun , that is to say upon the 1st . of ♉ ( for the 10. of April is still our Example ) and the Degree of the Aequator cut by the said String is the required Right Ascension , which counting from ♈ or East Point ( as you must always do ) happens to be 28 Degrees , or thereabouts . OPERATION XVIII . To find the Ascensional Difference . AS for the Ascensional Difference ( i. e. the Difference between the Right and Oblique Ascensions ) we have it here before our Eyes at a View , as being that portion of the Day 's Parallel which lyes between the Sun 's Rising or Setting , and the 6 a Clock Hour Circle , so that if he rises on the 10. of April at almost 5. and sets near 7. we may conclude that the Ascensional Difference is about 14. Degrees , for 15. make an hour . But if you will be exact , then lay the String from the Pole on the Point where the Sun rises or sets , and when it cuts the Aequator , count there the Degrees from the said String to the 6 a Clock Circle , and all is done . Thus then you see , that when we know the Ascensional Difference we have the time of the Suns Rising and Setting , for it is but adding it to 6 a Clock , if the Sun be in his Northern Declension , or substracting it in his Southern . The END of the first Section . SECT . II. Of the Operations that concern Geography . HAving given you a short account of the Operations immediately relating to the Sun , without reflecting upon any part of the Earth , but that , on which we then stand , wee 'l now descend to those that concern Geography , where you may have a view not only of all Countries , as to their Situations , Extent and the like , but see at one glance when you please , several other things appertaining to them worth the knowing , as , What a Clock it is in any place imaginable ; what People are Rising , who are going to Bed , and who to Dinner : as also , where it is they have no Night , where no Day , with divers particulars of the same nature , which were thought by many formerly not performable without Magic . That our Instrument is Geographical , no body will ( I dare say ) doubt , it being the Terrestrial Globe , and consequently the Epitome of the very Earth it self ; and besides its many other Operations ) it may be perchance useful in this , that all Countries are here more obvious , and consequently more easily found out than in any common Universal Map or Globe . Nor do's it a little contribute to it , and fix the Position and Order of the said Countries in our Memory , that not only the Divisions and Subdivisions of the Earth are ( by our present Directions ) clear and distinct , as far as this small bulk can afford , but freed also from the usual crowd of Towns and Places , very often neither of Note nor Use , unless for Distraction . For the business of a Terrestrial Globe , is to represent the situation of famous Regions and Provinces , and how they are distant each from the other ; to show us also where the late Discoveries are ; where more may chance to be made ; what proportion any Place bears to the known Parts , or they to the whole Terraqueous Mass . These ( I say ) and the like , are what a Globe is properly to represent ; for small and inconsiderable Places ought not to be there , as being the chief Object of Chorographical and Topographical Charts , to which the curious are to recur upon occasion . As for the first or grand Devision of this Globe , to wit , the four Quarters , their names are in the midst of them in remarkable Capital Letters ; nor is there any trouble about their Bounds , after that that joyns Europe and Asia is consider'd ; for bating the little Isthmus made by the Mediterranean and Marerubrum ( which contains the limits of Asia and Africa ) there is no part of the said Quarters , which is not surrounded by the Sea. For the separation then or Boundary between Europe and Asia , it is a fine black line , that beginning at the mouth of the Tanais , runs up the Stream to Tuia ( situated on its most Easterly F●exure , ) and thence going to the nearest Banks of the River Oby , accompanies it till it falls into the Northern Ocean . This I say is the separation drawn by me , and not from Tuia to the mouth of Duina at Arch-angel ; for since there are ( as to the Question in hand ) different and various Opinions among Geographers , I follow the rather this Devision than any other , since it contains almost all the vast Dominions of the Russian Emperor , and so makes him as it were an intire Europaean Monarc . The Devision of each modern Country from the other ( which have all their Names on them in small Capital Letters ) is also a black pric't line , and that you may have a glimps also of Antient Geography , I have exprest some of the most considerable old Nations and Empires , by Prick Lines of several colours ( as the directions on the Globe it self shews you ) to amplify or contract their Bounds , when they agree not with the present Limits ; but as for Cities and Towns , there are ( as I said ) but very few of any sort set down , for in all the Island of Great Britain , we mention but London and Edinburgh , besides a Port or two , in which proportion we proceed all along . Thus having acquainted you with these few Preliminaries , wee 'l now , after you have a little consider'd the Names of each Country , and how they all lye from your Zenith , where you are ever to suppose the Country or Place to be , which the Globe is made for ; I say , we will now , after you have a little considered these things , fall upon the Operations , an Employment commonly much more diverting and pleasant than Speculation . OPERATION I. How to find the Distance between any two places . IF the Question be ( for Example ) between Constantinople , and the Place you dwell at , ( which we shall for the Future suppose still to be at London ) Draw your String from the Zenith streight over Constantinople , and having mounted your Bead thither , bring it to the Meridian , or Quadrant of Altitude , and it will lye ( counting from the Zenith to it ) on the 24 Degree , or thereabouts , which multiply by 60 ( the number of Miles contained according to the Common Account in each Degree ) shews you that the Distance required is some 1440 Miles . But if it be demanded how far it is from Constantinople to Tangier , i. e. from any other two Places , when neither lye under your Zenith , then take a pair of Compasses , and placing one Foot on the first Town , and the other Foot on the second , find ( in the Meridian , Aequator , Horizon , or any other divided great Circle ) the Number of Degrees between the Feet , which making about 31. amounts to near 1860 miles . Or if you have no Compasses , fix the loose or Plummet end of your String with your Finger on Tangier , and drawing the rest of it streight over Constantinople , place there the Bead ; and if you measure that distance in any of the said devided Circles 't will give you the above mentioned Degrees and Miles . And here be pleased to remember that to free you from Multiplication in Relation to Miles , I have ordered a little Table to be plac't in the vacant part of the Globe towards the Southern Ocean , where you may find from 1. Degree to 20. how many Miles any number of Degrees give ; but if your Question contains more Degrees than are set down , as for Example 31. you are only to add 660. ( which you will see in the Table is the vallue of 11. Degrees ) to 1200 ( the value of 20. ) and the Sum Total makes 1860. Miles for the required distance . In this manner you must operate in other cases . The Table of Reduction is to be in the following manner . 1 60 11 660 2 120 12 720 3 180 13 780 4 240 14 840 5 300 15 900 6 360 16 960 7 420 17 1020 8 480 18 1080 9 540 19 1140 10 600 20 1200 OPERATION II. How to find the Latitude and Longitude of any Place . THe Latitude of a Place is its nearest distance from the Aequator ; If therefore you would know the Latitude of , ( suppose ) Constantinople , draw the String from the Pole over the said City , and placing thereon the Bead , bring it to the gradual devision of the Colurus Aequinoctiorum , or 6 a clock Hour Circle , and it will lye on the 43 Degrees , and about 5 minutes more , for the Latitude required . The Longitude of a Place is the number of Degrees ( reckon'd Eastwardly in the Aequator ) from the grand Meridian to the Hour Circle , or particular Meridian that passes through the Place required . As for the said Grand or General Meridian , 't is that from whence we begin our Reckoning ; and since it matters not ( as you will plainly see in the Memorandum of the third or following Operation ) where we commence , to wit whether from the Meridian that runs thro' London , or that thro' Paris , Rome or any other place , if people be acquainted with it before hand ; I say , since this is so , what wonder is it , ( there being by reason of some accidental Proprieties and Causes infinit fit Places ) if Geographers and other Learned men quarrel in the Affair , and earnestly strive to have the Prerogative granted that Countrey , which they are pleased to propose . Of all places , the Hesperides , Azores and Canaries , ( by reason of their Westerly Site , or the pretended non-variation of the Needle in some of them ) have had the most vogue ; but since each of the said Places make not one but many Isles , they afforded new occasion of Dispute ; for among the Hesperides , or Isles of Cape Verd , some would have Fuego to carry away the Bell , some St. Nicholas , but others St. Vincent , as appears by Hondius's Globe . Now Langrenius , in his , begins from St. Mary and St. Michael in the Azores ; Johnsonius in his Universal Map , counts from Corvo and Flores , whereas the Learned Dudley ( the late Titular Duke of Northumberland ) gives the honour to Pico , and has as much reason for it as the rest . Nor is there less do about the Canaries , for the French fix it at Ferro , several of the Hollanders at Teneriffa , and many other Nations at Palma , which is the Place I would willingly choose , ( since the great Ptolomy thought fit at last to assign it there ) were it as convenient for my present purpose as St. Vincent . 'T is St. Vincent then I here pitch upon for this Meridian to pase throu ' , because it differs in Longitude from London within less than 20 Minutes of just 30 Degrees , or 2 Hours , so that the 2 a Clock Circle will represent it ( within almost a Minute in time ) without need of drawing a Particular one , and the said Meridian is ( as I told you in the beginning ) distinguished from the rest by Pricks , which being distant from each other a quarter of a Degree , are useful on several occasions . Having thus fixt our Grand Meridian , or first Longitude , that of other Places follow 's with ease ; for if you would know the Longitude of Constantinople , draw but your String from the Pole over it , and it will cut the Aequator neer the 62. Degree for the Longitude required , as you may readily percieve by the lower little Aequinoctial Figures . OPERATION III. How to find out any Place , the Longitude and Latitude being given . THis Operation is not only usefull for the finding out of Towns express'd on the Globe , when you cannot guess whereabout they are situated , but also for the placing them truly in case they should chance not to be set down . Suppose then Constantinople were the Town sought for , and that you found its Latitude to be 43 g. 5′ . and Longitude 61 g. 46′ . in some book or Geographical Table ; I say supposing this , you have nothing to do , after having mounted your Bead ( by the help of the devided Colurus ) 43 g. 5′ . above the Aequator , but to move your String on its Noose from the Pole to 61. 46. in the said Aequator , and Constantinople will be just under your Bead ; and if ( in case of Omission ) it should not , you may then if you please marke it out your self , for that is its exact place . But by the way , if the Geographical Tables agree not with the Longitude of your Globe as telling you that ( v. g. ) Constantinople has but 54 g. 36′ , you are then to look from whence the said Tables begin , and finding their Commencement , suppose at Palma , and that Palma ( according to the former Operation ) has by your Globe 7 g. 10′ . of Longitude , you must add this number to your Tables , and then you will agree . OPERATION IV. To find the situation of any Place according to the Angle of Position , or Points of the Compass . DRaw the String from the Zenith over , v. g. Constantinople , and 't will cut the Horizon about 5 Degrees beyond E b S Eastward , for the true situation of the said Town from your Habitation ▪ according to the Points of the Compass . OPERATION . V. To find in what Clime or Parallel any Place lies . BEfore we can here well come to Operation , there are some few Particulars to be consider'd ; and first what a Clime is ; which is no hard thing to conceive , since most know that after the Vernal Equinox our Days not only exceed 12 houres , but that every neerer Countrey to the Pole has days of greater Length than the Remoter : Nor are there many ignorant , that when our Days ( that live on this side of the Line ) increase , theirs on the other side decrease proportionably , and when theirs encrease ours decrease ; so that no People are at a Constancy , but they that dwell exactly between both Poles , to wit under the Aequator . This Diversity was thought by the Ancients a thing so fit to be known , that they invented the Devision of the Earth into Climes , so that as soon they heard a Countrey named , they presently ( besides the fond Reflections concerning the Temperament of the Air , Ingeniety of men , &c. ) knew the length of its longest Day , and consequently how much any other Place exceeded or came short of that length . For suppose the first Northern-Clime were to pass over all the Places on this side of the Aequator , whose longest Day is 12 hours and 1 / 2 ; and the second Clime those of 13 hours , and so on towards the Pole by a half hourly Increment , what difficulty could there be to resolve immediately the Question , when we once know the Clime , or having the length of the longest Day to find out the very Clime it self . I Wonder therefore , that so ingenious a man as 〈◊〉 , should seem to assert , that this Devision is useless , it being as easy to find the longest Day as the Clime ; whereas , were Climes in esteem and fashion , the Memory would as soon conceive and remember in which of them any Countrey lay , as now it does it's Bounds , the manner of its situation , and the like ; and if so , one may quickly judge whether they are useless , and whether it be possible that the length aforesaid can be known by any other means so universally , and at so easy a rate . A Clime then ( generally speaking ) is a space contained between two Circles Parallel to the Aequator , having the Places thro' which they pass differing ( as to the length of their longest Days ) half an hour ; and this space takes the name of Clime from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Inclinare vel Deflectere ; for the greater our Deflection is from the Aequator or Right Sphere , the longer our Summer Solstitial Day will be . Nor were the Antients content with this large Devision of the Earth , but subdevided it into Parallels , so that Places differing a quarter of an Hour , were reckon'd to be under such and such Parallels , which some call Artificial ( from their relation to the Artificial Day ) to distinguish them from all others that occur . As for the Antiquity of Climes , 't is immemorial ; nor could there be many in the beginning by reason of the small extent of the known parts of the World ; For tho' Ptolemy reckons about 10 , that is to say 21 Parallels , as making them to reach as far as Thule ; yet Homer , Ovid and other Poets , so possess'd men with the Fancy , that from the Cimerians Northward , there was nothing by reason of the hideous vapours and exhalations , but a dubious and creperous light , that even Pliny , and after him the Arabians insisted only on seven , looking on all Countries that lay farther as not worth perchance the taking notice of . As for the seven in vogue with them ▪ and mention'd also very particularly by our Countryman Sacro-bosco ( whose credit and great Repute has perchance not a little kept up their Fame among the Moderns ) they were , Dia-Meroes , Dia-Syenes , Dia-Alexandrias , Dia-Rhodou , Dia-Romes , Dia-Boristheneos , and Dia-Riphoeon , being all names made by the Addition of the Greek Preposition 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ( i. e. per ) to some remarkable Town , River , or Place , thro' which the middle of each Clime past ; so that the middle of the first went thro' Meroe , an Ethiopian City on the Nile , where ( according to some ) Queen Candace Reigned ; the second thro' Syene in Egypt , lying just under the Tropic , the third thro' Alexandria ; the fourth thro' the Isle of Rhodes ; the fifth thro' Rome ; the sixth thro' the mouth of Boristhenes , now called Nieper by the Cossacks and the other Inhabitants ; and the seventh and last thro' the Riphoean Hills , part of which lay according to their account in or about , the Latitude of 50 Degrees , and consequently corresponded with the Cimerians . 'T was here then that Alfraganus and other Arabians ended Northwards , who besides several smal particulars , err'd not a little in making Rome and the Boristhenes only a Clime asunder , when as their longest days differ at least an hour . And as for the Southern Climes ( to wit those on the other side of the Aequinoctial ) they thought fit to consider them , but not knowing what to call them , as being ignorant ( for the most part ) of the Places they went through , they added 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ( i. e. Contra ) to the former Denominations , so that making Anti-dia Meroes serve for the first Clime , Anti-dia Sienes for the second , they proceeded in the same order with the Rest . But now before I end , I shall endeavour to solve a difficulty which startles not a few , viz. how it comes to pass ( seeing the Climes are assigned ( as we mentioned ) by the Antients , to know the length of the Summer Solstitial day in every Country ) that the middle of the first Clime ( which in rigour should lye no further from the Aequator , than to encrease the day a quarter of an hour ) runs over Meroe , where the Excess is at least an hour . I answer , the Antients , deeming it more equal that the middle of the Clime , and not the end of it should be the Point where the half hourly increment was to begin , fixt the Terme à quo , not in the Aequator , but a quarter of an hour further , and therefore Taprobane ( which some now think Sumatra ) was the place where Ptolemy commences all his Climes , making thereby the middle of his first to pass per Sinum Avalitum or ( Mouth of the Red Sea ) and the middle of his second per Meroen ; But the Arabians , thinking that for several Degrees from the Aequator all was either Sea , or ( by reason of the Heats ) scarce Habitable , or else judging it for their Honour , to have their own Country ▪ in the first Clime , began half an hour beyond Taprobane , and so Dia Meroes , ( tho the Days are there 13 hours long ) leads the Van in their Catalogue . These few things premis'd , I shall now shew you the way I take therein , which I think in all respects clear and ready . First , I make the primary Circle of Longitude to be the Circle particularly appropriated to this use , being devided and mark't according to the true distance of each Clime from the other ; and as to the place where they commence on our Globe , I rather follow Ptolomies Astronomical than Geographical Method ; for ( besides the aforementioned excess of the Arabians ) should we begin but a quarter of an hour from the Aequator , it makes a great space of the Earth , viz. from Taprobane to the Aequator , to be in no Clime at all ; and which is more , it causes a little confusion , when the length of the day is greater in every Clime , than what the said Clime can justly challenge , according to its Rank and Number ; I say , as for the place where the Climes commence , I rather follow Ptolomies Astronomical than Geographical way ; and therefore beginning at the very Aequator , my first Parallel ( or middle of my first Clime ) is supposed to run over the places that enjoy 12. hours and a quarter of Day , and the end of it ( noted on the primary Circle of Longitude or 2 a Clock Hour Circle with the Figure I. ) over the places that have 12. and 1 / 2 ; and thus we proceed to the Polar Circles , to wit , where the 24th . Clime , or 48th . Parallel terminates , so that from thence we come to the Devisions on the said Circle of Longitude , which show where the days are as long as an ordinary Week , where as long as a Month , and where as two , arriving at last at the Poles themselves , where there is a constant half year of light , and as much of Darkness . And to give you a Remembrance of the Names of the aforesaid old Climes , and that you may also see without Calculation or Trouble where the Ancients plac'd them , I have set down the first Syllable of their names ( as Mer. Sy. Al. &c. ) according to their respective Latitudes . To find then in what Clime any place is ( v. g. Constantinople ) you are only to draw your String from the Pole over that City , and mounting up the Bead thither , to move it to the said Primary Circle of Longitude , and 't will lye on the Clime or Paralel required . But if you would know what places are ( suppose ) under the 4th . Clime , throu'out the World , i. e. what places have their longest day just 14. hours ; Fix the Bead ▪ on the 4th . Clime and moving it on its Noose from the Pole round the Globe , you may conclude that every place it passes over , has the Sun exactly so long above the Horizon , when the days are at the longest ; and in the same manner you must proceed on the South of the Aequator , to find the Countrys that lye under the 4th . Southern Clime . In short , here we have , besides ( what has been already said ) a view not onely of the strange inequallity of the Climes , ( especially between the first and last ) but also of their exact distance in Degrees , and consequently in Miles , by help of our Table of Reduction , mentioned in the first * Operation of this Section . But seeing we are a little fallen into Speculation , 't will not be , perchance , improper to proceed yet further , and to consider here , as in a natural and fit place the Bounds and Terms of the five Zones , so called from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Cingulum , as enclosing the whole World within their respective Districts : 'T is with the Torrid one we 'l then begin , whose Bounds are the two Tropics , so that the Diurnal Parallels not only remarkably distinguish it from the other Zones , but shew why the several Inhabitants within this space were called by the Ancients AMPHISCII , i. e. Vtrinque umbrati , or men that had two shadows , from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 utrinque & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Vmbra ; nay , by the said Parallels you may find when the shade will change and be different ; For , since by these Paths or Traces the Sun ( as we often hinted ) passes from Tropic to Tropic , 't is evident that sometimes he must be on the Northside and sometimes on the Southside , of all that live here , which must then needs alter the shadow . And as for knowing the time of this change , we are only to consult the days of the Month on each Parallel ; for that which passes over the Heads of the propos'd Inhabitants , shews that from that time to the 11. of June ( or the Sun 's coming to Cancer ) and so till he comes again to be Vertical , their shade will be full South at noon : whereas from his said Vertical station to the 11. of December ( when that he enters into Capricorn ) and so till he comes again to them , their shadow will be directly North. From this Torrid and hot Residence ; we 'l now run to the other Extream , viz. to the two Frozen Zones , which lying from each Polar Circle to the very Poles themselves , are sufficiently distinguish'd from the rest . Now since the longest day within these Limits is at least 24. hours in length ( as we show'd you even now in treating of the Climes ) and since the Sun in this space of time , compasses the World , it must follow that here he runs round the Inhabitants , which gave the name of PERISCII to them , that is to say Circum Vmbrati , or surrounded with their shadow , from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Circum & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Vmbra . As for the two remaining Zones , they are the Temperate ones , bounded by the Tropic's and Polar Circles : Nor do the Inhabitants of this moderate and more excellent position want an appellation from the property of their shadow also ; for never having the Sun but on one side of them ( as still setting before he gets round ) and unable to pass , as he could in the Torrid Zone over their Heads , by reason he has no excursion beyond the Tropics ) it must needs follow that their shade who live in the Northern Zone , will ever fall North , and theirs in the Southern , South ; so that they were called HETEROSCII , i. e. Habentes alteram solum Vmbram , or People having but one kind of shadow , from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 alter & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Vmbra . So much then for the Climes and Zones , together with their various inhabitants , and now we will proceed to the Operations that follow . OPERATION VI. To know what a Clock 't is at any time , in any place of the World. THere is no Operation perchance in the whole Treatise , more diverting and pleasant than this ; nor scarce any more readily perform'd after a very little Reflection , even in the most difficult Cases . For having Compos'd your Globe , if it be then 12. a Clock with you , the standing Hour Circles or Meridians already described , will ( by the Common or little Figures which lye within or upon the Roman ones , that surround the Polar Circles , ) shew you exactly the Hour , wheresoever you cast your Eye ; That is to say , that 't is about 2. of the Clock at Constantinople , 3 at Aleppo , &c. But now , if it be not 12. with you ▪ but ( v. g. ) 3 in the afternoon , when you desire to know the then hour at Constantinople , add the said 3 a Clock to the Figure 2. ( which you see lyes , as I now mention'd on the Meridian or Hour-Circle , that runs near that City ) and 't will tell you that 't is about 5 a Clock there ; and thus you must always do , unless the time of the Day with you , and the Figure that lies on the Meridian of the place in question make a greater number than 12 ; for then the Hour sought for , is what remains above 12 ; as for Example , if it be 11 with you , then this with 2 , ( i. e. the Figure near the Meridian of Constantinople ) making 13 , do but cast away 12 , and you may conclude it there 1 in the Afternoon . There are several other ways of performing this Operation ; as finding the Difference of Longitude between you and the Place in Dispute , and so adding or substracting it ( as need requires ) from the true time of the Day , Or else by calling it always Mid day , there where the Hour Circle that shews your then true time of the Day ( which by our Example is 3 in the Afternoon ) crosses , for by counting from thence to the Meridian of the Place in question , either forwards or backwards ( as 1 , 2 , 3 , 4 , or 11 , 10 , 9 , 8 , &c. ) according as the said Place lies East or West from 3 , and all is done ; I say there are several ways to perform this Operation , but seeing the first is the most clear and expedite , I solely insist on it : and now because you may be perchance running over with your Eye , the whole Globe , and considering how one Situation or Country differs from another in time , 't will not be amiss to tell you that there are 3 Places , that have more particular Relation to your Dwelling or Habitation than any other . The first is that , which lies opposite to you in your own Parallel , whose Inhabitants are called by the Antients PERIAECI , or Circumcolae , from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Circum & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 habito , and though by the Word , all People are comprehended that dwell any where in the said Parallel , yet Geographers commonly mean those by it , that are thus Diametrically situated . These then live in the same Zone and in the same Clime , and cast the same kind of Shade with you : These enjoy your proportion of Heat and Cold , your Seasons of the Year , your Encrease of Days and Nights , and in short all things else of this kind , saving that your Hours are opposite ; their six in the Evening being your six in the Morning ; and your Noon their Midnight . The Second Place lyes under your very Meridian , or 12 a Clock Hour Circle , which makes your Hours and theirs the same , but by being 51 g 30′ . on the other side of the Aequator , it happens that tho you all agree in the Temperament of your Zones , number of Climes , in the Casting a Shadow on one side onely , and the like ; yet their Zone and Clime are Southern , their Shade falls toward that Pole , their Summer is your Winter ; and your Spring their Autumn ; so that from this contrariety they are named ANTAECI or Adversicolae from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 contra , & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Habito . The Last is the Nadir or Point on which the Globe stands , whose Inhabitants are called ANTIPODES . i. e. opposita habentes vestigia , or men that walk Feet to Feet with you , from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Contra , & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Pedes . These imply ( even by the vulgar acception of the word ) the height of Opposition ; and since they are the very Antaeci of our Periaeci , participating thereby of whatever was opposite to you in either of the former Places , it is no wonder that you enjoy together neither Day nor Night , nor Season of the Year , nor any thing else of this Nature . OPERATION VII . To find where 't is Day , and where 't is Night , all the World over . COmpose your Globe , and all People that live in the illuminated Hemisphere , enjoy DAY at that Moment ; and all that live in the Obscure One , NIGHT. OPERATION VIII . To know where at that Moment of time the Inhabitants enjoy nothing but DAY , and where nothing but NIGHT ; as also when the DAY and NIGHT will be thus perpetual in any place subject to this Alteration . DEscribe with your Eye an Imaginary Circle about the Illuminated Pole , its Radius being the Distance from the said Pole to the nearest part of the shade of Extuberancy , and all places within that Circle will have then no Night , and all places within the dark Circle of the like Radius , round the obscur'd or obumbrated Pole will have then no Day : Now if you desire to know , when 't will be in this manner perpetual Day or Night , at any Place between the Poles and the Polar Circles , ( for you know 't is never perpetual Day and Night any where else ) you have nothing to do but to measure with your String , or Compasses the Distance between the Place requir'd and the next Pole , which now for Examples sake , we will suppose the Northern Pole ; I say you have nothing to do , but to measure this Distance ; for placing one end of your String , or one Foot of your Compasses on the Interfection of the Meridian and the Aequator , if you observe what Northern Parallel the other end of your String , or Foot of the Compasses ( extended at the aforesaid Distance ) touches , 't will shew you by touching ( v. g. ) the Parallel mark't with the 10th . of April , and 12th . of July , that it begins to be on the said 10th . of April , perpetual Day there ; and so continues until the 12th . of July . Now if you measure from the before mentioned Intersection towards the Southern Pole , and find the End of your String , or Foot of the Compasses to touch the 13th . of October , and 9th . of January , 't is certain that from the said Day in October to that of January 't will be perpetual Night there , and consequently from the 12 of July to the 13th . of October , the Days and Nights succeed each other after the ordinary manner . OPERATION IX . To find where the Sun is Rising , and where He is Setting , all the World over . COmpose your Globe , and having consider'd the Confines or Extremity of the PRECEEDING and FOLLOWING Shades of Extuberancy , you may conclude that to all the Inhabitants under the first , the Sun is Rising , and to them under the Second , that He is then Setting . OPERATION X. To find where the Sun is Vertical at any time , i. e. what People have him just over their Heads . THE Sun is always Vertical to those that lye in the middle of the Illuminated part of the Globe , i. e. to those that dwell under his then present Place in his Parallel ; therefore ( as I show'd you in the * first Section ) if you Compose your Globe and hold up your String against the Sun from the Pole , till its Shade passes thro' the other , or from the Zenith , till it passes thro' the Nadir , 't will cut the Parallel of the Day at the Suns true Place , and consequently show you who they are , that have him then just over their Heads ; which happens ( for Examples sake , on the 10th . of April , about our 6 in the Morning ) to them that dwell about the middle of the Coast of Malabar . OPERATION XI . To know where they are Rising , where they are at Dinner , where at Supper , and where going to Bed all over the World. THis Operation depends on this Maxim , That it is the same Hour with all People that have the same Longitude , that is to say , that live under the same Semi-hour Circle , or Semi-Meridian , therefore as the drawing of your String from the Pole , over half the illuminated part of the Globe , i. e. over the Sun 's present Place , shows you that 't is Noon or Dinner-time with all that inhabit under the said String , so the drawing it over any Place distant 6 hours Westward ( i. e. over so many hours towards the left hand from the Vertical point ) shows where 't is then all the World over 6 in the Morning , or Tunc to Rise ; whereas had you drawn it six hours Eastward ( i. e. towards your Right-hand , ) it would have shewn you where 't was six in the Evening or Supper-time , and four hours further ( i. e. two hours short of Midnight , or the point opposite to Noon ) where 't is 10 of Clock , or Bed-time . OPERATION XII . How much any People ( if it be Day with them ) are past Morning , or want of Evening ; and ( if it be Night with them ) how much they are past Evening or want of Morning . IF the Place you propose has a Diurnal Parallel that runs over it , then see what Point of the said Parallel the Preceding shade of Extuberancy cuts , and if you count the Hour Circles or distance in time between the said Point and the proposed Place , 't will give you ( if it be there Night ) how much it lack 's of Morning ; and the distance in time between the said Place and the Point made by the Following shade of Extuberancy gives you how much it is since Evening . On the other side , if it be Day there , the distance between the said Place , and Poynt made by the Preceding shade tells you how long 't is since Morning , and the Following shade how long 't is since Evening . Now if there be no Parallel that run's over or neer your said proposed Place , mount your Bead to it , and moving your said Bead on the Noose from the Pole it will describe a Parallel , and then you may operate as before . The Reason of the Operation is this ; The shade of Extuberancy getting every hour in the Aequator ( as you saw * before ) fifteen degrees , 't will proceed in the same proportion on all Parallels over which it passes , therefore , if the Distance between any Point in the Aequator and the Following shade be the distance in time of the said Point from Evening or Sun-set , and if the distance there between any Point and the Preceding shade be the distance of the said Point from Morning or Sun-rising , it follows that the distance between any Point in an Aequinoctial Parallel and these two shades of Extuberancy that cut it , must be also it 's true measure or distance in time both from Morning and Evening . OPERATION XIII . To find the Sun's height in any Place , where the Globe shews 't is Day , or his Depression where it show's 't is Night ; as also what People throughout the World see the Sun , at the same Height . SUppose on the 10 of April ( Having compos'd your Globe , and found it about 6 in the morning with you ) you should desire to know how high the Sun is at Rome , as also all the People that then see him at that , or any other determin'd height , Measure by your String or Compasses , the nearest Distance between Rome and the shade of Extuberancy , and 't will give you in any great Circle about 22 Degrees for his Height there at that moment . And the reason of it is , because when the Sun ( i. e. the Place where he is Vertical ) is distant 90 Degrees from Rome , then Rome sees him in his Horizon , and as soon as he gets above the Horizon ( v. g. ) 22 Degrees , his Rayes will illuminate beyond Rome 22 Degrees ; for else there would not be always 90 Degrees from the Place where the Sun is Verticale to the Confines of the shade and Light , or utmost Extent of his Rayes ; but the distance from Rome to the nearest part of the shade of Extuberancy , is the distance of his Illumination beyond Rome ergo 'tis his true Height . In like manner if it be Night at any Place on your Globe , and you desire to know how much the Sun is there depress'd or under the Horizon : take the Distance ( as before ) between the said place , and the nearest Term of the shade of Extuberancy , and that ( for the former reason ) will be the required Depression . As for the finding out of all Places , that have the Sun ( suppose 22 Degrees above their Horizon , you are only to lay the Plummet end of your String or Foot of your Compasses on the middle of the Coast of Malabar ( where we now suppose the Sun to be Vertical ) and making your Bead or the other Foot of your said Compasses to lye on Rome , describe an imaginary Circle ; and then all People under the said Circle will have the Sun 22 Degrees high , since they are all distant from him like Rome ; and thus you must operate in all other Cases . OPERATION XIV . To know what a Clock 't is with you , the Italian , Babilonish , and Judaic way . YOU are first to know that as England , France , Spain , Denmark , Sweden , most part of Germany , and many other Places follow the Astronomical account in their Diurnal Computation of time , with this only difference that the Astronomers begin at Noon , and so go on from 1 to 24 ; whereas the aforesaid Nations begin at Mid-night , dividing the whole Natural Day into twice twelve hours ; I say , as these Nations begin their Account at Mid-Night , so the Italians do theirs at Sun-set , continuing to 24 without interruption , after the Athenian manner of old , which is also now usually observed in Bohemia , Austria , Silesia , &c. On the contrary some Places in Germany , and particularly Noremberg , still follows the antient Babilonian or Caldean Way , as commencing their 24 hours from Sun-rising : therefore the difficulty and seeming Confusion of counting by either of these 2 last wayes proceeds from the Sun's inconstancy in its Rising and Setting ; for when he is in the Aequinoctial our Globe show's us the hour , as soon after their manner as our own : As for example , if you would then know what hour 't is with you , the Babilonian way , Hold up your String against the Sun , and moove it on it's Noose from the Pole , till the shade fall on the contrary Pole , ( i. e. look what a clock 't is the * second Way , and where the shade of the String cuts the Aequator , the Roman Figures there will give you the true Babilonish Hour . Or ( which is all one ) see what a clock 't is by the shade of Extuberancy , or * 3d way , and finding the said shade to fall , suppose , on the 9 a clock hour-circle in the Aequator as the then true hour after our English Fashion ; do but cast your Eye on the Polar Circles , and the said 9 a clock hour-circle , will cut there at the Roman Figure 3. so that you may conclude it then 3 a clock the Babilonian way . Nor does the Italian manner materially differ from this , for 't is but adding 12 hours to the 3 found as before , and then 15 will be the true hour after that account . Now if you would know the hour when the Sun is out of the Aequator ( as for example , on the 10th . of April ) consider the Parallel of the Day , which giving you at first sight about one hour for the Ascensional Difference , ( as I show'd you in the former * Section ) do but add this hour to the three found , as we now show'd you , and 't will give you four for the true Babilonian hour ; whereas if you substract it from 3 ( i. e. from the aforefaid 15. ) you have the true Italian hour ; and thus you are to proceed in all other cases ; Only remember that when the Sun is in his Southern Declension the Substraction of his Ascentional Difference gives the Babilonian , and the Addition of it the Italian hour . But if you would have yet an easier way of performing this , consult the 12th . Operation , and the distance in time there from Day gives you the Babilonian , and the distance from Night the Italian hour . As for the Jews , they devided the day always into 12. equal parts , which they called hours , as appears by our Saviours demand ; Are there not 12 hours in the Day ? therefore when the Sun is in the Aequator ( as it happened about the time of the Passion ) this and the Babilonish way are the same , for then the 3d. hour is 9 a Clock with us ; and our 3 in the afternoon is their 9th hour ; so that at 6 our way , or at 12 theirs , the Sun Sets , and the Night begins , which they also devided into 12 equal parts ; I say , this is the same as the Babilonish way , when the Sun is at or about the Aequator , and consequently easy ; but afterwards , by reason of the strange inequallity of both Day and Night , the Computation must be troublesom , especially if we use Reduction ( the common prescribed way on the Globe ) for the Summer days with us contain above 16 of our hours , and the Winter ones not half so many , and yet both kind of Days are to be devided into 12 ▪ equal parts or hours ; Nor were the Jews the only people that reckon'd thus , for the manner was in use among the Romans , as we see by Persius his Drunkards , who lay a Bed to digest their Wine — Quinta dum line a tangitur Vmbra . Nay the Greeks followed it also , and had Machines or Clocks ( as Achilles Tatius tell us ) which could ( notwithstanding the forementioned strange inequality of Dayes ) measure their Time. But this seemingly odd and exotic account , may very exactly and expeditely be perform'd by our Globe ; for , if the Globe-maker devides each diurnal Parallel by distinct specks or pricks into twenty four parts , that is to say ; if he devides that part of each Parallel above the Horizon into 12 equal ones , and that below it into the like number , you have nothing to do but to hold up your String against the Sun , and if you move it from the Pole on its Noose , 'till its shade passes over the contrary Pole , then upon what prick soever the shade falls , that will be the requir'd hour ; and in like manner if you know the Sun's Depression , draw but your String over his then Place , and it will cut the Parallel at the true Judaical time of the Night . These Vnequal Hours were also called Planetary by the Ancients , who allowed to each a Planet to govern it ; so that the first hour ( suppose ) on Saturday , belonging to Saturn , if you go on still in the usual Coelestial Order , as 't is exprest * in the Margent , and consequently assign Jupiter to the second hour , Mars to the third , &c. the 25th ( i. e. the first hour of Sunday ) will happen to the Sun's Lot , and the first of Munday to the Moon 's , and so forward : and thus you may see how it came to pass that the dayes of the week succeeded in the present order , and not according to that of the Planets in the Heavens , that is to say , why Dies Lunae ( or Munday ) and not Dies Veneris ( or Fryday ) immediately follows Sunday . I shall now end this Discourse , after I have told you , that if we English-men think these Computations strange , they that use them , wonder as much at ours ; nay , each man pretends some particular Convenience and Advantage by his Method ; For first ; an Italian says , that without breaking ones Brains no body can tell our way when the Day-ends , so that idle men , who usually hate computing do often couzen themselves , and take false measures in their Affairs ▪ for ( continues he ) if they chance to get up at 8 of the Clock in Winter , they fancy a whole day ( even St. Barnabas's ) before them , when as this Hour or early rising to Him , is 16 of the Clock , which informs him at the very instant , there are but 8 hours to Night . The Caldean on the other side urges that Morning , being the most precious part of the Day , is fittest to be nicely known , and tho' his Hour gives him not presently the Distance to the Evening , yet it so alarms him , as to what relates to the Morning , that he cannot make the least slip therein , without being at the same moment conscious of his failure . Lastly , the Jew approving both Reasons highly , triumphs in his way ; for he no sooner looks ( he says ) upon his Dial , but sees there not only what hours are past , but also what remain , and are yet behind . But notwithstanding all these shews and pretences of Reasons our Account is so far from coming short of any , that in reality it surpasses all ▪ for we not only know exactly what we want every moment of Noon ( a thing of mighty Concern ) but can appoint positive hours all the Year long , for any Employment whether private or publick , whilst these other ways ( by reason of the Suns inconstancy in Rising and Setting ) have all orderly and set times ( as when to Dine , when to Sup , when to Rise , when to go to Bed , &c. ) still mutable and fleeting . OPERATION XV. How to make the Globe Universal . THis Operation is quite beyond both my Proposal and Design ; for I really intend nothing but a Dial , ( according to a Determin'd Elevation ) fraught with several easy and natural Performances , as well divertising as useful ; And if a man cannot be content with one for his Study or Garden , unless it may serve for Jerusalem also , he must not only quarrel with Mr. Oughtred's excellent Projection , and all particular Analems , Quadrants and the like , but with Stoffler's Astrolabe , an Instrument received with mighty applause by all . Besides , 't is forty to one ( especially since there are , as we already see , so many Vniversal Operations performable ▪ by our Globe , tho fixt for a particular Place , ) if there chance a case in seven years that would move one to wish the Elevation changed ; Yet least this might happen , the Instrument Maker will prepare a thin Brass Circle , gradually devided like the Horizon , and of the same bigness ; therefore if the new Elevation were ( suppose ) for Rome , open but your Compasses at 90 Degrees in any of the great Circles ▪ or , take the same distance with your String and Bead , and having designed by your said Compasses or String any two Points thus distant from Rome , clap over your new Horizon so , that it s devided edge rests on the said two Points ; or in short , let Rome be the Pole of the Brass Circle , and 't will cut all the Equinoctial Parallels , as if the Globe had been made for that City , and consequently you will soon have there , the Suns Rising , Setting , Amplitude , Ascensional Difference , &c. Moreover the Circle being exactly made , will stick of it self , or , at least by the help of any scrap of Paper between , so that if at any time you set but the Plumet-end of your String on Rome , you may then hold it down with one Finger , and operate as you would do from your own Zenith . But since I am fallen upon this needless affair , and since the Operation is in effect the changing of the fixt and standing Site of our Globe , 't will be perchance not amiss to inform you ( if you are not already well verst in the Sphere ) that there are three different and distinct Positions of it , which you will better comprehend , if you consider your self in these three Places . Sch. 1 Suppose first , that you were under one of the Poles , and for Example sake , the Northern one , it must needs follow that that Pin on your Globe will not only be useful there , in relation to the several Operations that must ( as we show'd you ) be done from the Polar Pin , but from that of the Zenith also ; because now 't is the Zenith there , and therefore the South-Pole being the Nadir , all Circles must lye as they are represented in Scheme the first . Seeing then that the Horizon is a great Circle , and always 90 Degrees from both Zenith and Nadir , it will necessarily happen that the Horizon and Aequator must concur , so that the Aequator describ'd on the Globe will serve for an Horizon in this Position of the Sphere , which is called by Geographers the Parallel one , because by reason of the concurrence aforesaid , all the Heavenly Bodies according to their Diurnal motion i. e. according to the motion of the Primum Mobile ) parallel to the Horizon ; so that the Sun cannot Set during the six Months of his Northern Declension , nor rise during the six of his Southern ; for his Rising and Setting imply the cutting or intercepting of some part of his daily Road or Track by the Horizon . Nor want the Stars here their particular Properties also ; for being carried daily on the Poles of the World , and consequently moving parallel to the Aequator , all that are above the Horizon cannot go under it , nor the others emerge , unless some , by their proper motion after a long series of time , change that Order . Having then in this Sphere the Zenith and Horizon , whatsoever is performable by your own Zenith and Horizon , may be here ( mutatis mutandis ) perform'd after the same manner . Sch. 2. Sch. 3. As for the oblique Sphere which is the third and last Position , and here express'd by the third Scheme , we are in it ( you must know ) our selves , and so are all other People and Places of the World that are in neither of the two former ones ; for take any point not under the Poles or the Aequator for your Zenith , and 't will be impossible to describe an Horizon or Circle 90 Degrees from it , which cuts not the Aequator and all its Parallels obliquely . 'T is this Obliquity then that gives name to the Position , and 't is this that makes the great inequalities in days and nights ; for if the Horizon has a greater portion of one Diurnal Parallel above it , than of another ( as it must needs have by its slanting ) 't will follow , when the Sun is in such a Parallel , that the Day will be longer than when the portion was less , and consequently ( since more of one Parallel is under the Horizon than of another ) that one Night is shorter than another ; and seeing the nearer the Pole is to the Horizon , the more equally it cuts the said Parallels , and the further it is from it , the greater the inequality happens to be , 't is no wonder that by how much the greater the Elevation is , by so much the longer the Days are ▪ and when the whole Horizon falls below some of the Parallels , that then ( during the Sun's aboad there ) the Inhabitants have no night at all ; therefore it follows that if a Star be neerer the Pole than is the Latitude of a Place , it can never set in that Place . Yet notwithstanding this strange inequality and disproportion of Day and Night , all People in all Positions ( by that time the Sun finishes his annual Course ) make them even , and thereby enjoy an equal share of both , for if under the Pole the Sun be six months above the Horizon , he is as long under it , and if we and the Rest , that live in the Oblique Sphere , have Summer Days of a mighty length , our Winter Nights are of the same Dimension ; therefore it follows , that at the long Run the Inhabitants under the Aequator , or in the Right Sphere ( who have always 12 hours of Day and as much of Night ) cannot boast of having more of the Suns Company than they that live in the two other , and consequently that the assertion is true . 'T is in the Oblique Sphere then that the above-mentioned Brazen Horizon is chiefly intended ; but as I said in the beginning , 't is forty to one ( so many Universal Operations being perform'd by the Globe in its set Posture ) that in 7 years a man lights on a Question , that could invite him to change it , were it moveable as other Globes are ; so that having show'd you that ( in case of Necessity ) it may be in effect altered even without stirring it from its Pedestal . I shall proceed . OPERATION . XVI . How to take the Elevation of the Pole in any place whatsoever . SUppose you were in a strange Place , and that your Globe being one , that had bin fitted for London , you desire to know the present Elevation . Expose your Globe to the Sun on a Meridian Line with the Pin or Needle in the * Hole on the Parallel of the 10 of April , or true day of the Moneth , and observing at 12 a clock ( when the Sun comes into the Plain of the Globes Meridian ) that the shade of the said Needle or Pin loses not it self as it would do were the Sun directly opposite to it , for so it had hapn'd at London , or in any place in the Latitude of 51 e 30′ . I say , having thus expos'd your Globe , and observing this , move your Pin or Needle from Hole to Hole , or from one Degree of the Meridian to the other , 'till it's shade be wholly lost , and finding the said Needle or Pin on the Parallel ( suppose ) of June 11th . which is about 11. 30′ higher then it 's proper place ( to wit the Parallel of the 10th of April ) you may conclude that your present Elevation is 63 degrees , i. e. 11. 30′ higher than the Globe's ; whereas had ▪ you bin oblig'd to move your Needle or Pin so many Degrees lower than the 10th of April , your Elevation had bin but 40. The Demonstration is obvious , for since the Earth is round ; as nothing perchance proves it better , than the Experience we have , that as so many miles ( suppose 60 ) elevates or depresses the Pole one Degree , so just 60 Miles more elevates or depresses it another : I say , since the World is round , and that the Degrees of the Globe answer to its Degrees , it must follow that the difference between the Pins situation now on the Globe and where it would have stood on it at London is the true difference of the two Elevations . OPERATION XVII . How to know in what Elevation the Sun Rises or Sets , an hour , or any other space of time , earlier or later than he do's in the Globes Elevation . IF the Sun rising at London on the 10th . of April about 5 , and setting about 7 , you would know in what Elevation or Latitude he then rises , ( for examples sake ) at 4 and sets at 8 , take the distance of 90 Degrees with your String or Compasses in any great Circle , and placing one end of your String or one foot of your Compasses , where the Parallel of the day intersects with the Hour-Circle of either 4 in the morning , or 8 at night , observe where , or at what point the other end of your said String or other foot of your said Compasses touches in the Meridian , or 12 a Clock Circle of the Globe , and you will find it to be at , or about 8 Degrees and 30 Minutes , beyond the Zenith towards the North Pole , so that the Elevation required is greater than your own by those 8 Degrees and 30 minutes , that is to say the Elevation is that of 60 or thereabout ; whereas had your String or Compasses touch't 8. ° 30 ′ on the other side of your Zenith , the required Elevation would have been less than your own so many Degrees , i. e. it would have been that of 43 Degrees or thereabout . This appears true by placing your Brazen Horizon , or by describing an imaginary one over the two points made by the Intersection of the Parallel of the Day , and Hour-Circles of 4 in the morning and 8 in the evening ; for in the Elevation belonging to such an Horizon , 't is evident that the Sun rises at 4 and sets at 8. Now the Pole of every Circle being 90 Degrees from it , and the Point in the Meridian being 90 Degrees from the aforementioned Intersection , it follows that the said Point in the Meridian is the Zenith or Pole of this new Horizon , and consequently by being distant from the Aequator 60 Degrees , that so many Degrees is the Latitude or Elevation required . The END of the second Section . SECT . III. Of the Moon . HAving now finish'd with the Sun , wee 'l make a step , if you please , to the Moon , and show you how to resolve all the useful ordinary Questions concerning her , whether we see her by Night or by Day ; for 't is equal to us whether she shines out right , and consequently casts a shade , or appears only faint and wan , by reason of thin Clouds , or by the excess of Light during the Sun's aboad above the Horizon . Let us then begin with her Almucantar and Azimuth , as being the Basis and Foundation of all Operations here relating to her ; nor can there be the least difficulty in any of them ▪ unless perchance in the 7th . since they have so great a Correspondence and affinity with those already handled in the former Sections . OPERATION I. To find the Moon 's Almucantar or Height . THIS is to be perform'd as well when she cast's a shade , as when she cast's none , by the two first ways of finding the Suns Almucantar , and therefore consult the * second Operation in the first Section . OPERATION II. To find the Moon 's Azimuth . THIS is also to be found by the two first ways of finding the Sun's Azimuth , treated of in the * 5th . Operation of the first ▪ Section . OPERATION . III. To find her true place on the Globe . IF she casts no shade , her place is to be found by her Almucantar and Azimuth , as we hinted in the * 6th . Operation of the first Section , since she must ever be where these two Circles intersect ; But if she shines out cleer , you have nothing to do ( having plac't your Globe on a Meridian Line ) but to see what hour the shade of the enlightned Pole , or that of your String ( passing over both Poles ) mark 's ; for this giving you her hour-Circle ( which we 'l call the Lunar hour hereafter ) her height or Almucantar must needs tell you in what part of the said Circle she resides . This Operation is to be well understood and readily perform'd , seeing most that follow are as it were Corollaries from it ; and for the better illustrating and explaining them , we will imagine the Moon 's Place to be in the hour Circle of 2 in the Afternoon , about 43 Degrees above the Horizon . OPERATION IV. To know the Moon 's Declension from the Aequator . THIS is only the nearest distance of her true Place from the Aequator , which your Bead or Compasses will show you to be about 12 Degrees Northward , if ( according to the foregoing Example ) she be 43 Degrees high , in the hour Circle of 2 in the afternoon . OPERATION V. To find the Moon 's Diurnal Parallel , and consequently how to Compose the Globe by the Moon . BY the Moons Diurnal Parrallel I mean a real or imaginary Circle Parallel to the Aequator , and answerable to her present Declension , which by the former Operation we suppose to be about 12 Degrees ; Having therefore this ▪ Parallel you may compose the Globe by the Moon , as you do by the * Sun. And here you must remember , that tho' the finding of the Parallel implies at first a Meridian Line , yet the knowing how to compose thus your Globe will not be useless ; for now you are no longer confin'd to one Place or Line , but may compose it where you please by the help of the said Parallel . OPERATION . VI. To find the Moon 's Bearing according to the Points of the Compasse . THIS is to be perform'd after the way of finding the Sun's Bearing , in the * 7th . Operation of the first Section ; for if you draw your String from the Zenith over the Moons present Place , the said String cuts ( by our Example ) the Horizon at S. W. and some few Degrees towards the South for her then Bearing . OPERATION VII . To know what a clock it is by the Moon . THere is no Operation treated of so intricate as this , and therefore if the Reader ( who would have his Curiosity satisfy'd ) has not Patience enough to descend to a little niceness , he had better ▪ fall upon another Subject ; but tho' we may be somewhat long at first , in laying down and explicating all Particulars , yet at the end we will contract the whole into half a dozen Lines , and thereby make the Operation very expedit , and easy ; I say , there is no Operation so intricate as this ; for , the Moon by reason of her different Place in her Epicicle , is so inconstant in her dayly Elongation from the Sun , that sometimes she spends from ( v. g. ) her Conjunction to her first Quarter above 8 days , tho ▪ at another time a great deal less than 7 will serve the turn ; and to this variety and skittishness is the space also between any of her other changes liable . If then her distance from the Sun be so uncertain , and yet is the thing that must be known before her Place , or shade on the Globe can give us the hour seek ▪ how strangely fallible is the usual way ( as well in some Authors of Note , as in ordinary Almanacks ) of finding it , to wit , the adding of as many 48 minutes to the hour she shows on a Dial , as she is days old ; for the Tables , made in pursuance of this Rule , suppose her always on the 15th of her Age to be at Full , which may happen ( as I now mention'd ) not only much sooner , but also much later , so that most commonly her true Age and the said Tables are at variance ; nay , when they agree , there can be no Reliance on them , seeing that if ( v. g. ) at 6 they show tolerably what a clock it is , yet by 12 there may happen an Error of near a Quarter , by reason that she is every moment at a new distance from the Sun , and at one also which presently becomes very sensible . Thus therefore we see that there must be Exceptions and Restrictions in any one Rule that appertains to this business ; nor is it to be perform'd by an Instrument in a trice , as the Operations commonly are belonging to the Stars , that have a Regular motion , or to the Sun , whose Extravagance is not soon perceptible ; I say , thus we see that there must be here Exceptions and Restrictions , and in truth nothing but a down right Astronomical Calculation can really perform it ; yet since such a critical Exactness in the hour is never necessary in our ordinary affairs , I shall propose this method , which will at least come always very near the Mark. When you desire to know what a clock it is by the Moon , take an Almanac ( for if you would only have her true Age , you must recur to one , or to something analogical ) and reckon therein how many dayes there are in the present Quarter from one Change to the other , i. e. from New Moon to her First Quarter , or from her first Quarter to her Full , and so on ; for I call any of these four Aspects a Cardinal Point , or Change , and the whole time between one Change and the other a Quarter ; I say , Reckon how many Days there are , in the then Quarter , and you will find either 6½ , or 7 , or 7½ , or 8 ▪ so that if the number be 6½ , her Elongation from the Sun is 55 Minutes and ½ , per Diem , if 7 Days 51′½ , if 7 days and half , 48′ ; and lastly if 8 Dayes , 48′ . I mean not nevertheless that from Change to Change there maynot sometimes happen 6 days and 16 hours or 6 Days and 20 hours , and several such Fractions and Deviations from the Positive Terms prefixt by me : but since the forementioned whole and half dayes will bring us to a knowledge exact enough of the hour sought for , we call 6 days and 16 hours 6 dayes and a ½ only , as coming neerer to it than 7 whole ones ; In like manner , we call 6 , and 20 hours 7 days , and deal in this Proportion with all other number of days and hours which the Ephemerides or Almanack give us concerning the length of the requir'd Quarter . And here you may be pleas'd to remember also , that it would not be amiss , in case you exceed much any of the foresaid terms , to add or cast away sometimes a minute or a little more , as you shall see Cause ; For if ( v. g. ) you find the Moon to be six days and 17 hours in her journey ( which according to our former Directions is to be reputed only six days and ½ ; and consequently the Elongation 55′½ , you may then cast away 1′½ , because of this great excess above the half day ; and if you should find her at another time to be 7 days and twenty houres , i. e. eight days , you may add for the want of the four hours a minute , and make her dayly Elongation , 46 instead of the forementioned 45 ; but here you may do as you you please , for the error will not be considerable . These Particulars being premis'd , let us come to an Example ; and Suppose then that on the fifth of January , finding the Moons shadow to marke two in the afternoon on your Globe for the Lunar hour , you should desire to know the true , or Solar hour . First your Almanac can tell you not only that the Moons last Cardinal Point , was ( v. g. ) her Conjunction , but how many Days and Hours she spends in going from it to the next Cardinal Point ; for finding there her said Conjunction to be on the first day ( suppose ) at seven at night , and that she comes to her first Quarter on the ninth day , near the same hour , you may presently conclude she is 8 whole Days in this Voyage , and consequently that her Diurnal Elongation from the Sun will be 45 minutes . Now because the said fifth day is the 4th of her Journey , if you multiply 45 by 4 , or lookin the Tables ( which we shall presently show you ) belonging to her 8 Days Journey , you 'l have three hours for the time that she is behind the Sun , so that the Solar or true hour must be five at night , wanting four minutes ; for you are always carefully to substract two minutes for every hour the Moon wants of compleating her whole Days march , which in the present case happens , not before seven at night ; whereas you must have added them , had the Solar hour bin nine at night , because then her Elongation from the Sun would have been 4 minutes more than the aforesaid three hours . 'T is in this manner you are to opperate in all cases ; but before we proceed , take these two Memorandums with you . First , That by the Moon 's compleating a day's journey , I mean 24 hours after the time ( let it happen by night or by day ) of her entring into her last Cardinal Point ; as for Example , If she comes to her Conjunction , or any other Cardinal Point , at 7 in the Evening on ( v. g ) Munday , then at 7 in the Evening on Tuesday , she has compleated one day's journey , and at the same hour on Wednesday two Dayes , and so on till she comes to her next Cardinal Point . The second Memorandum is , That whereas ( in the late Example ) her Elongation from the Sun was three hours ( because you sought what a Clock it was on her fourth days journey from her Conjunction to her First Quarter , at the Elongation of 45 minutes per diem . ) Now had she been thus advanced in her Course from her First Quarter to her Full , or from her last Quarter to her Conjunction , you must have added 6 hours to the said 3 hours , so that then the true hour would ( instead of 5 at night ) have been 11 ; and this is to be a general Rule . Thus much then for the way of finding what a Clock it is at any time by the Moon , and now let us make good what we have said . First we see , that to know the Hour by the Moon , is to know the difference between the Lunar and Solar hour , i. e. between the hour Circle she is in , and that in which the Sun happens ( at the same time ) to be ; or , in other Terms between the hour she marks on the Globe by her shade , and that which the Sun would mark did he then appear ; Now seeing that in her Course from one Cardinal Point to the other , she seldom spends the same number of days and half days , it follows ( as we hinted in the begining ) that no certain number of minutes , can be allowed for her daily Elongation ; But if we divide 6 hours , or 360 minutes ( i. e. her total Elongation from one Cardinal Point to another ) by the Days and half days she spends in the journey , the Quotient must be her Diurnal Elongation ( at least to sence ) during that Quarter . Now since the Diurnal Elongation is , as you see most commonly above three quarters , and somtimes almost an hour , the Horary one must be ( as I said ) considerable , seeing in the space of every 7 hours it may amount to above a quarter more ; therefore this inconvenience we obviate by allowing two minutes for each hour after her compleat days journey , and substracting them from what she wants of it . Here I confess there may be an Error , but it is hardly worth the mentioning ; for when she is either 8 days , or 7 , in her journey from one Cardinal Point to another ; i. e. when her Diurnal Elongation is either 45′ , or 51′ and ½ , the difference from 48 minutes a day ( or 2 minutes an hour ) cannot be but 3′ and ½ in a whole day : nay , when her Elongation is 55′ and ½ i. e. when she spends 6 days and ½ in her voyage , the difference is but 7′ and ½ from the aforesaid 48 minutes ; nor can this happen till the end of every compleat days journey , and consequently is not perceivable for the greatest part of it . But since we here see where and how any error may arise , it is easily remedied by an Allowance , if any man thinks it worth the while to be so exact . As for the Reason why , if she be in her Course from her first Quarter to her Full , or from her last Quarter to her Conjunction , we must add always six hours to the Elongation , which our Calculation or the Tables give , it is , because the said Elongation is only the precise time of her Departure from her last Cardinal Point , whereas if she be past her first Quarter in her Journey towards her Full , she is so much and six hours more , i. e. so much and the six hours , which happen from her Conjunction to her first Quarter . Now in rigor we should add twelve hours to the Elongation we find , when she is gone from her Full , towards her last Quarter , but seeing she is in the Plane of the same Hour-Circle or very near it , both at Full and in Conjunction , therefore the bare adding the said simple Elongation will serve as well in one case as in the other ; for if , the Full Moon ( at suppose 2 of the Clock at night ) casts really her Shadow on the Hour-Circle of 2 in the Afternoon , yet there 's no need of hints ( the thing being so plain ) to prevent your mistaking Day for Night . The like also is to be said of the last Quarter , whose Elongation should be in truth eighteen hours , but the additional six hours ( as we allow her after her first Quarter ) are sufficient , since no man can be so ignorant as to take the Morning for the Evening , notwithstanding the Lunar hour should be upon a Morning Hour-Circle . To facilitate then this Operation ( least what we have already said has proved tedious ) we will conclude ( as I promis'd ) with a short Recapitulation ▪ or Abstract , as also with the Tables of her daily Elongation , let the time be what it will ( as we said ) that she spends in her Journey from one Cardinal point to the other . The Abstract of the Operation in finding the true Hour by the Moon according to the late Example . AS for the Almanac , there are three things ( we see ) it informs us of , viz. 1. The Hour when the Moon came to her last Cardinal Point . 2. How many days she is going from the said Point to the next ; and , 3. In which Days Journey she is at present . Knowing then , according to the late Example that the Moon will be eight days running throu ' her Quarter , and that she is in the fourth Days Voyage ; 't will follow that the fourth day in the Table ( whose title is eight dayes ) will tell you that her present Elongation from the Sun is three hours ; so that the Lunar-hour being two in the afternoon , the true hour must be just five at night ; only twice two Minutes are to be abated , because she lacks 2 hours from compleating her said fourth days voyage ; for your Almanack ▪ ( according to our supposition ) informing you that it was seven at night when she set out from her last Cardinal Point , it must be still seven at night before she compleat's any whole day's Journey during that Quarter . This then is the summ of the whole Business , nor need you trouble your self with any other Reflexion unless it be to add six hours ( as I already said ) to the Elongation , in case she be going from her first Quarter to her Full , or from her Last to her Conjunction . And to conclude take notice , that the hour ( if you see the Moon , ) may be as well found by day as by night , for her Place on the Globe ( which the third * Operation show's how to find ) is always the true Lunar hour . Tables of the Diurnal Elongation of the Moon from the Sun , whether she goes in 6½ , 7 , 7½ , or 8 days , from one Cardinal Point to the other . 6. ½ Days Card. Point . 0. Days from her Cardinal Point . 0. Hor. 0. min. Elongation . 1. Days from her Cardinal Point . 0. Hor. 55. ½ min. Elongation . 2. Days from her Cardinal Point . 1. Hor. 51. min. Elongation . 3. Days from her Cardinal Point . 2. Hor. 46. ½ min. Elongation . 4. Days from her Cardinal Point . 3. Hor. 42. min. Elongation . 5. Days from her Cardinal Point . 4. Hor. 37. ½ min. Elongation . 6. Days from her Cardinal Point . 5. Hor. 33. min. Elongation . 6½ Days from her Cardinal Point . 6. Hor. 0. min. Elongation . 7. Days . Card. Point . 0. Days from her Cardinal Point . 0 Hor. 0. min. Elongation . 1. Days from her Cardinal Point . 0. Hor. 51. ½ min. Elongation . 2. Days from her Cardinal Point . 1. Hor. 43. min. Elongation . 3. Days from her Cardinal Point . 2. Hor. 34. ½ min. Elongation . 4. Days from her Cardinal Point . 3. Hor. 26. min. Elongation . 5. Days from her Cardinal Point . 4. Hor. 17. ½ min. Elongation . 6. Days from her Cardinal Point . 5. Hor. 9. min. Elongation . 7. Days from her Cardinal Point . 6. Hor. 0. min. Elongation . 7 ½ Days . Card. Point . 0. Days from her Cardinal Point . 0. Hor. 0. min. Elongation . 1. Days from her Cardinal Point . 0. Hor. 48. min. Elongation . 2. Days from her Cardinal Point . 1. Hor. 36. min. Elongation . 3. Days from her Cardinal Point . 2. Hor. 24. min. Elongation . 4. Days from her Cardinal Point . 3. Hor. 12. min. Elongation . 5. Days from her Cardinal Point . 4. Hor. 0. min. Elongation . 6. Days from her Cardinal Point . 4. Hor. 48. min. Elongation . 7. Days from her Cardinal Point . 5. Hor. 36. min. Elongation . 7½ . Days from her Cardinal Point . 6. Hor. 0. min. Elongation . 8 Days . Card. Point . 0. Days from her Cardinal Point . 0. Hor. 0. min. Elongation . 1. Days from her Cardinal Point . 0. Hor. 45. min. Elongation . 2. Days from her Cardinal Point . 1. Hor. 30. min. Elongation . 3. Days from her Cardinal Point . 2. Hor. 15. min. Elongation . 4. Days from her Cardinal Point . 3. Hor. 0. min. Elongation . 5. Days from her Cardinal Point . 3. Hor. 45. min. Elongation . 6. Days from her Cardinal Point . 4. Hor. 30. min. Elongation . 7. Days from her Cardinal Point . 5. Hor. 15. min. Elongation . 8. Days from her Cardinal Point . 6. Hor. 0. min. Elongation . These Tables are to be on the Globe in the most vacant and free parts of it . OPERATION VIII . To know how many hours the Moon has been up , and how many she lacks of her setting , as also how long she is to be that day above the Horizon . THis is done by numbring the Hours or Hour Circles between the Moons place in her Parallel on the Globe and the intersections of her said Parallel with the Horizon ; for having found that her Parallel cuts the Horizon in the East at the five a clock hour circle , and in the West at that of seven , and seeing that her present Place is ( v. g. ) at that of two in the afternoon , you may conclude that she has bin up nine hours wanting eighteen minutes , that is , eight hours and forty two minutes ; and will set within 5 hours wanting ten minutes , or four hours and fifty minutes ; for the Moon goes from East to West ( by the Motion of the Primum Mobile or Motum Raptus ) two Minutes ( as we suppose ) every hour ( take one time with the other ) slower than the Sun ; which happens by her being too quick for the Sun in her own Motion , that is to say , in the Motion of the Center of her Epicicle , which carries her from West to East ; therefore the Moon according to the present Example or Supposition will be above the Horizon fourteen Hours wanting twenty eight Minutes , i. e. about thirteen hours and a half . OPERATION IX . To find at what at lack the Moon rises and sets . BY the last Operation you are inform'd of the hours from her present station to her Rising and Setting , which hapning in the Example to be about eight hours and fourty two Minutes for the one , and four hours , and fifty minutes for the other , it must follow , ( having found the true hour to be within four minutes of five at Night ) that she rose about eight and fourteen minutes in the Morning , and will set at nine and fourty six minutes at Night . OPERATION X. To find how long the Moon shines every night . HAving found by the precedent Operation , that the Moon sets at 9 and 46 minutes at night , and that the Sun ( by the 12th . of the first * Section ) sets the same day , ( suppose the 8th . of February ) at 5 in the Evening , 't will follow that she shines four hours and 46 minutes . OPERATION XI . To find when the Moon comes to South , and consequently when t is high water at London Bridge . HAving found by the * third Operation the Moons place to be in the 2 a Clock Circle , you thereby see that she is past the South 2 hours and 4. minutes ; Now since it is always High-water at the Bridge three hours after her coming to South , and since the Solar or true hour is ( according to our Example ) 5 at Night , it follows 't was High-water at 4 minutes before 6. and consequently 't will be high water again at the same hour next morning , and 24 minutes ; for from one Tide to the other there are always about 12 hours and 24 minutes . OPERATION XII . To know in any Eclips of the Moon , what Countries see it wholly , what in part , and what not at all . PLACE your Globe on a Meridian Line , or otherwise Compose it , and when you percieve the Moon to begin to enter into the shade of the Earth , consider ( as you do when you seek by the * Suns Rays where 't is day and night ) what part of the Globe is illuminated , and what not ; for , since she appears to all Countries that lie in the Light , and is hid from those in the Shade , you have not only a view of what people see her in her then condition , but may ( till her total immersion ) perceive by her illumination how the Countries , that lye in or near the Following shade of Extuberancy , loose every moment the sight of her , and consequently , who they are that took leave of her in the beginning of her Eclips , who when she came to half of it , and who when wholly obscur'd , with infinite more Reflections of this nature . On the other side you may find , how some that lay in the preceding shade of Extuberancy saw nothing of her at first , but now begin to discover her in her Angony ; and if you draw on the Globe a little Circle with Chalk or the like , in the Confines of the obscurity and light , just as she begins to be wholly in the shadow , you will discern ( by the space between the said Chalk and the new shade of extuberancy at her Emersion ) what people never saw her , tho she were above their Horizon . Infinite are the Reflexions ( as I said ) of this nature , but these are sufficient to show you how to make more your self ; so that now I will end after I have remembred you , that the Sun being by his Opposition in the same hour Circle with the Moon , especially in all Central Eclipses , nay he is so ( as to sense ) for some time both before and after such Eclipses ; I say , the Sun being so , you may therefore not only ( by the bare shade of the String , or that of the illuminated Pole ) know what a Clock it is from time to time in the Polar Circles , but in the Aequator also , by the shade of Extuberancy , which performs the observations above mentioned ; and thus by the very same shade you find not only what People see the Eclipse , either in whole or in part , ( as we now told you ) but at what hour it appears to each of them , and how long ; as also the Duration of her Decrease and Encrease in light , together with the time of her total Obscurity ; moreover , this very shade gives you her Height and Azimuth all along , as you may see in the * Operations that concern them . OPERATION XIII . To represent the several Phases or Shapes of the Moon by the Globe . THIS is rather a Speculation than an Operation , Nor should I have mentioned it , were it not that several ( who know something in Mathematics ) cannot comprehend the Cause of the Moon 's continual Metamorphosis or Change , that is to say , why she should be now more , now less illuminated , and that also in so different a shape and manner . To comprehend therefore this , Expose your Globe ( elevated on a Stand or a Table as high as your Eye ) to the Sun or Moon , and place your self so before it as to see the whole illuminated half ; for ( as to sense ) the illuminated and shady parts of all Spheres are ( as we formerly mentioned ) equal . Having then a while consider'd this great Circle made by the Limb or Extremity of the illumination , remove your station a little on the one side ( as for Example towards the righthand ) and you will find the illuminated part to appear Gibbous or Oval , I mean not so broad as long , because so much of it is hid from you , as you can now discover of obscurity . From hence go yet farther side-wise , and the visible part of the Globe will be Dicotomous , or party per pale , that is to say the light and shade will become equal . After this make another Proportionable step , and all that is illuminated will appear Horned or Lunular , and the obscure part Gibbous ; But if you remove to the point opposite to your first Station , you will see nothing besides a dark and shadow'd Hemisphere ; whereas should you proceed further in the same Order , you would perceive Light on the other side , first Lunular , then Dicotomous , next Gibbous , and lastly totally predominant . Now as the Globe is always half illuminated , whether we see little or much of the illumination , so it happens with the Moon , who being in Conjunction appears all dark to us ▪ because her illuminated half is towards the Sun , and opposite to us ; but as soon as she gets from him , and consequently is no longer in the same Plane with him and our Eye , we must needs have a view of some part of the Illumination , seeing she can only appear wholly obscure when she is thus before the Sun. The said Illumination also ( since she is Spherical ) must seem as on the Globe the more Horned the less it is , and then blunter and blunter according to her Encrease or Elongation , till at last she becomes Dicotomous , afterwards Gibbous , and lastly Full ; for by being at her greatest distance from the Sun , or in Opposition with him ( which causes our Eye to be in the middle or between them ) 't is impossible she should appear otherwise than all Light : And here you may be pleased to take notice , that if you compass your Globe with a String or Thred that passes throu ' the Zenith and Nadir , and let one half of the describ'd Circle represent the Illumination and the other the Obscurity , you may perform this Operation at any time , whether the aforesaid Luminaries shine or no. How easy therefore is it to conceive the whole Mistery of the Moons four principal Changes , and what men mean by them . For first we see that as She is call'd New by an Astronomer from her being with the Sun , ( i. e. as fully between our Eye and the Sun , as her then Course permits ) so no sooner has he found by their several motions that she is gotten 90 Degrees or six hours from the Sun , but he says , she is in her first Quarter ; and when they are asunder 180 Degrees or 12 Hours ( to wit as far as ever they can be ) that she is Full ; and lastly , as soon as they are distant 270 Degrees or 18 hours on the same side , and 90 Degrees or six hours on the other , that she is in her last Quarter ; so that at their next meeting she becomes New again . OPERATION XIV . How to find how long the Moon wants of any Change , or Cardinal Point , and consequently how old she is . I Propose not this Operation as a thing exact , but seeing it is a Corollary of the former , I thought fit to hint it ; therefore pray take it ▪ for better , for worse , and make of it what you can : To resolve then these Questions by the Globe , you are to expose it as before to the Moon when she shines , and move about it till you can there just describe her shape ; and by the way you will come nearer the mark , if you only consider the Lunular or lesser Portion , whether it happen to be the obscure or the illuminated part of her whole Discus or Orbe ; I say , describe her Shape on the Globe , as neer as you can , and observe how many Degrees the breadth of the Horn'd or Lunular Portion will be in any great Circle , that crosses it in the middle at Right Angles , and that will give you taliter qualiter what you seek for , as appears more clearly by the ensuing Example . Having observ'd , suppose , the illuminated Portion of the Moon to be Lunular , expose your Globe , and move about it 'till you perceive on it an illuminated Lunula proportionable to the Real one , then finding its measure by some great Circle that crosses it at right Angles , to be 40 Degrees , these consequences will follow . First if the Moon be in her Encrease , she is past being New 40 Degrees , i. e. three days and about seven hours , seeing her hourly Elongation from the Sun ( is one time with another ) about half a Degree and half a minute ; but if she be in her Decrease , she wants so many days and hours from being again New. In the next Place it will happen that the obscure part of the Globe is 140 Degrees broad ; for ( both parts or portions making up the apparent Hemisphere ) the said obscur'd Part becomes the supplement of the former 40 Degrees ; so that 140′ amounting to about 279 hours , or 11 days and 15 hours , you may conclude that if she be Encreasing , she wants so much of being Full , as also that she is 50 Degrees or almost 100 hours ( i. e. four Days and almost four hours ) past her first Quarter ; whereas if she be Decreasing , she will want eleven Days and fifteen hours from her next Conjunction , and be four days and almost 4 hours beyond her last Quarter . As for knowing the Moons state in relation to her Waxing and Waining , you need only observe on what side of her Discus her illuminated Part stands ; for if it be on the West-side of it , she is in a Waxing Condition , if on the East-side in a Waining or Declining one : And here also remember that as to the measuring the aforesaid Portions of the Moons Discus , represented on your Globe , you may do it by the Horizon , if she illuminates not much beyond the Zenith , or by the Aequator , when the illumination reaches to the Pole or neer it , or by the Ecliptic when it extends it self a good way further ; for the said Portion of the Moons Discus is measur'd at first sight by that great Circle which lies equally distant from each Horn of the Lunula on the Globe , i. e. by that great Circle which crosses it ( as we said ) in the middle at Right Angles ; and when no great Circle does so . you had best measure it exactly with your Compasses , seeing that on the knowledge of its breadth , the Resolution of all the former Questions depend . Many things of great use may be drawn from knowing the true proportion of the illuminated and obscure parts of the Moons Orb , but this I leave to them that have exacter Instruments than the Globe , and more time to make Deductions . The END of the Third Section . SECT . IV. Shewing the Proportion between Perpendiculars and their Shades . SEeing there is the same proportion between all Shades and their Perpendiculars ; at least to sense , and seeing the several Almucantars of the two great Luminaries are the chief Cause of the lengthning or shortning of them , I have here adjoin'd a few by - Operations even in Altimetry it self , as belonging naturally to our Globe , since it not only shows us several ways of finding from time to time the said Almucantars , but gives us also at the same instant without trouble ( as appears by the ensuing Operations ) the above-mentioned Proportion , and consequently the height of all things Perpendicular to the Horizon . OPERATION I. How to find the Proportion between the Perpendicular and its Shade . COnsider the Northern or back part of the Globes Meridian , which we will call hereafter the Quadrant of Proportion , and which is not only devided like the Southern or fore-part into Degrees , but markt also ( in relation to the affair in hand , ) with several Figures , of which that next the Zenith is 17 , and the remotest 188. And by the way you must take notice , that when you see a Cross behind any Figure , it signifies half an Integer more , so that 17 + is 17 Degrees and a half , 26 + is 26 and a half , &c. When you would therefore Operate , Turn the Southern or fore-part of the Meridian towards the Sun , 'till they be both in the same Plane , i. e. 'till the shade of the Pin in the Zenith falls directly upon the Quadrant of Proportion , and what Figure soever , ( suppose 25 ) the shade of Extuberancy cuts , that will be the then Proportion between Perpendiculars and their Shades ; for here you may take notice , that we ever suppose the Shade to be 100. Nay , if finding ( by any of the * former ways ) the Sun's height to be ( suppose ) 14 Degrees , you rectify your Bead to 76 Degrees , or the Complement of it , you need only clap back your String , that is to say , draw it from the Zenith , over the Devisions of the afore-mention'd Quadrant , and then the Figures under the Bead ( to wit 25 ) will shew you the required Proportion ; In short , take but the Suns Height ( any how ) and reckon from the Zenith as many Degrees on your said Quadrant of Proportion , and the Figures at the end of your Account will give the Proportion sought for . Now if the Shade of Extuberancy , or the Bead marks not even Degrees for the Sun's Height , but ( for Examples sake ) 13 . 30′ , and consequently falls between the Figures of 23 and 25 in the Quadrant of Proportion , you had best ( to avoid all Calculation and Allowance ) expect a Moment longer , for then the Sun's Height being even , and without Fraction , you may operate as before . OPERATION II. How to find the height of a Tower by the Globe . THIS Operation appears at first Sight to be a Corollary of the former , for finding , as I showd you , that the Shade of Extuberancy falls in the Quadrant of Proportion , on the number ( v. g ▪ ) 25 , and that the said ▪ number represents a Perpendicular , do but measure the shade of any Tower and you will soon have its height , seeing that as 100 is to 25 ( i. e. as 100 is to the number found on the said Quadrant ) so is the Shade of the Tower , ( which being measur'd wee 'l suppose 80 yards long ) to a fourth number , viz. to 20 the required height . OPERATION III. How by the help of your Globe to measure any Tower or height , and yet not ▪ to seem to use any Instrument in the Operation . THIS Operation may perchance a little surprise some , and yet it differs not in reality from the former ; that showing you how to measure a height by your Globe upon the place , and this how to do it privately . To perform then the Operation , you must choose ( when you are alone ) any of the aforesaid Numbers , on the Quadrant of Proportion , as suppose 25 , and seeing that belongs to the 14th . Degree from the Zenith , rectify your Bead to the Complement , i. e. to the 76th from the Zenith in the said Quadrant ; this being done move your String hanging on the Zenith's Pin , till your Bead touches the Parallel of the Day , which we now suppose to be the tenth of May , and the Hour-Circle , that meets with it there ( to wit that of six in the morning , or six in the afternoon ) tells you that at those hours , on that day of the Month , the perpendicular will be the fourth part of the Shade , i. e. as twenty five to an hundred , so that having discours'd with some body of the possibility of measuring heights without an Instrument , repair with him to any convenient place , about the foresaid times of the day , and when you find by your Watch that 't is exactly six , do but measure the Shade and you will have the required height . And by the way take notice , that as it is in your power to choose what proportion you please , and the more odd and exotic it happens ( if you can quickly reduce it ) the better it is , for then People will not perchance so soon comprehend the Operation ; I say , as you can choose your Proportion , so you may choose the Hour also , for if your Bead be rectify'd to the chosen Proportion , according to the foregoing Example and Instructions , and brought to the hour pitcht upon ( suppose 3 in the afternoon ) the Parallel , ( to wit , that of the fifth of February , ) which meets with the the said Bead and Hour-Circle , tells you that then the Proportion will thus happen ; nay , you may choose what day and hour you please , if you will be content with the casual Proportion or number which the Bead , when rectify'd ( as we mentioned ) falls upon . OPERATION IV. How to find the Hour by your Stick . YOUR Stick being divided into ten equal parts , and each part by Pricks into as many equal Subdevisions , you must operate thus . Rectify your Bead ( on the tenth v. g. of April ) to the Sun's Meridian Altitude , and if you then move your String on the Pin of the Zenith , to the Quadrant of Proportion , the Bead will lye ( for Example ) on 87 , so that having writ this on Paper with the figures of 12 above it , draw your String from the Zenith over the next Hour-Circle on which hand you please , I mean either over that of 11. or 1. and where your String cuts it on the said Parallel of the day , there place your Bead , and 't will lye ( v. g. ) on 93 in the said Quardrant of Proportion ; noting then 93 in your paper under the hours of 11. and 1. proceed then in this manner from Hour-Circle to Hour-Circle , 'till you come to 6 , for after the Sun is within an hour of his Rising or Setting , you may easily guests what time of Day 't is ; besides shadows are then so long that they are troublesome to measure ; I say proceed in this manner to 6 , and a Table like that in the * Margin will show you the hour not only during that day , but during five or six successively ; without any considerable Errors , for you have nothing to do but to erect your Stick , as perpendicularly as you can , and to measure its Shade with it , so that finding the length of the said Shade to be , suppose 200 i. e. twice as long as the Stick , your Paper will tell you , that when this proportion happens , 't is either eight in the morning , or four in the afternoon . OPERATION . V. How to to take an Angle in Altimetry by the Globe . THIS Operation is to be perform'd like that of finding the height of the Sun and Moon when they shine not out , as I formerly * show'd you ; that is to say , you must place your Globe Horizontal , and having turned the Meridian towards ▪ the Tower , move your Eye along the said Meridian , till the Extuberancy of the Globe permits you only to see the top of the Tower , and then bring but your String , ( which we suppose you hold in both hands cross the Meridian ) towards you , till it just takes away the sight of the said Top , and the Degree which your String then lies on , ( counting from the Zenith ) is that of the required Angle , to wit , of the Angle which is ordinarily taken by any Quadrant , Jacobs Staff , &c. OPERATION VI. How to make and figure the Quadrant of Proportion , as also the Demonstration of the foregoing Operations . IT appears plainly by the Scheme here before us , that the Shade ( AB ) being Radius , the Perpendicular ( CB ) is Tangent of ( A v. g. 14. ) the Degrees of the Suns height , as also that the Perpendicular ( CB ) being Radius , the Shade ▪ ( AB ) is Tangent of the Complement of the said height ; therefore if the Radius being 100 , you mark from the Zenith to the Horizon each Degree of your Quadrant of Proportion with Figures according to the value of their respective Tangents , you must necessarily perform the late Operations , that give us the height of things , the hour of the Day , &c. For if your Bead be rectify'd ( from the Horizon of your Globe ) to ( 76 ) the Complement of the Suns height , it will be distant from the Zenith just as many Degrees as the Sun is high , to wit 14 , and consequently being moved to the Quadrant of Proportion ( which is figur'd we see , from the Zenith downwards ) must lye there on 25 , the Tangent of his said Height , therefore as the Radius 100 is to ( 25 ) this Tangent , so ( 80 ) the length of the Shade must be to the Perpendicular 20. In the next Place if your Bead be rectify'd every hour to the Suns height , it must ( when moved to the Quadrant ) still lye on Tangent Complement of his said hourly height ; Now the Shade being always as I told you the Tangent Complement of this height , the former little Tables must needs shew you the corresponding Hour , when we once know the value of the Shade , i. e. its proportion to the Stick . To conclude the Tangents of the first 10 Degrees are not exprest on the Quadrant ▪ because when the Sun is no higher , we may easily guess at the hour , and besides ( as we said ) the Shade is then extremely long , and consequently very troublesom to measure ; nor need we go further than 62 Degrees , since his greatest Meridian Altitude exceeds not that value . The End of the Fourth Section . SECT . V. Of Dialling . THE Performance of this Section no less appertains than the rest to our Globe ; since it not only represents to our view , what Dials are in themselves , and why they shew us the time of the Day , but afford's us also so natural and so easy a way of describing them , that no person can be hardly so ingnorant , who will not ( with the least Instruction ) in three hours time be able to make one on most Planes , unless perchance ▪ for want of a little Digestion and private practice , the Rules shove one another out of his Memory . Nay all the accidental Requisits to Dialling ( being these that follow ) are here performed without the help of any forrein Instrument . 1. To draw a Meridian Line . 2. To draw a Line Parallel to the Horizon on a Plane not Horizontal . 3. To find the Declension of a Plane . 4. To find how much a Plane Reclines . 5. To find how much a Plane Inclines . 6. To find how long the Sun shines on a Plane ; that is to say , when he 'l come on , and when He 'l go off it , at any time of the year . Besides we have already taught you , how to know when a Plane is * Level ▪ how to find the † Height ▪ of the Sun , and how his * Azimuth , all which properly appertain to this Science . These then are the Operations , I mean by Requisites , which shall be all treated of either immediately before , or immediately after each Dial that requires them . But tho' I intend to show you , as I now mentioned , this easy and natural way of Dialling , even in what bigness you please without need of Quadrant or Scale of Reduction , without your knowing the least Problem in the Mathematics , or my requiring any thing else of you , let that you can draw a Line from Point to Point , and describe a Circle , when the Radius is given ; I say , tho' I intend this , yet that you may not be wholly Ignorant of their Geometrical Construction , I shall teach you that also , and therein perchance something both expedite and new ; but then I must suppose ( for I have not time to instruct you , ) that you can Erect a Perpendicular , draw a true Parallel , and know so much of the * Sector as how ( besides the use of the Line of Lines ) to find the Chord and Sine of any Number of Degrees by it . I mention the Sector , not that any Ordinary Ruler , with a Line of Sines , Line of Chords , &c. is unsufficient , but because you have under the Pedestal of your Globe a Sector to your hand , which I have order'd there for two Reasons ▪ First it will be necessary , the Globe standing erect and at right Angles with the Horizon , to bring the edge of its Pedestal to your Plane in several Operations ; Now seeing this cannot be done unless the Pedestal be greater than the Globes Diameter ( which would , make it perchance cumbersome , and to take up too much room ) there are therefore under it two small wooden Rulers about half an Inch Broad , to slip in , or out to a determin'd length , so that it will be better to have one of them a Sector ( which is a very necessary Instrument ) than not , especially since 't is no hindrance to the use , we chiefly intend it for . Nor would I have any thing more on it ( to avoid the Confusion of Devisions ) than the Line of Sines on the one side , and the Line of Lines on the other ▪ and as for its length , if it be six inches , it will make an even Foot at full extension ▪ which renders it a very convenient standing measure . My second Reason for the said Sector is , because I will show you , how to find by it the TANGENT and SECANT of any degree even according to any Radius , and how usefull an Operation this is ( and particularly in Dialing , ) everybody well knows that has the least insight in it . Suppose then you desire the Tangent and Secant of 50 Degrees ; open your Sector , and taking ( GR ) the given Radius between your Compasses , put it over in the Line of Sines , at the Sine of 40 , viz. at the Complement of the Angle required , and the distance between the Figures of 50 and 50 , will be the Tangent sought for ; and the distance between the Figures of 90 and 90 will be the Secant of the said 50 Degrees . These two Problems I recommend to you because they are extremly ingenious and useful , found out it seems a while ago by Mr. Line ( the Author of that admirable Horological Pile in White-Hall Garden ) as , since his death , one of his Scholars ( that hinted them to me ) informed me , and upon consideration I found them exactly true , having thus demonstrated them . Sch. 1. 'T is evident by Sch. 1. that as the sine Complement AB is to the Sine CB , so the Radius AD is to the Tangent ED. Again 't is evident by Scheme 2. that as KC : KS : : CR : ST , but by Construction KC is on the Sector the Sine of 4 or Sine complement of 50 , and CS the Sine of 50 it self , therefore CR being the Radius given , ST must be the Tangent requir'd , viz. the Tangent of 50 , according to that Radius . On the other side we see by the said first Scheme that as the Sine Complement AB is to the Radius AD , so is the Radius AC . ( or AD ) to the Secant AE . Again you see by Scheme second , that KC : KD : : CR : DP ; but by construction KC is the Sine of 40 or Sine Complement of 50 , and KD is Sine of 90 or Radius of the Sector , and CR is the Radius given , ergo PD must be the Secant required . Having thus done with the Preliminaries , we 'l now come to the business it self , after I have told you there are five principal Planes on which a Dial may be made ; to wit the Horizontal , the Vertical , the Declining , the Reclining and the Inclining Plane ; and first of the Horizontal , since that Dial is the Basis and Foundation of all the Rest . Sch. 3. Sch. 4. Sch. 5. Sch. 6 Sch. 10. Sch. 7. Sch. 9. Sch. 8. Sch. 11. Sch. 12. Sch. 13 Sch. 14. Sch. 15. Sch. 16. Sch. 17 Sch. 18. Sch. 19. Sch. 20. Sch. 21. Sch. 22. Sch. 23. Sch. 25. Sch. 26. Sch. 27 Sch. 24 Sch. 28 Sch. 31 Sch. 32 Sch. 33 Sch. 34 Sch. 35. Sch. 36. Sch. 37. Sch. 39 Sch. 38 Sch. 41 Sch. 42 Sch. 34 OPERATION I. BEfore you proceed further , you must know Reader , that the Printer ( skipping a line in the last Paragraph , and then adjusting the number of Planes to those he found exprest ) has left out two , so that the before mentioned principal Planes are 7 ; viz. the Horizontal Plane , the Direct Vertical Plane , the Declining Vertical Plane , the Direct Reclining Plane , the Direct Inclining Plane , the Reclining Declining Plane , and the Inclining Declining Plane . First , then of the Horizontal , that Dial being ( as is said ) the Foundation of this Science , and afterwards of the rest in Order ; for the Author treats of all Dials that are to be described on the aforesaid Planes . J. M. How to describe an Horizontal Dial by the Globe , for the Elevation of London . The first way . OPen your Compasses at 60 Degrees in any great Circle of your Globe , and draw on a sheet of Paper a blind Circle with a fair Diameter throu ' it , for the Meridian or 12 a Clock hour line of your Dial ; Then take with your Compasses in the Horizon of your said Globe , the several Distances between the next 8 morning or evening hour Circles and its Meridian or ordinary 12 a clock hour Circle , and marking these Distances successively in the blind Circle on both sides of its Diameter , they and the Center will be the Points by which you may draw all hour Lines from 4 in the Morning till 8 at Night ; and if you would have a Dial bigger than the blind Circle , draw about it a bigger Circle , if a lesser a less : nay , if you describe any other Figure as an Oval , Square Oblong , &c. the said Points will as well guide your Ruler , as when the blind Circle it self was the Extremity or border of your Plane . But least this Direction should be too obscure for a Beginner , I will here adjoyn an Example . Having opened your Compasses , as I said , at 60 Degrees in any great Circle of your Globe , and describ'd a blind Circle , to wit , I p T c , as in Scheme third , draw a fair line IT any how throu ' the Center O for your Meridian or 12 a clock hour Line ; and by the way remember that in the Fabrique of this Dial you place the point I ever towards you , and T farthest from you , to the end you mistake not when directed to this or that hand . Having then proceeded thus far , put one foot of your Compasses on the Meridian or ( according to the Polar Figures ) the 12 a clock Circle of your Globe where it cuts the Horizon , and the other foot on the 1 a Clock Circle , and mark this distance in the blind Circle from I towards the left hand , to wit from I to k , and it will give you a point or mark for your 1 a Clock hour line , and from I to h towards your right hand the mark for your 11 a Clock hour Line . In the next place take in the said Horizon the distance between the 1 and 2 a Clock Circles , and place it from k onwards to l for a mark for your 2 a Clock Line , and from h to g for the 10 a Clock line , and so on till you come to r , 8 at night , and to a , 4 in the morning , which are the latest and earliest Summer hours . If then you would have a larger Dial describe a larger Circle , suppose , NESW ; or if a lesser Dial , a lesser Circle , as MPQR , and laying your Ruler on the Center O , and on each of the former Marks or Letters in the said blind Circle successively , draw but a fair line to the designed Limb or Border ( whether it be a Circle ; or the square VXYZ or any other Figure , ) and your Dial wants nothing bdt a Cock ; but remember that you need not draw your hour lines quite from the Center O , because meeting all there , they will be apt to blur ; therefore describe about the said Center , at what distance you please , a little Circle ( like γ ♌ λ ) and your lines will terminate there with more neatness and convenience . Now if you have a mind to put on half hours and quarters , you will not much err if you divide each hour into four parts , but to be exact you must make use of your String , thus . You know that the distance between each hour-Circle in the Aequator is 15 Degrees , Draw therefore your String from the Pole throu ' the Aequator of your Globe , over 7 degrees and 30 minutes , ( or half the distance between each Hour Circle ) and where the String cuts the Horizon there will be the true half Hour of that Hour ; so that if you mark with your Compasses the said distance on the blind Circle , between the corresponding hour lines , the Ruler ( passing throu ' that Mark and Center ) will give you in the Border the place of that half hour ; and in like manner you are to proceed in marking out the rest , as also the Quarters , and all other Subdivisions . As for the Stile or Cock of this Dial , it must always at the Center make an Angle with the Meridian or 12 a Clock Line ( OI ) equal to the Distance between the Pole and the nearest part of the Horizon of the Globe ; that is to say an Angle equal to the Elevation or Latitude of the Place ; therefore your Dial being made ( suppose ) for London , open your Compasses at the aforesaid distance , or at 51 Degrees and ½ , and placing one foot on I , the other will fall on K in the said blind Circle ; so that drawing the blind line OK to π , you will have the Triangle IO π , which if you so erect , that the Point O lyes just on the Center , and the Base IO on your 12 a Clock line ( or Substile ) your Dial is finish'd . And here you may take notice , that tho' this Stile be the Triangle IO π , yet you may fashion it into what shape you please , in case the side π O ( which indicates or shows the Hour ) makes still an Angle of 51 Degrees and 1 / 2 with the Meridian IO ; nay , you may make it a Pin or upright Stile , as appears by the Perpendiculars AB , GH and π I , for either of them will serve the turn by marking the hour with the shade of its Apex or Top : but then they must not be plac'd in the Center O , but thereon the Substilar , where ( falling from the Indicating side O π ) they stand Perpendicular to it ; that is to say , the Pin AB ( being part of the Triangle or Stile IO π ) must be erected at B , the Pin GH at H , and π I at I ; and the reason , why they perform this Office , as well as the whole Triangle IO π is , because their Tops are parts of the Line O π , which is the only side of the said Triangle , that shows the Hour , as we mention'd before . Now for the Demonstration of all , it follows in the next Operation . OPERATION II. How to describe an Horizontal Dial by the Globe for the Elevation of London . The second way . DEscribe a Circle of what bigness you please , and draw a Meridian , or 12 a Clock line throu ' it , as before ; then count in the Horizon of your Globe how many Degrees there are between the Hour-Circles of 12 and 1 , or , ( which is the same thing ) between 12 and 11 , and you will find their number to be about 11. 40′ . These place on both sides of your said Meridian Line by the help of a Quadrant , or Line of Chords , and they 'l give you ( if you lay your Ruler as before on the Center ) the 11 and 1′ a Clock Hour Lines of your Dial , to wit , the distance from I to k , and from I to h , as may be seen in the aforesaid third Scheme . Proceed then in this manner as to the rest of the Hour lines , and for your Stile and Substilar , the former Directions are sufficient . The Demonstration or Reason why these Dials show the Hour is not difficult ; for if : you consider your Globe , you will see that all its . Hour Circles are equally distant from each other , and that the Axis of the World ( of which the two Poles are the extremities ) lies in the middle of them , and is in truth a part of each , as being the common Section of them all ; therefore when the Sun comes into the Plane of any Hour Circle ( for example to that of 4 in the morning ) the shade of that Hour-Circle will fall there , where the said Hour Circle cuts the Horizon on the Opposite or Western side , and consequently the Axis being in that Plane , as a part of it , its Shade must needs fall there also . Now since the Blind Circle or Limb of the Dial described is a Circle representing the Horizon , and having by Construction its Hour-lines distant from each other as the Hour Circles of the Globe or World are distant in their Horizons , and since the Hour-lines of This ( and consequently of all other Dials ) are only the intersections of the Hour-Circles with their respective Planes , it must needs follow , if we place in the middle of the said Dial a Cock or Stile , making an Angle of 51 , 30 , with its Meridian line or Substilar ( to wit , the Angle which the Axis of the World makes with the intersection of the Meridian and Plane of the Horizon ) 't will cast a Shade directly on the Hour line corresponding to the Hour Circle in whose Plane the Sun then lies , in case the Meridian or 12 a Clock line of the Dial be plac't North and South , like the Meridian of the Globe when compos'd ; for the Globe it self without it be compos'd will not ( as we have formerly mention'd ) shew the Hour , because its Hour-Circles do not then correspond with the Heavenly ones . And as for the reason why the 12 a Clock line is the Substilar , 't is because the true Height of the Axis above the Plane ( which the Stile or Cock , as I showd you , represents ) is to be measured in the Hour Circle that falls on the Plane at right Angles , which being the Meridian or ordinary 12 a Clock Hour Circle , it follows that its Intersection with the Plane must be the Substilar , or Line with which the Stile is to make the Angle of the Elevation . All that we have then said of this Dial may be clearly seen by Sch. 5. which represents your Globe cut into an Horizontal Plane , with its Dial on it , as Sch. 4. does the Globe entire , when you consider it in the description of the said Dial ; for there you have before your eyes ( by the Letters I k , l , &c. ) not only how to open your Compasses from Hour-Circle to Hour Circle for the true placing the Distances of each Hour-Line on your blind Circle , but also the number of Degrees in the Horizon between every Hour Circle and the Meridian . Besides , by the Horizons oblique cutting the Hour Circles , you may see how that ( notwithstanding the equality of the Suns Horary motion ) the Hour-lines of this Dial must be unequal , and consequently that they are of different distances in different Latitudes . OPERATION III. To describe an Horizontal Dial Geometrically , for the Elevation of London . Describe a fair Circle as ABCD , and if you would have your Dial of another Shape , you may afterwards describe about it what Figure you please ; I say , describe the fair Circle ABCD , and draw throu ' its Center O the Line AOC for your Meridian or 12 a Clock hour line , and crossing it at right angles with BD for the Morning and Evening 6 a Clock hour lines , mark in it ( by the help of your Line of Sines or any way else ) from A the value of 51. 30. or Latitude of your dwelling , which happening to reach , ( for example sake ) to K , draw the blind line OK ; then throu ' any point of AO ( suppose A ) draw GH , another blind line , parallel to BD , or at right Angles with the said AO , and taking with your Compasses the nearest distance between A and OK , which being ( suppose ) the point L , let AL , by the help of your Sector ( according to our former * directions , ) be the Radius to the Tangent Line GH , so that marking in it on both sides of A , the Tangents of 15 , 30 , 45 , 60 , and 75 Degrees , the said Center O and the point 15 will give you the Hour-lines of 1 and 11 , the Center O and 30 , those of 2 and 10 , and in this manner proceed to 75 , which will give you the Hour-lines of 5 and 7 ; and as for those beyond the 6 a Clock lines , do but produce 8 in the Morning , and 't will give you 8 at Night , and 7 in the Morning 7 at Night , as will 4 and 5 in the Evening , the like forenoon Hours . Thus then you have not only an Horizontal Dial Geometrically described , almost as soon as the former , ( and this without embroyling the Plane with multiplicity of blind Circles and Lines ) but a way also ( in case you have no Sector ) how to make any Tangent Line serve your turn ; for , 't is but taking between the Compasses 45 Degrees of it ( i. e. a distance equal to its Radius ) and finding out ( by a trial or two ) the Point ( suppose ) R in the line OA , where one foot of your Compasses being placed , the other just touches M ( the suppos'd nearest point or distance in OK from the said R ) draw throu ' R a line at right Angles with the Meridian , and noting in it , as we show'd you before , the Degrees of each hour ( according to this new Tangent line ) the Center O and these Degrees will give you the points of each hour line ; for as the former Radius AL was to the several Degrees in its Tangent Line , so will the now Radius RM be to the several Degrees in its Tangent Line . As for the Demonstration or Reason of this Dial , every body that understands Gnomonics comprehends it , I doubt not , at the first sight ; for the Angle O in the Triangle KOA , being by construction equal to the Elevation , do but place the Base AO on a Meridian Line , and if you consider the Side KO as the Indicating Side of the Stile or Cock , it necessarily follows , that it will represent the Axis of the World ; for it is evident that its Top K will point directly to the Pole , and touch it , if produc'd , whilst O its other extremity passes throu ' the Center of the Horizontal Plane ; therefore if a Circle ( whose Radius is AL ) were so plac't on this Stile or Axis , that its Diameter crost it at right Angles at L , the said Circle would represent Circulum maximum semper apparentium , for that Circle in the Heavens ever touches the Horizon , as this would do at A. This Circle then being parallel to the Aequator , is divided by the Hour Circles into twenty four equal parts , and consequently each fifteen Degrees in its Tangent Line GH , will correspond with its said equal parts or Divisions . Now GH is also the Tangent Line of the Horizon , as touching it in the Point A , but where the Hour Circles cut the Horizon , or its Tangent line , there the Points will be , to which ( from the Center ) the Hour Lines in an Horizontal Dial are to be drawn ; ergo O the Center of your Horizontal Plane , and the several fifteen Degrees in the common Tangent GH are the true points of the Hour Lines . Besides as the distance ▪ between each Hour Line ( if AL , be the Radius ) is 15 Degrees , so if AO be Radius ( I mean OA the Radius of the Horizontal Plane ) the said Hour Lines will be distant as many Degrees asunder , as they are in the Horizon of the World , or as you found them in the Fabrick of the second Horizontal Dial by the Globe . Here also you may see , that the true place of this Dial is to be in the Center of the Earth , and not on its superficies , but by reason of the Suns vast distance , the Error , which thereby happens ) is not sensible ; nay , because the Error is not sensible , we may safely conclude , that the Sun is vastly distant from us . So much then for Horizontal Dials , since there now remains nothing necessary to be known , but how to find whether they stand Level or no ( which is handled in the first * Section ) and how to draw a Meridian Line for their true placing , which is learnt by the following Operation . But before we go further let me advise you ( whensoever you make a Dial of consequence , of what kind soever it be ) to describe it first on Paper , and thence to mark out the Lines on your real Plane , for thereby you will not only keep your said Plane neat , and more judiciously chuse the best place for the Center of your Dial , but ( besides the several conveniences which practice will show you ) the Lines themselves will be more exactly drawn , by reason you can manage your Paper draught as you please . OPERATION . IV. How to draw a true meridian Line on any Horizontal Plane . * COmpose your Globe on the Plane , or Place where your Dial is to stand , and making marks or pricks there ( on each side of the Pedestal ) at the Letters S and N , draw but a Line throu ' those marks , and that will be a true Meridian Line , and if you do the like under the Letters E and W , you will have a true East and West Line . OPERATION . V. How to Describe a Vertical , or an Erect Direct South Dial by your Globe for the Elevation of London . The first way . THIS Dial is made on the Plane of the Primary Vertical , which passes from the Zenith to the Nadir throu the East West points , and being therefore erect , and facing also directly the South , t is commonly called an Erect Direct South Dial ; so that if you draw but your String from the Zenith to the Nadir thro either of the Intersections of the Horizon with the Equator , 't will appear upon the Superficies of the Globe , like the emerging edge of a thin Plate , and consequently represent the said Plane , or at least as much of it as is requisite . This being don't open your Compasses at 60 Degrees , as * before , and describe on a sheet of paper the blind Semi-Circle I PC ( as in 〈◊〉 10 ) with the Diamiter or Meridian IOT throu ' it , then take with your Compasses the distance between the Zenith of your Globe , and the Intersection of your String with the nearest Hour Circle , and 't will in your Blind Circle on both sides of the Meridian or twelve a Clock Line , ( to wit from I to k , and I to h ) give you marks , by which you may draw from the Center O the Hour Lines of 1 and 11 ; as will the distance from k to l , and h to g ( viz. the distance from the said first Intersection to the second ) the marks of 2 and 10 ; and in this manner you must proceed to 6 and 6 , as the latest and earliest hours , that this kind of Dial shows ; for since its Sides lye full East and West , and that the Sun never comes to the East before 6 in the morning , nor is later in the West than 6 at night , 't is impossible that the Plane should significantly contain more Hour-Lines . And as for the Stile or Cock ▪ the distance on your Globe between the Zenith and the Pole ( being the Complement of the Elevation ) gives you from I to K the Degrees of its height above the Plane , so that you may easily place and erect it , the Substile being still the Meridian . The Rules in the first Horizontal Dial will show you also both how to contract and enlarge it , and how to resolve ( especially if you consult the 7th . 8th . and 10th . Schemes ) any difficulty that can possibly arise in the present Operation ; for Scheme the 7th . shows you the Globe it self with the String drawn from the Zenith to the Nadir throu ' the East Intersection of the Aequator with the Horizon ; and Scheme the 8th . the Globe cut into this Plane by the said String , and lastly the lower part of Scheme the 10th . ( to wit , the Semi-Circle PIC ) the Dial described by the foregoing Directions . Now for the Demonstration it follows in the 8th . Operation . OPERATION VI. How to make this Vertical South Dial by the Globe for the Elvation of London . The second Way . DEscribe a Blinde Circle of what bigness you please with a Diameter throu ' it , and placing your String on the East or West Poynt of the Globe as before , measure ( by your Bead or Compasses in any great Circle ) the distance between the Zenith and each Intersection of the said String with the Hour Circles , and you will have the Degrees of every Hour from 12 a Clock , as the before mentioned Seventh Scheme shows you ; so that by the help of your Sector ( or of any Line of Chords or Quadrant ) you may mark them successively in your Blind Circle on both sides of the Diameter , and then if you draw from the Center Lines throu ' those marks , your Dial is finish't ; for as to the Stile and Substilar , you need no other Instruction than what you had in the last Operation , which also directs you to the Demonstration , since the same serves both . OPERATION . VII . How to draw a Line Parallel to the Horizon ; together with two ways how to place truly all paper Draughts on their respective Plane . HAving lately advised you To Delineate all Dials on * Paper , before you draw them on your designed Plane , and having show'd you how to describe this Dial , 't is now time to teach you how to draw an Horizontal Line on this Plane , that you may thereby truly place your Draughts . Slip therefore out your two Rulers , which are under the the Pedestal ( as I already mentioned ) and placing the end of one on a convenient Center ▪ ( chosen by you ) in your Plane , you 'l have by the end of the other ( when the Plummet falls on the Asterisk or little Star ) a cond Point , and consequently marks to draw the required line by ; so that if you then place the Center of your said Draught on the Center of the Plane , and its 6 a Clock Hour Line on your Horizontal Line , all the other Lines will fall on their true places , and thereby show you where ( with a Cole or the like ) to mark out points for the perfect and final drawing of them . The Cock also of the Paper Dial , will direct you in the placing of the other ; for they are both to be of the same height above their respective Planes , with their Tops pointing the same way ; viz. downwards to the Horizon in all these South Dials . But if you will have yet a more easy way of placing a Paper Draught not only on this , but on any Plane for which 't is made , look what a Clock 't is by your Globe , and moving your said Draught on its Plane 'till it shows exactly the true Hour , do but fix it there , and you may mark out the Points for your fair Lines with all the ease imaginable . OPERATION . VIII . How to make a Vertical or Erect Direct North Dial for the Elevation of London . THERE is no difference between the Fabrick of this Dial and the former , unless it be in figuring it ; for a South Dial reverst is a North Dial , the After-noon Hour Lines being mark't with the Morning Figures , and the Morning ones with those of the Afternoon ; So that the Top of the Stile points now upwards , as may be seen by Scheme 9th , and by the upper part of Scheme 10th . to wit , by the Semi Circle PTC ; therefore when you chuse a Center in your design'd or real Plane for this Dial , let it be in the lower part of it to have Room for the Hour Lines to run upwards . And by the way you must here remember , that tho' I bad you in the making of this your Vretical South Dial , to take the distance between the Zenith and the Intersection of the String with the next Hour Circle for the 1 and 11 a Clock Hour Lines , &c , yet that Section of your Globe by your String from the Zenith as aforesaid , gives in truth a North Dial , and therefore in strictness you ought to have taken the Distance between the Nadir and the several Intersections of the Plane with the Hour-Circles ; but since both Dials are ( as I told you ) alike , 't is best always to operate thus from the Zenith , as being more at hand than the Nadir , and consequently more convenient . The Demonstration or reason why these Dials show the Hour , differs even at first Conception but little , and at the second not at all from that already given for the Horizontal Dial. By the first Conception I mean our considering these Planes as Vertical and Erect ; for since , the Hour-lines of all Dials are ( as I show'd you in the former Demonstration ) the Intersections only of the respective Hour-Circles with the Planes , and since the hourly indicating Shade , is the Shade of the Axis or of the Hour-Circle , which then lies in the Plane of the Sun , it must follow , that the Mark made ( for example sake ) by the 4 a Clock Morning Hour Circle on the String , and the Center of the said Plane ( which is the common passage of all the Hour-Circles ) will be two true Marks or Points for you to draw that hour-Line by , and consequently that the Shade of the Axis will still fall on the said hour-line as often as the Sun comes into the Plane of that Hour-Circle . Now your blind Circle is ( by construction ) equal to the Circle made by the String on the Globe , and the Marks on its Limb are equal to the Marks on the said String , therefore the Dial must be truly drawn , and the Stile plac't on the 12 a Clock line ( to wit on the intersection of that Hour-Circle , which falls on the Plane at right Angles ) must truly cast its shade from time to time , seeing by its Site and Angle it corresponds with the Axis of the World. As for our second Conception in reference to these Dials , we shall find by it that their Planes are real Horizontal ones to some People or other ; for this Section of the Globe being a great Circle will be the Horizon to those that live in the Pole of it , viz. to those under our Meridian 90 Degrees from our Zenith , which being a point in our Horizon , makes their Horizontal Dials always our Direct Vertical ones , and their Direct Vertical Dials our Horizontal ones . 'T is plain then , that the present Dials are exactly describ'd , if our former Directions and Proof of an Horizontal one be true ; for all the Hour Lines are here drawn from the Center to the several intersections of the Hour-Circles and Horizon , which ( as we are to suppose ) the String represents . Nor do's the Cock of these Dials differ from the former Rules ; for having the Meridian or 12 a Clock line for Substilar for the former reason , and being 38 Degrees and a half above it , it makes an Angle equal to the Elevation of the People , who have the said Plane for Horizon . OPERATION IX . To make the aforesaid North and South Dials Geometrically , for the Elevation of London . THere is no need of a Scheme for this Operation , since 't is a Corollary from what we have now said ; for make but an Horizontal Dial Geometrically ( as we formerly show'd you in Scheme the 6th ) according to the Complement of the Elevation of your Place , and that will serve ( the figuring only consider'd ) for either Dial. Here then you may see that OS , or ON the Basis or Foot of the Stile of these Dials , ( that is to say , the distance between its Center and its Horizontal edge or side ) is ever the Tangent of the Elevation ; for 't is the Tangent Complement of FS or NR the Stiles height above the Plane . And here also you see that the very same Dial ( the figures only transpos'd ) will serve both for an Horizontal and this Direct Vertical one to those that live in the Latitude of 45 Degrees , since the Elevation of the Pole and Complement of it is there the same . OPERATION X. To describe by the Globe , Meridian Dials , or ( as others call them ) East or West Dials for the Elevation of London . THese Dials tho' Vertical and Direct ( as passing thro' our Zenith , and facing also two Cardinal Points or Quarters of the World ) are very different from the former , nor has any body ( I believe ) taught yet their Description by the Globe . To perform therefore this Operation , you must by the help of your String or Compasses describe on your Globe , with Chalk ( or the like matter ) an Arch ( as in Sch. 11. ) which having its Pole at K ( the East-point , for examples sake , of the Aequinoctial ) cuts somewhere or other the 11 a Clock Northern hour Circle , I mean the 11 a Clock hour Circle on the Northern , or black part of the Globe ; and this Arch by reaching from the point C in the Aequinoctial Colure ( or 6 a Clock Circle ) to H in the Horizon on the said Northern side of the Globe , will be a piece of a little Circle parallel to the Meridian containing the Degrees of the Elevation of the Pole , and cutting all the Hour-Circles also from 6 to 11. But if this be thought too troublesom a work , the Globe-maker may avoid it by putting 6 Pricks or Asterisks upon the Globe , where the said Arch and Hour-Circles would intersect , as may be seen in the said 11 Scheme at C , O , S , T , V and Z ; so that if beyond C he adds one prick more , viz. at R , to give you from H the Radius , or 60 Degrees of the said Arch , you need nothing else . This being premis'd , describe on a sheet of paper ( HR , or 60 degrees of the said Arch being Radius ) a blind Circle as in Sch. 12 , and drawing the Line H h how you please throu ' K its Center to represent the intersection of the Horizon , open your Compasses to the said Arches full extent , to wit , from H to C , and putting one foot on the blind Circle at H , and the other marking there at C , draw the line PC π , throu ' the Center K , and 't will represent the intersection of the Aequinoctial Colure ( or 6 a Clock hour Circle ) with your said blind Circle or Plane ; so that if you take from off your Globe , the distances between the point C , and the several Intersections of the Hour Circles with the said Arch CH , and place them on your blind Circle on the right hand side of PC π , as well below the Horizon H h , as above it , and draw lines thro' them ( viz. O ο , S σ , T τ , V υ , and Z ζ ) you will have a compleat East Dial describ'd , after you have drawn 2 lines more on the left side of the said C π , to wit , the Line N ν distant from it as is O ο , and the Line M μ , as is S σ. As for the figuring each hour line , it must be according to the Figures of the corresponding Hour-Circles cut by the aforesaid Arch CH , and thus you will find them figured in the forementioned Scheme 12 , which shews you too how the Borders or Parallels are drawn for the said Figures to lye in , as being only double Lines ( equidistant at pleasure ) on both sides of the Horizon H h ; and here also by the blind Lines , and by the fair ones , you have before your Eyes what is necessary to be exprest on your fair Plane , and what not . Nor is there any difference in the Construction of a West-Dial , except it be in turning on your draught the Hour-Lines or Parallels the other way , to the end they may all point Northwards on their respective Planes ; for thus ( in Sch. 11. ) do the Prick Lines ( m 8 , n 7 , c 6 , o 5 , s 4 , t 3 , u 2 and z 1. ) which would truly represent this Dial , if they were produced in the said Scheme . Now for the Substilar 't is the 6 a Clock Hour Line , since that Hour Circle falls on the Plane at right Angles , and as for the Cock it may be a Gallows Stile ( as in Scheme 13 ) or a Pin ( as in Scheme 14 ) so it be plac't on the Substilar and perpendicular to it , having its height equal to the Distance between the Pricks or Asterisks C and P in the said 11 Scheme , or ( which is all one ) to the distance between K and X. viz. the nearest distance between the Substilar , and the 9 a Clock hour line in an East-Dial , and the Substilar and the 3 a Clock Line in a West Dial. But here you are to remember , that when I say , that the height of the Stile is to be equal to the distance between C and P. I mean in rigour equal to the Sine , and not the Chord of that Arch ; but seeing the Chord of 10 Degrees , differs not sensibly from the Sine ( and by the way the Arch CP on the Globe will not be above 10 Degrees from the Meridian , ) the interval between C and P will serve the Turn . But if you would be more exact take between your Compasses the distance of double CP , to wit the interval of ( suppose ) 20 degrees , and half of it is the required distance ; for half the Chord of 20 Deg. is equal to the Sine of 10. Or if you , please you may erect a needle at C Paralel to P ( the elevated Pole of the Globe ) and the distance between them will be the true Height of your Stile . To Conclude , You may contract and enlarge these Dials as you please , by drawing the hour-lines twice or thrice ( or according to any other proportion ) nearer or farther asunder , and so abateing or heightning in the like manner your Stile . The Demonstration is obvious , for since the points M , N , C , O , S , T , V and Z in the upper part of the blindCircle or Plane , and the Points μ , ν , π , ο , σ , τ , ● , ζ , on the lower part of it are ( by being equal in distance to those on the Arch ) the intersections of the morning hour Circles of 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 ▪ with the edges of the said Plane , it follows that the Lines drawn from the corresponding Points , must be the true hour lines of this Dial , since the hour Lines ( as we said ) of all Dials , are only the Intersections of the respective hour Circles with the Plane . Again the shade of the Axis ( the Axis being a part of all the hour Circles ) falls ever on the Hour-Line or Interfection of this or that Hour Circle , as often as the Sun comes into the Plane of that Hour-Circle , therefore the Stile of this Dial representing truly the Axis ▪ ( since 't is above the Plane , and distant from it as 't is on the Globe ) will cast its Shade every hour on the corresponding hour Line ▪ and as for the reason , why the height of the said Axis is equal to the distance between the 3 or 9 a Clock Lines and the Substilar , it shall be shown in the Demonstration of the next Operation . OPERATION XII . How to describe an East or West Dial Geometrically for the Elevation of London . DRAW the blind Line H h and cross it from your left hand ( as in Sch. 13. ) with AE ae another blind-line to make an Angle at their Intersection K equal to the Complement of the Elevation , then pricking in the said Line AE ae on the right side of K , the respective Tangents of 15. 30 45. 60. and 75 Degrees , as also on the left the Tangents of 15 and 30 , Draw but Perpendiculars through the Pricks , and you have an East-Dial ; whereas should you cross ( as in Sch. 14. ) H h with AE ae from the right hand , and pricking the aforesaid Tangents the other way , draw Perpendiculars through them , you would have a West-Dial . By these Schemes also you may know how each Dial is to be Figur'd , the East-Dial containing ( as you see ) all the hours from 4 in the morning 'till Noon : and the West all the hours from Noon to 8 at Night . Now for their Cocks , they are ( as I said , in the last Operation ) to be a Pin , or a Gallowes Stile , and in height equal to the Tangent of 45. Degrees , or distance between the 9 or 3 a Clock hour Lines and that of six , which is ever their Substilar . These Dials must be true , if their Planes lye in or Parallel to the Meridian ; for since the Line H h , by being plac'd according to our Hypothesis horizontal , represents the intersection of the Horizon , and the line AE ae that of the Aequator , by making an Angle with the said H h equal to the complement of the Elevation , the substilar must be the Intersection of the Aequinoctial Colure ( or 6 a Clock hour Circle ) with the Plane , since that Hour-Circle falls on the Plane at right Angles . If then a Gallows Stile be set on the said Substilar and Perpendicular to it , its Shade must needs constantly cross the Aequator AE ae at right Angles . Now when the Sun is in the Plane of the 6 a clock hour Circle , his Ray makes no Angle with the said Stile , because the Sun , and the Stile are in the same Plane , and so the shade falls directly along the Substilar ; but when he gets ( for examples sake ) into the next hour Circle , his Ray ( the height of the Stile being Radius ) makes an Angle of 15 Degrees with the said Stile , and consequently the distance of the two shades are in the line AE a the Tangent of those Degrees . The like therefore being said of the next Hour Circle and so on , it follows ( as I mention'd in the beginning ) that the pricking from the intersection K , the Tangents of 15 , 30 , 45 , 60 and 75 Degrees in the line AE ae , must give you points to draw the perpendiculars or true hour-lines of this Dial by , as also , that the Tangent of 45 Degrees gives the height of the Stile , since the Tangent of those Degrees , ( which you see gives the 3 and 9 a clock lines ) is equal to the Radius . Here also we see not only why these hour-lines are so unequally distant , since they are so many Parallels marshall'd according to the Divisions of a Tangent line , but why the 12 a Clock hour line can never be really express'd , for 't is the Tangent of 90 Degrees which is infinite . OPERATION XIII . How to describe a Declining Dial by the Globe for the Elevation of London . The first Way . THIS Plane ( as passing from the Zenith to the Nadir ) is still Vertical , and should ( you may suppose ) be by right the primary Vertical , but by its tendency towards the East or West Points , its Dial takes the Appellation of a Declining one , that is to say , of a Dial , whose Plane declines so many degrees from facing directly the North and South , as is its tendency towards the said East or West points . As for the way of making this Dial it differs little from the first Direct Erect one , already * treated of ; for supposing your present given Plane declines 40 Degrees from full South towards the East , you must draw your String ( which ever represents the Edges , as we have said , of your Plane ) not throu ' the East Point of the Horizon of your Globe , as before , but throu ' 40 Degrees further towards the North , for this makes the String to represent part of a Plane that comes nearer ( by so many Degrees ) the facing of the East than it did . Then opening your Compasses at 60 Degrees in any of the great Circles , and describing ( as in Sch. 17th . ) the blind one PZW , prick in it from its Meridian Line OZ , the distance between the Zenith of your Globe and the intersection of your String with the first Hour-Circle ( to wit between Z and b in Sch. 15. ) and it will give you a mark for the 11 a Clock line on your Dial ; and the distance between the Zenith and the Intersection of your String with the next Hour-Circle ( to wit between Z and c ) will give you the mark of the 10 a Clock line , and thus you must proceed to every Hour-Circle cut thus by your String , till it falls on the Horizon , that is to say from z to d , e , f , g , h , letters marking ( as you see in the said Scheme ) the 9 , 8 , 7 , 6 , 5 and 4 a Clock Hour Circles ▪ and consequently giving you those Hour-lines on your Dial. Now for the Afternoon hour lines ( which are no longer equal in distance to the Morning ones , ) you have nothing to do but to draw your String , on the West-side of your Globe , throu ' 40 Degrees in the Horizon the contrary way ( viz. from the West towards the South ) and the distance between the Zenith and the Point in the first Hour-Circle cut by your String ( to wit from Z to k in Sch. 16. ) will give you the mark for 1 a Clock , and the distance from thence to the next Point or Intersection gives you that of 2 , to wit , from Z to l , and in this Order you are to proceed to n , the ▪ 4 a Clock Hour Circle , that is to say , till you come to the intersection of the String with the Horizon on the West-side of your Globe . As for your Stile and Substilar they differ also from those of direct North and South Dials ; for the said Stile or Cock is to be no longer plac'd on the 12 à Clock Line , nor will its height now be equal to the Complement of your Elevation , therefore having drawn your String throu ' the Degrees of Declension in the Horizon as before , and putting one foot of your Compasses in the North Pole , find with the other the nearest Point on your String , to wit S ( as in Sch. 15. ) and the distance between S the said nearest Point and the Zenith of your Globe will be ZS in the blind Circle of Scheme the 17th , to wit the distance between the Meridian Line of your Dial and your Substilar , which in this our Example lyes from the Moridian towards your left hand or Morning hours , and the distance from the said Point in the String to the Pole ( being from S to P ) will in the said blind Circle be the height of your Stile ; so that if you erect and place your said Stile from the Center all along the Substilar OS it will continually show you the Hour . But if you fancy that the Extension of your Compasses from the Pole to the String will not give you precisely this Point , since your said Compasses may seem to touch it in several Points ; I say , if you doubt or fancy this , fasten a Thred on the Pole , and drawing it streight over the Horizon at 40 Degrees from the Meridian of your Globe Eastwardly ( i. e. till it passes thron ' the Pole of the Plane ) see where the said Thred crosses your String ( or edge of the Plane ) and there the true requir'd Point will be . The Demonstration of this Dial is in the following Operation . OPERATION XIV . How to describe by the Globe a Declining Dial for the Elevation of London . The second way . DRaw your String over at 40 Degrees in the Horizon from the East Northwardly , and from the West Southwardly , as before , and the respective distances between the Zenith and the Intersection of your String with the Hour-Circles will give you in any great Circle of the Globe the Degrees of their respective distances as well for the Morning as Afternoon , and the proportionable Degrees in any Circle will give you the Points for the Drawing of your Hour-lines , as I showd you in the Construction of the former Vertical North and South Dials ; and as for the Stile and Sub-stilar , you must operate as directed in the foregoing Operation , that is to say , the number of Degrees between Z and S gives you the Sub-stilar , and those from P to S the height of your Stile . As for the Demonstration or Reason why Dials thus made show the Hour , it is this ; First you see that the String , by being on one side removed 40 Degrees from the East point Northward , and on the other side 40 Degrees from the West Point Southward , represents on the Globe the requir'd Plane , and therefore wheresoever the Hour Circles cut it , there the Shade of the Axis will fall , as we show'd you before in the former Dials ; Now two Points made by the intersections of each Hour Circle with the Plane being given you ( to wit , the Center where they all meet , and their respective marks on the String , or supposed Edges of your Plane ) it must needs follow , that if you draw Lines throu ' those Points , they will be true Hour Lines ; for ( as we have often said ) the Hour-Lines of all Dials are only the intersections of the Plane with the hour Circles . In the next place , since PS by construction is the nearest distance from the Pole to your String or Plane , it appears that the Hour-circle which cuts the said Plane at S , falls on it at right Angles , and consequently that as PS ( the height of the Pole or Axis above the String or Plane ) gives the true height of the Stile of this Dial , so the intersection of the Plane with the said Hour-Circle must be the true Substilar ; for the Substilar ( as we already mention'd ) is only the intersection of the Plane with the Hour-Circle , which falls at right Angles on it ; Ergo The distance between Z and S gives in your blind Circle the distance from your 12 a Clock line to the Substilan , and PS the height of the Stile . And by the way , here it appears not only why the 12 a Clock Lines of Declining Dials continue perpendicular , but also why their Centers keep the same distance from the Horizontal Edges of their Planes , as do the Centers of the primary Vertical or direct North and South Dials ; I say , here all this appears ; for the 12 a Clock Line ( which is ever the intersection of your Meridian with these Planes ) being a Perpendicular in the primary Vertical Plane , becomes the Axis of the Horizon , and all Vertical Dia's ▪ by their Declension more only about it , so that both the Center and the said 12 a Clock Line remain the same in all ; therefore the Tangent of the Elevation , being ( as I * formerly show'd you , ) the length of the foot of the Stile , or distance between the Center of a Primary Vertical Dial and its Horizontal Edge is that of a Declining one also . But to proceed with the Demonstration ; you must remember that this Dial is an Horizontal one ( as we show'd you * before ) to those that dwell in the Pole of the Circle describ'd by the String , i. e. to those in our Horizon 40 Degrees Eastward from the Meridian , or ( which is all one ) to those that dwell where the Thred cuts the Horizon ; but all the Hour-Lines are truly drawn according to the former Rules of an * Horizontal Dial , to wit from the Center to the Points where the respective Hour Circles cut the String or Limb of the Plane , therefore it must truly shew the hour . OPERATION . XV. How to describe Geometrically a Declining Dial for the Elevation of London . The first way . THIS Dial being ( as I said ) an Horizontal one to those in our Horizon 40 Degrees Eastward from the Meridian , Find ( as we show'd you in the * Geographical or 20 Section ) what Elevation or Latitude they have , and describe Geometrically an Horizontal Dial on paper for the said Elevation . In the next place consider the difference between both Longitudes , to wit how many Hours the Sun comes sooner to their Meridian than yours , so that if he comes , suppose , 3 hours , 't will follow , that the 3 a clock hour line is to be the true 12 a clock line of this Plane , because 't is really so late with those People , when 't is but Noon with you , and consequently that their 4 will be your 1 a clock , and their 2 your 11. and in the like manner you are to mark the rest , having nothing more to do but to draw on your fair Plane a * Line Parallel to the Horizon , and to place on it at right Angles the true 3 a Clock Line , ( that is to say the 12 a clock line according to your now alteration or present figuring the Hour-Lines , ) for you will have all the requisite Marks or Points , not only to draw the other Hour Lines , but also plainly to see , where the Substilar will fall , and how high the Cock it self is to be ; for they are all to correspond with those in the said Horizontal or Paper draught . Now in case the difference of Longitude between these 2 Places happens to be a Fraction , as ( suppose ) one hour and 10 minutes , then ( if the Declination of your Plane be still Eastward as in the former example ) 10 minutes past 1 must be markt in the Horizontal Draught with the Figure 12 , as the Meridian Line , and 2 and 10 min. with Figure● . and so on all along ; whereas if the Declination were Westward , then 11 and 10 minutes will be the said Meridian Line , 10 and 10 minutes your 1 a Clock Line , for thus you must operate in all other Cases , that is to say , you must still allow by the new figures the difference of Longitude , that chances to be between you and them , to whom the Declining Plane is Horizontal . But because this manner of Dialling may seem to some troublesom and confus'd ( especially when the said Difference of Longitude happens to be a Fraction , and not even Hours ) I shall here adjoin a second Geometrical Way . OPERATION . XVI . How to describe Geometrically a Dial declining 40 Degrees Eastward , for the Elevation of London . The second way . HAving made an Horizontal Dial for this Elevation in the lower part of your Paper Plane , ( as 't is exprest by the prick lines in Scheme 18 ) and drawn from the Center A the several Hour-Lines upward as far as you think fit , and Figur'd them to show what Hour-Lines they are , chuse in AC ( the 12 a clock line ) any Point , suppose P , and draw throu ' it the blind Line GD making with the said AC an Angle of 50 Degrees or Complement of your Declension ; then erect the Perpendicular PB on the said blind line at P , and taking with your Compasses ( AP being your Radius ) the Tangent of 5● Degrees and ½ , or true Elevation of the Pole , put one foot on P , and where the other marks on the said Perpendicular ( suppose at F ) there will be the Center of your Declining Dial ; so that having bordred your Plane with fitting Parallels , to contain the standing Figures of each hour , you have nothing more to do , but to draw fair Lines from the said Center F , to your Border , throu ' the Intersections of the Line GD with the several Hour-lines of the Horizontal Dial ; that is to say , you have nothing more to do , but to draw fair Lines throu ' the Points KLMNO PQR which give the hours of 7 , 8 , 9 , 10 , 11 , 12 , 1 and 2 ; and by the way you may have as many other Morning or Evening hours as you please if you draw the said GD long enough for the other hour-lines of the Horizontal to meet with it . Nor is there more difficulty here about the Stile and Substilar than in any of the former Dials ; for ( AP being Radius ) 't is but taking the Sine of 40 Degrees ( or Declination of the Plane ) with your Compasses from the Sector , and putting one foot on your 12 a clock Line at P , the other foot will in the line GD ( to wit , at M ) give you the Point for to draw the Substilar FM , and the Sine Complement of the Declension , or Sine of 50 Degrees , will be XM the Stiles height . Nay , if ( for want of a Sector or the like ) you cannot conveniently find the Sine of the said Declension , do but observe where a Perpendicular from A falls on GD suppose at M , and PM will be the distance in the said GD between the 12 a Clock line of this Dial and its Substilar , and AM ( equal to XM ) the height of the Stile above it . Thus then we see that the Fabrique of a Declining Dial ( which is wont to terrify young Students ) is in a manner as quick and easy as that of the Horizontal , since two ordinary Lines more , viz. GD and BP give us all the Points necessary for its Description . The Demonstration and Reason of this Dial is evident ; for , the Horizontal being by construction true , any Erect Plane facing the South , that crosses its Meridian ( or 12 a clock line AC ) at right Angle● will represent a Primary Vertical or Direct South Plane , and then the Center of the Dial described on it will be distant from P the intersection of the two Planes on the said AC ) the Tangent of the Elevation , as I shew'd you * before . Now since GD is ( by Hypothesis ) the Edge of a Vertical Declining Plane , and since ( as we show'd you in the before cited place ) that the 12 a Clock line , as well in a Declining as in a Primary Vertical Dial , is Perpendicular to the Horizon , containing in it the Centers of the said Dials , it follows that FP ( being the Tangent of the Elevation , and Perpendicular also to the said DG where it cuts the 12 a Clock line of the Horizontal ) must be the 12 a Clock line , and F the Center of our present Dial , whose Declension is 40 Degrees Eastward , since FP declines so many Degrees from CP toward the morning Hours ; for the said CP and FP represent the 12 a Clock lines of a Direct , and of our thus Declining Vertical Plane , if you consider them flatted down , and lying in the Horizon . This being so , 't is evident that the Lines drawn from F to KLMN , &c. are the true Hour lines of our Dial , as falling from its Center to the several Points made on its Horizontal edge , by the Hour Circles or ( which is all one ) by their Intersections with the Horizontal Dial. As for the Stile and Substilar , let us but consider the Triangle AMP , and we shall find that P is by construction the Angle of 50 Degrees , and A that of 40 , as substended by the Sine of the Declension , so that A being a right Angle , AM must be a perpendicular ; therefore the Hour Circle , whose intersection the said AM happens to be , falls at right Angles on our present Plane , and consequently gives the Substilar ; Now since the Axis of the World passes through F and A , the Centers of the two Dials , when they are joyned ( as we now suppose them ) at GD the common Section of their Planes ; I say , since the Axis passes throu ' their Centers , its Elevation or Height above our Plane must be AM , as being the only Perpendicular that can fall from it upon the said Plane , and consequently its Measure ; but AM you see is the Sine Complement of 40 , since PM is the Sine of 40 , Therefore in all Declining Dials , The Sine of the Declension ( from their 12 a Clock Line ) gives in their Horizontal Edge their Substilar , and the Sine Complement their Stile . Q. E. D. OPERATION XVII . To take the Declension of a Plane . COmpose your Globe and find exactly the Azimuth , i. e. what Degree of the Horizon is cut by the String 's shade , when it passes throu ' the Zenith and Nadir , which wee 'l suppose to be the 50th from the South towards the West ; then having slipt out ( to an equal length ) the two Rulers from under your Pedestal , Hold your Globe level , and apply the said Rulers , as soon as you can , to your Plane , ( as you did when you drew an * Horizontal Line ) and find again the Azimuth , which now being ( for example ) 90 Degrees shows your Plane declines 40 towards the East , because , the Azimuth being now increast so many Degrees , the Meridian ( which by the help of the said Rulers was perpendicular to your Wall or Plane ) is turned thereby from true South ( as formerly it stood ) towards the East the above-mentioned number of 90 Degrees ; but had the shade fallen on the 10th . Degree , your Plane would ( for the same Reason ) have declin'd 40 Degrees towards the West . In short therefore , the difference of these two Azimuths is the thing that resolves the Question ; for when they are equal there is no Declension at all . Of Reclining Dials . THE Horizontal Plane lay open ( we saw ) to the whole Hemisphere , whilst each Vertical one enjoy'd but half of it ; for , by being Vertical , a moiety of the said Hemisphere is before , and the other behind it . Now the Reclining Plane ( which is exprest by Sch. 29. ) instead of being perpendicular to the Horizon bends towards it , yet so , that its bending has nothing in it of overwhelming or tendency towards those , that behold it ( as it happens to Inclining Planes exprest by * Scheme 30 ) but still receeds , according to the Degrees of its Reclination , farther * and farther from them , making thereby an obtuse Angle with the Horizon , and consequently faces more than half the apparent Heavens , as the Inclining one does less , whose Angle is therefore ever Acute . As for the kinds of Reclining Planes , there are ( I may say ) 4 , to wit , the Aequinoctial , the Polar , the Direct Reclining , and the Declining Reclining Plane ; for each of these appropriates to it self a particular Fabric , or way of making , and therefore we will Treat of them in Order . OPERATION XVIII . How to describe a Dial on an Aequinoctial Plane , both by the Globe , and Geometrically also . THIS Plane is represented by the Globe , when 't is Compos'd and cut ( as in Scheme 20 ) quite throu ' at the Aequinoctial , therefore open your Compasses at 60 Degrees there , and describing the Blind Circle ABCD in Scheme 21 , divide it as the Hour-Circles cut the said Aequinoctial ( in Sch. 19th . ) that is to say , divide it into 24 equal Divisions , and there will rest nothing more to be done , but to draw Lines from the Center O , through as many of those Divisions as you shall think necessary , and then to Figure them successively from Morning to Night . As for the Stile ( seeing the Axis of the World is at right Angles with any Diameter of the Aequator , and runs throu ' the Center of it ) it must needs follow that the Perpendicular Pin OP plac't in the Center of your Dial , will perform that Office ; for when it directly points to the Pole it represents the said Axis , as the divided blind Circle does the Aequinoctial , and its Divisions ; therefore since the Shade of the Axis ever falls ( according to the time of the Day ) on This or That intersection of the Hour-Circles with the Aequator , the Shade of the Pin must fall also on the corresponding Hour-line of the Dial , as being ( in the effect ) the same thing , in case the 12 a Clock Line be plac't on a Meridian line , and mounted at A ( its South side ) above the Horizon , the Complement of the Elevation of the Pole , i. e. 38 Degrees and a half for by this means your Plane , from an Horizontal one , will be perfectly that of the Aequator . Nor is it hard to mount thus the said South side of your Dial , since 't is but opening your Compasses , in any great Circle of your Globe at twice as many Degrees as is the Complement of the Elevation , to wit 77 Deg. and they will give you the true length of a Perpendicular to underprop withal the aforesaid A ▪ or Southern point of the 12 a clock line of your Dial. And the reason of it is , because AC the Diameter of your Dial being ( by Hypothesis ) equal to the Diameter of the Globe , becomes now ( C being Center of the new Arch , made by the mounting or raising the side of your Plane above the Horizon ) a Radius double to OA the former Radius . Therefore since the Chord of a double Arch is ever the Sine of the single Arch in a Circle , whose Radius is double the other , it follows that the Chord of 77 Degrees is ( in respect to the double Radius AC ) the Sine of 38 g. 30 m. and consequently will perform ( if erected Perpendicularly ) the design'd Operation . Now for the Geometrical Construction of this Dial , ( since it consists only in dividing a Circle into 24 equal parts , with a perpendicular Cock or Stile , ) there is no need of more words about it ; so that we 'l end here with a Memorandum , viz. that as the Reclining face of this Plane , shews the Hour from Spring to Autumn , so the Inclining Face , or other side of it does the same , for the remaining half year , to wit , from Autumn to the Spring . OPERATION XIX . How to describe a Polar Dial , both by the Globe , and Geometrically also . THE true Plane of this Dial is speculatively the Plane of the Aequinoctial Colure or 6 a Clock Hour-Circle , but in practice that of any Circle parallel to it , so that the Construction and Demonstration of a Dial on it , is ( mutatis mutandis ) the same with that on a Meridian Plane , of which we have already so fusely * treated . Make then by your Globe ( for example sake ) an East Dial on a Meridian Plane , according to any of the former ways , and if you alter but the Figures , that is to say , if having figur'd the Substilar instead of 6 with 12 , you mark the Morning 7 a Clock Hour line of the said East Dial with 1 , that of 5 with 11 , and so on in Order , it will be a true Polar Dial , showing you exactly the Hour , when it directly faces the South , and Reclines so , that the Apex or uppermost part of the Substiler or 12 a Clock line points just to the North Pole ; for then the back-part of the Plane makes an Angle with the Horizon equal to that of our Elevation . This Operation may be also perform'd of it self without the former consideration , since 't is but putting one foot of your Compasses on the Intersection of your Meridian or 12 a Clock hour Circle with the Aequator of your Globe ( to wit , on K in Scheme 22 ) and so describing with Chalk the Arch CAE , I mean an Arch which reaching from the said Meridian , cuts the Morning 7 a Clock , or if ( you please ) the Evening 5 a Clock Hour Circle somewhere or other ; for then if you draw a blind Circle ( as in Sch. 23. ) of the same bigness , and take the several distancces between the Pricks or intersections of the Hour-Circles with the said Arch , to wit , the distances between C and O , C and S , &c. and place them on the blind circle , on both sides of PCK π the Substilar or 12 a clock line , as well below the line AE ae , as about it ) the lines drawn from the said Pricks will be true Hour lines , and the distance between C and P or between K and X will ( for the reasons mentioned in the Description of the Meridian Dials ) be the height of the Stile . Now to describe this Dial Geometrically , 't is yet more easily performed , for if you draw ( as in Scheme 24. ) the Line AB parallel to the Horizon , and then take a Point in the middle of it ( suppose K ) do but prick on both sides of it the Tangent of 15 , 30 , 45 , 60 , and 75 , and the several Perpendiculars drawn throu these Pricks will be true Hour-lines , which you may figure as you see in the before mention'd 24th Scheme ; and as for the Stile the Tangent of 45 , ( or distance between the 12 a Clock line , and that of 9 or 3 ) gives you its height , which is to be a Pin or Gallowes Stile as before , and the 12 a clock line the Substilar . OPERATION XX. How to describe a Direct reclining North or South Dial. SUPPOSE then that the Plane lay directly South , and that its Reclination were 20 Degrees , you have nothing to do , but either Geometrically to make on it a direct Vertical South Dial for the Elevation of 71 Degrees and ½ ( I mean for a Plane 20 Degrees neerer the Pole than your own Zenith ) or to fix your String on 71 gr . and 30 min. in your Meridian ( that is to say at A in scheme 25th . and then to draw your said string over the East or West Points of your Globe , for 't will represent this Plane , since it Reclines or falls back from the Zenith 20 degrees ; therefore the Distances between the Hour-Circles that intersect with your String , must ( for the former reasons ) give you in any blind Circle ( which shall be equal to a great one on your Globe ) marks ( viz. b , c , d , e , f , g , ) for the corresponding Hour-lines ; and the Meridian being the Substilar ( since 't is the Hour Circle that falls on the Plane at right Angles ) the Height of your Stile must ( as in all Direct Vertical Dials ) be the distance from the Pole to A , the supposed Point , or Place where your String is fixed . Now had your Plane Reclin'd 20 Degrees the other way , that is to say ▪ had it Reclin'd so many Degrees facing the North , you must have fixed your String at N , viz. 20 Degrees short of the Zenith , and consequently your said String would have intersected with the Hour Circles at o , p , q , r , s ; therefore a Direct Vertical North Dial for the Latitude of 31 g. 30 m. will be the required Dial. OPERATION . XXI . How to make a Declining Reclining Dial by the Globe . SUppose your Plane declin'd 40 Degrees Eastward ( as did the late Declining * Vertical ) and then Reclin'd 20 Degrees with a Southern Aspect , and by the way you must remember , that I mean in general by a Planes Reclining with a Southern Aspect , its looking towards that Quarter , tho' it be turned more or less from Direct South towards the East or West ; in like manner a Declining Reclining Plane with a Northern Aspect turns from direct North towards one of the aforesaid Points . Supposing then a Plane thus Reclining , Do but describe or place it on your Globe , and your Operation will be as easy as any of the former . First mount your Bead 71 Degrees and half above the Horizon , that is to say fix it to 20 Degrees from the Zenith of the Globe ; then seeing your Plane has a Southern Aspect , ( and so lies beyond your said Zenith Northward ) move your String till it cuts in the Horizon 40 Degrees Westward from the Northern Meridian , or back part of the 12 a Clock Hour Circle . In the next place take a Thred and tying it about your Globe so , that it lies not only on your Bead , but crosses also the Horizon at 40 Degrees from the East point Northward , and 40 Degrees from the West Point Southward , the said Thred will represent your Plane Reclining and Declining , as aforesaid . Or , in short fix , a small Needle in the Point where the Bead lies ( which we suppose at A in Sch. 26. ) and fastning to it a Thred or part of the string , draw it over the Horizon at 40 Degrees from the East-Point Northwards , and it will give you the Eastern or Morning side of your Plane , as it will the Western or Afternoon side ; if you draw it ( as in Scheme 27. ) over 40 Degrees of the Horizon from the West-Point Southwards . This being done , describe a blind Circle or Semi-Circle equal to a great one on your Globe , for Example sake , the blind Semi-Circle A. T. C , and drawing from ( O ) the Center the blind Line OA perpendicular to the Horizontal line H h , take the distance with your Compasses between A the station of your Needle or Bead , and the point in the 12 a clock hour Circle crost by the Thred or Edge of your Plane , and this distance from A in your blind Circle , gives you there towards your left hand the Point k , to which if you draw a fair Line from the Center it will be the 12 a clock Line of your Dial , and the distance from the said station of your Bead or Needle to the intersection of the Thred with the next Hour-Circle will give you l , the mark of the 11 a clock Line ; and in this manner you must run over all other intersections of your Thred and Hour-Circles to the very Horizon on both sides of the Globe ( I mean on the Morning and Evening side of it , represented by Scheme 26 and 27 ) and placing their distances on your blind Circle , on both sides of the aforesaid OI , do but draw lines to them from the Center , and your Dial is describ'd . And here you must observe that I have ( in Scheme 26. or Eastern Face of the Globe ) plac't A ( the Station of the Bead or Needle ) above the Meridian , since its true place cannot be exprest ; for it ought to have bin on the other side of it , I mean on the Western side , which Scheme 27 is supposed to represent . Now for the Stile and Substilar there is no difference from the Rules of the Declining Vertical , since 't is but finding the nearest point on your Thred to the Pole by your Compasses ; for the distance between the said Point on your Thred and it's intersection with the 12 a clock Hour-Circle is the distance in the blind Circle between , k and M for the Substilar and the distance between the said neerest Point and the Pole , gives MX the height of the Stile above the Plane . Nay , if you measure the Distance between each Point and A in any great Circle , * 't will give you the Degrees or Distances between A and your Stile , Substilar , and each Hour-line , and consequently performs the second way ( as we have all along mention'd ) of describing Dials by the Globe . As for the Demonstration of this Dial , what we have formerly said about the rest proves it also ; for supposing that the Thred represents truly your Plane , and that the Hour lines of a Dial , are ( as I have show'd you all along ) the several intersections of the Hour-Circles with the Plane , this Dial must be true , since all the Lines on it are the said intersections , as drawn from its Center to the Points made by the Hour-Circles on its Edges : Nor can there be any error in the Substilar or Stile , the first being the intersection of the Plane with it's true Meridian of the Plane , I mean with that Hour Circle which falls on it at right Angles , and the other being the real Height ( as you see ) of the Pole above the Plane , ergo , the whole must be true . OPERATION XXII . How to describe by the Globe a Dial Declining and Reclining as the former , with a Northward Aspect . THere is no need here of a Scheme , the Construction of this Dial being in a manner the same as the former , only now you must draw your String and Bead ( fitted to the Reclination ) the contrary way , that is to say , over the South or forepart of the Globe throu ' the 40th Degree in the Horizon East-ward from the Meridian or 12 a clock hour circle , then fixing a Needle ( as * I show'd you ) on your Globe , or else tying a thred round it so , that it crosses still your Bead ▪ and the aforesaid two Points in the Horizon , you have there the Plane represented , and may consequently ( by the help of the former Instructions ) describe this Dial , whose Stile is to point upward , because of its Northern Aspect . OPERATION . XXIII . How to describe all Inclining Dials , whether Direct or Declining . AN Inclining Dial ( of what sort soever it be ) is the back or hinder part of a Reclining one of the contrary Aspect so that its hour-lines must be mark with the opposite Figures , and ▪ the Stile must point the other way ; therefore if you desire a Dial Declining East-ward 40 Degrees , and Inclining 20 with a Southern Aspect , describe only the last Dial , ( which has , you see , the ▪ same Declination and Reclination with a Northern Aspect ) and then if you mark the Morning hour lines with the Evening Figures , and place the Paper draught the contrary way , that is to say , let the Apex of the stile point downwards , you will perform the Operation . As for the Geometrical Description of Reclining or Inclining Dials since 't is very intricate , I shall not now trouble you with it , especially having already show'd you so facil a way by the Globe . OPERATION . XXIV . How to find the Degrees of the Reclination or Inclination of any Plane by the Globe . THere are two ways to perform this Operation ; for first ( as I show'd you in taking the * Level of a Plane , ) the String rests just on the Horizon of the Globe , when it stands on an Horizontal Plane , or one 90 Degrees from being Erect and Vertical . Draw therefore on the Reclining Face or side of the Plane ( represented by Scheme 29. ) a Line parallel to the Horizon ( suppose AB ) and let fall the Perpendicular CD , then place the Notches of the Pedestal of the Globe ( mark't with SN ) on the said Perpendicular , and consider what Degree in the Meridian ( counting from the Zenith ) the String just lyes or rests upon , and that will be as well the Inclination , if the Plane inclines , as the Reclination if it reclines ; for the Complement of this ( I mean the distance between the Point , or Resting place of the String and the Horizon ) showing always how much the Plane want's of being * Level or Horizontal , the Degrees from the Zenith , must needs show how much it wants of being Erect or Vertical . As for the second way , Draw a Perpendicular on the Reclining side of your Plane ▪ as I now show'd you , and placing on it ( after the same manner ) the Notches of the Pedestal , expect 'till the Shade of the Pin in the Zenith falls upon the Meridian of your Globe ; for this show's the Sun to be at that moment in the Plane of the said Meridian ; then observing on what Degree of it the Shade of Extuberancy falls , place but your Globe Level or Horizontal with your Meridian in the Plane of the Sun as before , and as the difference of these Degrees shows how much your Plane wants of being Horizontal , so that the Complement show's what it wants of being Erect , and consequently the value of it's Reclination if it reclines , or Inclination if it inclines . Sch 29. Sch 30 You may also if you please draw your Perpendicular on the Inclining side of your Plane ( as in Scheme 30th ) but then the requir'd Inclination , if it inclines , or Reclination if it reclines , will be the difference in Degrees between the aforesaid shades of Extuberancy , after you cast away 90 ; for by how much the Inclination happens to be , by so much the shade of Extuberancy exceed's 90 , since 90 is the difference between an Horizontal , and an Erect Plane . OPERATION XXV . How to find how long the Sun can possibly shine on a Plane , as also ( from time to time ) when we may expect him after his Rising to come on , or before his Setting to go off the said Plane . I Defer'd this Operation till we had treated of all Planes , because the applying of it would then be better understood . 'T is ( tho' obvious and easy , of great Use ) as not only showing us what Hour lines are absolutely necessary on all Dials , and what not , but telling us also at what a clock ( all the year long ) we may expect the Sun on our Plane , and at what a clock he must go off it ; for ( notwithstanding He be above the Horizon , He will not always so long shine on a Plane not Horizontal , as by the Earliest and Latest hour lines ( that may be justly exprest on it ) one might expect . If then you would find ( suppose on a Declining Plane ) what hour lines may be justly and necessarily drawn on it , I mean what the earliest and latest hour lines ought to be , you are only to draw you String from the Zenith ( according to the Declension ) on both sides of the Meridian ( or 12 a clock hour circle ) to the very Horizon ; that is to say , you must operate in the same manner as you do , when you describe the Plane in the Fabrick of this kind of Dial ; for the Hour circles cut by your said String in the Horizon show you exactly how early he can come on , and how late he can stay on it ; so that to express further Lines were needless . This then makes you stop at 4 in the Afternoon in your late * Example , where the Plane declines 40 Degrees Eastward , whereas had it declin'd but 20 your earliest hour ( as you may see if you try ) would have bin five in the Morning , and the latest five at Night . In short , describe your Plane ( let it be what it will ) on your Globe with your String , and your Hour circles , ( as we said ) that intersect with it in the Horizon answer the Question , since it clearly appear's ( your String ever representing the Edges of the Plane ) that if the Sun lyes Easterly in the Morning , and Westerly in the Evening of the Hour-circles , that meet your String in the Horizon , He must be behind your Plane ; therefore since he is not then able ( tho' up ) to shine upon it , 't were needless ( as we said ) to express more Hour lines . 'T is the Describing also of the Plane with your String that brings us to the knowledge of the second part of this Operation , I mean the knowing at all times when the Sun comes on , and goes off any Plane ; for having describ'd one ( Declining , v. g. 20 Degrees Eastward ) do but observe what Diurnal Parallels and Hour-circles intersect on the Edges of your Plane , and you have your Intent ; for you will by this means see , that , ( tho' the Sun rises ( for example sake ) on the 11 of June before 4 ) the first hour circle , which intersects with this Parallel on the Edges of the Plane , is that of a Quarter before six , whereas about the beginning of May , he is there at half an hour past five , and on the 10 of April at or near 5. Now if you consider in the same manner the West-side of the Globe , you will see from time to time at what hour he goes off it ; and thus you may do , let the Plane be what it will. Here therefore it evidently appears , if you should erect at any time ( suppose about the 10th of April ) a Perpendiculur stile on an Horizontal Plane , and draw every Hour a Line along the Shade of the said stile , why such a Dial will be false , as only telling you the true Hour twice in the year , to wit on the 10th of April , and about the 10th of August , viz. on the days on which the Sun run's in the same Diurnal Parallel ; I say , all this now evidently appears , since every Line thus drawn on an Horizontal Plane ( except the Meridian , or 12 a clock line ) is no Hour line but an Azimuthal Section ; I mean the Section of the said Plane , with a Circle that then passes over your head throu ' the body of the Sun ; so that if one of these Lines should Bear ( suppose ) almost SE , and be figur'd with 10 in the morning , Draw but your String from the Zenith , over that Bearing , or Point of the Compass in the Horizon of your Globe , and it will truly represent the said shade or Line on your Plane ; for it show's it to be 10 of the Clock on the Parallel belonging to the said 10th of April : But since your String cuts also on your Globe ( v. g. ) the Tropic of ♑ at a little before 9 , and the Tropic of ♋ at almost half an hour past 10 , you may conclude that this will be the true time of the Day on the 11 of December , and 11 of June , tho' the shade of the Perpendicular stile still show's 10 a clock at the aforesaid Bearing , let the Season of the year be what it will ; therefore a Dial thus made must be false . Of several ingenious and humersome Dials . HAving thus run throu ' all Planes , I shall at present show you how to make use of the former Principles , as to the ready Describing of several ingenious and humersome Dials , for all are now in a manner but Corollaries from what we have already said , and consequently easy both in Speculation and Practice . OPERATION XXVI ▪ How to make a Dial on any Plane whose stile shall be an Arrow fixt casually on it . EXamine what the Plane is , and having found it to be , suppose , a Vertical one Declining 40 Degrees East-ward , describe by your * former Rules : such a Dial on Paper with the Paper stile F x , M. ( as in Scheme 31. ) exactly set , and mounted ; then draw on the Plane an Horizontal Line H h , and place on it your said Paper draught so , that the 12 a clock Line FP may fall at right Angles on the said Horizontal line . Lastly , move your Draught along it , till some part of F x or Indicating side of the stile , ( suppose the Point A ) just touches the Top or most prominent Part of the Arrow , and fixing there the said Draught , if you draw fair Lines on your Plane under those on the Paper , the said Arrow will always show you the Hour with its Top. The Reason is plain : for you see by the said Top's just touching the Edge , or Indicating side of the Paper-stile , it has the effect of the Top of AB , I mean the Top of a Perpendicular falling from the said side on the Sub-stile , so that X the Top of XM ( both in the present Scheme and also in Scheme . * 18. or Example of a Declining Plane ) has this Effect also . Now since the Top of AB or XM or of any other Perpendicular , that falls from the Indicating side XF on the substile FM will perform the Office of the stile ( as we show'd you at large in Demonstration of the * first Horizontal Dial or first Example , ) it must necessarily follow , that A the Arrow's Top do's the like . OPERATION XXVII . How to make a Dial to show the Hour without a stile on any Plane . DEscribe ( as in Scheme 32. ) a Dial on P the given Plane , and erect for the present a true stile ( as FAB ) of Paper or the like , then fixing a Glass or any other transparent matter ( suppose G ) at what distance you please , before the said given Plane and Parallel to it , mark where A the Top of the Stile just touches the said Glass ; and if there you paint a little Asterisk or spot , it will ( as often as the Sun shines ) describe such another Figure ( at suppose D ) by its shade on the said Plane P , and move also from Hour Line to Hour Line , according to the true time of the day . The reason of this is also Evident ; for , if A the top of the real Stile show's the Hour by casting a Shade ( as we show'd you all along ) on the Hour Lines , then the Asterisk being there painted where the said Top touches the Glass , must do the like ; for it is , you see , the Stile 's Apex or Top , and consequently casts a true shade to know the Hour by . This Dial serves not only for all double Windows , or for Cavities that have over them any Glass or Transparent matter , but shows us how to make one for any Plane , that is illuminated by a Ray coming throu ' a Hole , since if you describe the Planes proper Dial on Paper , and move it duly ( as before ) on the said Plane , 'till the Stile , or ( if that be too short ) 'till a Thred drawn along its Indicating side , touches the Hole , it will give you marks for the drawing the fair and standing Hour-lines of your Plane , which the said Ray will dayly run over in order , and consequently show you from time to time the Hour ; for the Ray passing ( as you see ) throu ' the Hole ( v. g. ) at A , and falling on the true Hour Line at D , performs what A , the Apex of the true Stile ( FAB ) would do . OPERATION XXVIII . How to describe a Dial , having a Picture of a Man in it , that shall Point to the Hour from time to time with his Finger . THIS Dial is on several Planes of Mr. Lines his forementioned Pile in Whitehal Garden ; and as no Dial can be more useful , so perchance none ever struck the Fancy , both of the Ignorant and Learned , with a more sudden Admiration than this , as I have often found by Experience , both in England , and elsewhere . Nor truly can it but surprize one at first to think , that a Picture ( without a Machine or Movement ) should have his Finger ever on the Hour , and as duly attend the Sun's motion , as if he were alive ; I say , this cannot but surprize one , and yet this very Dial is as easy to be made , as any of the former . Suppose then ( as in Scheme 33 ) that the Plane given you were that of the Vertical Cavity , a b c d , lying directly South ; describe therefore on the Glass ( ABCD ) the contrary Dial , i. e. a Direct North Dial , with a Paper Style truly mounted ; and placing the said Glass over the Plane , and Paralel to it , see where the Stile just touches the said Plane , and at that point ( suppose E ) let the top of the Pictures Finger be painted ; then throwing away your Paper Stile , and now ( by the Help of a handsome Frame or the like ) fixing there your Glass , all its painted Hour Lines ( by hindring the Sun's Passage or Light ) will project so many Dark Lines on you Plane , whilst the then true one falls directly on the Mans Finger , and consequently shows you what a Clock it is . For if there were a Hole that passed at E ( the Top of the Mans Fingers ) throu ' the Center of the World to our Antipodes , it necessary follows ( by the Reasons in our former Operation ) that at 10 of the Clock , ( suppose ) at night , the Sun ( being then Northward ) must cast its Rays throu ' the said Hole or top of the Finger , on the 10 a Clock Line of this North Dial on the Glass ; but since at 10 a Clock in the morning , the Sun is in the same Plane as he was at 10 at night ( only his Station is contrary ) therefore he must now cast the Shade of the Hour Line the contrary way , i. e. on the Mans Finger ; for , in the day time the Hour-line is between the Sun and the Finger , whereas in the night time the Finger or Hole is between him and the Hour-Line . This Dial needs not always be made on a Glass , for 't is sufficient if you raise a thin Frame ( aaaa in Scheme 34. ) on the Pillars bbbb , above P your Plane , as high as the Glasse's true Station or Place , for then you may cross the said Frame with small Strings or Wyars , which will by their interposition cast the same shade as the Hour-lines of the Glass would have done ; so that if the Figures belonging to the said Lines be put on the Frame , at the end of each corresponding Wyar , and then pierc'd , the Sun Beams passing throu ' their Cavities , will distinguish each very perfectly on the Plane . Tho I have not time to show you all the particulars of this Learned Man's rare Invention in Dialling ; ( for most of the Dials on the aforesaid Pile may be naturally and expeditely describ'd by the help of this Globe ) yet I will give you two more , viz. the two following ones , because , besides their prettiness , we may have use of them , as you shall see by and by . OPERATION XXIX . To make a Dial by which a Blind man may constantly know the Hour . YOU must first get made in Brass the Armillary Hemisphere ABCDE ( as in Scheme 35 ) 8 Inches , suppose in Diameter , representing your Globe cut throu ' the Horizon ; but the said Hemisphere is not to have any thing solid remaining , besides the Horizon ABCE with the Pieces of the Hour Circles ( 1234 , &c ) that reach to it from the Nadir , or rather from the Tropic of Capricorn AFC on the Northernside , for the Southerly Circles are superfluous . Then having plac'd the said Hemisphere directly North and South , as your Globe stands when Compos'd , fix G a Glass Bowl of clear water 4 Inches in Diameter ( i. e. half the former ) in the midst or center of it ; for the Sun's Beames passing throu ' the Water will contract in a Point , and ever burn at ( suppose H ) the true Hour-Circle ; so that if a Blind-man puts but his Hand on the said Brazen Hour Circles , he will soon find by the Heat where the Sun marks , and consequently tell you the Hour ; for he may easily feel how far it is from the middlemost Hour Circle , I mean the 12 a Clock Circle or Meridian . As for the Reason of this Operation , 't is presently conceiv'd ; for when the Sun is over against ( suppose ) the 5 a Clock Hour Circle on the South-side of the Dial , he must needs be over against the same Hour on the North-side , both hours making but one Circle ; Now since the Center of the Bowl ( by being in the Center of the Hemisphere ) is in the Plane of all the Hour Circles , and since ( according to the nature of Refraction ) all Parallel Rays of the Sun , passing throu ' a Sphere of Water , are ( where they meet with the Direct Ray , that passes throu ' the said Center ) contracted into a point , viz. on the opposite side , at the distance of half its Diameter , or two Inches according to our present Example ; I say , seeing this , it must needs follow , that at 5 of the Clock , the Sun will burn on the corresponding Hour-Circle , and if so , then a Blind-man ( by feeling the Heat , and finding its distance from 12 ) must needs be able to tell you the true time of the Day . OPERATION XXX . To make a Dial to show the Hour when the Sun shines not . PRepare a Blew Glass Bowl , ( as in Scheme 36th ) and describe on it ( with their Respective Figures ) all the Hour-Circles of the Globe , or as many as you think fit ; then fixing it where you intend , and composing it truly by your Globe , if you place your self so at some Distance , that ( a little Hole being made at each Pole , to wit at P p ) you may see quite throu ' the Bowl , 't will follow that the Hour-Circle ( suppose A , which the Sun's Picture appears on ) will be the true time of the Day . I call this to know what a Clock it is when the Sun shines not , because now the least faint Appearance of him serves the turn , tho' it be not enough to cast any shadow ; nay let the Sun be quite cover'd , and if you can but guess ( by the Adjacent Brightness , ) whereabout he is , you will be able to guess the Hour without any sensible Error ; for the said Brightness appearing on the Bowl will be proportionably distant from the Sun 's true place there , as 't is from the Sun in the Heavens . 'T is clear that the Suns Picture must fall ( if any where ) on the true Hour-Circle , because ( by Composing the Bowl according to the true Position of the Heavens ) the Hour-Circles of the one concur with the other , and fall exactly in the same Plane ; therefore were your Eye in the Center of the Bowl , its true Hour Circle , ( i. e. that which corresponds with the time of the Day , ) would be just interpos'd between your Eye and the Sun ; but since the whole Axis is the common Section of the Hour-Circles , let your Eye be but in any part of it , the same Interposition must happen ; so that seeing the Suns Ray ( by reason of the Blew Colour ) penetrates not the Glass , his Picture must needs be on the outside of it , where the said Ray would have otherways past ; Now the Ray that goes from your Eye throu ' the two Holes being the Axis , therefore whilst your Eye remains in this Posture , it will follow that wheresoever you see the Suns Picture on the Glass , there his place must be , and consequently his said Picture must show the Hour . OPERATION XXXI . How to make an Horizontal Concave Dial by the Globe , and Geometrically also . COmpose so your Globe in the Concavity given ( suppose BAC in Scheme 37. ) that A the Center of the said concavity shall concurr with the Center of the said Globe ; then drawing your String over each necessary hour Circle on the Globe to the sides of the Concavity , mark as many Points , as shall be convenient for the Describing the corresponding hour Circles , and the Pin ( AD ) erected in the Nadir at D as high as the said Center A , I mean a Pin equal to the Semi-diameter of the Concavity , will with its Top always show you the hour . Tho the former way be impracticable when the Hole is less than the Globe , yet it serves to illustrate and make easy the Geometrical Operation ; for you have nothing ( you see ) to do , but to draw hour Circles within as you would without , were the said Concavity a whole Sphere , and then the Top of its Semi-Diameter ( i. e. the poynt which lyes in the Center A ) will perform the Stiles part ; for since the Sun is every Hour ( as we have before showd you ) in the same Plane of the true hour Circle , and since A the Top of the Semi-Diameter ( being in the Center of the Concavity , ) is part of the Axis ( or Common Section of all the Hour-Circles ) it follows , that its Shadow must fall on the true Hour . OPERATION XXXII . How to describe Geometrically a Cieling Dial. SEeing the Glass ( which reflects the Suns Rayes to show us the Hour ) is commonly fixt in the corners and by-places of Windows , the Globe can seldom be so well order'd ( by reason of its Bulk ) as to help us in the Construction of this Dial , therefore I shall only give you the Geometrical way , which is ( as I take it ) both short and new ; and because these Dials have commonly the Windows ( or inlets for the Sun ) Southerly , for otherwise they will show but very few hours , we 'l suppose ours also in the following Example to stand thus , and afterwards you shall see the difference between such a Dial , and those whose Windows have another Aspect . First make on any Past-board , Trencher , &c. an Horizontal Dial , as in Scheme 38. and fix in O its Center a Thred of a good Length , to wit OP ; then fasten the said Dial so with a Nail to a Long Masons Ruler , that its Fiducial edge ( KL ) may lye upon the Meridian or 12 a Clock Line , and having cemented and plac't Level a piece of Looking Glass ( of the bigness of a Three pence ) in the Window , or what convenient place else you please of your Chamber , ( which we 'l suppose to be G ) find by the Plumet AE the Poynt A in the Cieling ( WXYZ ) being the poynt ( in Scheme 39. ) directly over the said G , and draw throu ' it a Meridian line , viz. the Line AL. In the next place , fix one end of a piece of Packthred on G the Center of the Glass , and the other on some point of your Meridian line in such manner that it make an Angle with it of 51. 30′ . i. e. the Angle of the Elevation , which may be easily perform'd by the application of the side of a Quadrant to the said extended Packthread , and when 't is right , let the Point thus found in your Meridian line be called B. Lastly , take the distance between the aforesaid Points A and B , and marking it , suppose at C , on the edge of your Ruler from O , the Center , ( or fastning of the Horizontal ) place so the said Rulers Fiducial edge ( KCL ) along the Meridian line on the Cieling , that the point C may lye just on A , and all is done ; for then if you draw but the Thred OP streight over each Hour-line of the Horizontal , it shows you where you are to draw all the fair Lines of the required Dial. Sch. 40. As for the truth of this Dial , it appears ( in Scheme 40. ) by the right Angle Triangles OGH and GHF , where HF is part of HM , a suppos'd Meridian line on the Floor , under that in the Cieling , G the Station of the Glass in the Window , H the Point under the said Station , as formerly A was the Point over it , and to facilitate the Demonstration , let us imagine GH equal to GA , i. e. that the Glass lyes in the middle , between the Floor and Cieling ; This being so , suppose that GH ( instead of representing a Perpendicular Line in the Wall ( as here we conceive it ) had been a Perpendicular Stick , and that you were to describe an Horizontal Dial on the Floor , whose Stile was to be the said Stick ; I say supposing this , you must ( you know ) to perform the Operation , produce the Meridian Line MH to suppose N , and fastning a String on G , find in it the Point ( v. g. ) O for the Center of the Dial , ( I mean a Point , to which a String being extended from G , makes with the Meridian ( OH ) the Angle of the Elevation ) and so draw the several Hour-lines from the said O according to their respective Angles and Distances ; all which is exprest at large in the third * Scheme or first Horizontal Dial ; for there ( you see ) GH is a Perpendicular Stile , showing the Hour with its top , and that O is the Center of the Dial , having a Line drawn to it from G making the Angle of the Elevation with the Meridian OH : Now since O in our present case is a point without the Chamber and consequently the Line MH cannot be produc'd to it , you must draw your Thred from G to the said Meridian Line ( HM ) within the Chamber , and find in it the Point F , to wit the Point where the said Thred GF makes with it an Angle equal to that of the Elevation , for thereby you will have the distance of O , your true Center from H , as being the distance of F from H , seeing the side GH is common , and the Angles in both Triangles equal : This being so , if you put out of the Chamber an Horizontal Dial whose Center shall lye on O , and its Meridian Line concurr with HF , 't is but producing all its Hour-Lines on the Floor , and it must necessarily follow that G the Top of the Perpendicular Stile , will show you truly the time of the Day ; But by Construction all the hour-lines are thus drawn on the Cieling , and consequently are exactly over the supposed ones on the Floor , Ergo , the Reflext Ray from G must as truly show you the Hour above , as the Direct Ray below ; for both Rayes are ever in the same Plane . Nor is there to be any real Difference in the Operation tho' the Chamber-window should look another way ; for you are only to remember , that whilst it enjoys the least Point of South , the Center of your Dial is without the Chamber , when it looks full East or West 't is in the side or edges of it , and when it verges Northward , 't is altogether within ; so that in a full Southern Aspect , the said Center will be most abroad , and in a full Northern one the Contrary ; all which plainly appears to any one , that will consider an Horizontal Dial truly plac'd ( having a Perpendicular for its Stile ) if he draws over the Hour-lines , a Line that shall represent the aforesaid side of your Chamber according to its Position and Site . OPERATION XXXIII . To make a compound Dial to wit , one containing several useful Operations . INnumerable are the ingenious Dials that may be invented , but since we have been long enough on this Subject , either for my Reader 's Speculation or Curiosity , I will now conclude , and that with a Recapitulation or summing up of much of what we have already said , by showing the Fabrick of a Compound Dial ; that is to say , one that contains many useful Operations , besides the Hour ; for nothing rubs up the Memory more efficatiously , or makes us more Masters of our Rules , than a Practical Example . The said Dial shows as follows . 1. The Hour with us at all times . 2. The Hour in what other Countries you please . 3. The Sun's Place in each Sign . 4. The Day of the Month. 5. The time of the Sun 's Rising and Setting . 6. The Sun's Amplitude . 7. The Sun's Height . 8. The Sun's Azimuth . 9. The Sun 's Bearing according to the Points of the Compass . 10. The Proportion between Perpendiculars and their Shadows , and consequently the height of any Tower or the like . To make then this Dial , you must first describe an Horizontal ( as in Sch. 41. ) about a Foot in Diameter , and let B the Center of the Plane be the Point , where an Erect , or Vpright Stile ( according to our Directions in the * first Horizontal ; ) shews you with its Top the Hour . Now because the Shade of an Vpright Stile , unless it be very short , will presently fall out of the Plane , as well in the Morning as toward Night , therefore it will be convenient to have your Cock or Stile made so , that AB the Perpendicular or fore-part of it ( as in Scheme 42. ) should stand at B the said Center of the Plane , to represent this upright Stile , and its Angle AOB at O the Center of the Dial , or Point from whence all the Hour-lines are drawn ; for thus the side OA ( making with the Meridian line at O , the Angle of the Elevation ) represents the Axis of the World , and consequently casts its shadow on the Hour-lines , as the usual Cocks of all Horizontal Dials do . 2. Having chosen all the Places , which you desire from time to time to know what a Clock it is at , consider well your Globe , and find under what Hour-Circles the said Places lye ; as for Example , suppose Rome lies under the 11 a Clock Hour-Circle , Constantinople under that of 10 , Aleppo 9 , &c. Place therefore the said Towns towards the Limb of your Dial , under the corresponding Hour-lines , and you will constantly know the time of the Day in the said Places ; for calling it always Noon at each Place you seek after , you have nothing to do but to count the Hours from thence to the shade of the Stile ; as v. g. If it be 4 a Clock with you in the afternoon , and you would know the Hour at Aleppo , let Aleppo be 12 , and counting from thence ( 1. 2. 3. &c. ) 'till you come to the Hour of the Day , ( I mean the Hour then shown you by the Shade , ) you will find it to be 7 a Clock there ; for Aleppo is ( you see ) three hours Eastward of you ; now had the Hour with you been 4 in the morning , you must have counted backwards , as 11 , 10 , 9 , 8 , and consequently you would have found it there 8 in the morning . In this manner then you must operate all along . 3ly . and 4ly , Find by your Globe exactly the Sun's height every hour at his Entrance into each Sign , then take by the help of your Sector ( AB , the Erect Stile in Scheme 42. being Radius ) the Tangent Complements of the Heights , and putting one Foot of your Compasses on your Dial at B , make Pricks or Marks in each corresponding Hour-line accordingly ; that is to say , if the Sun be high ( suppose ) 50 Degrees at 12 of the Clock , when he enters ♉ or ♍ , then take the Tangent of 40 and prick that distance in the Meridian line , viz. From B to f ; and if his height at 1 and 11 a Clock be ( v. g. ) 48 degrees , take the Tangent of 42 , and prick that distance in the 11 and 1 a Clock lines , viz. from B to h and g , and when you have gone thus over all the Hour-lines , no sooner will the Sun come into ♉ or ♍ but the Shade of the Point or Apex of the Stile AB will fall every hour on the aforesaid Pricks , and consequently show you the Suns place in the Ecliptic . In like manner you must do with the rest of the Signs , and then with the 10th Degree of every Sign , placing still the Character of each Sign about the Limb of your Dial , near the last mark or Prick belonging to it . This being done , see by your Globe what day of the month corresponds with each Sign , and what with their Subdivisions , and if you mark this ( as the said 41th Scheme shows you ) on both sides of the Meridian , then the said Pricks will ( by the help of the Shade of the top of AB ) show you also the day of the month . I mention here Pricks not only as an easier way , but a better way than Lines ; for besides the great difficulty of drawing them , they embarras and confound a Dial very much , especially if there be many of them ; whereas the said Pricks are never out of an Hour-line , and consequently take up no new room . Now to avoid Confusion and Mistakes , I would have the said Pricks of 3 sorts at least , for if one Row were ( v. g. ) Astericks and another Crosses , and a 3d Plain Pricks , you would then know at first sight , to what Sign or Day of the month any of them belongs . 5ly . Instead of troubling you with deviding the Circle GKLT ( the upper part of the Border of the Dial ) for the finding out the time of the Suns Rising and Setting , you need only consult the Days of the Month on your Globe , first , when He rises earliest , Secondly , when He rises at 4 a Clock , Thirdly , when at 4½ ; Fifthly , when at 5 ; and in the like Proportion go on , till the Days come to their greatest Decrease , and putting the said days of the Month in Order ( as they are in the Scheme ) under the corresponding Hours on the morning side of your Dial for his Rising , do the like for his Setting on the Evening side of it , and you may perform the Operation with sufficient Exactness . In like manner you are to proceed for the Quarters , half Quarters , &c. if you would have them exprest . 6ly . To avoid also the trouble of deviding the Circle 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 according to the Suns Diurnal Increment and Decrement in Amplitude , you need only find by your Globe , what the said Amplitude amounts to on every of the aforementioned Days ( which are markt on your Dial for the Suns Rising and Setting ) and then put it in Figures under each Day , as the Scheme shows you . 7ly . Open your Compasses at the Tangent of 28 Degrees ( AB being the Radius ) and putting one Foot on B describe the Circle XYZ , afterwards describe another according to the Tangent of 35 Degrees , then a third , according to that of 40 , and so on in the same Proportion as far as your Plane permits . Now if you mark these Circles with the Figures of the Complement of their Degrees , that is to say the Circle of 28 Degrees with the Figure 62 , that of 35 with 55 , that of 40 with 50 , &c. you will always know the height of the Sun ; for what Circle soever the Shade of AB touches with its Top , that will be the requir'd Height ; and if it falls between 2 Circles , 't is but considering which of them it comes nearest to , and then you may guess at the Height with sufficient exactness . 8ly , and 9ly . Devide one of these Circles viz. SEWN into Degrees , and under each 11 Degree and ¼ , place the several Points of the Pixidis Nauticae , or Mariners Compass in the Order as they are express'd in our said Scheme , and you will not only have ( by the Shade of AB ) the Suns Azimuth at all times , but see also how he bears from you according to the Points of the Compass ; and if the Shade be at any time too short , lay on it but a Ruler , Label of Paper or the like , and that will truly lengthen the said Shade , and resolve your Question . 10thly . Devide AF the Northern half of the Meridian , as many times as you can by the Stile or Radius AB , and then each Devision into ten equal parts ( as you see it done in the said Scheme ) and by it you will know at all times the Proportion between any Perpendicular and its Shade , and consequently , ( besides many other things ) the height of any Tower , Tree or the like , for having found the Sun to be ( suppose ) 25 Degrees high , and that the Circle of Altitude cuts the Linc AF in the 22 Devision , if therefore you measure the Shade of your Tower , and finding it ( for Examples sake ) to be 66 Yards long , you have what you seek ; for as the said 22 is to 10 ( the Stiles height ) so is 66 the length of the Shade to 30 the height of the Tower. So much then for the Construction of Dials . And now let me desire all those that are pleased to follow this Geometrical way ( which perchance is as expedite a one , and as free from blind Lines as can be , ) not to rest satisfy'd till they fully comprehend what they do ; for the Mechanical way of Dialling is as soon lost as learnt , it being impossible ( without continual Practice ) not to forget the Rules , especially if one can make many Dials ; when as a man that understands the reason of the Operations ( by having in his Head a true Idea of the Sphere and its Projection ) will 20 years after without Memorandums or Notes , be able ( reflecting but a little ) to make not only all Dials he formerly knew , but new ones also at first fight . To Conclude , I here present my Reader with the Globe in a new Dress , for being painted or stain'd on Marble ( according to Sch. 43. ) 't will be fit for any Garden or open Portico ; and least it might appear too plain , the corners of its Base or Pedestal may be adorned with handsom well turn'd Branches , which not only embellish the whole Machin by their Make , But hold out Bowls of Glass and Wyar for use also . For on the First Corner , to wit , That markt with A , there is placed ( as a Rarity . ) The blind man's * Dial. On the Second markt with B. The † Dial that shows the Hour , when the Sun shines not , which will be often very useful . On the third , mark't with C , there is an Armillary Wyer Sphere having a Vane on the Top , that continually shows on the brass Plane within ( graduated and Nautically Character'd ) from what Quarter the Wind exactly blows ; as also , ( if you turn the said Vane into the Plane of the Sun ) his Azimuth and Bearing . Besides , the Sphere ( being an Horizontal Concave Dial ) shows the Hour too ; for the Shade of the Pin's top in the Center ever fall's on the true Hour-Circle , as I show'd in the * Construction of such a Dial. And by the way you must know this Branch stands not in it's true place in the Scheme ; I mean on the third Corner of the Base , because in Perspective 't will fall on the Globe it self , and consequently not appear well to the Eye in a Picture . Lastly , on the fourth Corner markt with D there is another Glass Bowl of the former Dimension , containing orderly all the Constellations , and remarkable Stars , and therefore , if you know the Hour , it will compose the said Bowl or Globe , and so represent the then position of the Heavens ; but ( tho you are Ignorant of the Hour ) if you see a known Star , and move the Bowl on its Axis , till the painted star on it lyes just between your Eye and the Real one , you have the Hour , and consequently may know ( the Globe being now Compos'd ) any Star or Constellation above the Horizon ; for the Axis of this Bowl having one end pointing directly to the North Pole , and the other fixt in the Center of a Rundle containing on its Limb the Days of each Month , fitted to the right Ascension of the Stars , and moving also on a Plane divided into 24 equal parts , figured with the hours of a Natural Day , 't will follow that the Day of the Month ( when the Globe is Compos'd ) must lye on the true Hour , as the true Hour move'd to the Day of the Month must Compose the Globe , as is before hinted . These short directions are sufficient for any Mathematician , or Instrument-Maker ; and as for the Branch it self , 't is ( as you see ) not in its true Place for the above mentioned Reason . J. Moxon To the Reader . HAving Courteous Reader * engaged to show you the Problems and Operations on the Sector , which the Noble Author supposes every one ( that studies the Geometrical way of Dialling ) to know , I shall here begin . I. Upon a Line given ( AB ) to erect ( CD ) a Perpendicular . IF there be a Point ( as C ) given in ( AB ) the Line on which the Perpendicular is to fall , Mark on both sides of the said Point ( with your Compass ) the equidistant Points M and N , then opening them at pleasure , put one foot on M and describe the blind Arch EF , and putting the other Foot in N , describe the blind Arch GH , and the fair line from ( D ) their Intersection to the Point C , will be the Perpendicular requir'd . Now if you have no Point assign'd ( in the said Line ( AB ) to terminate your Perpendicular by take two Points there at pleasure , as suppose M and N , and opening how you will your Compasses , describe the blind Arches EF and GH above your Line , and OP and QR below it , and the Intersections of these Arches ( to wit , D and S ) will be two points to draw your Perpendicular by . II. Upon ( C ) the end of ( AC ) a given Line , to draw ( DC ) a Perpendicular . OPEN your Compasses at a convenient width , and putting one Foot on C , let the other ( within reach of AC ) mark any where , as at F : then touching or cutting from thence the said AC ( with the moving Foot of your Compasses ) at , suppose , E , and describing on the other side of F the blind Arch GH , lay your Ruler on FE , and it will cut the said Arch , at , suppose D , so that DC will be the requir'd Perpendicular . III. A Line ( AB ) being given how to draw ( DG ) a Parallel to it . HAVING taken two points in the said Line , as suppose A and B , open your Compasses at what width you please , and putting one foot on A , describe the blind Arch CDE , and putting one foot on B describe the blind Arch FGH , then if you lay your Ruler on the highest part or greatest Extuberancy of the said Arches , to wit on the Points D and G , the Line so drawn will be the requir'd Parallel . IV. To describe a true Square . AB being a Line as long as the side of the Square you design , erect on the end A , the Perpendicular DA of the former length ; then taking between your Compasses the said AB , put one foot on D , and describe the blind arch EF , and again putting one foot on B , describe the blind arch GH , to cut EF , and if from their Intersection C , you draw the fair lines CB and CD , you have a true Square . V. To draw an Oblong , or ( as they commonby call it ) a Long Square . AB being the longest side of this Square , erect on the end A , the Perpedicular DA , of the length of the shortest ; then taking between your Compasses , the line AB , put one foot on D , and describe the blind arch EF : and taking between your Compasses the line AD , describe the blind arch GH , to cut the said EF , and if from their Intersection C , you draw the fair lines CB and CD , you have the Square you design . VI. To Describe an equilateral Triangle , or an Isosceles . OPEN your Compasses at AB , being the side of the Triangle you design , and putting one foot on A , describe the blind Arch EF , and again putting one foot on B , describe the blind Arch GH to cut the said EF , and if from their Intersection C , you draw the fair lines CA , and CB , you have a true equilateral Triangle ; Nor is there any difference in the Description of the Isosceles ASB , for the only difference between them is , that the sides AS and BS of the Isosceles are longer ( or if you please they may be shorter ) than the Base AB , whenas all three sides are equal in the equilateral Triangle . VII . To make a Triangle of three given Lines . SUPPOSE the first line given be AB , the second AC , the third BC , and that you are to make a Triangle of them : let AB be the Base , and taking the given line AC between your Compasses , put one foot on the Base at A , and describe the Blind Arch EF , then taking the given line BC , between your compasses , put one foot on the Base at B , and describe the Blind Arch GH , to cut the said Arch EF , and if you draw lines , from their Intersection at C , to A and B , on the aforesaid Base , you have your intent . VIII . To describe an Oval . CROSS RP at right Angles with IM , and taking with your Compasses ( on the said lines from the intersection O ) equal distances , to wit , OA , OB , OC , and OD , and draw through the point C , the lines AK and BH , each equal to twice AC , as also throu ' D the lines AN and BL , each equal to twice BC , then A and B being Centers , describe the Arches KPM , and HLR ; in like manner C and D being Centers , describe the Arches HIK , and LMN , and the figure thus drawn will be a perfect Oval . So much for the Geometrical Problems necessary for Dialling , and as for the Instrumental ones , i. e. those performed by the Sector , they are , as I may say , of two sorts , some belonging to one side of it , and some to the other ; for the side marked with L is divided into 100 equal parts , and called the LINE of LINES , and the side mark'd with S , the LINE of SINES . First then of the LINE of LINES , which by the way , tho' it be divided ( as I said ) but into 100 parts , may yet stand for 1000 , if you fancy every 10 Divisions a Line of 100 parts , and in like manner it will stand for 10000 parts , if every division be deemed 100 , therefore a Line ( v. g. ) of 75 equal parts , may be exprest by 75 of those Divisions , or by 7½ or by ¾ . The Use of the LINE of LINES marked with L. I. To divide a Line into any number of equal parts . SUPPOSE your Line were to be divided in 23 equal parts , take it between your Compasses , and opening your Sector , place one foot of your said Compasses on the 23 division of the Sector , and the other foot on the 23 over against it , and the distance between the Figures 1 and 1 ▪ on the said Sector will give you one equal Division of your Line , and the distance between 2 and 2 , will give you two equal Divisions of it , and in this manner proceed till you quite run over it , as you design . II. To find the proportion between any two Lines . SET over the greater Line at 100 , and 100 on the Sector , then taking the lesser between your Compasses , find where it will be just set over also , or lye parallel to the former , which hapning suppose at 50 and 50 , you may conclude , that the Proportion required , is as 100 to 50. III. To divide a Line as any other Line proposed is divided ; that is to say , according to any Proportion . SUppose you saw a Line , containing 65 equal parts of the Sector devided into three pieces , the first containing five equal parts of the Sector , the other fifteen , so that the last must be 45 ; then suppose you would divide ( after this proportion ) another Line , containing but thirteen equal parts of the Sector ; Open your Compasses at 13 , or length of the Line to be devided , and putting it over at 65 , and 65 on the Sector , the Parallel at 5 and 5 will be the first division of the Line to be divided , and one equal part of the Sector in value ; the Parallel at 15 and 15 will be the second , and three equal parts in value ; and the remainder ( being 9 in value , ) will be the third ; and thus you may do in all other cases . IV. To encrease or diminish a Line in any Proportion . SUppose the Proportion were as 4 to 7 , take the Line given between your Compasses , and setting it over on your Sector , at the Figures 4 and 4 , the distance from 7 to 7 will be a Line encreast ( in respect of the given one ) as is the Proportion of 4 to 7 ; In like manner you must do , if any other Proportion were requir'd . Now if you would diminish a Line as is 7 to 4 , put over the Line given at 7 and 7 , and the distance of 4 and 4 is the requir'd proportion . V. Two Lines being given , to find a Third Proportional . FIND by your Compasses how many parts of the equal Divisions of your Sector will measure both your given Lines , so that supposing the one to contain 10 parts , and the other 20 , set the second Line ( i. e. the Line 20 ) over at 10 , and 10 on the Sector , and the distance or Parallel at 20 , and 20 on the Sector , will be 40 , the requir'd Proportional . VI. Three Lines being given , to find a Fourth Proportional . THE value of the Lines being found as before , and supposing the first to be 10 , the second 20 , the third 30 , put over the second Line ( to wit , 20 ) at 10 and 10. ( the value of the first Line ) and the distance or Parallel at 30 and 30. ( or value of the third Line ) will be 60 , the required Proportional . Of the Use of the LINE of SINES , markt with S. I. How to find the Sine of any Angle , according to any Radius . SUppose the Sine of the Angle you require be 50 , take the Radius between your Compasses , and put it over at the extremity of the Sector , that is to say , at 90 and 90 , and the Parallel at 50 and 50 will be the Sine of 50 Degrees , according to that Radius . II. How to find the Chord of any Arch. SUppose you would have the Chord of an Arch of 50 Degrees , open your Compasses at the length of the given Radius , and put it over at 90 and 90 , then take with your said Compasses the Parallel , at the Figures 25 and 25 on the Sector , ( i. e. at the Figures of half the Degrees given ) and prick or measure it twice upon any streight Line , and that will be the required Chord . III. How to make an Angle of any value , as also how to find the value of any Angle already drawn . SUppose you are to make an Angle of 50 Degrees , draw a Line , as ( for Example sake ) AD , and taking any Point in it , as B , open your Compasses to a convenient Radius , and put one Foot on B , and describe the blind Arch CF , then taking between your Compasses the Chord of 50 , according to the Radius of the said Arch , put one Foot on C , and the other marking at suppose E , draw the Line BE , and you have the required Angle , to wit , the Angle EBC . But if the Angle you would make be above 90 Degrees , as suppose 130 , make the Angle of its Supplement , viz. the Angle of 50 as before , and the Angle on the other side , viz. EBA will be the Angle you look for : Here therefore you see how to find the value of any Angle already drawn , as suppose the Angle EBC , since 't is but describing a blind Arch , as CF , and setting over ( on the Sector ) the Radius of the said Arch at 90 and 90 ; for if you observe where the measure of this Arch ( viz. C. E ) marks a Parallel on the Sector , as before , the Figures there ( to wit , 25 ) being doubled ( and amounting consequently to 50 ) will be the requir'd Angle . As for the Tangent and Secant of any number of Degrees , the Noble Author has himself showd you how to find them at pag. 71. and so gentle Reader having finish'd my promise , I bid you Farewel . SECT . VI. Of the STARS . AS for the Stars , it is not my set business to meddle with them , nor is there any Instrument that so naturally resolves all the usual Questions concerning them , as the Coelestial Globe ; for there things appear as they do in the Heavens themselves ; But because such a Globe is not always at hand , I will shew you how its most necessary Operations may ( in case of necessity ) be perform'd , even by our present Globe , and then I shall treat of the Pedestal , on which all the appearing Stars are truly projected . The usual and most necessary Operations of the Coelestial Globe in relation to the Stars are these . 1. To find the Declination of any Star. 2. To find the Right Ascension of any Star. 3. To find the difference between the Suns Right Ascension , and that of any Star , or the difference between the Right Ascensions of any two Stars . 4. To find the true place of any Star on the Globe , i. e. the Point that corresponds there , with its then Place in the Heavens . 5. To find the Bearing of any Star according to the Points of the Compass . 6. To take the height of any Star you see . 7. To find the height of any Star by the Hour tho' unseen . 8. To find the Azimuth of any Star. 9. To find how many Hours any Star stays above or below the Horizon . 10. To find when any Star rises or sets . 11. To find what a Clock 't is by any Star. 12. To know the name of any Star you see . OPERATION I. To find the Declination of any Star. AS for the Declension of the Stars , since the Coelestial Globe and other Instruments , that shew their motions , perform this Operation by their make ( for on them the Stars are always plac'd , according to their respective Declensions ) we shall require here a proportionable Concession , viz. That in some of the vacant parts of our Globe there may be a little Table , containing the Declension and Magnitude of the most noted Stars , as also the Degree of the Ecliptick , which agrees with their respective Right Ascensions : that is to say , a Table containing their Declension and Magnitude , with the Suns Place in the Ecliptic , when his and their Right Ascension are the same ; and the said Table may be made in the following manner . The Table for the Stars . Mag. Name . Declension . Deg. Eclip . 1. Bulls Eye . 15 48. ♊ 6. 1. Lions Heart . 13 33. ♌ 26. 1. Arcturus . 51 4. ♏ 2. 2. Little Dog. 6 3. ♋ 19. 2. Medusa , or Algol . 39 40. ♉ 13. And so for as many as the Globe maker thinks fit to express . OPERATION II. To find the Right Ascension of any Star , v. g. of the Lion's Heart . HAving found by the Table , that the Lions Heart has the same Right Ascension with the Sun , when he is in the 26 of ♌ , draw your String over that Degree of the Ecliptic , and it will cut the Aequator at almost 148 Degrees , for the Stars Right Ascension . OPERATION III. To find the difference between the Suns Right Ascension , and that of any Star , as also the Difference of the Right Ascensions of any two Stars . HAving found by the former Operation , that the Right Ascension of the Lion's Heart is towards 148 Degrees , and that the * Suns ( on v. g. the 10 of April ) is near 28 , the difference ( by Substraction ) will appear to be about 120 Degrees , or ( by the intermediate Hour Circles ) 8 hours . In like manner having found ( for example sake ) the Little Dogs Right Ascension , to be about 110 Degrees , the difference between it and that of the Lions Heart is 38 , or 2 hours and a half . OPERATION IV. To find the Place of any Star on the Globe , i. e. the Point that corresponds with its then Place in the Heavens . HAving found by the foregoing Operation , that the difference between the Suns Right Ascension and the Lions Heart , is about 120 Degrees , or 8 hours , substract the said hours ( for so much the Sun Rises and Sets now before the Star ) from the time given ( suppose from 10 at Night ) and the remaining 2 hours shows you , that the Star is at that moment in some part of the Hour-circle of 2 in the afternoon , or thereabouts ; so that the Bead rectify'd to the Stars Declension , and moved on its Noose from the Pole to the said Hour-Circle , determins the very Point or Place requir'd , The like may also be performed by your Compasses open'd from the Pole , at the Complement of the Stars Declension . But here you must remember that the readiest way still to find the present place of a Star is by its Almucantar and Azimuth ; for where these Circles intersect , there the Stars then Place will be ; and as for the Almucantar and Azimuth of any Star , they are found by the 6th , and 8th , Operation of this Section . OPERATION V. To find the Bearing of a Star at all times . HAving found the true Place of the Lions Heart by the former Operation , if you draw your String over it from the Zenith , 't will cut the Horizon at or about S. W. for its then Bearing . OPERATION VI. To take the Almucantar or height of any Star you see . BEcause Stars cast no shade , you must take their Height as you do the Suns when he is overcast , and therefore consult the first Operation of the first * Section , or the 5th , of the * 4th . Section . OPERATION VII . To find the height of a Star at any time , by the hour tho' unseen . THE Hour being ( v. g. ) 10 at Night , on the 10 of April , the Suns place is where his Parallel cuts the 10 a Clock Hour Circle , so that knowing by the difference of their Right Ascensions that the Lions Heart is ( v. g. ) 8 hours behind the Sun , you may conclude the Star to be somewhere in the Hour-Circle of 2 in the afternoon , to wit , in that Point , which answers to the said Stars Declension ; having therefore its Place , draw but your String from the Zenith over it , and mounting your Bead to it , if you move your said Bead to the Meridian or Quadrant of Altitude , 't will lye on or about the 45th . Degree for the required Height . OPERATION VIII . To find the Azimuth of any Star. FInd but the Lions Heart's Bearing , or his then true Place in the Heavens as before , and the String will cut the Horizon on its true Azimuth . Now if you see the Star , you may perform this Operation without any of the former Postulats ; for placing your Globe on a Meridian Line , and holding your String streight from the Zenith , do but move it in that posture by the direction of your Eye ( as we show'd you in the first * Section ) till it be in the same Plane with the Star , and the Degrees of the Horizon under your String , give you the required Azimuth , which will now be about 45 Degrees Westward . OPERATION IX . To know how many hours any Star stays above or under the Horizon . REctify the Bead to the Declension of the Lions Heart , and moving your String on the Noose from the Pole , till the said Bead touches the Horizon on the West side , see what Hour-Circle cuts with it there , and you will find it to be that of 7 and a quarter or thereabouts ; and this doubled ( making in all some 14 hours and a half ) gives the true time of its stay above the Horizon ; so 4 and three quarters doubled ( I mean the Hour-Circle which Intersects with it on the East side ) gives you 9 hours and a half for its stay below the Horizon . OPERATION X. To find when any Star Rises or Sets . HAving found by the third Operation , the difference between the Suns Right Ascension and that of the Lyons Heart to be 8 hours on the 10th of April ; and having also found by the foregoing Operation , that it Rises where the Hour-Circle of 4 and 3 quarters cuts the Horizon , and Sets where that of 7 and a quarter do's the like , add the 8 hours difference ( because the Star is now so much behind , or too slow for the Sun ) to 4 and 3 quarters , which making 12 and 3 quarters in all , shows that the Star rises at 12 a Clock , and 3 quarters in the afternoon ; and by adding it to the aforesaid 7 and a quarter , that it sets at 15 and a quarter , to wit , at 3 and a quarter in the morning . OPERATION . XI . To find what a Clock 't is by any Star. HAving ( v. g. ) on the 10th . of April found the true place of the Lyons Heart , on the Globe , by some of the former ways , as ( for Example ) by its Height and Azimuth : I say ; having thus found the Stars true place on your Globe ( which hapning ( v. g. ) to be in the 2 a Clock Circle ) find by the third Operation the difference between its and the Suns right Ascension , which being 8 hours , add it to the said 2 ( for the Star is as we said 8 hours now behind or too slow for the Sun ) and the then true hour will be 10 at night . OPERATION XII . To know the Name of any remarkable Star which you see . BY a Stars Height and Azimuth you may ( as we have show'd you ) quickly find its present true place on the Globe , and consequently its Declension , as being the nearest distance between its said Place and the Aequator ; so that your Tables of Declension gives you its Name ; and if there should be two of the same Declension then their right Ascensions ( being different ) will resolve the Doubt . To conclude , all the former Operations may be yet more readily performed , and that without any Table , if the Globe-maker place 10 or 20 of the most noted Stars ( which will be enough to These Schemes are properly Sch 3d & 4 belonging to Page 141 as showing the way to describe the Projectiō but they may serve for Sch 1 & 2 Pag. 135. if on the higher the Constellation are supposd to be Engravd & on the lower a line was draw̄ frō the Center to lack hour in the limb & no Almucantar or Azi●●th exprest but by Pricks satisfy any ordinary curiosity ) on the Globe it self , according to their true Longitude and Latitude ; for then their Declensions , Parallels , and right Ascensions appear in a manner at first view , which must needs therefore facilitate the other Operations . Of the PEDESTAL . THUS you see that our Globe ( tho' it be a Terrestial one ) may ( in case of necessity ) be serviceable in relation to the very Stars ; but because all Operations that have the least Reflection in them , seem intricate and troublesome to some , I have here adjoyned ( for them that will be at the Expence of the best sort of these Globes ) a most Facile way , that shall resolve in an instant , all the former Questions and more ; for there is not only a Steriographical Projection on the Pedestal of the appearing Stars in our Horizon , but one also so ordered , that it obviates the inconveniences which make Stofflers admirable Astrolabe so much neglected of late ; for some say , there is no finding a Star on it without much poring , tho' we should know near what Constellation it lyes ; others , that when we see a Star there , we are still ignorant to what Constellation it belongs ; many quarrel at the great confusion which the Azimuths , Almucuntars , and other Circles exprest on it make ; and some again object , that the numeral Figures belonging to the said Circles are oftentimes so hid by the solid part of the Rete , that we cannot without a new trouble and motion perform the intended Operation . I say , this Projection on the Pedestal ( besides several other things ) obviates these inconveniences , as you will presently see . The Explanation of the Circles and Lines of the whole Projection or Pedestal . THE uttermost Circle ( in Sch. 1 ) or Limb SENW of the lower or first Plane , represents Circulum maximum semper latentium , or ( if you think that too large ) what Parallel you please . It may be conveniently nine Inches or a little more in Diameter , if the Globes be a Foot , and being of fine Pastboard or the like substance , it is to be let into the Pedestal , which is purposely made Cradle or Frame wise , that it may ( by your hand underneath ) be easily turn'd round , and be also taken quite out , if any particular or extraordinary occasion should require it ; Nay , the whole Pedestal may be pulled off , ( if you think fit ) from the handle or Fulerum , and us'd apart as a distinct Instrument . 2. The great Circles described on it are only two , viz. the Aequator ( ♈ AE ♎ ae ) and the Ecliptic ( ♈ ♋ ♎ ♑ ) divided into the 12 Signs , with their gradual subdivisions . Now ( since it will be no incumbrance to your Plane ) you may express on it also ( if you please ) the two Tropics , by two fine Circles , that of Cancer touching the Ecliptic at ♋ , and that of Capricorn at ♑ . And as for the Limb , it is divided into 360 Degrees , for being in Projection greater than the Aequator , 't will prove more useful in all the Operations , that concern such Divisions . Nor are the Circles or Stars placed here as on the Globe ( I mean according to the Degrees of a Quadrant equally divided ) but Steriographically projected by half Tangents , i. e. as they would appear and fall on an Aequinoctial Plane , or a Plane parallel to it , were our Eye in the Pole , of which more hereafter , as also the Centers and Radius's of each Circle , when we come to the Description and Demonstration of the whole Projection ; and in this manner also ( to wit , by half Tangents ) the Line P. E. is divided , which shows the Declension of any Star. Thirdly . The Stars being all plac'd on this Plane according to their respective Right Ascensions and Declensions ; and by the way , when you once know how to find by this Projection the Right Ascension and Declension of a Star ( as you will presently do by the following Instructions , that concern operation ) you will then also know by the help of Astronomical Tables ( which give each Star's Right Ascension and Declension ) how to place them here : I say , the Stars being all plac't on this Plane , according to their respective Right Ascensions and Declensions , they are to be Marshall'd and reduc'd into Constellations ; and therefore you must suppose either fit Pictures drawn about them to express what they are , or that the uttermost Stars of each be join'd by a fine Prick't Line , which will give you perchance , the most clear and just representation of them , and consequently prove the easiest way for the finding them out in the Heavens ; But since Pictures have conveniences and great ones also ; for thus without consulting the written names , we cannot only find presently ( even a far off ) the Constellation we seek after , but know at the same time the Place of each Star in it , which Place for the most part gives the Star its ordinary Name : I say , since Pictures have great Conveniences , let them be us'd ; but then they must be as faintly and simply express'd as can be ; for deep shadows , and unnecessary Flourishes both distract the Fancy , and cause even the Stars that are express'd to be less conspicuous and observ'd . Fourthly , When the first Plane is thus garnished and plac'd in its Frame , there is another of the same bigness , either of Glass , or Talk ( represented by Scheme the second ) to be put over it , and fixt or fastned in the uttermost Molding or Ledge of the Pedestal . And here be pleas'd ( for distinction sake ) to remember , that by the Terms First , and Second , these two Planes are distinguish'd , and that by Projection is meant the whole Pedestal , or Astronomical Machin , which ( as I said ) may be taken off , and used apart , as a particular Instrument . Lastly , the second Plane ( represented , as I said by Scheme the second ) has its Limb S. E. N. W : divided ( besides the subdivisions or Quarters ) into 24 equal parts , by so many streight Lines , drawn from the. Center P , and figur'd ( I. II. III , &c. ) according to the hours of a natural Day . As for the Circle HRST , it represents the Horizon ; and the Circular Pricks within it give the Almucantars and Azimuths of every 10 Degrees ; for ( on the one side ) if you consider the said Pricks as so many Circles ascending from the Horizon towards the Zenith , the Figures along the Lines , PS and PN give you from the Horizon upwards the height of that Star which touches any of them . On the other side , if you consider them in File , ( I mean as so many Arches passing thro' the Zenith , and terminating in the Horizon ) their distance from PS ( the Southern part of the Meridian ) shows the Azimuth of the Star next any of them , by the Figures round the Horizon ; and least you might not readily distinguish Arch from Arch , if the Pricks were all of the same kind or Species , there are two sorts here , viz. one of plain and simple Pricks the other of small Astricks alternatively plac'd ; so that 't is but observing of what Species the Prick next a Star is , ( as suppose an Astrisk , ) and then following with your Eye a File or Arch of Astrisks 'till you come to the Horizon ; for the Figures at their termination there give you the requir'd Azimuth . Thus then the confusion which the several Almucantars and Azimuths would make ( were they all describ'd on the Plane ) is avoided , seeing the Plane is now less fill'd than if the Almucantars were only exprest on it ; for disjoyn'd Pricks circularly plac'd occupy not the room of a continued Circle , and yet each Row or Circle of the said Pricks perform both the forementioned Offices . How to operate by the Projection or Pedestal . FIRST the Reader must remember , that I call Rectifying the first Plane ; the placing and adjusting it so that all the Stars may appear above and below the Horizon , as they then really do in the Heavens themselves ; which Operation being a main and principal matter ( for all the other are in Truth but so many Deductions or Corollaries ) I will now begin with it ; nor is there any thing here requir'd but the height of some Star in view ( as the Lion's Heart , or the like ) which you may find by the Globe as you do the * Sun 's or † Moons height as I mentioned * before . Now for cleerness sake , let us suppose this Star to be about 45 Degrees high Westwardly , and then if you move your Plane till the said Star , lyes thus under a Prick of this height , you have ( without ever moving more the Plane ) the several following Operations at a time . First , You see all the Stars that are then above the Horizon and below it ; for all the painted ones within the Circle HRST , on the second Plane represent the real ones then in sight , and the rest those that are below the Horizon . Secondly , You see what Stars are Rising , what are Setting , what are Culminating , and what are in their Lowest Depression . Thirdly , If you look after any particular Star ( suppose the Lion's Heart ) by seeing him on the West-side of PS ( the Meridian of the said second Plane ) you are sure he is not only in a Declining state but also ( by following the Prick next him to the Horizon , according to its Species ) that his Azimuth is 45 Degrees . Fourthly , You will see his Bearing , to be about S. W. if you follow the Azimuthal Arch to the Nautical Characters there . Fifthly , You see that the Hour of the Night is 10 , by observing under what Hour-Line the 10th . of April ( i. e. the day of the Month , the Suns place in the Ecliptick ) lyes . Sixthly , By any real or imaginary Hour Line that runs over the said Star , you find his Right Ascension to be near 148 Degrees ; for thus the said Hour Line cuts the Limb. Seventhly , By his being behind the Sun about 8 hours ( as appears by the Hour Lines that pass over the Star and the Suns place ) you have the difference of their Right Ascensions , which amounts to about 120 Degrees . Eighthly , Which is the most surprising ( and not performable even by a Coelestial Globe ) you no sooner see these things in relation to this or any other particular Star , but at the same time also ( even without touching your Projection ) you have them in relation to all the Stars in general ; for when the First Plane is rectify'd , we have ( besides the Hour ) the Heighths , Azimuths , Bearings , Right Ascensions , &c. of all the other Stars above the Horizon . Concerning the other Operations , they are more restrain'd , as being peculiar to the Star you enquire after ; for if you would know when the Lions Heart Sets , ( which for continuation's sake we will call the ninth Operation ) do but move your first Plane till the said Star touches the Horizon , and the imaginary Hour Line that passeth over the Sun's place in the Ecliptic , show's you , that 't will be then about 3 and a quarter in the morning . 10ly . By the Figures about the Horizon , you will see at the same time , that his Occasive Amplitude is near 23 Degrees ▪ Northward , and his then Bearing ( by the Nautecal Caracters ) to be WNW , or thereabouts . 11. By the imaginary Hour-line that then passes over the said Star ( viz. that of about 7 and a quarter ) you have half the time of his constant aboad above the Horizon , and consequently know , that from his Rising to his Setting there are about 14 hours and an half . 12. By reason that the imaginary Hour-line of about 7 and a quarter passes over the Star ( as we said ) at his Setting , it follows that it 's Ascensional difference ( i. e. the difference between its Right and Oblique Ascension ) is about an Hour and a quarter , or 18 Degrees . 13. By the Degree of the Ecliptic that Sets with the Star ( which is the 26 of ♌ ) and by the opposite Degree which then Rises ( viz. the 26. of ♒ ) you see that on the 8th . of August he Sets Achronically , and on the 2. of February Cosmically . 14. Remove the said Plane , till the said Star brushes the Horizon on the East-side , and by the precedent method ( mutatis mutandis ) you will find when he Rises , what his Ortive Amplitude is , how he then Bears , how long he is under the Horizon , when he Rises Cosmically , and when Achronically . 15. By placing the point of a Pin or Needle , on the Class over the Lions Heart , and then moving the first Plane , till the divided 6 a Clock Hour-line PE , lyes just under the said point the Divisions there will show its Declination to be about 13 Degrees and 33 Minutes . The like you may do with your Compasses ; for if you take the Distance between the Pole and Star , and measure it on PE , you have what you seek for . Many other Operations are performable by the Projection , touching the Stars ; but since these are the most material ones , and since I have not time to treat more fusely , I leave the rest to be found out by my Reader himself , who may easily do it , if he understands either the Caelestial Globe , or any Instrument belonging to the Stars . And here he is to remember , that knowing but the Hour at any time , let him put the Suns place , or day of the Month under the Hour-line , that corresponds with it , and the Projection will be rectified , and consequently ( having a true view of the then posture of the Heavens ) he may opperate as before . In the next place , if he knows but the Suns place in the Ecliptic of the first Plane , and opperates with the said place as if it were a Star , he may find out the former Operations in relation to the Sun it self ; that is to say , he may at that moment know his Height , Azimuth , Bearing , Amplitude , &c. 16. If you would know the Stars in the Heavens , you may also do it by the help of this Projection ; for your first Plane being rectified , it gives you ( as I said ) the true posture of all the Stars ; so that if those you seek after be near the Horizon , Meridian , or any other noted Quarter , those on your Plane near its Horizon , Meridian , or corresponding Quarter will resolve the Question . Or , if you take the height of a Star , and its Azimuth ( according to any of the former Directions ) then whatever Star on your Plane has the same , it will be that you seek after , and consequently you have its Name . Now knowing once a Star , your said first Plane shows you what they are that lye about it , and so by degrees you may run from one to another round the Heavens . Nor need you , as to the knowing of the Stars , be so exact ( either in rectifying your Projection , or in having the hour of the night , or in taking the Heights , and the like ) as in other Operations : for , by the bigness of the Star , by its nearness to some remarkable one , and by twenty other particular properties , you will be so regulated and confined , that you may safely conclude , when you examine your Projection , that the real Star you see , can be no other than such and such a one . How to Describe the PROJECTION . HAving thus show'd you the use of the Pedestal or Projection , I shall fall on the way of Describing it , and ( according to my manner all along ) on the Demonstration of it also , especially since it conduces to a more easy comprehension of all Steriographical Projections ; and if I be a little longer than ordinary , it is now no great matter , for I have ended all the Operations I intend at present , so that what is here further said may be omitted without inconvenience , if the Reader be disgusted at Speculation . As for the nature of the Projection , t is Optical , representing all things in the Heavens , as they appear to the Eye , from such and such a Station , and not according to their true and real distances . 'T is chiefly founded on the 20th . Proposition of the third Book of Euclid , which proves , that the Angle at the Periphery is but ½ that at the Center ; for from thence 't is infer'd , that if placeing our Eye on the superficies of the Sphere ( v. g. at the South Pole ) we look into its Cavity , the Angle made at our Eye , by the two Rayes that issue from it ( the one along or throu ' the Axis to the opposite Pole , and the other to a determined Point ) will be the Angle only of half the value of the Arch , or real distance between the two Objects , i. e. between the said Opposite Pole and Point ; now since any Diameter on the Plane of the Aequator ( for that , or some Parallel Circle to it , we now suppose to be the Plane of our present Projection ) meeting with those Rays , will be the Tangent of the Angle they make , which being in value ( as we said ) but half the real distance between the said Objects , it must need follow , if any Star or Point in the Heavens be distant from this opposite Pole , suppose 20. Degrees , That the Tangent of 10 Degrees from the Center of the Projection ( which represents the said Pole ) gives its true apparrent place there , and the like is to be said of any other distance . I shall not trouble the Reader with any Scheme to demonstrate this further , because ( being fusely treated of by Aguilonius and others ) 't is obvious enough to all Mathematicians ; and as for new Beginners ( if they desire a fuller conception of it ) let them but apply themselves to any man vers't in Projections , and in the space of ten Minutes he will shew it them more clearly and naturally , by Strings fitly placed on an Armillary Sphere , than I can here in many hours ; therefore supposing ( if to such , what I have already said be not evident ) that the Heavens may be thus projected by half Tangents , let us proceed to the way of doing it , that is to say , to the finding of the Centers and Radius's of all the Circles which conduce to the before mentioned Operations . As for the Concentric Circles of the first Plane , to wit , the Aequator , the Tropics , and the Limb , which is ( as I said ) Circulus maximus semper latentium , or some Parallel ▪ to it , there is no difficulty in describing them ; for having drawn at right Angles the Lines NS and EW ( representing the four Cardinal Points ) throu'P , the Center , or projected Pole , if you open your Compasses at the Tangent of 45 Degrees , and place one foot on the said P , you must needs project the Aequator ; because being distant from either Pole 90 Degrees , the Ray that touches it , and that which runs along the Axis to the opposite or North Pole , makes an Angle at your Eye ( as we said before ) of only half so much . In like manner , the Tropic of Cancer being 66 g. 30 m. from this Pole , the Tangent of 33 g. 15 m. gives his Radius , as the Tangent of 56. g. 45 m. does Capricorn , whose real distance from the said Pole is 113 g. 30 m. for it lies 47 Degrees beyond the former Tropick . And lastly , the Tangent of 64 g. 15 m. projects the Limb or uttermost Circle , if it be Circulus maximus super latentium , as being yet 15 Degrees further ; for the true distance of that Circle from the said Pole 128 Degrees and 30 Minutes . Now for the main matter , to wit , the great Circles which fall obliquely on the Plane , take this easy general Rule for them all , viz. That their Centers are distant from the Center of the Projection the Tangent of as many Degrees as their Poles are distant from the Pole of the Plane , on which the Projection is made ( that is to say , in our present Case , from the North-Pole of the World ) and the Secant of the said Degrees is their Radius . Suppose then you were to project ( v. g. ) the Ecliptic , which is the only oblique Circle of your first Plane ; you know that its Northern Pole , ( being in your Meridian ) is distant from the North Pole of the World 23 g. 30 m. Open therefore your Compasses at the Tangent of those Degrees , and place one Foot in P , and the other will give you in the Line PN ( the Northern half of the Meridian of your Plane ) or in the Line PS , ( the Southern half of the said Meridian ) the point D , for the requir'd Center . D then being the Center , open but your Compasses at the Secant of the said Degrees , and you have the Radius ; Nay , the Distance from D to e , or from D to w , the East and West Points of the Aequator ( or points where the Ecliptic intersects with the Aequator on the Sphere ) gives this Secant ; for if PD be the Tangent of 23 g. 30 m. then D e and D w are ( you see ) the Secants . But before we demonstrate the aforesaid Rule , let us make an end with the great Oblique Circles of the Transparent or second Plane , which are only the Horizon HRST , and the Azimuths of every 10 Degrees , exprest ( as I said ) by plain Pricks and Astrisks . As for the Pole of the Horizon , it is ( you know ) the Zenith , which being distant in your Meridian 38 g. 30 m. Southwards from the North Pole of the World , it must follow by the former Rule , that the Tangent of 38 g. 30 m. ( or Complement of the Elevation ) from P ( the Center of the Projection ) giving you ( Southwards in the Meridian of your Plane ) h , the requir'd Cent●● , the Secant of these Degrees will be the requir'd Radius ; Nay the distance from h to e , or from h to w the East and West points of the Aequator , ( or Points where the Horizon cuts the Aequinoctial Colure ) gives this Secant ; for if P h be the Tangent of 38 g. 30 m. h e and h w are the Secants . The Poles of all the Azimuths , are ( as every body knows ) in the Horizon ; now that of the Primary Vertical , being in the Meridian also , 't is distant in the Heavens ( on the North side of your Meridian ) the value of the Elevation , or 51 g. 30 m. so that by the foregoing Rule ( PV ) the Tangent of those Degrees will , from the Center P ( Northward , ) give you in the Meridian of the Plane the Center of this Circle , and the Secant the Radius . Nay , the distance from V to e , or from V to w , the East and West Points of the Aequator , ( or points where the said Primary Vertical cuts the Aequinoctial Colure ) gives this Secant ; for if PV be the Tangent of 51 g. 30 m. V e and V w are the Secants . Besides , where the moving foot of your Compasses ( thus extended ) touches the Meridian of the Plane , there will be the Zenith in projection , and consequently distant from P ( Southward , ) the Tangent of 19 d. 15 m. or half the Complement of the Elevation ; for our Zenith lyes in the Meridian 38 g. 30 m. beyond the Pole on the South-side of the Sphere or Heavens . As for the Centers of the other Azimuths , tho' there be no Tables calculated to shew how their repective Poles are distant from that of the Plane or Projection , and consequently the aforesaid Rule may seem useless , yet by resolving a Triangle , these Distances may be found , as also the value of the Angle , made by your Meridian ( or 12 a Clock hour Circle ) with the Meridian that passes throu ' the proposed Degree of the Horizon , so that the Rule serves as before ; for if you draw a blind Line thro' P , that makes an Angle with PN , answerable to the value of the Angle of those two Meridians in the said Triangle , the Tangent of the distance found between the Pole of the Plane and that of the propos'd Azimuth will still give you its Center from P in the said blind Line , and the Secant its Radius . But you may avoid the Resolution of a Triangle , by the usual expedite way , viz. by drawing thro' V ( the Center of the Primary Vertical , found as before ) the blind Line K. M. at Right Angles with P. N. ( the Northern part of the Meridian of your Plane ) and then pricking on both sides of the said V ( ZV being Radius ) the Tangents of all the Azimuths you would express , as ( for example ) those of 10 , 20 , 30 Degrees , &c. for the said Pricks give their Centers , and the Secant of those Deg. their Radius . This Way also agrees not a little with the above mentioned Rule ; for if the distance from V ( the Center of the primary Vertical ) to 10 ( the Center of the Azimuth of 10 Degrees ) be the Tangent of those Degrees , 't is evident , that the Radius Z 10 is the Secant ; and if this be the Secant , the distance from V to 10 is the Tangent . Thus then in short may be drawn ( mutatis mutandis ) all other great oblique Circles in any Steriographical Projection , when their Poles lye in one and the same Circle ; and now since the aforesaid Rule agrees even with this usual way of describing these Circles , I will here Demonstrate it , having done with the great Circles on both our Planes ; for as to the Hour Circles , they are all seen in Cultro , ( that is to say , they lye directly under your Eye , and consequently are in projection streight Lines , and distant ( as on the Sphere ) 15 Deg. asunder ; I say , since the Rule agrees not a little with this way , and that I have done with the great Circles both Planes , I will now demonstrate it by the two Lemmas that follow . The Demonstration . Sch. 5. I. THe Secant of any Arch is equal to the Tangent of the same Arch more by the Tangent of half its Complement . That is to say , CE the Secant ( for example sake ) of 60 Degrees ( in Scheme 5 ) is equal to EB ( the Tangent of 60 ) and to BA the Tangent of 15 , or half the Complement of 60 : For the Angle ECA being equal by Hyp. to the Angle ACH , becomes equal to * the Angle EAC . therefore EA is equal to † EC , and consequently EB plus BA is equal to EC . QED. Sch. 6. II. The Tangent of any Arch greater than 45 Degrees is equal to the Tangent and Secant of double its Excess above 45 Degrees ; that is to say , AB Tangent ( for example ) of 46 Deg. ( in Sch. 6th ) is equal to CD Secant of 2 Degrees plus DB Tangent of the said Degrees ; for the Angle DCA being by Hyp. † equal to the Angle ACH becomes equal to the Angle DAC ; therefore CD is equal to * AD , and consequently AD plus DB is equal to CD plus DB. These two Lemmas being premis'd , let us consider the Projection ( for example sake ) of the Ecliptic , and see how it agrees with our said Rule , to wit , That the Centers of all the projected great oblique Circles are distant from the Center of the Projection , the Tangent of as many Degrees as their Poles are distant from the Pole of the Plane on which the Projection is made and that the Secant of those Degrees gives their Radius's . The Ecliptic is to touch both Tropics on the Solstitial Colure or Meridian of the Plane , because it touches that Colure thus in the Heavens , and on the Sphere ; so that by Construction P ♋ ( the distance in Projection between the Center of the Plane and the Point where the Ecliptic touches the Tropic of Cancer ) is the Tangent 33. 15′ . or half 66. 30′ , ( its real distance on the Sphere from the North Pole ) and on the other side P ♑ ( the distance in Projection between the Center and the Point where the Ecliptic touches Capricorn ) is the Tangent of 56. 45. or half 113. 30′ . it s real distance as before . Now D by Construction being distant ( on the Meridian or Diameter of the Plane ) from the Center P the Tangent of 23 d. 30 m. ( or real distance between the Pole of the Plane of the Projection and that of the Ecliptic ) must needs be , according to our Rule , the Center of this Circle in Projection , and the Secant of those Degrees its Radius , if we prove the said D to be the middle of the Line ♋ ♑ ( or Diameter of the Ecliptic ) and D ♋ and D ♑ to be Secants of 23 d. 30 m. 'T is manifest that D ♋ is Secant of 23 d. 30 m. because 't is equal ( by Lem. 1. ) to PD , Tangent of 23 d. 30 m. plus P 69 Tangent of 33 d. 15 m. Again D ♑ is Secant of 22 d. 30 m. because P ♑ ( Tangent of 56 d. 45 m. ) is equal by Lemma the second to the Tangent and Secant of 23 d. 30 m. Now PD being Tangent of those Degrees , D ♑ must be Secant ; therefore D ♋ and D ♑ being equal , D is the middle of the Line ♋ , ♑ , and consequently PD ( the Tangent of 23 d. 30 m. from the Center of your Plane ) gives in its Meridian the Center of the Ecliptic , and the Secant of those Degrees the Radius , Q. E. D. and in this maner the way of projecting the other great oblique Circles is to be demonstrated . Nor do's this Rule solely serve for the Description of the great Oblique Circles on the present Planes , but for all that are expressed on Stofflers Astrolabe , or Mr. Oughtreds Horizontal ; Nay it shews not only how to draw the Meridians in Gemma Frisius his Projection , but , by the bare conversion of the Terms , the Parallels themselves , tho little Circles . For first as to the Meridians , whose Poles , ( as every body knows ) lye all in the Aequator , suppose you would describe the 10th . from the Limb or grand Meridian , which is to be the Solstitial Colure , since , in this Projection , your Eye lies in the East or West points of the Aequator , to wit in the Pole of the said Colure ; I say , suppose you were to describe the 10th . from the Limb , it follows by our Rule , because their Poles are 10 Degrees asunder on the Sphere and in the Heavens , that the Tangent of those Degrees gives from A ( the Center of the Projection in Sch. 7th . ) the requir'd Center B , and the Secant the Radius ; For this Circle on the Sphere cutting the Aequator at the 80th . Deg. from the Pole of your Plane , ( or point opposite to your Eye ) its extremity C must in Projection be distant from A the Tangent of 40 Deg. only ; Now since BC ( to wit BA plus AC the Tangents of 10 and 40 Deg ) is equal by Lemma the first ) to the Secant of 10 Degrees , and since BN . and BS ( or distance from B to the two Poles of the World ) are visibly the Secants of those Degreees , it necessarily follows , that the Meridian to be describ'd ( which pass we know throu ' the said three points C. N. and S. ) can have no other Center but B , nor Radius but the said Secant . Besides if if we make this Arch an entire Circle ( by the prickt Arch NAES ) then AB the Tangent of 10 Degrees plus BAE = BC ( the Secant of 10 ) is equal ( by Lemma the 2d . to the Tangent of 50 Degrees , but the other part of the said Meridian lyes ( we know on the Sphere ) 100 Degrees from the forementioned Pole of the Plane , and in projection the Tangent of 50 from the Center A ; ergo B is the true Center of the requir'd Meridian , and the Secant of 10 Degrees the Radius . Sch. 7. 2. For the Parallels or Circles of Latitude , the same Rule ( the Terms as I said being converted ) finds both their Centers and Radius's ; for if you would project ( suppose ) the 80th . Parallel from the Aequator , that is to say , the 10th . from the Pole of the World , 't is but saying , That the Secant of 10 Degrees from the Center of the Plane gives you the Center of the Parallel requir'd , and the Tangent of the same Degrees the Radius . To prove this , let AF ( in Sch. 7. ) be by Construction the Secant of 10 Degrees , and opening your Compasses at the Tangent of those Degrees place one foot on the said F , and describe the Circle KLPO ; Now because AF the Secant of 10 Degrees is equal ( by Lemma the 1st . ) to the Tangent of 10 and Tangent of 40 Degrees , therefore AK is the Tangent of 40 Degrees . Again because AF ( Secant of 10 ) plus FP = FK ( Tangent of 10 Degrees ) is ( by Lemma the 2d ) equal to the Tangent of 50 , ergo AP is Tangent of 50 ; but the Parallel requir'd is a Circle which on one side cuts ( in the Sphere ) the Aequinoctial Colure 80 Degrees from the Pole of your Plane ( or point opposite to your Eye ) and on the other side at 100 , or supplement of the said 80 Degrees , therefore seeing K and P the two extreme points of the projected Circle OPLK are distant from the Center A on the produc'd Axis ( or intersection of the Aequinoctial Colure with the Plane ) the Tangents of 40 and 50 Degrees ( to wit , the Tangents of half the real value of these Arches ) it must follow that the said OPLK truly represents the requir'd Parallel , and consequently that the Arch OKL is that part of it , which is farthest from your Eye , to wit , so much of the whole Circle as falls on the Plane . Thus much then for these Parallels , since all are to be describ'd after the same manner , and now having mention'd little Circles , 't is fit the Reader should know how the Circles of Altitude are to be describ'd on the second Plane of the Pedestal or Projection which are little Circles also . The way is easy for if you would have the Almucantar , ( suppose ) of 10 Degrees ( viz. abcd in Scheme 4th ) you must proceed thus . Because the Horizon in projection ( as we show'd you before ) is distant from the Center , ( on the North side of the Meridian ) the Tangent of 25 , 45m . or half the Elevation , to wit from P to H , and ( on the South side ) from P to S , the Tangent of 64. 15 , or half 128. 30′ . the supplement of the said Elevation , therefore the Almucantar of 10 Degrees ( being on the Sphere 10 Degrees neerer the Pole than the Horizon , ) will in projection be nearer the Center 5 Degrees . So that the Tangent of 20 , 45′ from the Center P giving ( a ) its extremity on the North side of the Meridian , and the Tangent of 59. 15. giving ( c ) its extremity on the South side , it follows that ( g ) half the distance between the said ( a ) and c becomes the Center to describe it by ; For since all the Circles of the Sphere are still Circles in projection ( except those that are seen in Cultro ( as we said ) if you have the Diameter ( or streight Line that joyns the extreme points of any of them ) half of it must needs give you the Center ; and in this manner then are the other Circles of Altitude , to be describ'd . But here take notice that whereas in Sch. 2. ( representing the second or trasparent Plane ) the Azimuths and Almucantars are found ( as I * show'd you ) by the consideration of the Pricks or Asterisks there exprest : Now , that the Reader may know how to Place them , the very Circles and Arches are describ'd on it , Sch. 4. as it represents for the said Pricks and Asterisks are ever to be in their intersections . And by way the Instrument maker may ( if he pleases ) make use of Pricks , and no Asterisks on the real Transparent Plane of the Pedestal ; for they will upon second thoughts perform better the Operation . The Conclusion . HAVING thus finish'd all the Operations that at present occur , I shall now end with what I promis'd in the * Beginning , to wit , with showing the Reader the particular Advantages of this Globe , which are of four kinds ; For , First it does several Operations not performable by the Ordinary Globes . 2ly . It does even the Operations ( which the other perform ) much easier and quicker . 3ly . It performs many at a view , which are to be done by the other ( for the most part ) successively . Lastly , It has several by-advantages and conveniences belonging to it by it's Make independent of the Operations . As to the Operations not performable by any other Globe , they are : 1. The placing of it self * Level , or Horizontal . 2. The ‡ Composing of it self to the Position of the Heavens . 3. The showing of the * Hour , even several wayes : and this not only at Home but at the same time also in all ‡ Places of the World. * 4. The knowing how much any place wants of Day , if it be Night there ; or of Night if Day there ; and consequently the ‡ Babilonish and Italian Hour without any Computation . 5. The showing the * Judaical Hour , without any Computation . 6. The showing the Sun 's true Place in the Heavens every * Moment , and consequently in what Countrey he is then Vertical . 7. The Sun's height at any time of the Day both at * home , and in all other ‡ Places , where the Globe show's 't is Day , as also his Depression where it show's 't is Night . 8. The Sun's * Azimuth and ‡ Bearing . 9. The Antient * Geography as well as Modern . 10. The Hour by the ‡ Moon ; with several other Operations concerning her . 11. The * proportion of Perpendiculars to their shades , with Corollaries in relation to Altimetry , and showing the Hour by your stick . 12. The performing of all the accidental * Requisites to Dialling , as how to draw Meridian Lines , and Lines Parallel to the Horizon , how to find the Declension of all Planes , as also their Reclination , Inclination , &c. But here the Reader must remember , that when I say none of the forementioned Operations are performable by other Globes , I mean not this alwayes in a strict sence ; for if ( suppose ) we have the Hour of the Day given , we may then ( as every body knows ) soon find by it the Sun's height , or if ( suppose ) we have his Azimuth , we have the Hour ; I say , I mean not this alwayes in a strict Sence , but call all these Operations not performable by other Globes , since they at first require ( for the Operations they do ) somthing as hard to be found as what we seek after ; whereas by exposing only of this Globe to the Sun , and having but the day of the Month , most of the Premises present themselves to us at all times with as much facility as the very Hour it self by an Horizontal Dial. Besides , the Reader must know , if a Brazen graduated Semi-Circle were hung on the Poles here , with an erected moveable Pin , or Cursor on it , there would be no need of the Holes ( I * formerly mention'd ) in each Parallel of the Globe , for the true Composing of it ; Nay this Semi-Circle ( omitting several other things ) will also give the hour , by being still directly over it , as often as 't is moved into the Plane of the Sun ; but seeing I pretend to show all the Operations here treated of , even on a naked and free Globe , by the sole help of a little String or Thred , I hint only the said Semi-Circle , that the Reader may use it , if he shall judge it any time fit for his business . In the second place , as to the Operations common to all Globes , but more easily perform'd by this , take some few Examples that follow . 1. If you would find ( suppose ) the Aurora by the Common Globes , you must ( after knowing the Day of the Month , or Suns place in the Ecliptic ) bring it to the Meridian ; then you must put the Index Horarius on 12 , and so move the said Sun's place to the East side of the Horizon . Afterwards you must find the opposit Point to the Sun's place , and fixing your Quadrant of Altitude in the Zenith ; you must mount the said opposite Point till it meet with the 18th Degree , and then the Index gives you what you seek for , whereas by This Globe you have nothing to do but to * depress your Bead 18 Degrees below the Horizon , and to move the String on the Zenith till the said Bead touches the Parallel of the Day on the East side of the Globe ; for then it lyes on the requir'd Hour . 2. If you would but know when the Sun rises by the other Globes ; you must ( after finding of the Sun's place ) lay your Index on 12 and when you have brought the said Place to the East side of the Horizon , the Index will show the Hour : Whereas now the * Intersection of the Parallel of the day with the Horizon performs the Operation without more a-doe . 3. If you would know the Ascensional Difference by the other Globes , you must first find the Right Ascension , then you must find the Oblique , and lastly you must substract the greater from the less ; whereas here the * distance on the Parallel of the day ( which the Hour-Circles measure ) between the 6 a clock hour circle and the intersection of the said Parallel with the Horizon gives at a view the requir'd Ascensional Difference in time , and consequently in Degrees . I shall not trouble my Reader with more Instances at present , leaving the rest to his own Observation , and he will still find ( at least generally speaking . ) That the Operations ( as I said ) common to both Globes are more easily and readily perform'd by this than by any other . As to the Advantages of the third kind , to wit , The performing several Operations at one view , which are perform'd successively by other Globes , there are at least 15 that present themselves to you ( the Globe being compos'd ) as soon as ever you have made the Shade of the String ( hanging on the Zenith ) to pass throu ' the Nadir ; for then you have before your Eyes . 1. The Hour of the Day ; by considering the shade of the * illuminated Pole. 2. The Day of the Month ; by considering on what Diurnal Parallel the Shade of the String marks the same Hour with that * shewn by the shade of the said illuminated Pole. 3. The Place where the Sun is Vertical ; by considering the Sun's * place in his Parallel , and consequently the Country under it . 4. The Sun's Sign or Place in the Ecliptic ; by considering ( according to the Increment or Decrement of the Days ) throu ' what part of the * Ecliptic the Parallel of the Day passes . 5. The Suns Declination ; by considering throu ' what * Degree of the Aequinoctial Colure , the Parallel of the Day passes . 6. The Sun's Azimuth and Bearing ; by considering what * Degree of the Horizon and what Nautical Character , are cut by the shade of the String hanging from the Zenith . 7. The time of the Sun 's Rising and Setting ; by considering on what * hour circle the Parallel of the Day and Horizon intersect on the East and West sides of the Globe . 8. The length of the Day and Night ; by considering how many Hour-Circles cross that part of the Diurnal Parallel * which is above the Horizon ; for they show the length of the Day , as the Hour-Circles , that cross the part under the Horizon , do the length of the Night . 9. The Sun 's Ascensional Difference ; by considering the * Hour-Circles on the Parallel of the Day between the 6 a clock Hour-Circle , and the intersection of the said Parallel with the Horizon . 10. The Sun's Amplitude ; by considering how many * Degrees in the Horizon the Sun rises from the true East Point , or sets from true West . 11. Where 't is Day or Night over all the World ; by considering the * illuminated and obscur'd parts of the Globe ; for the one show's ever where 't is Day , and the other where 't is Night . 12. Where they enjoy nothing but Day , and where nothing but Night : by considering the * Illumination and Obscuration about the Poles : for a Circle describ'd about the illuminated Pole , to the nearest shade of Extuberancy , shows , that all the Inhabitants within that Circle have nothing but Day , and that all they that dwell within the like Circle about the obscur'd Pole , have nothing but Night . 13. Where the Sun is Rising and Setting all the World over ; by considering the * preceeding and following shade of Extuberancy ; for the first , show's the people to whom the Sun then is Rising , and the other to whom the Sun is then Setting . 14. How many hours any place wants of day or night ; by considering first a Parallel to run over the Place propos'd , and then by reckoning the number of * Hours between the said place , and the preceeding , and following shade of Extuberancy ; the one bringing with it Day and the other Night . 15. What a clock 't is all the World over ; by considering ( according to the little Polar Figures ) the * Hour-Circle that passes over any place , and adding to the time thus found ( if it be in the afternoon ) as many hours as are past since Midday with you , or substracting ( if it be in the Morning ) as many Hours as you want of Midday . Now for the last kind of Conveniences , which this Globe Challenges , to it self , to wit. Those independent of the Operations , they are 4. 1. For , First It takes up little or no room wheresoever it stands , the bottom of the Pedestal not being ordinarily much bigger , than the foot of a large hour-glass , whereas other Globes are cumbersom , and embarras any Table or Place on which you set them . 2. It is wholly expos'd to our Eye as well below as above the Horizon ; whereas the Frame , Meridian , and the other Appendices of common Globes , always hide more than half of them . 3 It is as cheap as a single ordinary Globe , and yet performs the Operations of the Terrestrial and Celestial ones . 4. It never declines from its Position ; whereas other Globes by moving on their Poles encline presently more or less to this or that side of the Meridian and Horizon , so , that ( besides their usual grating ) all the Operations become sensibly false . FINIS . Decemb. 28. 1672. A Catalogue of GLOBES , Coelestial and Terrestrial , Spheres , Maps , Sea-Plats , Mathematical Instruments , and Books , with their prizes , made and sold by Joseph Moxon , on Ludgate-Hill , at the Sign of Atlas . GLOBES 26 Inches the Diameter . The price 20 l. the pair . GLOBES near 15 Inches Diameter . The price 4 l. GLOBES 8 Inches Diameter . The price 2 l. GLOBES 6 Inches Diameter . The price 1 l. 10 s. CONCAVE HEMISPHERES of the Starry Orb ; which serves for a Case to a Terrestrial Globe of 3 Inches Diameter , made portable for the Pocket . Price 15 s. SPHERES , according to the Copernican Hypothesis , both General and Particular , 20 Inches Diameter . Price of the General 5 l. of the Particular 6 l. of both together 10 l. SPHERES , according to the Ptolomaick System , 14 Inches Diameter . Price 3 l. SPHERES , according to the Ptolomaick System , 8 Inches Diameter . Price 1 l. 10 s. Gunter's Quadrant , 13 Inches Radius , printed on Paper , and pasted on a Board , with a Nocturnal on the back-side . Price 5 s. Gunter's Quadrant , 4 Inches Radius , printed on Paper , and pasted on Brass , with a Nocturnal on the backside , and a Wooden Case covered with Lether sit for it : A new Invention contrived for the Pocket . Price 6 s. A large Map of the World , 10 Foot long , and 7 Foot deep , pasted on Cloth and coloured . Price 2 l. A Map of all the World , 4 Foot long , and 3 Foot deep , pasted on Cloth and coloured , Price 10 s. in Sheets 2 s. 6 d. A Map of the English Empire in America , describing all Places inhabited there by the English Nation , as well on the Islands as on the Continent . Price 15 s. Six Scriptural Maps , 1. Of all the Earth , and how after the Flood it was divided among the Sons of Noah . 2. Of Paradise , or the Garden of Eden , with the Countries circumjacent inhabited by the Patriarchs . 3. The 40 years travel of the Children of Israel throug the Wilderness . 4. Of Canaan , or the Holy Land , and how it was divided among the twelve Tribes of Israel , and travelled through by our Saviour and his Apostles . 5. The Travels of St. Paul , and others of the Apostles , in their propagating the Gospel . 6. Jerusalem , as it stood in our Saviours time ; with a Book of explanations to these Maps , entituled , Sacred Geography . Price of the Maps 6 s. useful to be bound up with Bibles . price of the Book 1 s. 6 d. A Sea Plat , or Map of all the World , according to Mercator , in two large Royal Sheets of Paper ; set forth by Mr. Edward Wright , and newly corrected by Joseph Moxon , &c. Price 2 s. Sea-Plats for Sailing to all parts of the World. Price 6 d. the Sheet . The famous City of Batavia in the East Indies , built and inhabited by the Dutch , curiously Engraved , and Printed on four large Sheets of Royal Paper . Price 2 s. 6 d. A small Map of all the World , with Descriptions , on one Sheet . Price 6 d. BOOKS . A Tutor to Astronomy and Geography , or the Use of both the GLOBES , Celestial and Terrestrrial ; by Joseph Moxon , A Member of the Royal Society , and Hydrographer to the Kings most Excellent Majesty . Price 5 s. The Vse of the Copernican Spheres , teaching to salve the Phaenomena by them , as easily as by the Ptolomaick Spheres ; by Joseph Moxon , &c. Price 4 s. Wright's Correction of Errors in the Art of Navigation . Price 8 s. New and rare Inventions of Water-works , teaching how to raise Water higher than the Spring . By which Invention , the Perpetual Motion is proposed , many hard Labours performed , and varieties of Motion and Sounds produced . By Isaac de Caus , Engineer to King Charles the First . Price 8s . Practical Perspective , or Perspective made easie . Teaching by the Opticks how to delineate all Bodies , Buildings and Landskips , &c. By the Catoptricks , how to delineate confused Appearances , so as when seen in a Mirrour or Polish'd Body of any intended Shape , the Reflection shall shew a Design . By the Dioptricks , how to draw part of many Figures into one , when seen through a Glass or Christal cut into many Faces . By Joseph Moxon , &c. Price 7s . An exact Survey of the Microcosm , being an Anatomy of the Bodies of Man and Woman , wherein the Skin , Veins , Nerves , Muscles , Bones , Sinews , and Ligaments are accurately delineated . Engraven on large Copper Plates , Printed and curiously pasted together , so as at first sight you may behold all the parts of Man and Woman ; and by turning up the several Dissections of the Papers , take a view of all their Inwards ; with Alphabetical References to the names of every Member and part of the Body . Set forth in Latin by Remelinus , and Michael Spaher of Tyrol ; and Englished by John Ireton , Chyrurgeon ; and lastly , perused and corrected by several rare Anatomists . Price 14s . Vignola , or the Compleat Architect ; shewing in a plain and easy way , the Rules of the five Orders in Architecture , viz. Tuscan , Dorick , Ionick , Corinthian , and Composite ; whereby any that can but read and understand English , may readily learn the Proportions that all Members in a Building have to one another : Set forth by Mr. James Barrozzio of Vignola , and Translated into English by Joseph Moxon , &c. Price 3s . 6d . Christiologia , or a brief but true Account of the certain Year , Month , Day and Minute of the Birth of Jesus Christ. By John Butler , B. D. and Chaplain to his Grace James Duke of Ormond , &c. and Rector of Lichborough in the Diocess of Peterborough . Price 3s . 6d . A Tutor to Astrology , or Astrology made easie ; being a plain Introduction to the whole Art of Astrology ; whereby the meanest Apprehension may learn to Erect a Figure , and by the same to give a determinate Judgment upon any Question or Nativity whatsoever . Also new Tables of Houses , calculated for the Latitude of 51 degr . 32 min. Also Tables of Right and Oblique Ascensions to 6 degr . of Latitude . Whereunto is added an Ephemeris for three years ; with all other necessary Tables that belong to the Art of Astrology . Also how to Erect a Figure the Rational way , by the Tables of Triangles , more methodically than hath been yet published ; digested into a small Pocket Volume , for the conveniency of those that erect Figures abroad . By W. Eland . Price 2s . The Use of a Mathematical Instrument called a Quadrant , shewing very plainly and easily to know the exact Height and Distance of any Steeple , Tree or House , &c. Also to know the time of the Sun-Rising and Setting , and the Length of every day in the year , the Place of the Sun in the Ecliptick , the Azimuth , Right Ascension , and Declination of the Sun : with many other necessary and delightful Conclusions : performed very readily . Also the use of a Nocturnal , whereby you may learn to know the Stars in Heaven , and the Hour of the Night by them ; with many other delightful Operations . Price 6d . A brief Discourse of a Passage by the North-Pole , to Japan , China , &c. pleaded by three Experiments and Answers to all Objections that can be urged against a passage that way : As 1. By a Navigation into the North Pole , and two Degrees beyond it . 2. By a Navigation from Japan towards the North-Pole . 3. By an experiment made by the Czar of Muscovy , whereby it appears , that to the Northward of Nova Zembla is a free and open Sea as far as Japan , China , &c. With a Map of all the discovered Land nearest to the Pole. By Joseph Moxon , &c. Price 6d . Regulae Trium Ordinum Literarum Typographicarum ; Or , the Rules of the three Orders of Print-Letters , viz. the Roman , Italica , and English , Capitals and Small ; shewing how they are compounded of Geometrick Figures , and mostly made by Rule and Compass . Useful for Writing Masters , Painters , Carvers , Masons , and others that are lovers of Curiosity . By Joseph Moxon , &c. Price 5s . The Use of the Astronomical Playing Cards , teaching an ordinary Capacity by them to be acquainted with all the Stars in Heaven ; to know their Places , Colours , Natures and Bignesses . Also the Poetical Reasons for every Constellation . Very useful , pleasant , and delightful for all lovers of Ingeniety . By Joseph Moxon , &c. Price 6d . The Astronomical Cards . By Joseph Moxon , &c. Price plain 1s . Coloured 1s . 6d . best coloured , and the Stars Gilt. 5s . Geographical Playing Cards , wherein is exactly described all the Kingdoms of the Earth , curiously engraved . Price Plain 1s . Coloured 2s . best Coloured and Gilt 5s . the Pack . The Genteel House-Keepers Pastime ; or , the Mode of Carving at the Table , represented in a Pack of Playing Cards . By which , together with the Instructions in this Book , any ordinary Capacity may easily learn how to Cut up , or Carve in Mode , all the most usual Dishes of Flesh , Fish , Fowl , and Bak'd Meats : and how to make the several Services of the same at the Table ; with the several Sawces and Garnishes proper to each Dish of Meat . Set forth by several of the best Masters in the Faculty of Carving , and published for publick use . Price 6d . Carving Cards . By the best Carvers at the Lord Mayor's Table . Price 1s . Compendium Euclidis Curiosi . Or , Geometrical Operations , shewing how with one single opening of the Compasses and a straight Ruler , all the Propositions of Euclid's first five Books are performed . Translated out of Dutch into English . By Joseph Moxon , &c. Price 1s . An Introduction to the Art of Species . By Sir Jonas Moor. Price 6d . Two Tables of Ranges , according to the Degrees of Mounture . By Henry Bond Senior . Price 6d . Mechanick Exercises : Or , the Doctrine of Handy-Works , in nine Monthly Exercises . The first Three , viz. Numb . I. Numb . II. Numb . III. teaching the Art of Smithing . The second Three , viz. Numb . IV. Numb . V. Numb . VI. teaching the Art of Joynery . The third Three , viz. Numb . VII . Numb . VIII . Numb . IX . teaching the Art of House-Carpentery . Accommodated with suitable Engraved Figures . By Joseph Moxon , &c. Price of each Monthly Exercise 6d . Mechanick Dialling ; Teaching any man , though of an ordinary Capacity , and unlearned in the Mathematicks , to draw a true Sun-Dial on any Given Plane , however situated ; only with the help of a straight Ruler and a pair of Compasses ; and without any Arithmetical Calculation . By Joseph Moxon , &c. Price 1s . 6d . Mathematicks made Easie : Or , A Mathematical Dictionary , Explaining the Terms of Art , and Difficult Phrases used in Arithmetick , Geometry , Astronomy , Astrology , and other Mathematical Sciences , Wherein the true Meaning of the Word is Rendred , the Nature of Things signified Discussed , and ( where Need requires ) Illustrated with apt Figures and Diagrams . With an Appendix , exactly containing the Quantities of all sorts of Weights and Measures : The Characters and meaning of the Marks , Symbols , or Abbreviations commonly used in Algebra . And sundry other Observables . By Joseph Moxon . Price 2s . 6d . The English Globe , invented by the Right Honourable , the Earl of Castlemain , ( and of which this Book shews the use ) containing about a Foot in Diameter , are made by Joseph Moxon . Price ordinary made up 40s . and with the Projection described in Section 6. of this Book . Price 50s . At the place aforesaid , you may also have all manner of Maps , Sea-Plats , Drafts , Mathematical Books , Instruments , &c. at the lowest Prizes . FINIS . Notes, typically marginal, from the original text Notes for div A31232-e380 * pag. 24. Notes for div A31232-e1170 * p. 73. † p. 80. * p. 82. † p. 85. Notes for div A31232-e2460 Of the Circles describ'd on the Globe . The 4 Cardinal points of the Globe . * vid. Oper : 2. & 5. in Sect. 2. What the Operations of the Globe are perform'd with . A Memorandum . How the Treatise is divided . Notes for div A31232-e4180 The first way . A Memorandum . The second way . The Reason and Demonstration of the Operation . The first way . The Reason and Domonstration of the operation . How much the Sun illuminates more than half the Earth . How to know the terms of the shade of Extuberancy when the sun shines faintly . The second Way . The Third way . To know at any time whether it be Forenoon or Afternoon . * Operat . 1. pag. 4. A way to Compose the Globe by the Sun. * Operat . 2. pag. 7. A Memorandum . The first way of Composing the Globe . The Demonstration . The 2d way vid. Op. 10. The 1. way . The Second way . vid. Op. 10. The first way . * Operat . 3. pag. 8. The second way . The Third way . * vid. Oper. 2. pag. 5. A Memorandum . The 4th . way . The first way . The 2. way . * Op. 2. pag. 6. † Op. 5. pag. 10 A Memorandum . * Op. 3. pag. 8. The 1st . way . The 2. way . The 3d. way . * 2. pag. 6. The 4th . way . A Memorandum . * vid. the particulars in the conclusion or last Chapter . The 2d . way of composing the Globe by the shade . Demonstration . * Op. 3. pag. 8 The 3d. way of finding the day of the month . * Op. 2. pag. 6 & Op. 5. pag. 10. To find when , and at what declension , the Sun rises or sets earlier or later , accord - * Op. 6. pag. 11. * Vid. Oper. 13. Sect. 2. Notes for div A31232-e13600 Preliminary Considerations The grand Divisions of the Earth . The Boundary between Europ and Asia . The Division of each modern Country from the other The Ancient Limits of several Nations . A Table of reducing Degrees into Miles . What the Latitude of a Place is , and how to find it . What the Longitude is . Of the Grand Meridian . Of the most noted Places where Author 's have plac't the grand Meridian . Where we fix our Grand Meridian . How to find the Longitude of any place . A Memorandum : A preliminary Discourse of Climes . What a Clime is . What a Parallel is . Of the Antiquity and number of Climes . Of the 7 common Northern Climes . Of the 7 Southern Climes . Why the middle of the first Clime has 13. hours of day . How the first Circle of Longitude is divided as to the Climes . To find in what Clime any Place lies . Of the inequality of the Climes . * pag. 23. Of the 5 Zones . Of the bounds of the Torrid Zone , which contains the Amphiscii , To find when the shade changes side here . Of the bounds of the frozen Zones which contain the Periscii . Of the bounds of the Temperate Zones which contain the Heteroscij . First way . Second way . Third way . Of the Periaeci . Of the Antaeci . Where they have no Night , and where no Day . When 't will be perpetual Day or Night at any Place . * Op. 6. pag. 11. Where 't is Dinner-time all the World over . Where 't is the time of Rising all the World over . Where 't is Supper time all the World over . Where 't is Bed-time all the World over . The Reason or Demonstration of the Operation . * Oper. 10 sec . 1. pag. 14. To find the Sun's height in any place . The Reason of the Operation To find the Sun's Depression . To find all the Places , that have the Sun at the same height . How Astronomers begin their Computation of Time How the Italians . How the Babilonians . To find the Babilonish and Italian hour when the sun is in the Aequator . * Op. 10. sec . 1. pag. 14. * Op. 10. sec . 1. pag. 14. To find the Italian Hour when the Sun is in the Aequator . To find the hour both the said ways at any time . * Op. 18. p. 19 A most ready way of finding at any time the Babilonian and Italian Hour all the world over . Of the Judaic way of Computing time . A most ready way to find the Judaic Hour . Why the days of the Week being called by the Names of the Planets follow not each other after the order of the Planets * ♄ Saturn . ♃ Jupiter . ♂ Mars . ☉ Sol , ♀ Venus , ☿ Mercury , ☽ Luna . The Advantage in reckoning the Italian way . The Advantage in reckoning the Babylonian way . Of the Parallel Sphere . Oblique Sphere . All Positions ( taking the year round ) enjoy an equal share of the Sun's presence . * Vid. Op. 3. sec . 1. pag. 8. The Demonstration . How the Earth is prov'd Round . The Demonstration . Notes for div A31232-e26310 * pag. 5. * pag ▪ 10 ▪ * pag. 11 : * vid. pag. 8. & 15 : A Memoran . * p. 12. How you are to operate ; A Memorandum . An Example . Two Memorandums . The reason or demonstration of the Operation . A memorandum . Why 6 hours must be added sometime to the Tables . * p. 49. * p. 16. * pag. 49. * Op. 7. sec . 2. pag. 33. * Vid. Op. 1. & 2. pag. 49. A Corollary . An Example . Notes for div A31232-e32470 A memorandum . * Sect. 1. Op. 2. p. 5. *   1. 2. 3. 4. 6.   12. 11. 10. 9. 8. 7. 6. — — — — — — — 87. 93. 110. 140. 200. 300. 625. * Op. 2. Sect. 1. pag. 6. Notes for div A31232-e35120 A preliminary Discourse . * pag. 4. † pag. 5. * pag. 10 ▪ * ☞ Because every body ( that desires to know these and the following Problems ) has not perchance at hand Mr. Gunter's Book , I shall add them to this Treatise as the Reader will find at the end of it : J. Moxon . How to find the Tangent and Secant of any degree . Demonstration . A Memorandum . The Construction . An Example . How to draw the half hours , quarters , &c. The Construction . Demonstration . * pag. 71. The Demonstration . * pag. 4. A Memorandum . * pag. 8. * pag. 73. The Construction . The construction . * pag. 79. How to draw a Line Paralel to the Horizon , and how to place truly the draught on its Plane An easier way how to place any paper draught on its Plane . A Memorandum . Demonstration . A Memorandum . Some few things to be premis'd . The Construction of an East Dial. Of a West Dial. Of the Stile and Substilar . The Demonstration . The Construction . The Demonstration . The reason of the unequal distance of these hour-lines . What a Declining Plane is . The Construction . * pag. 80. To describe the Morning hours of a Declining Dial. To describe the Afternoon Hours . How to make the Stile and Substilar of a Declining Dial. A Memorandum . The Construction . The Demonstration of these 2 declining Dials . A Memorandum . * pag. 84. Another Demonstration . * pag. 83. * pag. 73. The construction . * pag. 23. * pag 8. The Construction . A ready way to find the Stile and Substile of a declining Dial. Demonstration . * pag. 92. The Demonstration of the Stile and Substilar . * pag. 82. * vid. pag ▪ 104. * vid. pag ▪ 105. The Construction and Demonstration . How to make an Horizontal Plane an Aequinoctial one . The Demonstration . The Geometrical Construction . A Memorandum . * pag. 8. The Construction . The Construction and Demonstration of a declining direct Dial facing the South . A Direct North reclining Plane . * pag. 89. How to describe the Plane of this Reclining Dial on the Globe . The Construction . A Memorandum . Of the Stile and Substilar * pag. 82. Another Demonstration : The construction . * pag. 2. First way . * pag. 4. * pag. 4. The second way . The first part of the Operation . * pag. 89. The second part of the Operation . Why every Erect Stile or perpendicular show's not always the true Hour . The Construction : * pag. 89. The Demonstration . * pag. 94. * pag. 75. Demonstration . The Advantage or use of this Dial. The Construction . Demonstration . Another Dial of the same nature . The construction . The Demonstration . The Construction . Demonstration . The Construction . The Geometrical way . The Demonstration . The Construction . The Demonstration . * pag. 73. How this Dial is to be made when the windows lye not Southward . The Construction of it , as to the Hour at home . * pag. 73. The Construction of it as to the Hour in other places . To find the Suns place and day of the Month. To find the Rising and Setting of the Sun. To find the Suns Amplitude . To find the Height of the Sun. To find the Suns Azimuth and Bearing . To find the Proportion of Perpendiculars to their Shades . The description of the Branches or Embellishments in Sheme 43. * p. 111. † p. 112. * vid. p. 113. * p. 71. Of the Sector . Notes for div A31232-e68720 * Op. 17. Sect. 1. pag. 19. A Memorandum . * p. 6. * p. 68. * Op. 5. way 2. p. 10. A Memorandum . Of the first Plane and its bigness . Of the Circles and Stars on it , and how they are placed . Of the second Plane , and it's bigness . * p. 6. † p. 68. * p. 132. Two Memorandums . The Principle on which this Projection depends . Of the Concentric Circles . The general Rule for projecting the great Oblique Circles . Of projecting the Ecliptic . Of projecting ▪ the Horizon . Of projecting the primary Vertical . Of projecting the rest of the Azimuths . An expedite way of finding the said Centers and Radius . Lemma 1. * Eucl. 27. 1 ▪ † 6. 1. Lemma 2. † Eucl. 27. 1. * 6. 1. The Ecliptic truly projected . A Memorandum . The way of describing G. Frisius's Meridians . The way of describing G. F. hia Parallels . How to describe the Circles of Altitude on the 2 Plane . * p. 138 and 139. Notes for div A31232-e82150 * p. ● . First kind . * pag. 4. ‡ p 8. & 15. * pag. 13. ‡ p. 31. * pag. 36. ‡ pag. 39. * p. 40. * p. 35. * p. 5. ‡ p. 37. * p. 10. ‡ p. 11. * p. 21. ‡ p. 51. * p. 65. * p. 70. A Memorandum . * p. 8. 2d kind . * p. 18. * p. 9. 3 kind . * p. 14. * p. 15. * p. 35. * p. 13. * p. 11. * p. 10. & 12 * p. 16. * p. 17. * p. 19. * p. 17. * p. 33. * p. 33. * p. 34. * p. 36. * p. 31. 4th kind . 
A51767	----	The five books of Mr. Manilius containing a system of the ancient astronomy and astrology : together with the philosophy of the Stoicks / done into English verse with notes by Mr. Tho. Creech. Astronomicon. English Manilius, Marcus. 1700 Approx. 502 KB of XML-encoded text transcribed from 160 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2005-12 (EEBO-TCP Phase 1). A51767 Wing M431 ESTC R28801 12579842 ocm 12579842 63721 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A51767) Transcribed from: (Early English Books Online ; image set 63721) Images scanned from microfilm: (Early English books, 1641-1700 ; 965:32) The five books of Mr. Manilius containing a system of the ancient astronomy and astrology : together with the philosophy of the Stoicks / done into English verse with notes by Mr. Tho. Creech. Astronomicon. English Manilius, Marcus. Creech, Thomas, 1659-1700. [2], 68, 134, 88, [7] p. : ill. [s.n.], London : 1700. Reproduction of original in Cambridge University Library. Index: p. [1]-[6] Errata: p. [7] Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. 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Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Astrology. Astronomy, Ancient. Stoics. 2005-07 TCP Assigned for keying and markup 2005-07 Aptara Keyed and coded from ProQuest page images 2005-08 Andrew Kuster Sampled and proofread 2005-08 Andrew Kuster Text and markup reviewed and edited 2005-10 pfs Batch review (QC) and XML conversion The Five BOOKS OF M. MANILIUS , Containing a SYSTEM OF THE Ancient Astronomy AND ASTROLOGY : Together with The Philosophy of the STOICKS . Done into English Verse with Notes . By Mr. THO. CREECH . Nunc autem quid est sine his cur vivere volimus ? Mihi vero cum his ipsis vix : His autem detractis , ne vix quidem . Cicero ad Var. LONDON , Printed , and Sold by the Booksellers of London and Westminster . 1700. AN ACCOUNT OF MANILIUS . SIR , THE Campaign being over , and Councils not yet begun , the World is very much at quiet ; nor can I find News enough to fill a Letter : But to keep up our usual Correspondence , I send you an Account of an old Latin Poet , very little known , tho' as worthy your Acquaintance , as many of those who are in Credit . He lay buried in the German Libraries , not heard of in the World , till Poggius Publish'd him from some old Manuscripts found there ; and tho' 1 Burde Cotzus , thinks Lucian consulted this Poet when he wrote his little Treatise of Astrologie ; tho' Julius Firmizus is 2 accus'd as an ungrateful Plagiary , for not acknowledging from whom he Transcrib'd the chiefest parts of his Books ; yet there is no good Evidence , that any one Writer mention'd this Author before Poggius . Pliny is suppos'd to speak of him as a 3 Mathematician , and Gerbertus , as an 4 Astrologer ; but concerning the Poet , there is as dead a silence as if he had never been ; nor can his greatest Admirers find any Character of him in old Writers . Yet it must be own'd , that he is an Author of some considerable Age ; for the Manuscripts which Poggius , Bonincontrius , Scaliger , and Franciscus Junius us'd , were ancient : Tanaquil Faber , Spanhemius , and the severest Criticks allow him to be as old as Theodosius the Great , and pretend to find some particular Phrases in him , which are certain Characters of that Time. Others , who believe they have very good Reasons to place him higher , find it very difficult to account for this universal silence : What they offer , is either bare May-be and Shift , and scarce ever amounts to a tolerable Reason : 'T is true , they say , he is not mention'd by Ovid in his 5 Catalogue of Poets , and no wonder , since he did not begin to write before the 6 Banishment of Ovid , and Published nothing before his Death ; Perhaps he was one of those Young Men , — 7 Quorum quod inedita cura est Appellandorum nil mihi juris adest . or his Fame did not reach so far as Pontus : Otherwise they are confident there are too many Graces in his Poem to be neglected ; at least , the singularity of his Subject would have deserved to be taken notice of , as well as that of 8 Gratius . But why Quintilian doth not propose him to his Orator , tho' he encourages him to 9 read Macer and Lucretius , and 1 affirms , that a competent skill in Astronomy is necessary to make him perfect in his Profession ? Why the following Philologers never use his Authority , tho' it might very often have been pertinently cited by Gellius and Macrobius ? Why the Grammarians and Mythologists , seem to be altogether unacquainted with his Writings ? They confess these are Questions not easie to be answer'd . Of this Poet , who is acknowledged by all Parties to have lain very long unknown , and about whom , since he first appear'd in the World , so many Controversies have risen , I am now to give you an account . His Name is commonly said to be Marcus Manilius , which in some Copies of his Poem is shortned into Manlius , in others softned into Mallius : This variation is inconsiderable , and the common fault of unaccurate Transcribers ; but 2 Bonincontrius affirms , that the Title of his very Ancient Copies was , C. Manilii Poetae illustris Astronomicon ; and that he had seen a Medal , in which was the Figure of a Man , but in a Foreign Habit , with a Sphere plac'd near his Head , and this Inscription , C. MANILI . 3 Lilius Gyraldus mentions another of the same stamp ; But that these Medals belong'd to this Poet , may be as easily deny'd , as 't is affirm'd , or rather , as 't is conjectured : However all Parties agree , that the most Ancient Copies constantly bear the Title of Manilius ; but whether the Books of Poggius and Bonincontrius , which call him Caius , or those of Scaliger and others , in which we find Marcus written , are to be follow'd , is submitted to every Man's Discretion ; the Matter is not of any Consequence , nor a fit Subject for Dispute , because impossible to be determin'd : Tho' if Conjecture may be admitted , I should fancy that it is more probable a Transcriber may err , when he puts M. before Manilius , than when he writes a C. because in the former case , the Sound of the following Word , which is the most considerable in the Title , and consequently the chiefest in his Thoughts , may pervert him ; but in the latter , He hath no temptation to mistake . This M. or C. Manilius , was born a Roman , and liv'd in Rome when Rome was in her Glory ; commanding the biggest part of the known World , and full of the greatest Men that ever any time produc'd : For the same Age that saw Manilius enjoy'd Varro , Lucretius , Cicero , Caesar , Virgil , Varius , Horace , and ( to close the Catalogue ) Augustus . In the beginning of this Astronomical Poem that Emperour is 4 invok'd , that very Emperour who was the 5 adopted Son of Julius Caesar , who 6 beat Brutus and Cassius at Philippi , 7 overthrew Pompey the Great 's Son , 8 who sent Tiberius to Rhodes , 9 who lost three Legions in Germany under the Command of Varus ; who 1 routed Anthony and Cleopatra at Actium , and sav'd the Roman Empire by turning that overgrown dissolute Republick into a well regulated Monarchy . Here are so many Characters , that the Person cannot be mistaken , not one of them agreeing to any but the first Great Augustus . So that this Author liv'd in that Age to which He pretends by so many very particular Circumstances , or else He is a most notorious Cheat , and one of the greatest Impostors in the World. It seems 2 Tanaquil Faber thought him to be so , since without giving any Reason He brings him down as low as the time of Theodosius : 3 Vossius was once of the same Opinion , having observed , as He then thought , some Measures , Words and Phrases peculiar to that Age , and therefore He concludes against Scaliger , that Julius Firmicus did not follow Manilius , but Manilius wrote in Verse what Firmicus had published in Prose under the Reign of Constantine the Great : But upon second Reading this 4 Critick alter'd his first Sentiments , and allows him to be as ancient as the Poet himself desires to be thought . 5 Gassendus often quotes him , and always sets him after Firmicus , as may be seen in many places of his Writings ; but gives no reason why he constantly observes that order : But Gevartius , who had study'd and design'd to publish Notes upon this Author , says in a Letter to Mr. Cambden , 6 I have been long acquainted with this Writer , and know him well , but cannot , with Scaliger and other learned Criticks , allow him to be as ancient as Augustus , for in my Notes I will demonstrate that he liv'd in the Age of Theodosius and his Sons Arcadius and Honorius , and that he was the same with Manlius Theodorus , upon whose Consulship Claudian writes a Panegyrick , in which he mentions his Astronomicon . The same thing he asserts in his Comments upon 7 Statius , and promises to do Wonders in his 8 Electa upon this Subject ; what his performance was I do not find taken notice of by any of the Criticks , nor am I concern'd for it , being certain that he fail'd in his Attempt , because it was ridiculous and rash : Yet the learn'd Ezechiel Spanhemius endeavours to support this Conjecture of Gevartius , 9 and tells us , that sub Armis , a Phrase familiar to Manilius , as lib. 1. v. 795. — Matrisque sub Armis Miles Agrippa suae — Lib. 4. v. 656. — Regnum sortita sub Armis . And in another place , — Quumque ipsa sub Armis Pax agitur — was us'd in the time of Theodosius , as appears by the following passage in that Emperour 's Code , 1 Quicunque sub Armis Militiae munus Comitatense subierunt . Scaliger himself unwarily gave a very great advantage to this Opinion , when he 2 affirm'd , that the word Decanus , which Manilius uses , was brought from the Camp , and that a Sign which govern'd ten Degrees was call'd Decanus , because an Officer who commanded ten Men in the Army had the same Title : But 3 Salmatius , who discover'd the Mistake , ( for Decanus was not heard of in the Roman Camp before the time of Constantine the Great ) hath so well corrected it , or rather 4 Huetius hath given so good an Account of that Word , that tho' an Argument drawn from it may be strong against the Critick , it will never be of any force against the Author . It is almost needless to mention the Exceptions of those Criticks who think his Stile impure , or , as they please to speak , too barbarous for the Age he pretends to ; Indeed 5 Gyraldus endeavours by this very Argument to prove he was no Roman born : But 6 Scaliger laughs at him for his Attempt , tells him that he does not distinguish between Idiotisms and Barbarisms , and that Vitruvius ( to whom he should have added Lucretius ) might be call'd barbarous as well as he : 7 Franciscus Junius commends the propriety of his Language , 8 Salmatius and 9 Huetius have approved many passages which lesser Criticks thought to be impure ; And the accurate Vossius , 1 after he had studied and considered him well , found nothing in him inconsistent with the Age of Augustus , and the Politeness of his Court. Indeed most of the Instances that are produc'd upon this head , do not fasten on the Author himself , but on the Transcribers and Publishers of his Writings . There ought to be a new Edition of his Astronomicon , and I do not despair of seeing one which will have a pure genuine Text , and free that Text from many of his Interpreters Comments , especially from the Notes of the miserable wretched 2 Fayus . You see , Sir , I have brought this diffus'd Controversie within a very narrow Compass ; Tanaquil Faber and Gassendus keep their ( if they had any ) Reasons to themselves . Their Authority I confess had been perswasive , had they considered , and after a fair hearing determin'd the Controversie ; but an incident declaration , and an unweigh'd Sentence concerning the Age of any Writer ought not to be submitted to , but appeal'd from : And therefore if I can shew the Observation of Spanhemius to be unconcluding , and refute the bold Conjectures of Gevartius , I shall leave Manilius in possession of that Age , which he so often , and with so much assurance claims . And here I am sure we should not have been troubled with Spanhemius's Observation , had he been pleas'd to consider , that sub Armis , and sub Armis Militiae , being very different from one another , might be us'd in very different Ages of the Empire ; and that he argues very ill , who says , the one was known in the Time of Theodosius , and therefore the other was not common in the Court of Augustus : 'T is certain that it was , for Virgil ( whom Manilius often imitates ) hath — Sedet circum castella sub Armis , — Equitem docuere sub Armis Insultare solo — And in another place , — Ludunt Belli simulachra sub Armis . And this Virgil himself borrow'd from Ennius , who says , Ter me sub Armis malim vitam cernere . I could produce more Authorities , were not these sufficient to secure Manilius from Spanhemius's Observation . But Gevartius , as he is bolder , so he is much more unhappy in his Conjectures ; he fixes upon the Man , and says this Manilius is Mallius Theodorus , celebrated by the Poet Claudian ; for the Author of this Astronomicon , is in many of the old Copies call'd Mallius , and this Mallius Theodorus , was a good Astronomer , and a Writer of great Industry and Reputation : But did Gevartius ever meet with the Astronomicon , under the Title of Fl. Mallius Theodorus ? Or of Fl. Mallius and not alwaies of C. or M. Manlius , Mallius or Manilius ? Doth Claudian commend the Poetry of his Consul , or mention his Acquaintance with the Muses ? or could a Poet forget , or not celebrate that Talent which he himself must look upon as a very great Perfection , and the Age would have highly valued , had he been the Author of this Poem ? Doth he say he wrote Books of Astronomy , knew the Depths of Astrology , and was admitted into the Councils of the Stars ? Here was a large Field for that luxuriant Wit to have wanton'd in , and it cannot be thought he would have conceal'd the deserts of his Patron when he study'd to commend him : But instead of this he praises his Justice , Integrity , Clemency and Honor ; he extols his Eloquence , and prefers the sweetness of it before all the delicate Charms of Poetry and Musick . 3 Ut quis non sitiens Sermonis Mella politi Deserat Orpheos blanda Testudine cantus ? And tho' all the Muses are concern'd for him , and busie in his Service , yet he is devoted to none of them but Ura●ie , who assisted him in his Astronomical Diversions . 4 Uranie redimita comas , quâ saepe Magistra Mallius igniferos radio descripserat Axes . Gevartius very well observes that this Consul Mallius was an Astronomer . 5 Invenit aetherios signantem pulvere cursus , Quos pia sollicito deprendit pollice Memphis : Quae moveant momenta polum , quam certus in Astris Error : Quis tenebras Soli causisque meantem Defectum indicat numerus . Quae linea Phoeben Damne , et excluso pallentem fratre relinquat That he publish'd some admir'd Books 6 Consul per populos , idemque gravissimus Author Eloquij , duplici vita subnixus in aevu● Procedat , libris pariter , fastisque legendus . But how doth it appear that Astronomy was his Subject , when Claudian himself tells us it was the Origine and Constitution of the World ? He represents him as well vers'd in all the several Hypotheses of the Natural and Moral Philosophers , acquainted both with the Physicks and Ethicks of the Greeks , and able to discourse of their Opinions very properly , and very elegantly in Latin. 7 Graiorum obscuras Romanis floribus Artes Irradias — But when he speaks of his Writings he says he describ'd the Origine and Disposition of the World , and gave very convincing proofs of his own Wit , Capacity , and Judgment , by his exact account of the beautiful Order , and regular Contrivance of that wonderful Machine . 8 Qualem te legimus teneri Primordia Mundi . Scribentem , aut Partes Animae per Singula , Talem Cernimus , et similes agnoscit Pagina mores . From these Verses and other passages in Claudian , as — 9 Quae vis animaverit Astra , Impuleritque Choros , quo vivat Machina motu ; it may be inferr'd that this Consul Mallius , was as to Natural Philosophy a Stoick , and built his World according to the Hypothesis of that Sect , and therefore wrote something very like what we find at large in the first Book , and hinted at in several passages of the other Books of Manilius . But this being the least part of our Author , and subservient to his greater and general design , it must not be suppos'd that Claudian should enlarge only upon this , and leave his whole Astrology untoucht ; unless we think Claudian as ridiculous as that Painter would be , who being to fill his Canvas with a noble Family should draw a single Servant , or paint only a Finger or a Nail when he had a large beautiful Body to represent . I have been the more particular in this matter , because Gevartius pretends to demonstration , tho' to confute his conjecture it had been sufficient only to observe , that it is the most ridiculous thing in the World to imagine that Mallius a Man well known both for his personal Endowments and publick Employments , who had been Governour of several Provinces , and at last Consul should publish a Treatise under his own Name , and yet in almost every Page of the Book endeavour to perswade his Readers it was written four hundred years before . For it must be granted that the Prince whom he 1 invokes in the beginning of his Poem , who is stiled Patriae Princepsque Paterque , who is deify'd whilst 2 alive , and ( not to repeat the other particulars I have already reckon'd up ) whose 3 Horoscope was Capricorn , was the first Great Augustus , and therefore there is no need of calling in the Authorities of 4 Horace , 5 and 6 Suetonius to prove it . This last Character puts me in mind of another Objection that may be drawn from F. Harduin's 7 Observation , for he says that Suetonius was himself deceiv'd , and hath deceiv'd all those who have thought Capricorn was concern'd in the Nativity of Augustus : For if this be true all the Pretences of Manilius are ruin'd ; but since that Writer doth not back his Assertion with any Reasons , I shall not submit to his bare Authority , nor wast my time in guessing what Arguments he may rely on , being not bold enough to conjecture what the daring Author may produce . Having thus fixt the Age of this Author , and prov'd him to have liv'd in the time of Augustus Caesar , I shall venture farther to affirm that he was born under the Reign of that Emperour , not only a Roman , but of illustrious Extraction , being a branch of that noble Family the Manilij , who so often fill'd the Consul's Chair , and supply'd the best and greatest Offices in the Roman Commonwealth . And here I must oppose many of the Criticks , and be unassisted by the rest : For 8 Scaliger confesses , that from his own Writings , it cannot be known what Countryman he was , and no other Authors give us any Information . Bonincontrius and Gyraldus endeavour to prove from the Medal already mention'd , that he was no Roman ; the Learned 9 Isaac Vossius thinks he was a Syrian , and all who look upon him to be the same with that Manilius mention'd by Pliny , Nat. Hist . lib. 35. cap. 17. say he was a Slave : Only Petrus Crinitus 1 affirms , he was Nobly Born , and Mr. Tristan will 2 have him to be that Manilius , of whom Pliny gives a very Honourable Character , in the Tenth Book and Second Chapter of his Natural History ; where he says , He was of Senatorian Dignity , an excellent Scholar , and ( If we believe Mr. Tristan ) a very good Astronomer . But since Crinitus doth not prove what he says , and Mr. Tristan but conjectures at best , and upon Examination , will be found to be very much mistaken in his Conjectures , therefore I cannot expect any assistance from either of these Authors . Now it is not certain that the Gentleman whom Pliny speaks of in the Second Chapter of his Tenth Book was Nam'd Manilius . Copies differ , and in the M. SS . of Salmasius 3 he is call'd Mamilius : Pliny doth not say one word of his skill in Astronomy ; he only 4 affirms , That he was the first of all the Romans who wrote concerning the Phoenix , that never any Man saw it feed , that in Arabia it is Sacred to the Sun , that it lives 660 Years , and that with the Life of this Bird is consummated the Conversion of the Great Year , in which the Stars return again to their first points , and give significations of the same Seasons as at the beginning : And all this any one may write who is in an entire Ignorance of the Courses and Influence of the Stars : But when Mr. Tristan farther observes that Pliny insinuates , besides a particular respect , a kind of Intimacy and Acquaintance between this Manilius and himself , he gives us a very convincing Argument against his own conjecture : for there is good reason to believe this Manilius the Poet dy'd before Augustus , and therefore could not be intimate with Pliny . To set this whole matter in its due light , I shall , as the learned and ingenious Sr. Edward Shirburn hath already done in his Preface to the Sphere of Manilius take a view of those , who have been by the name of Manilius deliver'd down to Posterity as Men of Letters , and then consider which of all those , or whether any one of them was this Manilius the Poet. Of that Manilius whom Pliny mentions in the second Chapter of his tenth Book I have already said enough ; and about that Manilius , whom Varro 5 cites , I shall not be concern'd , there being no ground to think he was the Author of this Poem . 6 Pliny lib. 35. cap. 17. tells us of one Manilius surnam'd Antiochus , who with Publius Syrus , and Staberius Eros were brought to Rome , all three of Servile Condition , but persons of good Literature . His words are these , Pedes Venalium trans mare advectorum [ Creta ] denotare instituerunt Majores ; Talemque Publium [ Syrum ] mimicae Scenae conditorem , et Astrologiae consobrinum ejus Manilium Antiochum , item Grammaticae Staberium Erotem , eadem navi advectos videre Proavi . Our Ancestors us'd to mark with Chalk the Feet of those Slaves who were brought over from beyond Sea to be sold ; And such an one was Publius [ Syrus ] the Founder of the Mimick Scene , and his Cousin German Manilius Antiochus of Astrology , and Staberius Eros of Grammar ; whom our great Grandfathers saw in that manner brought over in one and the same Ship : This Manilius Laurentius Bonincontrius ( who near two ages agoe commented on our Author ) conceives the same with Manilius who wrote this Astronomical Poem , to confirm which opinion he produces the evidence of a Silver Medal in his possession whereon was the figure of a Man , in an Exotick Habit with a Sphere plac'd near his Head , and this Inscription MANILI : The same is affirm'd says Lilius Gyraldus by Stephanus Dulcinus , and the said Gyraldus farther assures us that a familiar Friend of his , one Nicolaus Trapolinus , had another Medal of the like Stamp and Inscription . But against this opinion of Bonincontrius and Gyraldus , Scaliger opposes a double Argument , one drawn from the seeming inveracity of that suppos'd Evidence ; no such Medal being at this day to be found in the Cabinets of any , no not the most curious Antiquaries ; the other from the reason of Time , for Manilius Antiochus being brought to Rome in the beginning of Sylla's days ( for he was brought in the same Ship with Staberius Eros , who open'd his Grammar School in Rome whilst Sylla was alive ) must needs , if he were the Author of this Poem have been 120 Years old when he began to write , this piece being written in the latter years of Augustus . Besides , the Author in the Proem of this work wishes for long life to compleat his intended Poem , and therefore certainly he was not of that Age , it being ridiculous for a Man to wish for long life , when he is at the Extream already . The same Pliny , lib. 36. cap. 10. speaks of one Manilius a Mathematician , who when the Obelisk which Augustus erected in the Campus Martius for finding out the Hours of the day by the Shadow of the Sun , with the Increase or Decrease of the Days and Nights , plac'd a guilded Ball , Cujus Vertice Umbra colligeretur in semetipsam , alia atque alia incrementa jaculantem Apice , ratione ( ut ferunt ) à capite hominis intellecta , says Pliny , who commends the design . To this Person Scaliger conceives this work may with fairer probability be ascrib'd than to the former ; which Opinion is by divers other judicious Men embrac'd . The excellently learn'd Isaac Vossius conceives yet , that the Manilius Antiochus , and the Manilius Mathematicus before mention'd are not two distinct Persons , but one and the same under different Titles and Appellations , and the very Author of the Poem we now publish , whose particular Sentiments upon this Subject , and Arguments confirming the same , he was pleas'd not long since to impart to me , by his most obliging Letter , in answer to some Queries by me propounded in one of mine to him upon occasion of my intended publication of this piece , which for the Readers satisfaction , I shall here make publick , tho' not in his own words , yet as near as may be in his own Sense . And first in answer to Scaliger's Argument drawn from Reason to Time , against Manilius Antiochus , upon the supposition of Staberius Eros ( one of the Three before mention'd ) set open his Grammar School in the time of Sylla ninety five years before the death of Augustus ; and that therefore Manilius could not probably be ( according to Scaliger's Computation ) less than 120 Years old at the time when this Poem was written ; he urges by way of reply , that Suetonius ( from whom Scaliger takes the ground of his Argument ) doth not say that Staberius Eros open'd his School in Sylla's time , but that he taught gratis the Children of those who in Sylla's time were proscrib'd . The Words of Suetonius are these , Sunt qui tradunt tanta eum ( Staberium ) honestate praeditum , ut temporibus Syllanis Proscriptorum liberos gratis , et sine mercede ulla in Disciplina receperit . How long that was after the times of Proscription will be needless here to declare ; and that Manilius was not so old as Scaliger conceives , when this piece was written , may be made out from this , that he was the Cousin German of Publius Syrus , who that he was brought a young Boy to his Patron , Macrobius affirms , from whom likewise , and from the Verses of Laberius it may be collected , that he was but a Youth when he came upon the Stage against Laberius , which was but a little before the death of Julius Caesar and Laberius also ; to whom he succeeded on the Mimick Stage in the second year of 184 Olympiad , that is in the Year of Rome 711 , as Eusebius testifies . And therefore seeing it is , manifest that Manilius publish'd this Poem soon after the Varian Defeat , which happened in the Year 762 of Rome , it is as evident likewise that between the Youth or Adolescence of Manilius , and the time wherein he wrote this piece , there could not pass above one and fifty Years , and consequently there is no reason to assign so great an Age to Manilius , as Scaliger here doth , since perhaps he was not seventy years old when he had finish'd this his Astronomical Poem . As to what Scaliger subjoyns touching Manilius his wish for long life together with a cheerful old Age , and the Inference he thence makes that he could not reasonably be thought to be old then , who wish'd he might live to be so . The Argument is but weak , for Senium is one thing , and Senium Annosum is another ; Nor doth he simply wish for Vitam Annosam , but Vitam Annosam quae conjuncta sit cum molli Senecta , which may be wish'd for even by those who are very old . As for the name of Antiochus , he seems to have taken it from the famous Philosopher Antiochus Ascalonita , often mention'd by Cicero , Plutarch , Sextus Empiricus , and others , whose School not only Cicero , but Varro , Brutus , and divers others are said to have frequented , and in all probability this our Manilius also , as being not only of the same Nation , but happily born in the same Town ( Ascalon . ) So that it may seem no wonder if after the manner of those times , he took upon him the Name of his worthy Tutor and Instructor . For that he was a Syrian is not only manifest from his Consanguinity with Publius Mimus , but may likewise be collected from the Title or Inscription of this work , which is an ancient and excellent Manuscript in the Possession of Vossius is this M. MALLII POENI ASTRONOMICON DIVO OCTAVIO QUIRINO AUG . That the Phaenicians were by the Romans called POENI is manifest out of Horace , Cicero apud Nonium , and our Author in this very Poem ; he concludes therefore than this our Manilius , or ( as he is rather pleased to call him ) Manlius was a Phaenician , and in all probability Native of the same Town as Antiochus his Tutor , whose name he assum'd . From this Dedication of his Work to Augustus , by the Name of Quirinus , as the Inscription shews , will appear the Error of those , who who imagine the same to be Dedicated to Tiberius , or some later Roman Emperour : And the Reason of attributing the Name of Quirinus to Augustus , may be made clear from the Words of Suetonius , Censentibus quibusdam Romulum appellari oportere quasi et ipsum conditorem Urbis , &c. Dion likewise tells us 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , That Augustus Caesar extremely desir'd to be call'd Romulus : and Joannes Philadelphensis ( Scripto de Mensibus in Aug. ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Octavianus Son of Octavius was after his great Victories honoured with divers Names , for by some he was called Quirinus , as another Romulus , &c. As to that Manilius stiled by Pliny Mathematicus , he conceives that titular distinction to make no difference in the Person , but that he is the same with the former , further adding , Omnino existimo et illum quoque de nostro Manilio accipi debere . And whereas Salmasius affirms that the name Manlius or Manilius is not to be found in that place of Pliny in any ancient Manuscripts , he makes it appear that Salmasius is extreamly mistaken by the testimony of several antient Manuscript Copies of Pliny in his Possession , one of which was written above 8 or 900 Years agoe , in all which the Word Manlius is found , though with some small difference in writing of the name . Nor doth he think the name of Marcus prefixd to Manilius ought to be scrupled at , upon the Account that none of the Manlian Family after the 360th Year from the building of Rome could or did use that Praenomen , seeing the prohibition as Cicero intimates is only to be understood of the Patrician Race , Now that this Manilius , or ( as he calls him ) Manlius was before his Manumission a Slave , not only the place of Pliny already cited , but the very Agnomen of Antiochus sufficiently demonstrates , for as much as a Greek Agnomen joyn'd to a Roman Name is always a most certain Token of a Servile Condition . Thus far Sir Edward Shirburn , who is very much inclin'd to rest satisfied with this rational discourse of the incomparable Vossius , and thinks others should be so too ; but upon examination it will appear that Scaliger's Objections are still in force , and that Vossius's his reasonings are all to little purpose . It must be granted that the Agnomen Antiochus proves that Manilius to be of Servile Condition , tho' there is no need of this Argument , since Pliny in very express Terms asserts that he is so : T is likewise true that that Manilius was a Syrian , being a near Kinsman to Publius Syrus , and brought to Italy in the same Ship with him : But that that Manilius the Syrian was the same with Manilius the Poet , is a Question that still returns , and will not , I fear , be determin'd by the Title of that ancient and excellent Manuscript of Vossius : For if instead of M. MALLII POENI , we read M. MALLII POETAE , which is found in other Manuscripts , ( and every body knows there is so little difference in the traits of the Letters of those two words in ancient Copies , that they may very easily by Ignorant Transcribers be mistaken for one another ) then the Evidence drawn from this Inscription is lost : Besides that Title is not to be regarded , it not being written by the Author but affixt by some heedless Copyer of the Poem : For it is Divo Octavio , whereas Augustus was never stil'd Divus though often Deus before his Death , and the Writer of the Astronomicon , as will by and by appear , dy'd before Augustus . To speak out what I think will not be deny'd , Manilius the Author of this Poem was young when he wrote it , and dy'd young ; and therefore cannot be that Manilius Antiochus whom Scaliger reckons to be 120 , and Vossius is forced to confess was 70 years of Age about the time Varus was defeated by the Germans . The first part of this Assertion may be demonstrated from almost all the Pages of his Book , in which we meet with many things that are not to be accounted for on the Hypothesis of Sixty : He is too fierce and fiery for that Age , and bounds every Step he takes : In a Man of years when we find a Warmth we feel it to be regular , he never starts , his Pace is equal , and seldom varies but when his Subject forces him to a more than ordinary quickness . Judgment appears all thro' , and a strength well govern'd : When he rises he doth not affect to climb but to walk , like a sober Traveller , who knowing his own force seeks the easiest ascent , when his Ground is uneven , or he is oblig'd to take the advantage of a Prospect . But 't is not so in Youth whose Fancies as well as Passions are impetuous ; that pleases them most which is most daring , finding they have strength they use it to the utmost , and when at last they sink they seem rather worn out , than tired . I cannot compare the Spirit of Poetry possessing a Youth , of a strong generous Imagination and vigorous Constitution , to any thing better than to a Flame seizing on the Body of a Meteor , the whole Mass blazes , and mounts upon a sudden ; but its motion is all the way uneven , and it quickly falls in a despicable Gelly : He that looks on the Latin of Manilius will see that I do him no Injury when I compare him to this Meteor , for even when he is oblig'd to give rules , and is ty'd almost to a certain form of words , he struggles against those necessary Fetters , he reaches after the strongest Metaphors , uses the boldest Catachresis , and against all the rules of Decency labours after an obscure Sublime , when he should endeavour to be plain , intelligible and easy : But as soon as he hath room to get loose , how wildly doth he rove ? he is not free but licentious , and strives to err greatly . 'T is needless to produce particulars , since they are so visible in the Prefaces , Fables , and Descriptions thro' his Books : And upon the whole it may be affirm'd , there are so many boldnesses scatter'd thro' his Poem , and so much of Toysomness just by them , that a Man may read his Youth in his writings , as well as his Contemporaries could do it in his Face . I would mention and enlarge upon his conspicuous Vanity , and from thence endeavour to support the Judgment I have already pass'd ; but that I consider that fault when it hath once possess'd a Man is not to be cool'd by all the Frost and Snow of Age : Yet from the Vanity of Manilius I think a particular Argument may be drawn to prove him to be young , for he had a design to rival or perfect the inimitable Virgil. This is evident from the Preface to his third Book : — 7 Romanae Gentis Origo , Totque Duces Orbis , tot bella , tot otia , et omnis In Populi unius leges ut cesserit Orbis Differtur — For here it is plain he had this mighty project in his head , and after he had prepar'd himself by this Astronomical Poem , rais'd his Fancy and got a good turn of Verse , was resolv'd to prosecute it with his utmost vigour ; he saw the vastness of the design — 8 Spatio majore canenda Quam si tacta loquor — Yet he hop'd to live to finish it , though in the beginning of this Poem he wishes for old Age that he might compleat the Work he then had in hand ; yet having gone through the most difficult part of it sooner , and with more ease than at first he thought he should have done ; he sets up for new Schemes and thinks he shall have years enough before him prudently to begin , and Strength succesfully to carry on so great an Undertaking . In this very Preface he reckons up a great many other Subjects fit to employ a Poet , but in express terms lays them all aside . Colchida nec referam , &c. Non annosa canam , &c. But the Roman History is in his Thoughts tho' he will not begin to write , till his greater leisure gives him opportunity to do it . These two Observations perswade me , that Manilius was Young when he began this Poem , and that he dy'd Young , and did not live to finish his design , or accurately Revise what he had written , will I think be very evident from what follows : It cannot be deny'd , that this Poet had advanc'd very far in his Work , whilst Tiberius was at Rhodes , for in his fourth Book , he gives this Character of that Island : 9 Virgine sub casta felix Terraque Marique , Et Rhodos , Hospitium recturi Principis Orbem , Tuque domus verè solis , cui tota sacrata es , Cum caperes lumen magni sub Caesare Mundi . Now 1 Tiberius retired to Rhodes , when C. Antistius and L. Balbus , were Consuls ; he continu'd there Seven 2 Years , and return'd in the Consulship of P. Vinicius and P. Alfinius Varus ; and yet in the first Book we meet with the 3 Description of the Prodigies that appeared before the defeat of Varus in Germany which hapned when Poppaeus Sabinus and Q. Sulpicius Camerinus were Consuls , about eight years after the Return of Tiberius from Rhodes : What shall we say then ? was the fourth Book written and publish'd before the first ? or would the Poet have strain'd for that Complement to Rhodes after the Varian Defeat ? with what Propriety could that Island be call'd Hospitium recturi Principis Orbem , or with what Truth could it be said to contain the most glorious Luminary next to Caesar , when that imagin'd Star had not for many years been in that Horizon , and now shone in other quarters of the World ? No , this had been Banter and inexplicable Riddle : But if we suppose Manilius to have had this Work under his hand several years , to have revis'd it , and added what he thought would adorn his Poem , then we can easily give an account why his fourth Book should appear to be eight years younger than his first : A little before Tiberius's return from Rhodes he wrote his fourth Book , after that he composs'd his fifth , and sixth which is now lost ; then at several times revising his Work , and about the time of the Varian Defeat being upon the end of his first Book , he added to his discourse of Comets a short Account of those prodigious Meteors that then appeared , and which Historians 4 tell us were the most amazing that were ever seen : Soon after this he dy'd before he had corrected the fourth Book , as appears from the Character which in that Book he gives the Island Rhodes , and which his last and finishing hand could not have left there . These Observations will help us to give some tolerable account of the other difficulties relating to this Author , for to any one who enquires why the first Book is more correct than the rest ? why the Impurities of Stile the Criticks charge upon him are for the most part pickt out of the four last Books ? I would answer , we have only the first and rude Draughts of them ; and that as Poets and Painters are said to be very near ally'd , so they agree in nothing more than they do in this , that though in their Scetches we see the Master , yet we may find something that the Finisher would correct : To him who asks why there is no mention of this Poet in any of the Antients , I would reply , That Manilius having left an unfinisht Piece , his Family was studious both of his Credit and their own , they carefully preserv'd the Orphan , but would not expose it : In that Age when Poetry was rais'd to its greatest highth , it had argued the utmost Fondness or the extreamest Folly in a Noble Family to have publish'd a crude uncorrect Poem , and thereby engage their Honors to defend it . Besides , Augustus who was infinitely jealous of his reputation ( — Si palpere recalcitrat undique tutus , says Horace who knew his Temper very well ) would not have born the too officious Complement of being invok'd , unless the Poem had been as correct as Virgil's Georgicks , and fit for his Genius to inspire . Lucan afterward suffer'd for the like Complement , though indeed upon a far different account : He lost his Life for pretending to be inspir'd by Nero , when he made better Verses than the Emperour himself ; his Flattery to Nero was too great , as this of Manilius to Augustus had been too little , and a Defect in such Addresses was as dangerous under the wise , as an Excess in them was under the vain Emperors of Rome . You are sufficiently tired , I fear , with this long Discourse about Manilius full of guesses and conjectures , yet I cannot dismiss this Subject without adding something concerning his Quality , and place of Birth . His Quality he carries in his name , the Manilij being one of the best Families in Rome , which so often fill'd the Consul's Chair , and was employ'd in the greatest Offices of that Common-wealth . Indeed some have affirm'd that he was of Servile Condition , and being made free , according to Custom , took the name of his Patron : But since I have already prov'd , that he was not the Manilius Antiochus in Pliny , there is no reason left for any one to say he was a Slave ; he himself very expresly , I think , declares himself to be a Roman born , for in his fourth Book he shews a Concern for the Interests of the Roman Common-wealth down as low as the Age of Hannibal . 5 Speratum Hannibalem nostris cecidisse catenis : which he could not with any Propriety have done , had his relation to that State commenc'd so lately , or had his Ancestors had no Interest in the then Losses or Victories of Rome . And seeing he was born a Roman , and of the Family of the Manilij , we may farther from some other Evidences conclude that he sprung from a very considerable , if not one of the noblest Branches of it ; for if we reflect that tho' he dy'd young , yet he had been well instructed in the several Hypotheses of the Antient Philosophers , accurately taught the Doctrine of the Stoicks , led thro' all the intricate mazes and Subtilties of Astrology , that he was acquainted with the Mathematicks , knew all the Mythology of the Antients , and had run thro' the Greek Poets , we shall find in him all the signs of a very liberal and costly Education , and consequently of a considerable Quality , or at least a great Fortune . But if we reflect farther that he was conversant at Court , and acquainted with the modish , and nicest Flattery of the Palace , that he made his Complements in the same Phrase that the most intimate and finisht Courtier ever us'd , we may raise another probable Argument that his Quality was great : Now this reflection may be supported by one observation made on the Complement he pays Tiberius when at Rhodes : He stiles him 6 Magni Mundi Lumen , using the very same Word , which we meet with in Velleius Paterculus , who wrote all Court Language , upon the very same occasion . 7 Alterum Reipublicae Lumen is Tiberius , and he retir'd to Rhodes , ne Fulgor suus orientium Juvenum , C. et L. Caes. obstaret initiis , says that Historian . As to his place of Birth , since we find him at Rome when he wrote this Poem , 8 Qua genitus cum fratre Remus hanc condidit Urbem : and no Author settles him any where else , it may with some shew of Probability be concluded , that he was born in that City , in which we are certain he both studeid , and led his life : But if we consider farther that he takes all occasions to shew his respect for Rome , that with Zeal he mentions those extravagant Honours which the Flattery 9 of Asia , and the Vanity of her own Citizens had put upon her , we shall find so much Veneration in his Writings , that it could not well rise from any other Spring than that Piety which Men of generous Sense and Spirit always retain for the Places of their Birth . To close this Discourse , I have prov'd this Author was not the Manilius Antiochus mention'd by Pliny , Nat. Hist . lib. 35. cap. 17. Nor that Manilius lib. 10. cap. 2. and that both Vossius and Mr. Tristan are very much mistaken in their Conjectures . There remains another Manilius whom the same 1 Pliny , commends for his Skill in Mathematicks ; this Mathematician Scaliger thinks to be the same with the Poet , because he liv'd in the time of Augustus , and was conversant in the same Studies with our Author ; These I must own are not convincing proofs ; but as there are no good Arguments for , so there are no Objections against his pretences , and therefore he still stands fairest for the Person . This Manilius of a Noble Family , born in Rome , and living in the Age of Augustus , had a liberal Education suitable to his Quality and the time in which he liv'd : his Writings shew him to be well acquainted with the Principles of the several Sects of Philosophers , but addicted to the Stoicks , whose Hypothesis in all its out-lines bears a very near resemblance to some of the Theories that are now in Fashion . The Modern Philosophers build Worlds according to the Models of the Antient Heathens , and Zeno is the Architect . The Stoicks Principles were in short these : They say there is one Infinite , Eternal , Almighty Mind , which being diffus'd thro' the whole Universe of well order'd and regularly dispos'd Matter , actuates every part of it , and is as it were , the Soul of this vast Body : The Parts of this Body they say are of two Sorts , the Celestial , viz. the Planets and the fixt Stars , and the Terrestrial , viz. the Earth , and all the other Elements about it : The Celestial continue still the same without any Change or Variation ; but the whole Sublunary World is not only liable to Dissolution , but often hath been , and shall again be dissolv'd by Fire : From this Chaos which , because it is made by Fire , they call Fire , they say another System would arise , the several particles of it settling according to their respective Weights : Thus the Earth would sink lowest , the Water would be above that , the Air next , and the Fire encompass the other Three : But because all the Earthy parts are not equally rigid , nor equally dispers'd thro' the Chaos , therefore there would be Cavities and Hollows in some places fit to receive the Water , and to be Channels for Rivers : In other places Hills and Mountains would rise , and the whole System appear in that very form and figure which it now bears . They farther add , that this Infinite Mind hath made one general decree concerning the Government of the lower World , and executes it by giveing such and such Powers to the Celestial Bodies , as are sufficient and proper to produce the design'd Effects : This Decree thus executed they call Fate , and upon this Principle their whole System of Astrology depends : That some things happen'd in the World which were very unaccountable every days Experience taught them ; they learn'd also or pretended to have learn'd from very many accurate , and often repeated Observations , that there was a constant Agreement between those odd unaccountable Accidents and such and such Positions of the Heavenly Bodies , and therefore concluded that those Bodies were concern'd in those Effects : Hence they began to settle Rules , and to draw their scatter'd Observations into an Art ; And this was the State of the Hypothesis and Astrology of the Stoicks , ( I must call it so for distinction sake , tho' , neither the Hypothesis it self , nor the Astrology built upon it was invented by Zeno , but deliver'd down to him and his Scholars by the Chaldeans and other Philosophers of the East ) 'till the Greeks ambitious of making it appear their own , endeavour'd to establish support and adorn it with their Fables , and by that means made that which before seem'd only precarious , ( as all Arts which are drawn from bare Observation and not from any settled Principles in Nature must appear to be ) ridiculous Fancies , and wild Imaginations : But I do not design an Account , nor a defence of the Astrology of the Antients : You know , Sir , it hath been spoken against and derided on the one Hand , and supported and applauded on the other by Men of great Wit , Judgment , Piety , and Worth : and he who shall take a View of it , will always find enough in it to divert his leisure , if not to satisfie his Curiosity , and raise his Admiration . This is the Hypothesis which Manilius endeavour'd to explain in Latin Verse : Had he liv'd to revise it , we had now had a more beautiful and correct piece ; he had a Genius equal to his Undertaking , his Fancy was bold and daring , his Skill in the Mathematicks great enough for his Design , his Knowledge of the History , and Acquaintance with the Mythology of the Antients general : As he is now , some of the Criticks place him amongst the Judicious and Elegant , and all allow him to be one of the useful , instructive , profitable Poets : He hints at some Opinions which later Ages have thought fit to glory in as their own Discoveries . Thus he defends the Fluidity of the Heavens against the Hypothesis of Aristotle . He asserts that the fixed Stars are not all in the same concave Superficies of the Heavens , and equally distant from the Center of the World : He maintains that they are all of the same Nature and Substance with the Sun , and that each of them hath a particular Vortex of his own ; and lastly he affirms that the Milkie Way is only the undistinguish'd Lustre of a great many small Stars , which the Moderns now see to be such , thro' the Glass of Galilaeo : In short , we do not give him too great a Character , when we say he is one of the most discerning Philosophers that Antiquity can shew . In my Version I have endeavoured to render this Author in●●lligible and easie , and therefore have been sometimes forc'd to take a larger Compass than a strict Tra●slation would allow ; and have ●dded some Notes to make him ●ess obscure : Amongst those Notes y●u will find one relating to the Th●ory of the Earth , which I must desire you to lay aside , it being written and printed several years ago , and before I had well considered the weak unphilosophical Principles , and pernicious Consequences of that vain Hypothesis . And now , Sir , you are near the End of this long Letter , give me ●eave to tell you , that I have not tired ●ou half so much , as at first I design'd to do ; having left unsaid a great many things relating both to the Author and his Writings : Those perhaps will appear at the Head of a Latin Edition of his Works , which I shall think my self oblig'd to undertake , unless a very learned Gentleman , from whom I have long expected it , frees me from that trouble , and obliges the World with his own Observations . I am Your Humble Servant , T. C. All-Souls , Octo. 10●● 96. MANILIUS . The First Book . After a short Account of his Design , and a complemental Address to Augustus , he begins , 1. With the Rise and Progress of Astronomy , and other Arts : 2. Discourseth of the several Opinions concerning the Beginning of the World : 3. Describes the Order of it : 4. Proves the Earth to be the Centre of the World : 5. Proves it to be round : 6. Asserts the Soul of the World : 7. Reckons up the Signs of the Zodiack : 8. Describes the Axis : 9. The Northern Constellations : 10. The Constellations between the Tropicks and the South-pole : 11. Explains the Figures of the Constellations : 12. Asserts Providence against Epicurus : 13. Discovers the Bigness of the World : 14. Treats of the movable and immovable Circles : 15. Makes a long description of the Milky-way : 16. Reckons up the Planets : 17. Discourseth of Comets and Meteors , and concludes that they presage . STars conscious of our Fates and Arts 1 Divine , The wondrous work of Heaven's first wise design , In numerous Verse I boldly first inclose ; Too high a Subject , and too great for Prose . At what the Ancients with a wild amaze And ignorant wonder were content to gaze , My Verse brings down from Heav'n , design'd to show Celestial secrets to the World below : What yet the Muses Groves ne'er heard , I sing , And bring unusual offerings to their spring . Rome's Prince and Father , Thou whose wide command With awfull sway is stretcht o'er Sea and Land , Who dost deserve that Heaven thy Love bestow'd On thy great Father , Thou thy self a God , Now give me Courage , make my Fancy strong , And yield me vigour for so great a Song . Nor doth the World this curious search refuse , It kindly courts the daring of my Muse , And will be known ; whilst You serenely reign , Instruct our Labour , and reward our Pain . Wings raise my Feet , I 'm pleas'd to mount on high Trace all the Mazes of the liquid Sky , Their various turnings , and their whirls declare , And live in the vast regions of the Air : I 'll know the Stars , which yet alone to gain Is knowledge mean , unequal to the Pain ; For doubts resolv'd it no delight affords , But fills soft empty heads with ratling words : I 'll search the Depths , the most remote recess , And flying Nature to Confession press ; I 'll find what Sign and Constellation rule , And make the difference 'twixt the Wise and Fool ; My Verse shall sing what various Aspect reigns When Kings are doom'd to Crowns and Slaves to Chains . I 'll turn Fate 's Books , there reade proud Parthia's doom , And see the sure Eternity of Rome . Two Temples rais'd with sacred Incense shine , I bow at Nature's and the Muses shrine ; Both aids I need , for double Cares do throng , And fill my Thought ; the Subject and the Song : And whilst I 'm bound to Verse with Orbs immense The World rouls round me , and distracts my sense ; Vast is my Theme , yet unconceiv'd , and brings Untoward words scarce loosned from the Things . Who first below these wondrous secrets knew ? Who stole that knowledge which the World withdrew ? Whose soaring mind those Airy mazes trod And spight of Heaven desir'd to seem a God! Open the Skies , and teach how Stars obey , And run their race as Nature marks the way , Their Power and Influence , what directs their Course What whirls them round , and what confines their force . First Mercury disclos'd these mysteries , By Him we view the Inside of the Skies , And know the Stars , and now Mankind admires The Power , not onely Lustre of their Fires : By Him all know how great , how just and wise , And good is the Contriver of the Skies ; At whose Command the Stars in order met , Who times appointed when to rise and set ; That Heaven 's great secrets may lie hid no more , And Man instructed gratefully Adore . Nature disclos'd her self , and from her Springs Pure streams deriv'd o'erslow'd the Minds of Kings , Kings next to Heaven , who o'er the East did sway , Where swift Euphrates cuts his rapid way , Where 2 Nile o'erflows , and whence the Whirl restores The Day to Us , and passing burns the Moors . And next o'er Priests , whose constant Cares employd In publick service did obleige the God , His Presence did their holy minds inspire With sacred flames , and rais'd their fancies higher , Till by degrees to due perfection wrought He made himself the Object of their thought : Such were those wondrous Men who first from far Lookt up , and saw Fates hanging at each Star : Their thoughts extended did at once comprise Ten thousand revolutions of the Skies , They markt the Influence , and observ'd the Power Of every Sign , and every fatal Hour ; What Tempers they bestow'd , what Fortunes gave , And who was doom'd a King , who born a Slave ; How Aspects vary , and their change creates , Though little , great variety in Fates . Thus when the Stars their mighty Round had run , And all were fixt whence first their Race begun , What Hints Experience did to search impart They join'd , and Observation grew to Art ; Thus Rules were fram'd , for by Example shown They knew what would be , from what had been done ; They saw the Stars their constant Round maintain Perform their Course , and then return again ; They on their Aspects saw the Fates attend , Their change on their Variety depend ; And thence they fixt unalterable Laws , Settling the same Effect on the same Cause . Before that time Life was an artless State Of Reason void , and thoughtless in debate : Nature lay hid in deepest Night below , None knew her wonders , and none car'd to know : Upward men look , they saw the circling light , Pleas'd with the Fires , and wondred at the sight : The Sun , when Night came on , withdrawn , they griev'd , As dead , and joy'd next Morn when he reviv'd ; But why the Nights grow long or short , the Day Is chang'd , and the Shades vary with the Ray , Shorter at his approach , and longer grown At his remove , the Causes were unknown : For Wit lay unimprov'd , the desart plains Were unmanur'd , nor fed the idle Swains : Ev'n Gold dwelt safe in Hills , and none resign'd Their lives to Seas or wishes to the Wind ; Consin'd their search , they knew themselves alone , And thought that onely worthy to be known : But when long time the Wretches thoughts resin'd , When Want had set an edge upon their Mind ; When Men encreast , and Want did boldly press , And forc'd them to be witty for redress ; Then various Cares their working thoughts employ'd , And that which each invented all enjoy'd . Then Corn first grew , then Fruit enricht the grounds , And barbarous noise was first confin'd to sounds : Through Seas unknown the Sailer then was hurl'd , And gainfull Traffick joyn'd the distant World : Then Arts of War were found , and Arts of Peace , For Vse is always fruitfull in encrease . New hints from settled Arts Experience gains , Instructs our Labour , and rewards our Pains : Thus into many Streams one Spring divides , And through the Valleys rouls refreshing Tides . But these were little things compar'd , they knew The voice of Birds , in Entrails Fates could view ; Burst Snakes with charms , and in a Bullock's bloud , See Rage appeas'd , or fear an angry God. They call'd up Ghosts , mov'd deepest Hell , the Sun Could stop , and force a Night upon his Noon ; Then make him rise at Night , for all submit To constant Industry , and piercing Wit. Nor stopt they here , unwearied Industry Rose boldly up and mounted through the Sky , Saw all that could be seen , view'd Nature's Laws , And young Effects still lying in their Cause . What wings the Lightning , why from watry Clouds The Thunder breaks , and roars the wrath of Gods. What raiseth Storms , what makes the Winds to blow , Why Summer's Hail's more stiff than Winter's Snow : What fires Earth's Entrails , what doth shake the Ball , Why Tempests rattle , and why Rain doth fall : All this she view'd , and did their modes explain , And taught us to admire no more in vain . Heaven was disarm'd , mad Whirlwinds rul'd above And Clouds and Vapors thundred instead of Jove . These things explain'd , their hidden Cause known , The Mind grew strong , and ventur'd boldly on ; For rais'd so high , from that convenient rise She took her flight , and quickly reacht the Skies ; To every Constellation Shapes and Names Assign'd , and markt them out their proper frames Then view'd their Course , and saw the Orbs were mov'd As Heaven did guide , and as the World approv'd ; That Chance was baffled whilst their Whirls create The interchang'd Variety of Fate . This is my Theme , ne'er yet in Numbers wrought , Assist me , Fortune , and improve my thought ; Equal my Mind to my vast task ; prolong My life in ease , smooth as my flowing Song ; That while my Muse is working o'er the Heap , And forms this Chaos to a pleasing shape , I may with equal care , and equal heat , Declare the Little and disclose the Great . But now since Fate and Verse do joyntly flow From Heaven , and both rule equally below . First let my Muse whole Nature's Face design , Its Figure draw , and finish every Line . Whether from Seed it ne'er 3 began to be , Secure from Fate , and from Corruption free ; Knew no Beginning , and no Ending fears , But was , and will be , as it now appears . Or huddled 4 Chaos by a wondrous Birth Archt the vast Sky and fixt the solid Earth ; And when this shining World once rais'd its Head To Shades Infernal banisht Darkness fled . Or whether unseen 5 Atoms blindly thrown Compos'd it , and as Years whirle nimbly on , It must dissolve , and as it first was wrought From almost Nothing , fall to almost Nought . Or rose from working 6 Fire's enlivening Rays , Which form Heaven's Eyes , and live in every Mass . In Thunder roar , and in the Lightning blaze . Or whether 7 Water which combines the Frame Compos'd , and keeps it from the loosning Flame . Or whether 8 Water , Air , and Flame and Earth Knew no beginning , no first seeds of Birth ; But first in Being from themselves arose , And as four Members the vast God compose ; In which Thin , Thick , Hot , Cold , and Moist and Dry , For mutual Actions mutual parts supply . From whose agreeing disagreement springs , The numerous odd Variety of Things . These Qualities to act provoke the Seed , Make Vital Elements and Bodies breed . What 't was at first , and whence the All began Is doubted , and the Doubt too deep for Man ; And let it be , but whencesoe'er it came Its Face is certain , 't is an order'd Frame . Upward the 9 Flame on active Pinions fled , To Heaven's high Arch it rais'd its shining Head , There stopt as weary grown , and round the Frame For Nature's Bullwark roll'd a Wall of Flame . Then liquid Air spread through the empty space Less light and active took the second place . But next the Flame the lightest parts aspire To waste themselves , and feed the greedy Fire . The heavyer Water makes an humbler Claim , And lies the third in order in the Frame ; That Vapours rising may , like Seed , repair What Fire destroys , and feed decaying Air : Weight sank round Earth to the remotest place , And floating Sand in clinging Mud's embrace Stuck fast , whilst Seas squeez'd out flow'd o'er the Mass : As those grew limpid , and diffus'd the Waves , Through spacious Hollows and descending Caves Rocks started forth , their Heads the Mountains rear'd , And Earth surrounded by the Floud appear'd . Lowest of all , and in the midst it lies Compass'd by Seas , and cover'd by the Skies . The Place doth fix it , for still rising higher The other Elements equally retire , And that by falling stops its farther fall , And hangs the midst and lowest of them all , Its parts to one fixt point press jointly down , And meet , and stop each other from moving on . For did not Earth hang midst the airy space , How could the Sun perform his constant race ? Drive on the Day , fall headlong down the West , Force up the Stars , and rise again at East ? How could the Moon her usual Round maintain , Rise , set , and rise near the same point again ? Or He that leads the Stars at Night return To East again , and usher forth the Morn ? But since Earth did not to a Bottom fall , But hangs , and yielding Air surrounds the Ball , The way is open , and no stop to force The Stars return , or to impede their course . For who can think that when the 10 Sun doth rise He 's born anew , or when He sets He dies ? That when one Day He hath display'd his Light His Race is finisht , and goes out at Night ? Since He the same doth every Morn appear , And as He drives a Day He whirls a Year . From the same East He comes with equal pace , To the same West He still directs his Race ; And not one Change is seen in Nature's Face . The same Moon shines , and at a certain Day , Her light encreases , and Her Horns decay . The track she made Nature doth still pursue , Nor like a Novice wanders in a new . Phoebus still warms those signs where first he shone , And Day goes round with one eternal Sun. Thus prov'd : because by just Degrees the Hours In different Countries are the same with Ours . The Eastern Nations view the rising Fires Whilst Night shades us , and lazily retires . And as to distant West we nimbly run , That still removes , nor can we reach the Sun. No East begins , no West his race doth bound , But he drives on in one continued Round . Nor is it wondrous that one single Ball Should hang , since 't is the Nature of the All. No prop supports , but as their motions prove , The whole World hangs , and all that whirls above . The Sun doth drive his Race through yielding Skies , Wheel round the liquid Bound , and set and rise . Through Aether , Moon and Stars direct their Race , Like these Earth unsupported keeps its place , Though no fixt Bottom props the weighty Mass . Well then , the Earth hangs midst the yielding Air Not stretcht into a Plain , but every where It rises and declines into a Sphere . In other Parts this Figure Nature drew , The Sun and Stars , if we exactly view , Seem round , the Moon is vary'd every Night , Nor with an equal Face receives her Brother's Light. This proves her round since different rays adorn , Now shape , now bend , now fill her borrow'd Horn , This Form's Eternal and may justly claim A Godlike Nature , all its parts the same ; Alike and equal to its self 't is found , No End 's and no Beginning in a Round . Nought can molest its Being nought controul , And this enobles and confines the Whole . Hence every Countrey sees not every Sign , What Sailer views the bright 11 Canopus shine O'er Egypt's Shores , and when its Rays appear Who sees the little Circles of the Bear ? For Earth still rising to a Round denies , A larger Scene , and bounds our feeble Eyes . This Truth the 12 Moon confirms when deep in Night Earth interposes , and diverts her Light , She doth not all the World at once surprize , But now seems dark to these , now other Eyes . The Eastern Parts first view her darkned Face , Then o'er the South she rolls her broken Rays ; And then still prest by the obscuring shade , She hears the Western Brass resounding to her Aid . Now if the Earth were flat the darkned Moon Would seem to all Eclypst as well as one . At once presenting to the common view Her gloomy looks , and prove this fancy true . But since its Figure 's round , dim Cynthia's beams By just degrees must visit the Extremes ; Not all at once ; she must divide the Skies , And while she sets to some , to others rise . For in the mighty Concave whirl'd above She rising must , and must declining move ; Now climb this rising , and her Glories show , Then sink again , and scatter Beams below . This proves ( nor shall the subtlest Wits escape These twining Reasons ) the disputed Shape . By various Animals this Globe's possest , The Common House of Man , of Bird , and Beast ; The Northern 13 parts rise high , the Southern fall Beneath our Fee , the Adverse of the Ball. Yet as it lies its surface a Flat , Though false , its bigness doth improve the Cheat , And take the Roundness off , though every where It riseth and declines into a Sphere . Hence when with setting Beams the Sun withdrawn Beholds our East , they see the Morning dawn ; And when their Toils He with his Light restores , Sleep sits on Us , and gently easeth Ours . The Sea 14 runs round , and with its circling Waves The Floud at once divides , and joyns the Halves . To that vast Frame in which four parts conspire Of different form , Air , Water , Earth and Fire , United 15 God the World's Almighty Soul By secret methods rules and guides the Whole ; By unseen passes He himself conveys Through all the Mass , and every part obeys . To proper Patients He kind Agents brings In various Leagues binds disagreeing Things . Makes some Powers act , and some receive their Force ; And thus whilst Nature keeps her Vital Course , Though different Powers the several Things divide , The World seems One , and all its parts ally'd . Now Constellations , Muse , and Signs rehearse , In order , let them sparkle in thy Verse . Those which obliquely bound the burning Zone , And bear the Summer and the Winter Sun , Those first : then those which roll a different way From West : nor Heaven's Diurnal whirl obey : Which Nights serene disclose , and which create The steddy Rules , and six the Laws of Fate . First Aries , glorious in his Golden Wool , Looks back , and wonders at the mighty Bull , Whose back-parts first appear : He bending lies With threatning Head , and calls the Twins to rise , They clasp for fear , and mutually embrace ; And next the Twins with an unsteady pace Bright Cancer rolls : Then Leo shakes his Mane : And following Virgo calms his Rage again : Then Day and Night are weigh'd in Libra's Scales , Equal a while , at last the Night prevails , And longer grown the heavyer Scale inclines And draws bright Scorpio from the Winter Signs : Him Centaur follows with an aiming Eye His Bow full drawn and ready to let fly : Next narrow Horns the twisted Caper shows , And from Aquarius Urn a floud o'erflows . Near their lov'd Waves cold Pisces take their Seat , With Aries joyn and make the Round compleat . Now view the point where turn the shining Bears , And from their height look down on other Stars . Which never set but onely change their Sites To the same point ; and whirl the meaner Lights ; Thither the Axis runs , whose adverse Poles Bears the poiz'd World , and Heaven about it rolls ; No solid substance that the weight might bear But an imagin'd Line stretcht through the Air ; Begun from either Pole the Line extends Earth's Centre through , and in the other ends . For since the frame turns round , that fancy'd Line Which cuts the middle , too minutely thin By turning round it self to measure space , But still confin'd to one imagin'd place , Is call'd the Axis ; cause unapt to move It sees Stars whirl , the shining Planets rove , And swiftly measure the vast space above . Fixt near the Pole appear those friendly Stars Well known to wretched greedy Mariners ; Which guide their Sails , and which direct their Oars , When mad for gain they fly to foreign Shores. ( Whilst Heaven it self befriends their Avarice , What Pleas may wretched Mortals make for Vice ? ) Seven equal Stars adorn the greater Bear , Which measure larger Circles of the Sphere , And teach the Grecian Sailers how to steer . The smaller Bear , though less in size and light In narrower Circles she commands the Night , Yet Tyre prefers , for through the Ocean tost They sail by her and find the foreign Coast ; These stand not front to front , but each doth view The others Tayl , pursu'd as they pursue . Betwixt and round these two the Serpent twines , At once divides , and to their place confines ; Secure from meeting they 're distinctly roll'd , Nor leave their Seats , and pass the dreadfull fold : These keep the Vertex , but betwixt the Bear And shinning Zodiack where the Planets Err , A Thousand Figur'd Constellations roll , Some near the Zodiack , some plac'd near the Pole : Whose differing Powers by tempering Skies combin'd Make Seasons fruitfull , and refresh Mankind . First near the North , as conscious of his shame A Constellation kneels without a Name ; And next Bootes comes , whose order'd Beams Present a Figure driving of his Teams . Below his Girdle , near his Knees , He bears The bright Arcturus , fairest of the Stars . Behind his Back the radiant Crown is view'd , And shines with Stars of different magnitude ; One plac'd i' th' front above the rest displays A vigorous light , and darts surprizing rays . This shone since Theseus first his faith betray'd , The Monument of the forsaken Maid . Nor far from these distended Lyra lies , Well strung , the sounding glory of the Skies . This Orpheus struck when with his wondrous Song He charm'd the Woods , and drew the Rocks along ; When Hell obey'd , when Death resign'd her Chain , And loos'd his dear Eurydice again ; This gain'd it Heaven , and still its force appears , As then the Rocks it now draws on the Stars . The Planets dance , and to the tunefull sound The Heaven consents , and moves the fatal Round . Next Ophiuchus strides the mighty Snake , Untwists his winding Folds , and smooths his Back , Extends its Bulk , and o'er the slippery Scale His wide stretcht Hands on either side prevail : The Snake turns back his Head , and seems to rage , That War must last where equal Powers engage . Next view the Swan , whom Jove advanc'd above , That Form's reward by which He caught his Love. When shrouded in the fair deceitfull shape , He cheated trusting Leda to a Rape : Now grac'd with Stars his Wings stretcht o'er the Skies . And next the Swan the shining Arrow flies : The towring Eagle next doth boldly soar , As if the thunder in his Claws he bore : He 's worthy Jove , since He , a Bird , supplies The Heaven with sacred Bolts , and arms the Skies . Next rais'd from Seas the Dolphin's Tail appears , The Glory of the Floud and of the Stars . Whom while the Horse ( one radiant Star doth grace His generous Breast ) pursues with eager pace , His Legs before , as running , He extends , But clos'd in fair Andromeda he ends . Her Perseus joyns , her Foot his Shoulder bears Proud of the weight , and mixes with her Stars . Five splendid Stars in its unequal Frame Deltoton bears , and from the shape a Name ; But those that grace the sides dim Light display And yield unto the Basis brighter Ray. Next with her Cepheus Cassiopeia shines , Her posture sad , and mourns amongst the Signs ; She sees her Daughter chain'd , the rolling Tide The Monster spout , and curses her old Pride : She fears that Perseus will inconstant prove , And now in Heaven forget his former Love ; But He attends , and bears the Gorgon's head , His Spoil , and witness of a coming aid . Near the bent Bull a seat the Driver claims , Whose skill conferr'd his Honour and his Names , His Art great Jove admir'd , when first he drove His rattling Carr , and fixt the Youth above . Next stormy Hoedi shine which shut the Main , And stop the Sailers hot pursuit of gain . Then shines the Goat , whose Brutish Duggs supply'd The Infant Jove , and nurst his growing Pride . From that wild Food He did to Heaven aspire , Fierce Thunder throw , and dart the blasting Fire . Then mindfull of her Care the gratefull God Repaid her with those Skies which she bestow'd . Then Pleiades and Hyades appear , The sad Companions of the turning Year . Born by the Bull they lead they Tempests forth , And close the Constellations of the North. Farewell cold North , thy Ice benums my Muse , I fly from Thee , and warmer Regions chuse ; Betwixt the Tropicks of the Traveling Sun , I 'll trace the Signs that burn the torrid Zone , Then pass those bounds and view the Stars that roll Between cold Caper and the lower Pole. First next the Twins , see great Orion rise , His Armes extended stretch o'er half the Skies : His stride as large , and with a stately pace He marches on , and measures a vast space . On each broad Shoulder a bright Star's display'd , And three obliquely grace his hanging Blade . In his vast Head immerst in boundless spheres Three Stars less bright , but yet as great , he bears . But farther off remov'd , their Splendor's lost , Thus grac'd and arm'd He leads the Starry Host . Next barks the Dog , and from his Nature flow The most afflicting Powers that rule below , Heat burns his Rise , Frost chills his setting Beams , And vex the World with opposite Extremes . He keeps his Course , nor from the Sun retreats , Now bringing Frost , and now encreasing Heats : Those that from Taurus view this rising Star , Guess thence the following state of Peace and War , Health , Plagues , a fruitfull or a barren Year . He makes shrill Trumpets sound , and frightens Peace , Then calms and binds up Iron War in Ease . As he determines , so the Causes drawn , His Aspect is the World 's supremest Law. This Power proceeds from the vast Orb He runs , His Brightness equals or exceeds the Sun's . ●ut far remov'd he through the distant space ●arts feeble splendour from his Azure face . Yet others He excells , no fairer Light Ascends the Skies , none sets so clear a bright . Next Procyon view , view , and next the nimble Hare , Then Argo sailing through the liquid Air ; Advanc'd from all the Dangers of the Tides , Which first she stem'd , she now securely rides . Heaven is her Port , and now she rules the Flouds , A Goddess made for saving of the Gods. Close by the Serpent spreads ; whose winding Spires With order'd Stars resemble scaly Fires . Next flies the Crow , and next the generous Bowl Of Bacchus flows , and chears the thirsty Pole. The Centaur next in double shapes exprest , A Humane Body joyns a Horse's Breast . The World 's great Temple next , and Altar lies Grac'd with the Gifts of conquering Deities , When Earth-born Giants did the Skies invade , The lesser Gods implor'd the greater's Aid ; His Power Jove doubted when he view'd from far The threatning force of the unequal War. When He inverted Nature's Frame beheld , That Earth rose upward , and that All rebell'd . That Hills on Hills heap'd , rais'd their threatning Head , And frighted Stars approaching Mountains fled ; When impious Armies at a monstrous Birth Broke through the Bowels of the gaping Earth , Of disagreeing Forms , and frightfull Makes , Vast Humane Bodies twisted into Snakes . E'er this no Danger and no fear was known , And wanton Jove sate idly in his Throne . But lest some greater Power ( soft ease betray'd His Mind to doubt ) should yield the Rebels aid , He rais'd this Altar , and the Form appears With Incense loaded , and adorn'd with Stars . Next on his Belly floats the mighty Whale He twists his Back , and rears his threatning Tail ; He spouts the Tide , and cuts the foaming Way , Wide gapes his Mouth , as eager on his Prey ; Such on Andromede He rusht , and bore The troubled Waves beyond their usual shore . Next Swims the Southern Fish , which bears a Name From the South-wind , and spreads a feeble Flame . To him the Flouds in spacious windings turn , One Fountain flows from cold Aquarius Urn ; And meets the other where they joyn their Streams One Chanel keep , and mix the Starry Beams . Betwixt th' Eclyptick and the latent Bears Whose creaking Axis turns the rolling Spheres , Those stranger Skies are painted with these Stars . Which ancient Artists in their wondrous Lines Transmit to Fame , and call the Southern Signs . The other part lies hid , the vast abode Of unknown Nations , by our Feet untrod . From the same Sun they take their common Light , But different Shades : in an inverted site , Their Signs o' th' left Hand 16 set , and rise o' th' right . Their Skies as large , their Stars as splendid run , Equal i' th' rest , but are excell'd by One , By Caesar's Star which doth o'er us preside , Earth's present joy , and Heaven's future pride . For that the lower Pole resemblance bears To this Above , and shines with equal Stars ; With Bears averse , round which the Draco twines , At once divides them , and at once consines , That there as many Constellations move , We must believe from what we find above . For Fancy , which decaying Sense supplies , Not onely feigns a Vertex like to This , But all resembling Beauties of the Skies . These are the Stars which scattered o'er the Pole In different Places fixt complete the Whole ; But raise thy thought from sense , nor think to find Such Figures there , as are in Globes design'd ; Nor think that Stars set close compose the Frames , Or that the Signs are all continued Flames . For then we soon should see the World expire , Frail Nature could not bear so great a Fire ; Some Places vacant conscious of her State She leaves , unable for so vast a Heat . For 't is her kind intent alone to show By certain Stars , those Signs that rule below ; Such notice give , and such fair hints impart ; As Men may take , and may improve to Art : The Stars mark out the Shapes , the lower Beams Answer the high , the middle the extremes . Fansie those parts that lie obscur'd between , For 't is enough that some of them are seen : But chiefly then when Cynthia's beams are clear , And full , but few , though still the same , appear ; And whilst the vulgar fly , their place possess ; Nor lose their Light , nor mingle with the Less . Yet these still keep one Course , They still pursue Their constant track nor vary in a New. From one fixt point they start , their Course maintain Repeat their whirl , and visit it again : And this is strange , and this doth more surprize Than all the other wonders of the Skies , That such unwieldy frames their signs should draw , As mov'd by Reason , and confin'd by Law ; No change in distance nor in site appear , Though great their Number , long the rolling year . A most convincing Reason drawn from Sense , That this vast Frame is mov'd by Providence . Which like the Soul doth every Whirl advance ; It must be God , nor was it made by Chance ; As Epicurus dreamt , He madly thought This beauteous Frame of heedless Atoms wrought , That Seas and Earth , the Stars and spacious Air Which forms New Worlds , or doth the Old repair , First rose from these , and still supply'd remain , And All must be , when Chance shall break the Chain , Dissolv'd to these wild Principles again . Absurd and Nonsense ! Atheist use thine Eyes , And having view'd the order of the Skies , Think , if Thou canst , that Matter blindly hurld , Without a Guide should frame this wondrous World. But did Chance make , and Chance still rule the Whole Why do the Signs in constant order roll ? Observe set Times to shut and open Day , Nor meet , and justle , and mistake their Way ? Perform their Course as if by Laws confin'd , None hasten on , and leave the rest behind . Why every Day doth the discovering Flame , Show the same World , and leave it still the same ? E'en then when 17 Troy was by the Greeks o'er-thrown , The Bear oppos'd to bright Orion shone ; She near the Pole in narrow Rounds did move , He fac'd her then , and measur'd the vast space above . And e'en at Night when Time in secret flies , And veils himself in Shades from humane Eyes ; They by the Signs could know how fast He fled , And in the Skies the hasty Minutes read . How many Towns have fall'n , what well-built States , Since Troy , have sunk below oppressing Fates ? How many Times hath sporting Fortune hurld The Chance of Rule and Slavery through the World ? How hath she now reverst Troy's ancient Doom , And built her Relicks greater up in Rome ? Reviv'd old Ilium doth new Spoyls enjoy , And Greece now bends beneath the Fate of Troy. Why should I count how oft the Earth hath mourn'd The Sun's retreat , and smil'd when he return'd ? How oft he doth his various Course divide 'Twixt Winter's Nakedness and Summer's Pride ? All Mortal Things must change . The fruit full Plain , As Seasons turn , scarce knows her self again ; Such various forms she bears : large Empires too Put off their former Fance , and take a new . Yet safe the World , and free from Change doth last , No Years encrease it , and no Years can waste ; Its Course it urges on , and keeps its Frame , And still will be , because 't was still the same . It stands secure from Time's devouring Rage , For 't is a God , nor can it change with Age. And that the Sun ne'er drives the rising Day From North to South , nor leaves the beaten way ; That weary grown He still falls down the West At Night , nor turns his Horses to the East ; That Light by just Degrees the Moon adorns , First shews , then bends , then fills her borrow'd Horns , And that the Stars in constant order roll , Hang there , nor fall , and leave the liquid Pole ; 'T is not from Chance ; The Motion speaks aloud The wise and steddy conduct of the God. These equally dispos'd in Order lye , Make various Shapes , and chequer all the Skie . Above them nought ; To the World's Top they rose , Painting the Roof of Natures Common House ; Which in a wide Embrace doth all contain , The spatious Air , the Earth , and raging Main ; These Set in order , and in order Rise , As West drives down , or East brings up the Skies . But now how vast the Arch , how next immense The Zodiack's Round , though far remov'd from Sense , Plain Reason shews ; whose Active Force can pierce , The deep Recesses of the Universe . No Bars can stop it , through the World it flies , And Heaven it self lies open to its Eyes . As great a space as Earth , and humble Seas From Heaven divide , so great two Signs possess . The World 's 18 Diameter by Art is found , Almost the third Division of the Round . Therefore as far as four bright Signs comprize , The distant Zenith from the Nadir lies . And two thirds more almost surround the Pole , The Twelve Signs measure , and complete the Whole . But since the Earth hangs midst the spacious All , The Solid Centre of the Liquid Ball , Therefore as far as e'er our Eyes can pass Upward , or downward , could they pierce the Mass , Till bounding Sky the wearied Sight confines , Is equal to the distance of two Signs . And six such spaces the vast Round complete Where All the Signs their constant Whirls repeat , And each lies distant in an equal Seat. Nor must you wonder such Varieties Of different Fates from the same Stars should rise . Since great their Empire , and unlike their force , Their Seats so large ▪ and so immense their Course . Thus far advanc't my towring Muse must rise , And sing the Circles that confine the Skies , Describe the track , and mark the shining Way , Where Planets Err , and Phoebus bears the Day . One towards the North sustains the Shining Bear And lies divided from the Polar Star ; Exactly 19 six divisions of the Sphere . Another drawn through Cancer's Claws confines , The utmost Limits of the Fatal Signs ; There when the Sun ascends his greatest height In largest Rounds He whirls the lazy Night . Pleas'd with his Station there He seems to stay , And neither lengthens nor contracts the Day . The Summer 's Tropick call'd . — It lies the fiery Sun 's remotest Bound , Just five Divisions from the other Round . A third twines round , and in the midst divides The Sphere , and see the Pole on both its sides . And there when Phoebus drives , He spreads his Light , On all alike , and equals Day and Night . For in the midst , He doth the Skies divide , And chears the Spring , and warms the Autumn's Pride . And this large Circle drawn from Cancer's Flame , Just four Divisions parts the Starry Frame . Another Southward drawn exactly sets The Utmost Limits to the Sun's retreats ; When hoary Winter calls his Beams away , Obliquely warms us with a feeble Ray , And whirls in narrow Rounds the freezing Day . To Us his Journey 's short , but where He stands With Rays direct , He burns the barren Sands . To wisht-for Night he scarce resigns the Day , But in vast Heats extends his hated Sway. The last drawn round the Southern point confines Those Bears , and lies the Utmost of the Lines . Wise Nature constant in her Work is found : As five Divisions part the Northern ●ound ; From the North point , This Southern Round appears Just five Divisions distant from its Bears . Thus Heaven 's divided , and from Pole to Pole Four Quadrants are the Measure of the Whole . The Circles five , by these are justly shown , The Frigid , Temperate and the Torrid Zone . All these move Parallel , they set , they rise , At equal Distance moving with the Skies ; Turn'd with the Orbs the common Whirl repeat , Are fixt , nor vary their allotted Seat. From Pole all round to Pole two Lines exprest , Adversely drawn , which intersect the rest And one another ; They surround the Whole , And crossing make right Angles at each Pole : These into four just parts , by Signs , the Sphere Divide , and mark the Seasons of the Year . One drawn from Heaven's high top descends from far , And cuts the Serpent's Tail , and the dry Bear : The Equinoctial Scales , the Snake's Extremes , And next the Southern Centaur's middle Beams ; Then thwarts the Adverse Pole , and next divides The mighty Whale , and parts its scaly sides ; Bright Aries point , and splendid Trigon past , The fair Andromeda below the Waste , And next her Mother's Head it cuts , and then The Pole , and closeth in it self agen . Cross this , and from the Pole doth first appear The Other , through the forefeet of the Bear , And through its Neck ; ( which when the Sun retires First shines , and spreads black Night with feeble Fires ) Then parts the Twins and Crab , the Dog divides , And Argo's keel that broke the frothy tides . And then the Pole and other Circle crost To Caper turns contracted in his Frost : The Eagle cuts , and the inverted Lyre , Black Dracos folds — The hinder Paws o' th' Bear , and near the Pole It 's Tail , and closing there compleats the Whole . These Rounds immovable , their site the same , Here Seasons fix , nor vary in the frame . Two more are movable : one from the Bear Describ'd surrounds the middle of the Sphere , Divides the Day , and marks exactly Noon Betwixt the rising and the setting Sun : The Signs it changes as we move below , Run East or West , it varies as You go ; For 't is that Line , which way soe'er we tread , That cuts the Heaven exactly o'er our head , And marks the Vertex ; which doth plainly prove That it must change as often as we move . Not one Meridian can the World suffice , It passes through each portion of the Skies ; Thus when the Sun is dawning o'er the East 'T is their sixth hour , and sets their sixth at West : Though those two hours we count our days extremes , Which feebly warm us with their distant Beams . To find the other Line cast round thine Eyes , And where the Earth's high surface joyns the Skies , Where Stars first set , and first begin to shine , There draw the fancy'd Image of this Line : Which way soe'er you move 't will still be new , Another Circle opening to the view ; For now this half , and now that half of Sky It shews , its Bounds still varying with the Eye . This Round's Terrestrial , for it bounds contains That Globe , and cut the middle with a Plain ; 'T is call'd the Horizon , the Round's design , ( For 't is to bound ) gives title to the Line . Two more Oblique , and which in adverse Lines Surround the Globe , Observe : One bears the Signs Where Phoebus drives and guides his fiery Horse And varying Luna follows in her Course . Where Planets err as Nature leads the Dance , Keep various measures undisturb'd by Chance ; It s highest Arch with Cancer's beams do glow , Whilst Caper lies , and freezes in the low : Twice it divides the Equinoctial line , Where fleecy Aries , and where Libra shine . Three Lines compose it , and th' Eclyptick's found i th' midst ; and all decline into a Round . Nor is it hid , nor is it hard to find , Like others open onely to the Mind ; For like a Belt with studs of Stars the Skies It girds and graces ; and invites the Eyes : To twelve Degrees its Breadth , to thrice sixscore Its Length extends , and comprehends no more : Within these bounds the wandring Planets rove , Make Seasons here , and settle Fate above . The other Round from Bears oppos'd begun Runs adverse to the Chariot of the Sun , It leaves the Pole , and from its Round retires , And cuts inverted Casiopeia's Fires : Thence still descending and obliquely drawn It passes through the Body of the Swan , Then Cancer's fires , the headlong Bird of Jove , The Line and Zodiack where the Planets rove : And thence in various windings turns to meet The other Centaur , and entwines his feet : And thence to mount through Argo's Sails begins , The Line , and lowest portion of the Twins ; Then joyns the Driver , and from thence ascends O'er Perseus , and to Cassiopeia tends , There 't is receiv'd in her inverted Chair , In her the Round begins , and ends in Her. Twice cuts the Tropicks , Zodiack and the Line , And is as often cut by those agen . Nor need we with a prying Eye survey The distant Skies to find the Milky way , It must be seen by All , for every night It forcibly intrudes upon our sight , And will be mark'd for shining streaks adorn The Skies as opening to let forth the Morn . And as a beaten Path that spreads between A troden Meadow , and divides the Green. Or as when Seas are plow'd behind the Ship , Foam curls on the green surface of the Deep . In Heaven's dark surface such this Circle lies , And parts with various Light the Azure Skies . Or as when Iris draws her radiant Bow Such seems this Circle to the World below . It all surpriseth , our inquiring sight It upward draws , when through the Shades of Night It spreads its Rays , and darts amazing Light. Fond Men the sacred Causes strive to find , And vainly measure with a feeble Mind : And yet they strive , they madly whirl about Through various Causes , still condemn'd to Doubt . Whether the Skies 20 grown old , here shrink their Frame , And through the Chinks admit an upper Flame . Or whether here the Heavens two Halves are joyn'd But odly clos'd , still leave a Seam behind : Or here the parts in 21 Wedges closely prest , To fix the Frame , are thicker than the Rest , Like Clouds condens'd appear , and bound the Sight , The Azure being thickned into White . Or whether that old 22 Tale deserves our Faith , Which boldly says , that this was once the Path Where Phoebus drove ; and that in length of Years The heated track took Fire and burnt the Stars . The Colour chang'd , the Ashes strew'd the Way , And still preserve the marks of the Decay : Besides , Fame tells , by Age Fame reverend grown , That Phoebus gave his Chariot to his Son , And whilst the Youngster from the Path declines Admiring the strange Beauty of the Signs ; Proud of his Charge , He drove the fiery Horse , And would outdoe his Father in his Course . The North grew warm , and the unusual Fire Dissolv'd its Snow , and made the Bears retire ; Nor was the Earth secure , each Countrey mourn'd The Common Fate , and in its City 's burn'd . Then from the scatter'd Chariot Lightning came , And the whole Skies were one continued Flame . The World took Fire , and in new kindled Stars The bright remembrance of its Fate it bears . Thus Fame , nor must the softer Fable die That Juno's Breast o'erflowing stain'd the Skie , And made that Milky way , which justly draws Its Name , the Milky Circle from its Cause . Or is the spatious Bend serenely bright From little Stars , which there their Beams unite , And make one solid and continued Light ? Or Souls which loos'd from the ignoble Chain Of Clay , and sent to their own Heaven again , Purg'd from all dross by Vertue , nobly rise In Aether wanton , and enjoy the Skies . Great Atreus Sons , Tydides fixt above , And stout Achilles equal to our Jove ; With three-ag'd Nestor : He that bravely stood The Dangers of the Land and of the Floud . Vlysses , Nature's Conquerour , enjoy The Skies deserv●d ; with all the Chiefs at Troy. Jove's Son Sarpedon , He that Lycia sway'd : The black Merione , the Martial Maid , Had Fate stood Neuter , Troy's securest Aid . With all those Kings that Greece or Asia bore , Or Pella 23 greatest in her Conquerour . Next these the grave and prudent Heroes rise , Whose solid Riches lay in being Wise ; There good Zeleucus , stout Lycurgus shine , Solon the just , and Plato the Divine . His Master next , whose Bloud unjustly spilt On Athens still reflects a real Guilt . Next Persia's Scourge who strew'd the joyfull Floud With Xerxes fleet , and check'd the growing God : Who broke his Force , when Neptune bore the chain , And prov'd his juster Title o'er the Main . Here Romans joyn'd , the greatest Croud , reside , The Kings , e'er Tarquin stain'd the Throne with Pride . The Horaces our Army in our Wars , The Town which he defended , Cocles bears ; Next Clelia rides , the brightest Maid in Fame , And Scevola more glorious by his Maim . Then He on whom the Helping Crow bestow'd A Name , and in the Figure brought a God. Camillus who the Stars deserv'd to gain For saving Jove , when Thunder roar'd in vain ; Patient of wrongs , and whilst alive ador'd , The Founder of that Rome that He restor'd . Next Brutus sits , and next , unlearn'd in Fear , The fierce Revenger of the Pyrrick War , Papyrius shines ; The Decii , o'er their Foes In Triumphs Equal , Rivals in their Vows . Fabritius , Curius , for their Country bold , Alike in Courage , and too great for Gold. Marcellus , Sword of Rome , the third that bore A Royal spoyl , and Cossus grac'd before : Next Fabius sits , who left the Common way To Victory , and Conquer'd by Delay . Livy and Nero glorious for the fall Of haughty Carthage in her Asdrubal . The Scipio's Africks Fate both joyn'd in One , The latter ending what the first begun . Pompey by Thrice the Conquer'd World ador'd , Before God Caesar stoopt to be our Lord : The fam'd Metelli ; Tully , Rome's defence , Deserving Heaven for pretious Eloquence . The Claudian Race , and the Emilian Line With Fortune's Conquerour great Cato shine . But Venus Julian race , who drew their rise From Heaven ▪ return again and fill the Skies ; Where great Augustus , with his partner Jove Presides , and views his Father fixt above . Quirinus joyns him , and is pleas'd to see The Caesars grow Rome's Founders more than He. The highest Arch contains the greater Gods , The Godlike Heroes fill these next Abodes ; Those generous Souls , that ran an equal race In Vertues Paths , and claim a second place . Thus far my Muse hath with success been crown'd , Or sound no stops , or vanquisht those she found . And thus incourag'd now she boldly dares To sing the Fatal compacts of the Stars . But stop thy flight , sing all the Fires that shine And influence too , and finish thy design . Seven Fires refuse the Worlds Diurnal force , From West to East they roll their proper Course . Cold Saturn , Jove , fierce Mars , the fiery Sun , With Mercury 'twixt Venus and the Moon . Some swift ▪ some slow , they measure different Years , And make the wondrous Musick of the Spheres . But these are constant , these adorn the Night , Whilst Others seldom shine and then affright . For few have view'd a Comet 's dreadfull train , Which Wars foretells , and never shines in vain , Soon catch on Fire , and die as soon again . The Reason's this ; when days serenely fair Have chas'd the Clouds , and cleans'd the lower Air , And mists breath'd out from Earth rise through the Sky , The moister parts are conquer'd by the Dry. And Fire entic'd by the Convenient Mass Descends , and lights it with a sudden blaze : But since the Body's thin , the Parts are rare And Mists , like smoak , lie scattered through the Air ; As soon as e'er begun , the feeble fire Must waste , and with the blazing Mass expire . For did they long exist , their constant Light Would seem to bring new Day upon the Night ; Whole Nature's Course would change , and from the Deep The Sun would rise , and find the World a-sleep . But since in various Forms the Mists must rise , And shine in the same Figures o'er the Skies , These sudden Flames thus born by Chance at Night , Must shew as much variety of Light. Some equally diffus'd , like flaming Hair , Draw fiery Tresses through the Liquid Air. And streight the Mass that fiery Locks appear'd Grows short , and is contracted to a Beard . Whilst some in even and continu'd streams , Are round like Pillars , or are squar'd like Beams . And some with Belly'd Flames large Tuns present , Alike in shape , and equal in extent . Some ty'd in knots like hairy Curls are spread , A narrow Covering o'er the Comets Head. The Meteor Lamp in parted Flames appears , The Sheaf uneven shakes her bended Ears . But still when wandring Stars adorn the Night , The falling Meteors draw long trains of Light. Like Arrows shot from the Celestial Bow , They cut the Air , and strike our Eyes below : Fire lies in every thing , in Clouds it forms The frightfull Thunder , and descends in storms . ●t passes through the Earth , in Aetna raves , And imitates Heaven's Thunder in its Caves . ●n hollow vales it boyls the rising Flouds , ●n Flints 't is found , and lodges in the Woods , ●or tost by storms , the Trees in Flames expire , ●o warm are Nature's parts , so fill'd with Fire . Therefore when Mists , which wandring Flames retain , ●ursue and catch , and leave as soon again , Blaze o'er the Skies when through the parted Frame The Meteors break in one continued Flame , Or when midst Rain , or through a Watry Cloud Quick Lightning flies , or Thunder roars aloud , Wonder no more ; for o'er the spatious All Is fire diffus'd , and must consume the Ball. When eating Time shall waste confining Clay , And fret the feeble Body to decay . Thus far through paths untrod my Muse has gone , Found different Causes , but not fixt on One , Such various Flowers in Nature's field invite Her gathering Hand , and tempt her greedy sight ; That drawn by many she scarce one enjoys , Lost in the great Variety of Choice . For Earthy Mists involving Seeds of Flame May rise on high , and fiery Comets frame ; Or little Stars by Nature joyn'd in One May shine , though undiscover'd when alone . Or they are constant Stars , whose Natural Course The Sun o'er powers by his prevailing Force , Draws from their Orbs , and shadows by his Light , Then frees again , and opens to our sight . Thus Mercury , thus Venus disappears , Then shines again , and leads the Evening Stars . Or God in pity to our Mortal state Hangs out these Lights to shew approaching Fate ; They never idly blaze , but still presage Some coming Plague on the unhappy Age. No Crop rewards the cheated Farmer 's toil , He mourns , and curses the ungratefull Soil ; The meagre Ox to the successless Plow He yoaks , and scarce dares make another Vow . Or wasting Plagues their deadly Poisons spread , Encreasing the large Empire of the Dead . Men die by Numbers , and by heaps they fall , And mighty Cities make one Funeral . On groaning Piles whole huddled Nations burn , And Towns lie blended in one Common Urn. Such Plagues Achaia felt , the fierce Disease Laid Athens waste , and spoil'd the Town in Peace . It bore the helpless Nation to the Grave , No Physick could assist , no Vows could save ; Heaps fell on Heaps , and whilst they gasp'd for Breath , Heaps fell on those , and finisht half their Death . None nurst the Sick , the nearest Kinsmen fled ; None stay'd to bury , or to mourn the Dead . The Fires grown weary dy'd beneath their Spoils , And heapt-up Limbs supply'd the place of Piles . Vast Emptiness and Desolation reign'd , And to so great a People scarce one Heir remain'd . Such are the Plagues that blazing Stars proclaim , They light to Funerals their unlucky Flame . They shew not onely private Plagues to come , But threaten Mortals with the Day of Doom . When Piles Eternal Heaven and Earth shall burn , And sickly Nature fall into her Urn. They sudden Tumults , and strange Arms declare , And when close Treach'ry shall start up to War. When faithless Germans did of late rebell , And tempt their Fate , when Generous Varus fell , And three brave Legions bloud the Plains did drown , O'er all the Skies the threatning Comets shone . E'en Nature seem'd at War , and Fire was hurld At Fire , and Ruin threatned to the World. These things ▪ are strange , but why should these surprize , The Fault is Ours , since we with heedless Eyes View Heaven , and want the Faith to trust the Skies . They Civil-Wars foretell , and Brothers rage , The Curse and the disgraces of an Age. Never more Comets drew their dreadfull Hair Than when Philippi saw the World at War. Scarce had the Plains drunk up the former Bloud , On scatter'd Bones and Limbs the Romans stood And fought again ; disdaining meaner Foes , ( A wretched Conquest where the Victors lose ) Our Empire 's power did its own self oppose ; And great Augustus o'er the slaughter'd Heaps Pursu'd bright Victory in his Father's steps . Nor did the Rage end here , the Actian fight , That bloudy dowry of a wanton Night , Remain'd , and rais'd by Cleopatra's Charms The headlong Nations ran again to Arms. The Chance for the whole World was thrown again , And the Skies Ruler sought upon the Main , Then War obey'd a Woman , Timbrels strove With Thunder , Isis with the Roman Jove . Nor stopt it here , but the degenerate Son Stain'd all the Glory that his Father won . The Seas great Pompey freed He seiz'd again , His Pirates lay like Tempests on the Main . The Relicks of the Wars , the Impious Slaves Were arm'd for fight , and ravag'd o'er the Waves . Till the torn fleet di'd all the Seas with Bloud , And Asia's Chains reveng'd the injur'd Floud . Let this , O Fates ! suffice ; Let Discord cease , And raging Tumults be confin'd by Peace . Let Caesar triumph , let the World obey , And long let Rome be happy in his Sway. Long have him here , and when she shall bestow A God on Heaven enjoy his Aid below . The End of the First Book . NOTES . 1 Whether Divinas is to be rendred Divining or Divine is not yet agreed by the Interpreters of the Poet ; by rendring it Divine , Manilius is freed from a redundancy of Words , and the Origine of Astronomy , which he so often inculcates in other places , is hinted at : beside , Divinus seldom signifies Divining , but when a Substantive follows which determines it to that sense , as Divina imbrium , and the like , and in that case I find Milton venturing at it in his Poem : — Divine of future Woe . 2 It seems very plain that this whole description respects onely the Eastern Kings , and therefore Manilius must be reckoned amongst those who believed the head of Nile to be in the East ; and lest he might be thought to have forgotten the Egyptians , I am inclin'd to think he includes them under the Priests , to whose care Astronomical Observations were peculiarly committed . 3 This was the Opinion of Xenophanes , Melissus , Aristotle and others ; and Pliny thus concludes in the second Book cap. 1. of his Natural History : 'T is reasonable to believe that the World is a Deity , eternal and immense , that never had a beginning , and never shall have an end . As absurd an Opinion as ever was propos'd , and repugnant to all the Appearances of Nature ; look upon the Rocks on the Sea shore , and having observ'd their continual wearing , consider how few thousands of years they must have stood : direct thy eye to Heaven , and view the several changes in that which was thought impassible ; and in short , reflect on the essential vileness of matter , and its impotence to conserve its own being ; aud then I believe you will find reason to put this Opinion amongst those absurdities which Tully hath allotted to one or other of the Philosophers to defend . 4 This blind fancy we owe to the Phoenicians , who ( if Philo Biblius's Sancuniathon may be trusted ) taught that the Principles of the Universe were a Spirit of dark Air , and a confus'd Chaos ; this Spirit at last began to Love , and joyning with the Chaos , produced 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or slime , and thence fashioned the World. And hence likely the more sober part of the Greek Philosophers , ( for they were but borrowers of Learning ) who requir'd two eternal principles , the one active and the other passive , such as Plato , Anaxagoras , &c. took their notions , and having added some few new ornaments , vented them for their own . 5 The Philosophy of Epicurus is too well known to need any explication . 6 The Opinion of Heraclitus , concerning which see the first Book of Lucretius . 7 Thales the Milesian endeavoured to establish this by Arguments drawn from the Origine and Continuation of most things : The seminal Principle of Animals is humid , Plants are nourished by mere Water ; Fire it self cannot live without Air , which is onely water rarefied , and the Sun and Stars draw up vapors for their own nourishment and support . These were the considerations upon which he grounded his Opinion ; and hence 't is easie to guess that he kept up the credit of his School rather by those riches which he gain'd by his lucky conjecture at the scarcity of Olives , than by the strength of argument and reason . 8 The Assertion of Empedocles , agreeable to which Ovid sings , Quatuor aeternus genitalia Corpora Mundus Continet — . 9 There is something in this scheme of Manilius so like the ingenious conjecture of the excellent Authour of the Theory of the Earth , that what reflects on the one must have an influence on the other , and when the fiction is confuted the serious discourse will find it self concern'd : The Stoicks held the material part of their Deity to be changeable , and that too as often as the fatal Fire prevail'd , and reduc'd the Elements into one Chaos ; in such a confusion the Poet supposeth the first matter of his World , and then makes the different parts separate , and take proper places , according as they were light or heavy : agreeable to this Opinion the Theory of the Earth supposeth a Chaos , which he defines to be a Mass of Matter , fluid , consisting of parts of different sorts and sizes , blended together without any union or connexion . The solid and heavyer parts of this Chaos descend to the Centre , by their own weight , and there fixing and growing hard , compose the inward Body of the Earth ; the lighter parts fly upward , and being continually agitated , make that Body which we call Air ; the middle sort being somewhat heavyer , and not so much agitated , cover-over the solid interiour Body of the Earth ; and its fat and oily parts rising , and swimming on the surface , stop and detain those heavyer particles which upon the first separation were carried up by the Air , and afterward according to their several degrees of Gravity fell back again toward the Centre : These particles sticking in this oily matter , made a soft crust , which in time being hardned by the Sun and those breezes which always attend its motion , became the habitable Earth . This Earth thus form'd was solid , and without Caverns , nor had it any inequalities on its surface ; as to its site , its Axis was parallel to the Axis of the Ecliptick , both its Poles being equally inclin'd to the Sun ; and as to its figure it was Oval . These are the few easie principal parts of that excellent Hypothesis , settled on the obvious notions of Gravity and Levity , and on the acknowledged Nature , and allow'd Motion of a Fluid . And from these so many curious propositions are naturally deduced , so many difficulties concerning Paradise and the Floud happily explain'd , and all set off with that neatness and aptness of expression , and that variety of curious thought , that I am very much inclin'd to believe that Nature was never so well drest before , nor so artificially recommended . And it is pity that the first acknowledged Principles of Philosophy will not allow it to be true . Inherent Qualities are now generally exploded , as unphilosophical , not to be understood , and unfit to explain the Phaenomena of Nature . The Acceleration of a heavy Body in its descent ( beside a thousand other Arguments ) quite overthrows Gravity both as an accident of Aristotle , and as essential to Matter , according to the fancy of Epicurus ; so that this motion proceeds onely from external impulse , and depends upon the present order of the World. So that Philosophy will not allow the supposition of Gravity or Levity in a confus'd Chaos , since it can sufficiently demonstrate that they are neither inherent qualities , nor essential to matter , and that it is in vain to look after them , before the system of the World was settled in the present order . From this hint it is easie to infer that the supposed Chaos would have still continued such , the solid Parts would have been agitated this or that way indifferently by the restless particles of the Fluid , but there could have been no orderly separation , because no Principle of it . But suppose such a separation , why must the outward Crust of the Globe be without Caverns in its Body , and Inequalities on its Surface ? What Law of Nature doth necessarily prove that in such a confusion the solid parts must be equally dispersed through the Body of the Air ? If we trust our Eyes , and look upon a Dust raised by the ruin of a House , or onely consider what Confusion is , it will be very hard to find such a regular and orderly disposition . And since these solid Bodies may be unequally dispers'd , and every one of them tends to the Centre by a direct Line , whenever they settle , the Body which they compose must be unequal in its surface . Yet to let this Difficulty pass , its Figure according to this Hypothesis will be much more Oval than common observation will allow , for since it is said to be Oval because the Motion of the Aequator is swifter than that of the Polar Circles , the figure must be almost as much Oval , as the Circle of the Aequator is bigger than the Circle of the Pole ; there being nothing to hinder the utmost effect of this motion but the weight of the Fluid endeavouring to reduce it self to a Levell , which of what moment it will be in this Case I leave to be considered . And as for its site , that renders the torrid and the frigid Zones unhabitable ; intolerable Heats still burning the former , and the continual gathering and dropping of the vapours making the others too cold and moist to entertain either Man or Beast . And this one concession , I am afraid , spoils most part of the Contrivance ; for these portions of the Crust could never grow hard , being continually moistned by the Vapours , and so little expos'd to the Sun , or that breeze which attends its motion : And therefore , whenever Vapours were drawn from the Abyss in the Torrid Zone , these parts of the Arch being not firm enough to sustain themselves , must sink in ; and those Vapors that were imprisoned between the surface of the Abyss and the solid part of the Crust of the Earth , might have found an easie passage through this soft portion of the Crust , and therefore could not contribute to the general dissolution of the Frame . Besides , from such a muddy Fountain what could be expected but streams unwholsome and corrupted , and unfit for that end for which they were design'd , and for that use , to which sacred Scripture tells us they were imploy'd ? A great many other inconveniences in Nature may be observ'd to follow this Contrivance ; but because this Hypothesis was not set up for its own sake , but to give an intelligible account of Noah's Floud ; I shall close these reflexions with a few considerations upon that . And first the Authour pleads for an universal Floud , it being inconsistent with the demonstrated Nature of a Fluid , that Water should stand up in Heaps fifteen Cubits above the tops of the highest Mountains . This I am willing to admit , though there is no reason why Omnipotence might not be immediately concern'd in this , since he himself confesseth , that the forty days Rain cannot according to his Hypothesis be explain'd by any Natural Cause that he can find out . Secondly , He compares the height of the Mountains and the Depth of the Sea , and having as to both made allowable suppositions ( though the Course of the longest River , even the Nile it self , will not prove its head to be above three foot higher than its mouth ) he infers that eight Oceans will be little enough to make an universal Deluge : The Waters above the Firmament are exploded ; the Rain would afford but the hundredth part of such a Mass of Water , unless the showers were continual , and over the face of the whole Earth , and the Drops came down ninety times faster than usually they do . ( Though here a Man would be apt to think from the expressions in Genesis , The Windows of Heaven were opened , that there was somewhat very extraordinary in this Rain , and that all those requir'd conditions were observ'd . ) The Caverns of the Earth , if they threw out all the Water they contain'd , could afford but little in comparison of the great store that was requir'd ; And if the whole middle region of the Air had been condens'd , still there had not been enough , because Air being turn'd into Water filleth onely the hundredth part of that space which it formerly possess'd . Though all the other ways by which some have endeavour'd to explain the Floud , were demonstrably insufficient , yet this last which gives an account of it from so natural and easie a Cause as the condensation of the Air deserved to be considered a little more ; but it is the Art of a Disputer to touch that least which presseth most on that Opinion which he would advance . For it being allowed that Air by natural Causes may be chang'd into Water , and a Vacuum in this very Chapter being excluded , it necessarily follows , that as much Air as riseth fifteen Cubits higher than the tops of the Mountains is sufficient to make such a Deluge as is describ'd to have been in Noah's time . Because where there is no Vacuum , there can be no contraction into a less space , and every particle of Matter , whatever form or schematism it puts on , must in all conditions be equally extended , and therefore take up the same Room . But suppose a Vacuum , or ( as it happens in our imperfect condensations ) that a hundred cubical feet of Air would make but one foot of Water , yet sure the Region is large enough to make amends for this disproportion : Now since Nature is sufficient for condensation , and since its powers may be considerably invigorated for the execution of the Almighty's wrath ; why must it be thought so difficult to explain a Deluge ? and why should an excellent Wit waste it self in fashioning a new World , onely to bring that about which the old one would permit easily to be done ? It is above the Province of Philosophy to make a World , let that be suppos'd to have been form'd as it is reveal'd , it is enough for us to search by what Laws it is preserv'd ; and a system erected on this foundation will be agreeable both to Reason and to Religion . 10 He explodes the Opinion of Xenophanes , and the Fancy of Epicurus . Vid. Lucretius's fifth Book . 11 Canopus is a Star in the Southern Keel of the Ship Argo , of the first magnitude : These particulars as to the Appearance of the two Stars are not mathematically true , yet serve well enough for the Poets design , sufficiently proving the roundness of the Earth . 12 This Argument being taken from the Eclipse and not from the increase or decrease of the Moon , the Poet must be understood , not as to divers moments of Time , for the Moon at the same instant is seen Eclips'd by all to whom she appears above the Horizon , but as to the diversity of Hours at which the Eastern or Western People reckon the Eclipse to begin or end . 13 This is to be understood in respect of those who inhabit the Northern Hemisphere , to whom the North Pole is still elevated . 14 It was the Opinion of the ancient Poets , and some others , that the Sea was as a Girdle to the Earth , that it ran round it as an Horizon , and divided the upper Hemisphere from the lower . 15 Release this Soul from that union which the Stoicks foolishly assign'd , and then to hold a Soul of the World and Providence is all one . 16 Manilius is not constant in his Position ; most commonly as a Poet he turns his face to the West , and then the North is on his right hand , and the South on the left : sometimes as an Astronomer he turns his face to the South , and this is the position in this place . 17 Alluding to the two Verses in Homer's sixth Iliad , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . 18 Demonstrated by Archimedes in his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Prop. 3. That the Circumference of every Circle exceeds three times the Diameter thereof by a part that is less than 1 / 7th , and greater than 10 / 70. 19 Eudoxus divided the Sphere into sixty parts , and this division Manilius follows , and according to that describes the Position of the Celestial Circles . 20 The Opinion of Diodorus . 21 Macrobius reports Theophrastus to be the Authour of this Fancy . 22 From Plutarch we learn that Metrodorus and others asserted this , and Achilles Tacius fixes this foolish Opinion on Oenopides Chius . 23 The learned Mr. Hayns dislikes Scaliger's reading , which I have followed , and thinks that he meant that Pella was a Woman ; a more solemn foppery was never met with , and this Note , beside a great many others , may serve to credit the Dauphin Editions of the Classick Authours . MANILIUS . The Second Book . Manilius takes care frequently to tell his Reader that he is the first that ever ventur'd on an Astrological Poem ; He seems mightily pleas'd with his undertaking , hugs it as his First-born , and the Son of his strength , and is very troublesome in acquainting us with the pains which he suffered at its Birth ; and then reckons up the Beauties of the Child , and what great hopes he conceives of it : If ever he deserv'd Scaliger's Character , that he knew not when to leave off , it must be acknowledged that this is the Case in which it may be chiefly apply'd : We need look no farther than the beginning of this Book to be satisfied in this matter ; He spends about sixty Verses in reckoning up the chief Subjects of Homer , Hesiod , Theocritus and others ; all which being laid aside , he declares his design to be wholly new ; and then begins , 1. To prove the World to be one Animal : 2. The Influence of the Heavens : 3. He Describes the several species of the Signs . 4. The various configurations or aspects of the Signs ; and tells us what are Trines , what Quadrates or Squares ; what Hexagons or Sextiles ; and what are Right and Left in each of these . 5. What Signs are said to be conjoyn'd , what not , and what oppos'd ; to what Sign each part of Man's body is appropriate ; what Signs are said to hear , what to see one another ; what are friendly , and what not . 6. The friendly and unfriendly aspects of the Signs , and the various aspects of the Planets in the Signs . 7. The Twelfths or Dodecatemoria of the Signs and Planets . 8. The twelve Celestial Houses , and assigns to each its proper Planet . IN lasting Verse the mighty Homer sings The Trojan Wars , the King of fifty Kings , Stout Hector's brand , the bloudy dreadfull Field , And Troy secure behind the Hero's Shield : Vlysses wandrings , and his travelling years , In time and glory equal to his Wars : How twice with conquering Fleets he plough'd the Main , Whilst Scylla roar'd , and Neptune rag'd in vain . And how at Home he fixt his tottering Throne , Redeem'd his honour , and secur'd his Son : Usurping Woers felt his thundring Sword , And willing Nations knew their Native Lord. His Subjects these , and from his boundless Spring MANILIUS . The Second Book . Manilius takes care frequently to tell his Reader , that He is the first who ventur'd on an Astrological Poem : He seems mightily pleas'd with his Vndertaking , hugs it as his First-born , and the Son of his Strength : He at large acquaints us with the Pains which He suffer'd in bringing it to Perfection , and then reckons up the Beauty of the Child , and what great Hopes He conceives of it : ' If ever he deserves Scaliger's Character , That he knew not when to leave off , it must be principally then when He speaks of himself and his own Performance . We need look no further than the Beginning of this Book to be satisfied in this matter : He spends about Sixty Verses in reckoning up the chief Subjects of Homer , Hesiod , Theocritus , and other Poets , all which being laid aside . He declares his Design to be wholly new , and then begins , 1. To assert , that the whole Word is Animate , and God the Soul of it 2. The Influence of the Heavens . 3. He reckons up the several kinds or sorts of Signs , as , 4. Male and Female Signs : 5. Human and Brute Signs . 6. Single and Double Signs . 7. Pairs . 8. Double Signs made up of different Species . 9. Signs Double by Place , viz. Those that immediately precede the Four Tropick Signs . 10. Signs of Natural or Unnatural Postures . 11. Day and Night Signs . 12. Earth and Water Signs . 13. Fruitful and Barren Signs . 14. Signs of different Postures . 15. Maim'd and intire Signs . 16. Season Signs . 17. He sings the various Configurations or Aspects of the Signs : As , 18. Trines . 19. Quadrates or Squares ; shews what are to be accounted Right and what Left in these Figures : And , 20. Adds several Cautions concerning Squares and Trines . 21. He describes the Intercourse or Agreement of Trines and Quadrates . 22. Of Hexagons or Sextiles , of which he gives a particular Account . 23. Of Contiguous Signs . 24. Of Unequal Signs . 25. Of Opposites . 26. He shews what Gods are the Guardians of each Sign . 27. The Signs for the several parts of the Body . 28. What Signs See , Hear , Love , or Hate each other . 29. He makes a short Digression about Friendship . 30. He treats of the Friendly and Unfriendly Aspects . 31. Of the Dodecatemoria , or Twelfths . 32. Of the Dodecatemoria of the Planets , and proposes two ways to find them . 33. He describes the Celestial Houses , assigning them their Proper Charges and their Titles , together with the Planets which presided in them ; and then concludes this Second Book . THE mighty Bard in lasting Numbers sings Ilium's long Wars , the King of fifty Kings ; Brave Hector's Brand , the bloody dreadful Field , And Troy secure behind the Hero's Shield . He sings Vlysses , and his wandring Years ●n Time and Glory equal to his Wars : He sings how twice He conquering plough'd the Main Whilst Scylla roar'd , and Neptune rag'd in vain , And how at Home He fixt his tottering Throne , Redeem'd his Honour , and secur'd his Son : Usurping Woers felt his thundering Sword , And willing Nations knew their Native Lord. His Subjects these , from whose 1 abundant Spring ●ucceeding Poets draw the Songs they sing ; ●rom Him they take , from Him adorn their Themes , ●nd into little Channels cut his Streams , ●ich in his store — Next Hesiod sings the Gods Immortal Race , ●e sings how Chaos bore the Earthy Mass ; ●ow Light from Darkness struck did Beams display , ●nd Infant-Stars first stagger'd in their way : ●ow Name 2 of Brother vail'd an Husband's Love , ●nd Juno bore unaided by her Jove : ●ow twice-born Baccbus burst the Thunderer's Thigh , ●nd all the Gods that wander through the Sky . Hence He to Fields descends , manures the Soil , Instructs the Plowman , and rewards his Toil : He sings how Corn in Plains , how Vines in Hills Delight , how Both with vast Encrease the Olive fills : How Foreign Graffs th' Adulterous Stock receives , Bears stranger Fruit , and wonders at her Leaves : An useful Work , when Peace and Plenty reign , And Art joyns Nature to improve the Plain . The Constellation 's Shapes 3 some make their Themes , Sing whence they came , and how adorn'd with Beams , Andromeda enjoys kind Perseu's Aid , The Sire unbinds , the Mother mourns the Maid : Callisto ravisht now the Pole surveys , Nor grieves to change her Honor for her Rays : The Little Bear that rock'd the mighty Jove , The Swan whose borrow'd Shape conceal'd his Love Are grac'd with Light , the Nursing Goat's repaid With Heaven , and Duty rais'd the Pious Maid ; The Lion for the Honors of his Skin , The squeezing Crab , and stinging Scorpion shine For aiding Heaven , when Giants dar'd to brave , The threatned Stars ; and Thunder fail'd to save : And now the Fish ignoble Fates escape Since Venus ow'd her Safety to their Shape : The Ram having pass'd the Sea , serenely shines , And leads the Year , the Prince of all the Signs . Thus whilst by Fables They the Stars advance , They vainly make the Heaven one large Romance ; Earth fills the Sky , the Mass ignobly reigns , And Heaven 's upheld by that which it sustains : Fables absurd , which Nature's Laws reject , To make the Cause depend on the Effect . The sweet Theocritus with softest Strains Makes piping Pan delight Sicilian Swains ; Thro' his smooth Reed no Rustick Numbers move , But all is Tenderness , and all is Love ; As if the Muses sate in every Vale , Inspir'd the Song , and told the melting Tale. Some Birds , some Wars of Beasts , or Serpents write , Snakes in their Poems hiss , and Lions sight : Some Fate in Herbs describe , some Sovereign Roots , Or see gay Health spring up in saving Fruits : One breaks thro' Nature's stubborn Bars , invades The rest , and sacred Silence of the Shades , Turns up the inside of the World , and Night , And brings Eternal Darkness into Light. Of every Subject now the Muses sing , And Floods confus'd come tumbling from their Spring , Yet dry as fast , nor can Parnassian Streams Suffice the Throngs that crowd to common Themes . I seek new Springs which roul refreshing Waves Thro' Plains untrod , and Purls in hidden Caves , Kept pure for Me , which Birds did ne'er profane , And thirsty Phoebus oft hath sought in vain : My Verse shall be my Own , not stoln , but wrought ; Mine , not the Labor of Another's Thought . My Vessel 's trimm'd , tho' never launch'd before , I spread my Sails , and boldly leave the Shore : I 'll sing how God the World's Almighty Mind Thro' All infus'd , and to that All confin'd , Directs the Parts , and with an equal Hand Supports the whole , enjoying his Command : How All agree , and how the Parts have made Strict Leagues , subsisting by each others Aid ; How All by Reason move , because one soul Lives in the Parts , diffusing thro' the whole . For did not all the Friendly Parts conspire To make one Whole , and keep the Frame intire ; And did not Reason guide , and Sense controul The vast stupendous Machine of the whole , Earth would not keep its place , the Skies would fall , And universal Stiffness deaden All ; Stars would not wheel their Round , nor Day , nor Night , Their Course perform , be put , and put to flight : Rains would not feed the Fields , and Earth deny Mists to the Clouds , and Vapors to the Sky ; Seas would not fill the Springs , nor Springs return Their grateful Tribute from their flowing Urn : Nor would the All , unless contriv'd by Art , So justly be proportion'd in each part , That neither Seas , nor Skies , nor Stars exceed Our Wants , nor are too scanty for our Need : Thus stands the Frame , and the Almighty Soul Thro' all diffus'd so turns , and guides the whole , That nothing from its setled Station swerves , And Motion alters not the Frame , but still preserves . This God or Reason , which the Orbs doth move , Makes Things below depend on Signs above ; Tho' far remov'd , tho' hid in Shades of Night , And scarce to be descry'd by their own Light ; Yet Nations own , and Men their Influence feel ; They rule the Publick , and the Private Will : The Proofs are plain . Thus from a different Star We find a fruitful , or a barren Year ; Now Grains encrease , and now refuse to grow ; Now quickly ripen , now their growth is slow : The Moon commands the Seas , she drives the Main To pass the Shores , then drives it back again : And this Sedition chiefly swells the Streams , When opposite she views her Brother's Beams ; Or when she neer in close Conjunction rides She rears the Flood , and swells the flowing Tides ; Or when attending on his yearly Race The Equinoctial sees her borrow'd Face . Her Power sinks deep , it searches all the Main , Testaceous 4 Fish , as she her Light regains , Increase , and still diminish in her Wain : For as the Moon in deepest Darkness mourns , Then Rays receives , and points her borrow'd Horns , Then turns her Face , and with a Smile invites The full Effusions of her Brother's Lights ; They to her Changes due proportion keep , And shew her various Phases in the Deep . So Brutes , whom Nature did in sport create , Ignorant both of themselves , and of their Fate , A secret Instinct still erects their Eyes To Parent Heaven , and seems to make them wise : One at the New Moons ● rise to distant Shores Retires , his Body sprinkles , and adores : Some see Storms gathering , or Serenes foretel , And scarce our Reason guides us half so well . Then who can doubt that Man , the glorious Pride Of All , is nearer to the Skies ally'd ? Nature in Man capacious Souls hath wrought , And given them Voice expressive of their Thought ; In Man the God descends , and joys to find The narrow Image of his greater Mind . But why should all the other Arts be shown , Too various for Productions of our own ? Why should I sing how different Tempers fall , And Inequality is seen in All ? How many strive with equal Care to gain The highest Prize , and yet how few obtain ? Which proves not Matter sways , but Wisdom rules , And measures out the Bigness of our Souls : Sure Fate stands fixt , nor can its Laws decay , 'T is Heaven's to rule , and Matter 's Essence to obey . Who could know Heaven , unless that Heaven bestow'd The Knowledge ? or find God , but part of God ? How could the Space immense be e're confin'd Within the compass of a narrow Mind ? How could the Skies , the Dances of the Stars , Their Motions adverse , and eternal Wars , Unless kind Nature in our Breasts had wrought Proportion'd Souls , be subject to our Thought ? Were Heaven not interessed to advance our Mind , To know Fate 's Laws , and teach the way to find , Did not the Skies their kindred Souls improve , Direct , and lead them thro' the Maze above ; Discover Nature , shew its secret Springs , And tell the Sacred Intercourse of things , How impious were our Search , how bold our Course , Thus to assault , and take the Skies by force ? But to insist on tedious Proofs in vain , The Art defends it self , the Art is plain ; For Art well grounded forces to believe , It cannot be deceived , nor can deceive ; Events foretold fulfil the Prophesie , What Fortune seconds , how can Man deny ? The Proofs are Sacred , and to doubt would be Not Reason's Action , but Impiety . Whilst on these Themes my Songs sublimely soar , And take their Flight , where Wing ne're beat before ; Where none will meet , none guide my first Essay , Partake my Labors , or direct my way , I rise above the Crowd , I leave the Rude , Nor are my Poems for the Multitude . Heaven shall rejoyce , nor shall my Praise refuse , But see the Subject equall'd by the Muse ; At least those favour'd few , whose Minds it shows , The Sacred Maze , but ah ! how few are Those ! Gold , Power , soft Luxury , vain Sports , and Ease Possess the World , and have the luck to please : Few study Heaven , unmindful of their state , Vain stupid Man ! but this it self is Fate . My Subject this , and I must this pursue , This wondrous Theme , tho read , and prais'd by few ; And first the Signs in various Ranks dispose , As Nature prompts , or their Position shows : Six Male from Aries , from the Bull comprise ( See how he rises backward in the Skies ) Six Female Signs ; but intermixt they fall In order turn'd , 6 one Female , and one Male. Some Signs bear 7 Humane Shapes , some Signs exprest In single Figures bear the Form of Beast : These Shapes direct us , and from those we know How each inclines , what Tempers Signs bestow ; Their Figures will not let their Force escape , Their Tempers are agreeing to their Shape . These Signs are Single , now observe the 8 Pairs , Double Shapes confess a double Force in Stars : And each Companion still in each creates A Change , and vast Variety in Fates : Ambiguous Force from both exprest combines , No Single Influence flows from Double Signs . What Powers , or good or bad , one Part displays , They may be alter'd by the others Rays : Two of this kind in all the round of Sky Appear , the Pisces and the naked Gemini : These different Powers , tho both Pair Signs , possess , Because their Parts Position disagrees ; For tender Gemini in strict embrace Stand clos'd , and smiling in each others Face : Whilst Pisces glide in two divided Streams , Nor friendly seem , nor mix agreeing Beams . Thus tho in Both two parts compose the Frame , In Form alike , their Nature 's not the same . These Pairs alone an equal Frame can boast , No stranger parts are mixt , no parts are lost From their due Form ; whilst other Pairs are join'd Of Natures disagreeing in their kind ; Such is the Goat , he twists a Scaly Train , The Centaur such , half Horse , and half a Man. Observe this well , in these Mysterious Arts VVhether the Signs are fram'd of different parts , Or only Pairs , it much imports to know , For hence comes great Variety below . Midst double Signs the Pious Maid may claim A place , not from the Figure of her Frame , But ' cause in Her the Summer's Heats decay , And gentler Autumn spreads a weaker Ray. But to be short ; the same account defines That Double still precede the Tropick Signs , Because in those two Seasons mixt unite Their Powers , and make them double by their Site . Thus of the Twins the one the Bull requires , The other feels the Crab's unruly Fires ; One sees the fading Flowers , and Spring decline , The other Boy leads on the hottest Sign : But naked both , for both feel scorching Rays As Summer comes , or as the Spring decays . Thy Face , bright Centaur , Autumn's Heats retain , The softer Season suiting to the Man ; Whilst Winter's shivering Goat afflicts the Horse With Frost , and makes him an uneasie Course . Thus thou midst double Signs mightst doubly claim A place , both from thy Seat , and from thy Frame : The like in Pisces is observ'd , one brings The Winter's end , the other leads the Springs ; In them Spring 's Dews , with Winter's Rage combine , Both moist , and both agreeing to the Sign : How wise , and how obliging in her Grants Is Nature's Bounty suited to our Wants ! With Moisture she the Watry Signs supplies , And they enjoy their Ocean in the Skies . But there is War , Sign disagrees with Sign , And Three rise adverse to the other Nine : Bull 's Back , 10 Twins Feet , Crab's Shell do first appear , And stop the progress of the rising year ; Whilst others in their usual Postures rise , Nor shew unnatural Figures in the Skies : Since then thro' adverse Signs the Summer's Sun Makes way , no wonder that he drives so slowly on . How vast this Knowledge , and how hard to gain , The Subject still encreasing with the Pain ; Yet my swift Muse , like Larks on towring Wings Mounts to the Skies , and as she mounts she sings : She sees Signs various in her Aiery Flight Some Signs of Day , and other Signs of Night : Not so 11 distinguish'd Cause those Signs maintain Those times distinctly , and then choose to reign : For then as Years roul round , the Circling Lights Would all be of one kind Day 's all , or all the Night 's . But ' cause wise Nature in her first Designs By Laws Eternal fixt them to these Times : The Centaur , Lion , and the golden Ram , Fish , Crab , and Scorpio with his venom'd Flame Or near in Site , or in an equal space By two alike divided , are the Day 's : The rest the Night 's . But who can hope to see Opinion's join , or find the World agree ! Some with the Ram begin , and thence convey The Five in Order following to the Day . The rest from Libra are to Night confin'd : Whilst others sing Male Signs affect the Light , And Female safely wanton in the Night . But others , this is plain from common sense , demand Some Signs for 12 Sea , and other Signs for Land : Thus watery Pisces , and the Crab retain Their proper Nature , and respect the Main : The Bull and Ram possess their old Command , They led the Herds , and still they love the Land , Tho' there the Lion's Force their Rest invades , And poysnous Scorpio lurks in gloomy Shades ; The Danger is despis'd , the Ram , the Bull Keep Land , so powerful is the Lust of Rule : The Twins , the Centaur , and the Scales dispose In the same Rank ; and join the Maid with those . Of middle Nature some with Both agree , One part respects the Land , and one the Sea : The double Goat is such , whose wild Command Now Sea affects , and now enjoys the Land : And young Aquarius pouring out his Stream Here spreads a watry , there an Earthy Beam. How shall these things , yet they reward thy pain , Reason's in All , and nothing's fram'd in vain : The Crab 13 is fruitful , and a numerous Brood Pierce Scorpio yields , and Pisces fill the Flood ; The Lion's barren , and no Vows can gain The Maid ; Aquarius spends his Youth in vain , Ah too remov'd , too far disjoyn'd to prove The fruitful Pleasures of encreasing Love ! 'Twixt these two kinds a Third nor fruitful Beams Nor Barren spreads , but joyns the two Extreams : The Goat all Beast above , and Fish below , The Centaur glorious in his Cretian Bow , The Scales that Autumn's Equinoctial rule , The Twins , and Ram , to whom we join the Bull. Nor must you think it undesign'd , a Cast Of busie Nature as she wrought in haste ; That some shew running 14 Postures in their frame , The Lion , Centaur , and the turning Ram ; Erected some , Aquarius rears his Head , The Twins are upright , and the pious Maid : Some crouching Signs a lazy Posture show , Thus Taurus bends , as wearied by the Plough ; The Scales press'd down appear , and Caper lies By his own Frost contracted in the Skies : The Crab and Scorpio flat are found , they show The Postures there which they maintain below , Whilst watry Pisces low , and gently glide In Streams divided , always on their side . But search minutely , and you find a 15 Maim In many Signs , the mighty Bull is lame , His Leg turns under , Scorpio's Claws are lost In Libra's Scales , nor can the Centaur boast A Form compleat , tho' we distinctly find One Eye , the other 's lost , and Cancer's blind . Thus Heaven to wretched Mortals sends Relief By these Examples it corrects our Grief , Since Signs , on which our Fates depend , do share The like Misfortunes , which we grieve to bear . The different 16 Seasons likewise share the Signs , From Pisces Spring , and Summer from the Twins , From Centaur Winter , Autumn from the Maid begins : Each hath three Signs , and as the Seasons fight In the Years Round , so these lie opposite . Nor is 't sufficient that my Muse defines The Kinds , and Figures of the Single Signs , They work by Compact , they their Beams unite To mutual Aid determin'd by their site . From Aries rightways draw a Line , to end In the same Round , and let that Line subtend An equal Triangle ; now since the Lines Must three times touch the Round , and meet three Signs , Where e're they meet in Angles those are 17 Trines . Because they are at equal distance seen On either side , and leave three Signs between . Thus Aries sees on either side below The Lion roar , and Centaur draw his Bow : The Bull with Caper and the Maid are found In Trine : Thus fix the others of the Round . Signs Left and 18 Right are in the Trines agreed ; The Left still follow , and the Right precede ; The Maid is Left , and Caper to the Bull Is Right : Thus fix the others by this Rule . Tr : 1. ♈ ♐ ♌ Tr : 2. ♉ ♑ ♍ Tr : 3. ♊ ♒ ♎ Tr : 4. ♋ ♓ ♏ Q : 1 : ♈ ♑ ♎ ♋ Q : 2 : ♉ ♒ ♏ ♌ Q : 3 : ♊ ♓ ♐ ♍ But more , in Quadrates ; not in Trines alone Signs Right and Left are by Position shown ; In 19 Quadrates : which to know , the Round divide By Squares exactly equal on each side ; Where Angles close the Perpendiculars There lie the Signs agreeing in the Squares . To give an Instance then , observe the Site , The narrow Goat sees Libra on the Right , o th' Left the Ram , at equal distance lies The Crab , and on the Left sees Libra rise , To make a Square agreeing in the Skies . This single Instance all the rest declares , And shews that twice six Signs compose three Squares . But now should any 20 think their Skill designs The Squares aright , and well describes the Trines , And that they hit the Rule when e're they ' give Four Signs to Squares , to Trines allotting Five ; And thence presume to guess what mutual Aid The Signs afford , they 'll find their Work betray'd : For though on every side five Signs are found To make the several Trines that fill the Round , Yet Births in each Fifth Sign no Fates design To share th' united Influence of the Trine . They lose the Thing , though they preserve the Name , For Place and Number still oppose their Claim : For since the Round where Phoebus guides his Reins Three hundred , and thrice twenty parts contains , One third of those , as we the Round divide By Trines , to every Trine must make one side ; But Sign apply to Sign , not Part to Part , This Number 's lost ; and therefore false the Art. For tho Three Signs appear to interpose Between the Two in which the Angles close ; Yet take the Scheme as 't is expos'd to sight , And joyn the utmost parts of Left and Right ; Then count the number ; on the slightest view You 'll quickly find it much exceeds the true : Thrice fifty parts it holds , and thus one Line Defrauds the other , and destroys the Trine ; And therefore though the several Signs retain The Name of Trines , they claim the Parts in vain . The like Mistake , when you design a Square , Thy Art may baffle , and elude thy Care ; For as the Round we by Degrees divide To every Quadrate Ninety make one side : Now from the first from which begins the Line , Toth ' last degree of the succeeding Sign If you count on , twice sixty parts prepare To crowd upon thee , and deform the Square : Or from preceding Signs last parts descend To Signs succeeding , let the Reckoning end I' th' first Degree of those : the space consines But sixty parts , the number of Two Signs ; Thus count from Fourth to Fourth , Degrees too few , Or else too many will thy Work pursue , Elude thy Skill , and prove the Scheme untrue . Then take Advice , nor from my Rules depart Nor think thy Figures well design'd by Art , ' Cause Four in Squares , Three equal Lines in Trines In Angles meeting there divide the Signs ; For in all Trines the single sides require Sixscore Degrees to make the Scheme intire Squares ninety ask : but more or less proclaim The Figure , faulty , and destroy the Frame . And where the several Lines in Angles close , They there the Trines , or else the Squares dispose ▪ Sext : 1 : ♈ ♊ ♌ ♎ ♐ ♒ Sext : 1 : ♉ ♋ ♍ ♏ ♑ ♓ These mutual Aid by Nature's Laws convey , And jointly act with an agreeing Ray. And therefore every Birth , that Squares or Trines Enjoys , not always carries all the Lines ; And tho' the Signs the name of Squares may gain , Or Trines , they never shall their Force obtain : They cannot jointly act , their Rays unite , Tho Trines they seem , and shew like Squares to sight : For wide the difference , whether those Degrees , The Line takes up , which to it Art decrees ; Or from the Numbers , which the Circle fill , Detracting somewhat , it cludes thy Skill : For then of Signs too many or too few It will possess ; and make the Scheme untrue . Thus far of these : But now expect to share More vigorous Influence from the Trine than Square ; For Lines that measure Squares remotely tend , And almost close with the Celestial Bend ; But those that make up Trines to Earth repair , Downwards they shoot , from Signs the Influence bear , And with a nearer Ray infect our Air. From Signs Alternate little Friendship 's due , Asquint they look , and with a partial view ; The Line that measures them obliquely drawn , Thro' various Angles goes not freely on ; Many its stops , in every other Sign The Angle closing still diverts the Line ; Forward it darts , but soon it meets a Bound , And six times broak , it leisurely creeps round : From Taurus stretcht to Cancer , thence it bends To Virgo's Sign , and thence to Scorpio tends ; Cold Caper meets it next , and thence it goes To Aries , upward then to Taurus flows , Where , whence it first began , we find the Figure close . The Other , for the Round contains no more , Meets all the Signs the Second mist before ; Then passing those already sung , go on , To all the Others let the Lines be drawn , And equal Angles make the other Hexagon . You see their Site , and thus Oblique they lie , And view each other with a squinting Eye , Too near , because thus plac'd , for mutual Aid , Which freely flows in Lines direct convey'd . High in the Concave Signs Alternate lie , The Lines that mark them almost touch the Sky And therefore far from Earth thro' distant way They dart their Influence with a feeble Ray. And yet some Intercourse in these we find , For Signs Alternate are alike in Kind ; In the first He●agon six Males are found , With Females only is the Second crown'd : Thus Nature works , and , when the Place denies , Sex makes Agreement , and unites the Skies . In Concord no Contiguous Signs agree , For what can love when 't is deny'd to see ? They to themselves , which they behold alone , Their Passion bend , and all their Love 's their own Alternately of different Kinds they lie , One Male one Female fill the Round of Sky . From Signs unequal any way remove All Thoughts of Union , they 're averse to Love : Thus never think between the Sixths to find An Intercourse , nor hope to see them kind ; Because the Lines , by which we mark their place , In length unlike stretch thro' unequal space . For take the Zodiack , from the Ram begin , And thence on either side extend the Line To meet the Sixth from Aries , then dispose A Third , and let the Three in Angles close ; Between the Two first Lines Four Signs are found , The Third includes but One , for that fills up the Round . But more , the Signs oppos'd in Site , that lie With Beams directly darting thro' the Sky ; Tho' much remov'd they seem , yet mix from far Their friendly Influence , or declare for War ; As the Sun's Aspect and the Planet's Fire For Peace determine , or to Rage inspire . These Signs 21 adverse would you distinctly note ? Let Summer's Crab oppose the Winter's Goat . The Scales the Ram where Day and Night appear Equal in adverse Seasons of the Year : The Fish oppose the Maid , the watry Vrn With adverse Fires sees raging Leo burn . When Scorpio fills the highest Arch of Skies , Then bending Taurus in the lowest lies , And when the Centaur sets the Twins arise . Yet though in Site oppos'd these rowl above , Yet joyn'd by Nature or by Sex they love : Thus Males to Males strict Leagues of Friendship bind , And Female Signs to their own Sex are kind . The Fish and Maid oppos'd are friendly Signs , For Nature couples what the Place disjoyns : But Nature sometimes yields , the Trines prevail , And Females Females fight , and Males the Male : Tho' Female both the Goat the Crab defies Winter in this , in that the Summer lies ; Here Snow makes white , and Frost binds up the Fields ; There Sweat o'reflows and Winter's Rigor yields ; Here Day exults , there Night extends her Sway , And Winter's Darkness equals Summer's Day : Thus Nature sights , nor must we hope to find The Signs of disagreeing Seasons kind . Tho' differing Seasons hold the Scales and Ram , They are half Friends , and mix agreeing Flame : In this gay Flowers the painted Beds adorn , This fills the Plains , and stores the Barns with Corn ▪ Their Days and Nights in equal Balance meet , Not vext with too much Cold , nor too much Heat : They Summer's Wars and Winter's Rage compose , Nor will these Seasons let their Signs be Foes . Thus are the several Aspects taught — These things considered , press no more Divine ▪ And know the Gods the Guardians of each Sign Whom Nature order'd to controul their Course , Direct their Influence , and assist their Force : Great Powers are Godlike , we at least assign Gods to great Powers , to make them seem Divine For where Things want , high Titles there bestow Admir'd Worth , and makes them great in show . Pallas the Ram 2● , and Venus guides the Bull , The Twins share Phaebus , and enjoy his Rule ; The Crab is Mercury's , and Jove divides His Mother's Servant , and the Lion guides : Ceres the Maid , for this her Sheaf declares , And fighting Scorpio owns the God of Wars : Juno pours out the Vrn , and Vulcan claims The Scales , as the just Product of his Flames : The frozen Goat kind Vesta's Aid requires , She cheers his cold , and warms him with her Fire ▪ Diana draws the hunting Centaur's Bow , And mighty Neptune now is prov'd to know The Fish above , which He had fed below . And now that Reason guides , that Gods do move The various Orbs , and govern all above , Must needs erect thy Mind , it must impart Strong Inclinations to pursue the Art ; Since Man securely may his Thoughts advance , And hope to find , when undisturb'd by Chance . Now learn what Signs the several Limbs obey , Whose Powers they feel , and where Obedience pay . The Ram defends the Head , the Neck the Bull , The Arms , bright Twins , are subject to your Rule : I' th' Shoulders Leo , and the Crab's obey'd I' th' Breast , and in the Guts the modest Maid : I' th' Buttocks Libra , Scorpio warms Desires In Secret Parts , and spreads unruly Fires : The Thighs the Centaur , and the Goat commands The Knees , and binds them up with double Bands . The parted Legs in moist Aquarius meet , And Pisces gives Protection to the Feet . But Stars have proper Laws , and Signs maintain An Intercourse , and Compact in their Reign ; Some Hear each other , some each other See , Some fight and Hate , whilst some in Leagues agree : Some Foreign Passions cautiously remove , But make Themselves the Object of their Love. Thus Signs in Sex by Nature closely join'd Are Foes , whilst Signs in Sex oppos'd are kind ; And Signs , whose opposite Position tends To Disagreement , breed the greatest Friends . When God ordain'd this mighty Frame to rise , He setled these Affections in the Skies , That some might Hear , and some each other See , Some Hate and fight , and some in Leagues agree ; Some Love themselves alone ; All this appears In Men , who take their Tempers from the Stars . The Ram , as it becomes the Prince of Stars , Is his own Council , and Himself he hears ; He Libra sees , but unsuccessful proves In loving Taurus , for in vain he Loves ; Taurus ( for Aries finds but cold returns For all those Fires with which he freely burns ; Nay more , by Treachery all his Love 's repaid ) Sees , Hears the Fishes , and adores the Maid : Thus from the Tyrian Pastures lin'd with Jove He bore Europa , and still keeps his Love : The Twins see Leo , and they hear the Vrn Pouring out his Streams , but for the Fishes burn . The Crab ( as Caper adverse in the Skies ) First makes himself the Object of his Eyes ; He loves Aquarius Vrn , and then repays The friendly Goat by hearkning to his Rays . The Lion sees the Twins embracing Fires , He hears the Centaur , and the Goat admires : Mischief the Maid for Sagittarius brews , She hears the Scorpion , and the Bull she views . But Libra hears her self , her Mind applies To following Scorpio , to the Ram her Eyes : The Scorpion sees the Fish , the Maid he hears ; To Leo Sagittarius bends his Ears ; To young Aquarius he his Eyes resigns , His Love prefers the Maid to other Signs . The Goat admires , and loves himself alone , ( For since at 23 Caesar's Birth Serene he shone ; What Glory can be greater than his own ? ♈ Loves ♉ ♉ ♍ ♊ ♓ ♋ ♒ ♌ ♑ ♍   ♎ ♏ ♏   ♐ ♍ ♑   ♒ ♋ ♓   He hears the Crab : Aquarius hears the Twins , And sees the Centaur , and amidst the Signs The towring Crab alone his Mind can move , And is the only Object of his Love. Whilst Pisces to the Bull their Ears apply , And view the Scorpion with a longing Eye . These Powers the Tempers of their Births define , Each carries the Affection of his Sign ; These love to See and love to Hear create , And all the Intercourse of Love and Hate : Hence some embrace , and some as odly fly Each other ; Love and Hate , but know not why . Thus far of single Signs : But Trines engage With Trines , and all the Heaven is full of Rage : Signs War in Bodies , and in Parties fight , As adverse in their Manners , as in Site : The Ram , Lion , Centaur joyn'd in Trine oppose The Heavenly Scales , and to their Trine are Foes . And this on two Accounts ; Three Signs to Three Shine opposite , and who can hope to see Two differing Natures , 24 Man and Beast agree ? For he that holds the Scales Celestial , bears A Humane Shape , a Brute the Lion wears , And therefore yields , for Reason's Force controuls Brute Strength , and Bodies still submit to Souls . The Lion conquer'd to the Skies was thrown , And fleecy Aries flead before he shone ; The Centaur's Forepart still commands the rest , So much the Humane Form exceeds the Beast . No wonder therefore that with great Success The Scales fight Aries , and his Trine oppress . But this we may in one short rule comprise , For view the Signs that fill the round of Skies , And those that are in Humane Forms exprest Are conquering Foes to all the shapes of Beast . But yet their Hate not equally extends , Signs have their proper Foes , as well as Friends ; The Ram's Productions Friendly Leagues refuse To all the Fishes , Maid , or Scales produce : What Scorpio , Cancer , Pisces , Scales create Are Foes to Taurus , and his Births they hate : Whilst those Productions that the Twins design Are Enemies to Aries , and his Trine . Against the Crab and Bull the Goat declares , And Virgo too , and Libra feels his Wars : Nor shall ( could I write curious Verse , my Muse To shew her Art in Precepts would refuse ; I teach an Art , and 't is by all confest Instruction when 't is plainest than 't is best : ) The furious Lion rous'd with desperate Rage With fewer Enemies than the Ram engage . The double Centaur with his threatning Bow Affrights the Maid , the Bull that bends his Brow , With Caper , and with Pisces is her Foe . O're Libra's Sign a Crowd of Foes prevails , The Icy Goat , the Crab which square the Scales , With those of Aries Trine consent to hate The Scales of Libra , and her Rays rebate . Nor doth the Sign of fiery Scorpio find Foes less in number , or of better Mind ; The Urn , Twins , Lion , Bull , the Scales , the Maid He frights ; and they of him are equally afraid : Nor can the Centaur's Bow his Peace defend , The Twins , Vrn , Virgin force his Sign to bend By Nature's Law , nor are the Scales his Friend . The same oppress thy Sign with equal Hate Contracted Caper , and thy Force rebate . Whilst those that are in Brutal Forms exprest Afflict the Vrn , and all his Trine molest . The neighbouring Fish the Vrn with Hate pursues , And those the Maid , and those the Twins produce . And those that own the Centaur's angry Star He treats as Foes , and still afflicts with War. These Rules are true , but somewhat else defines The Friendship and the Enmity of Signs : Thus Thirds are Foes , for with a squinting Ray They view each other , and their Hate convey : Signs opposite , whatever place they fill Averse to Peace , and are unfriendly still : Thus Sevenths their adverse Sevenths are doom'd to loath , And Thirds from both , and which are Trines to both : Nor is it strange that Trines unfriendly prove When Kin to Signs that are averse to Love. So many sorts of differing Signs dispose Mens Tempers , and produce such Crowds of Foes ; Look o're the World , see Force and Fraud increase , Rapine in War , and Treachery in Peace ; But look for Truth and Faith , the Search were vain , No Mind is Honest , and no Thoughts are plain : What bulky Villanies bestride the Age ! What Envy pusheth on Mankind to rage ! Envy not to be dispossest , her Throne Is firmly fixt , and all the World 's her own ! Friends kill their Friends , a Husband stabs his Wife , Sons sell their Father's and their Mother's Life ; Bold Atreus feasts , and at the barbarous sight The Sun retires , and leaves the World to night . Whilst Brothers poyson , with a smiling Face They mix the Cup , and kill where they embrace : No place is safe , no Temple yields Defence Against secret Stabs , or open Violence ; And many a slaughter'd Priest profanely dies On the same Altar with his Sacrifice . Those most betray who kindness most pretend , And Crowds of Villains skulk behind the Name of Friend . The World 's infected , Wrong and Fraud prevails , Whilst Honesty retires , and Justice fails ; Nay Laws support those Crimes they checkt before , And Executions now affright no more . For disagreeing Stars that Men produce , Their Tempers fashion , and their own infuse : Hence Peace is lost , pure Faith we seldom find , Kind Leagues are rare , and then but feebly bind ; For as the Signs above , so Things below Do differing Minds and Inclinations show ; They form Men's Thoughts , and the obedient Clay Takes disagreeing Tempers from their Ray. Hence 't is that Friendship is so thinly sown , It thrives but ill , nor can it last when grown ; Rare it's Production : and the World pretends To boast but one poor single pair of Friends : One Pylades and one 25 Orestes name , And you have all the Instances of Fame ; Once Death was strove for , 't was a generous Strife , Not who should keep , but who should lose a Life Was their Dispute , contending to deny Each other the great Priviledge to die . The Surety fear'd his guilty Friend's return , The Guilty Friend did his own Absence mourn ; Careless of Life , impatient of Delay , He broak thro' hindring Friends that choak'd his way , And ran to Danger : Here they disagreed , One hop'd to free , One fear'd to be so freed . But now if you would know what Signs dispose To Leagues , and Peace , and friendly Thoughts disclose ; The Ram's bright Births you may securely joyn As Friends to the Productions of his Trine : But the Ram's Births are more sincerely plain , They give more Love than they receive again From thine fierce Leo , or than his can show That strides thro' Heaven , and draws the Cretan Bow : For 't is a Sign of thoughtless Innocence , Expos'd to Harms , unpractis'd in Defence ; Unus'd to Fraud or Wrong , but gentle , kind , And not more soft in Body than in Mind . The others carry Fierceness in their Ray , Their Nature's bruitish , and intent on Prey ; Ungrateful still , nor can they long retain A sense of Kindness , and unjust for Gain : But tho' by Nature these are both enclin'd To frequent Quarrels , yet expect to find More Force in that which is of double kind , Than in the Single Lion : Hence increase Some sudden Heats , but intermixt with Peace . The Bull and Goat are equally inclin'd To mutual Friendship , both alike are kind ; The Bull 's Productions love fair Virgo's Race , Yet frequent Jarrs disjoin their close Embrace . The Scales and Vrn one friendly Soul inspire , Their Love is setled , and their Faith intire ; To both their Births the Twins productions prove The surest Friends , and meet an equal Love. The Crab and Scorpion to their Births impart A friendly Temper , and an open Heart ; Yet Scorpio's ( Fraud amongst the Stars is found ) Tho' Friends they seem , yet give a secret Wound . But those whom Pisces watry Rays create , Are constant neither in their Love , nor Hate ; They change their Minds , now quarrel , now embrace , And Treachery lurks behind their fawning Face . Thus Signs or Love , or Hate : and These bestow Their differing Tempers on their Births below . Nor is 't enough to know the Signs alone , The Planets Stations must be justly known , And all Heaven's parts , because the Site and Line And Aspect change the Influence of the Sign : Thus when Oppos'd the Signs this Influence bear , In Trine a different they are known to share , In Sextile this , another when in Square . And thus the Sky now gives , now takes away The Influence , now it points , now blunts the Ray Here Hate infects them , when they thence remove ; They lose that Hate , or change the Rage to Love. For Signs , or when they rise , or culminate , Or set , send down a different sort of Fate . To Hatred Signs oppos'd in Site incline , The Quadrates Kinsmen aid , and Friends the Trine ; The Reason's obvious : The Celestial Round Observe , there Signs of the same kind are found In each fourth place : In each fourth Sign appear The several Seasons that command the Year ; Thus Aries gives the Spring , flat Cancer glows With Summer's Heat ; the generous Bowl o'reflows In Libra , Caper scatters Winter's Snows . Besides , by Signs in double Forms exprest Each fourth Celestial place is found possest , Two Fishes glide ; two smiling Boys embrace , A double Figure we in Virgo trace , The Centaur's double with a single Face . Next Simple Signs with their refulgent Stars Fill each fourth space , and still are found in Squares . Without a Rival Taurus fills his Throne , The dreadful Lion shakes his Mane alone , Th' 26 unbodied Scorpion no Companion fears , And still the Vrn a simple Sign appears . Therefore to each fourth place the Stars assign'd In Time agree , in Number , or in Kind ; This makes them Kindred Signs , and these preside O're Kinsmen's Minds , and their Affections guide . But those four Signs on which the Hinges move Belong to Neighbours , and direct their Love. The other Square with all its Stars attends On Guests , Acquaintance , and remoter Friends . Thus all the Signs as they are plac't obtain Their Rule , and with unequal Vigor reign . For tho' the Site and Form of Squares they bear , They work not like the other Signs in Square ; For whilst the Cardinals more Force confess , The rest , which we from Number nam'd express Double or Simple Signs , still work with less . The Line extended thro' the larger space With Trines determines , and makes out their place , Presides o're Friends , whose mutual Faiths supply The room of Blood , and draw a closer Tie : For as it measures a long space , to joyn The distant , stretching out from Sign to Sign . So those , whom Nature doth in spight remove , It brings together ; and knits in Bands of Love. And these before the others most commend , For tho' the nearest Kinsmen oft pretend Deluding Kindness ; who deceives a Friend ? No Sign nor Planet serves it self alone , Each blends the others Vertues with its own . Mixing their Force , and interchang'd they reign , Signs Planets bound , and Planets Signs again . All this my Muse shall orderly reveal , And keep the Method she begun so well ; She 'll sing what Parts the several Signs require , In what the Planets spread commanding Fire ; This must be shown , if in your search for Fate The Signs of Love you 'd know from those of Hate . Now with expanded Thought go on to know A Secret great in Use , tho' small in show ; For which our scanty Language , poor in words , No single fit expressive Term affords , But Greek supplies , a Language born to frame Fit Words , and show their Reason in the Name . 'T is Dodecatemorion 27 , thus describ'd — Thrice ten Degrees with every Sign contains Let Twelve exhaust , that not one part remains ; It follows streight that every Twelfth confines Two whole , and one half Portion of the Signs : These Twelfths in Number , as the Signs , are Twelve , And these the wise contriver of the Frame Plac't in each Sign , that all may be the same . The World may be alike , each Star may guide , And every Sign in every Sign preside ; That all may govern by agreeing Laws , And friendly Aids be mutual as their Cause . And therefore Births ; o're which one Sign aspires , In Powers are various , different in Desires ; Males follow Females , and from Man deprest Weak Nature sinks , and errs into a Beast : For all on Signs depend , in which succeed The different Twelfths , and vary in the Breed . Now whose , and how dispos'd , the Muse must sing , And draw deep Knowledge from its secret Spring ; Lest this unknown you should from Truth decline , Mistaking the chang'd Influence of the Sign : Each Sign 's first Twelfths is by its self possest , The others shar'd in Order by the rest ; Each hath its Twelfth , they take their equal Shares , ( Ambition is a Vice too mean for Stars ) Thus every Sign hath for its proper Throne Two whole , and one half Portion of its own ; Of other Signs that rowl in order on Each takes as much , till all the thirty parts are gone . But there are many sorts , to find the true Wise Nature orders we must all pursue ; This is her Will : Tho partial Search may fail , Yet He 's secure of Truth who seeks for All. For Instance , grant it were thy great Concern To know the 28 Planet's Twelfths ; securely learn ; I 'll shew the Method : As you count the Signs , First mark that Sign 's Degree where Phoebe shine And views the new-born Child ; that multiply By Twelve : ( because Twelve Signs adorn the Sky ) Observe the Product , and from thence assign To those gay Stars where Phaebe's found to shine Thrice ten Degrees : Then go in Order on , Assigning Thirty till the Number 's done ; And where the Number ends there fix the Moon : That is her Twelfth . The following Planets lie In following Twelfths , and there enjoy the Sky . Another Method claims my next Essay , Another differing from the former way ; This too I must explain , its Rules impart , And fix the subtle Niceties of Art , First take the 29 Sun 's true place , and that confest , Observe the Portion by the Moon possest : Count those Degrees the middle Space contains , Take all the Thirtys thence , and what remains Dividing into Twelfths , from thence assign To those gay Stars in which the Moon does shine One Twelfth : To Signs that orderly come on Apply their Twelfths , till all the Number 's done , And where the number ends there fix the Moon . That is her Twelfth . The following Planets lie In following Twelfths , and there enjoy the Sky . The Task 's not done : The Muse must next unfold A nicer thing , in fewer Numbers told : Which less in show and in extent appears , Yet than the Greater more of Force it bears : In every 30 Twelfth a Twelfth the Planets claim , The Thing is different though we use the Name ; 'T is thus describ'd . Five half Degrees do lie In every Twelfth , Five Planets grace the Sky , And every Planet in its proper Course One half Degree possessing there exerts its Force . 'T is useful therefore to observe the Sign , And mark the Twelfth in which the Planets shine ; For where the Planets , as they rowl their Course , A Twelfth possess , they there exert their Force . These must be jointly sung : yet these belong To future Thoughts , and claim another Song : 'T is now enough that I have clearly shown Things hid before , and made their Vses known ; Let it suffice , that I have brought the Muse Materials proper , and prepar'd for Use : When all is ready , let her build the Frame , And raise a lasting Monument of Fame : The single Elements distinctly known Thee sees her Way , and may go safely on ; And all the Parts describ'd the Verse will roul With freer Force , and orderly erect the whole . For as to Boys at School we first propound The Letters , show their Form , and teach their Sound , And then go on , instruct them how to Spell , And join their Letters in a Syllable ; Then to frame Words , and thence their Fancies raise , To bind these words in Verse , and reach the Bays . And as the Boys proceed , they find their past , And first Acquirements useful to their last ; For Precepts without Method got by pain , Prove empty , and the labour is in vain : So since my Songs Fate 's dark Intrigues reherse , Their Influence show , and bind the Stars in Verse ; Since they mount high , and from the Signs above , Bring down the God , and open hidden Jove : All must be taugth , and I must first impart The Elements peculiar to this Art ; That thence , as she proceeds , my labouring Muse May draw Materials , and go on to Use . And as wise Builders , who design a Town , First clear the Field , and cut the Forest down , And streight new Stars behold as new a Sun : From Antient Seats , and Hospitable Glades The Beasts are forc'd , and Birds forsake their Shades . Some Stones for Walls , some Marble square for Shrines , And suit Materials to their great Designs ; And when they have provided sit Supplies For future Art , the Piles begin to rise ; Nor doth the interrupted work disgrac't By any stop , accuse their foolish haste : So I , that raise this mighty Work , must choose Materials proper to employ my Muse , Bare fit Materials ; and not build one part 'Till all lies ready to compleat the Art ; Lest whilst my Thoughts the noble work pursue , As all Materials lay expos'd to view , They start surpriz'd , and stop amaz'd with new . Be careful then , and with a curious Eye , Observe the 31 four fixt Hinges of the Sky ; One constant point their settled place defines , Altho' they vary in their moving Signs : One fixt i' th' East , where with a gentle Ray The Sun views half the Earth on either way , And here brings on , and there bears off the Day . One in the West , from whose declining steep The Sun falls head-long , and enjoys the Deep : The Third in Heaven's high point , where midst the Course Bright Phoebus stops , and breaths his weary Horse ; He stands a while , and with an equal Ray , Views East and West , and then drives down the Day . Oppos'd to this , the Fourth securely lies , The immoveable Foundation of the Skies ; The lowest point , to which with steddy Rein The Stars descend , and whence they mount again : These Points in Fate the greatest Interest claim , Because they settle , and support the Frame ; In these fixt Points were not the Quarters ty'd . o th' Top , o th' Bottom , and on either side , The Ball would cleave , the whirls would dissipate The agitated parts ; and break strong Fate . Now different Powers these several Hinges grace And vary with the dignity of Place ; The chiefest that which on the Top doth lie , And with a narrow limit parts the Skye , There Glory sits in all her Pomp and state , The highest place requires the highest Fate ; Thence Places , Dignities , Preferments flow , And all that Men admire and wish below ; High Honours , Offices , in Suits success , Right to make Laws , and Power to give Peace ; Thence Scepters , and supreme Command accrne , And Power to give them , where Rewards are due . The next , ( tho' lowest and contemn'd it lies ) The fixt , and sure Foundation of the Skies , Great in effect , altho' it seems but small ; It governs Wealth , and Wealth 's the stay of all : It rules Estates , it shows what Mines contain , What secret Treasures we may hope to gain , Without this Power the other Fates were vain . As great in Power is that where Beams display Their rising luster , and renew the Day ; The Greek ( no other scanty Tongues afford A single proper and expressive Word ) Names this the Horoscope . This governs , Life , and this marks out our Parts , Our Humours , Manners , Qualities , and Arts ; This when and where the Birth is born declares And guides the various Vertues of the Stars : By this they are settled , and as this defines The Birth , enjoys the influence of the Signs . The Last , the Point , whence Stars descending fall , And view the lower surface of the Ball ; This rules the Ends of things , this Point declare The Period , and Result of all Affairs ; This governs Marriage , and on this depends Religion , Recreation , Death , and Friends . These Points considered , Their Powers distinctly seen , Observe the Spaces that are plac't between ; The Points are little , but the Spaces large , And every space has a proportion'd Charge . First then the Space that rising from the East Mounts upward , is by Infancy possest , There Childhood plays : From thence the Western space Gay Youth demands , and fills the second place . Next from the Western Point a space descends , Thro' under Heaven , and in the Lowest ends ; There Manhood , having past the various Maze Of Infancy and Youth , compleats its Race : To finish this ; The space that upward tends , And creeping slowly o're the steep Ascends To join the Round at East , is made the way Of feeble Age and flitting Life's decay . But more all Signs , whatever Form they bear , The several Vertues of their Stations wear ; With good or hurtful Powers those points their Ray , The Places govern , and the Signs obey : ♈ Hates ♍ ♎ ♒ ♉ ♋ ♎ ♏ ♓ ♊ ♈ ♌ ♐ ♋ ♑ ♎ ♍ ♉ ♌ ♍ ♎ ♒ ♍ ♈ ♐ ♓ ♑ ♎ ♈ ♉ ♋ ♌ ♑ ♏ ♈ ♌ ♐ ♒ ♊ ♉ ♍ ♎ ♐ ♊ ♎ ♍ ♒ ♑ ♊ ♎ ♍ ♒ ♒ ♈ ♉ ♋ ♌ ♏ ♑ ♓ ♓ ♒ ♊ ♍ ♐ They turn the Round , and as they wheel their Course , The Place now gives , and now takes off their Force ; For as the Planets thro' the stations Err , Those Places their own Ifluence transfer ; And force them , whilst within their bounds , to take Their ruling Vertues , and their own forsake . Hence now they smile , and now severely frown With Foreign Influence that Commands their own : Here sovereign send , there showr malignant Rays , And spread the fatal Venom of their Place . That station which above the East doth lie , The Third in order from the middle Sky , ●s an unhappy Seat ; destructive still To all Events , and too replete with Ill. Nor is this bad alone , the Seat that lies Below the Western Hinge oppos'd to this , ●s like it : Nor doth this that Seat surpass , 〈◊〉 Vertue of its Dignity of Place , ●s near the nobler Hinge : But both decline , ●●om both begin a wretched Round of time , ●f Labor full , for here you fall , and there you climb . Nor is the World with better stations blest Above the West , nor yet below the East , ●hat hangs above , this downward seems to bend , ●his in the neighbouring Hinge still fears an end , ●hat unsustain'd is eager to descend . Unhappy Seats ! Here Typho rules alone And fills a dark inhospitable Throne : ●his Typho Earth produc't , when Giants strove ●o Conquer Heaven , and shook the Throne of Jove . When Monsters rose , and at a wondrous Birth In bigness equal to their Mother Earth , Vast Sons broke forth : But Thunder stopt their Course , And tumbling Mountains dasht the Rebells Force . Typhorus fell : Earth was too weak to save , And War and He lay buried in one Grave ; Yet now he heaves in his Aetnean T●●●b , And Earth still fears new struglings in her Womb That next Heaven's topmost point , which riseth high , Almost it 's equal in the middle Sky With fairer Hopes , and better Fortune blest , Erects its Head , and much excells the rest ; Plac't near the highest Hinge , it riseth higher , This Empire 's Seat , and almost fills desire : It 's Title , the exalted Place may claim A glorious Patron , and as great a Name , Is Happy ; Happy , if that word can fill The Greek Expression and commend my skill . Here Jove presides in all his Pomp and State , And to this ruling Fortune trust thy Fate . Oppos'd , and next the bottom of the Ball There lies a Seat as wearied with its fall ; And yet prepar'd , tho' with a world of Pain For other Labour , and to mount again : About to bear , and destin'd to obey The Hinge's Power , submitting to its sway ; Yet prest not by the World , it gives a Scope To haughty Thoughts , and still permits to hop● In Greek Demonie : But our scanty Tongue Affords no proper word to grace my Song : Yet mind this station , it thy Thoughts may clai● Observe its Patron , nor forget the Name : Tho' troublesome it seems , no toil refuse The Labour 's great , but equal'd by the Vse . i th' Ninth , and Third gay strength and health Delight , Or Sickness arms its venom'd Darts for fight ; Why Contraries should thus these Seats possess 'T is hard to find , but Phoebus aids my guess ; The mighty Patrons , whom these Seats obey , In one determin'd time bear different sway And Day succeeds the Night , and Night the Day . That Seat which next the Highest Hinge doth lie The first declining from the middle Sky The Sun possesses : From his Rays we draw Our state of Health , He gives our Bodies Law : Its Title God. Oppos'd to this , which first begins to rise From Heaven's low bottom , and brings up Skies , A Seat appears just tipt with Light , and guides The Starry Night , in this the Moon presides . The Moon that sees her Brother's adverse Ray , That looks up to him as he guides the Day . And imitates his Influence the wrong way : She rules our Bodies , but her Face derives Moist rotting Powers , and wastes the Health He gives . It 's Title Goddess : But how mean these words Compar'd with those , expressive Greece affords ? But as for Heaven's high top , the utmost point Of Rising , and beginning of Descent , Where 'twixt the Eastern rise , and Western fall Jove hangs the Beam at which He weighs the Ball ; This Venus graceth , here she seats her Throne , And in the World 's high Face erects her own ; That Face , whose awful force Mankind admires , And yields Obedience to her pleasing Fires : Her Charge is Marriage , for what else can prove The Office of the beauteous Queen of Love ? Pleasure 's her aim , yet she forgets her Ease , And puts on Providence on design to please . Fortune 's the station 's Name ; observe the Place ; My Muse grows weary , and contracts her pace , Refusing to expatiate in her Race . But now go on , the lowest point of all The fixt Foundation of the solid Ball , Which looking upward , sees the circling Light , And lies it self immerst in deepest Night , Is Saturn's Seat ; tho' once he rul'd above , Enjoy'd that Power , and fill'd the Throne of Jove ; But thence thrown down , he makes his last retreat To this low place , and fills this humble Seat : Himself a Father , He pretends to bear Respect to Fathers , and makes Age his care : This only station double Cares enlarge , For Sons and Fathers Fortune are its charge : Severe and thrifty ; This the Greeks proclaim Demonium , its power expressing in its Name , Now turn thine Eye , and view the Eastern Plain , The space whence Stars renew their Course again ; Where moistned Phoebus from the Floods retires , Climbs up , and shakes the Water from his Fires , Then gathers Beauties , whose enlivening Heat First strike thee , Mercury , and refresh thy Seat. O happy Seat , on whom the Art that sways O're Heaven it self , bestows its 32 Authors rays ! The Fates of Children this is doom'd to bear , And all the Hopes of Parents are its care . One Seat remains , from whose declining steep , The Stars fall headlong , and enjoy the Deep , Which turns the World , and now can only trace The back of Phoebus , that once view'd his Face : No wonder Nature doth this Seat bequeath To Pluto , and inexorable Death ; For here the Day expires , this draws the light From all the World , and buries Day in Night , Nor is this all its care , on this depends , Faith , solid Constancy , and Friends , So great that Place's power , which waste the Ray , Which takes in Phoebus , and puts out the Day . The stations these , to which in constant Course The Stars arriving give and take new Force , Where Planets touching as they wheel their round , Mix foreign Powers , and with their own confound : Admitted once they make the Seat their own , And turn Usurpers in another's Throne . But this , if Fate my Life and Health prolong , Shall make the 32 subject of a future Song : Now ends the Book , which hath describ'd at large The Heavenly Houses , Guardians , and their Charge ; For which the Masters of the Art have found A proper Name , but of a foreign Sound ; 'T is Octotopos . With mighty labour I these Rules prepare , Forgetting Pleasure , and possest with Care : So hard it is in numerous Verse to close Unwieldy Words , and smooth uneven Prose . The End of the Second Book . NOTES . 1. Manilius having mention'd the chief Arguments of Homer's Poems , concludes with a high Character , stiling him the Fountain of all Poetry . Ovid. Amor. lib. 3. El. 8. to the same purpose , A quo , ceu Fonte perenni , Vatum Pieriis ora rigantur Aquis ▪ And Longinus ( de sublim . Sect. 13 ) says not only Stesichorus and Archilocus , but Herodotus the Historian , and Plato the Philosopher , owe their chiefest Beauties to that Poet. 2. Several Poems of Hesoid are lost , and Scaliger with other Criticks conjecture , That Manilius refers us to those lost Poems : But I think this and the preceding Verse ought to be Corrected , ( of this Correction perhaps I may give an account in a Latin Edition of this Author ) and then they will be found in those pieces of Hesiod that are now extant . 3. Eratosthenes a Greek Poet , flourished in the time of Ptolemy Euergetes , about the 138 Olymp. He wrote of the Stars and Constellations , and gave an account of all the Fables relating to them : I have not time to explain all these Fables and therefore shall only direct where they may be found . Concerning Perseus , Andromeda , her Father Cepheus , and her Mother Cassiopeia , vid. Ovid . Metam , lib. 4. ver . 665. Concerning Callisto , or the great Bear , Ovid. lib. 2. ver . 405. The Fable of the Little Bear may be found in Diodorus Siculus , lib. 4. Of the Swan in the First Book of Manilius . Of the Goat in the First Book of Manilius , and in Casaubon's Animadversions on Athenaeus : The Maid or Erigone , is said to be the Daughter of Icarus , who upon the Death of her Father , hang'd her self . The Nemean Lion being slain by Hercules , was plac'd amongst the Stars for his shining Skin . The Crab for pinching Hercules when he fought the Hydra : The Scorpion for Killing Orion , or rather , for assisting the Gods against the Giants . The Stories of Venus taking the shape of a Fish when she fled from the Giant Typho , and of the Ram who swam over the Hellespont with Phryxus and Helle on his Back , are well known , and may be found in Manilius , and Selden de Diis Syris . 4. This was a Fancy of the Antients , which some are not asham'd , after Experience hath so often Confuted it , to maintain still . 5. The Elephants do so , if we believe Pliny : Nat. Hist . lib. 8. cap. 1. 6. Aries is Male. Gemini M. Leo M. Libra M. Sagittarius M. Aquarius M. Taurus Female . Cancer F. Virgo F. Scorpius F. Capricornus F. Pisces F. 7. The Humane Signs are Gemini , Libra , Virgo , Aquarius . The Brute , Aries , Taurus , Sagittarius , Capricornus , Leo , Cancer , Scorpius , Pisces . 8. Of Double Signs some are Pairs , as Gemini , and Pisces : Others are made up of two different Species , such as Sagittarius and Capricornus . 9. The Tropick Signs are Aries , Libra , Cancer , and Capricorn . 10. Their Position is unnatural ; but this , as well as the fore-going Differences , will be easily understood upon view of the Signs upon a Globe . 11. Concerning Day and Night Signs , there are different Opinions : Some fancy that Aries , Taurus , Gemini , Cancer , Leo , Virgo , are the Days , and the other six the Nights . Others teach that the Male and Female are the same with the Day and Night Signs . But the Opinion that Manilius follows is this . Aries is a Day Sign , Taurus , Gemini , Night . Cancer , Leo , Day . Virgo , Libra , Night . Scorpius , Sagittarius , Day . Caper , Aquarius , Night . Pisces Day . So that begin with Pisces , and then you find two Day Signs together , and then two Night Signs , and so in Order . 12. The Water Signs are Pisces and Cancer . The Earth Aries , Taurus , Leo , Scorpio , Gemini , Sagittarius , Libra , Virgo : Capricornus and Aquarius belong to both Earth and Water . 13. The fruitful Signs are Cancer , Scorpio , Pisces . The Barren are Leo , Virgo , Aquarius . The remaining six are partly Barren , partly Fruitful . 14. The Running Signs are Leo , Sagittarius , Aries : The standing or Erected Signs , Aquarius , Gemini , Virgo . The Crouching Signs , Taurus , Cancer , Libra , Scorpius , Caper , Pisces . 15. The Maim'd signs , Taurus , Scorpius , Sagittarius , Cancer . 16. The Season signs are Pisces , belonging to the Spring . Gemini to Summer . Virgo to Autumn ; and Sagittarius to Winter . 17. Suppose in the Zodiack Circle Twelve Signs , and in every Circle 360 Parts or Degrees , and 30 of these Degrees to belong to each of the Twelve Signs . Begin at any of the Signs , for instance , Aries ; and in this Circle inscribe a Triangle , all whose sides are equal ; it is evident that the Arch of the Circle which each of these sides subtends , contains 120 Parts or Degrees ; and therefore between that Sign from which you begin to draw each side of this Triangle , and that to which you draw it , there must be Three Signs . But see Fig. 1st . 18. To shew what Signs are to be accounted Right , and what Left , the Poet mentions only the Trine of Taurus : Yet it is sufficient , upon View of Fig. 1st . direction for all the rest . 19. To know the Quadrate , begin from any sign , and in the Circle inscribe a Square , all whose sides are equal ; the Angles shew the Signs , and what are Right or Left , you may find that in Quadrates , as you did in Trines . 20. The meaning of all these Cautions concerning Trines and Quadrates , is in short , this , You must reckon by Degrees , and not by Signs ; for if you reckon by Signs , the Figures , as Manilius shews at large in each particular , will not be equilateral . See Fig. 1st . and 2d . 21. The Signs which have an Opposite aspect are , Aries . Taurus . Gemini . Cancer . Leo. Virgo . Libra . Scorpius . Sagittarius . Capricornus . Aquarius . Pisces . 22. The Guardians of the Signs . Of Aries . Taurus . Gemini . Cancer . Leo. Virgo . Libra . Scorpius . Sagittarius . Capricornus . Aquarius . Pisces Pallas . Venus . Phoebus . Mercurius . Jupiter . Ceres . Vulcan . Mars . Diana . Vesta . Juno . Neptune . The Reasons of this Assignment are to be taken out of the Old Fables . 23. Whether Capricorn was in the Horoscope of Augustus , when he was Born , or when he was Conceived , Is disputed : However 't is certain , Augustus took Capricorn for his Sign , and many times its Figure is found upon his Coins . vid. Sueton. vit . Aug. cap. 94. and Spanhemius de Nummis . p. 210. 24. See the Figures of these Signs on a Globe . 25. Pylades and Orestes being taken Prisoners , Orestes was condemned to Die , but was allow'd to go and settle some Affairs , upon Condition that Pylades would stay behind , and engage his Life for his return : Pylades becomes Surety : Orestes goes , settles his Affairs , and returns at the Day appointed . 26. So call'd , because in the Sign Scorpius we see nothing but the Claws . 27. The Dodecatemorion is the Twelfth part , or two Degrees and an half of a Sign . Every Sign containing Thirty Degrees ; for Twelve times two and an half make Thirty . Scaliger gives this Instance . Let the propos'd Degree be the Thirteenth Degree of Gemini , multiply Thirteen by Twelve , the Product is one hundred fifty six : Of these give Thirty to Gemini the propos'd Sign , Thirty to Cancer , Thirty to Leo , to Virgo Thirty , and Thirty to Libra : There remain Six , and therefore the Dodecatimorion of Gemini is in the Sixth Degree of Scorpius : But this instance doth not seem to agree with the Doctrine of Manilius . 28. Scaliger affirms , that Manilius proposeth two ways to find the Dodecatemoria or Twelfths of the Planets ; Huctius says he gives but one : This Dispute will be best determin'd by observing the Poet himself , and illustrating his Doctrine by two Instances : Let the Moon be in the Sixth Degree of Aries , multiply six by Twelve , the Product ●s Seventy two : Out of this Seventy two give the first Thirty to Aries , the second to Taurus , and ●hen there remain Twelve ; and therefore the Dodecatemorion of the Moon is in the Twelfth Degree of Gemini , that is , in the Second of the Five half Degrees of the Dodecatemorion of Gemini . 29. To this Method Scaliger applies this Example : Let the Sun be in the Thirteenth of Gemini , the Moon in the Twenty Third of Scorpius , the Arch of the Zodiack between the two Planets , contains one Hundred and Sixty Degrees : In this Number there are five Thirties , which being taken away there remain Ten ; divide these Ten by Twelfths , or two and an half , the Quotient is four Twelfths , or Dodecatemoria ; of which give one to Scorpius , another to Sagittarius , a third to Capricorn , and the fourth falling in Aquarius , shews the Moons Dodecatemorion to be in the twenty third Degree of that Sign . 30. The third sort of Dodecatemorion is this . In every Dodecatemorion or Twelfth , there are five half Degrees , and the Planets ( which the Antient Astrologers counted but five , not reckoning the Sun and Moon amongst the Planets ) have in each Dodecatemorion or Twelfth , one half Degree assign'd to every one of them . 31. From this Verse to the end of this Book , Manilius treats of the Twelve Celestial Houses , which he divides into the Four Cardines or Hinges , and the Eight Spaces that lie between these Hinges : The Hinges are the Eastern Point , the Middle Point , the Western Point and the lowest point of Heaven : The Spaces , &c. but see Fig. 10. 32. Manilius in the beginning of his first Book tells us Mercury was the Inventor of that Art , which he intended for the Subject of his Astrological Poem . 33. Either the Poet never finish'd this Part which he here promises , or it is now lost . MANILIUS . The Third Book . Manilius begins this Third Book as he did the Second , reckoning up and slighting the several Subjects which have imploy'd other Poets , and declaring his Design to be new and difficult : Then he proceeds to shew , 1. That the Twelve Signs of the Zodiack are the chief Disposers , and principal Governours of Fortunes . 2. That there are Twelve Lots belonging to these Twelve Signs . 3. He names and describes these Lots : The first is Fortune : The Second Warfare and Travelling : The Third , Civil Employments : The Fourth , Pleadings , and all the concerns of the Bar : The Fifth , Marriage Acquaintance , Guests : The Sixth , Plenty , Wealth , and the means of preserving it . The Seventh , Dangers : The Eighth , Nobility , Honour , Reputation : The Ninth , Children , Education . The Tenth , Manners , Institution , Family . The Eleventh , state of Health , Physick : The Twelfth , Wishes , and the ends of them . 4. He teaches how to suit these Lots , Labours , or Athla to the several Signs , when the Birth belongs either to Day , or Night . 5. He proposeth Rules how to find the Horoscope . 6. Refuting the Method prescrib'd by the Chaldaeans . 7. And shewing how to find the different lengths of Days and Nights , together with the several Risings and Settings of the Signs in order to find the Horoscope . 8. He resumes the Dispute against the Chaldaeans , and subjoins an Account of the several lengths of Days and Nights , in the three different Positions of the Sphere , Direct , Oblique , and Parallel . 9. He proposes another way to find the time of the Signs Rising and Setting . 10. He particularly Discourses of the Days Encrease from Capricorn to Cancer . 11. He shews what are the proper Years , Months , Days , and Hours of the Signs , and Confutes the Opinion of some Astrologers concerning them . 12. He sings how many Years belong to each Sign , and station . 13. And Concludes the Book with an Account of the Tropick Signs . I am not to Answer for the Astronomy , it is enough if I have made the Poet speak intelligible English . VVHilst I new ways attempt my groveling Name To raise from Earth , and wing my Flight for Fame ; Thro' Woods untrodden whilst I take my way , Ye Muses lead ; for I extend your Sway To larger Bounds , and make the World obey . No Heaven 's besieg'd , no Thunder thrown from far Intombs the Giants , and concludes the War : No fierce Achilles tells brave Hector's Spoil , Nor Priam bears the Hero to his Pile . No barbarous 1 Maid betrays her Father's trust , Nor tears her Brother to secure her Lust . No Bulls breath Fire , no Dragons guard the Prize , Nor from the poysnous seed Arm'd Harvests rise : No Youth returning here renews the Old , Nor treacherous Presents carry Flame in Gold. Nor will I sing the Babes Medea bore , Got by much Guilt , but ah ! destroy'd by more . The Theban Siege , the highest Pride of Fame , Nor how the Town by Thunder sav'd from Flame Lost whilst it 2 conquer'd ; nor how Spartans fought Round old Messana , shall enlarge my thought . No Sons 3 and Brothers shall be joyn'd in one , Nor Mother bear a Granchild in a Son ; No Murder'd Babes 4 shall feast their injur'd Sire , Nor Days break off , and frighted Suns retire . None shall defy the Sea , the Floods enslave , Sail o're the Mountains 5 , and walk o're the Wave : No Asian Kings . And thee , O mighty Rome , Thy Arms , thy Conquests , and thy World o'recome Thy Laws , thy Wars , thy Leagues my Verse refuse , Those claim the leisure of a greater Muse . Smooth Seas the Artless Sailer safely tries , And Flowers undress'd in fruitful Gardens rise ; He works securely , who in Gold designs , When e'en the rude unpolisht Metal Shines ; On specious Subjects common Wits compose , For where the Matter takes , the Fancy flows ; And every vulgar Author writes with ease , Secure of Credit , where the Themes can please . This way some take to Fame : Thro' Words unknown , And things abstruse my Muse goes boldly on , Observes all Interchange of Times , compares The fatal turns , and views the Leagues of Stars , Things so remote , so intermixt , and wrought With Parts in Parts ; they are too fine for thought . To know them is too much , but to explain How great ! to bind in Verse shews more than Man. Then come , who e're thou art that bring'st a Mind To know high Truth , and patient Thoughts to find ; Hear solid Reason , and go on to gain True serious Knowledge , but neglect the vain : No Kings at Aulis sworn , no tales of Troy With Priam's tears , or Helen's fatal Joy , Nor hope sweet Verse , and curious turns to find , I 'll leave thy Passions , and instruct thy Mind : And tho' some Words of foreign Stamp appear , Seem harsh , untun'd , uneasie to thy Ear ; This is the Subject's not the Writer's fault , Some things are stiff , and will not yield to thought ; I must be plain : And if our Art hath found Expressions proper , it neglects the Sound . Thy Mind well purg'd from vainer Cares compose , For now my Muse is eager to disclose , The nicest Secrets ; which observ'd , impart Fate 's Laws , and prove the surest Guides to Art. When Nature order'd this vast Frame to rise , Nature , the Guardian of these Mysteries , And scatter'd Lucid Bodies o'er the Skies ; When she the Concave , whence directly fall Streight Lines of Influence round the solid Ball , Had fill'd with Stars ; and made Earth , Water , Air , And Fire , each other mutually repair ; That Concord might these differing parts controul , And Leagues of mutual Aid support the whole ; That nothing which the Skies embrace might be From Heaven's supreme Command and Guidance free , On Man the chiefest Object of her Cares Long time she thought , then hung his Fates on Stars ; Those Stars , which plac'd i' th' Heart of Heaven , display The brightest Beams , and share the greatest sway ; Which keep a constant Course , and now restrain The Planets Power , now yield to them again ; Thus sometimes ruling , sometimes rul'd , create The strange and various Intercourse of Fate . To these her Powers wise Nature's Laws dispense Submitting all things to their Influence : But then as Emperours their Realms divide , And every Province hath its proper Guide , So 't is in Signs ; they have not equal Shares Of common Power , each Fortune claims its Stars . Our Studies , Poverty , Wealth , Joy and Grief , With all the other Accidents of Life She parcels out ; to proper Stars confines The Lots in number equal to the Signs . These grac'd with proper Names and Place contain The various Fortunes incident to Man , Yet so contriv'd , that they are always found In the same 6 Order , in the fatal Round . Yet are not Lots thus fixt to Signs to lie Possessing the same 7 Station in the Sky ; And from one place directing down to Earth An equal Influence work on every Birth ; But still the Time of every Birth confines These Lots to Seats , and makes them change their Signs , That every Lot from every Sign may flow , And vary the Nativity below . But lest Confusion too much Change produce , And make the Art too intricate for Vse ; 'T is order'd thus : — That when the Birth 's first Minute hath decreed The first Lot's Station , then the rest succeed In following Signs ; each Fortune takes its Seat In proper Order , till the Round's compleat : Take these short Rules till flowing Verse dilate , Unfolding all the Mysteries of Fate . These Lots which thus decreed to Signs contain The various Fortunes incident to Man ; As Planets joyn with a malignant Ray , Or Kind ; or as the rolling Skies convey To different Hinges , so the Fortune spreads , And well or ill the whole Design succeeds : Their Names and Kinds obliging Muse reherse , And sing their Titles in no vulgar Verse , That late Posterity with Joy may throng To Themes unknown , and crowd to learn my Song . Fortune 's the first : This Name our Art bestows , And what it signifies the Title shows . Here House is found , with all that may conduce To House , either for Ornament or Use : What train of Servants , what extent of Field Shall aid the Birth , or give him room to build : When large Foundations may be safely laid , Or Houses roof'd ; if Friendly Planets aid . Warfare's the next : And 't is in This decreed How every Native shall in Arms succeed : What Dangers wait them when abroad they roam , To pick up Follies which they miss at home . Civil Employments in the Third we find , Tho those too justly may be styl'd a kind Of Warfare ; when two different Interests jarr , Oppos'd in sides , and make a sort of War. Here 's Patronage , and here our Art descries What breaks its bands , what draws the closer ties , Shows what Rewards our Services may gain , And how too often we may court in vain : All this as Planets friendly Aids conspire , Or temper Signs with their unlucky Fire . Proceed , my Muse , for in the next appear The Court Concerns , and Fortunes of the Bar , The pleading Patron with the fearful Throng Of trembling Clients hanging on his Tongue . The smooth Perswader who shall teach the Laws , And settle Right , whilst Truth supports the Cause ; For from this Lot the Planets Rays dispense The various Powers of winning Eloquence . The Fifth to Marriage Sacred yet pretends To Guests , Acquaintance , Company , and Friends ; Here we discern the Common League that binds The Equal Souls , and joyns agreeing Minds . But in the sixth , rich Plenty takes her Throne , With Preservation : And from this 't is known What stores of Wealth shall come , how long their stay , As Planets tamper with their ruling Ray : The Seventh in horrid Dangers shall engage The Birth , if Planets not correct its Rage . The Eighth Nobility pretends to claim , Where Honour sits with her attendant Fame ; Where Family erect maintains her Place , And smiling Favour with her winning Face . The Ninth the doubtful Lot of Children bears With all the Pious Parents hopes and Fears , The Tutor's Industry , and Guardian 's Cares . The next to this the Act of Life contains , And shews how far a good Example reigns : How by their Masters form'd Slaves take their way To Tasks assign'd , and chearfully Obey . The following is a Lot of high concern , For hence the state of strength and Health we learn , When griev'd , we live obnoxious to Disease , Or free from Sickness , and consign'd to Ease : Let none who value Health , this Lot refuse , When they would time for wholsome Physick choose ; For hence we are with most exactness taught To gather Drugs , or mix the saving Draught . The Last , and which the Round concludes , contains The End of all our Wishes and our Pains , Shews if to what our several Aims address Obtain'd , shall crown our Studies with Success ; Whether with fauning Arts we court the Great , Or shunning Crouds , to Privacy retreat ; Whether we Plead at the Contentious Barr , Or Plough the Sea , and gather Wealth from far ; Or tear the Earth , to crowd our stores with Grain , Or bring unruly Bacchus to the Press again . For these , if Planets prosper the Effect , You may fit moments , and fit Days expect From this one Lot , and all the rest neglect . These Planets 8 Powers , and how their Rays infuse , Or Good , or Bad , shall then engage my Muse , When their Effects she Sings — But now lest hudled things confusedly wrought , Distract thy Mind , and discompose thy Thought ; Let Verse in Method orderly impart The single naked Elements of Art ; And since my ventrous Muse hath bound in Rhime , The various Labours of the Round of Time , ( What Greece calls Athla , happy Greece in Song , Are now call'd Labours in a meaner Tongue ) Which to Twelve Lots conveniently assign'd Determine all the Fortune of Mankind : Her Theme pursuing , she will next comprise The several Signs with which the Labours rise ; For to one Seat they are not always ty'd , Nor from one Sign at every Birth preside ; They change their station , as the Round they move , Yet still their Order is the same above . But lest you should imperfect Schemes compleat , Nor justly suit each Labour to its Seat ; First find the place by Fortune's Lot possest , ( Fortune the first , and Leader of the rest ) That done , to following Signs in order join The Lots , and give each Labour to its Sign : And to secure thy search for Fortune's place Two Rules shall guide thee , and enfold the Maze . The moment known when first the Birth began , The Planets join'd to Signs to form the Plan , And Scheme erected for the future Man ; If then the Sun with an exalted Ray Above the East and West commands his way , Then safely fix , and give the Birth to Day : But if through lower Skies he wheels the Light , The Day resigns , and yields the Birth to Night . This settled , if the Birth belongs to Day , The Rule is short , and not obscure the Way ; From that Degree , where then the 9 Sun presides , To that Degree where gloomy Luna rides : Count thro' the following signs , and as you pass , Exactly mark what Numbers fill the space : Thence from the Eastern point , which artful Greece Hath stil'd the Horoscope , an equal number of Degrees , Following the circling Zodiack as it bends , Count thro' the Signs ; and where the Number ends , There fix the Seat of Fortune ; thence confine In order , every Labor to its Sign . But if when Night her sable Wings hath spread , The Birth starts forward from his Genial Bed ; In different manner , then thy Numbers range , With Nature's Order , let thy 10 Method change ; The Moon , who imitates her Brother's Light , And governs in her own Dominion , Night , Observe : Thence thro' the Signs in order run , To find how far she 's distant from the Sun. The Native's Horoscope be next thy Care , And from that Point , begin to count as far As those Degrees permit thy Thoughts to pass ; And where they stop , there settle Fortune's place . And then to following Signs the rest confine In order , every Labor to its Sign . Perhaps these Precepts may appear too nice , For who can find the Horoscope in Skies Immense , still circling with impetuous force , In Motion restless , and so swift in Course ? Yet this not rightly fixt , our Art can boast No certainty , and all our Labour 's lost : As wretched Travellers are doom'd to stray , When those mistake , who should direct the Way . Because the Points which all the rest controul , Misplac'd at first , must influence the whole , And since the rouling Skies move swiftly on , A different Face is every moment shown , The Scheme must be uncertain , and the Birth unknown . Yet tho' of greatest Vse , 't is hard to gain This Knowledge ; and our Search is oft in vain : For who can in his narrow Breast comprise The World immense , and who observe the Skies , Which with eternal Revolutions move , And Circling , measure the vast Orb above ? What Diligence can e're describe its Face , What Art can fix in so immense a space ? Those Points where East and West exactly fall , Which Crowns the Top , and which supports the Ball ? I know the Method , the 11 Chaldaean Schools Prescribe , but who can safely trust their Rules ? To each ascending Sign , to find their Powers , They equal time allow , that time two Hours : And then from that Degree , from which the Sun Begins to start , his daily Course to run , Two Hours to each succeeding Sign they give , Still thus allowing , 'till their search arrive At the Degree and Sign they seek , for where The Number ends , the Horoscope is there . But false the Rule ; Oblique the Zodiack lies , And Signs as near , or far remov'd in Skies , Obliquely mount , or else directly rise : In Cancer , so immense his Round , the Ray Continues long , and slowly ends the Day ; Whilst Winter's Caper in a shorter Track Soon wheels it round , and hardly brings it back : Aries and Libra , equal Day with Night , Thus middle 12 Signs to the Extreams are opposite And Signs Extream too , vary in their Light. Nor are the Nights less various than the Days Equal their measure , only Darkness sways , In Signs 13 adverse to those that bore the Rays : Then who can think when Days and Nights are found , In length so differing thro' the Yearly Round , There should be given to every Sign in Skies , An equal Space , an equal Time to rise ? But more than this : The 14 Hours no certain space Of time contain , but vary with the Days : Yet every Day in what e're Sign begun , Beholds six Signs above the Horizon , Leaves six below ; and therefore Rules despise , Because the Hours no equal time comprise , Which give two Hours to every Sign to rise . The Hours in number Twelve divide the Day , And yet the Sun with an unequal Ray Now makes a shorter , now a longer stay . Nay farther , tho' you many ways pursue To find their length you 'l never meet the true , But thus : Take all that space of time the Sun Meets out , when every daily Round is Run , Let equal Portions next that time divide ; And then those Portions orderly apply'd To Days , will shew their length , from thence appears Their varying Measures through the rouling Years . The Standard this , by which our Art Essays Winter's slow Nights , and tries the Summer's Days . This must be fixt , when from th' Autumnal Scales , The Day declines , and Winter's Night prevails : Or in the Ram whence Winter's Nights retire The Hours restoring to the Summer's Fire : In those two Points , the Day and Night contain Twelve equal Hours . For with an even rein The Sun then guides , and whilst his Care doth roul Thro' Heaven's midd Line , he leans to neither Pole : But when remov'd , he to the South declines , And in the 15 Eighth Degree of Caper shines , The Winter 's hasty Day moves nimbly on , Nine 16 Hours and half ; so soon the Light is gone . But Night drives slowly in her gloomy Carr , Takes fourteen Hours and half for her unequal share ; Thus twice twelve Hours in Day and Night are found , To fill the natural Measure of the daily Round . Thence Light encreases still , as Nights decay , 'Till Cancer meets her in the Fiery way , And sets sure bounds to her encroaching sway . Then turns the Scene , and Summers day descends Thro' Winter's Hours , still losing as it bends : And then the Days of equal length appear , With Nights , ' th' adverse Season of the Year , And Nights with Days : For by the same Degrees That once they lengthened , now the Times decrease , These Times our Art can shew , but these belong To future Rhimes , and claim another Song . Thus measure those , who live where fruitful Nile , With Summer Torrents swoln o'reflows the Soil ; Whose seven large Mouths ; the Skies can boast no more Of Planets , vomit with impetuous Roar , And beat the Ocean from the foaming Shore . Now learn what 17 Stadia , learn what times in Skies Signs ask to Sett , and what they claim to Rise : Observe , short rules my Muse , but full she brings , And Words roul from Her , crowded up with Things . For Aries , Prince of all the Signs comprise Full forty Stadia , for his time to rise , But Eighty give him when He leaves the Skies : One Hour , and one third part his rise compleats , This space of time , He doubles when He sets . The following Signs to Libra rising , claim Eight Stadia more , and Setting lose the same . And thus in order following Signs require Still sixteen Minutes more to raise their Fire , And lose as much , when setting they retire : Thus signs to Libra , 18 as they rise increase ; And thus they lose when they descend to Seas : For all the Signs that do from Libra range , Take equal measures , but the Order change ; For Signs adverse to equal times engross , But setting Gain , and still arise with loss . Thus Hours and Stadia which bright Aries gets When rising , Libra loseth when she sets ; And all the time , which when He leaves the Skies , The Ram possesses , Libra takes to rise : By this Example , all the rest define , The following imitate the leading Sign . This rightly fixt , if you these Rules pursue , The Horoscope lies open to thy view ; Securely work , since you can fix in Skies The times , and Stadia , for the Signs to rise : From that Degree and Sign , in which the Sun Begins to start , his daily Course to run , Count fairly on , and all the work is done . Another method , if you this refuse , Shall lead thee right , and be as plain to use : For if the Horoscope you seek by Day , Observe these Rules , which shew the surest Way ; First find what 19 Hour , the Birth is born , and then Add five to that , and multiply by Ten : Add five , for every Hour the Signs ascend Thrice five Degrees , in the Celestial Bend : This done , take that Degree in which the Sign Then rouls the Sun , and to this Number join ; From this whole Sum , one Thirty parts apply'd To the Sun's Sign , nor to the rest deny'd , As following they in order lie , will show The thing you sought for , and design to know : For where the Number ends , that Sign and Part Is Horoscope : Thus speak the Rules of Art. By Night your search demands a different way ; To the Nights Hour , 20 add all the twelve of Day , From this whole Sum the Thirty parts apply To following Signs as they in order lie ; And where the Number ends , that Sign and Part Is Horoscope : Thus speak the Rules of Art. Thus you may find the Horoscope in Skies , And tho' Oblique the Circling Zodiack lies , This Point determin'd , you may fix them all , What Crowns the Top , and what supports the Ball : The Signs true Setting , and true Rising trace , Assign to each their proper Powers and Place , And thus what stubborn Nature's Laws deny , Our Art shall force , and fix the rowling Skie . Nor is o're all the Earth , the length of Night , And Day the same ; they vary with the sight ; Nor , would the Ram alone and Scales agree , In Day and Night ; in every Sign would be The Equinox , if as these Rules devise , Two Hours were given to every Sign to rise . In that Position where Direct's the Sphere , And in the Horizon both Poles appear ; The Day maintains an equal length to Night , And that Usurps not on the others Right : No Inequality in Skies is found , But equal Day , and equal Night goes round . Those Days and Nights which Spring and Autumn bear , They see unvary'd thro' the rowling Year , Because the circling Sun in every Sign Runs round , and measures still an equal Line ; Whether thro' Cancer's height he bears the Day , Or thro' the Goat oppos'd He bends his way , The Day 's alike , nor do the Nights decay . For tho' Oblique the Zodiack Circle lies , Yet all the Zones do at right Angles rise Still Parallel ; and whilst the Sphere is Right Half Heaven is Hid , and half expos'd to sight . Hence take thy way , and o're Earth's mighty Bend From this midst Region move to either End , As weary Steps convey thee up the Ball By Nature rounded and hung midst the All To either Pole ; whilst you your way pursue Some parts withdraw , and others rise to view . To you thus mounting as the Earth doth rise So varies the Position of the Skies , And all the Signs that rose Direct before Obliquely mount , and keep that Site no more ; Oblique the Zodiack grows , for whilst we range , Tho fixt its place , yet ours we freely change ; 'T is therefore plain that here the Days must prove Of different Lengths , since Signs obliquely move , Some nearer roul , whilst some remoter rove , And measure still unequal Rounds above . As nearer to the Arctick Round you go The Hours increase , and Day appears to grow ; The Summer Signs in ample Arch invade Our Sight , the Winter lie immerst in Shade ; The more you Northward move , the more your Eyes Their Lustre lose ; they set as soon as rise : But pass this Round , as you your way pursue , Each Sign withdraws with all its parts from view , Then Darkness comes , and chaces Light away , And thirty Nights excludes the Dawn of Day : Thus by degrees Day wasts , Signs cease to rise , For bellying Earth still rising up denies Their Light a Passage , and confines our Eyes . Continued Nights , continued Days appear , And Months no more fill up the rouling Year . Should Nature place us where the Northern Skies Creak round the Pole , and grind the propping Ice ; Midst Snows eternal , where th' impending Bear Congeal'd leans forward on the frozen Air ; The World would seem , if we survey'd the whole , Erect , and standing on the nether Pole. Its sides , as when a Top spins round , incline Nor here nor there , but keep an even Line , And there Six Signs of Twelve would fill the sight And never setting at an equal Hight , Wheel with the Heavens , and spread a constant Light. And whilst thro' those the Sun directs his way For long Six Months with a continued Ray He chaces Darkness , and extends the Day . But when the Sun below the Line descends With full Career , and to the lower bends , Then one long Night continued Darkness joins , And whilst he wanders thro' the Winter's Signs The Arctick Circle lies immerst in Shade , And vainly calls to feeble Stars for Aid : Because the Eyes that from the Pole survey The bellying Globe , scarce measure half the way , The Orb still rising stops the Sight from far , And whilst we forward look , we find a Bar : For from the Eyes the Lines directly fall , And Lines direct can ne'er surround the Ball ; Therefore the Sun to those low Signs confin'd Bearing all Day and leaving Night behind , To those that from the Pole survey denies His chearful Face , and Darkness fills their Eyes : Till having spent as many Months , as past Thro' Signs , he turns , and riseth to the North at last : And thus , in this Position of the Sphere One only Day , one only Night appear On either side the Line , and make the Year . What different sorts of Days and Nights are known In all Positions thus my Muse hath shown ; Her Work goes on , and she must next comprise What Signs appear , what Times they claim to rise In all Positions of the moving Skies : That when you follow Art , and boldly press To find the Horoscope , a just Success May meet thy search , and into knowledge raise thy guess . But who can all their various times reherse ? Compute so much , and state Accounts in Verse ? Therefore this part let general Rules define , Let those that follow my advanc'd Design Apply them right , but let the Rules be mine . Where-ever plac'd ; by these few Rules proceed , By Nature settled , and by Art decreed ; First count how many 21 Hours compleat the Night Or Day , when Cancer in the Summer's height Bears Phoebus , and short darkness bounds the light . Day 's Hours by Six divide , one sixth devise To following Leo as his time to rise : Night so divided too one Sixth bestow On Taurus , that his rising time will show : But then observe the difference of the time Which Leo takes , and which the Bull to climb , That into Three divide , and thence apply , Beside the time which Taurus takes to mount the Sky , One single Third to Naked Gemini . The like to Cancer , and the like Account To fiery Leo as his time to mount ; Then reckon all , you 'll find the Sum the same Which from the first Division to Leo came , When one sixth part of Day was given to raise his Flame . By the same Method Virgo's time define : But this Condition runs thro' every Sign , The following keeps those Hours the Sign before Obtain'd to rise , and vulgarly adds more : As these an orderly Encrease maintain , So Signs from Libra still decrease again ; But different Order they observe in Skies , The Hours these claim to Set , those take to Rise . But if you count by Stadia , change the Name , But keep the Method , for the Rule 's the same : Seven Hundred Twenty Stadia fill the Round , No more in Day , no more in Night are found : Hence take as many as compleat the Night , When glowing Cancer in the Summer's hight Bears Phoebus , and short darkness bounds the light . The rest by Six divide , one Sixth devise To fiery Leo as his time to rise ; Night 's Stadia so divide , one Sixth bestow On Taurus : Take the Difference twixt the Two , That Sum divide by Three , and thence apply , Beside the Stadia Taurus takes to mount the Sky , One single Third to naked Gemini . Thus to the rest proceed , but still confine To following Signs the Stadia of the former Sign , With one Third Part 's Encrease ; till Libra's Ray This Reckoning stops , and shews another way : For Signs from Libra different Rules comprise , A different Order they observe in Skies , The Stadia others claim to Set they take to Rise . Those Stadia too in which the rest ascend These Winter Signs in slowly setting spend . Thus having fixt the Stadia , now pursue The Horoscope , 't is open to thy view ; From that Degree in which the Sun doth mount Observe my Method , and begin to count ; Give proper Hours to every Sign to rise , And proper Stadia to ascend the Skies , Work by those Rules which I have shewn before , Securely work , for you can err no more . By what advance the Winter Months encrease , ( For they advance not by the same Degrees Thro' every Sign , till on the Ram they light , Which equals Time , and Day adjusts to Night ) Must next be shewn to all that press to learn , Short are the Rules , but yet of great Concern . First take the measure of the shortest Day And longest Night , when with unequal Ray Thro' Caper Phoebus drives the narrow way . Then count the 22 Hours which Day must yield to Shade , And in three Portions let the Sum be laid ; One of these Parts to th' Middle Sign apply'd Shews the Increase of Day on either side : For as the First is by the Midst surpass'd One Half , so that 's exceeded by the last . Thus thro' Three Signs the Day 's Increase is shown , The following takes what to the Last was grown , And adds an equal Portion of its own . For Instance : To the Conquest Night assign Full Fifteen Hours , and give the Day but Nine : Three Hours the difference . Now the Goat hath Power To lengthen Day the space of half an Hour , One Hour Aquarius adds , the Fishes joyn As much as Both , and with the rest combine ; Thus three Hours fill'd , adjusted Time they bring To Aries ; and he equals Day and Night in Spring . The Sixth part of the Time , or more or less , Whate're it proves , is the first Sign 's Increase ; The Second doubles what the First surpass'd , And gives it to be trebled by the last . But from the 23 Equinoctial point the Day Receives increase , but in another way ; For Aries takes as many Hours from Night , As Pisces seiz'd before in their own Right ; And to compleat the Rapine Taurus joins One Hour , one Half is added by the Twins ; Thus whilst these Signs the Time to Day restore , Night justly loses , as it gain'd before . From Caper thus Decreasing Nights appear , And Heaven turns up the right side of the Year ; The Day proceeds to lengthen all the way , Till high in Cancer rais'd it finds a Stay ; The Solstice then : when Day and Night are found Equal to Night and Day that drove the Winter round . Then by the same degrees again the Light Decreasing , what it took returns to Night . Thus far advanc't in Art my Verse defines The proper Years , Months , Hours , and Days of Signs : These must be shewn ; for Signs have Days & Hours , And Months , and Years when they exert their Powers . First then , that Sign in which the Sun appears , Because the Sun measures out the time in Years , Claims the first Year : On following Signs bestow The following Years as they in Order go . And so the Moon , for as she rounds the Skies , She measures Months , to Signs the Months applies . Of Days and Hours the Horoscope possest Of the first parts , to following . Signs commits the rest . This Nature orders , all her Months and Years , And Days , and Hours , she parcels out to Stars ; That as they run their Course they all may find The different Signs , and vary in their kind . This Nature orders too ; and hence there springs That various Discord that is seen in Things ; In one continued Stream no Fortune flows , Joy mixes Grief , and Pleasures urg'd by Woes : Inconstancy in every part appears , Which Wisdom never trusts , but Folly fears . Thus Years from Years , and as they roul the round The Months from Months , and Days from Days are found To differ : no returning Hours restore That sort of Fortune which they brought before : Because the Times , as round their Course they run , Meet different Signs , and are not bound to One ; The Days and Hours their ruling Signs obey , The Month 's the influence which they give convey And temper all things by their fatal Ray. Some Author's Write , ( for who can hope to see Opinions join , or find the World agree ? ) That from the Horoscope our Art defines The Days , the Hours , the Years , and Months of Signs ; From that alone let the Account begin , And all the rest will orderly fall in : And whilst the others , as before 't was shown , Three Heads of reckoning ask , the Moon , the Sun , And Horoscope , these still demand but One : Yet still as great , their difference must appear , Month disagrees with Month , and Year with Year , And Hours and Days : For with uneven pace , Tho' starting all together , they run the Race , And never make Returns in equal space : Twice to the Signs each 24 Hour the Days restore Twice every Month , brings round the Days , and more : Once every Year the Months to Signs are born , And when Twelve Years are run , the Years return . 'T is hard to think , and Nature's Laws reject One single Time , so differing in effect : That when one Sign for Years and Months appears , Bad Fate should clog the Months , Good Crown the Years : Or that the Sign which thro' the Months conveys Bright Fortune , should with Black infest the Days : Or that the Star , which with afflicting Power , The Day oppresseth , should exalt the Hour . Vain therefore their attempt , who fondly hope , The Times to reckon from the Horoscope , And think because with an unequal Date , They come to Signs , that these Returns create Their different , odd varieties of Fate . Absurd Opinion ! which with fruitless pain , They strive to prop with mighty Names in vain , It sinks , and falls with its own stupid weight again . This sung , and Times to Signs apply'd , the Muse Would beg release , and further Task refuse ; But lo the Subject grows : The next must show What length of Times the several Signs bestow : This must be known when in your search for Fate You measure Life , and fix the gloomy Date . Ten Years and One , but one third part withdrawn , The 25 Ram extends the wretched Life of Man ; Poorly he gives , as frugal of his Store , Whilst Taurus adds two Years to these ; the Twins two more . Full sixteen Years Eight Months , from Cancer flow , But two Years more the Lion's rays bestow . From Virgo twenty Years , eight Months convey'd , Enlarge the Birth : The Scales give equal to the Maid : Scorpio's as much as Leo's Rays dispense , The Centaur equals Cancer's influence : Of Years , twice seven , eight Months the Goat conveys ; Though young Aquarius shines with feebler rays , Four Years he trebles , and doubles six score Days . To the same space , with which the Ram began , The Fish plac't , next extend the Age of Man. But farther yet , 't is not enough to know The length of time which single signs bestow ; For you may Err , when in your search for Fate , You measure Life , and fix the gloomy Date ; Because the Heavenly Stations claim their share , As Planets intermix their Force declare , In this Contrivance , and make Life their Care. To single stations now what Years belong , ( With Planets join'd , they claim 26 another Song ) In well wrought Numbers let the Muse impart , And teach the simplest Elements of Art ; This done , these things prepar'd and sitly join'd , With greater Ease , she 'll raise the Work design'd , If when the Moon is in the Hinge at East , The Birth breaks forward from its native rest ; Full Eighty Years , if you two Years abate , This Station gives , and long defers its Fate : But if in Heav'ns midst point , this large Decree She shortens , giving fewer Years by three : With Eighty Courses in the Zodiack Round , Substracting Four , the Western Hinge is Crown'd . The lowest Hinge on all its Births , derives Years sixty two , and then concludes their Lives . The ninth , which makes upon the Right the Trine , Gives sixty Years , and bates but One of Nine . The Fifth o' th' Left , as frugal of its store , Gives sixty three , and can enlarge no more ; Th' Eleventh station , that which rises high , Almost an equal of the Middle Skie , Yields six score Springs , and lest that Gift should be Too scanty , lengthens that vast Summ by Three . The Third which lies at equal space below The Eastern point , doth fifty Years bestow , Mean is the station , and its Gift is so . The second Forty Courses of the Sun , And two bestows , and when that term is done , The Man goes off , e're half his race be run . The Twelfth gives twenty three , then hasty Death , Comes on , and in his Bloom , the Youth resigns his Breath . The Eighth next o're the Western Hinge can bring But fourteen Years , nor adds another Spring . The sixth but Twelve bestows , then Death destroys The Parents Hopes , and crops the growing Boys ; Diseases following , from their Birth create A feeble Frame , and sit the Prey for Fate . Now nicely view the Tropick Signs that lie Oppos'd in the four Quarters of the Skie ; Call'd Tropick Signs , because when these appear , The World then Turns the Seasons of the Year : Thus Spring in Cancer , in Autumnal Scales The Summer turns , in Caper Autumn sails ; Thence shivering Winter creeps congeal'd with Frost , Yet melts again ; and in the Ram is lost : These loose the Seasons , to their full Career , And make the Course of the Revolving Year ; And these being Hingers of the World , create New Powers in Stars ; and fix new Rules for Fate . In Heavens high Arch , and on the utmost Line Of Summers progross , Cancer seats his Sign : There stretches out the greatest length of Day , And then declines , and makes it soon decay ; But all the time which , as he bears the Light He takes from Day , He still conveys to Night . Then Corn grows yellow on the fruitful Soil , And lusty Reapers bare their Limbs for toil : Then Seas grow warm , the Floods forbear to roar , And Billows languish on the quiet Shore . Then Mars goes forth , nor is the Scythian Coast From Roman Arms defended by her Frost : And whilst their Pools and Marshy Grounds are dry , Fearing our Force , the conquer'd Germans fly : Then Nile o'reflows , and Egypt's fruitful Plain , Rich Harvests yields , nor needs the aid of Rain . Thus lies the World , when with exalted Ray , I' th' Summer Solstice Phoebus bears the Day Thro' Cancer's Sign , and drives the highest Way . Oppos'd the Goat in narrowest rounds of Light , Wheels Winter on , but long extends the Night ; Yet soon Ascending , He contracts the Shade , To Day returning all the waste he made ; The Fields unwrought , then lie , unplough'd the Seas , And Mars in Quarters , lies consign'd to Ease : Rocks cleave with Frost ; and by the Cold , opprest , All Nature's Powers , are stiffned into Rest . The next in Power are those two Signs that rise With equal Revolutions of the Skies ; Which times of Day and Night adjust , and bring The Autumn on , or else advance the Spring . The Sun returning in his Yearly Race , To Cancer's Sign meets Aries midst the Space , Seated between the Point , from whence he bends His upward Course , and that in which he ends . There plac'd as Umpire in the midst o th' way , Contracted Night , he well adjusts to Day . And as thro' him the Sun goes on to climb The Heavenly steep , He makes a change in time ; For Day , that shorten'd in the Winter Bend , The Ram first lengthens ; and the next extend , 'Till rais'd in Cancer , to the utmost height Of Summer's pitch , He wheels the longest Light. Then Seas lie husht : Then Earth grows bold to bear , And trusts young Flowers to the serener Air : Then Beasts in Fields , and Birds in every Grove , Press on with Fury to consummate Love. With joyful Songs the vocal Forests Ring , And various Leaves adorn the gawdy Spring : With such brisk Powers are Nature's parts possest , When wak'd , she rouses from her Winter's Rest . Oppos'd to Aries , Libra's Stars appear With the like power to sway the rouling Year , She equals Day and Night : But soon the Scale O'repois'd by Darkness , le ts the Night prevail ; And Day , that lengthned in the Summer's height , Shortens 'till Winter , and is lost in Night . Then from the burthen'd Elms , the generous Vine Descends , and Presses over-flow with Wine : Then Wheat is sown , whilst Autumn's heats remain To loose the Clods , and mollifie the Grain . These have their Powers , and as these Signs create A turn in Seasons , so they doe in Fate : From Tropick Signs ( for by their name , we guess Their turning Natures ) who can hope for less ? But wide in their mistake , who think to see These Powers spread equally in each Degree ; Not every Portion of the Tropick Signs Turns Seasons , and the Planets force confines , But one Day only , in the blooming Prime Of Spring , in Autumn One adjusts the Time , One Day in Aries doth to Time restore Equality , and Libra boasts no more ; One Longest Day in Cancer's Sign is born , One Night of equal length in Capricorn : The other Days roul on with different Light , Now gaining from , now losing time to Night . Thus One Degree in Tropick Signs creates A change in Heaven , and turns the Rules of Fates ; No fixt Decree's secure , their boundless sway , Extends to all , and makes the Stars obey . But which that is that governs , Fate 's Decree , There Authors differ , nor can Art agree ; For some the Eighth , and some the Tenth assign , The First Degree — is only Thine , Thine , but the Muse with scorn , forbears the Name ; Unworthy mention , and too mean for Fame . The End of the Third Book . NOTES . 1. This and the seven following Verses relate to the several particulars of Medea's story . 2. I use this Interpretation rather than that of Scaliger and others , because I think Manilius speaks only of that famous Siege of Thebes , when the seven Generals attackt it ; and as the Story says , Capaneus had almost ruin'd the Town before he was struck with Thunder . 3. Oedipus Married his own Mother Jocasta , and had Children by her ; so that each Son was Brother to the Father , and Grand-Child to the Mother . 4. This respects the Story of Atreus and Thyestes . 5. Xerxes is said to have dug a Channel round Mount Athos , and to have made a Bridge over the Hellespont . 6. Thus , for instance , in whatever Sign the Lot of Fortune is plac'd , the next that belongs to the next Sign , is the Lot of Warfare : Civil Employments must be given to the third , &c. 7. For the Lot of Fortune being in all Nativities that belong to Day to be accounted for from the Sun , and in all Nativities that belong to Night from the Moon ; and those two Planets not always possessing the same place in every Nativity , and the other Lots following the disposition of that of Fortune ; it is very evident that the same Lot is not to be always applyed to the same Sign . 8. The Poet never finisht this part , or it is now lost . 9. For instance , let the Sun be in the 20th Degree of Aries , the Moon in the 10th Degree of Libra ; from the 20th Degree of Aries ( counting thro' the following Signs Taurus , Gemini , &c ) to the 10th Degree of Libra ; are 170 Degrees : Let the Horoscope be the 10th Degree of Cancer ; from that 10th Degree of Cancer , count thro' the following Signs , viz. Leo , Virgo , &c. and you will find the Number 170 to end in the 10th Degree of Capricorn : Therefore in the 10th Degree of Capricorn place the Lot of Fortune : This I take to be the meaning of Manilius . 10. Suppose the Sun to be in the 21 , 49 ' ' ' ' ' of Leo , the Moon in the 26 , 31 ' ' ' ' ' of Virgo ; the Horoscope in the , 1 , 0 ' ' ' ' ' of Leo ; The Moon is distant from the Sun 325 , 18 ' ' ' ' ' , which number being distributed amongst the Antecedent Signs , viz. Cancer , Gemini , Taurus , &c. ends in the 5 , 42 ' ' ' ' ' of Virgo , that there is the place of the Lot of Fortune . 11. To explain this Method which the Chaldeans us'd to find the Horoscope , Scaliger gives this instance : Let the Sun's place be the 13 , 25 ' of Libra , let the Birth be at the end of the Seventh Hour of the Day : Now because every Sign hath thirty Degrees , and fifteen Degrees make one Hour , these Seven Hours are three Signs and an half , or one Hundred and five Degrees : Now reckon those Degrees thro' the following Signs , viz. Scorpius , Centaurus , &c. The Number ends in the 28125 ' ' ' ' ' of Capricorn , and therefore that is the Horoscope . 12. Sic media extremis , &c. The middle Signs here are Aries and Libra , and these are said to be opposite to the Extremes , Cancer and Capricorn , because in them the Days are equal , but in the others unequal to the Nights : This I take to be the meaning of the Poet , rather than what Scaliger and other Interpreters pretend . 13. Thus in Cancer the Days are longest ; in Capricorn , which is a Sign adverse to Cancer , the Nights are of the same length , that the Days were of in Cancer : The like holds in Leo , and Aquarius , and so in the rest . 14. The Italians divided all the time betwixt the Rising and Setting of the Sun into Twelve Hours , and all the time between the Setting and Rising of the Sun into Twelve Hours : And therefore , those times being various and unequal , the Hours must likewise be unequal . 15. According to the Opinion of some Ancient Astronomers , who plac'd the Winter Solstice in the Eighth Degree of Capricorn , the Summer Solstice in the Eighth Degree of Cancer , and the Equinox in the Eighth Degrees of Aries and Libra : Thus in the End of this Book , Has quidam vires octava in parte reponunt . 16. Eudoxus wrote of the Sphere at the 36th Degree , Elevation of the Pole , and Manilius follows him . 17. A Stadium in Manilius is half of a Degree , and therefore in the whole Zodiack there are 720 Stadia . In the Zodiack are 360 Degrees , to every Hour we reckon , 15 Degrees , therefore every Hour is equal to 30 Stadia , and for the same Reason , each Hour containing 60 Minutes , every Stadium is equal to two Minutes . 18. The rising and Setting of the Signs according to Manilius . Rising . Signs . Stadia . Hours . Minutes . Degrees . Aries . 40 1 20 ' ' ' ' ' 20 Taurus . 48 1 36 ' 24 Gem. 56 1 52 ' 28 Cancer . 64 2 8 ' 32 Leo. 72 2 24 ' 26 Virgo . 80 2 40 ' 40 Libra . 80 2 40 ' 40 Scorp . 72 2 24 36 Cent. 64 2 8 ' 32 Capr. 56 1 52 ' 28 Aquar . 48 1 36 ' 24 Pisces . 40 1 20 ' 20 Signs Stadia . Hours . Min. Deg. Setting Signs . Stadia . Hours . Min. Deg. Aries . 80 2 40 ' ' ' ' ' 40 Taur . 72 2 24 ' 36 Gem. 64 2 8 ' 32 Canc. 56 1 52 ' 28 Leo. 48 1 36 ' 24 Virg. 40 1 20 20 Lib. 40 1 20 ' 20 Scorp . 48 1 36 ' 24 Cent. 56 1 52 ' 28 Capr. 64 2 8 ' 32 Aquar . 72 2 24 ' 36 Pisces . 80 2 40 ' 40 Signs . Stadia . Hours . Min. Deg. 19. Let the Child be born in the Fourth Hour of the Day , add five to four , the Sum is 9 , Multiply 9 by 10 , the Product is 90. Let the Sun be in the 10th Degree of Gemini , add 10 to 90 , the Sum is 100 , of this 100 give 30 to Gemini , the Sign in which the Sun is , 30 more to the following Sign Taurus : 30 to the next Aries , 10 remain , therefore the 10th Degree of Pisces is the Horoscope . 20. Let the Birth be in the Seventh Hour of Night , add to that the Twelve Hours of the Day , and that Seventh Hour will be the Nineteenth , from the Suns Rising : Then add , multiply , and work , as in the former Method . 21. Let the longest Day in Cancer be of 16 Hours , the shortest Night of 8 : Divide those 16 Hours into 6 parts , each part contains 2 Hours 40 Minutes : Therefore allow Leo 2 Hours 40 Min. for his Rising time : Divide likewise the 8 Hours of Night into 6 parts , each part will contain 1 Hour 20. m. and that is the rising time of Taurus . The Difference between the Rising Times of these two Signs is 1 Hour 20 Min. Divide this Difference into three equal parts , each part will contain 26 Min. 40 Sec. Add these 26 Min. and 40 Sec. to the Rising time of Taurus , and the whole Sum makes up the Rising time of Gemini , viz. 1 Hour , 46 Min. 40 Sec. To this add another third part to make up the Rising time of Cancer , viz. 2 Hours 13 Min. 20 Sec. And so of the rest , as in the following Scheme . Signs Hours Min. Sec. Signs Aries . 0 53 20 Pisces . Taur . 1 20 0 Aqua . Gem. 1 46 40 Capr. Cancer 2 13 20 Cent. Leo. 2 40 0 Scorp . Virg. 3 6 40 Libra . But it must always be observed , that the Southern or Winter Signs are oppos'd to the Northern or Summer Signs . The Rising-time of the Summer is the Setting-time of the Winter ; and the Setting-time of the Summer the Rising-time of the Winter Signs . 22. The Example which Manilius himself gives , sets this Doctrine in its true Light. Let the longest Night in Capricorn be of 15 Hours , the Day consequently must be of 9. Thus the Night exceeds the Day by 3 Hours . Divide these 3 Hours into 3 Parts , give one Part , that is , 1 Hour to the Middle Sign , viz. Aquarius , and thence conclude that in Capricorn the Day encreases half an Hour , and in Pisces an Hour and half ; Aquarius being the Middle Sign in which the Days encrease one Hour . 23. According to the Doctrine of Manilius ( let the Example be the same with that in the preceding Note ) in Aries the Day encreases one Hour and half , in Taurus one Hour , in Gemini half an Hour . 24. There being 24 Hours belonging to each Day , and but 12 Signs , more than 24 Days in each Month , and 12 Months in every Year . 25. A Table of the Years and Months that belong to each Sign . Signs . Years . Months Signs . Aries . 10 8 Pisces . Taurus . 12 8 Aquar . Gemini . 14 8 Capr. Cancer . 16 8 Sagit . Leo. 18 8 Scorp . Virgo . 20 8 Libra . 26. This was never finished by the Poet , or is now lost . MANILIUS . The Fourth Book . After a short Reflection on the vain Cares of Mankind , he brings several Arguments to prove Fate : 1. Several unaccountable passages in the Roman and Grecian Histories : 2. Sudden Death , and unexpected Recoveries , contrary to all the powers of Art and Physick : 3. The difference between the Children of the same Parents : 4. The fewness of Worthy Men , and the certainty of Death : 5. The ill successes of Wise and Good Men , and the prosperity of Knaves and Fools ▪ 6. Monstrous Births : 7. Prophesy : And then endeavours , 8. to take off some Objections that might be rationally propos'd against this Doctrin : Then. 9. He shews what Tempers and Inclinations the twelve Signs singly consider'd do bestow , and to what Arts they incline : 10. Vnder the Ram , are born all sorts of workers in Wool , Broakers , Men of unsetled Fortunes , fearful , inconstant , and covetous of Praise : 11. Vnder the Bull , Plowmen , Aspiring , Reserv'd , Strong , and Amorous : 12. Vnder the Twins , Musicians , Songsters , Men of merry Tempers , and Astronomers : 13. Vnder the Crab , Covetous Fellows and Vsurers : 14. Vnder the Lion , Hunters , Beast-keepers , Plain , Open-hearted , easily provok'd , and easily appeas'd : Vnder the Maid , Philosophers , Orators , Notaries , shamefac'd and indifferently good : 16. Vnder the Scales , Measurers , Gagers , Accountants , Lawgivers , Lawyers , and Judges : 17. Vnder the Scorpion , Hunters , Gladiators , Men of Warlike and Military Dispositions : 18. Vnder Sagittarius , Chariot-Racers , Horse-breakers , Tamers of Wild Beasts , Men of acute Vnderstandings , and strong and nimble Bodies : 19. Vnder the Goat , Miners , Coyners , Goldsmiths , Bakers , Broakers , Inconstant and Lascivious in their Youth : 20. Vnder Aquarius , Men skill'd in making Aqueducts , and Water-works , and Spheres , and Globes , tractable and prodigal : 21. Vnder Pisces , Mariners , Pilots , Shipwrights , Rowers , Fishers , Fruitful but Inconstant : 22. He Discourses of the Tenths of each Sign , and what Sign is Lord of each third part of every Sign : 23. He encourages his Scholar to go on , tho the Task seems to grow upon him , and to be very difficult , because 't is a Noble Study , and the Object truly great : 24. He shews what degrees of each Sign are hurtful , what not : 25. He Teaches , that the Tempers of those that are Born when the Sign riseth , are different from those that are Born at other times : 26. He draws a Map of the Earth and Seas , and Teaches what Signs govern particular Countries : 27. He shews what Signs are call'd Eccliptick , and why : 28. He proposeth such Objections as are made to deter Men from this curious search , and answereth them . WHy should our Time run out in useless years , Of anxious Troubles and tormenting Fears ? Why should deluding Hopes disturb our ease , Vain to pursue , yet eager to possess ? With no Success , and no Advantage crown'd , Why should we still tread on th' unfinisht Round ? Grown gray in Cares , pursue the senseless strife , And seeking how to Live , consume a Life ? The more we have , the meaner is our Store ; The unenjoying craving Wretch is Poor : But Heaven is kind , with bounteous Hand it grants A fit supply for Nature's sober wants : She asks not much , yet Men press blindly on , And heap up more , to be the more undone : By Luxury , they Rapine's Force maintain , What that scrapes up , flows out in Luxury again ; And to be squander'd , or to raise debate , Is the great only use of an Estate . Vain Man forbear , of Cares , unload thy Mind , Forget thy Hopes , and give thy Fears to Wind ; For Fate rules all , its stubborn Laws must sway The lower World , and Man confin'd obey . As we are Born we Dye , our Lots are cast , And our first Hour disposeth of our last . Then as the influence of the Stars ordains , To Empires Kings are doom'd , and Slaves to Chains . Then Poverty , that common Fate comes down , ( Few Stars are Regal , and design a Crown ) What make a Wit , a Knave , a Saint , or Dunce , Are hudled then together , and fixt at once . The Ills that are ordain'd we must endure , From not Decreed how fatally secure ? Prayers are too weak to check fixt Destinies , And Vows too slow to catch the Fate that flies . Whether with Glory rais'd , or clogg'd with Scorn , The State , that then is setled , must be born . For did not Fate preside , and Fortune lead , Had parting Flames the good 1 Aenaeas fled ? Had Troy's sunk Fortune been sustain'd by 2 one ? And only Conquer'd then , when overthrown ? And did not Stars the rise of States dispose , Had mighty Rome from such beginnings rose ? Had 3 Shepherds built , or Swains without controul Advanc'd their 4 Cottage to a Capitol ? Plac'd on whose heights , our Caesars now survey The lower Earth , and see the World obey ? From their 5 burnt Nest , had Conquering Eagles flown , And the World yielded to a ruin'd Town ? Had Jove been storm'd ; or 6 Mutius safe return'd From baffled Flames , or vanquish'd whilst he burn'd ? Our Towns and Bridges guard , had 6 Cocles stood , Or the weak 6 Virgin swam rough Tiber's Flood ? Had one 6 Horatius our sunk hopes restor'd , Or Three have fall'n beneath a single Sword ? O Glorious Victory ! what Arms before , E're won so much , none ever fought for more ; Rome and her hopes of Empire hung on One , His o're matcht Lot was Hers , a Yoke or Throne . Why should I 8 Cannae's bloody Plains relate , And Africk's Ensigns threatning at our Gate , How Thrasymene Drown'd Flaminius's Shame , And after Fabius , wise Retreats o'recame , The Conquer'd Carthage shone with Roman flame ? How Hannibal on the Campanian Plains , Rome's Terror once , then destin'd to our Chains ; Whilst waiting on his Proud Bithynian Lord , Stole a base Death , and scap't our Nobler Sword ? But turn and view the 9 Civil Wars of Rome , There opens wide a various Scene of Doom : See Marcus ride with Cimbrian Lawrels Crown'd , Then in the Dungeon stretcht upon the groun'd ; Now Slave , now Consul , Consul , Slave again , His Curule Chair , succeeded by a Chain ; Now a mean Ruin on the Lybian Sands Despis'd he lies , and streight the World Commands ; Like Thunder from low Earth exhal'd , he rose From the Minturnian Pools , And scatter'd Vengeance on his haughty Foes . These wondrous Changes Fate and Stars advance , O mighty turns , and much too great for Chance ! Who 10 Pompey could ( that saw thy Conquering Fleet Regain the Seas , and Kings beneath thy Feet , Proud Pontus yield , fierce Tyrants make thy Train , And crowding Monarchs beg thy leave to Reign , That saw Victorious Lawrels Crown thy Head , And Worlds in thy repeated Triumphs lead ; And all that Glory which thy Sword had won , Fixt and supported by as great a 11 Son ) Have thought that Thou , upon a Foreign Sand , Should'st steal a Burial from a common Hand ; That shatter'd Planks , the Sea 's dishonest spoil Should hiz beneath thy Trunk , and be thy Pile ? That Thou , the mighty Thou , should'st want an Urn , What Power , but Fate , could work so strange a turn ? E'en 12 Caesar sprung from Heaven , and now a Star , Tho' midst the dangers of the Civil War , Secure He stood , and careless of Repose , Was ne're surpriz'd by his most watchful Foes ; Yet Crown'd with Peace , in all his Pomp and State He fell a Victim to o're-ruling Fate : No dark suspitions , but bright hints were brought , He knew what Cassius spoke , and Brutus thought ; How far advanc'd , how far they meant to go , And saw the minute of the fatal Blow : Yet dark Oblivion did his Memory blot , He all his warnings , and Himself forgot ; And in the Senate , whilst his Right Hand held The faithful Bill , which all the Plot reveal'd ; To prove that Fate will sway , and Stars controul , He fell , and with his Blood defac'd the Scroul : O mighty power of Fate , and prov'd too well ! The Best , the Wisest , and the Greatest fell . Why should I mention Kings 13 and Empires falls , Shew Conquering 13 Cyrus on the Sardian Walls ? Or Croesus shrinking at the rising Flame ? Or 13 Priam's Trunk , a thing without a Name ? Unhappy Prince ! the Beasts and Vultur's spoil , His Troy was burnt , but Priam wants a Pile . The Wreck of 13 Xerxes , who wou'd scourge the Gods , A Wreck , much greater than the threatned Floods ? Or 13 Tullus's Reign , who by the power of Fate , Was born a Slave , yet Rul'd the Roman State ? Or shew 13 Metellus snatch the Vestal Fire , And as he pass'd , prophaner Flames retire ? How oft do suddain Deaths the Healthy seize , Without the formal warning of Disease ? And yet how often from the Piles retire , E'en 14 fly themselves , and wander thro' the Fire ? Thus some have from their Graves return'd , and known Two Lives , whilst others , scarce enjoy but One. A small Disease destroys , whilst greater spare , Good Methods fail , and Men are lost by Care. Some temperate Diet , with Diseases fills , And Poyson 's Innocent , when Physick Kills . Some Children prove a mean degenerate Race , Some shew their Father's Mind , as well as Face ; In One , their Vertue , and their Fortune rise To greater height , and in Another dyes . One 15 mad in Love , to Troy will carry War , Or swim the Flood , and view the Torch from far , The Other is determin'd to the Bar. A Son his Father , Father kills the Son On mutual Wounds two headlong Brothers run ; These Combats prove the force of ruling Powers , For they are too unnatural to be Ours . That every Age no new Camilli's breath , The 16 Decij dye , or 16 Cato conquer Death , 'T is not but that the Seed can still receive As noble Stamps , but Fates refuse to give . To fewer Days they do not cramp the Poor , Nor brib'd by Wealth , enlarg'd the Rich with more ; There Riches lose their force , the shining Years Of glorious Tyrants must be turn'd in Tears ; They dig a Grave for Kings , and fix the Day ; How great must be that Power which Crowns obey ! Successless Vertue sinks whilst Vice prevails , And Folly wins the Prize when Prudence fails : He argues ill that from the Fortune draws The goodness or the badness of a Cause : Success or Merit do not always Crown , Midst good and bad Men they are blindly thrown , Without Respect , sixt fatally on One. For some superior Power 's impetuous force Marks out our way , and still directs the Course ; The Years that we must run , the length , the pace , And all the various turnings of the Race . Besides , what Monstrous Births , the Nurses fear And Mother's shame , half Man , half Beast appear ? Such wondrous Creatures ne're from Seed began , For what hath Beast that 's common to a Man ? And what mean Soul would with his Lust comply , And Sin on purpose for a Prodigy ? No ; Stars dispose , they Counterfeit a Rape , And mix a Monster of amazing shape . Besides , were not Events by Fates enrol'd , How can their certain Order be foretold ? How can the Prophets Sing of future Doom , And in the present read the Age to come ? To this there 's one Objection ; Fate denies Rewards to Vertue , and must plead for Vice : Absurd ; for who less hates a Poysonous Weed Because 't is bred from Necessary Seed ? Or who loves Corn the less ; who hates the Vine . Because by Nature rais'd , and not Design ? Thus Virtuous Minds deserve the greater Love , Since Heaven consents , and all the Stars approve ; And we should hate those more whom Fates have sent To commit Crimes and suffer Punishment ; For how , or whence these noxious faults begin No matter , since each is certainly a Sin. Nay this Opinion's settled by Debate , 'T is Fate that we should thus dispute of Fate . This settled , I must now attempt to climb Celestial steps , and run the Round of Time , The Zodiack travel , go through every Sign , Their Powers rehearse , and sing how all incline . First Aries shines , and as he oft doth lose His Fleece , and then as frequently renews , 'Twixt sudden Ruin , and a fair Estate He fixes the variety of Fate ; He gets , then loseth , then returns to Gain , Then Loss steals in , and empties all his pain ; He rears new Lambs , he doth encrease the Fold , And makes the Rams to shine in native Gold ; Betters the Wool , and whilst the Subject grows He forms Mens Minds to use what he bestows ; To Pick , to Card , to Spin , and Weave , to deal In Cloath with gain ; to Buy , Exchange , and sell : All useful Arts , whose constant Works supply Mens real Wants , not only Luxury : This 17 Pallas owns , nor doth disdain to claim Arachne's conquest as her greatest Fame . These are the manners , these the various Arts Which Aries Rays , and secret force imparts ; To anxious fears he troubled Minds betrays And strong Desires to venture all for Praise . Dull Honest Plowmen to manure the Field Strong Taurus bears , by him the Grounds are till'd : No gaudy things he breeds , no Prize for worth , But Blesseth Earth , and brings her Labour forth : He takes the Yoke , nor doth the Plough disdain , And teacheth Farmers to manure the Plain : He 's their Example , when he bears the Sun In his bright Horns , the noble toyl's begun : The useful Plowshare he retrieves from Rust , Nor lies at ease , and wants his strength in Dust . To him the 18 Curij , and to him we owe The brave Serrani , he i' th' Fields did Rods bestow , And sent a great Dictator from his Plow . Reserv'd , aspiring Minds , Limbs slow to move But strong in Bulk his powerful Rays improve , And on his 19 Curled Front sits wanton Love. Soft Gemini to easier Arts incline For softer Studies fit an Infant Sign . They tune rough Words , or they incline to Sing , To stop the Pipe , or strike the speaking String ; Through Reeds they blow the Natural Sound in Measure , Gay their delight , and e'en their Pains are Pleasure ; Wars they avoid , Old Age they chace with Song , And when late Death o'retakes them they are Young. Sometimes to Heaven they mount , and trace the Stars , Then fix in Globes , or turn the Signs in Spheres : Their Wit reigns o're their Nature , and refines Its Powers ; This is the Influence of the Twins . But glowing Cancer ( where the Summer Sun With fiery Chariots bounds the Torrid Zone , Drives fiercely up , then with a bending Rein Sinks down , and runs in lower Rounds again . ) As close in 's Shell he lies , affords his Aid To greedy Merchants , and inclines to Trade : His Births shall sail , through Seas and Dangers tost To reap the Riches of a Foreign Coast . What thrifty Nature hath but thinly sown In Many Countries , they shall bring to One ; Intent on gain ne're heed the Poors complaint But thrive on Scarcity , and live on Want : For Wealth undaunted gather every Wind , Out-sail good Fame , and leave Repute behind , And when their greedy Hands have seiz'd the Store Of this , search other Worlds , and seek for more . Or else at home prove griping Vsurers , Complaining at the slowness of the Years , Wish swifter Suns , and set too vast a rate On Time it self , to raise a quick Estate : Their Bodies shall be Strong , inur'd to Pain , Their Wits Contriving , and intent on gain : What Inclinations Leo's Rays dispense Is quickly known , 't is plain to Common Sense , He gives his Own ; for he the Woods infests The mighty Terror of the meaner Beasts : He lives on Rapine , ranges all the Day , And sullenly at Night groans o're his Prey . Hence he inclines Mens Minds to Hunt , and fills Our Nobles spacious Halls with grinning spoyls ; There Skins and Horns do spread a dismal grace , And stand as certain Heraulds of their Race ; This Beast was mine , and that my Father's Game , They cry , these are the Annals of their Fame : That generous Youth which France and Spain did fear Now prove the Humble Terror of a Deer . Nay some in 20 Towns pursue this wild delight , There barbarous grow , and breed up Beasts to fight ; Then bring them out for sight in Theaters , And feast their Luxury with Bruitish Wars ; Cruel in Sport : Their Posts are grac't with Spoyl , And they get shameful Honour without Toyl : He makes Men warm , their Passions quickly rais'd , Like Boys soon angry , and as soon appeas'd : But Plain and Honest all their Thoughts sincere ; Pure as the Sun , and like the Water clear . But modest Virgo's Rays give polisht parts , And fill Mens Breasts with Honesty and Arts ; No tricks for Gain , nor love of Wealth dispense , But piercing Thoughts , and winning Eloquence ; With words persuasive , and with Rhetorick strong They rule , and are e'en Monarchs by their Tongue . Through Nature's Secrets too , they boldly press , Tho' deeply hid , and meet a just success ; In Short-Hand skill'd , where little Marks comprise , Whole words , a Sentence in a Letter lies ; And whilst Obedient hands their Aid afford , Prevent the Tongue , and Fix the falling Word . But bashful Modesty , casts down their Eyes , The best of Vices , yet 't is still a Vice , Because it stifles , checks , or nips like Frost A blooming Vertue , and the Fruit is lost . Besides , though strange such Influence should come From Virgo's Rays , she gives a fruitful Womb. Libra , whose Scales , when Autumn turns the Signs , And ruddy Bacchus treads the juicy Vines ; In equal Balance , poize the Night and Day , Teach how to measure , and instruct to weigh : And Rival 21 Palamed , ( who Numbers found , And into Letters fram'd unpolisht sound ; To Him the Art of Words , and Speech we owe , Till then Men only Spoak , but knew not how . ) Besides , He 'll know the Niceties of Law ; What guard the Good , and what the Guilty awe , What Vengeance wait on Crimes , with Skill declare , His private Chamber , still shall be the Bar. What He determines , that for Right shall stand , As Justice weigh'd her Balance in his Hand . This Rul'd at 22 Servius's Birth , who first did give Our Laws a Being , rather than Revive ; The Tables seem'd Old , Reverend Senseless Lines , Meer waxen Things , and fit to serve Designs , As Fools mistook , or Crafty Knaves would draw ; Till He infus'd a Soul , and made them Law. Bright Scorpio Arm'd , with poys'nous Tail prepares , Mens Martial Minds , for Violence and Wars ; His Venom heats , and boyls their Bloods to Rage , And Rapine spreads o're the unlucky Age. Yet , when the Sun drives there , Men tear the Earth , And cast their Seed to an increasing Birth , As if he led mistaken Men to toil , And sweat for Matter for a future spoil . Yet 't is not Prey they seek , as much as Blood , For e'en in Peace they fiercely trace the Wood , O're Forests range , and every Plain infest , Now Fight with Man , and now Engage with Beast ; To please the Crowd , they unprovok'd engage , And sell their Lives , to the dishonest Stage ; And when calm Peace doth Publick Rest bestow , Yet still to Fight , each seeks himself a Foe . They spend their leisure Hours in fierce Alarms , And all their Recreation is in Arms. The double Centaur different Tempers breeds , They break the Horse , and tame the fiery Steeds ; They love the sounding Whip , the Race , the Rein , And whirl the Chariot o're the dusty Plain : Nor is their Humor to the Fields confin'd , They range the Woods , and tame the Savage Kind ; Young Bears they break , and Tygers heats asswage , And hear Young Lions roaring without Rage . Discourse the 23 Elephant , and Teach the Mass A mimick Action , and a decent Grace ; To Act in Plays , or raise th' unweildly load , To Dance , and be the Darling of the Crowd . For in the Frame , in double forms exprest , The Man is uppermost , and rules the Beast ; His Bow full drawn implies , his Rays impart , Strength to the Limbs , and Vigor to the Heart . Quick active Motions , full of warmth and heat , Still pressing on , unknowing to retreat . But Sacred Vesta guards thy fatal Fire , And thence 't is guess'd , what Minds thy Rays inspire , Contracted Goat ; by thee that Art 's infus'd , Which Fire assists , and where a Flame is us'd ; By thee the Miners burn the Womb of Earth ; And see the place of Metals fatal Birth : By thee they melt ; by thee they work the Mould , Refine , and Stamp it into mighty Gold : By thee , the Silver , Iron , Gold , and Brass , The Forge dissolves , and forms the easie Mass : By thee , the Ovens heat , and Baths acquire , And Happy 24 Chymists blow enriching Fire : Thy Cold ( for thou o're Winter Signs dost reign , Pull'st back the Sun , and send'st us Day again ) Makes Brokers Rich , for whilst you spread your Ice , Their Wares go off , and they enhance the Price : From thee our Youth unconstant Tempers prove , And eagerly pursue unlawful Love , ' Cause Goat above ; but these the Fish behind Corrects in Age , and fixes the soft Mind . Aquarius pouring out his Urn , imparts An useful Knowledge in resembling Arts , To find out Springs , and with new Streams supply The Barren Countries , and refresh the dry ; To raise in Pipes , or to extend in Beams , And in high Rooms imprison Foreign Streams ; Affront the Sea , for State , not use , restrain The Waves with Moles , and curb the raging Main ; Or Engins raise , whence Waters mount above , And mix the lower , with the higher Jove . A thousand other Arts , which Waters sway , As Channels lead , or else as Pipes convey , Depend upon the influence of his Ray. And to his Births the World oblig'd shall owe Spheres , Cycles , Orbs , and turn new Skies below . Soft , easie Tempers , loving Coin for use , Not sorbid , but inclin'd to be profuse ; Not pincht , nor yet too swelling in Estate ; Thus flows the Vrn , and fixes this for Fate . Last double Pisces , from their shining scale , Spread watry influence , and incline to Sail ; To trust their Lives to Seas , to plow the Deep , To make fit Rigging , or to build a Ship. In short , what e're can for a Fleet be fram'd , A thousand Arts , too numerous to be nam'd . Beside to steer , observe the Stars , and guide As they direct , and never lose the Tide ; To know the Coasts , the Winds , the Ports , and Shores ; To turn the Helm , or ply the bending Oars ; To sweep smooth Seas with Nets , to drag the Sand , And draw the leaping Captives to the Land , Lay cheating Wires , or with unfaithful bait , The Hook conceal , and get by the deceit : To fight at Sea , to stain the Waves with blood , Whilst War lies floating on th' unstable flood : Fruitful their Births , of Pleasure fond , engage In Love , are quick , but changing with their Age. Thus rule the Twelve , these Powers they singly own , And these would give if they could work alone . But none rules All its own degrees , they joyn Their friendly forces with some other Sign , As 't were compound , and equal parts receive From Other Signs , as they to Others give : Thus each hath Thirty parts , and each resigns Two Thirds of those degrees to other Signs : We call these portions ( Art new words will frame , ) The Tenths , 25 the Number doth impose the Name : So hid is Truth , so many Vails are spread Coy Nature's Face , and hide her Gloomy Head , So many are the little Niceties , So intricate , and puzling are the Skies , Not easie to be read by common Eyes . For one appearance in another lies , Conceals its Powers , and Acts in disguise ; And that which Lurks , and subtly interferes Hath different Powers from that which then appears . Not Day , but piercing Thought must clear this Sky , The Labour of thy Mind , not of thy Eye ; Press bravely on , and pass the Gloomy Cloud , Enter , and view the inside of the God ; The Path is dark , and lest thy Mind should stray I 'll boldly lead , and shew the nearest way ; I 'll Sing what League the different Parts combines , And shew how others Rule in other Signs . For instance , Aries shakes his shining Fleece , And governs the First Ten of his Degrees : But next the Bull , and next the Twins do claim The second , and third Portions of the Ram : Thus three times Ten Degrees the Ram divide , And He , as many others as preside In his Degrees , so many Fates affords His proper Powers being temper'd by his Lords . Thus lies the Ram , next view the threatning Bull , His case is different , he hath none to Rule : For in his First Ten Parts the Crab's obey'd , I' th' Second Leo , and i' th' Third the Maid . Yet he seems stubborn , and maintains his Throne , And all Their Powers he mixeth with his Own. The feeble Twins just Libra's Scales possess , Then Scorpio , and the rest of their Degrees Bold Sagittarius subjects to his flame , With Bow full drawn , as to defend his claim . An equal share in Empire all maintain , But keep not the same order in their Reign . For Cancer's Sign , as in the Goat he sways , Resigns his first third Portion to His Rays : For when he bears the Sun oppos'd in site , His Day is equal to the Others Night : This is the Reason why these Two combine , And each hath the same Portion in each Sign . His second part the Vrn with watry Beams O're-flows , and Pisces rule in the Extreams . The Lion minds his Partner in the Trine , And makes the Ram first Ruler in his Sign ; And then the Bull , with whom he makes a Square , I' th' Second Reigns ; His Sextile Twins declare Their Third pretence , and Rule the other share . The Crab is chiefly Honour'd by the Maid , The first place his , and there his Sway 's obey'd ; The next is Leo's , and the last her own , She Rules unenvy'd in her petty Throne . The Ram's Example Libra takes , and bears A likeness in this Rule , as in the Years ; For as He in the Spring , Her Scales do weigh In Autumn equal Night with equal Day : The first She Rules her self , next Scorpio's plac't , And Sagittarius Lords it o're the last : In Scorpio's first Degrees the Goat presides , Next Young Aquarius pours his flowing Tides ; Next Pisces Rules , for they in Waves delight , The Flood pursue , and claim an easie Right . The grateful Goat doth Cancer's Gift repay , His First Third part resigning to his Ray ; I' th' next the Lion shakes his flaming Manc , The last feels modest Virgo's gentle Rein. The Young Aquarius Libra's Scales command , Restrain his Youth , and check his turning Hand ; The next Ten parts bright Scorpio's Rays enjoy , Then Sagittarius Rules the giddy Boy : Pisces comes last , and sheds a watry flame , Its First Degrees resigning to the Ram : The Bull 's the next , his own the last are found , Content with the last Portion of the Round . This thing consider'd well thy Mind prepares To know the secret guidance of the Stars ; They interchange their Powers , they mix their Laws , And all agree to make one Common Cause ; For these Divisions do unite the Sky , The more they part the closer is the Tye. But now , lest Error should thy Mind surprise , Believe not the Appearance of the Skies ; They make a shew , they spread a Glaring Light To lead thee on , but never guide thee right ; Let Active Thought assisting Sense pursue Goy Truth 's retreat , and take an open view : What ever Things are born , their Minds receive The fatal Temper which that sign can give That governs in the Tenths , the Foreign Ray , Tempers the Mass , and forms the easie Clay . A Thousand Reasons for this Truth appear From different Births belonging to One Star ; Of all those Creatures , that at once do see The Light , scarce Two can perfectly agree ; But different Tempers all the shapes adorn , As various as the Bodies that are born : For though one Chiefly Rules , yet others joyn And change the proper influence of that Sign : These Interchanges all our Thoughts distract , We think on other Signs , whilst others Act. Thus neither singly will the Ram bestow A Love to Cloathing , nor the Bull to Plough ; To Hunt the Lion , nor the Crab to Trade ; Learning the Twins , nor Eloquence the Maid ; The Scales to weigh , to measure , and to gage , Nor Poys'nous Scorpio arm unhappy Rage ; The Fish to Sail , nor the Youth's Urn inspire To work in Water , nor the Goat in Fire . But many joyn , and these mixt Signs bestow Mixt Inclinations on the Births below : A subtle and surprizing Task is shown , Much have I past , yet still you lead me on ; These things seem dark , whilst I the rest explore , Enjoy my Precepts , and complain no more . 'T is God you search for , by my Aid you trie To climb , and view the inside of the Sky ; Confin'd by Fate , you search its boundless sway , And seek to know the Laws you must Obey : The narrow Bounds of your own Breast you pass , Enjoy the World , and rove in the vast space : Painful , but always noble things are hard , Great is the Task , but equal the Reward : Nor let the various Maze thy Thoughts repress , Enter , and you are certain to possess . Is Gold thy Aim ? What mighty Pains attend ? Mountains are level'd , and the Mines descend Through Earth's deep Center ; though she hides her Store We tear her up , and reach the hidden Oar : For shining Gems we cut the burning Zone , Such Dangers are the value of a Stone : The fearful Farmer makes his Yearly Vow , And Pain still presseth the deceiving Plow : In War no Danger 's shun'd , we fight for Spoyl , E'en lazy Luxury leads us on to Toyl ; For Food● and Cloaths from East to West we run , And Spendchrists often sweat to be undone . Are perishing Goods worth so much Pains and Cost , Hard to be got , and in injoyment lost ? Then what must Heaven Deserve ? 26 That Gold , that buys The rest , how disproportionate a Price ! It asks a higher value , and to gain The God , lay out thy self , The Price is Man : Thus Fate 's dispos'd , but yet the Work 's not done ; For though the Powers of all the Signs are known , And how they joyn , how each rules every part , The Skill is small , and incompleat the Art : Observe the numerous parts of the Degrees What Heat doth scorch or what the Cold doth freeze , ( Unfruitful both ) where too much Moisture flows , Or Drought doth drain , and various Fates dispose : For different Qualities in Signs controul , There 's nought all-over-equal in the whole . For view the Earth , the gliding Streams , or Flood , Faults are on all sides , Bad is mixt with Good. Thus Barren Seasons midst the Best appear , And a small Turn blasts all the Blooming Year . A Port turns Shelf , and the inglorious Sand Forfeits that Praise which once its Safety gain'd . Now Streams through Plains in smooth Meanders play , Then Roar o're Rocks , and force a rugged way . Such Inequality above appears , And thus the Sky is vary'd in the Stars ; As Sign from Sign , so from it self the same Doth disagree , and spread unequal Flame ; And Signs , whose Sovereign influence Births do find In One Degree , are in the next unkind : Those things these parts o're-rule , no Joys shall know Or little Pleasure over-mixt with Woe . These parts , if such can be to Verse confin'd , My Muse must Sing , and ease my troubled Mind ; For though 't is various , yet the Subject's bound To words but few , and all of equal sound ; So that it must be mean , it must refuse The turn of Verse , though fashion'd by a Muse . And that , though labor'd , Line must bald appear That brings ungrateful Musick to the Ear. But since I must the Laws of Fate rehearse The settled Matter must direct my verse ; No Room for Fiction , I must things declare , Not as they may be feign'd , but as they are . It is enough the God is barely shewn , Rich in himself he shines , and great alone : Nor should the World be so to Words betray'd As to be thought ennobled by their Aid : This spurs me on , and I forget my Ease , The World must be oblig'd , and I must please ; I must , if plainly I these parts comprise ; Then learn the noxious portions of the Skies . The Fourth , and the Sixth Portions of the Ram Are hurtful parts , and spread unlucky flame ; Nor doth the Seventeenth or the next display A kinder face , or shed a milder Ray : The Twenty First , Fifth , Seventh spread noxious Beams The Twelfth , and Fourteenth leaning to Extreams . The Bull 's Ninth portion , did the Sign depend On me , should never shine upon a Friend : Add Three to Ten , or double Ten and Three , Take Two from Thirty , all these parts agree ; Twice Twelve , and twice Eleven count , and joyn The Seventeenth part as noxious in this Sign , Nor is the Thirtieth better than the Rest . The Twins First part doth hurtful Rays dispense , Nor doth their Childhood prove their Innocence ; They 're froward , pettish , and unus'd to smile , Their Third , and Seventh Degrees agree in Ill : The Fifteenth equals these , and Twenty sees Close on each side immoderate Degrees : To Twenty reckon Seven , or Five , or Nine , And all are hurtful portions of this Sign . Should Cancer boast a kind and gentle Reign , The First , and Third , and Sixth would plead in vain ; The Eleventh , Fifteenth , and the Eighth Degrees , The Twentieth too could hope no more success : The Twenty Fifth , Seventh , Ninth , severely sway , The Seventeenth too with a malignant Ray Rules o're the Birth , and stamps the easie Clay . The flaming Lion in the First we fear , Nor doth the Fourth a milder Image bear ; The Twenty Second , the Fifteenth , Tenth presage With th' Eight and Twentieth an unhappy Age. With hurtful Powers the Twenty Fifth is Curst , The Thirtieth too as noxious as the First . The First , and the Eleventh of the Maid , The Sixth , the Fourteenth , Eighteenth parts are bad : The Twenty First , and Fourth this Sign disgrace , Nor can the Thirtieth shew a better Face . Next view the Scales , the Seventh , and Fifth degree Is bad , add Eight to Ten , or Ten to Three : To Ten twice told add Seven , or Four , or Nine , All like the Thirtieth hurtful in this Sign . I' th' First , Third , Sixth , and Tenth black Scorpio 's Claws And in the Fifteenth make Malignant Laws ; The Twenty Second , Eighth , Fifth , and Ninth betray His poys'nous Rage in an unhappy Ray : Would Fate allow thee choice , forbear to choose The Centaur's Fourth Degree , the Eighth refuse ; The Twelfth , the Sixteenth , Twentieth parts portend A wretched Life , and an untimely End : The Twenty Fourth , Sixth , Eighth Degrees molest , Nor is the Thirtieth better than the Rest . The Thirteenth of the Goats contracted Star , Nor Seventh , nor Ninth shall be my earnest Prayer ; Nor that which Twenty doth of One deprive , Or Three , or adding gives it Six or Five . To Ten add One , or Five , or Nine , or Three And you are sure to find a bad Degree : Add One , Five , Nine to Twenty , hurtful Streams Flow from the Vrn , and spread unlucky Beams . The Fishes close the Signs , their parts confest As noxious , and as guilty as the Rest ; For Three , Five , Seven , or Ten when joyn'd with Seven , Or One , mark hurtful Portions of the Heaven . Five multiply'd by Five is hardly clear'd , And Seven to Twenty added 's to be fear'd : All these are noxious Portions of the Sky , Too Hot , or Cold , or else too Moist , or Dry. This known , the Work is not compleatly done , The Labours still increase as you go on ; The Time makes difference , as they Rise , new force They gain , and after lose it in their Course . Thus when the Ram ascends , and proudly turns His bending backward Neck before his Horns To Mortal Eyes , the wretched Births are Curst With Ravenous Tempers , and inflam'd with Lust : All Modesty shall be to Gold betray'd , Nor Parents Care secure the easie Maid : These Tempers are his own ; as Fancy leads He roves , and wantons o're the flowry Meads : Forward to push , and as the Grass renews His wasted Strength , he Courts the willing Ews . To Travel he inclines through Lands unknown , He Ploughs new Seas , and makes the World his own : This he prefigur'd when his Back convey'd Young Phryxus safe , and lost the falling Maid . The Bulls bright part that first appears , creates Vile Pathicks scandals to the other Fates . The Cause , if it be fit to search for one When Nature works , may easily be shewn ; His Back-part first appears , in that he bears The narrow Cloudy Train of Female Stars : And thus the Posture , and the Sex combine To shew the Influence of the rising Sign : He bends to Plow , and o're the Fruitful Plains The Labouring Ox grows Fat upon his Pains . But when their Feet the rising Twins do shew , And half appear above , half lye below , The Births are happy , all their Parts refind , And Arts enrich the Treasures of their Mind ; Ready their Wit , persuasive is their Tongue , In Musick skill'd , and excellent in Song : These are the Powers their rising Rays dispense , They Wit bestow , and fix that Wit with Sense . When rouling Cancer riseth vaild in Clouds , I' th' Skies as deeply hid as in the Floods , The Moon resembling when depriv'd of Light ; The Births are Blind , and wish in vain for sight : By Fates a Verse condemn'd to double Death , Dead whilst Alive , and Buryed whilst they breath : But when the Lion shews his ravenous Jaws Prepar'd for Rapine , and unsheaths his Paws , A Spendthrift's born , who minds himself alone , He wrongs his Father , and he cheats his Son ; His Race in vain with expectation wait , For in himself he buries his Estate ; So vast his Gluttony , his Lust so wild That he devours himself , yet is not fill'd : And whilst his Appetite proceeds to crave He eats his Funeral , and he spends his Grave . When Virgo rises , ( who whilst Right prevail'd Rul'd here below , retreating when it fail'd ) To awful Honors all the Births must rise Profoundly skill'd in Sacred Mysteries : Good , Pious , Just , Devout , unus'd to Rage And great Examples to the looser Age : But when Autumnal Scales do first appear Happy the Birth , he shall be known from far , The Glory of the Bench , and of the Bar ; He justest Laws shall make , and Life and Death Depend upon the Issues of his Breath ; Him Towns shall fear , the Earth observe his Nod , And after Earth the Heaven enjoy a God. Thus Act these Signs , but Scorpio's Tayl displays A double Influence from his Forked Rays ; For when that first appears , tho Peaceful Child Shall Cities Raise , and be inclin'd to build ; The World shall see him with his 28 Plow surround The place design'd , and mark the fatal Bound ; Or he shall wast what others Pains did raise , Where Populous Cities stood , there Beasts shall graze , Or Harvests grow ; He leads to these Extreams , And Power agreeing waits upon his Beams . Bold Sagittarius , when he first appears , Heats the gay Birth , and makes him fam'd for Wars ; In Triumphs great , the Wonder of the Crowd , By Captives carry'd , he almost a God Shall climb the Capitol , bright Fame pursue , Old Cities raze , or grace the Earth with New : But ill succeess , ( his Forehead 's wreath'd with Frowns ) Shall wast his Fame , and blast his gather'd Crowns . Thus Conquering Hannibal , by this Sign betray'd Before his slight perceiv'd his Wreaths to f●de , He paid for Trebia's and for Cannae's fame , And recompenc'd our Losses by his shame . But when the narrow Goat erects his Tail He drives to Sea , and much inclines to Sail , Ignoble Trade then Ploughs the dangerous Main , And precious Life is meanly stak'd for Gain . The Good , the Pious , and the Just are born When first Aquarius pours out his Vrn. But could I rule , could I the Fates design , The rising Fishes ne're should govern mine ; They give a Hateful , Pratling , Railing Tongue , Still full of Venom , always in the wrong ; That blows up Jealousies , and heightens Fears , By mutterring Poys'nous Whispers in Mens Ears . Faithless the Births , and full of wild desire ; Their Faith is Treachery , and their Love is Fire . For when the Skies grew weak , when Giants strove , And snaky Typhon shook the Throne of Jove ; Fair Venus fled , and in a Fish's shape ( This Syria knows ) secur'd her mean escape ; Then did she through the Scaly Kind inspire New Heats , and with the Ocean mixt her Fire . No single Births , for when this Sign begins , Twins shall be Born , or those that shall have Twins . Now learn what Signs o're different Lands controle , But first take this short figure of the whole : East , West , and North , and South , on either side , These Quarters lie oppos'd , the World divide : As many Winds from these four Quarters flie , And fight and rattle , thro' the empty Sky : Rough Boreas from the North , bears Frost and Snows , And from the East , the gentle Eurus blows . Wet Auster from the torrid South is thrown , And pleasing Zephyrus cools the setting Sun. 'Twixt these two other Winds their Seats do claim , Alike in Nature , different but in Name . Around the Earth the liquid Ocean plays , The Ball enclosing with a soft Embrace ; But yet on many parts , Earth's bending sides , Or open Bays receive the flowing Tides . The Sea admitted from the Western Shores , Doth on the Right Hand wash the swarthy Moors ; And Lybia's Sands , where once great Carthage stood , Then o're the Syrtes whirls the rapid Flood ; And thence to Egypt it directly flows , Where what dry Heaven denies , the Nile bestows . The Left Hand Sea by Spain and France extends , And follows Conquering Italy as it bends ; Till into Streights the barking Sylla draws , And whirls it round Charybdis greedy Jaws ; Loos'd from these Streights , the Flouds spread wide again , And freely flow in the Ionian Main : Then on the left they turn , and winding flow , Fair Italy surround , and drink the Po. Then make rough Adria's Gulph ; the other side Illyrium washes with a gentle Tide , Sees Epire's Cliffs , and Corinth's lofty Towers , Then winds round plain Morea's open Shores. Thence Northward into vast recesses tost The Sea confines the Learn'd Achaia's Coast : Thence North and Eastward the unwilling Flood Consin'd by Streights , and stain'd with Helle's Blood To fam'd Byzantium cuts its winding way , And joyns Propontis to the Euxine Sea ; Behind whose back the Lake Meotis lies Receives full Tanais , and the Sea supplies . Hence when the Circling Waves return again The weary Sailer to the Open Main , He cuts th' Icarian , and th' Aegaean Tide By Asia's Coasts , and wonders at their Pride : And whilst the left hand Course he still pursues As many Trophies , as he places views ; A thousand Nations , 29 Taurus mount , that threats The Floods , the Bay that from the Sea retreats Parcht Syria's Plains , and the Cilician Seats , Till he at last to Egypt turns his Oars And sees the Waves dye on the swarthy Shores. Thus ruling Nature draws her bounding Lines , Checks midland Seas , and all their Rage confines . Yet midst this Sea a thousand Islands rise ; Shap'd like a Foot the low Sardinia lies Near Lybia's shores ; Trina●rid fill'd with Fires , But just cut off from Italy , retires , And adverse Greece Euboean Cliffs admires . Jove's Birth-place Crete appears , a goodly Isle , And Cyprus beaten by the adverse Nile . A thousand lesser Isles Command these Seas , Rhodes , Delos , and the equal Cyclades , Fam'd Aulis , Tenedos , and by Sardinia's side Lies Corsica , and breaks the coming Tide ; Near the Streight's Mouth the Baleares Reign , And strong Ebusus Triumphs o're the Main . Ten thousand smaller Rocks the Waves disperse , Too little to be nam'd , too mean for Verse . Nor doth the Ocean but one single way Attempt the Earth , and force an open Bay , It tries on every side , but Mountains bound Insulting Billows , and preserve the Ground ; For 'twixt the Summer East and Northern Pole Through narrow Channels secret Waters roul , Till spread at last upon the open Plain They make the Caspian like the Euxine Main . Southward encroaching Waters doubly press , O'reflow the Earth , and in a vast recess One part more East runs on , and breaks a way Through Persia's Banks , and makes the Persian Bay : More West the other soft Arabia beats Where Incense grows , and pleasing Odor sweats , Which sends us Gums soft Luxury to please , And reconcile the angry Deities : Strange that the same , when differently apply'd , Should calm the Rage of Heaven , and serve our Pride . This Bay is call'd th' Arabian Gulph , the Name The Country gives it , and 't is great in Fame . Thus lie the Seas ; Earth midst this mighty Flood Contains , first Africk , where proud Carthage good ; Once great in Arms , and whose extended sway O're Libya stretcht , and made the Spains obey : When Hannibal wrapt Alban Towns in flame , And eterniz'd the bloody Trebia's Name ; When led by Fate he March'd to overcome , And pour'd his swarthy Libya upon Rome : When gasping Consuls groan'd on every Plain , And Canna's Fields were burd'ned with the slain . Here Nature angry with Mankind prepares Strange Monsters , Instruments 30 of future Wars ; Here Snakes , those Cells of Poyson , take their Birth , Those living Crimes and grievance of the Earth ; Fruitful in its own Plagues , the Desart shore Hears Elephants , and frightful Lions roar ; Serious it seems in all these Monstrous shapes , But sports in the lewd Limbs of Mimick Apes . The Country's large , the Barren Plains extend A mighty space , and then in Egypt end . Thence Asia spreads , a fruitful Soil , the Streams Roul Golden Sand , the Ocean shines with Gems ; The Trees drop Balsom , and on all the Boughs Health sits , and makes it Sovereign as it flows . Thence India lies , a Land more large than thought , The Parthians oft , though not securely fought ; They flying still delude Rome's firmer Powers , And yet Command a different World from Ours . These Taurus bounds , whose threatning Mountains rise To awful Hights , and wound the lower Skies ; A thousand Nations lie by Tanais flood Which cuts the Scythia's , stain'd with humane blood ; By Lake Meotis , and the Euxine Tide Which Nature sets as bounds to Asia's Pride . Europe remains , which first the Beauteous load Receiv'd , and where the Bull confess'd the God ; Hence came its Name , in that the grateful Jove Hath Eterniz'd the Glory of his Love : Here Greece is seen , with Ruin'd Antient Troy , And shew'd what Fates attend unlawful joy : A Country Rich in Men of wondrous parts , The place of Learning , and the Seat of Arts : Here Athens stands , which makes the best pretence To Sovereignty in Wit and Eloquence : For Courage Sparta , and for Deities Fam'd Thebes , whose Heroes People half the Skies : Epirus , Thessaly , whose lasting Praise One single Pyrrhus , and Achilles raise . To these Illyrium joyns , and Warlike Thrace , The Seat of Mars , and breeds a stubborn Race . Thence 31 Germany , a mighty Country runs , And wonders at the vastness of her Yellow Sons . Thence South and Westward in a fertile Plain Lies France , for Tribute fam'd , for Battels Spain : But Italy Crowns all , whom Rome hath given Command of Earth , and joyns 32 her self to Heaven : These Bounds the Earth , and these the Seas confine , And God allots to every part a Sign ; No Land is free , no stately Town deny'd The kind Protection of a Starry Guide : For as in Man , the work of Hands Divine , Each Member lies allotted to a Sign ; And as the Body is the common care Of all the Signs , each Limb enjoys a share : ( The Ram defends the Head , the Neck the Bull , The Arms bright Twins are subject to your Rule ; I' th' Shoulders Leo , and the Crab's obey'd I' th' Breast , and in the Guts the modest Maid ; I' th' Buttocks , Libra , Scorpio warms desires I' th' secret parts , and spreads unruly fires : The Thighs , the Centaur , and the Goat Commands The Knees , and binds them up with double bands . The parted Legs , in cold Aquarius meet , And Pisces gives protection to the Feet . ) So in the greater World , the Members share Celestial Rulers , and enjoy their Care : Hence different Men , in different Climes we view , They vary in their shape , or in their Hue ; The Matter 's common , and in all the same , But private Stamps , distinctly mark the Frame . Vast Yellow Offsprings are the German's Pride , Whilst Neighbouring France is not so deeply dy'd : But hotter Climates narrower Frames obtain , And low-built Bodies are the growth of Spain : Hesperia mixeth sweet with many Grace , And temper'd Mars appears in every Face : Whilst active Greece produceth finer parts , Their looks betray their Exercise and Arts : Short Curl'd up Hair the Sons of Syria grace , Whilst Ethiopia's Blackness stains the Face , With Horrid Shapes she does her Sons expose , Distends their swelling Lips , and flats their Nose : Less India blackens , less it Crusts the Mass , And mixeth Colours in the Tawny Face : But Egypt's slimy Plains affect the sight With brighter Colours , and approach to White . Parcht Lybia burns her Sons , the vilest Shapes She shews , and scarce divides her Men from Apes : Whilst Mauritania doth disgust the Eye , ( Her Name betrays it ) with the blackest Dye . Tho' each Speech Organs fram'd alike employs , How many Languages confound the Voice ? How different Vertues Reign , how different Crimes ? Mens Manners are as various as the Climes . Like Trees transplanted by the Farmer 's Toyl ; Vice turns to Vertue , in another Soyl. Tho' Seed the same , yet different Fruits are born , Thus Yellow Ceres varies in her Corn. Nor doth the Vine on every Hill produce Like Grapes , nor Bacchus press an equal Juice . Rich Cinnamon , not every Country bears , Nor are all Fields bedew'd with Myrrha's Tears . Nor is this great variety exprest In Man , and Fruits alone , but it divides the Beast : Here Lions roar , and there in dreadful Wars The high-built Elephant his Castle rears ; Looks down on Man below , and strikes the Stars As many parts , so many Worlds appear , For every part is subject to a Star ; They spread their Influence , and the Countreys pay A due compliance to the Fatal Ray. Plac't midst the pleasing Vernal Signs , the Ram Commands the narrow Streight o're which he swam ; When from the Mothers Rage , his Fleece convey'd The Brothers safe , and dropt the falling Maid ; Content he swam , and with his Burthen pleas'd , He mourn'd his Loss , and griev'd to be so eas'd : The near Propontis too his Beams obeys , And Syria feels the Influence of his Rays : The loose Garb'd Persians , know his gentle Rule , Their Garments bear Relation to his Wool : With Nile that swells at Fiery Cancers Beams , And Egypt drown'd by its ore-flowing Streams . Cold Scythia's Rocks ; Arabia's wealthy Groves , And powerful Asia , Taurus Empire proves , Rich in their Corn , and wanton in their Loves . The boysterous Euxine , bent like Scythian bows . Beneath the Twins subjection gladly flows , And they of Ganges infant Streams dispose . The swarthy Indians Fiery Cancer sways , His Rule the Blackness of their Hue betrays , And Ethiopia's heated with his Ray. The Phrygian Plains the large Bithynian Woods The 33 Servant of the Mother of the Gods , The Lion own , the Cappadocian Shoar With fierce Armenia , hear the Lion Roar. And Macedon , that all the World subdu'd , Submits to the Great Monarch of the Wood. In happy Rhodes the gentle Maids ador'd , Rhodes , the retirement of our future 34 Lord : Blest Island truly Sacred to the Sun , E're since in thee the Glorious Coesar Shone , The World 's great Light , whom with expecting Eyes ; Mankind desires , and longs to see him rise . The Dorick Plains , the rich Ionian Towns , Arcadia Rival to the waining Moons : With Warlike Caria high in Antient Fame Owe all Subjection to her modest Flame . What Sign , could you dispose the Signs , should fall To Latium's share , but that which poizeth all ; To which by Nature , it must needs belong To value things , and separate Right from Wrong . In which the Times are weigh'd , and Day with Night Are met , the Darkness equal to the Light : The Scales rule Italy , where Rome Commands , And spreads its Empire wide to Foreign Lands : They hang upon her Nod , their Fates are weigh'd By her , and Laws are sent to be obey'd : And as her powerful Favour turns the Poize , How low some Nation 's sink and others rise : Thus guide the Scales , and then to fix the Doom , They gave us 35 Caesar , Founder of our Rome . The following Sign rules Carthage Conquer'd Towers , Subject they lie , to Scorpio's Scaly Powers ; With Lybia's Sand , and Egypt's fruitful Soil , The slimy 36 Gift of the o're-flowing Nile . Large Bounds , but yet too narrow to confine The vast Ambition of this craving Sign ; He claims the Isles of the Italian Main , And low Sardinia's subject to his Reign . To Crete the Centaur makes an hateful claim , And still keeps up the Memory of its shame : It bore a Centaur once , and that confines The Isle to the same Figure in the Signs : To him their Skill and Darts , the Cretans owe , And imitate the sureness of his Bow. Trinacria follows , Crete's Example draws Her Sister Isle , and yields it to his Laws ; And Latium's Shores , which narrow Friths disjoyn , Here baffle Nature , and in him combine , Nor would be differenc'd by another Sign . The West , and Northern Parts , rich France and Spain , Contracted Goat , are subject to thy Reign , And Germany , since 37 Varus stain'd thy Shore , A Seat for Beasts , and fit for Man no more : This monstrous Sign hath variously engrost , ( He Rules at Sea and Land ) thy doubtful Coast , Now Earth appearing , now in Water lost . But Young Aquarius with his watry Fires , From Egypt to the Clydae Isles retires ; The stout Cilicians , and the Neighbouring Plain With Sailing Tyre are subject to his Reign . When Heaven grew weak , and a successful fight The Giants rais'd , and Gods were sav'd by flight ; From Snaky Typhon's Arms , a Fishe's shape Sav'd Venus , and secur'd her from a Rape : Euphrates hid her , and from thence his Streams Owe all Obedience to the Fish's Beams . Wide Parthia's Plains confin'd by mighty Rocks , The Nations round , long bent unto its Yokes With Tigris Streams , the Red-Sea's shining Shores Are Subject to the Heavenly Fish's Powers . Thus Earth's divided , these the Signs that sway Its Portions , and the Parts their Beams obey ; These Signs the Tempers of their Empires show , The Parts above , directing those below , Their Powers infuse : And thus as Ruling Signs Are now Oppos'd , and now agree in Trines , Or other Site maintain , which Site directs Their Fatal Influence , various in Effects ; So Towns with Towns , and roaring Seas with Seas , And Land with Land , or differs or agrees . And as these Signs direct , so Men should choose This Town , this Country , or that Seat refuse ; Here Hate expect , there surest Friendship prove , As Heaven directs , and Stars decree above . But now attend , for Signs Eccliptick claim Thy Care , and learn the Reason of the Name : For some , as weary'd in their tedious Race , Grow restiff , dull , nor keep their usual pace . Nor is this strange , for through the mighty Frame There 's nothing that continues still the same : As Years wheel round , a change must needs ensue , Things lose their former State , and take a new . Now tir'd with Births , the Fields refuse to bear , Now unmanur'd , prevent the Tiller's care . Dilated Vapours tear the solid Earth , Strong the Convulsions at the Fatal Birth ; Vast Mountains sink : And now his large Command ▪ Neptune extends , and Seas o're-spread the Land , Contemning Shores : Thus were the Towns o're-flow'd When Mankind's single Heir Deu●alion stood On steep Parnassus , to repair the Stock , The spacious World possessing in one Rock . And when bold Phaeton , with unequal force The Chariot fill'd , and drove the Flaming Horse ; The Earth took Fire , Heaven saw the Stars recoil , And frighted Nature fear'd one common Pile . So much as Years roul round , the mighty Frame Is chang'd , yet still returns to be the same : And so the Stars , whilst they revolve their Course , Now lose their Power , and now regain their force . The Reason's plain , for when depriv'd of Light , The Moon Ecclipst , lies vail'd in sudden Night ; Whilst hindring Earth diverts her Brother's Ray , These Signs Eccliptick feel the same decay ; They feeble grow , they hang their bending Head , And mourn , and pine , as if the Moon were dead . Now Signs Eccliptick ( see the Name betray Unusual Languor , and a weak decay , ) Grow weak by Pavis , and those not Neighbouring Signs , But Opposite ; for thus our Art defines , Because the Moon then only feels decay , When Opposite unto her Brother's Ray. Nor is this Languor , nor these Times of Grief Alike to All , fome quickly find relief ; Some Languish long , and e're their Mourning 's done , The Sun goes round , and all the Year is run . But when their Grief is o're , the next in turn Begin to Languish , and prepare to Mourn ; The next in turn , that are in Order plac't On either side , the Two that Languish't last : To speak distinctly , 38 those two Signs that view And leave the Earth before the former two . Not that the Earth doth noxious Powers dispense , Or Subject Heaven to its dull Influence ; But since the World turns round , the Orb obeys , And Signs abate the vigour of their Rays , Not by Earth's Influence , but by their place . But what avail my Songs , if all refuse The profer'd Aid of my obliging Muse ? If puny fear forbids our Hopes to rise , To enter boldly , and enjoy the Skies ? What Nature hides , ( for thus Objections teach ) Is deeply hid , too deep for Man to reach . Vast the Recess ! Though stubborn Fate should Reign , And we know this , yet all the search were vain , Since none can find the Links that make the Chain . Fond Mortals ! why should we our selves abuse ? Nor use those Powers which God permits to use ? Basely detract from the Celestial mind , And close our Eyes , endeavouring to be blind ? We see the Skies , then why should we despair To know the Fatal Office of each Star ? To open Nature , to unvail her Face , Go in , and tread the Order of the Maze ? Why should we not employ the Gifts bestow'd By Heaven , in knowing the kind Author of the Good ? Our Work grows short , we may surround the Ball , Make the whole World our own , and live in all : Through what remains , we now with Ease may pierce , Take , and enjoy the Captive Universe : Our Parent Nature we , her parts , descry , And Heaven-born Souls affect their Father Skie : For who can doubt that God resides in Man , That Souls from Heaven descend , and when the Chain Of Life is broke , return to Heaven again ? As in the Greater World aspiring Flame , Earth , Water , Air , make the Material Frame ; But through these Members a Commanding Soul Infus'd , directs the Motions of the whole ; So 't is in Man , the lesser World , the Case Is Clay , unactive , and an Earthly Mass ; Bloods Circling Streams the Purple Soul convey , The Ruling Mind uniting to the Clay : Then who can wonder that the World is known So well by Man , since he himself is One ? The same Composure in his Form is shew'd , And Man 's the little Image of the God. Now other Creatures view , how mean their Birth , The Rubbish , and the Burdens of the Earth : Some hang in Air , some float upon the Waves , Born for our use , and bred to be our Slaves . All their Enjoyments are confin'd to Sense , The easie Works of wary Providence . But since they Reason want , their Tongues are mute , How mean , how low a Creature is a Brute ? No Mysteries disclos'd , commend their Parts , Nor are they Subjects capable of Arts ; How hard the Labour , yet how often vain To bring them foolishly to Ape a Man ? But ruling Man extends his larger sway Beyond himself , and makes the World obey ; Wild Beasts are tam'd , The Fields are forc't to bear , And Recompence the Labours of the Share . In vain the Sea disjoyns the distant Shores , His Sails the Winds command , the Floods his Ores . Alone erect his Form doth nobly rise , Up to the Stars he lifts his Starry Eyes , And takes a nearer Prospect of the Skies : He searches Jove , and whilst his Thoughts do trace His kindred Stars , in them he finds his Race . No outside Knowledge fills his vast Desires , The more he riseth , he the more aspires . We think it Reason that in Augury We should on Birds , and slaughter'd Beasts rely ; And can the Fates be less in Stars exprest , Than in a Bird , or Entrails of a Beast ? When God his Mind in meaner things declares , Should he neglect the Glory of the Stars ? Besides , the World is eager to be known , Our search provoking still ; for rouling on It shews us all its parts , displays its Light , And constantly intrudes upon our Sight : His Face unvail'd , God doth so plainly shew , That if we will but look , we needs must know : He draws our Eyes , nor doth our search forbid ; What Powers he hides not , he would not have hid : Then who can think it impiously bold To search what we 're encourag'd to behold ? Nor think thy force too small , too weak thy Mind Because to Clay unequally confin'd ; Its Power is wondrous Great ; how small a Mass Of Gold or Gems , exceeds vast Heaps of Brass ? How little is the Apple of the Eye ? And yet at once , he takes in half the Sky : Nor dreads the disproportion to the Sense , The Organ small , the Object is immense : And from the narrow limits of the Heart , The Active Soul doth vigorous Life impart To all the Limbs , its Sway the Members own , Wide is its Empire from its petty Throne . Man know thy Powers , and not observe thy Size , Thy noble Power in piercing Reason lies , And Reason conquers all , and rules the Skies . Nor must you vainly doubt that Man 's allow'd To know Heaven's mind , since Man can make a God : A Star 39 new rais'd , the Skie enlarg'd contains , And Heaven must still encrease whilst Caesar Reigns . The End of the Fourth Book . NOTES . 1 The Poet did not think of the Palladium as Scaliger imagines , but only of the Fire at Troy , which parted to let Aeneas go through with his Father , and his Household Gods. 2 Manilius makes only short Reflections on History , and therefore is frequently obscure : He says here , that it was impossible one single Aeneas should have rais'd the Glory and Reputation of ruin'd Troy , and made it then conquer , when it was overthrown , by building Rome which subdu'd the whole World ; for Rome rose out of the Ruins of Troy ; unless some over-ruling Power and Fate had ordain'd it should be so . 3 Romulus and Remus , the Founders of Rome , were but Shepherds . 4 I chuse to read Auxissent Culmina rather than vexissent , or duxissent Fulmina , and render Culmina a Cottage . 5 If Manilius be suppos'd to keep the Order of Time in his Historical Reflections , I must own I have not hit his meaning in this place ; for no doubt he had an Eye upon the Wars between the Sabines and Romulus : but then I cannot imagine what those Words Captus & à Captis Orbis foret mean : I cannot think with Scaliger and Huetius that he runs back to Troy , which he had left several Verses before , and therefore apply this passage to the taking and burning of Rome , and the besieging the Capitol by the Gauls : And 't is certain the Poet in his following Reflections neglects the Order of Time very much . 6 The Stories of Mutius Scaevola , Horatius Cocles , the Virgin Claelia , and the Combat between the three Horatij on the Roman , and the three Curiatij on the Alban side , are well known . 8 Short Reflections on the great Accidents in the Second and Third Carthaginian Wars , together with the Death of Hannibal . 9 He goes on with the Roman History , the unaccountable Fortunes of the Great Marius . 10 Pompey the Great , was a very notable Example of the variety of Fortune , being on a sudden rais'd to the highest , and as soon thrown down to the lowest Condition in the World. 11 Cum jam etiam posses alium cognoscere Magnum : I hope I have given this Verse a better Sense , than the other Interpreters have done . 12 Caesar is said to be sprung from Heaven , because he was descended from Aeneas the Son of Venus : After his Murther an unusual Star appear'd , which the Flatterers of Augustus said was the Soul of his Father Caesar . 13 The Poet closeth his Examples with Reflections on the overthrow of Croesus , the Famous wealthy King of Lydia , who was taken by Cyrus ; on the wretched Condition to which old Priam was reduc't ; on the unaccountable overthrow of Xerxes ; on the Advancement of Servius Tullus , who was the Son of a Bond-Woman , and yet came to be King of Rome , and on the Conduct of Metellus , who broke into the Temple of Vesta when it was on Fire , and brought out the Image of the Goddess . 14 — Mortes seque ipsae rursus fugiunt , errantque per Ignes . 15 To reconcile the different Interpreters , I have hinted at both Paris , ( or rather Hercules ) and Leander . 16 Furius Camillus was the restorer of Rome , after it had been taken and burnt by the Gauls : Of the Family of the Decij there were Three , who voluntarily devoted themselves to Death , for the Good and Prosperity of their Country : Cato Vticensis , who kill'd himself that he might not survive the Liberty of Rome . 17 Alluding to the Tryal of skill between Pallas and Arachne , describ'd by Ovid , in the Sixth Book of his Metamorphosis . 18 M. Curius Dentatus and Serranus were both fetcht from the Plough , to Command the Roman Armies , fought bravely , and Triumpht . 19 For this the Poets fancy'd to be the Bull that carry'd Europa into Crete . 20 Scaliger thinks Manilius means such as keep Beasts for publick Shews , and to fight in the Theaters ; and this Interpretation I rather follow than that of Huetius , who fancies the Poet means by this pompous Description no more than innocent , honest Butchers . 21 Palamedes is said to be the first Man amongst the Greeks , who invented Cyphers , and taught Men to cast Account : I have enlarg'd his Character , and taken notice of his invention of Letters . 22 Servius Sulpitius , the Great Lawyer , and Acquaintance of Cicero . 23 Of the Docility of Elephants , we meet with numerous Examples : Seneca mentions one , that play'd at Ball : Another , that would Dance on a Rope , &c. The Travellers in the East are full of strange Stories concerning those Animals ; and Lipsius in his Epistles , will furnish any Man with more Stories than he will readily believe . 24. If Alchymy was more Antient than Manilius , as Huetius himself grants , I see no Reason why the Poet might not speak of the Alchymists : The Interpretation I have given , I am sure , sounds better than that of Huetius . 25 The Tenths : This is a new word , but answers to Decanica in Manilius : Decanica signifies Ten Degrees , and the Decanus is Lord of Ten Degrees : The several Lords are these , In Aries Aries Taurus Gemini In Taurus Cancer Leo Virgo In Gemini Libra Scorpius Sagittar . In Cancer Capricor . Aquarius Pisces In Leo Aries Taurus Gemini In Virgo Cancer Leo Virgo In Libra Libra Scorpius Sagittar . In Scorpius Capricor . Aquarius Pisces In Sagittar . Aries Taurus Gemini In Capricor . Cancer Leo Virgo In Aquarius Libra Scorpius Sagittar . In Pisces Aries Taurus Pisces 26 Quantum est quo veniat Omne , I have follow'd the Interpretation of Scaliger ; but do not reject the Opinion of Huetius : Though of less force than Scaliger's . 27 The Hurtful Degrees . In Aries 4. 6. 12. 14. 17. 18. 21. 25. 27. In Taurus 9. 13. 17. 22. 24. 26. 28. 30. In Gemini 1. 3. 7. 15. 19. 21. 25. 27. 29. In Cancer 1. 3. 6. 8. 11. 15. 17. 20. 25. 27. 29. In Leo 1. 4. 10. 15. 22. 25. 28. 30. In Virgo 1. 6. 11. 14. 18. 21. 24. 30. In Libra 5. 7. 13. 18. 24. 27. 29. 30. In Scorpio 1. 3. 6. 10. 15. 22. 25. 28. 29. In Sagittar . 4. 8. 12. 16. 20. 24. 26. 28. 30. In Capric . 7. 9. 13. 17. 19. 25. 26. In Aquarius 11. 13. 15. 19. 21. 25. 29. In Pisces 3. 5. 17. 11. 17. 25. 27. 28 Alluding to the Custom of the Romans , who , when they design'd to build a City , took a Plow ▪ and made Furrow a where the Walls were to stand . 29 Vossius , In his Observations on Catullus , P. 204. Reads , — Taurumque minantem Fluctibus . — 30 Pyrrhus made use both of Elephants and Snakes , in his Wars against the Romans . 31 Germany , which comprehends all the Northern tract of Land beyond Thrace . 32 Rome had Temples Dedicated to her , and was look'd upon to be a Goddess . 33 The Poets feign'd that Cybele , the Mother of the Gods , rode in a Chariot drawn by two Lions . 34 Tiberius being under the displeasure of Augustus , was sent to the Island Rhodes , and liv'd there some time . 35 Vossius out of his Ancient Manuscript Reads , Qua genitus Caesarque meus qui hanc condidit urbem . 36 I know Donata Regna may bear another Sense , but this will do as well . 37 Whom ▪ in the time of Agustus , the Germans destroy'd , and cut off all the Legions he Commanded . 38 Thus when Aries and Libra are Eccliptick , the two next Eccliptick are Pisces and Virgo . 39 Alluding to Julius Caesar , Deify'd by Augustus . MANILIUS . The Fifth Book . Having explain'd the general influence of the Twelve Signs of the Zodiack , and given a particular account of their interchanges with one another , and how they incline when they rise ; after a short Preface , in which he magnifies his own Industry , and unweary'd diligence in this Subject : He goes on , 1. To shew what Constellations rise with the several Degrees of the Twelve Signs , and then what Tempers they bestow , and to what Studies they incline : For instance , 2. The Northern Rudder of the Ship , riseth with the fourth Degree of Aries , and those that are then Born , shall be inclin'd to Sail , and prove good Pilots : 3. Orion riseth with the same Degree of Aries , and those that are Born under his Influence , shall be Men of busie , active Tempers , Solicitors , cringing Parasites and Flatterers : 4. Heniochus or the Driver , riseth with the fifteenth Degree of Aries , and makes Charioteers , Horse-Racers , and Men skill'd in all sorts of Horseman-ship : 5. With the Twentieth Degree of Aries , the Hoedi or the Kids rise , and those , being wanton Stars , produce nothing that is Vertuous or Noble : Their Births are wanton , light , and lustful , and never Couragious , but in pursuit of some shameful lewd Pleasure ; some of their Births , are peculiarly delighted in feeding and keeping Goats : 7. With the Twenty-seventh Degree of Aries , rise the Hyades : And their Births are always turbulent and Seditious , prone to Factions , restless Phanaticks , or else , they give their Minds to Country Affairs , feed Cattle , or turn Waggoners : 7. With the Thirtieth Degree of Aries , the Goat riseth ; and those that are Born under that influence , shall be fearful , jealous , suspicious , and inconstant , or else inclin'd to Travel : 8. He says the Pleiades rise with the sixth Degree of Taurus ; and the Men that are then Born , shall be gay , and humorous , witty , but too effeminate and soft , minding nothing but Dress , Gate , and Love : 9. The Hare riseth with the seventh Degree of Gemini or the Twins ; and her Births are active and nimble , fit for all sports , all feats of activity , and slight of hand : 10. The Asses rise with the first Degree of Cancer ; and those that are Born under their influence , shall be employ'd in all sorts of Hunting and Fishing : 11. With the twenty-seventh Degree of Cancer , Procyon or the little Dog rises , and that produceth such as weave Nets , make Spears , and all other Instruments of Huntsmen : 12. The Great Dog riseth with Leo , and being himself a Constellation of excessive heat ; those that are Born under his influence , shall be full of Passion , Hate , Jealousie , and ungovernable suspicion , and given to excess in Wine ; their Heat shall lead them on to to dangers , and engage them to hunt wild Beasts . 13. With the last Degree of Leo , the Bowl appears , and inclines to plant and dress Vines ; the Births shall be somewhat intemperate , inclin'd to Merchandise , and to trade in those Commodities , which cannot be brought to perfection without moisture : 14. With the fifteenth Degree of Virgo , the Crown of Ariadne riseth , and then the Births shall be Florists ; they shall delight in making and perfuming Garlands , be Gay ; Amorous , and affect neatness in their Habit. 15. The Sheaf riseth with the tenth Degree of Virgo , and inclines Men to look after Corn , to build Barns , to Grind and Bake Grain , and make it useful : 16. With the eighth Degree of Libra , the Arrow rises , and then are Born expert Darters , and good Bow-Men , such as Philoctetes , Teucer , and Alcon . 17. The Goat or Hoedus , riseth with some part of Libra , and produceth Tempers quick and active , fit for Business , and covetous of Employment : somewhat loose , but honest to their Country , and Enemies to Knaves . 18. The Harp rising with some part of Libra , breeds Songsters and Musicians ; such as affect to Sing in Company , and are always humming to themselves . 19. The Altar rising with the eighth Degree of Scorpio , breeds Priests , Servants in Temples , and such as take care of and consult Oracles . 20. The Southern Centaur rising with the twelfth Degree of Scorpio , breeds Horse-Men , Charioteers , and Farriers . 21. With the fifth Degree of Sagittarius , Arcturus appears , and breeds Collectors of Customs , Treasurers for Kings , or Stewards for private Mens Estates . 22. With the thirtieth Degree of Sagittarius , the Swan rises ; and then are Born all kinds of Fowlers ▪ such as Teach Birds to speak , to sing , or to decoy , &c. all their Employments shall be about Birds . 23. With some part of Capricon , Ophieuchus , or the Snake-holder riseth , and produceth such as are skill'd in during poison'd Persons , and such as cannot be poison'd themselves . 24. With the last Degrees of Capricorn , the Southern Fish rising , breeds Anglers , Divers , Fishers for Pearls , &c. or at least , Traders for Fish and Pearls . 25. With some part of Capricorn the Harp , ( or rather the Strings of it , for of the Shell Manilius hath already spoken ) riseth , and produceth subtle Accusers , Justices that shall examine nicely , and determine justly ; or such as shall torture , and force the Guilty to Confession . 26. With some Degree of Capricon , the Dolphin riseth , and breeds all sorts of Swimmers , such as are nimble and active , and perform feats of activity , either in the Water , or on Land. 27. Cepheus rising with some Degree of Aquarius , breeds Men of Morose Tempers , such as are design'd for Guardians , or Tutors , Tragick Poets , and sometimes Comedians , Stage-Players , Pantomimes , and all sorts of Actors . 28. With , the twelfth Degree of Aquarius , the Eagle riseth , and breeds Men of the most violent Tempers , head-strong , and bloody , greedy of spoyl , and destroying every thing that opposeth them ; under-Officers in an Army , and ▪ Armor-bearers to a General . 29. Cassiopeia rising with the twentieth Degree of Aquarius , breeds Founders in Metals , Goldsmiths , Jewellers , &c. 30. With the twelfth Degree of Pisces , Andromeda riseth , and breeds Goalers , and all sorts of Exceutioners , cruel , pitiless and bloody . 31. With the twenty-first Degree of Pisces , the Horse riseth , and breeds strong , vigorous , active Men , excellent Horsemen , either for the Race or War , Farriers , and Physitians 32. With the thirtieth Degree of Pisces , the kneeling Constellation , or Hercules appears ; and his Births are Lewd , Treacherous Villains , given to no useful Arts , at best Juglers and Rope-dancers . 33. With the same Degree of Pisces , the Whale riseth , and produceth Fishers , Fishmongers , makers of Salt , &c. 34. The Bears ( Manilius tells us , what he means by their rising ) are joyn'd with Leo and Scorpio , and breed such as are employ'd in breeding Beasts , and particularly Bears . 35. There follows a fragment , in which the Poet Treats of the several magnitudes or sizes of the Stars , that make up the several Constellations . It is confess'd that Manilius shews no great exactness in the Astronomical part of this Book ▪ but the Astrology is perfect and , may for the most part be apply'd to the most correct Astronomy . HEre at the Signs , those Paths of yearly light , Weak Minds would stop ; nor dare a farther flight : But through the Planets Orbs would take their Course At one full stoop from Heaven , and mark their force ; What Mercury design'd , what Mars did dare , Or Luna thought on in her Gloomy care : What Sol would work , how Saturn look'd on Jove , And Venus manag'd her Intriegue of Love : No farther would their feeble Thoughts aspire , And other Stars had roul'd unheeded Fire . But since I 'm once on wing , and rais'd on high , I 'll boldly soar , and compass all the Sky ; I 'll visit every Star , and strive to know Their proper Powers , and how they Rule below : Avoid no labour , and no toyl refuse , Whilst constant Industry can aid my Muse . Here vast Orion Heaven's great part , the Streams , Whose Spacious Windings mix agreeing Beams ; The Hero's Ship which now midst Stars doth Sail , The frightful Centaur , and the gaping Whale , The Dog , whose Fires o're all the World are rould , The watchful Keeper of the growing Gold ; And Heaven 's high Altar grac't with Gifts invite My eager Muse to take a larger flight . There where the Serpent twines betwixt the Bears , Where rouls the Driver , and still minds his Cares : Where slow Bootes drives his lingring Teams , Or Ariadne's Crown spreads Heavenly Beams : Where Perseus soars with Gorgon's Spoyls above , And weilds his Fauchion to secure his Love : Where wretched Cepheus and his Wife beside The fair Andromeda still Curse their Pride ; Or where 1 oppos'd the scaly Dolphin lies To the swift Shaft , or where the Eagle flies , Or Starry Horse still runs , my Muse must move , And boldly visit every Star above . These I must Sing , their proper Powers explain , How when they rise , how when they set they Reign : And what Degrees they claim from every Sign , And what extend their force , and what confine : For when the World was Fram'd , the Mighty Cause These Powers bestow'd , and did Enact these Laws ; How Signs should singly work , how Stars agree , And settled all things by a firm Decree . First Golden Aries Shines , ( who whilst he swam Lost part of 's Freight , and gave the Sea a Name : Whose 2 Skin destroy'd himself , whose Golden Spoyl Forc't fierce Medea , from her Native Soyl ; Then Magick Arts to Cholchis Shores confin'd First Sail'd abroad , and Poyson swell'd the Wind : ) And now as Victor o're the Conquer'd Deep He keeps his Power , and still Commands the Ship : For when the 3 Northern Rudder rears its Flame , And in the fourth Degree , first joyns the Ram : Who ever 's born , shall be to Sail inclin'd , He 'll Plow the Ocean , and he 'll tempt the Wind ; He o're the Seas shall Love , or Fame pursue ; And other Months , another 4 Phasis view : Fixt to the Rudder , he shall boldly Steer , And pass those Rocks which 5 Tiphys us'd to fear . Had no such Births been born Troy's Walls had stood , No 6 Wind-bound Navy , bought a Gale with Blood ; No 7 Xerxes Persia o're the Ocean roul'd , Dug a new Sea , nor yet confin'd an old . No Athens sunk by 8 Syracusian Shores , Nor Lybia's Seas been choakt with Punick Oars , Nor had the World in doubt at Actium stood , Nor 9 Heaven 's great Fortune floated on the Flood : Such Births as these their hopes to Seas resign , Ships spread their Sails , and distant Nations joyn , The World divided , mutual Wants invite To close again ; and Friendly Ships unite . But when Orion on the left doth rise , Orion 10 the large Portion of the Skies ; At whose appearance Day the Night invades , And frighted Darkness folds her Gloomy Shades : One fit for Business , quick of Mind is wrought , Of Body nimble , and of Active Thought : As if he were the 11 People , all the Town He shall inhabit , every House his own : And one Salute , when 12 Morning peeps , extend Through every Street , to All a Common Friend . But when the Ram first shews thrice five Degrees , The Driver rears his Chariot from the Seas ; And climbs that Steep , whence blustering Boreas brings His North-East Blasts , and shakes their freezing Wings . He keeps his old Concern , and thence bestows Those various Arts which here on Earth he chose . To drive the 13 Chariot , to direct the Course , And hang with forward Lashes on the Horse ; Now press directly , now wheel nimbly round , Out-strip the Wind , nor raise the dusty Ground ; Or cross athwart , and force the rest to yield , Disperse the Crowd , and clear the gapeing Field : And tho' outstript , yet scorn to stoop to Fear , But , drive on Hope , and leave behind Despair . Or midst the Race from 14 Horse to Horse to leap , Sport o're their Backs , and fix the dangerous step : Or singly mounted break the Foaming Jaws , Throw ▪ well the Dart , and force a just applause . Hence influenc't at his Birth 15 Salmoneus strove To vye with Lightning , and to Rival Jove ; His Brazen Bridge , and Chariots fiercely hurl'd Must roar like Thunder , and must shake the World. Vain the attempt : But yet his Pride was high , And now he thought he had brought down the Sky : Proudly he rode , but winged Bolts pursue , And his feign'd Thunder's noise provok'd the True ; He fell , and by his sad Example shew'd 'T was Fate for Man , to be esteem'd a God. The fam'd Bellerophon first view'd the Light When this appear'd , and took his Aery Flight : O're Seas and Land he fled , and first began Through pathless Skies , a way unknown to Man. But when the Ram twice Ten Degrees doth shew , Where on the Right rough Boreas Tempests blow ; The Kids appear : But never hope to find Severe in Manners , nor correct in Mind Their Births ; from them no Censuring Catos come To settle Vertue , and adorn their Rome . No temperate Scipio's , whose obliging Charms The Spaniards Conquer'd , and excell'd their Arms : Too great a work for them , their Rays inspire Soft Love , then heat that Love to fierce Desire : Still urging on , they boyl that Lust to Rage , And Lust , not Courage , make the Youth engage : By Death bafe Pleasure is ignobly bought , And the Misfortune hightned by the Fault : By them are some to keeping Goats inclin'd , The Kids being always mindful of their Kind : Thence Goatherds rise , whose Pipes in every Vale Soft Love inspire , and tell the moving Tale. But when the Ram hath doubled Ten Degrees , And joyn'd seven more , then rise the Hyades ; Whose Births delight in Tumults , hate soft Peace , Seditions seek , and live averse to Ease : The Desks the 17 Gracchi , Souldiers crowd the Town They love to see , and scorn the peaceful Gown . They seek Contention , and when none appears They heighten Jealousies , and nourish Fears . Or meanly bent , they o're the fruitful Plain Their Cattel feed , or drive the lazy Wain : Such Minds these give , such Tempers these bestow , Curst Influence ! rais'd too high , or bent too low . But when the Ram hath trebled Ten Degrees , Shines all above , excluded all from Seas ; The Goat ( whose Bruitish Dugs did once improve The mighty Babe , and nurst the growing Jove ; Who gave him strength to Thunder ) first appears , Breeds timorous Births , and fills their Breasts with Fears . On slight Occasions , they with Doubts are Curst , Suspicious , jealous , fearing still the worst . Or Travellers bent on foreign Lands they breed ; Thus o're the Rocks Goats wander as they feed : Now seek this Plain , and then as fast pursue What tempts their sight , leave old , and seize the new . Thus far the Ram's concern'd , and next the Bull Joyns other Stars , and varies in its Rule : For mounting upward in his backward rise When Six Degrees appear , and grace the Skies , He shews the Pleiades : Whose Rays incline To Joys of Venus , and the Charms of Wine : Feasts their delight , where witty biting Drolls Raise Mirth , and Health swims round in flowing Bowls . Such are these Stars gay Births ; their Face , their Dress They chiefly mind , and 't is their work to please : Offended with their Sex , their Manly Hair With Pumice kill , and Curse those Limbs that bear . Female they seem ; now borrow'd Curls must raise Their Heads , and Love must play in every Maze : Now Gems must bind them up , now loose behind Their Locks must flow , and wanton in the Wind : Affected in their Gate , grow Fops by Rule , And with great study , finish Nature's Fool. Yet high Ambition , and a Thirst to please ( The Name of Vertue covers the Disease : ) Still fire their Breasts , nor from their Souls remove , They would not only Love , but would be known to Love. The Twins succeed , and when their Seventh Degree Swims rising o're the Surface of the Sea ; The Hare appears , whose active Rays supply A nimble force , and hardly Wings deny : The Whirlbats falling Blow they nimbly shun ; And win the Race , e're they begin to run . Let Feasts unbend the Clowns , let Labour yield To Sport and Mirth , and Pastime Crown the Field ; None give so sure , and none avoid the Fall So well ; or catch and turn the flying Ball. To vigorous stroak their active Arms command , Or with their Foot supply the place of Hand . Or when in Sport they shall the 18 Balls divide From Hand to Hand , and toss on every side ; Now throw the flying Globes , and now retain , Or play them back upon themselves again : Now back , now forward , round , and every way O're all their Limbs the active Balls shall play , As taught to know their meaning , and obey . Whilst Crowds admire , and think the constant cares Of Art effect what is the work of Stars . Wak't whilst asleep , they tame by active Pleasure Their growing Troubles , and Sports employ their leisure . Thus those agree . And next my Songs comprise Stars near the Crab , with whom the Asses rise : Then Births appear , whose Skill infests the Woods , Lay Snares for Beasts ; nor do they spare the Floods : On all they Prey , they boldly search the Caves ; Nor are the Fish secure in deepest Waves : Then 19 Meleager rose , whose fatal Brand , And Life too wasted in his Mother's Hand ; Unhappy Noble Youth ! who must attone Her wretched Brothers Slaughter by thy own ! Half bury'd whilst alive ! Whom Love betray'd To give the Hero's Honors to the Maid ; To rob thy jealous Uncles of their Fame , And by their Death secure the Beauty's claim . Then Atalante rose , who prest for Fame Through thickest Woods , and saw and overcame ; Her Dart first reacht the Boar , and wan the Prize , She Conquer'd with her Arrow , and her Eyes ; The Monster groan'd , and Meleager found As much disquiet , and as deep a Wound . Some pitch strong Nets , and some the Woods surround With 20 fear of Death , or slip the faithful Hound : Some dig the treacherous Pits , some spread the Toyls , Or hunt with Spears , and Grace their House with Spoyls . Another puts to Sea , infests the Lakes , Draws monstrous Fish , and starts at what he Takes . Whilst some through Nets the wandring Waters strein , Their Game they follow thro' the pathless Main , Where no Scent lies , yet seldom Hunt in vain . As if the Earth were not profusely stor'd , They fly to Seas , they search what Floods afford , And Nereus from his Waves supplies the Glutton's Board : But when the Crab hath doubled Tèn Degrees , And rear'd seven more , bright Procyon leaves the Seas : His Influence mean ; But tho' his feeble Flame No Hunters breeds , yet it supports the Game : Inclines to Weave strong Nets , to Train the Hound , To know the Breed , and to improve the Sound . To shave the Spear , and follow every Trade , That Love of Sport , and Hope of Gain persuade . But when the Lion's gaping Jaws aspire , The Dog appears , and foams unruly Fire . In Caves scorcht Neptune mourns contracted Floods , Herbs dye , and Beauteous Greenness leaves the Woods ; To other Climates Beasts and Birds retire , And Feverish Nature burns in her own Fire . So vast the Heat , such Flames increase the Sun , As if all Heaven 's great Fires were joyn'd in one . Air 's turn'd to Dust , the Earth's low Entrails burn , And dying Nature fears one common Urn. When this appears , his rising Beams presage Ungovern'd Fury , and unruly Rage ; A flaming Anger , universal Hate With Jealousie make up his Births unhappy Fate : Each little Cause doth scorching Thoughts inspire , Their Soul 's inflam'd , and Words break out in Fire : Yet crowd so fast , they justle as they rise , And part flies out in Sparkles through their Eyes . Their Tongue 's on Foam , and with their Teeth they break Their Words , and Bark when they design to Speak . Besides , excess in Wine inflames their Fire , And Bacchus makes their Fury blaze the higher . They fear no Rocks , nor Woods , but love to Gore The furious Lion , and the Foaming Boar ; They dread no Beasts , but with blind Warmth engage , And to their natural strength infuse their Rage : Nor is it strange that from his Beams should rise Such Tempers ; for above through yielding Skies Averse to Peace , he cuts his furious way , And hunts the Hare , intent upon his Prey . The Lion mounts , and with his last the Bowl Studded with Stars comes up , and cheers the Pole : And then who e're are born , their Minds incline To water Meadows , and to dress the Vine . To Hills , Lakes ; Rivers : To what e're produce The generous Liquor , and improve the Juice : Now Bridegroom Elms they shall in order place , And bring the blushing Brides to their embrace ; Entwine their Boughs : Or when the Stock 's display'd Without support , nor needs a Foreign Aid , In Branches lead it ; and uncurious grown Trust reeling Bacchus to himself alone . Or from the Stock , the hopeful Tendrils tear , Plant them anew , and teach the Twigs to bear . Use all improving ways that Art hath sought , By long Experience , or wise Nature taught : When ripe their Bowls the generous Wine shall Crown , Soften their Cares , and all their Wishes drown ; They largely shall enjoy their Fruits , nor spare The pleasing Recompences of their Care : Happy this State ; but Stars still force them on , And urge their greedy Minds to be undone : For Corn , and Foreign Stores which moisture yields , They 'll Plow the Ocean , and forsake their Fields Till tost by Storms , they midst the Waves resign Their baffled Hopes : And thus the Bowl inclines . Next Shines the Maid , and when the Maid ascends Thrice Five Degrees , the glorious Crown attends . The Crown , since Theseus first his Faith betray'd , The Monument of the forsaken Maid : They give Soft Arts , for here the Virgin Shines , And there the Virgin 's Crown , and each combines Soft Beams agreeing in the same Designs . Births influenc'd then shall raise fine Beds of Flowers , And twine their creeping Jasmine round their Bowers ; The Lillies , Violets in Banks dispose , The Purple Poppy , and the blushing Rose : For Pleasure shades their rising Mounts shall yield ▪ And real Figures paint the gawdy Field : Or they shall wreath their Flowers , their Sweets entwine , To Grace their Mistress , or to Crown their Wine ▪ The Odors fair Arabia's Groves dispense Sovereign for Health , or grateful to the Sense , Shall bath these Wreaths ; for when the Sweets unite , The new Adultery heightens the delight . Besides they 'll study Neatness , learn to dress , Affected grow , and think it Art to please : The present Pleasures Court , and gay desires ; For this the Virgin 's Age ; and this the Crown requires . When with her Tenth Degree , the Sheaf appears , Shews her full Corn , and shakes her loaden Ears : The Fields may fear , for those that shall be born Shall Plough the Ground , and be intent on Corn : They 'll trust their Seed to Clods , whose large produce Shall yield the Sum , and give increase by Vse . Build Barns for Grain , for Nature those contrives , And in the Ear it self a Pattern gives ; In that the Corn lies safe , her Laws ordain A proper different Cell for every Grain : How blest the World , had this been only known , Had Gold lain hid , and Corn been born alone ! Then Men were rich , when they could Want suffice , And knew no Baits for Lust , and Avarice . Yet had they still employ'd their Cares on Corn Alone , those Arts would have been slowly born , Which make Grain useful , and for Common good Grind , Mould , and Bake , and work it up to Food . Now Southward bend , and see in Southern Skies With Libra's Eighth Degree the Arrow rise : Their Beams are strong : They curious Arts bestow , To dart the Javelin , and to draw the Bow ; Or sling the Bullet ; from the lofty Clouds Swift Birds shall drop , nor shall the deepest Floods Secure their Fish : But both shall surely feel The fatal force of the unerring Steel : What powerful Stars but these drew here below Brave 21 Philoctete's and sure 22 Teucer's Bow ? One Hector's Flames repell'd , the angry Fire Did fear his Shafts , and sullenly retire ; The other bore Troy's Fate , more dreadful far , He sate Exil'd , than all the Greeks in War. He own'd those Stars , 23 who when the Serpent lay Twin'd round his Child , and Suckt the Bleeding Prey ; Ventur'd to shoot : The pious Arrow fled As sent by Fate , and pierc'd the Dragon's Head : To be a Father then was Art , and Love By Stars unaided , had but vainly strove ; They drew the Bow , restor'd the flying Breath To the lost Boy , and wak'd the Youth from Death . But when the heedless Goat 24 Exalts his Beard , Alone , as stragling from the other Herd ; Then Tempers quick , and piercing Minds are wrought , With Cares unweary'd , and of active Thought : They scorn that Rest , which private Minds enjoy , But fawn upon the Crowd , and Court Employ ; That 's their delight , and they 're enlarg'd by Fate To serve the Many , and be Slaves of State. Whilst they survive , smooth Knaves shall fear to Cheat In hopes of scapeing , or of grownig Great ; They shall espouse their injur'd Country's Cause , And be severe , yet not exceed the Laws ; Imprison Cheats , or else with rigorous Fines Break their Estates , and curb their lewd Designs . Happy this Temper , would they still pursue These useful Pleasures , and affect the True ; But they 'll from Business , and from Court retire , ( Loose are their Words , and looser their Desire ; ) Lewd Love and Wine indulge , and wast their Age In Mimick Dancing , or affect the Stage . Next shines the Harp , and through the Liquid Skies The Shell as lightest , first begins to rise ; This when sweet Orpheus struck , to listning Rocks He Senses gave , and Ears to wither'd Oaks ; Parch'd Pluto's 25 Cheeks grew moist , and Death resign'd Her Spoil , and unrelenting Fates grew kind . These skill in Musick , and in Songs impart ; How Sound is vary'd into Notes by Art Their Births shall know : Their Mouths shall Pipes inspire With voice ; Their Hands shall strike the speaking Lyre : At merry Feasts they shall the Guests delight , Smooth Wine with Songs , and stay the flying Night . Nay e'en when Troubles , and when Cares oppress , Their Mournful Lays , shall give their Sorrows Ease . Low Murmurs shall employ their warbling Tongue , And their own Ears shall always hear a Song : Below fierce Scorpio , when his Eighth Degree Appears , the Altar riseth from the Sea : No Lightning arm'd Jove's Hand , no Thunder roard Till here as Priest he stood , and first ador'd ; Then Powers unknown assisted , Clouds did swell With Fire , and the Devoted Giants fell : And who should then be born , but those that wait On Sacred Temples , and converse with Fate ? That Hymn in Holy Quires , know what 's to come , Are almost Gods , and can dispose of Doom ? With Twelve Degrees the Centaur's Form appears , And gives a Temper from the shape he bears ; For he that then is born , and feels his force , Shall harness Mules , or he shall drive the Horse ; Or he shall proudly mount the ratling Car , Or Arm the Steed , and lead him forth to War ; Or he shall study what Disease infests , And Ease apply to uncomplaining Beasts ; Or he shall keep them sound , his Art be shown In sure Prevention , nor expect a Groan . Next Sagittarius mounts with threatning Bow , Whose Fifth Degree doth bright Arcturus show : And he that then is born shall ne're be Poor , To him rich Fortune shall entrust her Store ; King's Treasures he shall keep , and Reign alone , Whilst those sit only higher in the Throne : Or if a Private House confine his Care , Blest he shall live , and see the thriving Heir In Wealth increast ; Or he shall still defend The People's Right , and be a Common Friend . But when this Centaur hath advanc'd his Fire Thrice Ten Degrees , and shews his Horse entire ; The Swan displays his Wings ; And then by Fate The Birds for an Enployment , and Estate Are given to every Birth : Nor can the Skies Make better claim to every Fowl that flies ; And hence to seize their own , they oft declare Against the Sky it self an open War ; They take them flying , or they set their Toyls On Boughs or Fields , and catch the Feather'd Spoils . Sometimes besiege their Nestswith treach'rous Reed , Or draw the Net , and take them whilst they feed : Thus Luxury toyls ; bold Luxury ventures far To Foreign Lands , and Travels more than War : Numidia's Plains , and Cholcos Woods afford Delicious Tribute to the Glutton's Board . Or Nature's stubborn Laws their Art shall break , Enlarge Converse , and teach the Birds to speak . The 26 Swan still shrouds a God , 't is more than Fowl , The Feather'd part confines a noble Soul ; And when cold Death comes on , the God dilates His Powers , and softly murmurs o're his Fates . Or they on Doves shall all their Cares employ , To make them Thrive , or teach them to decoy , Or carry Messages ; the Birds convey Their Masters Orders , nor mistake their way : They know this Star , and they this Influence own , Who carry sportive Birds about the Town ; Who with one Sparrow wretched Life maintain ; These are his Powers , and thus inclines the Swan . When Ophieuchus mounts , and joyns the Goat , Those that are born shall live an Antidote To strongest Poyson ; they may safely take The frightful Serpent , and the Venom'd Snake Into their Bosom : Whilst the Monster 's Cling About their Bodies kils their fiercest Sting . When the South Fish doth leave the Floods , and rise To Airy Seats , and swims in Liquid Skies ; Those that are born in every Shore shall lay Their Lines and Hooks , and catch the hanging Prey ; No Fish in their own Shells shall safely live By Nature fortify'd , whilst these can dive , All shall be dar'd ; and they immerst shall rove Thro' Depths , despair'd , and lost to those above ; Till with their dancing Prey they mount again ; So small is the reward of all this Pain ! Or Fish for Pearls , for Avarice cheats the Mind By valuing Things not for their Worth , but Kind . Vile Shells , which Nature midst the Floods hath laid , Asham'd of the mean work that she hath made ; When drawn up hither equal Provinces ; Nor can the Land now bear the Riches of the Seas : Such are the Tempers , and Success that waits On these Stars Influence , and compleats their Fates . Or free from danger they incline to gain By Merchandise , what others get by Pain . Before I sung the Harp's Commanding Powers , And taught the Influence of its fatal Hours ; Back to the same my Muse doth now retire , Pleas'd with the sounding Vertues of the Lyre : For when its gay Harmonious Strings appear , Let Sin grow Pale , and Villains learn to fear : For subtle Judges , whose Demands shall draw Pale sculking Guilt within the reach of Law , Shall then be born ; or else the Births shall dare To screw the Rack , and make the Wretch his Sin declare ; Steel'd against Pity , and averse to Spare . All Pains inflict , be Cruel without Hate , And make stern Justice wield the Sword of Fate : Or if soft Methods can prevail , the Cause They gravely shall determine by the Laws : As Wisdom gave the Sentence , Strife shall cease , Both sides be pleas'd , at least consent to Peace . But when the Dolphin's Fires begin to rise With Stars like Scales , and swim in Liquid Skies ; It shall be doubtful which shall most Command The Inclination for the Sea or Land : Both shall conspire , and in one Mass combind , Now this way draw , now that way force the Mind : For as the Dolphin mounts , now dives again , Now turns , now leaps , and figures all the Main : So those that shall be born shall now divide With wide stretcht Arms , and beat the swelling Tide ; Now thrust them downward , and with secret Oars Their Bodies row , and visit Foreign Shores ; Now tread the Water , with their Feet maintain Themselves Erect , and wade the deepest Main , As t' were a shallow ; like the firmest Field , The Floods shall bear them , and refuse to yield : Now on their Backs or Sides securely keep One constant place , and lie upon the Deep : No Oar to Boy them up ; but Floods forget Their natural yielding , and sustain the Weight : Or they shall dive , through boundless Oceans go , And visit Nereus , and the Nymphs below ; Or take up Shipwracks , Merchants Spoils restore , And rob the greedy Ocean of its Oar. To these joyn those , who from an 27 Engine tost Pierce through the Air , and in the Clouds are lost ; Or poize on Timber , where by turns they rise And sink , and mount each other to the Skies : Or leap through Fire , and fall on hardest Ground As on soft Seas , unhurt , and safe from Wound : Tho' void of Wings , their Bodies boldly rear , And imitate their Dolphin in the Air. Or if they want the skill , yet Nature's part Perform'd , they shall be nimble without Art : Not run , but rather fly , be swiftly born O're Fields of Wheat , nor bend the standing Corn. When with Aquarius Cepheus mounts , require No sportive Tempers from so grave a Fire : But stiff , morose , severe , affected Fools , With Looks as starcht , and heavy as their Souls : Whose Guardian 's roughness , or an Uncle's force Praise , and in Cato's Sentences Discourse : Design'd for Tutors , whom the noble Heir , Altho' he keeps them , shall be forc'd to fear ; Shrink at their Nods , and of their Looks afraid , Worship th' Imperious Idol he hath made . Or Tragick Poets ; Those whose Style must slay In Paper , and be Barbarous in a Play : Who must kill Heroes to delight the Crowd , And seek to please with Horror , and with Blood : Antigone 28 must fall the Tyrant's Spoil , And Brothers disagree upon their Pile : Thyestes eat his Babes , the Sun retire , And jealous Rage the mad Medea Fire ; Her Father , Brother , Sons must Murder'd lie , Whilst Dragons bear her through the Guilty Sky : Or she must Youth renew ; such Themes as these Shall raise their Thoughts , and make them strive to please . But then if softer Themes their Fancies move In Comedy , the heated Youth shall Love ; The Maid be stoln , the witty Slave defeat The covetous Father , and enjoy the Cheat. Thus fam'd 29 Menander in immortal Rhymes Exposeth Humour and instructs the Times ; Nature to him her Parts might safely trust , His Words expressive , and his Thoughts were just ; And when he copy'd her , she hardly knew Her own Original ; he wrought so true . But if unequal to a Poet's Rage They cannot Write , yet they shall serve the Stage . Their graceful action and their voice shall raise The native value of another's Plays ; The School's Simplicity , the Court's Address , The Souldier's Huff so decently express ; As if they acted not another's part ; And all was simple Nature , and not Art. In one short view they shall present to sight Whole Crowds , make Kings engage , and Armies fight : Before the pleas'd Spectators Troy shall lye In ruins , and the wretched Priam dye . But now the Eagle must my Songs employ , He shines upon the left hand of the Boy , Whom first from Earth he did to Skies convey , And now with wide stretcht Wings hovers o're his Prey . This Bird , the Armour-bearer of the Skies , Brings back thrown Thunder , Jove with Arms supplies , And with the Youth 's twelfth part begins to rise . And then shall spring a violent ravenous Brood , Eager to rob , and purchase Spoil with Blood : On Men and Beasts with equal Lust they seize , Nor make a difference between War and Peace . Their Friends and Enemies alike they awe , They every thing to wild contention draw , Their Will their Ruler , and their Sword their Law. But if their Violence aright they place , Their Vice turns Vertue ; conquer'd Spoils shall grace Their happy Country ; when in Arms they dare , Success shall wait , and Victory crown their War. But since the Eagle is employ'd above Not to throw Thunder , but to wait on Jove , And bring him Arms , they hope in vain to bear The highest Office , and Command in War ; They must be meaner , equal to their Star : Wait on a General , bear his ponderous Shield , And serve him bravely in the dangerous Field . When mourning Cassiopeia , grac'd with Stars , Upon the left hand of the Youth appears , And joins twice ten Degrees , her Beams impart In Metals skill , and fill the Births with Art : The precious Matter they shall nobly mold , And raise the native value of the Gold ; Hence shine our Temples , and our Roman Jove Fills here a Heaven as bright as that above ; Happy this Art employ'd on things Divine , To frame a Statue , or adorn a Shrine ; But now how low her Head she strives to hide , Whilst chain'd to Luxury , and a Slave to pride ! Now precious Metals common Roofs enfold , Rival the Temples , and we feast in Gold. But great Augustus doth its state maintain , Shews its old worth , and makes it rise again ; His Temples shine , and now such Works are wrought As Mithridates lost when Sylla fought ; The Sun 's outshone , and Caesar's glorious Gems Excel the native lustre of his Beams : And hence with joy we view that wondrous Prize , The Monuments of 30 Pompey's Victories ; Though those did first a Lust for Gems inspire , Which still burns new , and spreads a growing fire ; The Ornaments of Kings now serve to grace A shape , and raise the value of a Face ; Now Neck , Feet , Hands are deckt , and every Dress Shines with the Spoils of groaning Provinces ; Yet 't is the Ladies Sign , their wants supply'd Advance its worth , they love what decks their Pride : Lest want of Matter should the Work restrain , The Art grow idle , and the Sign be vain , By the same Powers are wretched Men decoy'd To dig for Oar , and work to be employ'd ; To turn the Globe to search where Metals breed , And see young Gold first blushing in its Seed ; Harmless it lies , 'till the mistaken worth Deludes poor Man , and brings the Monster forth . And lest Temptations too obscure should lye , Too far remov'd from every common Eye , Mixt with the Sands they shine on every Shore , These he shall gather , and extract the Oar , Or dive for Jewels , and , intent on Gain , Pierce thro the Floods , and search the deepest Main ; Draw Gold and Silver from the Waves embrace , And work them singly , and adorn the Mass ; Or in Electrum both ignobly join : These are the Powers and Tempers of this Sign . Next shines Andromeda ; she leaves the Sea , And on the Right joins Pisces twelfth Degree . Bright she appears , and gay with sparkling Fires , As when young Perseus first felt warm desires . Unhappy Maid ! expos'd to rage Divine , A faultless Victim for her Mother's Sin : When Seas let loose o'reflow'd the fruitful Plain , And Earth now fear'd its ruin from the Main ; Nought could appease , but to the injur'd Flood The Maid resign'd , to quench its rage with Blood. This was her Bridal , in her Robes of State ; But not provided for so sad a Fate , Glorious she lookt , and like the setting Sun , Greater , tho not so sierce , her Beauty shone . No joyful Torch its ominous Flames did spread , No Vows were heard to crown her fruitful Bed ; But Groans and Tears , e're Death pronounc'd her doom The Maid was born alive to her own Tomb. Hence fly my Muse , and on the naked Shore Leave the poor Maid , and dare to look no more ; 'T will melt thy Song to turn again to view , The weeping Parents bid their last adieu ; To see her fetter'd , and expos'd to pain , Design'd by Nature for another Chain : To see her hang on Rocks , and by her side Grim Death appear , and point to the swoln Tide . Yet turn , and view how she her Shape retains , How fair she looks , and glorious in her Chains : With what becoming fear her flowing Vest Forsakes her Limbs , and leaves her naked Breast : What hidden Beauties are expos'd to sight , Like Lightning glare , but must be lost in night . By her the Halcyons mourn'd , and round the Coast , That so much Beauty should in vain be lost , The Nymphs repin'd ; and Nereis from the Deep Bewail'd her Fate , and did consent to weep : The gentle Breeze that fann'd her golden Locks , Turn'd into Sighs , and murmur'd to the Rocks : All Nature seem'd concern'd , despairing Grief Was general , but too weak to yield relief . Then Perseus , glorious with the Gorgon's Spoil , By Love directed to a nobler Toil , Kind Fortune brought ; and at the wondrous sight He checkt his Horse , and stopt his airy flight ; His Hand scarce held his Spoil , Medusa's Eyes He bore , but now grew stiff at this surprise ; The Chains that held her , and the burth'ned Stone He happy call'd , and envy'd joys unknown . Amaz'd a while he hung , her Form survey'd , Then heard the Story from the weeping Maid ; Streight in his Breast high generous thoughts were bred , To spoil the Ocean to adorn his Bed : And should a thousand frightful Gorgons rise ; He would oppose them for so vast a Prize : Fixt on these Thoughts he leaves the mournful Shore , Her Parents chears , and bids them weep no more , For Aid was come : And their Consent desir'd Was granted soon , and nobler warmth inspir'd . Back he returns : Now teeming Seas did roar , Waves fled the Monster , and o'reflow'd the Shore ; High rais'd his Head , he spouts the Floods around , All Nereus ecchoes , and the Shores resound : Wide gapes his Mouth , and as on a vast Rock Dasht on each Tooth the foaming Billows broke : His winding Tail o're half the Main was spread , The Ocean groan'd , Rocks fear'd , and Mountains fled : Unhappy Maid ! though such an Aid was near , What was thy Mind , and how surpris'd with fear ? How pale thy Look ? and how thy Spirit fled In a deep sigh , and hover'd round thy Head ? How bloodless all thy Limbs , when from deep Caves The Monster rush'd , and bore the foaming Waves And Fate along ? and all design'd for thee A Prey how little , for so vast a Sea ! But Perseus nimble Aid descends , and hides The Gorgon's Fauchion in his scaly Sides ; He twists upon the Wound , then strives to rear His head , and shoots up forward thro the Air : Perseus retires , and still deludes his Foe , Hangs in the Sky , and aims a surer Blow : He presses on , and casts his Jaws around , Bites at the Air , but bites without a Wound . Then tosses Seas to Heaven , spouts purple Floods At his high ●oe , and drowns him in the Clouds . The Maid beheld this Fight , and , grateful grown , Fear'd for his danger , but forgot her own ; Doubtful which way the various Fate inclin'd , In Body less suspended than in Mind : Her doubt not long ; for now Success did prove The great advantage , and the force of Love ; The Monster groan'd , and from his Wounds there flow'd A mighty Stream , and stain'd the Seas with Blood. Down deep he sinks , but soon he floats again , And his vast Carcass covers all the Main ; Breathless he lay , yet then his shape did fright ; Tho dead , he was too dreadful for her sight . Now big with Conquest , from the cleansing Flood Bright Perseus rose , and more August he stood ; Then to the Rocks with eager haste he flies , Unbinds the Virgin , and enjoys the Prize . And thence Andromeda now shines a Star , The Cause , and the Reward of such a War , As freed the Ocean , and restor'd the Main To Neptune's sway , and fixt him in his Reign . And he that sees her rising Beams , shall draw The Sword of Justice , and shall smite by Law ; Dungeons shall be , and Whips and Racks his care , Steel'd against Pity , and averse to spare . At his stern feet shall wretched Wives complain , And weeping Mothers tell their grief in vain : Though late at night to kiss a parting Son , And draw his flying Soul into his own ; A Father sues , in unrelenting Ears His Prayers are lost , nor shall he yield to Tears . Or lean pale Hangmen shall her Beams create , Those solemn Murderers and Salves to Fate : Who on the Curses of the pitying Crowd Ignobly thrive , and live on shedding Blood. But he that sees her chain'd to Rocks , shall find A meaner Fortune , though as fierce a Mind ; A Goaler he shall be , secure for pains Poor Slaves , and be a 31 partner of their Chains . With Pisces twenty first Degree to fly The Horse begins , and beats the yielding Sky ; His Births shall Health , and vigorous Strength enjoy , For Action quick , and nimble for employ . They in thick rounds shall rein the manag'd Steed , Or sweep the Plain , deceiving with their speed : Or proudly mounted they shall boldly dare Heroick Acts , and lead the Crowd to War : Or else be nimble Messengers , and move With greater swiftness than a flying Dove ; Send both with like Advice , the one shall bring Returns , whilst t'other lags with lazy Wing . Or they shall study Herbs , and strength impart To Beasts , and e'en to Man enlarge their Art. But now go on ; with Pisces last Degrees , The humble Constellation on his Knees O' th' Right appears : And those that then are born No vertuous Powers , nor useful Arts adorn , But they 're for treachery , mischief , spoil design'd , Guilt 's in their looks and Rapine in their mind . Or if to Arts he shall incline the Breed , Such , where the Danger doth the Skill exceed , They chiefly follow ; 't is their only scope To mount a Precipice , or dance a Rope ; Tread 32. Airy steps , and whilst thro Clouds they reel , Draw up the Crowd , and hang them at their heel . But on the Left is open'd to our view The Whale , who now doth thro the Skies pursue With eager haste , as thro' the injur'd Flood The fair Andromeda , and still thirsts for Blood. And He that then is born shall be inclin'd To spoil the Sea , and kill the Scaly Kind , No Fish shall swim secure whilst Nets can sweep The troubled Ocean , and confine the Deep : Those that but now could wanton or'e the Main Shall lye fast bound , and wonder at their chain ; Till with a touch He shall the Cords command , And draw the Dancing Captives to the Land. Or whilst He shoals expects e'en midst the Flood Destroy , and stain the Ocean with their Blood. Yet then his works not cease , or pains decay , His various Arts encreasing with his prey : For on the Shore He shall his spoil divide For different uses . This when lightly dry'd Is better Meat ; and that when moist is good , Whilst other parts are hardned into Food . Could Gluttons see , they would not bear the sight Of preparations for their Appetite , Whilst Blood and Guts in a polluted Mass Lye mixt , and are corrupted into Sauce ; Till all in filthy Gore distils to treat The fashionable Palate of the Great . Or if to meaner Arts his Thoughts encline , Then Salt's his care ; he shall the Floods confine In narrow Pitts , and to the Beams expose , Till what was liquid now a solid grows , Then lay the crusted froth with careful hand In heaps , and cleanse it , and divide the Sand. And thus the brackish and unwholesom Flood Proves vital Salt , and Poyson 's turn'd to Food . The Great and Lesser Bear which still maintain One constant Round , and never touch the Main , Scarce know a Rise ; yet when each front appears , Take that to be the rising of the Bears . The First with Leo , and the last is join'd With Scorpio , and prove friendly to their kind . For those that then are born to Beasts shall bear Kind tempers , and oblige them by their Care ; Give Law to Lions , with a Panther play , Teach Tigers peace , and make a Wolf obey ; Maintain Converse , and give them Arts unknown , And such as Nature never thought her own . But yet their thoughts to Bears shall most incline , And there improve the Kindred of their Sign . Or ride the Elephant , his Bulk command , And make the Monster tremble at their Wand . Base the submission , where such strength in vain Possess 't must tamely yield to feeble Man : The third siz'd Stars the Pleiad's form do grace , They shine with virgin blushes in their face : Four in the Dolphin are observ'd to rise , And in Deltoton Three of equal size : The same the Eagle , and the Bear display , Nor can the Draco boast a greater ray ; Of size the Fourth and Fifth securely take A measure from the others of the Snake . But yet the greatest part we spare to note , Too small to be discern'd , or too remote : These lye obscure , and seldom spread their light , But when the Moon 's withdrawn to lower Night , When great Orion from the Skies retires , Plunges in Waves , and quenches his bright Fires ; Or when gay Phoebus doth his sway resign To shades , then They have a short leave to shine , Then Heaven with little Lights is spangled o're , That not the Sand upon the crooked Shore , That not the Billows in Tempestuous Floods , That not the leaves when Autumn shakes the Woods , Can equal the great Train ; they all surmount , E'en Number is too short for the account . And as in Cities , where in ranks decreed First 33 Nobels go , and then the Knights succeed , The next in order may the People claim ; The Rabble next , a Croud without a Name : So is the Heaven by different ranks possest ; Some like the Nobles with more rays are drest , Some shine with less , the numerous crowd with least : Were these endow'd with a proportion'd heat , Were they in Power , as they 're in number great ; They long ago must have dissolv'd the Frame , Nor could the world have born so fierce a Flame . The End of the fifth Book . NOTES . 1. — Celerique Sagittaè Delphinus certans — We may read , — Celerique Sagitta Delphinus certans — and interpret the words , not as others do , The Dolphin seated opposite to the Arrow : But The Dolphin of equal swiftness with the Arrow . 2. The Ram having a Golden Fleece , as the Poets fancy'd , the King of Jolcos kill'd him that he might enjoy the Treasure , and Jason being sent to fetch this Golden Fleece carried away Medea the King's Daughter . 3. The Ship hath two Rudders , a Northern , and a Southern Rudder . 4. A River of Jolchos , whither Jason with the Argonauts first Sailed . 5. Typhis , the Pilot to the Argonauts , who in his Voyage steer'd thro' the dangerous moving Rocks called the Symplegadae . 6. The Graecian Navy lay Wind-bound till Iphigenia was Sacrificed , and appeased the anger of Diana . 7. Vossius , in his Observations on Catullus , Reads — Invehet undis Persida — The Expression is bold , and therefore proper for the Poet . That Xerxes dug a new Channel , and made a Bridge over the Hellespont , are known stories . 8. Manilius mentions several notable defeats at Sea , such was that of the Athenians near Syracuse , which brought the Athenians very low : such were those of the Carthaginians by the Romans : And that of Antony by Augustus near Actium . 9. Heavens great Fortune : Because the Conquerour was to be deify'd . 10. Orion is a very large and bright Constellation , and deserves this pompous Description . 11. Instar erit Populi : This is one of Manilius's bold Expressions , which my English cannot reach . 12. Alluding to the officious Salutations , which the Clients amongst the Romans carried early every Morning to their Patrons . 13. Manilius is very accurate in describing the particular Niceties observ'd in the Roman racing : Those are not now observ'd amongst us , and therefore we must be content with such Expressions as our Language will afford . 14. An Exercise much us'd amongst the Romans ; the Horse-man rode one Horse , and led another , and in the midst of the Race would throw himself on the led Horse , and so back again as often as he was required ; or else would stand upon the Horses back , and in that posture ride the Course . 15. Salmoneus built a Bridge of Brass , and driving Chariots over it fancy'd he Thundred : This he did to procure himself divine Honours , but was kill'd by a Thunder-bolt for his impious attempt . 16. The Poets fancy'd Bellerophon rode upon the flying Horse Pegasus . 17. A Family amongst the Romans , famous for their seditious Harangues , which they made to the People of Rome out of the Desks , or Rostra , standing in the Market place . 18. Amongst the Romans one Man would take several Balls , and toss them , sometimes behind , and sometimes before , now on this hand , and now on the other , so that some of them should be always up in the Air : And this feat of Activity Manilius Describes . 19. The Story of Meleager runs thus : At his Birth his Mother heard one of the Destinies say , the Child should live till the stick that then lay in the Fire was burnt : The Mother snatch'd the stick out of the Fire , and perserv'd it . When Meleager was grown a Man , he with a great many others went to hunt a Wild Bore ; at the same time Atalante a Nymph of extraordinary Beauty came into the Field , and had the good Fortune to wound the Bore first : Meleager fell in Love with Atalante , and having kill'd the Bore presented the Head to her : His two Uncles who were present at the Hunting thought themselves injur'd , and would not suffer a Woman to carry off their Spoil . Meleager in defence of Atalante kills his two Uncles : Meleager's Mother , to revenge the Death of her two Brothers , puts the stick into the Fire , as that burnt Meleager wasted . 20. Formidine Mortis : Huetius Reads Formidine Pennae : For when they Hunted , they us'd to see stakes in the ground , to which they ty'd Feathers which frighted the Deer , and made them keep within that compass , or take that way the Hunters thought most convenient for their sport . 21. Philoctetes was Servant to Hercules , and when Hercules burnt himself , he left his Bow and Arrows to Philoctetes : Without these Arrows Troy could not be taken : Now it happened that Philoctetes , either by a contrivance of Vlysses , or because , being wounded by one of the Poisoned Arrows , he became offensive to the Grecian Camp , was sent away to Lemnos : But the Siege going on slowly , he was fetcht back again : With his Arrows he killed the chiefest of the Remaining Commanders , and so Troy was taken . 22. Teucer was Brother to Ajax , and he with his Bow beat back Hector when he came to burn the Grecian Navy . 23. The following Verses relate to Alcon the Cretan , who shot a Snake that lay twisted round the Head of his Son , and did not touch the Boy . 24. This Goat or Hoedus Scaliger could not find , but Huetius says , the Single Hoedus is put by Manilius for those two Haedi that are in the left hand of Heniochus , or the Driver . Thus Horace . — Archeri cadentis Impetus , aut orientis Hoedi , and Propertius Purus & Orion , purus & Hoedus erit . 25. The Poets fancy'd Orpheus went down to Hell , charm'd Pluto and the Destinies , and brought back his Wife Eurydice . 26. Alluding to the Fable , which says Jupiter Courted Leda in the shape of a Swan . 27. Several Feats of Activity amongst the Romans , in which they equall'd if not excell'd all the following Ages . 28. The common Subjects upon which Sophocles , Euripides , and other Tragaedians amongst the Ancients wrote their Plays . 29. A fam'd Comedian , who flourish'd in the hundred and fourteenth Olympiad . 30. Pompey having conquered Mithridates , brought to Rome more valuable Jewels than ever had been seen there : And from that time , as Pliny in the first Chapter of his 37th . Book complains , the Romans began to value and admire Jewels . 31. The Romans did not only put Notorious Malefactors in Chains , but likewise chained them to their Keepers ; and this Custom the Poet hints at . 32. Vossius out of his Ancient Manuscript reads , Et Coeli meditatus iter vestigia perdet , Et Perna pendens populum suspendet ab ipsa . 33. These were the several Orders in the Roman Common-Wealth . FINIS . INDEX . A. AStronomy , its rise and progress , part 1. p. 3. Axis of the World , part 1. p. 13. Plague of Athens , part 1. p. 34. Aspects , part 1. p. 60. Aspects friendly and unfriendly , part 1. p. 74. Aries's Influence , part 2. p. 9. et 24. Aquarius's Influence , part 2. p. 15. et 27. Astronomy to be studied , part 2. p. 39. Aries's Influence when join'd with other Constellations , part 2. p. 56. Aquarius's Influence when joyn'd with other Constellations , part 2. p. 72. The Fable of Andromeda , part 2. p. 76. C. Northern Constellations , part 1. p. 14. Southern Constellations , part 1. p. 17. Figures of the Constellations not real , part 1. p. 20. Northern Polar Circle , part 1. p. 24. Tropical Circle of Cancer , part 1. p. 24. Equinoctial Circle , part 1. p. 24. Tropick of Capricorn , part 1. p. 24. Southern Polar Circle , part 1. p. 25. The Colures , part 1. p. 25. Comets presage , part 1. p. 34. Chaldeans refuted , part 1. p. 106. and 110. Cancer's Influence , part 2. p. 11 et 25. Capricorn's Influence , part 2. p. 14. et 27. Countries govern'd by particular Signs , part 2. p. 36. The Influence of Cancer join'd with other Constellations , part 2. p. 61. Capricorn's Influence when join'd with other Constellations , part 2. p. 70. D Dodecatemorion , part 1. p. 76. Dodecatemoria of the Planets , part 1. p. 77. Day Births , part 1. p. 104. Bad and good Degrees of Signs , part 2. p. 21. E. Earth the Center of the Vniverse , part 1. p. 9. Earth round , part 1. p. 10. Geographical description of the Earth , part 2. p. 28. Eccliptick Signs , part 2. p. 38. F. Friendship , part 1. p. 72. Fortune's Lot , part 1. p. 103. Fate , part 2. p. 4. G. Guardians of the Signs , part 1. p. 66. Gemini's Influence , part 2. p. 10. et 25. The Influence of Gemini when join'd with other Constellations , part 2. p. 60. H. Horizon , part 1. p. 26. Influence of the Heavens , part 1. p. 51. Signs hear and see , love and hate each other , part 1. p. 67. The Celestial Houses , part 1. p. 80. Horoscope , part 1. p. 105. Hours various , part 1. p. 106. L. Twelve Lots of the twelve Signs , part 1. p. 99. Leo's Influence , part 2. p. 11. et 26. Libra's Influence , part 2. p. 13. et 26. Leo's Influence when join'd with other Constellations , part 2. p. 63. Libra's Influence when join'd with other Constellations , part 2. p. 66. M. Meridian part 1. p. 26. Milky way , part 1. p. 27. Various Opinions about the milky way , part 1. pag. 29. Meteors , part 1. p. 32. The several Magnitudes of the Stars , p. 2. p. 82. N. Night Births , part 1. p. 104. P. Southern Pole like the Northern , part 1. pag. 19. Providence asserted against Epicurus , part 1. pag. 21. Planets , part 1. pag. 32. Pisces's Influence , part 2. p. 15. & 27. Pisces Influence joyn'd with other Constellations , part 2. pag. 76. Q. Quadrates , part 1. pag. 61. S. Soul of the World , part 1. p. 12. & 51. The several kinds or sorts of Signs , part 1. p. 55. Sextiles , part 1. p. 63. Stadia , part 1. p. 108 , The several positions of the Sphere , part 1. p. 110. Scorpio's Influence , part 2. p. 13. et 26. Sagittarius Influence , part 2. p. 14. et 27. Sagittarius Influence when join'd with other Constellations , part 2. p. 69. Scorpio's Influence when join'd with other Constellations , part 2. p. 68. T. Trines part 1. p. 60. Taurus's Influence , part 2. p , 10. et 25. Tenths , or Lords of the Signs , part 2. p. 16. The Influence of Taurus join'd with other Constellations , part 2. p. 60. V. Virgo's Influence , part 2. p. 12. et 26. Virgo's Influence when join'd with other Constellations , part 2. p. 65. W. Different Opinions about the Beginning of the World , part 1. p. 7. The order of the World , part 1. p. 8. The bigness of the World , part 1. p. 23. The World animate , part 1. p. 51. Winds cardinal and collateral , part . 2. p. 28. Z. Signs of the Zodiack , part 1. p. 13. Zodiack , part 1. p. 27. ERRATA . Part I. PAg. 5. lin . 7. read lookt . pag. 12. l. 2. r. feet . p. 15. l. 27. r. stretch . p. 16. l. 33. r. the Tempests . p. 19. l. 15. r. their starry . p. 24 l. 15. r. Light. l. 18. r. Summer's Solstice . l. 22. r. sees . p. 46. l. 19. r. Fayus . p. 47. last line r. World. p. 49. l. 6. r. preside . p. 51. l. 22. r. Purle . p. 53. l. 2. r. draws . p. 59. l. 13. r. Cretan . p. 65. l. 31. r. Times . p. 66. l. 17. r. to more . p. 70. l. 16. r. then . p. 75. l. 26. r. which , and marks . p. 76. l. 21. r. which . p. 77. l. 10. r. Twelfth . p. 82. l. 32. r. point . p. 83. l. 6. r. Influence . p. 84. l. 6. read Typhoeus . l. 16. r. t is . p. 86. l. 17. r. the. p. 97. l. 9. r. sells . p. 100. l. 27. r. speeds . p. 104. l. 4. r. unfold . p. 107. l. 23. r. Carr. p. 109. l. 8. r. do equal . p. 110. l. 26. r. site . p. 114. in the margin blot out the Trine . l. 24. r. regularly . p. 116. l. 13. r. longest . p. 119. l. 15. r. she . p. 121. l. 28. r. fails . p. 124. l. 8. r. is . Part II. PAg. 4. lin . 24. read Marius . p. 8. l. 10. r. enlarge . l. 19. r. Successes . p. 10. l. 18. r. wasts . p. 16. l. 28. r. o're-spread . p. 17. l. 2. r. in a Disguise . p. 26. l. 3. r. averse . p. 31. l. 2. r. stood . p. 32. l. 7. r. which . p. 33. l. 21. r. manly , l. 28. r. flats . p. 39. l. 7. r. Pairs . p. 55. l. 9. r. Carr. l. 30. r. Carrs . p. 59. l. 6. r. makes . p. 67. l. 18. r. growing . p. 70. l. 18. r. kiss . p. 72. l. 33. r. who . p. 83. l. 22. r. nor . Notes, typically marginal, from the original text Notes for div A51767-e230 1 Vid. Not. ad Lucianum . 2 By Scaliger and Huetius . 3 Nat. Hist . lib. 36. cap. 10. 4 Gerbertus Rhemensis Bishop of Ravenna , and afterward Pope of Rome , Epist . 130. Age verò , Te solo conscio , ex tuis sumptibus fac mihi scribantur Marcus Manilius de Astrologia , Victorinus de Rhetorica , &c. 5 De Ponto , lib. 4. Ep. 16. 6 This Huetius affirms , but is undoubtedly mistaken . 7 Ovid. ibid. 8 Aptaque venanti Gratius arma dedit . Ovid. ibid. 9 Instit . lib. 10. Cap. 1. 1 Instit . lib. 1. cap. 10. 2 Praef. 3 Lib. de Poet. Hist . dial . 4. 4 Lib. 1. v. 7. 5 Lib. 1. v. 10. 6 Lib. 1. v. 906. 7 Lib. 1. v. 918. 8 Lib. 4. v. 763. 9 Lib. 1. v. 896. 1 Lib. 1. v. 912. 2 Not. in Lib. 6. Lucretij . 3 De Arte Gram. lib. 2. cap. 26. 4 Lib. de Poet. Lat. 5 Phys . Sect. 2. lib. 6. cap. 2. Ptolomaeus , Firmicus , Manilius primarij hujus Artis Script●res . vid. etiam p. 717. & pag. 740. 6 vid. Cambd. Epist . p. 260. 7 Vid. Not. in Statij . lib. 3. Syl. Carm. 3. 8 His Electa were almost finisht A. D. 1618. vid. Cambd. Epist . p. 259. 9 De praestantia & Vsu Numismatum . pag. 643. 1 Cod. Theod. l. 38. t. 1. de Decur . 2 Not. ad Manil. 3 Sal. de An. Climact . p. 560. 4 Not. ad lib. 4. v. 298. 5 Lib. de Poet. 3. Dial. 4. 6 Scal. Proleg . in Manilium . p. 3. 7 Praef. ad Not. 8 Not. ad Aug. script . 9 Vid. Not. in Manil. 1 De Poet. Lat. 2 The Editor of Manilius in usum Delphini . 3 De Mallii Theod. Consul . v. 251. 4 ibid. 274. 5 ibid. v. 126. 6 ibid. v. 332. 7 ibid ! v. 84. Ibid. v. 65. 8 Ibid. v. 253. 9 ibid. v. 101. 1 Lib. 1. v. 7. 2 lib. 1. v. 9. et 924. 3 lib. 2. v. 509. 4 Car. lib. 1. Od. 2. Hic ames dici Pater atque Princeps . 5 Virg. Ec. 1. et Georg. 1. 6 〈…〉 Aug. cap. 94. 7 de Num. Herod . p. 9. 8 Proleg . in Manil. p. 2. 9 Vid. Sir Edward Shirburn's Preface to the Sphere of Manilius . 1 De Poet. Lat. 2 Hist . Com. Tom. 1. 3 Vid Salmatium ad Solinum , p. 4 Vid Plin. Nat. Hist . lib. 10. cap. 2. 5 De Ling. Lat. lib. 4. et 6. 6 Sir Edward Shirburn's pref . 7 Lib. 3. v. 22. 8 Lib. 3. v. 21. 9 Lib. 4. v. 761. 1 Dion Cassius , p. 634. 2 Vell. Paterculus , lib. 2. cap. 99. 3 lib. 1. v. 894. 4 Dion Cassius , lib. 56. 5 Lib. 4. v. 40. 6 Lib. 4. v. 764. 7 Lib. 2. cap. 99. 8 Lib. 4. v. 7●5 . 9 Italia summà , quam rerum maxima Roma Imposuit terris , Coeloque adjungitur Ipsa . Lib. 4. v. 692. 1 Lib. 36. cap. 10. Notes for div A51767-e7840 The Subject of the Poem . The Invocation . The Difficulty . I. The Rise and Progress of Astronomy , II. Different Opinions about the beginning of the World. III. The Order of the Frame . IV. The Earth lies in the midst of the World. V. The Earth is round . First Argument . Second Argument . VI. God the Soul of the World. VII . The Signs of the Zodiack . VIII . The Axis . IX . The great Bear. The little Bear. The Serpent . Hercules . Bootes . Arcturus . The Crown . The Harp. Ophiuchus . The Swan . The Arrow . The Eagle . The Dolphin . The Horse . Andromeda . Perseus . The Triangle . Cepheus and Cassiopcia . Heniochus . The Hoedi . The Goat . The Pleiades and Hyades . X. Orion . The Dog-Star . Procyon . The Hare . Argo . The Serpent . The Crow . The Cup. The Altar . The Whale . The Southern Fish . The Flouds . The Southern Pole. XI . The Figures of the Constellations onely fansied . XII . Providence against the Epicureans . XIII . The bigness of the World. XIV . The Northern Polar Circle . The Tropical Circle of Cancer , or Summer Solstice . The Equinoctial . The Tropick of Capricorn . The Southern Polar Circle . The Colure . The Aequinoctial Colure . The Solsticial Colure . The Meridian . The Horizon . The Zodiack . XV. The Milky way . Various Opinions about the Milky way . XVI . The Planets . XVII . Meteors . Several sorts of Meteors . Stella Crinita . Barbara ▪ Trabs . Pithetes . Bostruchias . Lampadias . Stipulae ardentes . Stella cadens . Acontiae . Different Opinions about Meteors . Comets presage . The Plague of Athens . Wars . Notes for div A51767-e29170 Homer . Homer . Hesiod . Eratosthenes . Theocritus . Macer . Nicander . Some old Poet who describ'd Hell. 1. The World an Animal , and God the Soul of it . 2. The Influence of the Heavens . 3. 4. Male and Female Signs . 5. Humane and Brute Signs . 6. Single and Double Signs . 7. Pairs . 8. Double Signs of different Species . 9. Double Signs by Place . 10 Signs of natural or unnatural Postures . 11 Day Signs and Night Signs . 12 Earth and Water Signs . 13 Fruitful and Barren Signs . 14 Signs of different Postures . 15 Maimed and intire Signs . 16 Season Signs . 17 The various Configurations or Aspects . See Fig. 1. 18 Trines . 19 Quadrates . See Fig. 2. 20 Cautions concerning Squares and Trines . 21. The Intercourse of Trines and Squares . See Fig. 3. 22. Of Sentiles See Fig. 4. 23. Of Contiguous Signs . 24. Of Vnequal Signs . See Fig. 4. 25. Of Opposites . See Fig. 4. 26. The Guardians of the Signs . 27. Signs for the several parts of the Body . 28. Signs that See , Hear , Love , or Hate . See Fig. 5. 6 , 7 , and 8. 29. A short digression concerning Friendship . 30. The friendly and unfriendly Aspects . See Fig. 1. Trines . See Fig. 1. 31. Dedecatemorion . 32. The Dodecatemoria of the Planets . XXXIII . The Celestial Houses . The Hinges . See Fig. 10. The Medium Coeli . The Imum Coeli . The Horoscope . or Eastern Point . The Western Point . The intermediate Spacers . See Fig. 9. The Twelfth and Sixth Houses . See fig 9th . The Second and Eighth Houses . See fig. 9th . The Eleventh house See fig. 9th . The fifth House . See fig. 9th . The third and ninth Houses . See fig. 9. The ninth House . The third House . The tenth House . See fig. 9. The fourth House . See fig. 9. The first House . See fig. 9. The seventh House . Notes for div A51767-e58300 1. 2. The twelve Lots of the twelve Signs . 3. First Lot. Vid. Fig. 11 Second Lot. Third Lot. Fourth Lot. Fifth Lot. Sixth Lot. Seventh Lot. Eighth Lot. Ninth Lot. Tenth Lot. Eleventh Lot. Twelfth Lot. IV. How the Lots are to be suited to the Signs . When the Birth belongs to Day . When to Night . V. How to find the Horoscope VI. The Chaldaeans refuted . The first Argument against the Chaldaeans . The Second Argument . VII . How to find the different lengths of Days and Nights , and to find the Horoscope . The rising and Setting of the Signs first . By Stadia : and Hours . Another Method . VIII . Third Argument against the Chaldaeans . The length of Days and Nights in a Direct Sphere . In an Oblique Sphere . On this side the Arctick Circle . Beyond the Arctick Circle . In an erect or parallel Sphere . 9. Another way to find the Trine the Signs Rising and Setting by Hours . By Stadia . 10. How Days encrease from Capricorn 〈◊〉 Cancer . 11. The Years , Months , Days , and Hours of Signs . Some Astrologers Opinion . concerning the Years , Months and Days of Signs . Refuted . 12. How many Years belong to each Sign and Station . Vid. Fig. 9. 13. The Tropick Signs Cancer . Capricorn Aries . Libra . What Degrees in the Tropick Signs are to be considered . Notes for div A51767-e78140 Short Reflections on the Cares of Men. 1. The first Argument for Fate . II. Second Argument . III. Third Argument . IV. Fourth Argument . V. Fifth Argument . VI. Sixth Argument . VII . Seventh Argument . VIII . An Objection answer'd . IX . The Influence of the Signs . X. Of Aries . XI . Of Taurus . XII . Of Gemini . XIII . Of Cancer . XIV . Of Leo. XV. Of Virgo . XVI . Of Libra . XVII . Of Scorpio . XVIII . Of Sagittarius . XIX . Of Capricorn . XX. Of Aquarius . XXI . Of Pisces . XXII . The Tenths and the Lords of the third part of each sign . Of Aries . Of Taurus . Of Gemini . Of Cancer ▪ Of Leo. In Cancer . In Libra . In Scorpio . In Capricorn . In Aquarius . In Pisces . The usefulness of this Doctrin of the Lords . XXIII . Encouragements to this Study . XXIV . The Good and Bad Degrees of each Sign . The difficulty of putting this Doctrin into Verse . The hurtful Degrees in Aries . In Taurus . In Gemini . In Cancer . In Leo. In Virgo . In Libra . In Scorpio . In Sagittarius . In Capricorn . In Aquarius . In Pisces . XXV . How the Signs Act when they rise . Aries . Taurus . Gemini . Cancer . Leo. Virgo . Libra . Scorpio . Sagittarius . Capricornus . Aquarius . Pisces . The winds call'd Cardinal . The Collateral winds . The Mediterranean Sea and and the several parts of it . The Islands of the Mediter-anean . The Caspian Sea. The Persian Gulph . The Arabian Gulph . Africa . Asia . Europe . What Signs govern each Country . Why different Countreys bear Men of different Shapes and Colours . What Countreys are govern'd by Aries . By Taurus . By Gemini . By Cancer . By Leo. By Virgo . By Libra . By Scorpio . By Sagittarius . By Capricornus . By Aquarius . By Pisces . What Influence these Signs have in the seveveral Countries subject to their Rule . XXVII . What Signs are Eccliptick . Why call'd Eccliptick . In what Order the Eccliptick succeed one another . XXVIII . This Artho ' difficult , yet may be obtain'd . Notes for div A51767-e105240 The design of the Fifth Book . The Southern Constellations . The Northern Constellations . II. What Constellations rise with Aries . The Ship. III. Orion . IV. Heniochus , or the Driver . V. The Hoedi , or the Kids . VI. The Hyades . VII . The Goat . VIII . What Constellations rise with Taurus . The Pleiades . IX . What Constellations rise with the Twins . The Hare . X. What Constellations rise with Cancer . The Asses . XI . Procyon , or the little Dog. XII . What Constellations rise with the Lion. The great Dog. XIII . The Bowl . XIV . What Constellations rise with Virgo . The Crown● XV. The Sheaf . XVI . What Constellations rise with Libra . XVII . The Goat . XVIII . The Harp. XIX . What Constellations rise with Scorpio . The Altar . XX. The Centaur . XXI . What Constellations rise with Sagittarius . Arcturus . XXII . The Swan . XXIII . With Capricorn riseth Ophieuchus . XXIV . The South Fish . XXV . The Strings of the Harp. XXVI . The Dolphin . XXVII . What Constellations rise with Aquarius . Cepheus . XVIII . ●he Ea●●e . XXIX . Cassiopeia . XXX . What Constellations rise with Pisces . Andromeda . XXXI . The Horse . XXXII . Hercules , or the Kneeling Constellation . XXXIII . The Whale The rising of the two Bears . The several magnitudes of the Stars . 
A51553	----	A tutor to astronomie and geographie, or, An easie and speedy way to know the use of both the globes, coelestial and terrestrial in six books : the first teaching the rudiments of astronomy and geography, the 2. shewing by the globes the solution of astronomical & geographical probl., the 3. shewing by the globes the solution of problems in navigation, the 4. shewing by the globes the solution of astrological problemes, the 5. shewing by the globes the solution of gnomonical problemes, the 6. shewing by the globes the solution of of [sic] spherical triangles : more fully and amply then hath ever been set forth either by Gemma Frisius, Metius, Hues, Wright, Blaew, or any others that have taught the use of the globes : and that so plainly and methodically that the meanest capacity may at first reading apprehend it, and with a little practise grow expert in these divine sciences / by Joseph Moxon ; whereunto is added Antient poetical stories of the stars, shewing reasons why the several shapes and forms are pictured on the coelestial globe, collected from Dr. Hood ; as also a Discourse of the antiquity, progress and augmentation of astronomie. Moxon, Joseph, 1627-1691. 1659 Approx. 618 KB of XML-encoded text transcribed from 140 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2005-12 (EEBO-TCP Phase 1). A51553 Wing M3021 ESTC R23159 12493266 ocm 12493266 62439 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A51553) Transcribed from: (Early English Books Online ; image set 62439) Images scanned from microfilm: (Early English books, 1641-1700 ; 769:16) A tutor to astronomie and geographie, or, An easie and speedy way to know the use of both the globes, coelestial and terrestrial in six books : the first teaching the rudiments of astronomy and geography, the 2. shewing by the globes the solution of astronomical & geographical probl., the 3. shewing by the globes the solution of problems in navigation, the 4. shewing by the globes the solution of astrological problemes, the 5. shewing by the globes the solution of gnomonical problemes, the 6. shewing by the globes the solution of of [sic] spherical triangles : more fully and amply then hath ever been set forth either by Gemma Frisius, Metius, Hues, Wright, Blaew, or any others that have taught the use of the globes : and that so plainly and methodically that the meanest capacity may at first reading apprehend it, and with a little practise grow expert in these divine sciences / by Joseph Moxon ; whereunto is added Antient poetical stories of the stars, shewing reasons why the several shapes and forms are pictured on the coelestial globe, collected from Dr. Hood ; as also a Discourse of the antiquity, progress and augmentation of astronomie. Moxon, Joseph, 1627-1691. Hood, Thomas, fl. 1582-1598. [14], 224, 40 p., 1 leaf of plates : ill., port. Printed by Joseph Moxon ..., London : 1659. First edition. Running title: A tutor to astronomy and geography. Includes bibliographical references. Added, engraved t.p.: Ductor ad astronomiam & geographiam, vel usus globi. "Ancient stories of the several stars ... collected from Dr. Hood," p. 200-224. Reproduction of original in Huntington Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. 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Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Astronomy -- Early works to 1800. Globes -- Early works to 1800. Sundials -- Early works to 1800. 2005-02 TCP Assigned for keying and markup 2005-03 Apex CoVantage Keyed and coded from ProQuest page images 2005-04 Judith Siefring Sampled and proofread 2005-04 Judith Siefring Text and markup reviewed and edited 2005-10 pfs Batch review (QC) and XML conversion DUCTOR ad ASTRONOMIAM & GEOGRAPHIAM . vel usus GLOBI , Celestis quam Terrestris . In Libris sex , viz. Astron. & Geogr. Rudimē . Astrō . & Geogr. Problē . Nautica . Problē . Astrologica . Problē . Gnomonica . Problē . Sphaeric . Triang . Problē . Per Josephum Moxon . LONDINI , Sumptibus Josephi Moxon . A TUTOR to ASTRONOMIE and GEOGRAPHIE : Or an Easie and speedy way to know the Use of both the GLOBES , Coelestial and Terrestrial . In six BOOKS . The First teaching the Rudiments of Astronomy and Geography . The 2. Shewing by the Globes the solution of Astronomical & Geographical Probl. The 3. Shewing by the Globes the solution of Problemes in Navigation . The 4. Shewing by the Globes the solution of Astrological Problemes . The 5. Shewing by the Globes the solution of Gnomonical Problemes . The 6. Of Spherical Triangles . More fully and amply then hath ever been set forth either by Gemma Frisius , Metius , Hues , Wright , Blaew , or any others that have taught the Use of the Globes : And that so plainly and methodically that the meanest Capacity may at first reading apprehend it ; and with a little Practise grow expert in these Divine Sciences . By Joseph Moxon . Whereunto is added the Antient Poetical Stories of the Stars : shewing Reasons why the several shapes and forms are pictured on the Coelestial Globe . Collected from Dr Hood . As also a Discourse of the Antiquity , Progress and Augmentation of Astnonomie . Psal. 111. 2. The Works of the Lord are great : sought out of them that have pleasure therein . Job . 26. 13. By his Spirit he hath garnished the Heavens : His hand hath framed the crooked Serpent . LONDON , Printed by Joseph Moxon : and fold at his Shop on Corn-hill , at the signe of Atlas . 1659. A Catalogue of Books and Instruments , Made and sold by Joseph Moxon , at his shop on Corn-hil , at the Signe of Atlas . GLobes of all sizes ; Coelestial and Terrestrial . Sphears , according to the Ptolemean Tychonean Copernican Systeme The Catholick Planisphere , call'd Blagrave's Mathematical Jewel ; made very exactly on Past-boards ; about 17. inches Diameter . And a Book of the Use of it newly set forth by I. Palmer M. A. The Spiral Line . Gunters Quadrant and Nocturnal ; Printed and pasted , &c. Stirrups Universal Quadrat . Printed and Pasted , &c , Sea-Plats , Printed on Paper , or Parchment , and Pasted on Boards . Wrights Corrections of Errors , in the Art of Navigation . The third Edition , with Additions . Vignola , or the Compleat Architect , useful for all Carpenters , Masons , Painters , Carvers , or any Gentlemen or others that delight in rare Building . A new Invention to raise Water higher then the Spring . With certain Engines to produce either Motion or Sound by the Water : very useful , profitable and delightful for such as are addicted to rare curiosities : by Isaac de Caus. A Help to Calculation By J. Newton . A Mathematical Manuel , shewing the use of Napiers bones , by J. Dansie . A Tutor to Astrology , with an Ephemeris for the Year 1659. intended to be Annually continued , by W. E. Also all manner of Mathematical Books , or Instruments , and Maps whatsoever , are sold by the foresaid Joseph Moxon . To the Reader . Courteous Reader , IFormerly Printed a Book of the Use of the Globes , Intituled A Tutor to Astronomy and Geography : The Book was Composed by William Blaew , but the Title was mine own ; and therefore I hope I may be the bolder to use it when and where I list . The sale of that Impression had almost perswaded me to have Printed it again : But when I considered it wanted many necessary Problemes , both in Astronomy , Navigation . Astrology , Dyalling , and the whole Doctrine of Triangles by the Globe ; And also that the Examples throughout that Book were made for the Citty of Amsterdam ; which by the general sale of the Book I found rendred it less acceptable then it would have been if they had been made for London ; And when I considered that to add so many Problemes , and alter all the Examples would both Metamorphose that Book , and be as Laborious a work to me as if I should write a new one ; Then I resolved to take this Task upon me ; which at length with Gods Assistance I have finished ; And now expose it to thy acceptance . The Globes is the first Studie a Learner ought to undertake : for without a competent knowledge therein he will never be able to understand any Author either in Astronomy , Astrology , Navigation , or Trigonometry : Therefore my aim hath been to make the Use of then very plain and easie to the meanest Capacities : In prosecution of which Designe , I doubt the Learneder sort may be apt to Censure me guilty of Prolixity , if not Tautology : Because the Precepts being plain , they may account some of the Examples Useless . But I desire them to consider that I write not to expert Practitioners , but to Learners ; to whom Examples may prove more Instructive then Precepts . Besides , I hope to encourage those by an ample liberal plainness to fall in love with these Studies , that formerly have been disheartned by the Crabbed brevity of those Authors that have ( in Characters as it were ) rather writ Notes for their own Memories , then sufficient Documents for their Readers Instructions . The Globes for which this Book is written are the Globes I set forth about four years ago : which as I told you in my Epistle to the Reader of Blaew's Book differs somewhat from other Globes , and that both the Coelestial and the Terrestrial ; mine being the latest done of any , and to the accomplishing of which , I have not only had the help of all or most of the best of other Globes , Maps , Plats ; and Sea-drafts , of New Discoveries that were then extant , for the Terrestrial Globe , but also the Advice and directions of divers learned and able Mathematicians both in England and Holland for Tables and Calculations both of Lines and Stars for the Coelestial : upon which Globe I have placed every Star that was observed by Tycho Brahe one degree of Longitude farther in the Ecliptick then they are on any other Globes : So that whereas on other Globes the places of the Stars were correspondent with their places in Heaven 58. Years ago , when Tycho observed them , and therefore according to his Rule want about 47. minutes of their true places in Heaven at this Time : I have set every Star one degree farther in the Ecliptick , and Rectified them on the Globe according to the true place they will have in Heaven in the Year 1671. On the Terrestrial Globe I have inserted all the New Discoveries that have been made , either by our own or Forraigne Navigators , and that both in the East , West , North , and South , parts of the Earth . In the East Indies we have by these later Times many spacious Places discovered , many Ilands inserted , and generally the whole Draft of the Country rectified and amended , even to the Coast of China , Japan , Giloli , &c. In the South Sea between the East and West Indies are scattered many Ilands , which for the uncertain knowledge former Times had of them are either wholely left out of other Globes , or else laid down so erroneously that little of credit can be attributed unto them : California is found to be an Iland , though formerly supposed to be part of the main Continent , whose North West shoar was imagined to thrust it self forth close to the Coasts of Cathaio , and so make the supposed Straits of Anian . The Western Shoars of the West Indies are more accurately discribed then formerly , as you may see if you compare my Terrestrial Globe with the Journals of the latest Navigators : And if you compare them with other Globes you will find 5 , 6 , yea 7 , degrees difference in Longitude , in most Places of these Coasts . Magellanica which heretofore was thought to be part of the South Continent called Terra Incognita is now also found to be an Iland . All that Track of Land called Terra Incognita I have purposely omitted , because as yet we have no certainty whether it be Sea or Land , unless it be of some parts lately found out by the Dutch ; who having a convenient Port at Bantam in Java , have from thence sent forth Ships Southwards , where they have found several very large Countries ; one whereof they have called Hollandia Nova , another Zelandia Nova , another Anthoni van Diemans Land ; and divers others ; some whereof lies near our Antipodes ; as you may see by my Terrestrial Globe . Again , Far to the Northwards there are some New Discoveries , even within 6. degrees of the Pole : The Drafts to the North Eastwards I have laid down even as they were discribed by the Searchers of these Parts , for a Passage into the East Indies . And also the Discoveries of Baffin , Capt. James , and Capt. Fox , ( our own Country men that attempted the finding a passage that way into the South Sea. I also told you what difference there is in several Authors about placing their first Meridian , which is the beginning of Longitude ; that Ptolomy placed it at the Fortunate Ilands , which Mr Hues pag. 4. chap 1. in his Treatise of Globes proves to be the Ilands of Cabo Verde , and not those now called the Canary Ilands ; because in his Time they were the furthest Places of the Discovered World towards the Setting of the Sun : Others placed it at Pico in Teneriffa ; Others at Corvus and Flora ; because under that Meridian the Compass had no Variation , but did then duely respect the North and South ; Others for the same Reason began their Longitude at St Michaels ; and others between the Ilands of Flores and Fayal : And the Spaniards of late by reason of their great Negotiation in the West Indies , have begun their Longitude at Toledo there , and contrary to all others account it Westwards . Therefore I seeing such diversity among all Nations , and as yet a Uniformity at home , chose with our own Country men to place my First Meridian at the Ile Gratiosa , one of the Iles of the Azores . By the different placing of this first Meridian it comes to pass that the Longitude of places are diversly set down in different Tables : For those Globes or Maps that have their first Meridian placed to the Eastwards of Gratiosa have all places counted Eastward between the first Mertdian and the Meridian of Gratiosa in fewer degrees of Longitude : And those Globes and Maps that have their first Meridian placed to the Westwards , have all Places counted Eastwards from the Meridian of Gratiosa and their first Meridian in a greater number of degrees of Longitude , and that according as the Arch of Difference is . I have annexed a smal Collection out of Dr Hood , which declares the Re son why such strange Figures and Forms are pictured on the Caelestial Globe : and withall the Poetical Stories of e-every Constellation . I also thought good to add at the latter end of this Book a smal Treatise , intituled The Antiquity , Progress , and Augmentation of Astronomy . I may without Partiallity give it the Encomium of a Pithy , Pleasant , and Methodical peece : It was written by a Learned Author ; and is worthy the Perusal of all Ingenuous Lovers of these Studies . Joseph Moxon . Encomiastic Achrosticon Authoris . IT s now since Atlas raign'd thousands of Years , OF whom 't is Fabl'd , Heavens hee did Uphold , SO Ancient Authors write : But it appeares EXcell he others did , for we are told PRoject he did the Sphear : and for his Skil HE had therein , his Fame will Flourish still . MUst we not also Praise in this our Age OUr Authors skill , and Pains , who doth ingage X Thousand Thanks , not for this Book alone OF his , But for the Globes he makes there 's none NOw extant made so perfect : This is known The Contents of the First Book . Chap. 1. WHat a Globe is . fol. 4 2. Of the two Poles . 4 3. Of the Axis . 4 4. Of the Brazen Meridian . 4 5. Of the Horizon . 5 6. Of the Quadrant of Altitude . 6 7. Of the Hour-Circle , and its Index . 6 8. Of the Nautical Compass , or Box and Needle . 7 9. Of the Semi-Circle of Position . 7 Chap. 2. Of the Circles Lines , &c. described upon the superficies of the Globe ; beginning with the Terrestrial Globe ; and 7 1. Of the Equator . 7 2. Of the Meridians . 8 3. Of the Parallels . 8 4. Of the Ecliptique , Tropicks , and Polar Circles . 8 5. Of the Rhumbs . 9 6. Of the Lands , Seas , Ilands , &c. Discribed upon the Terrestrial Globe , 9 7. Longitude . 10 8. Latitude . 11 Chap. 3. Of the Celestial Globe , or the Eighth Sphear , represented by the Celestial Globe : its motion , and of the Circles , Lines , Images , Stars , &c. described thereon . 11 1. Of the eight Sphear . 11 2. Of the Motion of the eighth Sphear . 12 3. Of the Equinoctial . 13 4. Of the Ecliptick . 15 5. Of the Poles of the Ecliptick . 15 6. Of the Axis of the Ecliptick . 16 7. Of the Colures , and Cardinal Points . 16 8. Of the Tropick . fol. 16 9. Of the Circles Arctick and Antarctick . 17 10. Of the Images called Constellations , drawn upon the Celestial Globe . 17 11. Of the number of the Stars . 19 12. Of the Scituation of the Stars . 20 13. Of the Magnitudes of the Stars . 20 The proportion of the Diameters of the fixed Stars ; Compared with the Diameter of the Earth . 21 The proportions of the fixed Stars Compared with the Globe of the Earth , 22 14. Of the Nature of the Stars . 23 15. Of Via Lactea , or the Milky way . 23 The Contents Of the Second Book . Prob. 1. SOme Advertisements in Choosing and Using the Globes . 35 To find the Longitude and Latitude of Places , on the Terrestrial Globe . fol. 37 Prob. 2. The Longitude and Latitude being known , to Rectifie the Globe fit for use . 38 Prob. 3. To find the Place of the Sun in the Ecliptick , the day of the Moneth being first known . 39 Prob. 4. To find the Day of the Moneth , the Place of the Sun being given . 40 Prob. 5. The Place of the Sun given , to find its Declination . 40 Prob. 6. The Place of the Sun given , to find us Meridian Altitude . 41 Prob. 7. The Suns Place given , to find the Hour of Sun Rising , and the length of the Night and Day . 42 Prob. 8. To find the Hour of Sun Set. 42 Prob. 9. To find how long it is Twilight in the Morning and Evening . 43 Prob. 10. The Suns Place given , to find its Amplitude ; And also to know upon what point of the Compass it Riseth . 44 Prob. 11 , The Hour of the Day given to find the Height of the Sun. 45 Prob. 12. The Altitude of the Sun , and Day of the Moneth given , to find the Hour of the Day . fol. 46 Prob. 13. How to know whether it be Before or After Noon . 47 How to take Altitudes by the Quadrant , Astrolabe , and Cross-staff . 47 To take Altitudes by the Astrolabe . 50 To take Altitudes by the Cross-staff . 51 Prob. 14. To observe with the Globe the Altitude of the Sun. 52 Prob. 15. To find the Elevation of the Pole● by the Meridian Altitude of the Sun , and Day of the Moneth given . 53 Prob. 16. To take the Altitude of any Star above the Horizon ; by the Globe . 54 Prob. 17. By the Meridian Altitude of any Star given , to find the Height of the Pole. 54 Prob. 18. Another way to find the Height of the Pole by the Globe ; if the Place of the Sun be given : and also to find the Hour of the Day , and Azimuth , and Almicanter of the Sun , 56 Prob. 19. To observe by the Globe the Distance of two Stars . 57 Prob. 20. How you may learn to give a guess at the number of degrees that any two Stars are distant from one another ; or the number of degrees of Altitude the Sun or any Star is Elevated above the Horizon : only by looking up to Heaven , without any Instrument . 58 Prob. 21. The Day of the Moneth , and Altitude of any Star given , to find the Hour of the Night , 59 Prob. 22. The Place of the Sun , and Hour of the Day given , to find its Azimuth in any Latitude assigned . 60 Prob. 23. The Place of the Sun , and Hour of the Day given , to find the Almicantar of the Sun. 61 Prob. 24. The Place of the Sun given , to find what Hour it comes to the East , or West , and what Almicantar it then shall have . 61 Prob. 25. To know at any time what a clock it is in any other Part of the Earth . 62 Prob. 26. To find the Right Ascension of the Sun , or Stars . 63 Prob. 27. To find the Declination of the Sun , or Stars . 64 A Table of the Right Ascensions and Declinations of 100. Select fixed Stars ; Calculated by Tycho Brahe , for the Years 1600 , and 1670. As also their Difference of Right Ascensions and Declinations , in 70. Years . 65 Prob. 28. The Place of the Sun or any Star given , to find the Right Descension , and the Oblique Ascension , and the Oblque Descension . fol. 71 Prob. 29. Any Place on the Terrestrial Globe being given , to find its Antipodes . 72 Prob. 30. To find the Perecij of any given Place , by the Terrestrial Globe . 73 Prob. 31. To find the Antecij of any given Place , upon the Terrestrial Globe . 73 Prob. 32. To find the Longitude and Latitude of the Stars , by the Coelestial Globe . 73 Prob. 33. To find the Distance between any two Places on the Terrestrial Globe . 74 Prob. 34. To find by the Terrestrial Globe upon what point of the Compass any 〈◊〉 Places are scituate one from another . 75 Prob. 35. To find by the Coelestial Globe the Cosmical Rising and Setting of the Stars . 76 Prob. 36. To find by the Coelestial Globe the Acronical Rising and Setting of the Stars . 77 Prob. 37. To find by the Coelestial Globe the Heliacal Rising , and Setting of the Stars . 78 Prob. 38. To find the Diurnal and Nocturnal Arch of the Sun , or Stars , in any given Latitude . 79 Prob. 39. To find the Azimuth and Almicantar of any Star. 81 Prob. 40. To find the Hour of the Night , by observing two known Stars in one Azimuth , or Almicantar . 81 Prob. 41. The Hour given that any Star in Heaven comes to the Meridian , to know thereby the Place of the Sun , and by consequence the Day of the Moneth , though it were lost . 82 Prob. 42. The Day of the Moneth given , to find in the Circle of Letters on the Plain of the Horizon , the Day of the Week . 83 Prob. 43. The Azimuth of any Star given , to find its Hour in any given Latitude . 84 Prob. 44. How you may learn to know all the Stars in Heaven , by the Coelestial Globe . 84 Prob. 45. How to hang the Terrestrial Globe in such a position that by the Suns shining upon it you may with great delight at once behold the demonstration of many Principles in Astronomy , and Geography . 89 Prob. 46. To know by the Terrestrial Globe in the Zenith of what Place of the Earth the S●● is . 91 Prob. 47. To find in what different Places of the Earth the Sun hath the same Altitude , at the same time . 92 Prob. 48. To find the length of the Longest and shortest Artificial Day or Night . 95 Prob. 49. To find how much the Pole is Raised , or Depressed , where the longest Day is an Hour longer or shorter then it is in your Habitation . 96 Prob. 50. The Suns Place given , to find what alteration of Declination he must have to make the Day an Hour longer , or shorter : And in what number of Daies it will be . 97 Prob. 51. Of the difference of Civil and Natural Daies , commonly called the Equation of Civil Daies . And how it may be found by the Globe . 99 Prob. 52. How to find the Hour of the Night , when the Moon shines on a Sun Dyal , by help of the Globe . 101 Prob. 53. To find the Dominical Letter , the Prime , Epact , Easter Day , and the rest of the Moveable Feasts , for ever . 102 Prob. 54. The Age of the Moon given , to find her place in the Ecliptick according to her mean motion . 104 Prob. 55. Having the Longitude and Latitude , or Right Ascension and Declination of any Planet , or Comet , to place it on the Globe , to correspond with its place in Heaven . 105 The Contents Of the Third Book . Prob. 1. THe Suns Amplitude and difference of Ascension given , to find the Height of the Pole , and Declination of the Sun. 108 Prob. 2. The Suns Declination and Amplitude given , to find the Poles Elevation . 108 Prob. 3. The Suns Declination and Hour at East given , to find the Heigth of the Pole. 109 Prob. 4. The Declination of the Sun and his Altitude at East given , to find the Heigth of the Pole. 110 Prob. 5. By the Suns Declination and Azimuth at 6 , of the Clock given , to find the Heigth of the Pole , and Almicantar at 6. 11● Prob. 6. By the Hour of the Night and a known Star Observed Rising or Setting , to find the Heigth of the Pole. fol. 112 Prob. 7. Two Places given in the same Latitude , to find the Difference of Longitude . 112 Prob. 8. Two Places given in the same Longitude , to find the difference of Latitude . 113 Prob. 9. Course and Distance between two Places given , to find their difference in Longitude and Latitude . 113 Prob. 10. To find how many Miles are contained in a Degree of any Parallel . 114 Prob. 11. The Rhumb you have sailed upon , and the Latitudes you departed from , and are arived to , given , to find the Difference of Longitude , and the number of Leagues you have Sailed . 114 Prob. 12. The Longitudes and Latitudes of two Places given , to find Course , and Great Circle distance between them . 116 Prob. 13. The Latitude you departed from , and the Latitude you are arrived to , and the number of Lagues you have sailed given , to find the Rhumb you have sailed on , and difference of Longitude . 116 Prob. 14. To find by the Globe the Variation of the Needle ; commonly called the Variation of the Compass . 117 Prob. 15. To keep a Journal by the Globe . 118 Prob. 16. To Steer in the Night by the Stars . 119 Prob. 17. How to platt on the Globe a New Land , never before Discovered . 119 Prob. 18. Seeing two known points or Capes of Land , as you sail along , how to know the distance of your Ship from them . 120 Prob. 19. Of Tides , and how by help of the Globe you may in general judge of them . 121 The Contents Of the Fourth Book . Prob 1. To Erect a Figure of the 12 Houses of Heaven . 123 Prob. 2. ●o Erect a Figure of Heaven according to Campanus . 128 Prob. 3. To find the length of a Planetary Hour . 129 Prob. 4. The length of a Planetary Hour known ; to find what Planet Reigneth any given Hour of the Day , or Night . fol. 131 Prob. 5. To find Part of Fortune by the Globe . 132 Prob. 6. To find in what Circle of Position any Star , or any degree of the Ecliptick is . 133 Prob. 7. To find the Right Ascensions , the Oblique Ascensions , and the Declinations of the Planets . 133 Prob. 8. How to Direct a Figure , by the Globe . 134 Prob. 9. Of Revolutions : and how they are found by the Globe . 135 Prob. 10. How a Figure of Heaven may be erected by the Revolution thus found . 135 The Contents Of the Fifth Book . Prob. 1. HOw by one position of the Globe to find the distance of the Hour lines on all manner of Planes . fol. 143 Prob. 2. To make an Equinoctial Dyal . 147 Prob. 3. To make an Horizontal Dyal . 149 Prob. 4. To make an Erect Direct South Dyal . 153 Prob. 5. To make an Erect Direct North Dyal . 156 Prob. 6. To make an Erect Direct East Dyal . 156 Prob. 7. To make an Erect Direct West Dyal . 159 Prob. 8. To make a Polar Dyal . 159 Prob. 9. To make Erect South Dyals , Declining Eastwards , or Westwards . 160 Prob. 10. To make a North Erect Dyal declining Eastwards or Westwards . 163 Prob. 11. To make Direct Reelining or Inclining Dyals . 164 Prob. 12. To make Declining Reclining , or Declining Inclining Dyals . 164 Prob. 13. To make a Dyal upon a Declining Inclining Plane . 168 Prob. 14. To find in what Place of the Earth any manner of Plane that in your Habitation is not Horizontal , shall be Horizontal . 171 Prob. 15. To make a Dyal on the ●e●ling of a Room , where the Direct Beams of the Sun never come . 175 Prob. 16. To make a Dyal upon a solid Ball or Globe , that shall shew the Hour of the Day without a Gnomon . 178 Prob. 17. To make a Dyal upon a Glass Globe , whose Axis shall cast a shadow upon the Hour of the Day . 180 The Contents Of the Sixth Book . Of the Parts and Kindes of Spherical Triangles . fol. 183 Prob. 1. The Legs of a Right Angled Spherical Triangle given ; to find the Hypothenusa , and the two other Angles . 184 Prob. 2. A Leg and the Hypothenusa given , to find the Rest. 187 Prob. 3. The Hypothenusa and an Angle given , to find the Rest. 187 Prob. 4. A Leg and Angle adjoyning given , to find the Rest. 188 Prob. 5. A Leg and the Angle opposite given , to find the Rest. 188 Prob. 6. The Angle given , to find the Sides . 189 Prob. 7. Oblique Triangles . The three Sides given , to find the Angles . 190 Prob. 8. Two Sides and the Angle contained between them given , to find the Rest. 193 Prob. 9. Two Sides and an Angle opposite to one of them given , to find the Rest. 194 Prob. 10. Two Angles and the Side comprehended between them given , to find the Rest. 194 Prob. 11. Two Angles and a Side opposite to one of them given , to find the Rest. 195 Prob. 12. Three Angles given , to find the Sides . 196 Prob. 13. How to let fall a Perpendicular that shall divide any Oblique Spherical Triangle into two Right Angled Spherical Triangles . 198 The Poetical Stories of the Constellations in Heaven . 200 The First BOOK . Being the first RUDIMENTS of Astronomy & Geography . Or A Description of the Lines , Circles , and other Parts of the GLOBE . PRAEFACE . THe Students of all Arts and Sciences have ever proposed a Maxime , whereon ( as on an allowed Truth ) the whole Science hath dependance : and by so much the more demonstrable that Maxime is , so much the more of Excellency the Science may claim . This of Astronomy and Geography comes not behind any ; for herein we shall only admit ( with the Ancients ) that the Form of the visible World is Spherical : Neither shall we beg our Ascertion any farther then Occular Appearance will demonstrate : every Mans Ey being his Judge , if he be either on a Plain field , or at Sea , where nothing can hinder a free inspection of the Horizon . Vpon good grounds therefore they ascerted the Spherical form of the Whole : and also concluded the Parts to be Round : I meane , very intire Subsistence , as the Stars , Planets , and the Earth . In the Celestial Bodies ( as the Stars and Planets ) this is also visible ; and therefore un-controullable : But that the Earth is Round proves with the unskilfull matter of dispute ; they frequently objecting with S. Austine the words of the Scripture , which say , He hath stretched forth the corners of the Earth ; not considering whether those words were spoken as alluding to the amplitude of Gods Omnipotence ; or that the Corners were meant Capes of Land , which indeed are stretched forth into the Sea. But that the Earth is Round is proved by divers certain and infallible Reasons , As first , By the Navigations of our Age , Divers able and honest Mariners having Sailed and continued an Easterly Course , have at length arrived ( without turning back ) to the same place from whence they set forth : witness Magellanicus , Sr. Francis Drake , Tho. Cavendish , Oliver vander Noort , W. Schouten , &c. Secondly , By the length of degrees in every Parallel ; for it is found by Dayly observation that the degrees of every Parallel upon the Earth , hold the same proportion to the degrees of the Equinoctial , as the degrees of the same Parallel upon an Artificial Globe or Sphear do to the degrees of the greatest Circle of the same : This Argument alone is sufficient : yet take one more from Visible Appearance : And that is this : The shadow which the Earth and Water together make in the Eclipse of the Moon is alwaies a part of a Circle ; therefore the Earth and Water which is the Body shadowing must also be a Circular or round Body ; for if it were three square , four square , or any other form , then would the shadow which it makes in the Moon be of the same fashion . Besides , Of all figures the Sphear or Globe is most perfect , most Capacious , and most intire of it self , without either joynts or Angles ; which form we may also perceive the Sun , Moon , and Stars to have , and all other things that are bounded by themselves , as Drops of Water , and other liquid things . But there is another frequent Argument against the Globulus form of the Earth ; and that is , That it seems impossible that the Earth should be round , and yet also Inhabible in all Places : For though we that inhabite on the top of the Earth go with our heads upwards ; yet those that inhabite underneath us must needs go with their Heads downwards , like Flyes on a Wall or Ceeling ; and so be in danger of falling into the Air. For Answer hereunto , first , You must understand that in the Center of the Earth there is an Attractive and drawing power , which draws all heavy substances to it : by vertue of which Attractive power , things though loosed from the Earth will again incline and cling to the Earth , and so much the more forcibly , by how much the heavier they are ; as a bullet of Lead let fall out of the Air , inclines towards the Earth far more violently and swiftly then a bullet of the same bigness of Wood , or Cork . Secondly , you must understand that in respect of the whole Vniverse there is no part either upper or under , but all parts of the Earth are alike incompast with Heaven ; yet in respect of the Earth , it is Heaven , which we take for the upper part ; and therefore we are said to go with our heads upwards , because our head ( of all the parts of our body ) is nearest to Heaven . Now that this Attractive power lies in the Center of the Earth , is proved by this Argument : If the Attractive power were not in the Center , a Plumb-line let fall would not make Right Angles with the Superficies of the Earth ; but would eb Attracted that way the Attractive vertue lies , and so make unequal Angles with the Superficies : But by so many Experiments as hath yet been made , we find that a Plumb-line continued , though never so deep , yet it alters no Angles with the Superficies of the Earth ; and therefore undoubtedly the Attractive power lies in the very Center , and no where else . CHAP. I. I. What a Globe is . A Globe according to the Mathematical Definition , is a perfect and exact round Body contained under one surface . Of this form ( as hath been proved ) consists the Heavens and the Earth : and therefore the Ancients with much pains Study and Industry , endeavouring to imitate as well the imaginary as the real appearances of them both , have Invented two Globes ; the one to represent the Heavens , with all the Constellations , fixed Stars . Circles , and Lines proper thereunto , which Globe is called the Celestial Globe ; and the other with all the Sea Coasts , Havens , Rivers , Lakes , Cities , Towns , Hills , Capes , Seas , Sands , &c. as also the Rhumbs , Meridians , Parallels , and other Lines that serve to facilitate the Demostration of all manner of Questions to be performed upon the same : and this Globe is called the Terrestrial Globe . II. Of the two Poles . Every Globe hath two Poles , the one North , the other South . The North Pole is in the North point of the Globe : The South Pole in the South point . III. Of the Axis . From the Center of the Globe both waies , proceeds a line through both the Poles , and continues it self infinitely ; which is called the Axis of the World ; and is represented by the two wyers in the Poles of the Globe : Upon these two wyers the Globe is turned round , even as the Heavens is imagined to move upon the Axis of the World. IIII. Of the Brasen Meridian . Every Globe is hung by the Axis at both the Poles in a Brasen Meridian , which is divided into 360 , degrees ; ( or which is all one ) into 4 Nineties : the first beginning at the North Pole , is continued from the left hand towards the right till the termination of 90 degrees , and is marked with 10 , 20 , 30 , &c. to 90. from whence the degrees are numbred with 80 , 70 , 60 , &c. to 0. which is in the South Pole : from whence again the degrees are numbred with 80 , 70 , 60 , &c. to 0 , and lastly , from 0 the degrees are numbred with 10 , 20 , 30 , to 90. which is again in the North Pole. This Brasen Meridian is of great use ; for by help of it you may find the Latitude of all Places , the Declination of all the Stars , &c , and rectifie the Globe to any Latitude . V. Of the Horizon . The Horizon is a broad wooden Circle , encompassing the Globe ; having two notches in it ; the one in the North the other in the South point : The notches are made just fit to contain the Brasen Meridian that the Globe is hung in : In the bottom or under Plane of the Horizon there stands up a rop or ( as it is called ) a Bed , in which there is also a notch , into which notch the Brasen Meridian is also let , so lo , as that both it and the Globe may be divided into two equal halfs by the upper Plane of the wooden Horizon . These Notches are as gages to keep the Globe from inclining more to the one side of the wooden Horizon then the other . Upon the upper Plane of the Horizon is several Circles delineated : as first , the inner Circle , which is a Circle divided into twelve equal parts , viz. into twelve Signes ; every Signe having its name prefixed to it ; as to the Signe of ♈ is the word Aries ; to ♉ the word Taurus , &c. every Signe is again divided into 30 equal parts , which are called Degrees , and every tenth degree is marked with 10 , 20 , 30. Next to the Circle of Signes is a Kalender or Almanack , according to the Old stile used by us here in England , each Moneth being noted with its proper Name ; as January , February , March , &c. and every day distinguished with Arithmetical figures , as 1 , 2 , 3 , 4 , &c. to the end of the Moneth . The other Calender is a Calender of the New stile ; which is in a manner all one with the Old ; only in this Calender the moneth begins ten daies sooner then they do in the other : and to this Calender ( because it was instituted by the Church of Rome ) there is annexed the Festival daies Celebrated by the Romish Church . The two other Circles are the Circles of the Winds ; the innermost having their Greek and Latine names ; which by them were but twelve ; and the outermost having the English Nanes , which for more preciseness are two and thirty . The use of the upper Plane of the Horizon is to distinguish the Day from the Night ; the Rising and Setting of the Sun , Moon , or Stars , &c. and for the finding the Azimuth , and Amplitude , &c. VI. Of the Quadrant of Altitude . The Quadrant of Altitude is a thin brass plate , divided into 90. degrees ; and marked upwards with 10 , 20 , 30 , 40 , &c. to 90. It is rivetted to a Brass Nut , which is fitted to the Meridian ; and hath a Screw in it , to screw upon any degree of the Meridian . When it is used it is screwed to the Zenith . It s use is for measuring the Altitudes , finding Amplitudes , and Azimuths , and discribing Almicantaraths . It would sometimes stand you in good steed if the Plate were longer by the bredth of the Horizon then 90. degrees ; for then that length being turned back will serve you instead of an Index , when the Nut is screwed to the Zenith , to cut either the degrees or Daies of either Style , or the Points of the Compass in any of those Circles concentrical to the innermost edge of the Horizon , which the Ey cannot so well judge at . VII . Of the Hour Circle , and its Index . The Hour Circle is a smal Brasen Circle , fitted on the Meridian , whose Center is the Pole of the world : It is divided into the 24 hours of the Day and Night , and each hour is again divided into halfs and quarters , which in a Revolution of the Globe are all pointed at with an Index , which to that purpose is fitted on the Axis of the Globe . The use of the hour Circle is for shewing the Time of the several mutations and Configurations of Celestial Appearances . VIII . Of the Nautical Compass , or Box and Needle . Just under the East point of the Horizon , upon the undermost Plane , is sometimes fixed a Nautical Compass , whose North and South line must be Parallel to the North and South line of the Horizon . The use of it is for setting the Angles of the Globe correspondent to the Angles of the World. IX . Of the Semi-Circle of Position . This is a Semi-Circle made of Brass , and divided into 180. degrees , numbred from the Equinoctial on either side with 10 , 20 , 30 , &c. to 90. at the two ends there is an Axis , which is fitted into the two hole , of two smal studs fixed in the North and South points of the upper Plane of the Horizon : upon this Axis it is moved up and down , according to the intent of your operation . The use of this Circle of Position is , for the finding the twelve Astrological Houses of Heaven ; and also for finding the Circle of Position of any Star or Point in Heaven . Thus much may serve for the lineaments Circumjacent to the body of the Globe . The next discourse shall be CHAP. II. Of the Circles , Lines , &c. discribed upon the Superficies of the Globe ; beginning with the Terrestrial Globe ; and I. Of the Equator . THe Equator is a great Circle , encompassing the very middle of the Globe between the two Poles thereof , and divides it into two equal parts , the one the North part , and the other the South part . It is ( as all great Circles are divided into 360. equal parts , which are called Degrees . Upon this Circle the Longitude is numbred , from East to West : and from this Circle both waies , viz. North and South the Latitude is reckoned . It is called the Equator , because when the Sun comes to this line ( which is twice in one year , to wit , on the tenth of March , and the eleventh of June ) the Daies and Nights are equated , and both of one length . II. Of the Meridians . There are infinite of Meridians , for all places lying East or West from one another have several Meridians ; but the Meridians delineated upon the Terrestrial Globe are in number 36. so that between two Meridians is contained ten degrees of the Equator . From the first of these Meridians ( which is divided into twice 90 degrees ) accounted from the Equator towards either Pole ) is the beginning of Longitude , which upon our English Globes is at the Ile Gratiosa , one of the Iles of the Azores , and numbred in the Equator Eastwards , with 10 , 20 , 30 , &c. to 360. round about the Globe , till it end where it began . They are called Meridians , because they divide the Day into two equal parts : for when the Sun comes to the Meridian of any Place , it is then Midday , or full Noon . III. Of the Parallels . As the Meridians are infinite , so are the Parallels ; and as the Meridian lines delineated upon the Globe are drawn through no more then every tenth degree of the Equator , so are the Parallels also delineated but upon every tenth degree of the Meridian ; lest the Globe should be too much filled with superfluity of lines , which might obscure the smal names of Places . The Parallel Circles run East and West round about the Globe , even as the Equator ; only the Equator is a great Circle ; and these are every one less then other , diminishing gradually till they end in the Pole. The Parallels are numbred upon the Meridian with 10 , 20 , 30 , &c. to 90. beginning in the Equator , and ending in the Pole. They are called Parallels ; because they are Parallel to the Equator . IIII. Of the Ecliptick , Tropicks , and Polar Circles . These Circles though they are delineated upon the Terrestrial Globe , yet they are most proper to the Celestial ; and therefore when I come to the Celestial Globe , I shall define them unto V. Of the Rhumbs . The Rhumbs are neither Circles nor straight lines , but Helispherical or Spiral lines : They proceed from the point where we stand , and wind about the Globe till they come to the Pole ; where at last they loose themselves . They represent the 32 winds of the Compass . Their use is to shew the bearing of any two places one from another : that is to say , upon what point of the Compass any shoar or Land lies from another . There are many of them described upon the Globe , for the better directing the ey from one shoar to the other , when you seek after the bearing of any two Lands . Some of them ( where there is room for it ) have the figure of the Nautical Card drawn about the Center or common intersection , and have ( as all other Cards have ) for the distinction of the North point , a Flowerdeluce pictured thereon . They were first called Rumbs by the Portugals ; and since used by Latine Authors , and therefore that name is continued by all Writers that have occasion to speak of them . VI. Of the Lands , Seas , Ilands , &c. Described upon the Terrestrial Globe : The Land described upon the Globe is bounded with an irregular line , which runs turning and winding into Creeks and Angles , even as the shoar which it represents ( doth ) For the better distinction of Lands , &c , this line is cullered close by one side thereof with divers Cullers , as with red , yellow , green , &c. these cullers distinguish one part of the Continent from the other ; and also one Iland from another . That side of the line which incompasses the Cullers , is the bounds of the Land ; the other side of the line which is left bare without Cullers , is the limits of the Water . The Land is either Continents , or Ilands . A Continent is a great quantity of Land , not interlaced or separated by the Sea , in which many Kingdomes and Principalities are contained ; as Europe , Asia , Affrica , America . An Island is a part of the Earth , environed round with Waters ; as Britain , Java , S. Laurence Isle , Barmudas , &c. These again are sub-divided into Peninsula , Istmus , Promontorium . A Peninsula is almost an Island ; that is , a track of Land which being almost encompassed round with Water , is joyned to the firm Land , by some little Istmus ; as Molacca in the East-Indies , &c. An Istmus is a little narrow neck of Land , which joyneth any Peninsula to the Continent ; as the Straits of Dariene in Peru , and Corinth in Greece . Promontorium , is some high Mountain , which shooteth it self into the Sea , the utmost end of which is called a Cape , as that great Cape of Good Hope , and Cape Verde in Africa . The Water is either Ocean , Sea , Straits , Creeks , or Rivers . The Ocean is that generall collection of all Waters , which invironeth the whole Earth on every side . The Sea is a part of the Ocean ; to which we cannot come , but through some Strait , as Mare Mediterraneum , Mare Balticum , and the like . These two take their names either from the adjacent places , as the Brittish Ocean , the Atlantick Sea , &c. or from the first discovere as Mare Magellanicum ; Davis , and Forbishers Staits ; &c. Or from some remarkable accident , as Mare Rubrum , from the red colour of the Sands ; Mare Aegeum , Pontus Euxinus , and the like . A Strait , is a part of the Ocean restrained within narrow bounds , and opening a way to the Sea ; as the Straits of Gibralter , Hellespont , &c. A Creek is a crooked shoar , thrusting out as it were two armes to imbrace the Sea , as Sinus Adriaticus , Sinus Persicus &c. A River is a small branch of the Sea , flowing into the Land ; as Thames , Tiber , Rhine , Nilus &c. Now that these Lands , Ilands , Towns , Seas , Rivers , &c. may at the first search be found upon the Globe , all Geographers have placed them thereon according to Longitude , and Latitude , VII . Longitude . The Longitude is an Arch of the Equator , comprehended between the first Meridian and the Meridian of the Place you inquire after . It is numbred on the Equator from the West to the Eastwards , with 10 , 20 , 30 , to 360. degrees , till it end where it began . VIII . Latitude . The Latitude is an Arch of the Meridian , comprehended between the Equator and the place enquired after . It is numbred on the Meridian , from the Equator both waies , viz. North and South , till it come to the Poles , or 90 degrees . Thus much may serve for the description of the Terestrial Globe : I therefore come to treat of the Celestial . CHAP. III. Of the Celestial Globe , or the Eighth Sphear , represented by the Celestial Globe : its motion , and of the Circles , Lines , Images , Stars , &c. described thereon . I. Of the eighth Sphear . THe eighth Sphear which is the starry Heaven , is represented by the Celestial Globe , because upon the Convexity of it all the Stars and visible appearances are placed according to the order that they are situated in the concavity of the eighth Sphear . It is called the eighth Sphear , because between it and us are contained seven other Heavens , or Sphears ; as 1. the Moon , 2. Mercury , 3. Venus , 4. the Sun , 5. Mars , 6. Jupiter , 7. Saturn . and eighthly the starry Heaven . The antients have made the Systeme of the world to consist of 2 other Sphears , called the Chiristiline Heaven , and the Primum Mobile , or first Mover : as in the following figure is represented . A figure wherein may be seen the Composition of the whole frame of the World. II. Of the Motion of the eighth Sphear . There hath bin attributed to the eighth Sphear a twofold motion ; the one called its Diurnal Motion , which is made from East to West upon the Poles and Axis of the World : And the other called its Second motion ; which is made from West to East upon the Poles and Axis of the Ecliptick . The Diurnal motion is caused by the violent Motion of the Primum Mobile ; for in 24 hours it carries along with it , not only the eighth Heaven or Orb of fixed Stars , but the Orbs of the Sun , the Moon , and all the rest of the Planets . It is called the Diurnal Motion because it is finished in one Day . The second Motion is unproperly attributed to the eighth Sphear ; it being indeed the Motion of the Equinoctiall ; tho Authors sometimes carelesly mention the one insteed of the other . Therefore in the next Section , where I treat of the Equinoctial , I shall at large explain unto you the nature of this mis-called Second Motion . III. Of the Equinoctial . The Equinoctial upon the Celestial Globe , is the same line formerly called the Equator upon the Terrestrial ; only with this difference , that the Equator remains fixt upon the Terrestrial Globe , but the Equinoctial upon the Celestial Globe is moveable ; ( or at least must be imagined to move ) contrary to the Diurnal motion from West to East , upon the Poles of the Ecliptick : I say imagined to move , because in the Heavens it doth really move , tho on a material Globe it would be inconvenient to make a moveable Equinoctial , and therefore it hath one fixed : which for this and the next age will sufficiently serve , without much deviation from the truth it self . Now that the difference between the Equator upon the Terrestrial Globe , and the Equinoctial upon the Celestial , may be proved ; and the motion of the Equinoctial be the better understood ; I shall only bring this example , All places that were formerly under the Equator , do and will keep the same Longitude , and remain still under the Equator : as may be proved by comparing the Ancient and modern Geographers together : but those Stars that were formerly under the Equinoctial , do not keep the same Longitude , nor remain under the Equinoctial : because the Equinoctial ( as aforesaid ) hath a motion from West to East , upon the Poles of the Ecliptick . But the Stars being fixed in their one Sphear , like knots in wood , and therefore move not , are by the Precession of the Equinox left behind the Equinoctial Colure , and so are caused to alter their Longitude ; as by comparing the Observations of ancient and modern 〈◊〉 together , it will appear : for about 346 years before Christ , the first Star in the Rams horn was by the Egyptian and Grecian Astronomers observed to be in the Equinoctial Colure : and 57 years ago , when Tycho observed , it was found to be in 27 degrees 37 minutes of ♈ . So that in about 2000 years it is moved forwards 28 degrees , and will according to Tycho's opinion , finish its Revolution in 25412 years : According to which motion , I have Calculated this following Table , for finding the Degrees and Minutes of the Equinoctial motion , answerable to any number of years within the said Revolution . ye . deg . m years . deg . m. 1 0 0¾ 100 1 25 2 0 1½ 200 2 50 3 0 2½ 300 4 15 4 0 3⅓ 400 5 40 5 0 4¼ 500 7 5 6 0 5 1000 14 10 7 0 5¾ 2000 28 20 8 0 6½ 3000 42 30 9 0 7¼ 4000 56 40 10 0 8½ 5000 70 50 20 0 17 10000 141 40 40 0 34 20000 283 20 60 0 51 25000 354 10 80 1 8 25412 360   This Table may be of use for finding the Equinoctial position of any Star , for any year either past , present , or to come . It s use is very easie , for if you desire to know the motion of the Equinox for any number of years , you need but seek your number in the Collumn of years , and against it you have the degrees and minutes of the Equinoctial motion . But tho the Stars have this motion one way , viz. in Longitude , yet do they not at all alter their Latitudes ; because the motion of the Equinoctial is made upon the Poles of the Ecliptique . IIII Of the Ecliptique . The Ecliptique is a great Circle , lying oblique or aslope from the Equinoctial , making an Angle of 23 ½ degrees with it : It cuts the Equinoctial into two equal parts , and is cut by the Equinoctial in two opposite points , viz. ♈ , and ♎ . It divides the Globe into two equal parts , called Hemisphears ; the one the Northern and the other the Southern Hemisphear . It is divided into 12 equal parts , which are called the twelve Signes , every part being noted with the Character of the Signes belonging unto it ; as unto Aries , ♈ : to Taurus , ♉ : to Gomini , 〈◊〉 ; and so of the rest . From every one of these 12 divisions proceed both waies viz. North , and South , Circles of Longitude , into the Poles of the Ecliptique . Each of these twelve Signes is divided into 30 equal parts , which are called degrees ; and are numbred upon every tenth degree with 10 , 20 , to 30 , and upon may new Celestial Globe , for more preciseness , every degree is again divided into halfs . It is called the Ecliptique as being derived from the Greek word : 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 which signifies to want light , because in and about it happen all the defects and Eclipses both of the Sun and the Moon . It is also called the Way of the Sun , because the Sun goes alwaies under it , passing through it in all his Annual Course . V. Of the Poles of the Ecliptick . There are two Poles of the Ecliptick , the one the North Pole , the other the South Pole ; and are called North or South according to their position next the North or South Pole of the World. Each it distant from its correspondent Pole of the World 23 degrees 30 minutes . As on the Terrestrial Globe all the Meridians discribed thereon meet in the Pole of the World , so on the Celestial all the Circles of Longitude drawn through the twelve Signes meet in the Poles of the Ecliptick . VI. Of the Axis of the Ecliptick . Through the two Poles of the Ecliptick is imagined to pass a straight line , through the Center of the Plain of the Ecliptick ; which is called the Axis of the Ecliptick , upon which the second motion of the Ecliptick is performed : even as the Diurnal motion is performed upon the Axis of the World. VII . Of the Colures , and Cardinal Points . There are two great Circles cutting one another at right angles in the Poles of the World , which are called the Colures . Each Colure receives an additional name from the point in the Ecliptick that it Cuts ; as the one passes from Pole to Pole through the beginning of ♈ and ♎ , which being two Equinoctial Signes , name therefore that Colure the Equinoctial Colure : The other passes through the beginning of ♋ and ♑ , which are Solsticial Signes , and therefore names that the Solsticial Colure . These Colures by intersecting one another , divide themselves into four Semi-circles ; and these Semi-circles divide the Ecliptick into four equal parts . viz. in ♈ , ♋ , ♎ , and ♑ , The points of the Ecliptick that these intersections pass through , are called the four Cardinal points , and are of great use in Astronomy ; for according to the Suns approach to any of them , the Season of the year is altered into Spring , Summer , Autumn , Winter : as shall be shewed hereafter . VIII . Of the Tropicks . There are two smaller Circles Parallel to the Equinoctial , which are called the Tropicks ; the one called the Tropick of Cancer , the other the Tropick of Capricorn : they are distant from the Equinoctial 23 degrees 30 minutes ; and therefore are the bounds of the Ecliptick . They receive their names from the Celestial Signe that they are joyned unto ; as the one the Tropick of Cancer , because it touches the Signe of Cancer ; the other the Tropick of Capricorn , because it touches the Signe of Capricorn . IX . Of the Circles Arctick and Antarctick . About the Poles of the World are two smal Circles described ; the one called the Arctick , the other the Antartick : That in the North is called the Arctick Circle : that in the South the Antarctick Circle . They have the same distance from the Poles of the World that the Tropicks have from the Equinoctial Circle , ( viz. 23 degrees 30 minutes ) and that the Ecliptick hath from the Poles of the World ; and therefore run through the Poles of the Ecliptick . X Of the Images called Constellations , drawn upon the Celestial Globe . Here I think fit to be beholding to Dr. Hood . for the paines he hath taken in his comment upon the Images and Constelations . He saith , The stars are brought into Constellations , for instructions sake : things cannot be taught without names , to give a name to every star had been troublesome to the Master , and for the Scholler ; for the Master to devise , and for the Scholler to remember : and therefore the Astronomers have reduced many stars into one Constellation , that thereby they may tell the better where to seek them ; and being sought , how to express them . All the Constellations formerly notified by the Antients were in number 48. twelve whereof we call the twelve Signes of the Zodiack , viz. 1 Aries , ♈ . 2 Taurus , ♉ . 3 Gemini , ♊ . 4 Cancer , ♋ . 5 Leo , ♌ . 6 Uirgo , ♍ . 7 Libra , ♎ . 8 Scorpio , ♏ . 9 Sagittarius , ♐ . 10 Capricorn , ♑ . 11 Aquarius , ♒ . 12 Pisces . ♓ . One and twenty more are Placed in the North Hemisphear , and are called 1 Ursa minor , 2 Ursa Major , 3 Draco , 4 Cepheus , 5 Bootes , 6 Corona Septentri , 7 Hercules , 8 Lyra , 9 Cygnus , 10 Cassiopeia , 11 Perseus , 12 Auriga , 13 Serpentarius , 14 Serpens Ophiuchi , 15 Sagitta , 16 Aquila , 17 Delphinus , 18 Equiculus , 19 Pegasus , 20 Andromeda , 21 Triangulum . The other 15 are scituated in the South Hemisphear , and called 1 Cetus , 2 Orion , 3 Eridanus , 4 Lepus , 5 Canis Major , 6 Canicula , 7 Argo Navis , 8 Hydra , 9 Crater , 10 Corvus , 11 Centaurus , 12 Lupus , 13 Ara , 14 Corona Austrina , 15 Pisces Austrina . Besides there are 2 other Constellations in the North Hemisphear , viz. Antinous , and Coma Berenices : which because they were not specified by the Ancients are here inserted apart . Now the Astronomers did bring them into these figures , and not into other , being moved therto by these three reasons : first these Figures express some properties of the stars that are in them ; as those of the Ram to bee hot and dry ; Andromeda chained , betokeneth imprisonment : the head of Medusa cut off , signifieth the loss of that part : Orion with his terrible and threatning gesture , importeth tempest , and terrible effects : The Serpent , the Scorpion , and the Dragon , signifie poyson : The Bull , insinuateth a melancholy passion : The Bear inferreth cruelty , &c. Secondly , the stars , ( if not precisely yet after a sort ) do represent such a Figure , and therefore that Figure was assigned them : as for example , the Crown , both North , and South ; the Scorpion and the Triangle , represent the Figure which they have . The third cause , was the continuance of the memorie of some notable men , who either in regard of their singular paines taken in Astronomy , or in regard of some other notable deed , had well deserved of man kind . The first Author of every particular Constellation is uncertain ; yet are they of great antiquity ; we receive them from Ptolomte , and he followed the Platonicks ; so that their antiquity is great . Moreover we may perceive them to be ancient by the Sciptures ; and by the Poets . In the 38 Chapter of Job there is mention made of the Pleiades , Orion , and Arcturus , and Mazzaroth , which some interpret the 12 Signes : Job lived in the time of Abraham , as Syderocrates maketh mention in his Book de Commensurandis locorum distantiis . Now besides all this , touching the reason of the invention of these Constellations , the Poets had this purpose , viz. to make men fall in love with Astronomy : And to that intent have to every Costellation invented strange conceited stories , ( as you may read at the latter end of this Book ) therein imitating Demosthenes , who when he could not get the people of Athens to hear him in a matter of great moment , and profitable for the Commom-wealth , he began to tell them a tale of a fellow that sold an Ass ; by the which tale , he so brought on the Athenians , that they were both willing to hear his whole Oration , and to put in practice that whereto he exhorted them . The like intent had the Poets in of those Stories : They saw that Astronomy being for commodity singular in the life of man , was almost of all men utterly neglected : Hereupon they began to set forth that Art under Fictions ; that thereby , such as could not be perswaded by commodity , might by the pleasure be induced to take a view of these matters : and thereby at length fall in love with them . For commonly you shall note this , that he that is ready to read the Stories , cannot content himself therewith , but desireth also to know the Constellation , or at leastwise some principal Star therein . There are in Heaven yet twelve Constellations more , posited about the South Pole , which were added by Frederic● Ho●tmanno , inhabiting on the Island Sumatra who being accommodated with the Instruments of that immortal Tycho , hath observed the Longitude and Latitude of those Stars , reduced them into Constellations , and named them as follows , 1 The Crane , 2 The Phenix , 3 The Indian , 4 The Peacock , 5 The Bird of Paradice , 6 The Fly. 7 The Camelion . 8 The South Triangle , 9 The Flying Fish , 10 Dorado , 11 The Indian Fowl , 12 The Southern Serpent . XI . Of the Number of the Stars . Although in Heaven there be a very great number of visible Stars , which for their multitude seem innumerable ; yet no wise man will from thence infer that they are impossible to be counted : for there is no Star in Heaven that may be seen , but its Longitude and Latitude may with meet Instruments for that purpose be exactly found ; and being once found , it may have a name allotted it , which with its Longitude and Latitude may be Catalogized either for the memory of the Observer , or the knowledge of Posterity . Now therefore if any one Star may be observed , they may all be observed ; and then may they all have Names given them ; which tho to the ignorant it seem uncredible , yet to the sons of God , ( as Josephus call Astronomers ) who herein participate of their fathers knowledge , it is easie to number the Stars , and call them all by their Names Psal. 97 , 4. But tho all the Stars in Heaven may be numbred and named , yet have not the Ancient Astronomers thought fit to take notice of more then 1025 of the chiefest that are visible in our Horizon , they being sufficient for any purpose that we shall have occasion to apply them unto . Yet of late the industry of Frederick Houtman aforesaid , hath added to the Catalogue 136 Stars , with their Longitude Latitude and Magnitude , and given Names unto them : which upon my New Globes I have also ascerted , as may be seen about the South Pole thereof . So that with these 1025 , observed by the Ancients , and these 136 , the whole number of the Catalogue is 1161. Some other Stars of late have been also observed by Bai●rus , among the several Constellations aforesaid ; but none of any Considerable Magnitude , and therefore I think fit to pass them by , and come to their scituation in Heaven , according to Longitude and Latitude . XII . Of the Scituation of the Stars : The Stars are Scituate in Heaven according to their Longitude and Latitude As the Longitude of any Place upon the Terrestrial Globe is an Arch of the Equator , Comprehended between the first Meridian and the Place . So the Longitude of any Star upon the Celestial Globe is an Arch of the Ecliptick , contained between the first point of ♈ and the Star inquired after . But yet because the Ecliptick is divided into twelve Signes , the Longitude of a Star is therefore ( in the most Customary account ) an Arch of the Ecliptick comprehended between the Semi-circle of Longitude passing through the beginning of the Signe the Star is in , and the Semi-circle of Longitude passing through the Center of the Star. The Latitude of a Star is either North or South : North , if on the North side of the Ecliptick ; South , if on the South side of the Ecliptick . As the Latitude of any Place upon the Terrestrial Globe is an Arch of the Meridian , contained between the Equator and the Parallel of the Place , So is the Latitude of any Star upon the Celestial Globe an Arch of a Semi-circle of Longitude , comprehended between the Equinoctial and the Star inquired after . XIII . Of the Magnitudes of the Stars : For the better distinction of the several sizes of Stars , they are divided into six several Magnitudes . The biggest and brightest Stars are called Stars of the first Magnitude : Those one degree inferiour in light and bigness are called Stars of the Second Magnitude , Those again one degree inferiour to the Stars of the second Magnitude , are called Stars of the Third Magnitude , and so the Stars gradually decrease unto the sixth Magnitude , which is the smalest , some few obscure Stars only excepted , which for their Minority and dimness are called Nebula . These several Magnitudes of the stars are expressed on the Globe in several shapes , as may be seen in a small Table placed on the Globe for that purpose . Now for your further satisfaction and delight , I have inserted a Collection of D. Hoods , wherein is expressed the measure of every Magnitude , and the proportion it hath , first , to the Diameter , and secondly , to the Body of the Earth . The greatness of any thing ( saith he ) cannot be better expressed then by comparing it to some common measure , whose quantity is known : The common measure whereby Astronomers express the greatness of the Stars , is the Earth ; Sometimes they compare them with the Diameter of the Earth , sometimes with the Globe thereof : The Diameter according to their account which allow but 60 miles to a degree , containeth 6822 8 / 11 miles ; and the whole soliditie of the Globe containes 165 , 042 , 481 , 283. miles and 79 / 137. According to Ptolome , who allotteth to every degree 62½ miles , the Diameter containeth 7159 miles 1 / 11 , and the whole soliditie of the Globe , hath 192 , 197 , 184 , 917 , 473 / 1331 miles . The proportion of the Diameters of the fixed Stars ; Compared with the Diameter of the Earth . The Diameter of a fixed Star of the first Magnitude compared with the Diameter of the Earth hath such proportion to it , as 19 hath to 4 : therefore it containeth the Diameter of the Earth 4 times and ¾ . The Diameter of a Star of the second Magnitude is unto the Diameter of the Earth as 269 is to 60 : therefore it containeth it 4 ⅙ times . The Diameter of a fixed Star of the third Magnitude is unto the Diameter of the Earth as 25 unto 6 : therefore it containeth it 4 ⅙ times . The Diameter of a fixed Star of the fourth Magnitude is unto the Diameter of the Earth as 19 unto 5 : therefore it containeth it 3 ⅘ times . The Diam . of a fixed Star of the fifth Mag , is unto the Diameter of the Earth , as 119 unto 36. therefore it containeth it 3 11 / 36 times . The Diam . of a fixed Star of the sixth Mag. is unto the Diame● of the Earth , as 21 unto 8 ; therefore it containeth it ⅝ times . As for the proportions of the cloudie and obscure Stars , they are not expressed because they are but few , and of no great account in respect of their smalness . The proportions of the fixed Stars compared with the Globe of the Earth , are as follow . A Star of the first Magnitude is to the Globe of the Earth , as 6859 , to 64. therefore it containeth the Globe of the Earth 107 ⅙ times . A Star of the second Magnitude is to the Globe of the Earth , as 19465109 is to 216000. therefore it containeth it 90 ⅛ times . A Star of the third Magnitude is to the Globe of the Earth , as 15625 is unto 216 : therefore it containeth it 72 ⅓ times . A Star of the fourth Magnitude is to the Globe of the Earth as 6850 is unto 125 : therefore it containeth the Globe of the Earth 54 11 / 12 times . A Star of the fifth Magnitude is to the Globe of the Earth , as 1685159 : is unto 46656 : therefore it containeth the Globe of the Earth 36 ⅛ times . A Star of the sixth Magnitude is to the Globe of the Earth , as 9261 is unto 512 : therefore it containeth the Globe of the Earth 18 1 / 10 times . I confess all this may seem matter of incredulity to those whose understanding is swayed by their visual sence ; but if they be capable to consider the vast distance of those Huge Bodies , ( the Stars ) from the face of the Earth , and also the diminutive quality of Distance , their reason will be rectified , and their incredulity turn'd into an acknowledgement of the unspeakable wisdom of Almighty God ; and they will say with the Psalmist , Great is our Lord , Great is his Power , his Wisdom is infinite . Psal. 147. 5. The distance of the Stars therefore from the Earth , is according to M. John Dee's Computation , 20081 ½ Semidiameters of the Earth . The Semidiameter of the Earth containeth of our common miles 3436 4 / 11 , Such miles as the whole Earth and Sea round about is 21600 : allowing for every degree of the greatest Circle 60 miles : so that the distance of the Stars from the Earth is in miles 69006540. Now as M. Dee saith , ( almost in these same words ) if you weigh well with your self this little parcel of fruit Astronomical ; as concerning the bigness and distance of the Stars , &c. and the Huge massiness of the Starry Heaven , you will find your Consciences moved with the Kingly Prophet to sing the confession of Gods Glory ; and say , The Heavens Declare the Glory of God , and the firmament sheweth forth the works of his Hands . XIIII . Of the Nature of the Stars . To many of the Principal Stars there is in Planetical Characters prefixed their Planetical Natures . The Astrologers make great use of them for knowing the nature of the Stars : for those Stars that have the character of ♄ adjoined are said to be of the nature of ♄ : those that have ♃ adjoined , are of the nature of ♃ : and so of the rest . If a Star have the characters of two Planets adjoined , that Star participates of both their Natures , but most of that Planets whose character is first placed . The use Astronomers make of those characters , is for knowing that culler of any Star ; as if a Star have ♄ adjoined , it is of the culler of ♄ ; if ♃ , it is the culler of ♃ , &c. The fixed Stars are known from the Planets by their continual twinckling ; for the Planets never twinckle , but the fixed Stars do . XV. Of Via Lactea , or the Milky way . This subject because it is already so fully handled by D r. Hood , that more then he hath written cannot well be said , either of his own oppinion or other mens , I think fit therefore to give you his own words : which are as follow . VIA LACTEA ▪ or Circulus Lacteus ; by the Latines so called ; and by the Greekes , Galaxia ; and by the English , the Milky way . It is a broad white Circle that is seen in the Heaven : In the North Hemisphear , it beginneth at Cancer , on each side the head thereof , and passeth by Auriga , by Perseus , and Cassiopeia , the Swan , and the head of Capricorn , the tayl of Scorpio , and the feet of Centaur , Argo the Ship , and so unto the head of Cancer . Some in a sporting manner , do call it Watling street ; but why they call it so , I cannot tell ; except it be in regard of the narrowness that it seemeth to have , or else in respect of that great High way that lieth between Dover and S. Albons , which is called by our men Watling street . Concerning this Circle there are sundry opinions : for there is great difference among some writers , both touching the place , matter , and efficient cause thereof . Aristotle dissenteth from all other , both Philosophers and Poets , in the place , matter , and cause of this Circle ; saying , that it is a Meteor ingendred in the Air , made of the vapors of the earth , drawn up thither by the heat of the Sun , and there set on fire . But his opinion is of all men confuted . First , touching the place , it cannot be in the Air ; for whatsoever is in the Air , is not seen of all men , at all times , to be under one and the same part of Heaven . If we see it in the South , they that are in the West shall see it under the East side of the Heaven ; and they that are in the East , shall see it in the West part of the Heaven ; but this Circle is of all men seen alwaies under the same part of Heaven , and to be joyned with the same Stars ; therefore it cannot be in the Air. Again , for the matter , it cannot be made of that which Aristotle nameth ( i. e. ) the vapours of the earth , because of the long continuance of the thing , and that without any alteration : for it is impossible that any Meteor made of vapours drawn up from the water , or exhalations from the earth , should last so long ; as may be seen in blazing Stars ; which though they have continued long , as namely , 16. moneths , some more , some less ; yet at the length they have vanished away : whereas this Circle hath continued from the beginning unto this day . Besides , put case it were made of these exhalations , Whence will they infer the uniformity thereof ? The Comets do alter diversly , both in the fashion of their blazing , and also in their several quantities ; whereas in this Circle , there is nothing but the same part , alwaies of one form and of one bigness . In the e●●cient cause therefore he must needs err : for if it be neither in the Air , nor made of the exhalations of the earth , it cannot be caused by the Sun ; for the one is the place and the other the matter , wherein , and whereupon the Sun sheweth his power . All other , ( besides Aristotle ) agree in the place , but dif●er in the efficient cause thereof : and they are either Philosophers , or Poets . Both these affirm that it is in the Firmament ( i. e. ) in the eight Sphear ; but they disagree in the cause thereof . The Philosophers ( and chiefely Demecritus ) affirm the cause of the thing , to be the exceeding great number of Stars in that part of Heaven , whose beams meeting together so confusedly , and not coming distinctly to the ey , causeth us to imagine such a whiteness as is seen . But the best opinion is this , that this Milky way is a part of the Firmament , neither so thin as the other parts thereof are , not yet so thick as the Stars themselves . If it were as thin as the other parts of the Heaven besides the Stars , then could it not retain the light , but the light would pass through it and not be seen : If it were as thick as the Stars , then would the light be so doubled in it , that it would glister and shine , as the Stars themselves do : but being neither so thin as the one , nor so thick as the other , it becommeth of that whiteness we see . Bla●u saith , This Lactean whiteness and clearness ariseth from a great number of little Stars , constipated in that part of Heaven : flying so swiftly from the sight of our eyes , that we can perceive nothing but a confused light : this the Tubus Diopticus ( more lately found out ) doth evidently demonstrate to us : by the benefit of which little Stars ( otherwise inconspicuous to our eyes ) are there clearly discerned . About the Southern Pole are seen two white spots , like little clouds , colured like the via Lactea . One of which is trebble the Latitude of the other ; some Mariners call them Nubecula Magellani . This Milkie way is discribed on the Globe between two tracks of smal Pricks , running through the Images mentioned in the beginning of this Section . Thus have you the definition of the Globes ; with the description of all the lines , Circles , &c. described thereon . I shall now explain unto you the meaning of Several words of Art , which in the use of them you will meet with , and then come to the Use it self . And first , what is meant by the word Horizon . When I spake of the Horizon before , I only mentioned the wooden Horizon or frame about the Globe ; which because it represents the Mathematical Horizon , is therefore called the Horizon : but the word Horizon is to be considered more particularly , two manner of waies : as First , the Natural Horizon . Secondly , the Mathematical Horizon . The Natural Horizon is that Appearent Circle which divides the Visible part of Heaven from the invissible ; it extends it self in a straight line from the Superficies of the Earth , every way round about the place you stand upon , even into the very Circumference of the Heavens . It is onley discerned at Sea , or on plaine ground , that is free from all hinderances of the sight as Hills , Trees , Houses , &c. The Mathematical Horizon ( which indeed is meant in this Treatise , so oft as I shall have occasion to name the word Horizon ) is a great Circle which divides that part of Heaven which is above us , from that which is under us , precisely into two equal parts : whose Poles are the Zenith and Nadir . In this Circle the Azimuths or Verticle Circles are numbred : and by this Circle our Daies and Nights are measured out unto us : for while the Sun is above the Horizon it is day ; and when it is under the Horizon it is Night . This Circle is represented unto us by the upper Plain of the wooden Horizon : Therefore so oft as you are directed to bring any degree or Star &c. to the Horizon , it must be understood that you must turn the Globe till the degree or Star come just to the upper inner edge of the wooden Horizon . The Zenith , and Nadir , are two points opposite to one another . The Zenith is that point in Heaven which is directly over our Heads : and the Nadir is that point in Heaven which is directly under our feet . The Azimuths or Verticle Circles are great Circles passing through the Zenith , and Nadir , whose Poles are the Zenith and Nadir . And as the Meridians cut the Equator , and all Parallels to the Equator at Right Angles , so the Azimuths cut the Horizon and all Almicanthars at Right Angles also . The Azimuths ( as the Meridians ) are infinite ; and are numbred by degrees from the East and West point towards the North and South in the Horizon : as also is the Amplitude . The Almicanthars are Circles Parallel to the Horizon , whose Poles are the Zenith and Nadir . They are also called Circles of Altitude , because when the Sun Moon or any Star , is in any number of degrees above the Horizon , it is said to have so many degrees of Altitude , which degrees of Altitude are numbred upon the Verticle Circle from the Horizon upwards , towards the Zenith . The Almicanthars are also infinite : as Parallels , Meridians and Azimuths are . The Amplitude is the number of degrees contained between the true East or West point in the Horizon , and the rising or setting of the Sun , Moon , or Stars . &c. The Declination is the number of degrees that the Sun , Moon , or any Star , is distant from the Equinoctial , towards either Pole : and hath a double Denomination , viz. North Declination , and South Declination : for if the Sun Moon or Star swarve towards the North Pole , they are said to have North Declination ; if towards the South Pole , South Declination . The Right Ascension is the number of degrees of the Equinoctial ( accounted from the first point of Aries ) which comes to the Meridian with the Sun Moon or Star , or any other point in Heaven proposed . The Oblique Ascension is the number of degrees of the Equinoctial which comes to the East side of the Horizon with the Sun Moon or any Star. The Oblique Descension is the degrees of the Equinoctial which comes to the West side of the Horizon with the Sun Moon or any Star. The Ascensional Difference is the number of degrees after subtraction of the Oblique Ascension from the 〈◊〉 〈◊〉 ●scension , . So many degrees as you are said to sail towards the Pole , you are said to Raise the Pole ; and so many degrees as you sail from the Pole , you are said to Depress the Pole. Course , is the point of the Compass you sail upon ; as if you sail East-wards , it is an Easterly Course , if West , a Westerly Course &c. Distance is the number of leagues you have sailed from any Place , upon any Course . A Zone is a space of Earth contained between two Parrallels . The ancient Geographers made five Zones in the Earth . Two Frozen , Two Temperate , and one Burnt Zone . The two Frozen Zones are those parts of the Globe , comprehended between the North Pole and the Arctick Circle , and the South Pole and the Antarctick Circle ; by the Ancients called inhabitable ; because the Sun being alwaies far remote from them , shoots its beams Obliquely upon them , which Oblique beams are so very weak , that all their Summer is but a continued Winter , and the Winter ( as they thought impossible to be at all indured . The Temperate Zones are the space of Earth contained between the Arctick Circle and the Tropick of ♋ , and the Antarctick Circle and the Tropick of ♑ : by the Ancients called Temperate and Habitable ; because they are composed of a sweet Mediocrity , between outragious Heat and extremity of Cold. The Burnt Zone is the space of Earth contained between the Tropick of ♋ , and the Tropick of ♑ , called by the Ancients Unhabitable ; because in regard the Sun never moves out of this Zone but darts its Beames perpendicularly upon it , they imagined the Air was so unsufferable Hot , that it was impossible for any to inhabite in this Zone . So that as you see they held the two Temperate Zones only habitable ; and the two Frozen Zones and one Burnt Zone , altogether unpossible to be inhabited . But their Successors either animated by industry , or compeld by necessity , have apparently confuted that Assertion ; for at this time many thousands can witness that their bloods are not so greasie as to be melted in the Scortching heat of the one , or so watry as to be congealed in the Icy frosts of the other . The Ancients have yet otherwise divided the Earth into four and twenty Northern Climates , and four and twenty Southern Climates : so that in all there is eight and forty Climates . The Climates are altered according to the half hourly increasing of the longest daies ; for in the Latitude where the longest daies are increased half an hour longer then they are at the Equator ( viz. longer then 12 hours ) the first Climate begins ; and in the Latitude where they are increased an whole hour longer then in the Equator , the second Climate begins ; where the daies are increased three half hours longer then in the Equator , the third Climate begins ; and so onwards , the Climates alter according as the longest day increases half an hour , till you come to find the longest day 24 hours long Now the Ancients ( in those times ) knowing no more then nine Habitable Climates , gave names only to nine . The first they called Dia Meroes , after the name of a famous Inland Iland , which is scituate about the middle of that Climate , and is now called Gueguere . The second Climate they called Dia Syenes , after the name of an eminent Citty in Egypt , lying about the midst of that Climate . The third Dia Alexanderas , after the name of the Metropolitan Citty of Egypt . The fourth Dia Rhodes . The fifth Dia Romes . The sixth Dia Ponton . The seventh Dia Boristheneos , The eighth Dia Ripheos . The ninth Dia Daniam . These names belong only to the Climates on the North side of the Equator . But those on the South side ( in regard of the smal Discoveries those Ages had on that side the Equator ) were distinguisht only by the addition of the word Anti , to the same Southerly Climate : as the first Southern Climate ( which is that Climate that lies as many degrees to the South-ward as the first doth to the North-ward ) they called Anti Meroes . The second Anti Syenes . The third Anti Alexanderas : and so on to the ninth . In every Climate is included two Parallels , which are of the same nature with the Climates , save only that as the Climates alter by the half hourly increasing of the longest day , the Parallels alter by the quarter hourly increasing of the longest day . Furthermore , in respect of the Horizon , we find the Sphear constituted into a threefold Position : as first , into a Direct Sphear , Secondly , a Parallel Sphear , Thirdly , an Oblique Sphear . A Direct Sphear hath both the Poles of the World in the Horizon , and the Equinoctial transiting the Zenith . In a Direct Sphear all the Circles Parallel to the Equator make right angles with the Horizon , and are also divided into two equal parts by the Horizon : and in a Direct Sphear the Sun Moon and Stars are alwaies twelve hours above the Horizon , and twelve hours under the Horizon , and consequently make twelve hours Day , and twelve hours Night . It is called a Direct Sphear because all the Celestial Bodies , as Sun Moon and Stars &c. by the Diurnal Motion of the Primum Mobile , ascend directly above , and descend directly below the Horizon . They that inhabite under the Equator have the Sphear thus posited ; as in the Iland Borneo , Sumaira , Celebes , St. Thomas a great part of Africk , Peru in the West-Indies : &c. as you may see by the Globe it self ; if you move the Brasen Meridian through the notch in the Horizon , till the Poles thereof touch the Horizon . As in this Figure . A Parallel Sphear hath one Pole of the VVorld in the Zenith , the other in the Nadir , and the Equinoctial line in the Horizon . In a Parallel Sphear all the Circles Parallel to the Equinoctial are also Parallel to the Horizon , and in a Parallel Sphear from the 10th of March to the 11th of September ( the Sun being then in the Northorly Signes and consequently on the North side the Horizon ) there is six Moneths Day in the North , and six Moneths Night in the South : and contrarily from the 11th of September to the 10th of March , ( the Sun being then in the Southerly Signes , and therefore on the South side the Horizon ) there is six Moneths Day in the South , and six Moneths Night in the North. It is called a Parallel Sphear , because the Sun Moon or Stars in a Diurnal Revolution of the Heavens , neither ascend higher or descend lower , but alwaies move Parallel to the Horizon . The Earth is thus Posited under both the Poles , viz. in 90 degrees of Latitude ; as may be seen by the Globe , if you turn the Brasen Meridian till either of the Poles be elevated 90 degrees above the Horizon . As in this figure . An Oblique Sphear hath the Axis of the World neither Direct nor Parallel to the Horizon , but lies aslope from it . In an Oblique Sphear all the Celestial Bodies , as Sun Moon or Stars &c. have ( in respect of the Horizon ) Oblique and unequal Ascensions and Descensions , and all the lines Parallel to the Equator make unequal Angles with the Horizon , and are cut by the Horizon into unequal parts ; for those lines towards the elevated Pole , have a greater portion of a Circle under the Horizon then above it : only the Equator because it hath the same Center with the Horizon , doth divide the Horizon into two equal parts , and is also divided into two equal parts by the Horizon . Hence is follows that when the Sun is in any part of the Ecliptick that declines towards the elevated Pole , the Daies in the elevated Hemisphear shall be longer then the Nights : and when the Sun is in any part of the Ecliptick that declines towards the Depressed Pole , the Nights shall be longer then the Daies . But when the Sun is in the Equinoctial , ( because whether the Pole be either Raised or Depressed ) equal portions remain both above and under the Horizon , therefore the Daies are of the same length with the Nights , and the Nights with the Daies . Also in an Oblique Sphear , all those Stars that have as great or greater number of degrees of Declination then is the elevated Poles Complement of Latitude to 90 , never set or come under the Horizon , and those Stars that have the same Declination about the Depressed Pole never rise . It is called an Oblique Sphear , because all the Circles of the Sphear move Obliquely about the Horizon . The Earth is thus Obliquely posited to all those Nations that inhabite under any degree of Latitude either North or South-wards between the Equator and either Pole : as may variously be seen by the Globe , when the Axis lies not on the Horizon , nor the Equator is Parallel to the Horizon . As in this following Figure . Moreover all Places have their Antipodes , Peraeci and Antae●i . The Antipodes of any Place is the opposite degree on the Globe . As if a Perpendicular were let fall from the Place you stand on , through the Center of the Earth , and continued till it pass quite through the Superficies of the Earth , on the other side ; then in the point where the Perpendicular cuts the Superficies of the Earth on the other side , is the Antipodes of that Place . The Inhabitants of any two Places that are in Antipodes to each other , go with their Feet directly against one another : and have a contrariety in the Seasons of the Year , and Risings , and Settings , of the Sun Moon Stars , and all other of the Heavenly Bodies : so that when with us it is Spring , with them it is Autumn ; when with us the Sun Rises , in our Antipodes it Sets ; and therefore their Morning is our Evening , their Noon our Midnight , their Evening our Morning ; and their Longest Day our shortest . The Periaeci of any Place is that point in the same Parallel which comes to the Meridian with the Antipodes . In the Periaeci of any Place , there happens not that Contrariety of Seasons in the Year , that doth in the Antipodes ; nor in the Length of Daies : for the Daies in both Places are of equal length : but in the times of the Day , there is the same contrariety , for ( though their Spring be our Spring , and therest of their Seasons of the year the same with ours , yet ) their Morning is our Evening , their Night our Day , &c. The Antaeci of any Place is the point under the same Meridian that is distant from the Equator on the South side so many degrees as your Place is distant from the Equator on the North side . In the Antaeci there happens not that contrariety in the Daies as doth in the Antipodes , but in the Seasons of the Year there is the same contrariety ; for in our Antaeci their Morning is our Morning , their Noon our Noon , their Night our Night : but herein is the Difference , their Spring is our Fall , their Summer our VVinter , &c. and their Longest Day our shortest : as in the ●ntipodes . The Second Book . Shewing the Practical Use of the GLOBES . Applying them to the Solution of Astronomical and Geographical Problems . PRAEFACE . Some Advertisements in Choosing and Using the GLOBES . 1. SEE the Papers be well and neatly pasted on the Globes : which you may know , if the Lines and Circles discribed thereon meet exactly , and continue all the way even and whole : the lines not swerving out or in , and the Circles not breaking into several Arches ; nor the Papers either come short , or lap over one the other . 2. See that the Culler be transparent , and ly not too thick on the Globe ; lest it hide the superficial Descriptions . 3. See the Globe hang evenly between the Meridian and Horizon , not inclining more to one side then the other . 4. See the Globe swim as close to the Meridian and Horizon as conveniently it may ; lest you be too much puzzeld to find against what point of the Globe any degree of the Horizon or Meridian is . 5. See the Equinoctal line be one with the Horizon , when the Globe is set in a Parallel Sphear . 6. See the Equinoctal line cut the East and West point of the Horizon , when the Globe is set to an Oblique Sphear . 7. See the Degrees marked with 90. and 00 , hang exactly over the Equinoctial line of the Globe . 8. See that exactly half the Meridian be above the Horizon , and half under the Horizon : which you may know if you bring any of the Decimal Divisions to the North Side of the Horizon , and find their Complement to 90. int h South . 9. See that when the Quadrant of Altitude is placed at the Zenith , the Beginning of the Graduations reach just to the superficies of the Horizon . 10. See that while the Index of the Hour Circle ( by the motion of the Globe ) passes from one hour to the other , 15. degrees of the Equator pass through the Meridian . 11. If you have a Circle of Position , see the Graduations agree with those of the Horizon . 12. See that your wooden Horizons be made substantial and strong ; for ( besides the Inconveniences that thin wood is subject unto , in respect of warping and shrinking ) I have had few Globes come to mending that have not had either broken Horizons , or some other notorious fault , occasioned through the sleightness of the Horizons . In the Using the Globes . KEep the East side of the Horizon alwaies towards you , unless your Proposition requires the turning of it : which East side you may know by the Word East , placed on the outmost verge thereof . For then have you the graduated side of the Meridian alwaies towards you ; the Quadrant of altitude before you , and the Globe divided exactly into two equal parts . So oft as I name to , at , of , or under the Meridian , or Horizon , I mean the East side of the Meridian , and Superficies of the Horizon : because the East side of the Meridian passes through the North and South points , both of the Globe and Horizon ; and agrees just with the middle of the Axis : And the Superficies of the Horizon divideth the Globe exactly into two equal parts . It you happen to use the Globes on the South side the Equator , you must draw the wyers out of either Pole , and change them to the contrary Poles ; putting the longest wyer into the South Pole. And because on the other side the Equator the South Pole is elevated , therefore you must elevate the South Pole of the Globe above the Horizon ; according to the South Latitude of your Place ; as shall be shewed hereafter . In the working some Problems it will be required that you turn the Globe to look on the West side thereof : which turning will be apt to jog the Ball , so as the degree that was at the Horizon or Meridian , will be moved away , and thereby the Position of the Globe altered . To avoid which inconvenince you may make use of a Quill , thrusting the Feather end between the Ball and the Brazen Meridian , and so wedge it up , without wronging the Globe at all , till your Proposition be answered . PROBLEME I. To find the Longitude and Latitude of Places , on the Terrestrial Globe . SEek the Place on the Terrestrial Globe , whose Longitude and Latitude you would know , and bring that Place to the Brazen Meridian ; and see how many degrees of the Equator is cut by the Meridian , from the first general Meridian , ( which on my Globes pass through Gratiosa , one of the Isles of the Azores , ) for that number of degrees is the Longitude of the Place . Example . I desire to know the Longitude of London , and close to the name London I find a smal mark 0 thus , ( which smal mark is in some Globes and Maps adorned with the Picture of a Steeple , &c. ) therefore I do not bring the word London to the Meridian , but that smal mark ; for that alwaies represents the the Town or Citty sought for : And keeping the Globe steddy in this Position , I examine how many degrees of the Equator are contained between the Brazen Meridian , and the first general Meridian ; which I find to be 24. deg . 00. min. Therefore I say the Longitude of London is 24. degrees 00. min. For the Latitude . See on the Brazen Meridian how many degrees are contained between the Equator and the mark for London ; which in this Example is 51½ : therefore I say London hath 51½ degrees North Latitude . PROBLEME II. The Longitude and Latitude being know , to Rectifie the Globe fit for use . 1. WHen you rectifie the Globe to any particular Latitude you must move the Brazen Meridian through the notches of the Horizon till the same number of degrees accounted on the Meridian from the Pole ( about which the Hour-Circle is ) towards the North point in the Horizon ( if in North Latitude , and toward the South if in South Latitude ) come just to the edge of the Horizon . Example . By the former Proposition I found the Latitude of London to be 51½ degrees North Latitude : therefore I count 51½ degrees from the Pole downwards towards my right hand , and turn the Meridian through the notches of the Horizon till those 51½ degrees comes exactly to the uppermost edge of the North point in the Horizon ; and then is the Meridian rectified to the Latitude of London . 2. Next rectifie the Quadrant of altitude , after this manner , Screw the edge of the Nut that is even with the graduated edge of the thin Plate , to 51½ degrees of the Brazen Meridian , accounted from the Equinoctial on the Southern side the Horizon , which is just the Zenith of London : and then is your Quadrant Rectified . 3. Bring the degree of the Ecliptick the Sun is in that day , to the Meridian : which you shall learn to know by the next Probleme , and then turn the Index of the Hour Circle to the hour 12. on the South side the Hour Circle , and then is your Hour Circle also rectified fit to use , for that Day . 4. Lastly If you will rectifie the Globe to correspond in all respects with the Position and Scituation of the Sphear , you must set the four Quarters of the Horizon . viz. East , West , North , and South , agreeable with the four quarters of the World ; which you may do by the Needle in the bottom of the Horizon ; for you must turn the Globe so long till the Needle point just to the Flower de luce . Next you must set the Plain of the wooden Horizon parallel to the Horizon of the World ; which you may try by setting a common Level on the four Quaters of the Horizon . And then positing the degree of the Ecliptick the Sun is in , to the Height above , or depth below the Horizon , the Sun hath in Heaven , ( as by the 11th Probleme ) your Globe is made Correspondent in all points with the frame of the Sphear , for that particular Time , and Latitude . PROBLEME III. To find the Place of the Sun in the Ecliptick , the Day of the Moneth being first known . SEek the Day of the Moneth in the Circle of Moneths upon the Horizon , and right against it in the Circle of Signes is the degree of the Ecliptick the Sun is in . Example . Imagine the Day to be given is May 10. therefore I seek on the Horizon in the Circle of Moneths , for May , and find the Moneths divided into so many parts as there is Daies in the Moneth ; which parts are marked with Arithmetical figures , from the beginning of the Moneth to the end , and denote the number of the Day of the Moneth that each Division represents : therefore among the Divisions I seek for 10 , and directly against it in the Circle of Signes , I find ♉ 29. degrees . Therefore I say May 10. the Suns Place is in 29. degrees of ♉ . But note , that if it be Leap Year , instead of the 10. of May you must take the 11. of May : because February having in a Leap Year 29. Daies , the 29. of February must be reckoned for the first of March , and the first of March for the second of March ; the second of March for the third of March ; and so throughout the year . The Leap Year is caused by the six od hours more then 365. daies that are assigned to every common Year : so that in a Revolution of 4. Years , one Day is gained , which is added to February ; and therefore February hath every fourth or Leap Year 29. Daies . PROBLEME IIII. To find the Day of the Moneth , the Place of the Sun being given . AS in the last Probleme it was your task to find on the Horizon the Day of the Moneth first , so now you must first seek the Signe and degree the Sun is in , and against it in the Circle of Moneths you shall see the Day of the Moneth : As against ♉ 29. you have May 10. PROBLEME V. The Place of the Sun given , to find its Declination . HAving by the third Probleme found the Suns Place on the Plain of the Horizon , you must seek the same degree in the Ecliptick , on the Globe ; then bring that degree to the Brazen Meridian ; and the number of degrees intercepted between the Equinoctial and the degree just-over the degree of the Ecliptick the Sun is in , is the Declination of the Sun for that Day : and bears its Denomination of North or South , according to its Position either on the North or South side the Equinoctial . Example . By the third Probleme aforesaid , of May 10. I find ♉ 29. the Suns Place ; Therefore I seek in the Ecliptick Line on the Globe for ♉ 29. and bring it to the East side of the Brazen Meridian , which is the graduated side ; and over ♉ 29. I find on the Brazen Meridian 20. deg . 5. min. ( numbred from the Equinoctial : ) and because ♉ is on the North side the Equinoctial , therefore I say , The Sun hath May 10. North Declination 20. degrees 5. min. PROBLEME VI. The Place of the Sun given , to find its Meridian Altitude . THe Globe rectified , Bring the degree of the Sun to the Meridian , ( or which is all one , the degree of the Ecliptick the Sun is in ; ) and the number of degrees contained between the Horizon and the Suns Place in the Meridian , is the number of degrees that the Sun is Elevated above the Horizon at Noon , or ( which is all one ) the Meridian Altitude of the Sun. Example . To know what Meridian Altitude the Sun hath here at London , May 10. I bring the Suns Place ( found by the third Probleme ) to the Meridian , and count on the Meridian the number of degrees contained between the Horizon and the degree just over the Suns Place ; which in this Example I find to be 58½ ▪ Therefore I say the Suns Meridian Altitude May 10. is here at London 58½ degrees . PROBL. VII . The Suns Place given , to find the Hour of Sun Rising , and the length of the Night and Day . THe Globe and Hour Index rectified , Seek the degree the Sun is in on the Globe , and bring that degree to the Eastern Side of the Horizon ; and the Index of the Hour Circle will point at the Hour of Sun Rising . Example . To know the Hour of Sun Rising here at London , May 10. The Suns Place ( as before ) is ♉ 29. Therefore the Globe being rectified ( as before ) I seek ♉ 29. degrees on the Globe , and bring that degree to the East Side of the Horizon ; and looking on the Index of the Hour Circle , I find it point at 4. a clock and ⅙ part of an hour more towards 5 ; therefore I say May 10. the Sun rises here at London at ⅙ ( which is 12. minutes ) after 4 a clock in the Morning . If you double 4 hours 12. minutes , it gives you the length of the Night , 8 hours 24. minutes . And if you substract the length of the Night 8. hours 24. minutes , from 24. hours , the length of Day and Night ; it leaves the length of the Day 15. hours 36. minutes . PROB. VIII . To find the Hour of Sun Set. TUrn the Place of the Sun to the West side of the Horizon , and the Index of the Hour Circle shews on the Hour-Circle the hour of Sun set ; which on the 10th of May aforesaid , is 〈◊〉 parts of an hour after 〈◊〉 7. a clock at Night , Viz. the Sun Sets at 48. minutes past 7. a clock . PROB. IX . To find how long it is Twilight in the Morning , and Evening . TWilight is that promiscuous and doubtfull light which appears before the Rising of the Sun in the Morning , and continues after the setting of the Sun in the Evening : It is made by the extension of the Suns beams into the Vapours of the Air , when the Sun is less then 18. deg . below the Horizon : for the Sun ere it Rises , and after it Sets , shoots forth its Beams through the Air , and so illuminates the Vapours of the Air ; which illumination does by degrees enlighten the Horizon , and spreads through the Zenith , even into the West , ere the Sun Rises ; and also continues above the Horizon , afte● the Sun sets . Now though it be Twilight when the Sun is 18. degrees below the Horizon ; yet the duration of Twilight ( is alterable both in respect of Time ) and Place : for at such Time at the Sun is farthest distant from any Place , the Twilight shall be greater , then when it is neerest . And in respect of Place , All Places that have great Latitude from the Equator , have longer Twilight than those that are neerer to the Equator : for as Authors say , under the Equator there is no Twilight ; when again in many Climes both Northward and Southward , the Nights are indeed no Nights but only ( as it were ) a little over-spread with a cloudy Shade ; and is either increased or diminished according to the ●autation of Meo●erological Causes . Therefore to know the beginning of Twilight in the Morning here at London , May 10 ; you must ( having the Globe rectified ) turn the degree of the Ecliptick which is opposite to the Place of the Sun till it be elevated 18. degrees in the Quadrant of Altitude above the Horizon in the West ; So shall the Index of the Hour-Circle point at the Hour that Twilight begins : Then subtract the Hour and Minute that Twilight begins from the Hour and Minute of Sun Rising , if in the Morning , or substract the Hour of Sun sett from the Hour of Twilight , if at Night ; and the remainder is the length of Twilight . Example . The Globe Quadrant and Hour-Index being rectified , as before ; and the Suns place given , ♉ 29. I seek the opposite degree on the Globe , after this manner ▪ I bring ♉ 29. to the Meridian , and observe what degree of the Ecliptik the opposite part of the Meridian cuts ; and because I find it cuts ♏ 29. therefore I say ♏ 29. is opposite to ♉ 29. Having found the opposite degree , I bring it into the West , and also the Quadrant of Altitude , and joyn ♏ 29. to 18. degrees ( accounted upwards on the Quadrant ) so shall ♉ 29. be depressed 18. degrees in the East Side the Horizon : Then looking what Hour the Hour-Index points at in the Hour-Circle , I find it to be , 1. Hor. 8. Min. which shews that Twilight begins at 8. Minutes past 1. a clock in the Morning . And if you substract 1. Hour 8. Minutes , from 4. Hours 11. Minutes , the time of Sun Rising , found by the 7th . Probleme , it leaves 3. Hours 3. Minutes for the length of Twilight : And if you double 1. Hour 8. Minutes , the beginning of Twilight , it makes 2. Hours 16. Minutes for the intermission of Time between Twilight in the Evening , and Twilight in the Morning . So that May 10. absolute Night is but 2. Hours 16. Minutes long , here at London . The reason why you bring the degree opposite to the Suns Place to the West , is , because the Quadrant containing but 90. degrees will reach no lower then the Horizon ; but this Probleme requires it to reach 18. degrees beneath it : therefore by this help , you have the Proposition Answered , as well as if the Quadrant did actually reach 18. degrees below the Horizon . This shift you may have occasion to make in some other Problemes . If you would know when Twilight ends after Sun set ; you shall find it by bringing the degree of the Ecliptick opposite to the Place of the Sun to 18. degrees of the Quadrant of Altitude , on the East side the Horizon ; for then shall the Index of the Hour-Circle point at 10. Hours 52. Minutes : which shews that it continues Twilight till 52. Minutes past 10. a clock at Night , May 10. here at London . PROB. X. The Suns Place given , to find its Amplitude ; And also to know upon what point of the Compass it Riseth . THe Globe &c. rectified : Bring the Suns Place to the East Side the Horizon ; and the number of degrees intercepted between the East point of the Horizon and the Suns Place , is the number of degrees of Amplitude that the Sun hath at its Rising ; and bears its denomination either of North or South , according to its inclination to either point in the Horizon . Or , if you would know upon what point of the Compass the Sun Rises , Look but in the Circle of Winds ; and against the Place of the Sun you have the name of the point of the Compass upon which the Sun Riseth . Examples of both . May 10. the Suns Place is ♉ 29. There●●re ● the Globe being rectified ; I bring ♉ 29. to the East side the Horizon , and find it touch against 33 , degrees 20. Minutes from the East point towards the North : Therefore I say the Sun hath North Amplitude 33 , degrees 20. Minutes . And to know upon what point of the Compass the Sun rises ; I keep the Globe to its Position , and look in the Circle of Winds , in the outmost verge of the Horizon , and find the Suns Place against the Wind named North East and by East ; Therefore I say May 10. here at London the Sun riseth upon the North East and by East point of the Compass . PROBL. XI . The Hour of the Day given , to find the Heigth of the Sun. THe Globe &c. Rectified . Turn about the Globe till the Index of the Hour-Circle point ( in the Hour-Circle ) to the Hour of the Day : Then bring the Quadrant of Altitude to the Suns Place in the Ecliptick , and the degree on the Quadrant which touches the Suns Place , shall be the number of degrees of the Suns Altitude . Example . May 10. here at London ; At 53. Minutes past 8. a clock in the Morning , I would know the Heigth of the Sun above the Horizon . Therefore I turn about the Globe till the Index of the Hour-Circle come to 53 : Minutes past 8. a clock ( which is almost 9. ) in the Hour-Circle : And keeping the Globe to this Position , I bring the Quadrant of Altitude to the Suns place , viz. 〈◊〉 29. ( found by the third Probleme ) and because the Suns Place touches upon 40. degrees of the Quadrant , therefore I say May 10. 53. Minutes past 8. a clock in the Morning , here at London , The Sun is just 40. degrees above the Horizon ; or which is all one , hath 40. degrees of Altitude . PROB. XII . The Altitude 〈◊〉 Sun , and Day of the Moneth given , to find the Hour of the Day . AN Hour is the 24th . part of a Day and a Night , or the space of time that 15. degrees of the Equator takes up in passing through the Meridian ; for the whole Equator which contains 360. degrees , passes through the Meridian in 24. Hours , therefore 15. degrees which is the 24th . part of 360 , pass through in one Hour . These Hours are Vulgarly divided into halfs , quarters , and half quarters ; but Mathematically into Minutes , Seconds . Thirds , Fourths , &c. A Minute is the 60th . part of an Hour , so that 60 , minutes make an Hour , 30 , half an Hour , 15. a quarter of an Hour : A Second is the 60th part of a Minute : a third is the 60th part of a Second : a Fourth is the 60th part of a Third : and so you may run on to Fifths , Sixths , Sevenths , &c. if you please . 12. of these Hours make a Day , and 12. more make a Night : so that Day and Night contain 24. hours as aforesaid ▪ which are Volgarly numbred from Noon with 1 , 2 , 3 , to 12 , at Night ▪ and then begin again with 1 , 2 , 3 , till 12 at Noon : But by Astronomers they are Numbred from Noon with 1 , 2 , 3 , &c. to 12. at Night ; and so forward to 13 , 14 , 15 , till 24 ; which is just full Noon the next Day . Yet in this Treatise I shall mention the Hours as they are Vulgarly co●●ted , viz. from 〈◊〉 . after noon , to 12. at Night , and call the Hours after Midnight by 1 , 2 , 3 , 4 , &c. in the Morning , to 12. at Noon again , the next Day . But to the operation . The Globe , &c. Rectified , Bring the Place of the Son to the Number of degrees of Altitude accounted upon the Quadrant of Altitude , and the Hour-Index shall point at the Hour in the Hour-Circle : yet herein respect must be had to the Fore or After noons Elevation ; as shall be shewed in the next Probleme . Example . May 10. The Sun is elevated 40. degrees above the Horizon , here at London : Therefore having found the Place of the Sun , by the third Probleme , to be ●29 . I move the Globe and Quadrant till I can joyn the 29. degree of 〈◊〉 to the 40. deg , upon the Quadrant of Altitude ; and then looking on the Hour-Circle , I find the Index point at 53. Minutes past 8. a clock , for the Fore noon Elevation ; and at 3. hours 7. Minutes for the After noons Elevation . Therefore if it be Fore-noon , I say , It is 53. Minutes past 8. a clock in the Morning . But if it be After noon I say , It is 7. Minutes past 3. a clock in the After noon . PROB. XIII . How to know whether it be Before or After Noon . HAving made one Observation , you must make a Second a little while after the First ; and if the Sun increase in Altitude , it is Before Noon : but if it decrease in Altitude , it is After Noon . Example . The Sun was at 8. hor. 53. Min. elevated 40. degr . above the Horizon : A little while after ( suppose for examples sake aquarter of an hour , ) viz. at 9. hor. 8. Min. I observe again the heigth of the Sun , and find it 42. degrees high ; so that the Altitude is increased 2. degrees ; Therefore I say , It is Fore-Noon : But if the Sun had decreased in Altitude , I should have said it had been After-Noon . How to take Altitudes by the Quadrant , Astrolabe , and Cross-staff . There are divers Instruments whereby Altitudes may be taken : but the most in use are the Quadrant , Astrolabe , and Cross-staff . A Quadrant is an Instrument comprehended between two Straight lines making a Right Angle , and an Arch discribed upon the Right Angle , as on the Center , containing 90. degrees , which is a quarter of a Circle : and therefore the Instrument is called a Quadrant . See this Figure . A prepresents the Center ; upon which is fastned a Plumb-line , A B the one side , A C the other side , upon which the Sights are placed : B C the Arch or Quadrant , which is divided into 90. equal parts , and numbred from B to C. D one Sight , E the other Sight : F the Plumbet fastned to the Plumb-line . When by this Instrument you would observe the heigth of the Sun , you must turn the Center A to the Sun , and let the beams thereof dart in at the hole in the first Sight D , through the hole in the second Sight E ; so shall the Plumb-line ly upon the degree in the Limb , of the Suns Elevation : As if the plumb-line ly upon the 20th degree , then shall the Altitude be 20. degrees ; if on 25. the Altitude shall be 25. degrees : and so for any number of Degrees the thred or Plumb-line lies on , the same number of Degrees is the Altitude of the Sun. But if it be a Star whose Altitude you would observe ; you must hold up the Quadrant , and joyn the Limb to your Cheek bone , and turn the Center towards the Star : then winking with one Ey , look through the holes of the Sights with the other Ey , till you can see the Star through those holes ; so shall the Plumb-line ( as before in the Sun ) hang upon the degree in the Limb of the Stars Elevation . Another sort of Quadrants is made with a moveable Index , as is represented in this Figure . A is the Center , A Band A C the two sides , B C the Limb , D E two Sights fixed upon a moveable Index or Label ; F G two other Sights , for observing the Horizon . When by this Quadrant you would observe an Altitude , the side B A must be parallel to the Horizon , and the Index must be moved till the Object ( be it either the Sun Moon or any Star ) be seen through the holes or slitts of the Sights placed on the Index ; for then the Arch D B shall be the Elevation required . You may know when the side B A is parallel to the Horizon , by observing the parting of Heaven from the Earth through the Sights on the Side B A. To take Altitudes by the Astrolabe . The Astrolabe is a round Instrument , flat on either side , upon one of the flats or Plains is discribed a Circle as B C D E , divided into 360 , equal parts or degrees , numbred from the line of Level B A C , with 10 , 20 , 30 , &c. to 90. in the Perpendicular D C. Upon the perpendicular is fastned a Ring as F , so as the Instrument hanging by it , the line of Level may hang parallel to the Horizon . Upon the Center is a moveable Label or Ruler , as G H , whereupon is placed two Sights as I K. If you desire further instructions for making this Instrument , you may peruse M r Wright in his Division of the whole Art of Navigation , annexed to his Correction of Errors : where he also shews the use of it at large ; which in brief is as follows . You must hold the Astrolabe by the Ring in your left hand , and turning your right side to the Sun , lift up the Label with your right hand , till the beams of the Sun entring by the hole of the uppermost Vane or Sight , doth also pierce through the hole in the nethermost Vane of Sight ; and the deg . and part of deg . that the Label lies on is the height of the Sun above the Horizon . But if it be a Star you would observe ; you must use the Astrolabe as you were directed to use the Quadrant , holding it up to your Cheek bone , and looking through the Sights , &c. To take Altitudes by the Cross-staff . This Instrument consists of a Staf about a yard long , and three quarters of an inch square : Upon it is fitted a Vane , ( or sometimes two , or three , ) so as it may slide pretty stiff upon the Staff , and stand at any of the Divisions it is set to . The making is taught by M r Wright , aforesaid : But the use is as follows . You must put that end of the Cross-staff which is next 90. degrees to your Cheek bone , upon the outter corner of your Ey , and holding it there steddy , you must move the Vane till you see the Horizon joyned with the lower end thereof , and the Sun or Star with the higher end ; then the degree and part of degree which the Vane cutteth upon the Staff , is the height of the Sun or Star. Some of these waies for taking Altitudes have been formerly taught by others , that have treated upon the Use of Globes : and therefore because some would be apt to think this Treatise uncompleat if I did not shew these waies also , I have thought fit to insert them : Yet the same things may be performed by the Globe alone , without troubling your self with multiplicity of Instruments ; if your Globe be made with a hollow Axis ; for then if the Globe stand Horizontal , you shall by Observing the Object through the Axis have the degree of Elevation , noted by the superficies of the Horizon . PROB. XIV . To observe with the Globe the Altitude of the Sun. PLace the Globe so that the upper plain of the Horizon may stand parallel to the Plain of the Horizon of your Place ; as was taught by the Second Probleme ; then turn the North Pole towards the Sun , and place it higher or lower , by moving the Meridian through the notches of the Horizon , till the beams of the Sun pierce quite through the Axis of the Globe : So shall the arch of the Meridian comprehended between the Pole and the Horizon , be the number of Degrees that the Sun is elevated above the Horizon . Example . March 20. just at noon , here at London , I would observe the Meridian Altitude of the Sun. Therefore placing the Horizon Horizontal , as by the Second Probleme : I turn the North Pole towards the Sun , and move it with the Meridian upwards or downwards , either to this side or that , till I can fit it to such a Position that the Sun Beams may dart quite through the Axis of the Globe ; which when it does , I look on the Meridian and find 42. degrees 25. min. comprehended between the Pole and the superficies of the Horizon ; Therefore I say the Meridian Altitude of the Sun March 20. here at London , is 42. degrees 25. min. PROB. XV. To find the Elevation of the Pole , by the Meridian Altitude of the Sun , and Day of the Moneth given . THe Day of the Moneth is March 20. By the 4th Prob. you may find the place of the Sun to be ♈ 10. Therefore bring the Place of the Sun to the Meridian , and elevate it above the Horizon the same number of degrees it hath in Heaven ; so shall the arch of the Meridian comprehended between the Pole and the Horizon , be the elevation of the Pole , in your Place . Otherwise . The Day of the Moneth given is March 20. so that by the fourth Prob. you have the Suns Place ♈ 10 ; and by the fifth , the Declination of the Sun 3. 55. North : therefore the Declination being North , and you on the North side the Equator ; you must substract 3. 55. from the Meridian Altitude 42. 25. and there remains 38 , 30. for the heighth of the Equinoctial above the Horizon ; but if your Declination had been South , you must have added 3 55. to the Meridian Altitude , and the Sum would have been the Elevation of the Equinoctial . Having the Elevation of the Equinoctial , you may easily have the Elevation of the Pole ; for the one is alwaies the Complement of the other to 90. Thus the Height of the Equinoctial 38. 30. subtracted from 90. leaves 51. 30. for the Elevation of the Pole , here at London . And thus it follows , that the Latitude of any Place from the Equinoctial , is alwaies equal to the Elevation of the Pole : for between the Zenith and the Equinoctial is contained the Complement of the Heighth of the Equinoctial above the Horizon to 90. PROB. XVI . To take the Altitude of any Star above the Horizon ; by the Globe . THe Horizon of the Globe set parallel to the Horizon of the World , as before : Turn the North Pole towards the Star , and when you can see the Star through the Axis , the Northern notch of the Horizon will cut the degree of Elevation on the Meridian . Example . April 19. at 11. a clock at Night , I would observe the Altitude of Spica Virgo : Therefore I set the Horizon parallel to the Horizon of the World , as by the Second Probleme , and turn the Northern Pole till it point towards the Star : Then looking in at the South Pole of the Globe through the Axis , I shall see the Star , and have on the Meridian the Question resolved . But if it point not exactly , then I move the North Pole upwards or downwards , either to the right hand , or to the left , according as I may find occasion , till I can see the Star through the Axis : and then the edge of the notch in the Horizon cuts 28. degrees 57. min. on the Brazen Meridian . Therefore I say April 19. at 11. a clock at Night , here at London , the Altitude of Spica 〈◊〉 is 30. degrees above the Horizon . PROB. XVII . By the Meridian Altitude of any Star given , to find the Height of the Pole. JOyn the Star to the Meridian , and place it to the Altitude observed ; so shall the number of degrees intercepted between the Pole and the Horizon , be the Elevation of the Pole. Example . Spica Virgo is observed to have 28. degrees 57. min Meridian Altitude ; therefore I bring Spica Virgo to the Meridian , and raise it or depress it higher or lower as I find occasion , till it is just 28. degrees 57. min. above the Horizon : Then I count the number of degrees between the Pole and the Horizon , and find them 51½ . Therefore I say the Elevation of the Pole is here at London 51½ . Yet note , If the Star whose Altitude you observe have fewer number of degrees of Declination from the Pole , then the Elevation of the Pole , you may be apt to mistake in its coming to the Meridian ; for those Stars never set ; and therefore are twice Visible in the Meridian in 24. hours , once above the Pole , and once under the Pole. If your Star have greater Altitude then the North Star , it is above the Pole ; but if it have less , it is below the Pole : so that if you know but whether it be above or below , it is enough ; for so you may accordingly raise it to the Altitude on the Meridian it hath in Heaven , and joyn it to the Meridian either above or beneath the Pole , as the Star is placed in Heaven : and then the arch of the Meridian comprehended between the Pole and the Horizon , is the Elevation of the Pole , as aforesaid . Otherwise . Having the Meridian Altitude of the Star , you must find its Declination by the 27. Probleme : and if the Declination be South , and you on the North side the Equator , you must ad the Declination to the Meridian Altitude , and the sum of both makes the Altitude of the Equinoctial : But if the Declination be North , and you on the North side the Equator , you must substract the Declination from the Meridian Altitude , ( as was taught by the 15. Prob. in the Example of the Sun ) and the remainder is the Altitude of the Equinoctial Then ( as was taught by the 15 Probleme aforesaid ) substract the Altitude of the Equinoctial from 90 , the Remainder is the Elevation of the Pole in your Place . Example . By the last Probleme the Meridian Altitude of Spica Virgo was 28 degrees 57 min , and the Declination of Spica by the 27th Probleme is found 9. degrees 33. min. South : therefore because the Declination is South , I ad 9. degrees 33. min. to the Meridian Altitude , which makes 38. deg . 30. min. for the Elevation of the Equinoctial : which 38. deg . 30. min. substracted from 90. leaves 51. degrees 30. min. for the Elevation of the Pole here at London . PROB. XVIII . Another way to find the Height of the Pole by the Globe ; if the Place of the Sun be given : and also to find the Hour of the Day , and Azimuth , and Almicantar of the Sun. THis must be performed by help of a Spherick Gnomon , ( as Blaew calls it , ) which is a small Pin or Needle fixed perpendicularly into a smal Basis with an hollow concave bottom , that it may stand upon the convexity of the Globe . Therefore the Horizon of the Globe being set parallel to the Horizon of the World , ( as by the Second Probleme ) the Spherick Gnomon must be set exactly upon the Place of the Sun ; and then turning the Globe about ( upon its Axis ) either from East to West , or contrarily from West , to East ; or else by the Meridian , through the notches of the Horizon , till the Spherick Gnomon cast no shadow on any side thereof ; you have on the Meridian in the North point of the Horizon the number of degrees that the Pole is elevated above the Horizon . Example . Imagine the four Quarters of the Horizon of the Globe correspond with the four Quarters of the Horizon of the World ; and the Plain of the Horizon of the Globe is parallel to the Plain of the Horizon of the World : The Suns Place is ♉ 29¼ , which I find on the Globe , and place the Spherick Gnomon thereon ; Then at a guess I move the Globe both on its Axis , and by the Meridian , ( as neer as I can ) so as the Spherick Gnomon may cast no shadow ; yet if it do , and the shadow fall towards the North Pole ; then I elevate the North Pole more , till the shadow fals just in the middle of it self : but if the shadow fall downwards , towards the South Pole , then I depress the North Pole : If the shadow fall on the East side , I turn the Globe on its Axis more to the West ; and if the shadow fall to the West , I turn the Globe more into the East : and the degree of the Meridian which the North point of the Horizon touches , is the degree of the Poles Elevation : which in this Example is 51½ . the Latitude of the City of London . By this Operation you have also given the Hour of the Day in the Hour-Circle , if you keep the Globe unmoved : and the Azimuth , and Almicantar , if you apply but the Quadrant of Altitude to the Place of the Sun , as by the 22 , and 23. Problemes . PROB. XIX . To observe by the Globe the Distance of two Stars . YOu must pitch upon two Stars in the Meridian ; and observe the Altitude of one of them first , and afterwards the Altitude of the other : Then substract the lesser Altitude from the greater , and the remainder shall be the distance required . Example . March 7. at 11. a clock at Night here at London , I see in the Meridian the two Stars in the foremost Wheels of the Waggon , in the Constellation of the Great Bear , called by Sea-men the Pointers , ( because they alwaies point towards the Pole-Star . ) Therefore to observe the distance between these two Stars , I first observe ( as by the last Probleme ) the Altitude of the most Northern to be 77. degree 59. minutes , and set down that number of Degrees and minutes with a Pen and Ink on a Paper , or with a peece of Chalk or a Pencil on a Board : and afterwards I observe the Altitude of the other Star which is under it , as I did the first , to be 83. deg . 21. min. and set that number of degrees and minutes also down , under the other number of degrees and minutes : Then by substracting the lesser from the greater , I find the remainder to be 5. degrees 22. min. which is the distance of the two Stars in the Great Bear , called the Pointers . PROB. XX. How you may learn to give a guess at the number of degrees that any two Stars are distant from one another ; or the number of degrees of Altitude the Sun or any Star is elevated above the Horizon : only by looking up to Heaven , without any Instrument . BEtween the Zenith and the Horizon is comprehended an Arch of a Circle containing 90. degrees ; so that if you see any Star in or neer the Zenith , you may know that Star is 90. or neer 90. degrees high ; and by so much as you may conceive it wants of the Zenith , so much you may guess it wants of 90. degrees above the Horizon . By this Rule you may guess at an Arch of Heaven containing 90. degrees , or at an Arch of Heaven containing 45. degrees ; if by your imagination you divide the whole Arch into two equal parts , for then shall each of them contain 45. degrees ; And if by your imagination you divide the Arch of 90. into 3. equal parts , each division shall contain an Arch of 30. degrees , &c. But this way is a little too rude for guessing at Stars elevated but few degrees , or for Stars distant but few degrees from one another . Therefore that you may learn to guess more precisely at Distances in Heaven , you may either with a Quadrant , Astrolabe , or the Globe ; find the exact distance of any two known Stars that are but few degrees asunder , and by a little revolving the distance of those Stars in your fancy , you may at length so imprint their distance in your memory , that you may readily guess the distance of other Stars by the distance of them . Example . You may find either by the Globe , Quadrant , or As●rotabe , ( for they all agree ) 3. degrees comprehended between the first Star in Orions Girdle , and the last ; therefore by a little 〈◊〉 nating upon that distance , you may imprint it in your fancy for 3. degrees , and so make it applicable to other Stars , either of the same distance , or more , or less : And the Pointers ( by the last Probleme ) are distant from one another 5. degrees and almost an half : These are alwaies above our Horizon , and therefore may alwaies stand as a Scale for five and an half degrees ; So that by these for 5½ degrees , and those in Orions Girdle for 3. degrees , and others observed , either of greater or lesser distance , you may according to your own Judgement shape a guess , if not exactly , yet pretty neer the matter of Truth , when you come to other Stars . Thus you may exercise your fancy upon Stars found to be 10. or 15. degrees asunder , or more , or less ; and with a few experiments of this nature enure your Judgement to guess distances , and enable your memory to retain your Judgement . This way of guessing will be exact enough for finding the Hour of the Night by the Stars , for most common Uses ; or the Hour of the Day , by guessing at the Altitude of the Sun ; if after you have guessed at the Altitude , you shall work as was taught by Prob. 12. for the Hour of the Day : and as shall be taught in the next Probleme , for the Hour of the Night . PROB. XXI . The Day of the Moneth , and Altitude of any Star given , to find the Hour of the Night . THe Globe , Quadrant , and Hour Index rectified : Bring the Star on the Globe to the same number of Degrees on the Quadrant of Altitude that it hath in Heaven : So shall the Index of the Hour-Circle point in the Hour-Circle at the Hour of the Night . Example . March 10. the Altitude of Arcturus is 35. degrees above the Horizon , here at London : Therefore having the Globe , Quadrant and Hour Index rectified , I bring Arcturus on the Globe to 35. degrees on the Quadrant of Altitude : And then looking in the Hour-Circle , I find the Index point at 10. a clock ; which is the Hour of the Night . PROB. XXII . The Place of the Sun , and Hour of the Day given , to find its Azimuth in any Latitude assigned . THe Globe , &c. rectified to your Latitude : Turn the Globe till the Index of the Hour-Circle come to the given hour ; and bring the Quadrant of Altitude to the Place of the Sun : so shall the number of degrees contained between the East point of the Horizon and the degree cut by the Quadrant of Altitude on the Horizon , be the number of degrees of the Suns Azimuth , at that time . Example . May 10. at 53. minutes past 8. a clock in the Morning , I would know the Azimuth of the Sun : Therefore ( the Globe being first rectified ) I turn about the Globe till the Index of the Hour-Circle point to 53. minutes past 8. a clock , or which is all one , within half a quarter of an hour of 9 ; then I move the Quadrant of Altitude to the degree the Sun is in that Day , and there let it remain till I see how many degrees is contained between the North point and the Quadrant ; which in this Example is 108. deg . 25. min. And because this distance from the North , exceeds 90. degrees ; therefore I substract 90. degrees from the whole , and the remains is 18. degrees 25. min. for the Azimuthal distance of the Sun from the East point towards the South . But if it had wanted of 90. degrees from the North point , then should the Complement of 90. have been the Azimuthal distance of the Sun from the East point . PROB. XXIII . The Place of the Sun , and hour of the Day given , to find the Almicantar of the Sun. THe Almicantars of the Sun is upon the matter the same thing with the Altitude of the Sun : only with this distinction . The Almicantars are Circles parallel to the Horizon , discribed by the degree of the Quadrant of Altitude upon the Zenith as its Center , by turning the Quadrant round about the Globe till it comes again to its first Place : But the Altitude is an Arch of the Vertical Circle , comprehended between the Horizon and any point of the Globe assigned . Their agreement consists in this ; When the Sun or any Star ha●● any known Almicantar , they are said to have the same number of degrees of Altitude ; As if the Sun be in the 20th Almicantar ; he hath 20 degrees of Altitude ; if in the 30th Almicantar , he hath 30. degrees of Altitude , &c. Now because the Operation is the same for finding the Altitude and Almicantar , I shall refer you to the 11th Probleme ; which shews you how to find the Altitude or Heighth ; and by consequence the Almicantar . PROB. XXIV . The Place of the Sun given , to find what Hour it comes to the East , or West , and what Almicantar it then shall have . THe Globe , Quadrant , and Hour Index rectified , Bring the Quadrant of Altitude to the East point in the Horizon , if you would know what hour it comes to the East ; or to the West point , if you would know what hour it comes to the West : Then turn about the Globe till the place of the Sun come to the Quadrant of Altitude ; and the Index of the Hour Circle shall point at the hour of the Day : which on the Day aforesaid will be 7. hor. 7 min. in the Morning , that the Sun commeth to the East , and 4 hor. 53. min. after noon , that the Sun commeth to the West . And if you then count the number of degrees from the Horizon upwards on the Quadrant of Altitude , it will shew you the Almicantar of the Sun for that time ; which will both Morning and Evening be 15 , deg . 30. min. as was taught you by the last Probleme . PROB. XXV . To know at any time what a clock it is in any other Part of the Earth . THe difference of Time is reckoned by the access and progress of the Sun : for the Sun gradually circumvolving the Earth in 24. hours , doth by reason of the Earths rotundity enlighten but half 〈…〉 at one and the same moment of Time ; as shall be shewed hereafter : so that hereby it comes to pass , that when with us here in England it is 6. a clock in the Morning , with those that have 90. degrees of Longitude to the Westward of us , it is yet Midnight : with those that have 180. degrees of Longitude from us , it is Evening ; And with those that have 90. degrees of Longitude to the Eastwards , it is Noon . So that those to the Eastward have their Day begin sooner then ours : But to the Westward their Day begins after ours . Therefore that you may know what Hour it is in any Place of the Earth , of what distance soever it be , you must first Bring the Place of your own Habitation to the Meridian , and the Index of the Hour Circle to 12. on the Hour Circle ; Then bring the other Place to the Meridian , and the Arch of the Hour Circle comprehended between the hour 12. and the Index , is the difference in Time between the two Places . Example . London in England , and Surat in the East Indies : First I bring London to the Meridian , and turn the Index of the Hour-Circle to 12 ; then I turn the Globe Westward , because London ●s Westward of Surat , till Surat come to the Meridian ; and see at what Hour the Index of the Hour Circle points , which in this Example is 5. hor. 54. minutes : And because Surat lies to the Eastward of us so many degrees , therefore as was said before , their Day begins so much before ours : So that when here at London it is 6. a clock in the Morning , at Surat it will be 11. a clock 54. minutes ; when with us it is 12. a clock , with them it will be 5 a clock 54. minutes afternoon . If you would know the difference of Time between London and Jamaica ; Working as before , you may find 5. hor. 15. min. But Jamaica is to the West of London ; therefore their Day begins 5. hor. 15. min. after ours : so that when with us it is Noon , with them it will be but three quarters of an hour past 6. a clock in the Morning : and when with them it is Noon , with us it will be one quarter past 5. a clock after Noon , &c. Or you may yet otherwise know the difference of Time , if you divide the number of Degrees of the Equinoctial that pass through the Meridian while the Globe is moved from the first Place to the second , by 15. so shall the product give you the difference of hours and minutes between the two Places : as you will find if you try either of these Examples , or any other . PROB. XXVI . To find the Right Ascension of the Sun , or Stars . THe Right Ascension of any point on the Globe is found by bringing the point proposed to the Meridian , and counting the number of degrees comprehended between the Vernal Colure , and the Meridian . Example , for the Sun. June 1. I would know the Right Ascension of the Sun : His Place found , as by the third Probleme , is ♊ 20. Therefore I bring ♊ 20. to the Meridian ; and then the Meridian cuts the Equinoctial in 79. degrees 15. minutes , accounted from the Vernal point ♈ : Therefore I say the Right Ascension of the Sun June 1. is 79. deg . 15. Minutes . Example , for a Star. I take Capella , alias Hircus , the Goat on Auriga's sholder , and bring it to the Meridian ; and find the Meridian cut the Equinoctial ( counting as before from the Vernel point ♈ ) in 73. degrees 58. minutes : Therefore I say , the Right Ascension of Hircus is 73. degrees 58. min. Do the like for any other point of the Globe proposed . PROB. XXVII . To find the Declination of the Sun , or Stars . THe Declination of any point on the Globe is found by bringing the point proposed to the Meridian , and counting the number of degrees comprehended on the Meridian between the Equinoctial and the point proposed : and bears its Denomination of North or South , according as it is scituate on the North or South side the Equinoctial . Example , for the Sun. June 1. I would know the Declination of the Sun. His Place found , as before , i● ♊ 20. Therefore I bring ♊ 20. to the Meridian ; and find 23. degrees 8. min. comprehended on the Meridian between the Equinoctial and ♊ 20. and because ♊ is on the North side the Equinoctial ; Therefore I say , June 1. The Sun hath North Declination 23. degrees 8. minutes . Example , for a Star. I take Hircus aforesaid , and bring it to the Meridian , and find 45. degrees 40. minutes comprehended on the Meridian between the Equinoctial and the Star Hircus . And because Hircus is on the North side the Equinoctial ; Therefore I say , Hircus hath North Declination 45. degrees 40. min. Do the like for any other point on the Globe proposed . But Note , The Right Ascension and Declination of the Sun alters dayly ; for in twelve Moneths he runs through every degree of Right Ascension , and in three Moneths to his greatest Declination : But the Right Ascension and Declination of the Stars is scarce perceiveable for some Years : Yet have they also an alteration of Right Ascension and Declination : For , those Stars that have but few degrees of Right Ascension , will in process of Time have many ; and those Stars between the Tropick that have North Declination , will in length of Time have South Declination ; and the contrary ( as shall be more fully shewed hereafter : ) For , the Stars moving upon the Poles of the Ecliptick go forwards in Longitude one whole Degree in 70½ Years ( as hath been shewed before , Book 1. Chap. 3. Sect. 3. ) and so alter both their Right Ascension , and Declination ; as may be seen by this following Table of Right Ascensions and Declinations of 100. of the most eminent fixed Stars , Calculated by Tycho Brahe , for the Years 1600. and 1670. which I have inserted ; partly , because by it you may see the differences of their Right Ascensions and Declinations in 70½ Years ; and partly to Accomodate those that may have occasion to know their Right Ascensions and Declinations neerer than the Globe can shew them . A Table of the Right Ascensions and Declinations of 100. Select fixed Stars ; Calculated by Tycho Brahe , for the Years 1600 , and 1670. As also their Difference of Right Ascensions and Declinations , in 70. Years .   1600   Differentia . 1900 Names of the Stars . R. Asc. Declin .   R. As. Decl. R. Asc. Declin . Scedir , in Casssopeae . 4 36 54 21 N 1 22 34 S 5 58 54 55 The Pole Star. 5 47 87 9½ N 3 59 34 S 9 46 87 43½ Southern in the whales tail . 5 51 20 12 S 1 17 34 N 7 8 19 38 Cassiopeae's Belly . 8 21 58 33 N 1 27 34 S 9 48 59 7 Girdle Andromeda . 11 50 33 32 N 1 23 33 S 13 13 34 5 Knee of Cassiopeae . 15 3 58 7 N 1 35 33 S 16 38 58 40 1. in ♈ horn . 22 56 17 19 N 1 23 31 S 24 19 17 50 Whales belly . 22 59 12 16 S 1 15 31 N 24 14 11 45 2. in ♈ horn . 23 10 18 50 N 1 22 31 S 24 32 19 31 South foot of Andromeda . 24 55 40 23 N 1 29 30 S 26 24 40 53 In the Knot in the line ♓ . 25 22 0 50 N 1 18 30 S 26 40 1 20 * Star in ♈ head . 26 23 21 33 N 1 25 30 S 27 38 22 3 * In the wtales jaw . 40 25 2 29 N 1 15 25 S 41 40 2 54 Caput Medusae 40 38 39 22 N 1 37 25 S 42 15 39 47 * In Persons side . 44 2 48 22 N 1 28 21 S 45 30 48 43 * In the Pletades . 50 57 22 49 N 1 29 21 S 52 26 23 10 In the Nostrils of ♉ . 59 16 14 37 N 1 25 17 S 60 41 14 54 North Ey of ♉ . 61 21 18 14 N 1 24 17 S 62 45 18 31 Aldebaran . 63 16 15 38 N 1 26½ 15 S 64 43 15 53 Hircus , Capella . 71 49 45 30 N 1 49 10 S 73 38 45 40 * Orions foot , Rigel . 73 51 8 43 S 1 15 9½ S 75 7 8 33½ North Horn ♉ . 75 16 28 12 N 1 37 8 S 76 53 28 20 Orions left sholder . 75 58 5 55 N 1 19 3 S 77 17 6 3 Belly of the Hare 77 48 71 6 S 1 5 7 N 78 53 20 59 1. In Orions Girdle 77 58 〈◊〉 39 S 1 17 7 N 79 15 0 32 Uppermost in Orions face 78 21 9 36 N 1 22 7 S 79 41 0 43 South Horn ♉ . 78 26 20 51 N 1 31 7 S 79 57 20 58 2. In Orions Girdle . 79 1 1 30 S 1 17 6 N 80 18 1 24 Last in Orions Girdle . 80 10 2 12 S 1 16 5 N 81 26 2 7 Auriga's right Sholder . 82 40 44 50 N 1 55 4 S 84 35 44 54 Orions right Sholder . 83 26 7 16 N 1 22 4 S 84 48 7 20 * Foot ♊ . 93 38 16 40 N 1 28 2 N 95 6 16 38 Great Dog Sirius . 96 53 16 11 S 1 7 4 S 98 0 16 15 Head of Castor , the first Twin . 107 9 32 41 N 1 44 11 N 108 53 32 30 The little Dog , Procyon . 109 37 6 12 N 1 20 12 N 110 57 6 0 Head Pollux , second Twin . 110 13 28 55 N 1 34 12 N 111 47 28 43 * In the Stern of the 117 39 23 11 S 1 4 15 S 118 43 23 26 Praesepe ♋ 124 20 21 2 N 1 28 19 N 125 48 20 43 Northern Asse ♋ Ship. 124 58 22 51 N 1 30 20 N 126 28 22 31 Southern Asse ♋ 125 27 19 35 N 1 27 20 N 126 54 19 15 The Heart of Hydra . 137 1 6 57 S 1 15 25 S 138 16 7 22 South of 3. in neck ♌ 146 22 18 42 N 1 28 28 N 147 50 18 14 Lions Heart , Basiliscus . 146 45½ 13 53½ N 1 53½ 28½ N 148 8 13 25 North of 3. in neck ♌ 148 33 25 23 N 1 23 29 N 150 1 24 54 Middle of 3. in neck ♌ 140 〈◊〉 21 50 N 1 50 29 N 150 51 21 21 First lowest in 〈◊〉 Vrsa Ma● . 159 12 58 31 N 1 37 32 N 160 49 57 59 First upper in □ Dubbe 159 37 63 54 N 1 41 32 N 161 18 63 22 * back ♌ . 163 10 22 43 N 1 27 34 N 164 37 22 9 Lions tail . 172 9 16 49 N 1 19 34 N 173 28 16 15 following lowest in □ Ursa Major . 173 3 55 57 N 1 23 34 N 174 26 55 23 Uppermost following in □ . 178 50 59 15 N 1 20 34 N 180 10 58 41 Girdle 〈◊〉 . 188 53 5 37 N 1 18 34 N 190 11 5 3 Rump Ursa Major , Aliot . 189 1 58 10 N 1 19 33 N 190 10 57 37 Vindemiatrix , ♍ . 190 36 13 8 N 1 17 33 N 191 53 12 35 Spica ♍ . 196 4 9 1 S 1 19½ 32½ S 197 23½ 9 33½ Middle tail Ursa Major . 196 54 57 3 N 1 3 32 N 197 57 56 31 End Tail Urs. Major . 202 54 51 22 N 1 2 31 N 203 56 50 51 Arcturus . 209 23½ 21 18½ N 1 11 29½ N 210 34½ 20 49 Left Sholder of Bootes . 214 2 40 3 N 1 2 27 N 215 4 39 36 South Scale ♎ . 217 14½ 14 18 S 1 23 27 S 218 37½ 14 45 North Scale ♎ . 223 54½ 7 50 S 1 21½ 24 S 225 16 8 14 * Northern Crown . 229 26 28 6 N 1 5 21 N 230 31 27 45 * Serpents neck . 231 12 7 46 N 1 15 21 N 232 27 7 25 Northern of 3. * in front ♍ . 235 34 18 38 S 1 28 19 S 237 2 18 57 Lest hand Ophiucus . 238 25 2 37 S ●1 23 18 S 239 48 2 55 Heart 〈◊〉 . Antares , 241 18 25 26 S 1 32 16 S 242 50 25 42 Right Shold ▪ Hercules . 243 15 22 27 N 1 5 15 N 244 20 22 12 Left knee of Ophiucus . 243 49 9 39 S 1 23 15 S 245 12 9 54 Right knee of Ophiucus . 251 50 15 7 S ●0 50 10 S 252 40 15 17 Head of Hercules . 254 6 14 55 N 1 8 8 N 255 14 14 47 Left Sholder of Hercules . 254 40 25 22 N 0 52 8 N 255 32 25 14 Head of Ophiucus . 259 5 12 56 N 1 11 7 N 260 16 12 49 Right Sholder of Ophiucus . 260 56 4 49 N 1 13 5 N 262 9 4 44 * head of the Dragon . 266 52 51 37 N 0 35 2 N 267 27 51 35 * Lyrae . 275 52 38 28 N ●0 50 4 S 276 42 38 32 Most Eastern in Head ♐ . 281 32 21 35 S 1 31 8 N 283 3 21 27 Vultures tail . 281 47 13 20 N 1 13 8 S 283 0 13 28 In the Swans Beak . 288 40 27 10 N 1 1 11 S 289 41 27 21 * in Vulture . 292 49 7 54 N 1 17 13 S 294 6 8 7 In the Swans North wing . 293 10 44 12 N 0 48 14 N 293 58 44 26 Upper horn ♑ . 289 57 13 40 S 1 25 16 N 300 22 13 24 Lower horn ♑ . 299 39 15 57 S 1 27 17 N 301 6 15 40 In the Swans breast . 302 1½ 39 1 N 0 53½ 18 S 302 55 39 19 Left hand of ♒ . 306 32 10 53 S 1 16 19 N 307 48 10 34 Swans Tail. 306 57 43 53½ N 0 51½ 20½S 307 49 44 14 In the Swans South wing 307 31 32 30 N 1 0 21 S 308 31 32 51 Left Sholder ♒ . 317 37 7 15 S 1 21 26 N 318 58 6 49 1. In tail ♑ . 319 28 18 21 S 1 26 26 N 320 54 17 55 In Cepheus Girdle . 320 46 68 50 N 0 22 26 S 321 8 69 16 In Pegasus mouth . 321 10 8 5 N 1 18 26 S 322 28 8 31 2. in tail ♑ . 321 16 17 51 S 1 25 27 N 322 41 17 24 Right Sholder of ♒ . 326 19 2 13 S 1 20 29 N 327 39 1 44 Fomahant , ♒ . 338 46 31 39 S 1 25 31 N 340 11 31 8 Scheat . P●gasus . 241 9 25 56 N 1 12 32 S 342 11 26 28 Marchab , Pegasus . 341 15 13 5 N 1 15 32 S 342 30 13 37 Mouth of Southern fi●h . 344 9 1 7 N 1 17 33 S 345 26 1 40 Head of Andromeda . 356 59 26 54 N 1 17 34 S 358 16 27 28 * Cassiopeae's chair . 357 5 56 58 N 1 15 34 S 358 20 57 32 End of Pegasus wing . ( tail . 358 14 12 58 N 1 16 34 S 359 30 13 32 Northern in the wh●les 359 49 11 1 S 1 18 34 S 1 7 10 27 The Vse of this Table . The first Collumne on the left hand is the names of the Stars . The Second Collumne shews the degrees and minutes of Right Ascension , for the Year 1600. The third the Declination for the same Year . The fourth shews whether the Declination be North or South ; N stands for North , S for South . The fifth shews the difference in degrees and minutes of Right Ascension of the Stars , between the Years 1600 ▪ and 1670. The sixth shews the Difference of Declination ; and whether it be North , or South . The seventh shews the Right Ascension in degrees and minutes , for the Year 1670. The eighth shews the D●clination in degrees and minutes for the same Year . By this Table you may perceive the fixed Stars increase in Right Ascension , till they come to the Vernal Colure ; from whence the number of their Right Ascension is reckoned : and by the Collumne of their Difference of Right Ascension , you may see how much they increase in 70. Years ▪ And if you would know how much they increase for any other number of Years , you must find what proportion they have to 70 , and the same proportion the Difference of the Right Ascension of the Stars will have to the Difference in the Table . Example . I would know the Difference of Right Ascension the Pole-Star will have in 35. Years . I find in the fifth Collumne the Difference of Right Ascension of the Pole Star to be 3. degrees 59. min. Therefore by the Rule of Proportion . I say , If 70. Years give 3. degrees 59. min. 35. Years shall give 1. degree 59½ ▪ min : and so proportionably for any other number of Years . Though this Rule serves for finding the Difference of Right Ascension of any Star ; Yet it will not serve for finding the Difference of any Stars Declination . For the Stars on the North side the Equinoctial between the Hyemnal and Solsticial Colures , and on the South side the Equinoctial between the Solsticial and Hyemnal Colures , increase in Declination . But the Stars on the South side the Equinoctial between the Hyemnal and Solsticial Colures , and on the North side the Equinoctial between the Solsticial and Hyemnal Colures , Decrease in Declination : as you may yet more plainly see by the Globe , if you bring 66½ deg . of the Meridian to the North side of the Horizon , and screw the Quadrant of Altitude to 66½ degrees in the Zenith , and Declination of the Pole of the Ecliptick ; and bring the Hyemnal Colure to the Meridian ; for so shall the Pole of the Ecliptick be joyned with the center of the Quadrant of Altitude , and the Ecliptick with the Horizon ; and all the Circles that the several degrees on the Quadrant make in a Revolution from West to East upon the Poles of the Ecliptick , represent the great Revolution of every Star that each degree on the Quadrant cuts . And thus demonstratively will be represented the progress of the fixed Stars through every degree of Longitude , and by consequence the alteration of their Right Ascension , and Declination . For , Imagining that degree of the Quadra●t of Altitude to be the Star , which just reaches the Star ; you may by turning about the Quadrant , see how Obliquely the Star ( or the degree representing the Star ) either moves about , or cuts the Equinectial , and all Circles parallel to the Equinoctial ; and thereby observe it sometimes to incline in motion to , and other times to decline in motion from the Equinoctial . But how long time it will be ●re the Star inclines to , or declines from the Equinoctial , you may know by finding the distance of Longitude in degrees it hath from either the Solsticial or Hy●mnal Colure ; and with respecting the foregoing Rules in its Position , you may by the Table in Book 1 , Chap. 3. Sect. 3. satifie your self . Example . The most Northerly Star in the Girdle of Orion doth yet decrease in Declination . But I would know how long it shall decrease ; Therefore by the 32. Probleme , I find the Longitude of that Star to be for the Year 1670. 77. deg . 51. min. which subducted out of 90 , ( the distance of the Solsticial Colure from the Equinoctial , ) leaves 12. 9 , for the distance of that Star from the Solsticial Colure . Therefore by the Table aforesaid , I find what number of Years answers to the motion of 12. deg . 9. min. And because I cannot find exactly the same number of degrees and minutes in the Table , I take the number neerest to it ; which is 14. degrees 10. minutes , and that is the motion of the Ecliptick in 1000. Years . But because this 14. degrees 10. minutes is 2. degrees 1. minute too much , I seek 2. degrees , 1. min. in the Table , and the number of Years against it I would subduct from the number of Years against 14 , deg , 10. min. and the remainder would be the number of Years required : But 2. deg . 1. min. I cannot find neither , therefore I must take the number of degrees and minutes neerest to it , which is 2. deg . 50. min. and that yeelds 200. Years ; which subducted out of 1000. leaves 800. Years . But because this is also too much by the motion of 49. min. Therefore I seek for 49. min. in the Table , and subduct the number of Years against it from 800 , and the remainder would be the number of Years required . But 49. min. is not in the Table neither , Therefore I take the neerest to it , which is 51. min. and that yeelds 60. Years ; which subducted out of 800. leaves 740. But this is likewise too much by the motion of two min. Therefore I seek 2. min. in the Table , but cannot find it neerer then 2½ , and against it I find 3. Years , which 3. Years I subduct out of 740 , and the Remainder is 737. the number in Years required . You may if you please for exactness , subduct for the ½ min. 8. Moneths ; so have you 736 , Years 4. Moneths , for the Time that the most Northerly Star in the Girdle of Orion will decrease in Declination after the Year 1670. which will be till An. Dom. ●406 . after which time it will increase in Declination for 12706. Years together , till it come to have 47. degrees 8. min. of Declination : at which time it will be in or very neer the place of the most Southerly Star of the Southern Crown ; and that Star in its place . And thus the Pole Star is now found to increase in Declination , and will yet this 421 Years : after which time it will decrease in Declination for 12706 Years together , till it come to be within 42. degrees 42. minutes of the Equinoctial , in the void space now between Draco and Lyra ; at which time Lyra will be almost as neer the Pole , as the Pole Star now is ; and then the most proper to be the Northern Pole Star : And the last Star in the Stalk of the Doves mouth will be then very neer the Southern Pole , and therefore most fit to be the Southern Pole-Star . PROB. XXVIII . The Place of the Sun or any Star given , to find the Right Descension , and the Oblique Ascension , and the Oblique Descension . BRing the Place of the Sun or the Star to the Meridian under the Horizon , and the degree of the Equator that comes to the Meridian with it is the Degree of Right Descension . For the Oblique Ascension . Bring the Place of the Sun or the Star to the East side the Horizon , and the degree of the Equator cut by the Horizon , is the Degree of Oblique Ascension of the Sun or Star. For the Oblique Descension . Bring the Place of the Sun or Star to the West side the Horizon , and the degree of the Equinoctial cut by the Horizon is the Degree of Oblique Descension . They need no Examples . PROB. XXIX . Any Place on the Terrestrial Globe being given , to find its Antipodes . BRing the given Place to the Meridian , so may you ( as by the first Probleme ) see its Longitude and Latitude ; then turn about the Globe till 180. degrees of the Equator pass through the Meridian ; and keeping the Globe to this Position , number on the Meridian 180. degrees from the Latitude of the given Place : and the point just under that degree is the Antipodes . Example . I would find the Antipodes of Cuida Real , an Inland Town of the West Indies , which lies upon the River Parana , an Arm of Rio de la Plata : Therefore I bring Cuida Real to the Meridian , and find ( as by the first Probleme ) its Latitude 23. 50 : South ; and its Longitude 333. degrees : Then I turn about the Globe till 180. degrees of the Equator pass through the Meridian ; and keeping the Globe to that position , I number so many degrees North Latitude as Parana hath South , viz. 23 , 50 , and just under that degree I find Lamoo , a Town lying upon the Coast of China , in the Province of Quancij : Therefore I say Lamoo is just the Antipodes of Cuida Real . Another way . Bring the given Place to the North or South point of the Horizon , and the point of the Globe denoted by the opposite point of the Horizon , is the Antipodes of the given Place . PROB. XXX . To find the Perecij of any given Place , by the Terrestrial Globe . BRing your Place to that side the Meridian which is in the South notch of the Horizon , and follow the Parallel of that Place on the Globe till you come to that side the Meridian which is in the Northern notch of the Horizon ; and that is the Perecij of your Place . PROB. XXXI . To find the Antecij of any given Place , upon the Terrestrial Globe . BRing your Place to the Meridian , and find its Latitude by the first Probleme ; If it have North Latitude , count the same number of degrees on the Meridian from the Equator Southwards ; But if it have South Latitude , count the same number of degrees from the Equator Northwards : and the point of the Globe directly under that number of degrees is the Antecij of your Place . PROB. XXXII . To find the Longitude and Latitude of the Stars , by the Coelestial Globe . THe Quadrant of Altitude will reach but 90. degrees , as was said Prob. 9. Therefore if the Star you enquire after be on the North side the Ecliptick , you must elevate the North Pole 66½ degrees above the North side the Horizon : If on the South side the Ecliptick , you must elevate the South Nole 66½ degrees above the South side the Horizon : Then bring the Solsticial Colure to the Meridian on the North side the Horizon , and screw the Quadrant of altitude to the Zenith , which will be in 23½ degrees from the Pole of the World : So shall the Ecliptick ly in the Horizon , and the Pole of the Ecliptick also ly under the Center of the Quadrant of Altitude ( as was shewed Prob. 27. ) Now to find the Longitude of any Star , do thus Turn the Quadrant of Altitude about till the graduated edge of it ly on the Star ; and the degree in the Ecliptick that the Quadrant touches is the Longitude of that Star. Example , for a Star on the North side the Ecliptick . I would know the Longitude of Marchab , a bright Star in the wing of Pegasus : I find it on the North side the Ecliptick , Therefore I elevate the North Pole , and placing ♋ on the North side the Meridian , I screw the Quadrant of Altitude to the Zenith , as aforesaid : Then laying the edge of the Quadrant of Altitude upon that Star , I find that the end of it reaches in the Ecliptick to ♓ 18. 56. Therefore I say , the Longitude of Marchab is ♓ . 18. 56. For the Latitude of a Star. The Degree of the Quadrant of Altitude that touches the Star is the Latitude of the Star. Example . The Globe and Quadrant posited as before , I find 19. deg . 26. min. ( accounted upwards on the Quadrant ) to touch Marchab aforesaid : Therefore I say , the Latitude of Marchab is 19. deg . 26. min. And thus by elevating the South Pole and placing the Globe and Quadrant of Altitude as aforesaid , I shall find Canicula have 15. degrees 57. min. South Latitude , and 21. degr . 18. min in ♋ , Longitude . PROB. XXXIII . To find the Distance between any two Places , on the Terrestrial Globe . THis may be performed either with the Quadrant of Altitude , or with a pair of Compasses : with the Quadrant of Altitude , 〈◊〉 : Lay the lower end thereof to one Place , and see what degree reaches the other Place , for that is the number of degrees between the two Places . If you multiply that number of Degrees by 60 the Product shall be the number of English Miles between the two Places . Example . I would know the distance between London and the most Easterly point of Jama●ca ; I lay the lower end of the Quadrant of Altitude to Jamaica , and extending the other end towards London , I find 68½ . deg . comprehended between them : Therefore I say 68½ is the number of degrees comprehended between London and Jamaica . If you would find the Distance between them with your Compasses , you must pitch one foot of your Compasses in the East point of Jamaica , and open your Compasses till the other foot reach London ; and keeping your Compasses at that Distance apply the feet to the Equinoctial line , and you wil find 68½ degree comprehended between them : as before . If you multiply 68½ . by 60 , is it gives 4110. English miles . If you multiply it by 20 , it gives 1370. English Leagues . If you multiply it by 17½ , it gives 1199. Spanish Leagues . If you multiply it by 15 , it gives 1054 Dutch Leagues . PROB. XXXIV . To find by the Terrestrial Globe upon what point of the Compass any two Places are scituate one from another . FInd the two Places on the Terrestrial Globe , and see what ●umb passes through them ; for that is the point of the Compass they bear upon . Example . Bristol and Bermudas are the Places : I examine what Rhumb passes through them both : and because I find no Rhumb to pass immediately through them both , Therefore I take that Rhumb which runs most Parallel to both the Places ; which in this Example is the tenth Rhumb counted from the North towards the left hand ; and is called as you may see by this following Figure West South West ; Therefore I say Bermudos lies scituate from Bristol West South West ; and by contraries Bristol lies cituate from Bermudas East North East . PROB. XXXV . To find by the Coelestial Globe the Cosmical Rising and Setting of the Stars . WHen any Star Rises with the Sun , it is said to Rise Cosmically . And when any Star Sets when the Sun Rises , it is sa●d to Set Cosmically . To find these , Rectifie the Globe to the Latitude of your Place , and bring the Place of the Sun to the East side the Horizon ; and the Stars then cut by the Eastern Semi-Circle of the Horizon , Rise Cosmically ; and those Stars cut by the Western Semi-Circle of the Horizon , Set Cosmically . Example . Novemb. 9. I would know what Stars Rise and Set Cosmically ▪ here at London . The Suns Place found , as by the third Probleme is 〈◊〉 27. Therefore I bring 〈◊〉 27. to the East side the Horizon , and in the Eastern Semi-Circle I find Rising with the Sun the right Wing of Cygnus , the Star in the end of Aquila's tail , Serpentarius and Centaurus : Therefore these Constellations are said to the Cosmically . In the Western Semi-Circle of the Horizon I find Setting Andromeda , the Triangle , Taurus , Orion , ( anis Major , and Argo Navis ; Therefore I say , these Constellations Set Cosmically . PROB. XXXVI . To find by the Coelestial Globe the Acronical Rising and Setting of the Stars . THe Stars that Rise when the Sun Sets , are said to Rise Acronically . And , The Stars that Set with the Sun , are said to Set Acronically . To find these , Rectifie the Globe to the Latitude of your Place , and bring the Place of the Sun to the West side the Horizon ; and the Stars then cut by the Eastern Semi-Circle of the Horizon , Rise Acronically : And those Stars cut by the Western Semi-Circle of the Horizon , Set Acronically . Example . November 9. I would know what Stars Rise and Set Acronically here at London . The Suns Place as before , is 〈◊〉 27. Therefore I bring 〈◊〉 27. to the West side the Horizon ; and in the Eastern Semi-Circle I find Rising the Southern Fi●h , Fomahant , Ce●us , Taurus , Auriga , and the Feather in Castor's Cap. Therefore these Constellations are said to Rise Acronically . In the Western Semi-Circle of the Horizon I find Setting the Lyons tail , Virgo , Scorpio , and Sagittarius , Therefore I say , these Constellations Set Acronically . PROB. XXXVII . To find by the Coelestial Globe the Heliacal Rising , and Setting of the Stars . WHen a Star formerly in the Suns Beams gets out of the Suns Beams it is said to Rise Heliacally . And. When a Star formerly out of the Suns Beams , gets into the Suns Beams , it is said to set Heliacally . A Star is said to be in the Suns Beams , when it is made inconspicuous by reason of its neerness to the Suns Light. The Bigger Stars are discernable more neer the Suns Light , then the Lesser are : For , Stars of the first Magnitude may ( according to the received Rules of ancient Authors ) be seen when the Sun is but 12. degrees below the Horizon but Stars of Second Magnitude cannot be seen unless the Sun be 13. degrees below the Horizon : Stars of the third Magnitude require the Sun to be 14. degrees below the Horizon ere they can be seen ; of the fourth Magni●ude 15. degrees . of the fifth Magnitude 16. degrees of the sixth Magnitude 17 degrees ; the Nebulous ones 18. degrees . Yet this Rule is not so certain but that either clear or cloudy weather may alter it . Read more of this subject in M r Palmer on the Plamsphear . Book 4. Chap. 20 Now to find the Time that any Star shall Rise Heliacally . Do thus Rectifie the Globe and Quadrant of Altitude to your Latitude . Then bring the given Star to the East side the Horizon , and turn the Quadrant of Altitude into the West side , and see what degree of the Ecliptick is elevated so many degrees above the Horizon as the Magnitude of the Star you enquire after requires , according to the foregoing Rules ; for the opposite degree of the Ecliptick is the degree the Sun shall be in when that Star Rises Heliacally . Having the degree of the Ecliptick the Sun is in , you may find the Day of the Moneth , by the 4th Probleme . Example . I would know when Cor Leonis shall Rise Heliacally here at London : Therefore I Rectifie the Globe and Quadrant of Altitude for London , and bring Cor Leonis to the East side the Horizon , and turn the Quadrant of Altitude into the West ; and because Cor Leonis is a Star of the first Magnitude , therefore I see what degree of the Ecliptick is elevated in the West side the Horizon 12. degrees on the Quadrant of Altitude , and find ♓ 9. deg . Now the degree of the Ecliptick opposite to ♓ 9. is 〈◊〉 9. Therefore I say , when the Sun comes to 〈◊〉 9. degrees ( which by the 4th Probleme I find is August . 23. ) Cor Leonis shall Rise Heliacally . For the Heliacal Setting . The Globe , &c. Rectified , as before : Bring the Star to the West side the Horizon , Then see what degree of the Ecliptick is elevated on the Quadrant of Altitude so many degrees as the Stars Magnitude requires ; for when the Sun comes to the opposite degree of the Ecliptick that Star shall set Heliacally . Example . I would know when Bilanx a Star in the Beam of the Scales , will Set Heliacally here at London . The Globe and Quadrant Rectified , I bring Bilanx to the West side the Horizon , and turn the Quadrant of Altitude into the East ; Then I examine what degree of the Ecliptick is elevated 13. degrees of the Quadrant of Altitude ( because Bilanx is a Star of the second Magnitude ) and find ♉ 4½ . opposite to ♉ 4½ . is 〈◊〉 4½ . Therefore I say , When the Sun comes to 〈◊〉 4½ . ( which by Probleme 4. will be October 18 ) Bilanx shall set Heliacally . PROB. XXXVIII . To find the Diurnal and Nocturnal Arch of the Sun , or Stars , in any given Latitude . THe Semi-Diurnal Arch is the number of degrees of the Equator that passes through the Meridian whiles the Sun or any Star is ascending above the East side the Horizon to the Meridian . To know the number of degrees it contains , Rectifie the Globe to the given Latitude , and bring the Place of the Sun or Star to the East side the Horizon , and note what number of degrees of the Equinoctial is then cut by the Meridian : Then remove the Place of the Sun or Star to the Meridian , and see again what number of degrees of the Equinoctial is then cut by the Meridian , and substract the former from the latter , and the remainder shall be the number of degrees of the Sun or Stars Semi-Diurnal Arch. But Note , If the Equinoctial point ♈ pass through the Meridian while the Sun or Star is turned from the East side the Horizon to the Meridian , then you must substract the number of degrees of the Equinoctial cut by the Meridian when the Sun or Star is at the East side the Horizon from 360. degrees , and to the remainder ad the number of degrees of the Equinoctial that comes to the Meridian with the Place of the Sun or Star , and the Sum of them both is the number of degrees of the Sun or Stars Semi-diurnal Arch ; which being doubled is the number of degrees of the whole Diurnal Arch : and which being substracted from 360 , given the Nocturnal Arch. Example , of the Sun. Having Rectified the Globe , I would May 10. know the Diurnal Arch of the Sun : His Place found by Prob. 3. is 8 29. Therefore I bring ♉ 29. to the Fast side the Horizon , and find then at the Meridian 299. degrees 30. min. of the Equinoctial ; then I turn the Place of the Sun to the Meridian , and find 56. deg . 30. min. of the Equinoctial come to the Meridian with it . Here the Equinoctial point ♈ passes through the Meridian while the Sun moves between the Horizon and the Meridian ; Therefore as aforesaid , I substract the first number of degrees and minutes viz. 299. deg . 30. min. from 360. degrees , and there remains 60 ▪ degr . 30. min. for the number of degrees and minutes contained between the degree of the Equinoctial at the Meridian and the Equinoctial point ♈ ; and to this 60. deg . 30. min. I ad the second number of degrees and minutes , viz. 56. deg . 30. min. the number of degrees and minutes between the point ♈ and the deg . of the Equinoctial at the Meridian , and they make together 117. degrees , for the Suns Semi diurnal Arch ; By doubling of which , you have 234. degrees , for the Suns Diurnal Arch ; And by substracting 234. ( the Diurnal Arch ) from 360. you have 126. degrees , for the Suns Nocturnal Arch. Example , for a Star. I take Sirius , a bright Star in the Great Dogs mouth . The Globe rectified , as before ; I bring Sirius to the East side the Horizon , and find then 29. degrees 30 minutes of the Equinoctial at the Meridian , then I turn Sirius to the Meridian and find 97. degrees 38 minutes of the Equinoctial come to the Meridian with it : Therefore I substract the first number viz. 29. degrees 30. minutes , from the second , 97. 38 , and the remains is 68. degrees 8 minutes , for the Semi-diurnal Arch of Sir●us . His Nocturnal Arch you may find as before . PROB. XXXIX . To find the Azimuth and Almicantar of any Star. THis Probleme is like the 22 , and 23. Problemes , which shew the finding the Azimuth and Almicantar of the Sun ; only , whereas there you were directed to bring the degree of the Sun to the Quadrant of Altitude , you must now bring the Star proposed to the Quadrant of Altitude ; and by the Directions in those Problemes the resolution will be found . PROB. XL. To find the Hour of the Night , by observing two known Stars in one Azimuth , or Almicantar . REctifie the Globe Quadrant and Hour Index . Then find the two known Stars on the Globe ; and if the two Stars be in one Azimuth , turn about the Globe and Quadrant of Altitude till you can fit the two Stars to ly under the graduated edge of the Quadrant of Altitude : so shall the Index of the Hour-Circle p●int at th● Hour of the Night . If the two Stars be in one Almicantar , Turn the Globe forward or backward till the two Stars come to such a Position that by moving the Quadrant of Altitude , the same degree on it will ly on both the Stars ; so shall the Index of the Hour-Circle point at the Hour of the Night . PROB. XLI . The Hour given that any Star in Heaven comes to the Meridian , to know thereby the Place of the Sun , and by consequence the Day of the Moneth , though it were lost . BRing the Star proposed to the Meridian , and turn the Index of the Hour-Circle to the Hour given , Then turn about the Globe till the Index point at the Hour of 12 , for Noon ; and the Place of the Sun in the Ecliptick shall be cut by the Meridian . Example . March 7. at 11 , aclock at Night the Pointers come to the Meridian of London . Therefore I place the Pointers on the Caelestial Globe under the Meridian , and turn the Index of the Hour-Circle to 11. past Noon , afterwards I turn back the Globe till the Index point to 12. at Noon ; Then looking in the Ecliptick , I find the Meridian cuts it in ♓ 26. 45. minutes ; Therefore I say , when the Pointers come to the Meridian at 11. a clock at Night , the Place of the Sun is ♓ 26. 45. Having thus the Place of the Sun , I may find the Day of the Moneth by the fourth Probleme ; and so either know the Day that the Pointers come to the Meridian at 11. a clock at Night , or at any other Hour given . The Day of the Moneth might also be found by the Declination and the Quarter of the Ecliptick the Sun is in , given : For the Meridian will cut the degree of the Suns Place in the Ecliptick in the Parallel of Declination : So that having respect to the Quarter of the Ecliptick , you 'le find the Suns Place ; and having the Suns Place , you may as aforesaid find the Day of the Moneth . PROB. XLII . The Day of the Moneth given , to find in the Circle of Letters on the Plain of the Horizon , the Day of the Week . THe seven Daies of the Week were by the Idolatry of the ancient Roman Heathenish Times Dedicated to the Honour of seven of their Gods , which we call Planets . The first is the most eminent , and therefore doubtless by them set in the first Place , called Dia Solis , or the Suns Day : The second Dia Luna , the Moons Day : The third Dia Martis , the Day of Mars : by us called Tuesday : The fourth Dia Mercurius , Mercuries Day : by us called Wednesday ; from Woden , an Idol the Saxons Worshipt , to whose Honour they Dedicated that Day , and is by all those Germain Nations still called Wodensdagh : The fifth Dia Jovis , Jupiter or Joves Day : which doubtless the Saxons ( from whom probably we receive it ) called Donder-dagh , because Jupiter is the God of Thunder ; and we either by corruption or for shortness , or both , call it Thursday : The sixth Dia Veneris , the Day of Venus : but the Saxons transferring her Honour to another of their Goddesses named Fria , called it Fridagh : and we from them call it Fryday : The seventh is Dia Saturnis , Saturus Day . The same Day of the Moneth in other Years happens not on the same Day of the Week , therefore the Dominical Letter for one Year is not the same it is the next : Now because you cannot come to the knowledge of the Day of the Week unless you first know the Sundaies Letter , therefore have I in Prob. 5● inserted a Table of M r Palmers , by which you may find the Dominical or Sundaies Letter for ever ; and having the Dominical Letter you may in the Circle of Letters on the Horizon find it neer the day of that Moneth , and count that for Sunday , the next under it for Monday , the next under that for Tuesday , and so in order , till you come to the Day of the Moneth . Example . I would know what Day of the Week June 1. Anno 1658. Old Style , falls on ; I find by the Table aforesaid the Dominical Letter is C , then I look in the Calender of Old Style for June 1. and against it I find Letter E , which because it is the second Letter in order from C , therefore it is the second Day in order from Sunday , which is Tuesday . PROB. XLIII . The Azimuth of any Star given , to find its Hour in any given Latitude . THe Hour of a Star is the number of Hours that a Star is distant from the Meridian . To find which , Rectifie the Globe and Quadrant of Altitude , and bring the Star proposed to the Meridian , and the Index of the Hour-Circle to 12. Then place the lower end of the Quadrant of Altitude to the given Azimuth in the Horizon , and turn the Globe till the Star come to the graduated edge of the Quadrant of Altitude ; so shall the Index of the Hour-Circle point at the Hour of the Star. Only this caution you must take ; If the Star were turned from the Meridian towards the Eastern side of the Horizon , you must substract the number of Hours the Index points at from 12. and the remainder shall be the Hour of the Star. But if the Star were turned from the Meridian towards the West side the Horizon , the Hour the Index points at is ( without more adoe ) the Hour of the Star. PROB. XLIV . How you may learn to know all the Stars in Heaven , by the Coelestial Globe . REctifie the Globe , Quadrant , Hour-Index and Horizon , as by Prob. 2. Then turn about the Globe till the Index of the Hour-Circle point at the Hour of the Night on the Hour-Circle . Then if every Star on the Globe had a hole in the midst , and your Ey were placed in the Center of the Globe ; you might by keeping your Ey in the Center and looking through any Star on the Globe see its Ma●ch in Heaven : that is , the same Star in Heaven which that Star on the Globe represents : for from the Center of the Globe there proceeds a straight line through the Star on the Globe , even to the same Star in Heaven . Therefore those Stars that are in the Zenith in Heaven , will then be in the Zenith on the Globe ; those that are in the East in Heaven , will be in the East on the Globe ; those in the West in Heaven , in the West on the Globe ; and those Stars that are in any Altitude in Heaven , will at the same time have the same Altitude on the Globe ; So that if you see any Star in Heaven whose Name you desire to know , you need but observe its Azimuth and Altitude , and in the same Azimuth and Altitude on the Globe , you may find the same Star : and if it be an eminent Star , you will find its Name adjoyned to it . Example . December 10. at half an hour past 9. a clock at Night , here at London , I see two bright Stars at a pretty distance one from another in the South ; I desire to know the Names of them ; Therefore having the Globe rectified to the Latitude of London , and the Quadrant of Altitude screwed to the Zenith , the Hour-Index also Rectified , and the Horizon posited Horizontally , as by Prob. 2. I observe the Altitude of those Stars in Heaven , ( either with a Quadrant , Astrolabe , Cross-staff , or the Globe it self , as hath been shewed Prob. 13 , 16. ) to be , the one 78. degrees , the other 42 , degrees above the Horizon . Therefore having their Altitudes , I count the same number of degrees as for the first 78. upon the Quadrant of Altitude upwards , and turn it into the South , under the Meridian , and see what Star is under 78. degrees , for that is the same Star on the Globe which I saw in Heaven . Now at the first examination of the Globe you may see that that Star is placed in the Ey of that After time which is called Caput Medusa , and indeed , that being the only Star of Note in that Constellation , bears the Name of the whole Constellation . The other Stars about it you may easily know by their Scituation . As , Seeing two little Stars to the Westwards of that Star in Heaven , you may see on the Globe that the hithermost is in the other Ey of Caput Medusa , and the furthermost in the Hair or Snakes of the same Asterisme . Looking a little to the Southwards of those Stars in Heaven , you may see two other smal Stars a little below those in the Eyes ; Therefore to know those also , you may look on the Globe , and see that there is one on the Nose , and another Starre in the Cheek of Caput Medusa In like manner for the second Star in the Meridian , which is 42 degrees above the Horizon : If you move the Quadrant of Altitude ( as before ) to the South or Meridian , and count 42 degrees upon the Quadrant of Altitude , you will find a Star of the second Magnitude in the Mouth of the Whale : Therefore you may say , that Star in Heaven is in the Mouth of the Whale : and because close to it on the Globe is written Menkar , Therefore you may know the name of that Star in Heaven is Menkar . In the South East and by South 56 degrees above the Horizon , I ●ee a very bright Star in Heaven ; therefore I bring the Quadrant of Altitude to the South East and by South point in the Horizon , and find under 56 degrees of the Quadrant of Altitude a great Star , to which is prefixed the name Occulus Taurus ; Therefore I say , the name of that Star in Heaven is Occulus Taurus . In the South East in Heaven you may see three bright Stars ly directly in a straight line from one another , the middlemost whereof is 25. degrees or thereabouts above the Horizon , therefore bring the Quadrant of Altitude to the South East point of the Horizon , and about 25 degrees above the Horizon you will see the same great Stars on the Globe , in the Girdle of Orion : Therefore those Stars are called Orions Girdle . At the same time South East and by East you have about 10 degrees above the Horizon the brightest Star in Heaven , called Sirius , in the Mouth of the Great Dog ; Canicula a bright Star in the Little Dog East and by South , about 25 degrees above the Horizon : Cor Leonis just Rising East North East : you have also at the same time on the East side the Horizon , the Twins , Auriga , the Great Bear ; and divers other Stars , eminent both for their splendor and Magnitude . In the West side the Horizon you have South West and by West about 4 degrees above the Horizon a bright Star in the Right Leg of Aquarius : and all along to the Southwards in Cetus the Whale , you have other eminent bright Stars : More upwards towards the Zenith you have a bright Star in the Line of the two Fishes : Higher yet , you have the first Star in ♈ , an eminent Star , because the first in all Catalogues that we have cognizance of ; and therefore probably in the Equinoctial Colure when the Stars were first reduced into Constellations : yet more neer the Zenith you have a bright Star in the Left Leg of Andromeda : From thence towards the North , you find other very eminent bright Stars in Cassiopea , Cepheus , Ursa Minor , in the Tail whereof is the Pole Star : and Draco : Hecules : where you turn back , to Lyra , Cygnus , Pegasus , the Dolphin , &c. all which , or any other , you may easily know by their Altitude above the Horizon , and the point of the Compass they bear upon . Thus knowing some of the most eminent Fixed Stars , you may by the Figure of the rest come to the knowledge of them also . For Example , Looking towards the North North East in Heaven , you may see seven bright Stars constituted in this Figure ; Therefore looking towards the same Quarter on the Globe , you may ( without taking their Altitude ) see the same Stars lying in the same Figure in the hinder parts of the Great Bear ; from whence you may conclude , that those Stars in Heaven are scituate in the hinder parts of the Asterisme called Ursa Major . Yet nevertheless you may see some Stars of Note in Heaven , which you shall not find on the Globe , and those in or neer about the Ecliptick : They are called Planets , and cannot be placed on the Globe , unless it be for a particular Time , with Black Lead , or some such thing that may be rubbed out again : Because they having a continual motion alwaies alter their Places . Of those there are five in number , besides the Sun and Moon , which are also Planets , though they shew not like Stars . These five are called Saturn , Jupiter , Mars , Venus , Mercury ; yet Mecury is very rarely seen : because he never Rising above an Hour before the Sun , or Setting above a Hour after , for the most part hath his light so overspread with the dazelling Beams of the glittering Sun , that sometimes when he is seen he seems rather to be a More in the Suns Beams , then a Body endowed with so much brightness as Stars and Planets seem to be . Now there are divers waies ( by some of which you may at all times ) know those Planets from the Fixed Stars : as first , Their not twinkling , for therein they differ from fixed Stars ; because they most commonly do twinkle , but Planets never ; unless it be ♂ Mars ; and yet he twinkles but very seldom neither . Secondly , They appear of a considerable Magnitude , as ♃ sometimes appears greater ly far then a Star of the first Magnitude ; and ☿ many times bigger then he . They are both glittering Stars , of a bright Silver collure ; but ♀ most radient , especially when she is in her Perigeon . ♂ appears like a Star of the second Magnitude ; and is of a Copperish colloure . ♄ shewes like a Star of the third Magnitude , and is of a Leaden Collour ; and he ( of all the others , ) is most difficult to be known from a fixed Star ; partly because of his minority , and partly because of the slowness of his motion . ☿ is very seldom seen ( as aforesaid ) unless it be in a Morning when he Rises before the Sun , or in an Evening when he Sets after the Sun : He is of a Pale Whitish Collour , like Quick silver , and appears like a Star of the third Magnitude . He may be known by the Company he keeps , for he is never above 29. degrees distant from the Sun. Thirdly , The Planets may be known from fixed Stars by their Azimuths and Altitudes observed : ( as hath been taught before ) for if when you have taken the Azimuth and Altitude of the Star in Heaven you doubt to be a Planet , and you find not on the Globe in the same Azimuth and Altitude a Star appearing to be of the same Magnitude that that in Heaven appears to be , you may conclude that that in Heaven is a Planet . Yet notwithstanding it may happen that a Planet may be in the same degree of Longitude and Latitude in the Zodiack that some eminent fixed Star is in ; as in the degree and minute of Longitude and Latitude that Cor Leonis , or the Bulls Ey , or Scorpions heart is in , and so may eclipse that Star , by being placed between us and it : But that happens very seldom and rarely ; but if you doubt it ▪ you may apply your self to some other of the precedent and subsequent Rules here set down for knowing Planets from fixed Stars . The fourth way is by shifting their Places ; for the Planets having a continual motion , do continually alter their Places : as ♂ moves about half a degree in a day : ♀ a whole degree ; but ♃ and ♄ move very slowly ; ♃ not moving above 5. minutes , and ♄ seldom above 2. minutes . Yet by their motions alone the Planets may be known to be Planets , if you will precisely observe their distance from any known fixed Star in or near the Ecliptick as on this Night , and the next Night after observe whether they retain the same distance they had the Night before ; which if they do , then are they fixed Stars ; but if they do not then are they Planets : yet this Ca●●on is to be given you in this Rule also , That the Planets sometimes are said to be Stationary , as not altering 1. minute in Place , forwards , or backwards in 6. or 7. daies together . Therefore , if you find cause to doubt whether your Star be a Planet , or a fixed Star , you may for the help of your understanding confer with some of the former Rules , unless you are willing to wait 8 or 9 daies longer , and so by observation of its motion resolve your self , Or , Fifthly , you may apply your self to an Ephemeris for that Year , and see if on that day you find any Planet in the degree and minute of the Zodiack you see the Star you question in Heaven ; and if there be no Planet in that degree of the Zodiack , you may conclude it is no Planet , but a fixed Star. PROB. XLV . How to hang the Terrestrial Globe in such a position that by the Suns shining upon it you may with great delight at once behold the demonstration of many Principles in Astronomy , and Geography . TAke the Terrestrial Ball out of the Horizon , and fasten a thred on the Brazen Meridian to the degree of the Latitude of your Place ; by this thred hang the Globe in a place where the Suns Beams may have a free access to it ; Then direct the Poles of the Globe to their proper Poles in Heaven , the North Pole to the North , and the South Pole to the South ; and with a thred fastned to either Pole , brace the Globe , so , that it do not turn from his position : then bring your Habitation to the Meridian ; so shall your Terrestrial Globe be Rectified to correspond in all respects with the Earth it self ; even as in Prob. 44. the Celestial Globe doth ; the Poles of the Globe , to the Poles of the World ; the Meridian of the Globe , to the Meridian of the World ; and the several Regions on the Globe made Correspondent to the same Regions on the Earth : So that with great delight you may behold , 1. How the counterfeit Earth ( like the true one ) will have one Hemisphear Sun shine light , and the other shadowed , and as it were dark . By the shining Hemisphear you may see that it is Day in all Places that are scituate under it ; for on them the Sun doth shine ; and that it is Night at the same time in those Places that are situate in the shadowed Hemisphear ; for on them the Sun doth not shine ; and therefore they remain in darkness . 2. If in the middle of the enlightned Hemisphear you set a Spherick Gnomon Perpendicularly , it will project no shadow , but shews that the Sun is just in the Zenith of that Place ; that is , directly over the heads of the Inhabitants of that Place : and the point that the Spherick Gnomon stands on , being removed to the Meridian , shews the Declination of the Sun on the Meridian for that Day . 3. If you draw a Meridian line from one Pole to the other , in all Places under that line , it is Noon : in those Places scituate to the West , it is Morning ; for with them the Sun is East : and in those Places scituate to the East , it is Evening ; for with them the Sun is West . 4 : Note the degree of the Equator where the enlightned Hemisphear is parted from the shadowed ; for the number of degrees of the Equator intercepted between that degree and the Meridian of any Place , converted into Hours ( by accounting for every 15. degrees 1. Hour ) shews , if the Sun be Eastwards of that Place , how long it will be ere the Sun Rises , Sets , or comes to the Meridian of that Place : or if the Sun be Westward of that Place , how long it is since the Sun Rose , or Set , or was at the Meridian of that Place . 5. The Inhabitants of all Places between the enlightned and shadowed Hemisphear , behold the Sun in the Horizon : Those Westwards of the Meridian Semi-Circle drawn through the middle of the enlightned Hemisphear behold the Sun Rising : Those in the East , see it Setting . 6. So many degrees as the Sun reaches beyond either the North or South Pole , so many degrees is the Declination of the Sun , either Northwards or Southwards : and in all those Places comprehended in a Circle described at the termination of the Sun-shine , about that Pole , it is alwaies Day , till the Sun decrease in Declination : for the Sun goes not below their Horizon : as you may see by turning the Globe about upon its Axis : and a the opposite Pole at the same distance , the Sun-shine not reaching thither , it will be alwaies Night , till the Sun decrease in Declination : because the Sun Rises not above their Horizon . 7. If you let the Globe hang steddy , you may see on the East side of the Globe , in what Places it grows Night ; and on the West side the Globe how by little and little the Sun encroaches upon it ; and therefore there makes it Day . 8. If you make of Paper or Parchment a narrow Girdle , to begirt the Globe just in the Equinoctial , and divide it into 24. equal parts , to represent the 24. hours of Day and Night , and mark it in order with I , II , III , &c. to XII . and then begin again with I , II , III , &c. to the other XII . you may by placing one of the XII s. upon the Equinoctial under the Meridian of your Place , have a continual Sun-Dyal of it , and the hour of the Day given on it , at once in two places ; one by the parting the enlightned Hemisphear from the shadowed on the Eastern side , the other by the parting the enlightned Hemisphear from the shadowed on the Western side the Globe . Much more might be said on this Probleme : But the Ingenuous Artist may of himself find out diversities of Speculations : therefore I forbear . PROB. XLVI . To know by the Terrestrial Globe in the Zenith of what Place of the Earth the Sun is . THis may be performed by the former Probleme in the Day time , if the Sun shines : but not else . But to find it at all times , do thus . Bring the Place of your Habitation to the Meridian , and the Index of the Hour-Circle to 12 ; Then turn the Globe Eastwards , if Afternoon , or Westwards , if Before Noon , till the Index of the Hour-Circle pass by so many Hours from 12. as your Time given is , either before or After-Noon : so shall the Sun be in the Zenith of that Place where the Meridian intersects the Parallel of the Suns Declination for that Day . Example . May 10 at ¾ of an hour past 4. a clock After Noon ▪ I would know in what Place of the Earth the Sun is in the Zenith . My Habitation is London . Therefore I bring London to the Meridian , and the Index of the Hour-Circle to 12. and because it is After Noon : I turn the Globe Eastwards , till the Index passes through 4 hours and 3 quarters , or ( which is all one ) till 70 degrees 15 minutes of the Equator pass through the Meridian . Then I find by Prob. 5. the Suns Declination is 20. degrees 5. minutes which I find upon the Meridian , and in that Place just under that degree and minute on the Globe , the Sun is in the Zenith : which in this Example is in the North East Cape of Hispaniola . Having thus found in what Place of the Earth the Sun is in the Zenith . Bring that Place to the Meridian , and Elevate its respective Pole according to its respective Elevation ; so shall all Places cut by the Horizon have the Sun in their Horizon : Those to the Eastwards shall have the Sun Setting ; those to the Westward shall have it Rising in their Horizon : those at the Intersection of the Meridian and Horizon under the Elevated Pole , have the Sun in their Horizon at lowest , but Rising ; those at the Intersection of the Meridian and Horizon under the Depressed Pole , have the Sun in their Horizon at highest , but Setting . Thus in those Countries that are above the Horizon it is Day-light , and in those but 18 degrees below the Horizon , it is Twilight : But in those Countries further below the Horizon it is at that time dark Night : And those Countries within the Parallel of the same number of degrees from the Elevated Pole that the Suns Declination is from the Equinoctial , have the Sun alwaies above the Horizon , till the Sun have less Respective Declination then the Elevated Pole ; and those within the same Parallel of the Depressed Pole have the Sun alwayes below their Horizon , till the Sun inclines more towards the Depressed Pole ; As you may see by turning about the Globe ; for in this position , that portion of the Globe intercepted between the Elevated Pole , and the Parallel Circle of 20. degrees 5. minutes from the Pole doth not descend below the Horizon : neither doth that portion of the Globe intercepted between the Depressed Pole and the Parallel Circle within 20. degrees 5. minutes of that Pole , ascend above the Horizon . PROB. XLVII . To find in what different Places of the Earth the Sun hath the same Altitude , at the same time . FInd by the former Probleme in what Place of the Earth the Sun is in the Zenith , and bring that Place on the Globe to the Zenith , and on the Meridian [ there ] screw the Quadrant of Altitude , and turn it about the Horizon , describing degrees of Almicantars thereby , as by Prob. 23. and all those Countries in any Almicantar on the Globe shall have the Sun Elevated the same number of degrees above their Horizon . Thus those Countries in the tenth Almicantar shall have the Sun Elevated 10. degrees above their Horizon ; those in the 20 th Almicantar shall have the Sun Elevated 20 degrees above their Horizon ; those in the 30 th , 30. degrees &c. So that you may see , when the Sun is in the Zenith of any Place , All the Countries or Cities in any Almicantar have the Sun in one heighth at the same time above their Horizon . But to find in what different Places the Sun hath the same heighth at the same time , as well Before or After Noon , as at Full Noon ; and that in Countries that have greater Latitude then the Suns greatest Declination , ( and therefore cannot have the Sun in their Zenith , ) requires another Operation . Therefore , Elevate its respective Pole according to your respective Latitude ; and let the Degree of the Brazen Meridian which is in the Zenith represent your Habitation , and the degree of the Ecliptick the Sun is in represent the Sun : Then bring the Sun to the Meridian , and the Index of the Hour-Circle to 12 , and turn the Globe Eastwards , if Before Noon , or Westwards , if After Noon , till the Index point to the Hour of the Day : Then place the lower end of the Quadrant of Altitude to the East point of the Horizon , and move the upper end ( by sliding the Nut over the Meridian ) till the edge of the Quadrant touch the place of the Sun : Then see at what degree of the Meridian the upper end of the Quadrant of Altitude touches the Meridian and substract that number of Degrees from the Latitude of your Place , and count the number of remaining degrees on the Meridian , on the contrary side the degree of the Meridian where the upper end of the Quadrant of Altitude touches the Meridian , and where that number of degrees ends on the Meridian , in that Latitude and your Habitations Longitude , hath the Sun the same heighth at the same time . Example . May 10. at 53. minutes past 8. a clock in the Morning I would know in what Place the Sun shall have the same Altitude it shall have at London , London's Latitude found by Prob. 1. is 51½ degrees Northwards : And because the Elevation of the Pole is equal to the Latitude of the Place ( as was shewed Prob. 15. ) Therefore I Elevate the North Pole 51½ degrees , so shall 51½ degrees on the Meridian be in the Zenith : This 51½ degrees on the Meridian represents London . The Suns Place found by Prob. 3. is ♉ 29. Therefore I bring ♉ 29 to the Meridian , and the Hour Index to 12. on the Hour Circle : Then I turn the Globe Eastwards ( because it is before Noon ) till the Index point at 8. hours 53 minutes on the Hour-Circle , and place the lower end of the Quadrant of Altitude to the East point in the Horizon , and slide the upper end either North or Southwards on the Meridian till the graduated edge cut the degree of the Ecliptick the Sun is in : Then I examine on the Meridian what degree the upper end of the Quadrant of Altitude touches ; which in this example , I find is 38½ degrees . Therefore I substract 38½ from 51½ Londons Latitude , and there remains 13. Then counting on the Meridian 13. degrees backwards , from the Place where the Quadrant of Altitude touched the Meridian , I come to 25½ on the Meridian , Northwards . Therefore I say , In the North Latitude of 25½ degrees , and in the Longitude of London ( which is in Africa , in the Kingdom of Numidia ) the Sun May 10. at 53. minutes past 8. a clock in the Morning hath the same Altitude above the Horizon it hath here at London . The Quadrant of Altitude thus applyed to the East point of the Horizon makes right angles with all points on the Meridian , even as all the Meridians proceeding from the Pole , do with the Equator : therefore the Quadrant being applyed both to the East point , and the Suns Place , projects a line to intersect the Meridian Perpendicularly in equal degrees ; from which intersection the Sun hath at the same time equal Heighth , be the degrees few or many ; for those 5. degrees to the Northwards of this intersection , have the Sun in the same heighth that they 5 degrees to the Southwards have it : and those 10 , 20 , 30. degrees , more , or less , to the Northwards , have the Sun in the same heighth that they have that are 10 , 20. 30. degrees more or less to the Southwards : So that this Prob. may be performed another way more easily , with your Compasses , Thus : Having first rectified the Globe , and Hour Index , Turn about the Globe till the Hour Index point to the Hour of the Day ; Then pitch one foot of your Compasses in the Suns Place , and extend the other to the degree of Latitude on the Meridian , which in this example is 51½ degrees North ; then keeping the first foot of your Compasses on the degree of the Sun , turn about the other foot to the Meridian , and it will fall upon 25½ . as before . Blaew commenting upon this Probleme , takes notice how grosly they ere that think they can find the heighth of the Pole at any Hour of the Day , by the Suns height : because they do not consider that it is impossible to find the Hour of the Day , unless they first know the height of the Pole. PROB. XLVIII . To find the length of the Longest and Shortest Artificial Day or Night . THe Artificial Day is that space of Time which the Sun is above the Horizon of any Place : and the Artificial Night is that space of Time which the Sun is under the Horizon of any Place . They are measured in the Hour Circle , by Hours and Minutes . There is a constant unequallity of proportion in the Length of these Daies and Nights ; which is caused both by the alteration of the Suns Declination , and the difference of the Poles Elevation . Those that inhabite on the North side the Equator have their longest Day when the Sun enters ♋ ; and those that inhabite on the South side the Equator , have their longest Day when the Sun enters ♑ . But to know how long the longest Day is in any North or South Elevation , Raise the North or South Pole according to the Elevation of the Place , and bring ♋ for North Elevation , or ♑ for South Elevation to the Meridian , and the Index of the Hour Circle to 12. Then turn the Globe about till ♋ for North Elevation , or ♑ for South Elevation , come to the West side the Horizon and the number of Hours and minutes pointed at on the Hour Circle , doubled , is the number of Hours and minutes of the Longest Day . The length of the Night to that Day is found by substracting the length of the day from 24. for the remainder is the length of the Night . The shortest Day in that Latitude is the length of the shortest Night , found as before . And the longest Night is of the same length with the longest Day . Example . I would know the length of the longest Day at London . Therefore I Elevate the North Pole 51½ degrees , and bring ♋ to the Meridian , and the Index of the Hour Circle to 12. Then I turn ♋ to the Western side the Horizon , and find the Index point at 8. hours 18. minutes , which being doubled makes 16. hours 36. minutes , for the length of the longest Day here at London . PROB. XLIX . To find how much the Pole is Raised , or Depressed , where the longest Day is an Hour longer or shorter then it is in your Habitation . REctifie the Globe to the Latitude of your Place ; and make a prick at that point of the Tropick which is at the Meridian ; I mean at the Tropick of ♋ , if your Habitation be on the North side the Equator ; or ♑ , if your Habitation be on the South side the Equator : And if you would know where the longest Day is just an hour longer then it is at your Habitation , turn the Globe to the Westward till 7½ degrees of the Equato● pass through the Meridian , and make there another prick on the Tropick : Then turn about the Globe till the first prick come to the Horizon ; and move the Meridian through the notches of the Horizon till the second prick on the Tropick come to the Horizon ; so shall the arch of the Meridian contained between the Elevation of your Place , and the Degree of the Meridian at the Horizon , be the number of Degrees that the Pole is Elevated higher then it is in your Latitude . Example . I would know in what Latitude the longest Day is an Hour longer then it is at London . Therefore I Rectifie the Globe to 51½ deg . and where the Meridian cuts the Tropick of ♋ I make a prick ; then I note what degree of the Equator is at the Meridian , and from that degree on the Equator count 7½ degrees to the Eastwards , and bring those 7½ degrees to the Meridian also ; and again where the Meridian cuts the Tropick of ♋ I make another prick , so shall 7½ degrees of the Tropick be contained between those 〈◊〉 pricks . Then I turn the Globe about , till the first prick comes to the Horizon , and ( with a Quill thrust between the Meridian and the Ball ) I fasten the Globe in this position : Afterwards I move the Meridian through the 〈◊〉 of the Horizon , till the second prick rises up to the Horizon , and then I find 56½ degrees of the Meridian cut by the Superficies of the Horizon : Therefore I say , In the Latitude of 56½ degrees , the longest Day is an Hour longer then it is here at London . But if you would know in what Latitude the Dayes are an Hour shorter , you must make your second prick 7½ degrees to the Westwards of the first , and after you have brought the first prick to the Horizon , you must depress the Pole till the second prick descends to the Horizon : so shall the degree of the Meridian at the Horizon , shew in what Elevation of the Pole the Daies shall be an Hour shorter . By this Probleme may be found the Alteration of Climates : for ( as was said in the Definition of Climates , Book 1. fol. 28. ) Climates alter according to the half-hourly increasing of the Longest Day : therefore the Latitude of 56½ degrees having its Daies increased an whole Hour ) is distant from the Latitude of London by the space of two Climates . PROB. L. The Suns Place given , to find what alteration of Declination be must have to make the Day an Hour longer , or shorter : And in what number of Da●es it will be . REctifie the Globe to the Latitude of the Place , and b●ing the Suns place to the East side the Horizon , and note against what degree of the Horizon it is : then bring one of the Colures to intersect the Horizon in that degree of the Horizon , and at the point of Intersection make a prick in the Colure ; and observe what degree of the Equator is then at the Meridian : Then turn the Globe Westward , if the Daies shorten ; but Eastwards , if they lengthen , till 7½ degrees of the Equator pass through the Meridian , and where the Horizon intersects the same Colure , make another prick in the Colure : Afterwards bring the Colure to the Meridian , and count the number of degrees between the two pricks , for so many degrees must the Suns Declination alter to lengthen or shorten the Day an Hour . Example . The Suns Place is ♉ 10. I would know how much he must alter his Declination before the Day is an Hour longer here at London . Therefore I rectifie the Globe to the Latitude of London , and bring ♉ 10. to the East side the Horizon , and find it against 24½ degrees from the East point : therefore I bring one of the Colures to this 24½ degrees , and close by the edge of the Horizon I make a prick with black lead , in the Colure : then keeping the Globe in this position , I look what degree of the Equator is then at the Meridian , and find 250¼ , and because the Daies lengthen , I turn the Globe Eastwards , till 7½ degrees from the foresaid 250¼ pass through the Meridian : then keeping the Globe in this position I make another prick in the Colure , and bringing this Colure to the Meridian , I find a little more then 5 degrees of the Meridian contained between the two pricks : therefore I say , when the Sun is in ♉ 10. degrees , he must alter his Declination a little more then 5 degrees , to make the Day an Hour longer . Now to know in what number of Daies he shall alter this Declination , you must find the Declination of the two pricks on the Colure as you found the Suns Declination by Prob. 5. and the Arch of the Ecliptick that passes through the Meridian while the Globe is turned from the first pricks Declination to the second pricks Declination , is the number of Ecliptical degrees that the Sun is to pass while he alters this Declination : and the degree of the Ecliptick then at the Meridian is ( with respect had to the Quarter of the Year ) the place the Sun shall have when its Declination shall be altered so much as to make the Day an Hour longer Thushaving the Suns first place given , and its second place found ▪ you may by finding those two places on the Plain of the Horizon , also find the number of Daies comprehended between them , as you are taught by the fourth Probleme . This Probleme thus wrought for different Times of the Year , will shew the falacy of that Vulgar Rule which makes the Day to be lengthned or shortned an Hour in every Fifteen Daies : when as the lengthning or shortning of Daies keeps no such equality of proportion : for when the Sun is neer the Equinoctial points the Daies lengthen or shorten very fast : but when he is neer the Tropical points , very slowly . PROB. LI. Of the Difference of Civil and Natural Daies , commonly called the Equation of Civil Daies . And how it may be found by the Globe . THe Civil Day is that space of Time containing just 24. Hours , reckoned from 12 a clock on one Day to 12 a clock the next Day ; in which space of Time the Equinoctial makes upon the Poles of the World a Diurnal Revolution . The Natural Day is that space of Time wherein the Sun moveth from the Meridian of any Place to the same Meridian again . These Daies are at one time of the Year longer then at another ; and at all Times longer then the Civil Daies . There is but smal discrepancy between them , yet some there is , made by a two-fold Cause . For first , The Suns Apparent motion is different from his true motion ; He being much slower in his Apogeum then he is in his Perigeum : For when the Sun is in his Apogeum he scarce moves 58 minutes from West to East in a Civil Day , but when he is in his Perigeum he moves above 61 minutes in a Civil Day : and therefore increases his Right Ascension more in equal Time. The second Cause is the difference of Right Ascensions answerable to equal parts of the Ecliptick : for about ♋ and ♑ the differences of Right Ascensions are far greater then about ♈ and ♎ : for about ♈ and ♎ the Right Ascension of 10. degrees is but 9. degrees 11. minutes ; but about ♋ and ♑ the Right Ascension of 10 degrees will be found to be 10. degrees 53. minutes , as by the Globe will appear . But because of the smalness of the Globes graduation ▪ you cannot actually distinguish to parts neer enough for the solution of this Probleme , if you should enquire the difference in length of two single Daies ; it will be requisite to take some number of Daies together ; Suppose 20. Therefore find by Prob. 3. the Places of the Sun for the beginning and ending of those Daies you would compare ; and find the Right Ascensions answerable to each place in the Ecliptick ; and also the differences of Right Ascensions answerable to the Suns motion in each number of Daies : Then compare the differences of Right Ascensions together ; and by substracting the lesser from the greater , you will have the number of degrees and minutes of the Equator that have passed through the Meridian more in one number of Daies then in the other number of Daies : which degrees of the Equator converted into Time , is the number of minutes that the one number of Daies is longer then the other number of Daies . Example . I would know what difference of Time there is in the length of the first 20. Daies of December , and the first 20 , Daies of March. I find by Prob. 3. the Suns place December 1 , is 〈◊〉 19. 45. at the end of 20 Daies . viz. on the 21 Day his place is 〈◊〉 10. 11. The Suns place March 1. is ♓ 21. 16. at the 20. Daies end , viz. March 21 , his place is ♈ 11. 3. I find by Prob. 26. the Right Ascension answerable to ♐ 19. 45 is 258. 10. ♑ 10. 11 280. 25. ♓ 21. 16 352. 00. ♈ 11. 3 9. 40. and the difference of Right Ascensions contained between the first Day in each Moneth , and the 21 of the same Moneth , by substracting the lesser from the greater is for 258. 10. And for 352. 00. 280. 25. 9. 40. 22. 15 17. 40. But note , because the Vernal Colure , where the degrees of Right Ascension begin and end their account , is intercepted is the Arch of the Suns motion from the first to the 21. of March , therefore instead of substracting the lesser number of degrees of Right Ascension from the greater , viz. 9. 40 from 35. 2. I do for finding the difference of the Right Ascensional arch of the Suns motion in those 20 Daies , sustract the foresaid 352 degrees from 360 , and the remains is 8. which is the difference of Right Ascension from ♓ 21 , 16. to the Equinoctial Colure : to which 8 adding 9 degrees 40 minutes , the Right Ascension from the Equinoctial Colure . to ♈ 11. 3. it makes 17 degrees 40. minutes for the difference of Right Ascensions between ♓ 21 , 16. and ♈ 11. 3 Then I find the difference of this Difference of Right Ascension , by substracting the less from the greater , viz. 17. 40. from 22. 15. and the remains is 4. degrees 35. minutes , for the number of degrees and minutes of the Equator that pass through the Meridian in the first 20 Daies in the Moneth of December more then in the first 20 Daies of the Moneth of March : which 4. degrees 35. minutes converted into Time , gives 19. minutes , that is , a quarter of an Hour and 4 minutes that the first 20 Daies of December aforesaid , are longer then the first 20 Daies of March. PROB. LII . How to find the Hour of the Night , when the Moon shines on a Sun Dyal , by help of the Globe . REctifie the Globe , and find by Prob. 54. or an Ephemeris , the Moons place at Noon : Bring it to the Meridian , and the Index of the Hour Circle to 12. and turn about the Globe till the Index of the Hour Circle points to the same Hour the shade of the Moon falls on , on the Sun Dyal . Then by Prob. 3. find the Suns place at Noon , and see how many degrees of Right Ascension are contained between the Suns place and the degree of the Equator at the Meridian , when the Index of the Hour Circle is brought to the Hour the Moon shines on in the Sun Dyal ; for those number of degrees converted into Time , shall be the Time from Noon , or the Hour of the Night . Only note , Respect must be had to the motion of the Moon from West to East , for so swift is her mean motion , that it is accounted to be above 12. degrees in 24. Hours ; that is 6 degrees in 12 Hours , 3 degrees in 6 Hours , &c. and this also converted into Time , as aforesaid , you must add proportionably to the Time found from Noon ; and the sum shall give you the true Hour of the Night . Example . Here at London , I desired to know the Hour of the Night January 6. this present Year 1658. The Moons place found by an Ephemeris , or for want of an Ephemeris , by Prob. 54. is in ♊ 21. degree 22 , minutes ; Therefore I rectified the Globe to Londons Latitude , and brought ♊ 21. 22. minutes to the Meridian , and the Index of the Hour Circle to 12. then by Prob. 3. I found the Suns place in ♑ 26. degrees 46. minutes , and by Prob. 26. I found his Right Ascension to be 300 degrees ; Then I turned about the Globe , till the Index of the Hour Circle pointed at 10 Hours , and at the degree of the Equator at the Meridian I made a prick ; then I counted the number of degrees of the Equater contained between the foresaid 300 deg . and this prick and found them 111¼ degrees which converted into Time , by allowing 15 degrees for an Hour , gives 7 hours , 25 minutes , Time from Noon : which if the Moons motion were not to be considered , should be the immediate Hour of the Night : But by the Rule aforesaid , the Moons motion from West to East , in 7 hours 25 minutes is 3 degrees 42 minutes , and this 3 degrees 42 minutes being converted into Time , is 14 minutes more , which being added to 7 hours 25 minutes : make 7 hours 39 minutes , for the true Hour of the Night . PROB. LIII . To find the Dominical Letter , the Prime , Epact , Easter Day , and the rest of the Moveable Feasts , for ever . THough these Problemes cannot be performed by the Globe , because of the several changes , and irregular accounts that their Rules are framed upon , yet because they are of frequent and Vulgar use , and for that the solution of many other Questions will have dependency on the knowledge these ; Therefore I have thought fit here to inserte this Table of M r Palmers , by which you may find them All. I shall not insist upon the Reasons of the several changes of Letters , and Numbers , Himself having already very learnedly handled that subject , in his Book of the Catholick Planisphear , Book 1. Chapter 11. ( to which I refer you ) Neither shall I need to give you any other Instructions for finding what is here proposed , then what himself hath given in his fourth Book , Chapter 66 , and part of 67. Therefore take it as he there delivers it . An Example , shall serve here instead of a Rule . For the Year 1657. I would know all these : wherefore I seek the Year 1657. in the Table of the Suns Cycle , and over against it , I find 14. for the Year of the Cycle of the Sun , and D for the Dominical Letter . And note here , that every Leap-year hath 2 Dominical Letters ( as 1660 , hath A G ) and the first ( viz. A ) serveth that Year till February 25 , and the second ( G ) for the rest of the Year . And note that these Letters go alwayes backwards when you count forwards ( as B A , then G F , &c. not F G , and , then A B ) as you may see by the Table . To find the Age of the Moon . Remember first that the Epact begins with March , which must be here accounted the first Moneth : Then if you add to the Epact the number of the Moneth current , and the number of the day of the Moneth current , the sum or the excess above 30 , is the Moons age . Example . January 20. 1656. According to the accompt of the Church of England , ( who begin the Year with March 25. which was the Equinoctial day about Christ time ) the Epact is 14. January is the 11 th Moneth , and the 20 th day is proposed ; now add 14. 11. and 20. together , they make 45. out of which I take 30. and there remains 15 , the Moons age . PROB. LIV. The Age of the Moon given , to find her place in the Ecliptick according to her mean motion . THis Probleme may be performed exact enough for Common uses by the Globe , but in regard it only shews the Moons place in the Ecliptick according to her meat motion , it will often fail you some few degrees of her true Place . The work is thus , First set figures to every twelth degree of the Equinoctial , accounted from the Equinoctial Colure , marking them with 1 , 2 , 3 , 4. &c. to 30 which will end where you began viz. at the Equinoctial Colure again : so shall the Equinoctial be divided into 30 equal parts , representing the 30 Dayes of the Moons Age These figures ( to distinguish them from the degrees of the Equator ) were best be writ with Red Ink. When you would enquire the Moons Place , Elevate the North Pole 90 degrees , that is , in the Zenith , so shall the Equator ly in the Horizon : Then bring the Equinoctial Colure against the Day of the Moneth in the Horizon , so shall the Moons Age written in Red figures , stand against the Signe and degree in the Horizon that the Moon is in at that Time. Example . September 28. 1658. I would know the Moons place in the Ecliptick , she being then 12 Daies old . Therefore I Elevate the North Pole 90 degrees above the Horizon , and turn the Globe about till the Equinoctial Colure come to September 28. in the Circle of Daies on the Horizon ; then looking against what Signe and degree of the Ecliptick Circle in the Horizon the 12 th division in Red figures stands , I find ♓ 9. which is the Signe and degree the Moon is in , according to her mean Motion . This Probleme may be applyed to many Uses : for , having the Moons Place you may find the Time of her Rising , Southing , Setting , and Shining &c. by working with her , as you were taught to work with the Sun , in several fore-going Problemes , proper to each purpose . PROB. LV. Having the Longitude and Latitude , or Right Ascension and Declination of any Planet , or Comet , to place it on the Globe , to correspond with its place in Heaven . PLanets and Comets cannot be placed on the Globe so as their places will long retain correspondence with their places in Heaven ; Because as was said Chap. 44. they have a continual motion from West to East upon the Poles of the Ecliptick : yet never-the-less you may by having their Longitude and Latitude , or Right Ascension and Declination , for any set Time , place a Mark for them on the Globe , either with Ink if your Globe be Varnisht , for then you may with a wet finger wipe it off again ; or with Black-lead , if it be not Varnisht , and then you may rub it out again with a little White Bread : which Mark for that Time , will as effectually serve you to work by , as any of the Fixed Stars placed on the Globe will do . Therefore if the Longitude and Latitude of any Planet , or Comet , be given ; Do thus , Elevate the North Pole , if the Latitude given be North ; but if the Latitude given be South , Elevate the South Pole 66 ½ degrees ; and place the Pole of the Ecliptick in the Zenith , and over it screw the Quadrant of Altitude : so shall the Ecliptickly in the Horizon ; and the Quadrant of Altitude being turned about the Horizon shall pass through all the Degrees of Longitude : Then find the point of given Longitude in the Ecliptick , and bring it to the Quadrant of Altitude , and hold it there : Then count upwards on the Quadrant of Altitude the number of degrees and minutes of given Latitude , and at the point where the number ends , close to the Quadrant of Altitude , make a smal Prick , and that Prick shall represent the Planet or Comet you were to place on the Globe . If it be the Right Ascension and Declination of a Planet or Comet that is given ; you must find the degree and minute of Right Ascension on the Equinoctial , and bring it to the Meridian , and keep the Globe there steddy ; then find the degree and minute of Declination on the Meridian , and under that degree and minute on the Globe make a Prick , and that Prick shall represent the Planet , or Comet , as aforesaid , If it be ♄ or ♃ that this Prick is to represent , it may stand on the Globe sometimes a Week or a Fortnight , without much difference from the Planets place in Heaven . But if the Prick were to represent the other Planets , you must ( in regard of their swift motion ) alter it very often , especially for the Moon ; for so swift is her motion , that in every two Hours she alters about a degree in Longitude . Having thus placed this Mark on the Globe , you may find out the Time of its several Positions , and Aspects , if you work by it as you are directed to work by the Sun , in the several respective Problemes throughout this Book . The End of the Second Book . The Third BOOK , Being the Practical Use of the GLOBES . Applyed to the Solution of Problemes In the Art of NAVIGATION . PRAEFACE . BEcause the Art of Navigation consists aswell in the knowledge of Astronomical and Geographical Problemes , as in Problemes meerly Nautical ; Therefore I must desire the Artist to seek in the last Book such Problemes as are only Astronomical or Geographical . For my Designe is here to collect such Problemes as are only used in the Art of Navigation , some few particulars excepted , as for finding Latitude , Longitude , Course ; Distance , &c. Which though they are handled in than Book , yet for their exceeding Vtility in the Art of Navigation , and for that what there is given , cannot alwayes be had to work by ; therefore in this Book I have mentioned divers other Observations , which being made or had , you may by the Rules proper for each Observation find what shall be proposed . PROB. I. The Suns Amplitude and Difference of Ascension given , to find the Heigth of the Pole , and Declination of the Sun. ELevate the Pole so many degrees as the Difference of the Suns Ascension is , and screw the Quadrant of Altitude to the Zenith , and bring the first point of ♈ to the Meridian , then number on the Quadrant of Altitude upwards the complement to 90. of the Suns Amplitude , and move the Quadrant of Altitude till that number of degrees cuts the Equator ; So shall the Quadrant cut in the Horizon the degree of the Pole Elevation ; and in the Equator the degree of the Suns Declination . Example . The difference of Ascension is 27. degrees 7. minutes . Therefore I Elevate the Pole 27. degrees 7. minutes above the Horizon , and screw the Quadrant of Altitude to 27. degrees 7. minutes , which is in the Zenith : then I bring the first point of ♈ to the Meridian , and number on the Quadrant of Altitude upwards 56. degrees 40. minutes , the Complement of the Suns Amplitude , and bring that degree to the Equator ; then I see in what degree of the Horizon the Quadrant cuts the Horizon , and find 51 ½ , which is the Elevation of the Pole : then looking in what degree of the Equator the Quadrant of Altitude cuts the Equator , I find 20 degrees , 5 min. which is the Declination of the Sun at the same Time. PROB. II. The Suns Declination and Amplitude given , to find the Poles Elevation . ELevate the Pole so many degrees as the Complement of the Suns Amplitude is ; and screw the Quadrant of Altitude in the Zenith , and bring the first point of ♈ to the Meridian : Then count on the Quadrant of Altitude to the Degree of the Suns Declination , and bring that degree to the Equinoctial ; and the degree of the Equinoctial cut by that degree of the Quadrant of Altitude , is the degree of the Poles Elevation . Example . The Suns Amplitude is 33. degrees 20. minutes , his Declination is 20 degrees 5 minutes , his Complement of Amplitude to 90. is 56 degrees 7 minutes . Therefore I Elevate the Pole 56. degrees 7 minutes above the Horizon , and screw the Quadrant of Altitude to 56 degrees 7 minutes which is in the Zenith : Then I bring the first point of ♈ to the Meridian , and number on the Quadrant of Altitude upwards 20. deg . 5 min. for the Suns Declination , this 20 th degree 5 minutes , I bring to the Equinoctial , and find it cut there 51 ½ . degrees , for the Heigth of the Pole. PROB. III. The Suns Declination and Hour at East given , to find the Heigth of the Pole. ELevate the Pole so many degrees as the Suns Declination is , and screw the Quadrant of Altitude in the Zenith : Then convert the Hours or minutes past 6. given into degrees ; by allowing 15 degrees for every Hour of Time , and for every minute of Time 15 minutes of a Degree ; and number those degrees or minutes in the Horizon from the East Southwards ; so shall the Degree of the Quadrant of Altitude cut by the Equator be the Complement of the heigth of the Pole. Example . The Suns Declination is 20 deg . 5 min. Therefore I Elevate the Pole 20 degrees 5 minutes , and also screw the Quadrant of Altitude to ●0 degrees 5 minutes which is in the Zenith : the Hour the Sun comes to be at East is 8 a clock 53 minutes , that is , 1 Hour 7 minutes after 6. Therefore I convert 1 Hour 7 minutes into Degrees , as before , and it gives 16 degrees 50 minutes ; which number of degrees and minutes I count from the East point Southwards , and thither I bring the Quadrant of Altitude : Then I look in what degree of the Quadrant of Altitude , the Equator cuts , and find 38 ½ , which is the Complement of the Poles Heigth , viz. 51 ½ degrees for the Heigth of the Pole. In this Probleme the Declination of the Sun and Elevation of the Pole bears the same Denomination of either North or South , for when the Declination and the Elevation are different the Sun cannot come to the East point . PROB. IIII. The Declination of the Sun and his Altitude at East given , to find the Heigth of the Pole. ELevate the Pole to the Complement of the Suns Altitude , and screw the Quadrant of Altitude to the Zenith : Then bring the Equinoctial point ♈ to the Meridian , and number on the Quadrant of Altitude the degrees of the Suns Declination , and bring that degree to the Equinoctial , and note the degree it cuts ; for its Complement to 90 is the Heigth of the Pole. Example . May 10. The Suns Declination is 20 degrees 5 minutes ; His Altitude at East is 25 degrees 55 minutes here at London : I enquire the Heigth of the Pole. Therefore I substract 20. 5 min. from ●0 the remains is 69 deg . 55 min. for its Complement ; wherefore I bring 69 deg . 55 min. of the Meridian to the Horizon ; and to 69 deg . 55 min. which is in the Zenith , I screw the Quadrant of Altitude then I bring ♈ to the Meridian , and count on the Quadran : of Altitude upwards 20 deg . 5 min , and move it about the Equinoctial till those 20 deg . 5 min. touch the Equinoctial , which I find to be in 38 ½ degrees , Therefore I substract those 38 ½ from 90 , and the remains is 51 ½ degrees , Therefore I say the Pole here at London is Elevated 51 ½ degrees . The Declination and the Elevation is alwaies the same , either North or South , for when they alter their Denomina ions the Sun at East can have no Altitude , neither can it indeed reach the East point : and therefore in this example , because the Declination of the Sun is North , it is the North Pole that is Elevated here at London . To perform the same otherwise , with a pair of Compasses . Take off with your Compasses from the Equator or Quadrant of Altitude the number of degrees of Altitude observed , and place one foot at the beginning of ♈ on the inner edge of the Horizon , and extend the other directly upwards towards the Zenith : Then move the Brazen Meridian through the notches of the Horizon till the other point of your Compasses ( respecting the Zenith ) reach the Parallel of the Suns Declination : So shall the number of degrees on the Meridian be the number of degrees that the Pole is Elevated above the Horizon ; and is either North or South according as the Suns Declination is : as before . This may yet otherwise be performed with the Quadrant of Altitude , by taking the Nut off the Meridian , and laying the edge of its Index ( specified in Chap. 1. Sect. 6. of the first Book ) exactly on the East line of the Horizon : for when that lies straight between the point of East on the outer Verge of the Horizon , and the beginning of ♈ in the inner Verge of the Horizon , then shall the upper end of the Quadrant of Altitude point directly to the Zenith : and if then you turn the Meridian through the notches of the Horizon till the Suns Altitude on the Quadrant of Altitude cut the Parallel of Declination , you will have on the Meridian the heigth of the Pole : as before . PROB. V. By the Suns Declination and Azimuth at 6. of the Clock given , to find the Heigth of the Pole , and Almicantar at 6. ELevate the Pole so many degrees as the Suns Azimuth is at 6. and screw the Quadrant of Altitude in the Zenith , and bring the first point of ♈ to the Meridian : Then number on the Quadrant of Altitude upwards the Complement of the Suns Declination , and bring that degree to the Equator : So shall the degree of the Horizon cut by the Quadrant of Altitude be the Complement of the Poles Elevation ; and the degree of the Equator cut by the Quadrant of Altitude shall be the Almicantar of the Sun at 6. of the clock . Example . The Suns Azimuth at 6 is 12¾ degrees : Therefore I Elevate the Pole 12¾ , and screw the Quadrant of Altitude to 12¾ degrees which is in the Zenith : Then I bring the first point of ♈ to the Meridian ; The Suns Declination is 20 degrees 5 minutes . Therefore I number on the Quadrant of Altitude 69 deg . 55 min. which is the Complement of 20 deg . 5 min. to 90. this 69 deg . 55 min. on the Quadrant of Altitude I bring to cut the Equator , and find when 69 deg . 55 min , cuts the Equator , that the Quadrant of Altitude cuts the Horizon , in 38½ deg . which is the Complement of the Poles Elevation : and at the same time the Quadrant of Altitude also cuts the Equator in 15½ degrees which is the Almicantar or Altitude of the Sun at 6. a clock . PROB. VI. By the Hour of the Night and a known Star Observed Rising or Setting , to find the Heigth of the Pole. REctifie the Hour Index , by Prob. 2. of the former Book ; and turn the Globe Westwards till the Hour Index points at the Hour of the Night ; fasten the Globe there , and turn the Meridian through the notches of the Horizon till the know● Star come to the East side the Horizon , if the Star be Rising , 〈◊〉 the West if it be Setting ; so shall the degrees of the Poles El●vation be cut by the Horizon under the Elevated Pole ; and 〈◊〉 North or South according as the Elevated Pole of the Globe 〈◊〉 PROB. VII . Two Places given in the same Latitude , to find 〈◊〉 Difference of Longitude . BRing the first Place to the Meridian , and note the number of degrees of the Equinoctial that comes to the Meridan with it ; then Bring the other place to the Meridian and note the number of degrees of the Equator that comes to the Meridian with it : and by substracting the lesser number from the greater you have the difference of Longitude , This needs no Example . PROB. VIII . Two Places given in the same Longitude , to find the Difference of Latitude . BRing the Places to the Meridian , and the degrees of the Meridian over the two Places is the Latitudes of them both , and by substracting the lesser number of degrees from the greater you will have the difference of Latitude . PROB. IX . Course and Distance between two Places given , to find their Difference in Longitude and Latitude . SEek the Rhumb you have failed upon , as in Prob , 34 , of the last Book , and upon that Rhumb make a mark for the Place you departed from ; then with your Compasses take off from the Equinoctial the number of Leagues you have failed upon that Rhumb , by allowing a degree for every 20. Leagues and place one foot of your Compasses upon that mark , and where the other foot falls on that Rhumb make a second mark ; then by bringing the first mark to the Meridian , you will see on the Meridian the Latitude of that mark , and in the Equator the Longitude as in Prob. 2. of the last Book : and by bringing the second mark also to the Meridian , you will as before , find the Longitude and Latitude of the second mark also . Then by substracting the lesser Latitude from the greater Latitude , and the lesser Longitude from the greater Longitude , you will have the difference remaining , both of Longitude and Latitude you are arived into . PROB. X. To find how many Miles are contained in a Degree of any Parallel . EVery Degree of the Equinoctial contains 20. English Leagues and every League 3. English Miles : But in every Parallel to the Equinoctial , the Degrees diminish more and more even to the Pole , where they end in a point . Therefore a Degree in any Parallel cannot contain so many Miles as a Degree in the Equinoctial . Now that you may know how many Miles are contained in a Degree of any Parallel to the Equinoctial . Do thus , Measure with your Compasses the width of any number of Degrees in any given Parallel ; suppose ( for Examples sake ) 10. Degrees in the Parallel of 51½ ; Examine in the Equator , how many Degrees of the Equator they will make , and you will find 6⅕ . Therefore 1. Degree in the Equator making 60 Miles 6. Degrees makes 360 , to which add for the 〈◊〉 part 12 Miles , makes ●72 Miles , to be the Measure of 10 Degrees in the Parallel of 51½ . So that by dividing 372. by 10. you have ●7 Miles for the length of a Degree , from East to West in the Parallel of 51½ Degrees . PROB. XI . The Rhumb you have sailed upon , and the Latitudes you de●arted from , and are arived to , given , to find the Difference of Longitude , and the number of Leagues you have Sailed . FIrst seek the Rhumb you have sailed on , and pass it through the Meridian till it cuts in the Meridian the Latitude you departed from ; and keeping the Globe there sted●y make a mark close by the Meridian , under that Latitude and in that Rhumb on the Globe , and note in the Equinoctial the degree of Longitude at the Meridian : then pass that Rhumb through the Meridian again , till it cuts in the Meridian the Latitude you are arived to ; and in that Rhumb and Latitude make on the Globe another mark , and examine in the Equinoctial the Longitude of the second mark ; for the difference between the first and second mark , is the difference of Longitude . Then open your Compasses to one Degree of the Equinoctial , and by measuring along in the Rhumb count how many times that Distance is contained between the two points in that Rhumb : for so many times 20. Leagues is the Distance you have sailed . Example . I sail upon the North West Rhumb from the Latitude of 1● ▪ degrees , into the Latitude of 30. degrees 40. minutes . Therefore I find the North West Rhumb ▪ and turn the Globe through the Meridian till this Rhumb cut the Meridian in the first Latitude , viz. in 10. degrees and directly under 10. degrees upon the Rhumb I make a prick , and also find 10 degrees 3 minutes , of the Equator at the Meridian , for the Longitude of the First Place . Then I turn the Globe again through the Meridian , till the same Rhumb cut the Meridian in the second Latitude . viz in 30 degrees 40 minutes , and directly under those 30 degrees 40 minutes upon the same Rhumb , I make another prick , which represents the Place I am arrived to : I examine the Longitude of this prick , as before , and find it 32 degrees 10 minutes . Therefore I substract the first Longitude , viz. 10 degrees 3 minutes from the second Longitude , viz. 32 degrees 10 minutes , and there remains 22 degrees 7 minutes , for the Difference of Longitude . Then for examining the Distance I open my Compasses to 1. degree on the Equinoctial and measure upon the Rhumb how oft that Distance is contained between the two pricks , and find 29¼ , that is , 29 degrees 15 minutes , which multiplyed by 2● . gives 585 , for the number of Leagues failed upon that R●umb . The reason why I open the Compasses no wider then to 1 degree , is because the Rhumbs being Circular or 〈◊〉 lines the distance on them may be measured more exactly by often counting that 1 degree in them the● if the 〈◊〉 had bin op●red to many degrees . Thus if the Compasses had been opened wide enough to reach between the two pricks aforesaid . I should not have had above 583 Leagues for the distance between the two Places : neither is there indeed more great Circle distance between them ; But I sailed upon a Rhumb , that is , I follow●d the Course of a Circular winding line , and so fetcht a Compass about to come to these two pricks ; and therefore I have in truth sailed 585. Leagues . For the segment of a Rhumb between two Places is alwaies greater then a straight line drawn betwixt them ; yea sometimes by half or more in Places neer either Pole. Note , If you be not very curious in opening your Compasses to this smal distance , you may in oft turning them about upon the Rhumb commit error in your measuring : therefore when you have taken the Distance of one degree , try if you neither gain or loose any thing in measuring 10 , or 20. degrees of the Equinoctial by them : for then your Compasses are opened to a width exact enough for your purpose . PROB. XII . The Longitudes and Latitudes of two Places given , to find Course , and Great Circle distance between them . FInd on the Globe the Longitudes and Latitudes given , and make pricks to either Longitude and Latitude : If any Rhumb pass from one place to the other , that is ( without more a doe ) the Rhumb sought . But if no Rhumb pass through ; Take the Rhumb that runs most Parallel to the two pricks : for that shall be the Rhumb or the neerest Rhumb that these two pricks Bear on . An Example of this , see in Prob. 34. of the Last Book : And the Great Circle Distance between these two pricks , you may find as by Prob , 33. of the same Book . PROB. XIII . The Latitude you departed from , and the Latitude you are arrived to , and the number of Leagues you have sailed given , to find the Rhumb you have sailed on , and difference of Longitude . MAke a prick on the Globe in the Latitude you departed from : then open your Compasses to the number of Leagues you have sailed , by taking for every 20. Leagues 1. degree of the Equator , half a degree for 10 Leagues , a quarter of a Degree for 5 Leagues , and so proportionably for any other number of Leagues : Place one foot of your Compasses in the prick made for the Latitude you departed from , and extend the other towards the Latitude you are arived to , and discribe an occult Arch ; Turn the Globe till this occult Arch come to the Latitude on the Meridian , and where the Latitude cuts this occult arch make another prick to represent the Latitude you are arived to ; so shall the Rhumb passing through those two pricks ( or that is most Parallel to those two pricks ) be as in the last Prob. the Course or the Rhumb those two pricks Bears on . The difference of Longitude you may find as by Prob. 11. PROB. XIV . To find by the Globe the Variation of the Needle ; commonly called the Variation of the Compass . OBserve by a Compass whose wyer is placed just under the Flower deluce , what point of the Compass the Sun Rises or Sets on , Morning , or Evening : Then examine by Prob : 10. of the second Book , what degree of the Horizon the Sun Rises or Sets on by the Globe also ; and if the Rising or Setting be the same , both on the Globe and Compass , there is no Variation in your Place , But if there be difference between the Rising or Setting by the Compass and the Globe , then is there Variation in your Place . If the point the Sun Rises upon in the Compass be neerer the North point , then the point the Sun Rises upon by the Globe , the Variation is Westwards . If the point the Sun Sets upon in the Compass be neerer the North then the point it Sets upon by the Globe , the Variation is Eastwards . If the point the Sun Sets upon in the Compass be further from the North point , then the point the Sun Sets upon by the Globe , the Variation is Westwards . If the point the Sun Rises upon in the Compass be further from the North point then the point the Sun Rises upon by the Globe , the Variation is Eastwards . And so many degrees as there is between the point of Rising or Setting found by the Compass , and the point of true Rising or Setting found by the Globe , so many degrees is the Variation from the North towards the East , or West point . Otherwise , when the Sun hath Altitude . Having the Altitude of the Sun ; find by Prob. 22. of the second Book , its Azimuth : Then examine by a Compass whether the true Azimuth found by the Globe , agree with the Azimuth found by a Nautical Compass : If they agree there is no Variation : But if the Azimuth of the Compass before Noon be neerer the North then the true Azimuth found by the Globe , the Variation is Westwards . If the Azimuth by the Compass Afternoon be neerer the North , the Variation is Eastwards . If the Azimuth by the Compass Afternoon be further from the North , the Variation is Westwards , If the Azimuth by the Compass before Noon be further from the North , the Variation is Eastwards . And this Variation shall be as aforesaid so many degrees as there is between the Azimuth Observed by the Compass , and the true Azimuth , Observed by the Globe . PROB. XV. To keep a Journal by the Globe . BY some of these foregoing Problemes you may Dayly ( when Observations can be made find both the Longitude and Latitude on the Globe of the Places you are arived to , and also the Way the Ship hath made , and make pricks on the Globe in their proper Places for every Da●●s Journey , so truly and 〈◊〉 naturally that if you kept your reckoning aright you may be sure you cannot miss any thing of the truth it self ; and that with less trouble and greater advantage , then keeping a Book of every Daies Reckoning . PROB. XVI . To Steer in the Night by the Stars . REctifie the Globe and Hour Index as by Prob. 2. of the last Book , and turn about the Globe till the Index of the Hour Circle points to the Hour of the Day or Night : Then turn the Globe till the Difference of Longitude between the Place you depart from , and the Place you sail to pass through the Meridian and if any Star in the Latitude of the Place you sail To come to the Meridian , or neer the Meridian with the degree of the difference of Longitude , that Star is at that time in or neer the Zenith of that Place you sail to : and by finding the same Star in Heaven , as by Prob , 44. of the last Book you may direct your ship towards that Star , and fail as confidently ( saies M r Blagrave ) as if Mercurie were your Guide . But because this Star moves from the Zenith of this Place you must often examine what Star is come to the Zenith , and so often charge the Star you Steer by , as the length of your Voyage may require . PROB. XVII . How to platt on the Globe a New Land , never before Discovered . THese two following Problemes are 2. Chapters of M r Wrights , delivered by him as follows . It may sometimes fall out in new Discoveries , or when your Ship by means of a Tempest is driven out of her right Course , that you shall come to the sight of some Isle , Shoald , or new Land , whereof the Mariner is utterly ignorant : And to make some relation of the same . or to go unto it some other time , if you desire to set it down on your Globe in the true place , you may do it after this manner : So soon as you have sight thereof , mark it well first with your Compass , observing diligently upon which Point thereof it lieth , And secondly , you must there take the heigth of the Sun , or of the Pole-star , as you were taught Prob. 13. of the second Book , that you may know in what Point your Ship is , and that point you must call the First Point ; which being so done , your Ship may sail on her Course all that day , till the day following , without losing her Way : and the next day mark the Land again , and see upon what Point it lieth ; and then take your heigth , and with it cast your Point of Traverse once again ; and that you may call your second Point . Then take a pair of Compasses , and placing one foot upon the First Point , and the other upon the Rhumb towards which the Land did Bear , when you Cast your First Point : set also one foot of another pair of Compasses in the second Point , and the other foot upon the Rhumb upon which the Land lay when you cast your second Point ; and these two Compasses thus opened , you must move by their Rhumbs , till those two feet of both Compasses do meet together , which were moved from the foresaid two Points : and where they do so meet together , there may you say is the Land which you Discovered ; which Land you may point out with the In lets and Out-lets , or Capes and other Signes , which you saw thereupon . And by the graduation you may see the Latitude thereof ; that thereby you may find it , if a any time after you go to seek for it . PROB. XVIII . Seeing two known Points or Capes of Land , as you sail 〈◊〉 long , how to know the distance of your Ship from them ▪ PItch one foot of one pair of Compasses upon one of the two foresaid Capes , and the other foot upon the Rhum● which in this Compass pointeth towards that Cape . 〈◊〉 in like manner shall you do with another pair of Compasses , placing one foot thereof upon the other known Cape , 〈◊〉 the other foot upon the Rhumb , which stretcheth towards 〈◊〉 said second Cape ; and moving the two Compasses ( so opened ) by these two Rhumbs off from the Land , the very same Point where the two feet which came from the two Capes do meet , you may affirm to be the very Point where your Ship is . And then measuring by the degrees of the Equinoctial , you may see what distance there is from the said Point to either of the foresaid Capes , or to any other place , which you think good , for it is a very easie matter , if you know the point where your Ship is , PROB. XIX . Of Tides , and how by help of the Globe you may in general judge of them . DIvide the Equinoctial into 30 equal parts , as was directed in Prob. 54. of the last Book . These 30. equal parts represent the 30. daies of the Moons Age. Then on the North and South point of the Compass in the outmost Verge of the Horizon , Write with red Ink 12. From the North Eastward , viz. at the Point North and by East , Write 11 ¼ . At the next point to that the same way , viz. North North East , Write 10 ½ . At the next , viz. North East and by North , Write 9 ¾ . And so forward to every point of the Compass ; rebating of the last hour ¾ till you come to 12. in the South ; where you must begin again to mark that Semi-Circle also in the same order you did the last . In this Circle is then represented the Points of the Compass the Sun and Moon passeth by every Day ; and the Figures annexed represent the twice 12. hours of Day and Night . Having thus prepared your Globe and Horizon , you may by having the Moons Age , and the point of the Compass on which the Moon maketh full Sea at any Place given , find at what Hour of Day or Night it shall be high Tide in the same Place . Thus , It is a known Rule that a North and South Moon makes high water at Margarate . Therefore Bring the first point of ♈ to the North or South point in the Horizon , and Elevate the North Pole into the Zenith : Then count in the Equinoctial the Daies of the Moons Age numbred in red figures ; and the Hour and minutes written in red figures annexed to the names of the Windes ) that stands against the Moons Age shall be the Hour of High Tide on that Day or Night at Margarate . The End of the Third Book , The Fourth BOOK , Shewing the Practical Use of the GLOBES : Applying them to the Solution of Astrological Problemes . PRAEFACE . THe Practise of Astrology is grounded upon a two-fold Doctrine . The first , for erecting a Figure of Heaven , placing the Planets in it , finding what Aspects they bear each other , and in what Places they are constituted , &c. and this we call the Astronomical part of Astrology . The second is , how to judge of the events of things by the Figure erected : and this is indeed the only Astrological part . The first of these I shall briefly handle ; because what therein is proposed may be performed by the Globe , both with speed , ease , delight , and demonstration . The second I shall not meddle with , but refer you to the whole Volumnes already written upon that Subject . PROB. I. To Erect a Figure of the 12 Houses of Heaven . BEfore you erect a Figure of the 12 Houses of Heaven it will be requisite you place the Planets , ☊ , and ☋ , according to their Longitude and Latitude upon the Globe , as was directed in Prob. 55. of the second Book : for then , as you divide the Houses of your Figure by the Circle of Position , you may by inspection behold in what Houses the Planets are scituated , and also see what fixed Stars they are applying to , or separating from . But to the matter . There is disagreement between the Ancient and Modern Astrologers , about erecting a Figure of Heaven . M r Palmer in his Book of Spherical Problemes Chap. 48. mentions four several waies , and the Authors that used them ; whereof one of them is called the Rational way used by R●giomontanus ; and now generally practised by all the Astrologers of this Age. This way the face of Heaven is divided into twelve parts , which are called the twelve Houses of Heaven numbered from the Ascendent or angle at East downwards , with 1 , 2 , 3 , &c , As in the following Figure . In a Direct Sphear , viz. under the Equator these twelve Houses are twelve equal parts : but in an Oblique Sphear they are unequal parts , and that more or less according to the quantity of the Sphears obliquity . These twelve Houses are divided by 12. Semi-Circles of Position ; which are Semi-Circles passing from the two intersections of the Horizon and Meridian through any Star , degree , or point in the Heavens . The degrees and minutes of the Ecliptick upon the Cusps of these four Houses ( that is , upon the beginning of these Houses ) are found all at once only by bringing the Rising degree of the Ecliptick to the Horizon : ( for the Horizon represents the Cusp of the Ascendent : ) and then shall the Meridian cut the degree of the Ecliptick on the Cusp of the tenth House . The Western Semi-Circle of the Horizon shall cut the degree of the Ecliptick on the Cusp of the Seventh House : and the Semi-Circle of the Meridian under the Horizon shall cut the degree of the Ecliptick on the Cusp of the fourth House . If you have the day of the Moneth , you may by Prob. 3. of the second Book find the Suns Place ; and if you have the Hour of the Day you may by first rectifying the Globe , as by Prob. 2. of the same Book , turn about the Globe till the Index of the Hour-Circle point to the same Hour in the Hour-Circle , and you will then at the Eastern Semi-Circle of the Horizon have the degree of the Ecliptick that is Rising , and by Consequence ( as aforesaid ) all the Cardinal points in their respective places . Now to find what degree of the Ecliptick occupies the Cusps of the other eight Houses of Heaven ; Do thus , The Globe rectified , as aforesaid , Move the Semi-Circle of Position upwards till 30 degrees of the Equator shall be contained between it and the Eastern Semi-Circle of the Horizon ; so shall the Semi-Circle of Position cut in the Ecliptick the degree and minute of the Ecliptick on the Cusp of the twelfth House ; and its opposite degree and minute in the Ecliptick shall be the Cusp of the sixth House , ( for you must note that if you have but the degree and minute of the Ecliptick upon the Cusps of six of the Houses , the opposite degrees and minutes of the Ecliptick shall immediately possess the Cusp of every opposite House . ) Then move the Circle of Position over 30. degrees more of the Equinoctial , so shall the degree of the Ecliptick cut by the Circle of Position be the degree of the Ecliptick , upon the Cusp of the eleventh House ; and its opposite degree in the Ecliptick shall be upon the Cusp of the fifth House . The degree of the Ecliptick upon the Cusp of the tenth and fourth Houses was found as before . Then remove the Circle of Position to the Western side of the Meridian , and let it fall towards the Horizon till 30. degrees of the Equator are contained between the Meridian and it , so shall the degree of the Ecliptick cut by the Semi-Circle of Position be the degree of the Ecliptick on the Cu●p of the Ninth House ; and the opposite degree of the Ecliptick shall be upon the Cusp of the third House . Let the Semi-Circle of Position fall yet lower , till it pass over 30. degrees more of the Equator , so shall the degree of the Ecliptick cut by the Semi-Circle of Position be the degree of the Ecliptick on the Cusp of the eighth House ; and the opposite degree of the Ecliptick shall be upon the Cusp of the second House . The degrees of the Ecliptick on the Cusp of the seventh House , and Ascendent , were found as before . Example . I would erect a Figure of Heaven for July 27. 5. hours o● minutes Afternoon , 1658. in the Latitude of London , viz. 51½ degrees , North Latitude . I first place the Planets , ☊ , and ☋ , on the Globe , as by Prob. 55. of the Second Book was directed : yet not exactly as I find them in the Ephemeris , for that shews only their place in the Ecliptick at Noon : Therefore I consider how many degrees or minutes each Planets motion is in a whole Day or 24. Hours , by substracting the Ecliptical degrees and minutes of the Planets place that Day at Noon from the Ecliptical degrees and minutes of the Planets place the next Day at Noon : or contrarily if the Planet be Retrograde : for the remains of those degrees and minutes is the motion of the Planet that Day ; Therefore proportionably to that motion I place the Planet forward in the Ecliptick : ( or backward if it be Retrograde : ) As if the Sun should move forward 1 degree , that is 60 minutes in a whole Day , or 24 Hours , then in 12 hours he should move 30 minutes , in 6 hours 15 minutes , in 4 hours 10 minutes , in 1 hour 2½ minutes , and so proportionably for any other space of Time : which I consider before I place the Planets on the Globe . PROB. II. To Erect a Figure of Heaven according to Campanus . REgiomontanus as aforesaid makes the beginning of every House to be the Semi Circle drawn by the side of the Semi Circle of Position according to the succession of every 30 th degree of the Equator from the Horizon But Camp 〈◊〉 make it to be the Semi-Circle drawn by the side of the Semi-Circle 〈◊〉 Position according to the succession of every 30 th degree of 〈◊〉 Prime Verticle , or East Azimuth ; which is represented by the Quadrant of Altitude placed at the East point . The four Cardinals are the same , both according to Regiomontanus , and Campanus : but the other eight Houses differ : Therefore when you would find them according to Campanus ; Rectifie the Globe and Quadrant of Altitude , and bring the lower end 〈◊〉 the Quadrant of Altitude to the East point in the Horizon : Then count from the Horizon upwards 30 degrees o● the Quadrant 〈◊〉 Altitude , and bringing the Circle of Position to those 30 degree● examine where the Circle of Position cuts the Ecliptick , which 〈◊〉 the aforesaid time is in 〈◊〉 29. 40 for that degree and minute upon the Cusp of the twelfth House , and its opposite degree 〈◊〉 minute in the Ecliptick viz. ♉ 29. 40. is upon the Cusp of 〈◊〉 sixth House : Lift up the Circle of Position 30 degrees high● upon the Quadrant of Altitude ( viz. to 60 degrees ) and 〈◊〉 Circle of Position will cut the Ecliptick in 〈◊〉 15. degrees for the Cusp of the eleventh House , and its opposite degree and minute in the Ecliptick viz. ♉ 15. is upon the Cusp of the first House . The degree and minute of the Ecliptick on the Cusp 〈◊〉 the Tenth and Fourth Houses is at the Meridian . Then transfering the Circle of Position to the West side of the Meridian and the Quadrant of Altitude to the West point in the Horizon , Let the Semi-Circle of Position fall 30 degrees from the Meridian on the Quadrant of Altitude , and it will cut in the Ecliptick ♎ 16 degrees , for the Cusp of the ninth House , and its opposite degree and minute in the Ecliptick viz. ♈ 16. is upon the Cusp of the third House : Let fall the Circle of Position 30 degrees lower on the Quadrant of Altitude , and it will cut the Ecliptick in 〈◊〉 2 degrees , for the Cusp of the eight House , and its opposite degree viz. ♓ 2. degrees is on the Cusp of the second House : The Cusps of the Seventh and Ascendent is the same with Regiomontanus viz. 〈◊〉 27. 47 , and ♐ 27. 47. The Figure follows . PROB. III. To find the length of a Planetary Hour . AStrologers divide the Artificial day ( be it long or short ) into 12 equal parts , and the Night into 12 equal parts : These parts they call Planetary Hours . The first of these Planetary Hours takes its denomination from the Planetary Day ; and the rest ●re named orderly from that Planet according to the succession of the Planetary Orbs : As if it be Munday that is , the Moons day , ( as by Prob. 42 , of the second ●ook ) the Planet reigning the first Hour shall be●● , the Planet ruling the second Hour shall be ♄ , the third Planetary Hour shall be 〈◊〉 , the fourth 〈◊〉 , the fifth ☉ , the sixth ♀ , the seventh : Thee begin again with 〈◊〉 for the eight Planetary , 〈◊〉 for the ninth and so through the whole Day and Night , till the Sun Rise again the next Day . The length of this Planetary Hour is found by the Globe , thus : The Globe rectified ; Bring the Suns place to the East side the Horizon and make a prick at the degree of the Equator that comes to the Horizon with it . Then remove the Suns place to the Meridian , and count the number of degrees of the Equator comprehended between that prick and the degree now at the Horizon ; and divide that number of degrees and minutes by 6. because there is 6 Planetary H●urs past since Noon ; and the Q●●tient shall shew the number of d●g●●●s and minutes that pass through the Meridian in one Planetary Hour . Example . J●ly 27. 1658. I would know the length of the Planetary 〈◊〉 here at Lonaon : I Rectifie the Globe , and bring the Sun ▪ place viz ♌ 〈◊〉 . 50. to the Eastern side the Horizon and find 115 degrees of the Equator come to the Horizon with it ; to this 115 degrees I make a prick : Then I turn the Suns place to the Meridian and find 22● degrees of the Equator at the Horizon , Therefore I either count the number of degrees between the pricks and the degree of the Equator at the horizon , or else sub●●r●ct the 〈◊〉 from the greater but both waies I find 111 deg●ees of the Equator to pass through the Meridian ( or the Horizon in six Planetary Hours Therefore dividing 111. by 6. I 〈◊〉 〈◊〉 . degrees ●0 minutes of the Equator to pass through the M●●●●●an in one Planetary Hour : which 18. degrees 30 minutes reduced into Time yeelds 72. minutes , by accounting for every 15. degrees one Hour for 1. degree 4. minutes , and for half a degree 〈◊〉 . minutes of Time and so proportionably ▪ so that the le●g●h of a Planetary Hour , July 27 is 1 co●●on Hour and ●4 minute , here at London . PROB. IV. The length of a Planetary Hour known , to find what Planet Reigneth any green Hour of the Day , or Night . THe Globe Rectified as in the last Probleme , Turn about the Globe till the Index of the Hour Circle points to the Hour of the Day in the Hour Circle . Then count the number of degrees comprehended between the degree of the Equator at the Horizon and the prick in the Equator , made as in the last Probleme , and reduce that number of degrees into minutes of Time , by re●koning 4. minutes of Time for every degree of the Equator . Reduce also the number of degrees and minutes that pass through the Meridian in one Planetary Hour into minutes by allowing ( as aforesaid 4. minutes for every degree , and then divide the 〈◊〉 〈◊〉 by the second and the Quotient shall be the number of 〈◊〉 〈◊〉 since Sun Rising Having the number of Planetary Hours since Sun Rising R●ckon the first Planetary H●ur by the ●ame of that Planet that bears the denomination of the Day the second Planetary Hour by the Planet succeeding that in order ●he th●●d by the next in order and so for all the rest 〈◊〉 you c●me to the last Planet viz. 〈◊〉 ; and then begin again with 〈◊〉 , and so 〈◊〉 〈◊〉 &c. 〈◊〉 you have 〈◊〉 so many Planets as there are Planetary Hours si●ce M●●●●ing . and that Planet the number ends on shall be the Planet Reigning that Planetary Hour . Example . July 27. 1658. aforesaid , I would know what Planet Rules at 5 a clock past Noon : The length of the Planetary Hour this Day ●ound by ●he last Probleme ▪ is 1. hour 14. minutes ▪ Therefore the Globe Rectified . I bring the Index of the Hour Circle to the Hour of the Day viz. 5 a clock in the Hour-Circle , and then count the number of degrees between the Prick made , as by the last Probleme and the degree of the Equator at the Horizo● ; and find them 187. which I reduce into minutes , by allowi●g for every degree 4 minutes ; and that gives 748 minutes . This 〈◊〉 minu●es I divide by the minutes contained in one Planetary Hour this Day , viz. by 72. and find 10. hours 8. minutes ; which shews there are 10. Planetary Hours and 8. minutes past and gon since Sun Rising . Therefore ♂ being the Planet after whose name the Day is called viz. Dia Martis , ♂ is as aforesaid , the Ruler of the first Planetary Hour : From him I count the Planet succeding , which is ☉ for the second Hour ; from ☉ I count the Planet succeding , which is ♀ for the third Hour , and so on to ♀ , and ☽ : and then I begin the Round again with ♄ , ♃ , ♂ , and ☉ , till I come again to ♀ , which is the tenth Planetary Hour since Sun Rising ▪ and the minutes remaining being 8. shews that there is 8. minutes past since she began to Reign . PROB. V. To find Part of Fortune by the Globe . COunt the number of degrees and minutes contained between the Suns place and the Moons place , begining at the Suns place and counting according to the succession of Signes till you come to the Moons place : and having found that number of degrees and minutes , add them to the number of degrees and minutes Ascending , reckoned from the first point of ♈ . If the sum exceed 360 , east away 360 , and the remainder shall be the number of degrees and minutes from the first point in 〈◊〉 , in which Part of For●●ne falls . But if it do not exceed 360 , you have already the number of degrees and minutes from the first point of ♈ in which you must place Part of Fortune . Example . I would find the place of Part of Fortune for the time of ou● Figure : I seek the two pricks representing ☉ and 〈◊〉 , and find ☉ in ♌ 14. 9. and ☽ in ♏ 19. 44. therefore counting from the Suns place to the Moons place according to the succession of Signes , I find 95. degrees 35. minutes , contained between them : This 95. degrees 35. minutes I add to 267. degrees 47. minutes , the degree and minute contained between the first point of ♈ and the Ascendent ; and they make together 363. degrees 22. minutes . This exceeds 360. therefore I cast away 360. and the remains are 3 degrees 22. minutes , for the place in the Ecliptick of Part of Fortune , reckoned from the first point of ♈ ▪ Therefore this character ♁ which represents Part of Fortune , I set in its proper place of the Figure , as I did the Planets . PROB. VI. To find in what Circle of Position any Star , or any degree of the Ecliptick is . CIrcles of Position are numbred from the Horizon upwards , upon the Quadrant of Altitude placed at the East or West point of the Horizon , Therefore when you would find what Circle of Position any Star or degree of the Ecliptick is in , Rectifie the Globe and Quadrant of Altitude , and bring the lower end of the Quadrant of Altitude to the East or West point of the Horizon , and lift up the Circle of Position till it come to the Star or degree of the Ecliptick proposed : and the number of degrees the Circle of Position then cuts in the Quadrant of Altitude is the number of the Circle of Position that the Star or degree of the Ecliptick is in . If the Star or degree of the Ecliptick be under the Horizon , turn the Globe about till 180 , degrees of the Equator pass through the Meridian , then will the Star or degree of the Ecliptick be above the Horizon : Lift up then the Circle of Position ( as before ) to the Star or degree of the Ecliptick and the number of degrees of the Quadrant of Altitude the Circle of Position cuts on the East side , is the number of Circles of Position the Star was under the Horizon on the West side : Or so many degrees as the Circle of Position cuts on the Quadrant of Altitude in the West side the Horizon is the number of the Circles of Position the Star or degree of the Ecliptick was under the Horizon on the East side . PROB. VII . To find the Right Ascensions , the Oblique Ascensions , and the Declinations of the Planets . EXamine the Right Ascensions and Declinations of those pricks made to represent each Planet , in Prob. 1. of this Book ; and work by them as you were directed to work by the Sun , in Prob. 26 , 27 , 28. of the second Book , PROB. VIII . How to Direct a Figure , by the Globe . TO Direct a Figure is to examine how many degrees of the Equinoctial are moved Eastwards or Westwards , while any Planet or Star in one House comes to the Cusp or any other point of any other House . When you would Direct any Promittor to any Hylegiacal point examine the degree of the Equator at the Meridian ; then turn about the Globe till the Promittor come to the Hylegiacal point , and examine again the degree of the Equator at the Meridian : and by substracting the lesser from the greater you will have the number of Degrees that passed through the Meridian whiles the place of the Promittor was brought to the Hy●●g●●cal point : and that number of degrees shall be the Arch of D●rection . Example . I would Direct the Body of the Moon in our Figure aforesaid to Medium C●●● , or the tenth House : I find by the Globe 20● . degr●es 30. minutes of the Equator at the Meridian with the ●eath House and turning the Globe till the prick made to represent the Moon come to the Meridian . I find 227 , degrees 20 , minutes of the Equator come to the Meridian with it . Therefore I 〈◊〉 the lesser from the greater viz. 2●3 degrees 3 ▪ minutes from 227. degrees 2● . minutes , and have remaining 2● ▪ degrees 50 minutes . This 〈◊〉 . degrees 50. minutes shews that 23. Years 1● . Moneths must expire ere the Effects promised by the Moons present position shall opperate upon the signification of the 〈◊〉 House . If the Body of the Moon had been Directed to any other point the● 〈◊〉 Meridian or Horizon ; you must have Elevated the Circle of 〈◊〉 〈◊〉 the point proposed ; and have under-propped it to that 〈◊〉 , and 〈◊〉 ▪ have turned about the Globe till the prick 〈◊〉 the Moon , had come to the Circle of Position ; and then 〈◊〉 degrees of the Equator that should have passed through the Meridian whiles this motion was making , should be the number of degrees of Direction ; and signifie in Time as foresaid , PROB. IX . Of Revolutions : and how they are found by the Globe . BY Revolution is meant the Annual Conversion of the Sun to the same place he was in at the Radix of any Business . When you would find a Revolution by the Globe , first find the Right Ascension of M●d Heaven at the ●●adix of the Business , as by Prob ▪ 26. of the second Book you were directed to find the Right Ascer●●on of the 〈◊〉 ; and 〈◊〉 add 87 degrees for every Y●a● since the Radix : Then substract 360 so o●● as you can from the whole and the R●m●●●s shall be the Right Ascension o● Mid H●aven for the A●●●al Revolu●●on . I● y●u 〈◊〉 the number of degrees of the Equator contained between the R●ght A●cension of the Mid H●aven and the Right Ascension of the Sun , and convert that number of degrees 〈◊〉 Time by allowing for every 15. degrees 1 Hour of Time it will shew , if the Suns place be on the Western side of the Meridian the number of Hours and minutes Afternoon the Revolution shall h●ppen on , but if on the East side the Meridian , the number of Hours and minutes Before-noon the Revolution shall happen on . PROB. X. How a Figure of Heaven may be erected by the Revolution thus found . SEek the degree of Right Ascension of Mid Heaven , and bring it to the Meridian , so shall the four Cardinal points of the Globe be the same with the four Cardinal points in Heaven at the time of the Revolution . The other H●●●ses are 〈◊〉 by the Circle of Position : as in the first Probleme of this Book ▪ The End of the Fourth Book . The Fifth BOOK , Shewing the Practical Use of the GLOBES : Applying them t● the Solution of Gnomonical Problems PRAEFACE DYals are of two sorts , Pendent , and Fixed . Pende● are such as are hung by the hand , and turned towards the Sun ; that by its Beams darting throug● smal Pin-holes made for that purpose , the hour of the Da● may be found . These are of two sorts , Vniversal , and P●●ticular . Vniversal Dyals are those commonly called Equi●oc●●● or Ring-Dyals : They are used by Sea-men and Tr●vellers , that often shift Latitudes . Particular are such as are made and only serve for Particular Latitudes . Of these sorts are the several Dya●● discribed on Quadrants , Cilinders , &c. Fixed Dya●s shall be the matter of this discourse ; and they are such as are made upon fixed Planes , and shew the Hour of the Day by a Stile or Gnomon made Parallel to the Axi● of the World. Of the several Kinds of Dyal Plains : and how you may know them . A Plain in Dyalling is that flat whereon a Dyal is discribed . There is some disagreement among Older and Later Authors in the naming of Plains : for some name them according to the Great Circle in Heaven they ly in : and others according to the scituation of the Poles of the Plains . Thus they which name them according to the Great Circle in Heaven their Plains ly in , call that an Horizontal Plain , which others call a Vertical Plain ; those Vertical , which others will call Horizontal ; and those Polar , which others call Equinoctial . However they be called it matters not , so you can but distinguish their kinds , which with a little consideration you may easily learn to do : For remembring but upon what grounds either the Order or Later Authors gave the Plains their Names , upon the same grounds you may also learn to know them . I confess both waies admit of some just exception against for in the Older Rule a Plain about the Pole , is called an Equinoctial Plain ; when as to a sudden apprehension it would sound more significant to call it a Polar Plain , as Later Authors do : Again , Later Authors call an Horizontall Plain a Vertical Plain ; when as it sounds more significant to call it an Horizontal Plain , as Older Authors do because it lie flat upon the Horizon : But I shall give you the names according to both Rules , and leave you to your liberty to accept of which you please . First therefore , you have an Equinoctial Plain otherwise called a Polar Plain . This Plain hath two Faces , upper , and under : These two Faces ly in the Plain of the Equinoctial : the upper Face beholding the Elevated Pole , the under Face the depressed Pole. 2. An Horizontal Plain , otherwise called a Vertical Plain : it lies in the Plain of the Horizon , directly beholding the Zenith . Erect Plains , otherwise called Horizontal Plains are the sides of Walls , and these are of seven sorts , viz 1. Erect Direct Vertical , North or South , 2. Erect Direct , East or West . 3. Erect Vertical Declining . 4. Erect Inclining Direct . 5. Erect Inclining Declining . 6. Erect Reclining Direct . 7. Erect Reclining Declining . 3. Erect Vertical , North or South Direct , otherwise called Direct North or South Horizontals , behold the North or South Directly , and ly in the East or West Azimuth . 4. Erect Direct East or West , otherwise called Direct East or West Equinoctials , behold the East or West Directly , and lies in the Plain of the Meridian , having its Poles in the Equinoctial . 5. Erect Vertical Declining Plains , otherwise called Declining Horizontals , do not behold the North or South Directly , but swerves from them so much as the Azimuth Parallel to their Plains swerves or Declines from them . 6. Erect Inclining Direct Plains , have the upper side of their Plains Inclining or coming towards you , and their Plains do exactly behold either the East , West , North , or South . 7. Erect Reclining Direct Plains , have the upper side of their Plains Reclining or falling from you , and their Plains exactly beholding either the East , West , North , or South . 8. E●●ct Reclining Declining , or Erect Inclining Declining Plains are those Plains which are either Inclining or Reclining , but 〈◊〉 behold the East , West , North or South , Directly but 〈◊〉 or Decline more or less from them . 9. Polar Plains are Parallel to the Axis of the World , and to the M●ridians that cuts the East and West , or North and South , points of the Horizon . All these kinds of Plains have two Faces ; the one beholding the North Pole with the same respect that the other beholds the South Pole ; except the Equinoctial Plain , which , because neither Pole is Elevated , hath but one Face : yet that one contains as many Hour lines as two other Faces . These two Faces or Plains will receive just 24. hour lines , fo● the 24 Hour-lines of Day and Night : for so much as the one side or Face wanteth or exceedeth 12. the other side shall either exceed or want of 12. Every Dyal Plain is Parallel to the Horizon of some Country or other in the World : therefore a Dyal made for any Horizon in the World may be set to such a Position that it will shew you the Hour of the Day in your own Habitation : At least for so long as the Sun continues upon that Plan● . All Plains may be aptly demonstrated by the Globe , by setting it correspondent to all the Circles in Heaven , as by Prob. 2. of the second B ok : for if you imagine the Globe in that Position were prest flat into the Plain of any Circle , that Flat shall represent a Dyal plain , which shall be called after the name of that Circle it is prest into . Thus if the Quadrant of Altitude be applyed to any degree of Azimuth , and you imagine the Globe were prest flat to the edge of the Quadrant of Altitude , so much as that Azimuth Declines from the East , West , North , or South , in the Horizon , so much shall that flat on the Globe be said to Decline either from the East , West , North , or South . Or if you imagine the Globe were prest flat down even with the Plain of the Horizon , that flat shall represent an Horizontal Plain ; because as was said before , the Plain lies in that Circle cal'd the Horizon . The Style or Gnomon is that straight wyre that casts the shadow upon the Hour of the Day : it is alwaies placed Parallel to the Axis of the World. There are several waies to find the scituation of all Plains ; but the readiest and speediest is by a Clinatory . The Clinatory is made of a square board , as A B C D , of a good thickness , and the larger the better ; between two of the sides is discribed on the Center A a Quadrant as E F divided into 90 equal parts or degrees , which are figured with 10 , 20 , 30 , to 90 ; and then back again with the Complements of the same numbers to 90 : between the Limb and the two Semidiameters is made a Round Box , into which a Magnetical Needle is fitted ; and a Card of the Sea Compass , divided into 4 Nineties , beginning their numbers at the East , West , North , and South points of the Compass , from which points the opposite sides of the Clinatory receives their Names of East , West , North , or South . Upon the Center A whereon the Quadrant was discribed is fastned a Plumb-line , having a Plumbet of Lead or Brass fastned to the end of it , which Plumb-line is of such length that the Plumbet may fall just into the Grove G H below the Quadrant , which is for that purpose made of such a depth that the Plumbet may ride freely within it , without stopping at the sides of it . See the Figure annexed . But admit there be Variation , Having by Prob. 19. of the third Book found the number of degrees of this Variation towards the East , or West , count the same number of degrees from the North point in the Card either to the Eastwards or Westwards , and note the degree in the Card terminating at that number , for that degree shall be the North point ; and its opposite degree the South point : 90. degrees from it either way shall be the East and West points . Therefore , whereas before you were directed to turn the Clinatory till the North point of the Needle point to the Flower-de-luce on the ●aid you m●st now turn ( or move ) the Clinatory till the North point of the Needle ●arg just over the degree of Variation thus sound ; and then a line drawn as aforesaid , by the side of the Clinatory Paral●el to the Needle shall be a North and South line or ( to speak more properly ▪ a Meridional line . You may fi●d a M●ridian li●e several other waies ; as first ; If the Sun shine just at Noon , hold up a Plumb-line so as the shadow of it may fall upon your Plain ; and that shadow shall be a Meridian li●e . Secondly , on the backside the Clinatory discribe a Circle , and draw a line through the Center to both sides the Circumference ; cross this line with an other line at R●ght Angles in the Center , so shall the Circle be divided into four equal parts . These four parts you must ma●k with East , West , North , South and divide each of them into 90. degrees . In the Center of this Plain erect a straight wyer prependicularly : when you would find a Meridian line examine by the tenth Prob. of the second Book the Amplitude of the Suns Rising or Setting from the East or West points , and waiting the just Rising or Setting that Day , turn the Instrument about till the shadow of the wyer falls upon the same degree from the East or West the Amplitude is of , for then the North and South line in the Instrument will be the same with the North and South line in Heaven . Thirdly by the Suns Azimuth : Find the Azimuth of the Sun by Prob. 22. of the second Book : and at the same instant turn the Instrument till the shadow of the wyer fall upon the degree on the Instrument opposite to the degree of the Suns Azimuth ▪ so shall the Meridional line of the Instrument agree with the Meridional line in Heaven . You may the same way work by the Azimuth of any Star. Only , whereas the shadow of the wyer should fall upon the opposite degree aforesaid : Now you must place a Sight or Perpendicular upon that opposite degree , and turn the Instrument about till the wyer at the Center , the Sight in the opposite degree of the Stars Azimuth , and the Star in Heaven , come into one straight line , so shall the Meridian line of the Instrument agree with the Meridional line in Heaven . Fourthly It may be found by any Star observed in the Meridian , if two Perpendiculars be erected in the Meridian line of your Instrument ; for then by turning the Instrument till the two Perpendiculars and the Star come into a straight line , the Meridian line of your Instrument will be the same with the Meridian line in Heaven . See more waies in Mr. Palmer on the Planisphear Book 4. Chap. 9 : If your Plain either Recline or Incline , apply one of the sides of your Clinatory Parallel to one of the Semi-diameters of the Quadrant to the Plain , in such sort that the Plumb-line hanging at liberty may fall upon the Circumference of the Quadrant , for then the number of degrees of the Quadrant comprehended between the side of the Quadrant Parallel to the Plain , and the Plumb-line shall be the number of degrees of Reclination , if th● Center of the Quadrant points upwards , or Inclination if th● Center points downwards . If your Reclining or Inclining Plain Decline , draw upon it a line Parallel to the Horizon , which you may do by applying the back-side of the Clinatory , and raising or depressing the Center of the Quadrant till the Plumb-line hang just upon one of the Semi-diameters , for then you may by the upper side of the Clinatory draw an Horizontal line if the Plain Incline , or by the under side if it Recline . If it neither Incline or Recline , you may draw● an Horizontal line both by the upper and under sides of the Clinatory . Having drawn the Horizontal line , apply the North 〈◊〉 ● of the Clinatory to it , and if the North end of the Needle 〈◊〉 directly towards the Plain , it is then a South Plain . If the 〈◊〉 point of the Needle points directly from the Plain , it is a Nor●● plain : but if it points towards the East , it is an East Plain : if towards the West a West Plain . If it do not point directly 〈◊〉 East , West , North , or South , then so many degrees as the 〈◊〉 declines from any of these four points to any of the other of 〈◊〉 four points , so many degrees is the Declination of the Plain , 〈◊〉 respect ( as aforesaid ) had to the Variation of the Compass . Or if you find the Azimuth of the Sun by its Altitude observed just when its beams are coming on or going off you● Plain , that Azimuth shall be the Azimuth of your Plain . Or you may erect a wyer Perpendicularly on your Plain , and wait till the shadow of that wyer comes to be Perpendicular with the Horizon , which you may examine by applying a Plumb-line to it , for then the shadow of the Plumb-line and the shadow of the Perpendicular will be in one : then taking the Altitude of the Sun you may by Prob. 22. of the second Book find its Azimuth , and thereby know in what Azimuth the Plain of your Dyal lies : for the Azimuth your Plain lies in is distant from the Azimuth of the Sun just 90. degrees . PROB. I. How by one position of the Globe to find the distances of the Hour-lines on all manner of Plains . YOu may have Meridian lines drawn from Pole to Pole through every 15. degrees of the Equinoctial , to represent the Horary motion of the Sun both Day and Night ; and when the Pole of the Globe is Elevated to the height of the Pole in any Place and one of these Meridian lines be brought to the Brazen Meridian , all the rest of the Meridian lines shall cut any Circle which you intend shall represent the Plain of a Dyal in the number of degrees on the same Circle that each respective Hour-line is distant from the Noon-line point in the same Circle . Thus if you should enquire the distance of the Hour-lines upon an Horizontal Plain in Londons Latitude ; The Pole of the Globe as aforesaid ) must be Elevated 51½ degrees , and one of the Meridian lines ( you may chuse the Vernal Colure ) be brought to the Brazen Meridian , which being done , you are only to examine in the Horizon ( Because it is an Horizontal Plain ) at what distance from the Meridian ( which in Horizontals is the Noon-line ) the several Meridians drawn on the Globe intersect the Horizon , for that distance in degrees shall be the distance on a Circle divided into 360. degrees that each respective Hour-line must have from the Meridian or a Noon line chosen in the same Circle ; and lines drawn from the Center of that Circle through those degrees shall be the Hour lines of an Horizontal Plain . If your Plain be not Direct but declines East or West ▪ 〈◊〉 must number the Declination Eastwards or Westwards re●pectively in the degrees of the Horizon and ( the Quadrant 〈◊〉 Altitude screwed to the Zenith , ( as aforesaid ) bring the lower end of the Quadrant of Altitude to the said degrees of Declination , and the number of degrees cut by the Meridians in the Quadrant of Altitude numbred downwards , is the number of degrees that the Hour-lines are distant from the Noon line in a Circle of 360 , degrees : And lines drawn from the Center of that Circle through those degrees be the Hour lines of half the Day . And if you turn about the Quadrant of Altitude upon the Zenith point till the lower end of it come to the degree of the Horizon opposite to the degree of Declination found before , the Meridian lines on the Globe ( as before ) shall cut the Quadrant of Altitude in the number of degrees ( counted downward ) that each Hour-line is distant from the other side the Noon-line : And lines drawn from the Center of that Circle through those degrees shall be the Hour-lines of the other half of the Day , If your Plane Decline , and also Recline or Incline , you must use the Gnomonical Semi-Circle , discribed in Prob. 12 ▪ which must be Elevated on the Quadrant of Altitude when it is set to the Declination ( as by the former Rule ) according to the complement of Reclination , or Inclination : But if your Plane be Direct , and Recline , or Incline , it must be set to the Meridian , and the Meridians on the Globe shall cut that Semi Circle in the number of degrees counted from the Quadrant of Altitude if the Plane Declines , or from the Brasen Meridian , if it be Direct , that the several Hour lines are distant from a line Perpendicular to an Horizontal line , in a Circle divided into 360 degrees ; And lines drawn from the Center through those degrees shall be the Hour-lines of such Reclining or Inclining Planes . The moving this thred from wyer to wyer represents the motion of the Sun , which as it passes over all the Meridians causes the shadow of that Meridional Semi Circle which it is directly over ▪ and the Axis , and the Meridional Semi-Circle directly opposite to the upper Meridional Semi-Circle to fall all into one straight line : And upon what point in the East and West line ( mentioned before ) that shadow-line shall fall is marked ●ut by the application of the thred as aforesaid : and is an Hour-line on any of the foresaid Planes . If you understand this Probleme rightly , you do already know how to draw the Hour lines upon all manner of Planes , and need no further Instructions ; yet partly fearing a raw Student should not clearly understand these Rules , and partly doubting ) because other Authors have been more Copious upon this Subject ) that I should be censured to be too sparing of my pains , if I should lightly touch so eminent a Doctrine as Dyalling is : Therefore I shall more distinctly handle Dyalling by the Globe , according to the way or Method that other Authors have used , and that after so plain a manner as possibly my Genius can devise . PROB. II. To make an Equinoctial Dyal . DIscribe a Circle , on a square board or Plane as B C E D , and through A the Center thereof draw a straight line Parallel to one of the sides , as B E ; Cross that straight line with another straight line as C D at Right Angles , so shall the Circle be divided into 4 equal parts : Divide each of these four equal parts into 90. degrees ; as in the Figure . This Circle shall represent the Horizon . Erect a wyer exactly perpendicular to the Center of the Plane ; and that wyer shall be the Gnomon or Style of the Dyal . Then Elevate one of the Poles of your Globe into the Zenith , and bring the Equinoctial Colure to the Meridian . And because in every hours Time 15 degrees of the Equator passes through the Meridian in Heaven , therefore turn the Globe till 15 degrees of the Equator pass through the Meridian of your Globe ; so shall the Colure pass by 15 degrees of the Horizon also . Therefore from the Center of your Plane draw straight lines through 15 ▪ degrees from one of the Semidiameters both waies : and those straight lines shall be two Hour-lines : Then turn the Globe till 15 degrees more of the Equator pass through the Meridian , and you will find as before , the Colure pass by 15 degrees more of the Horizon : therefore on your Plane number 15. degrees further beyond both the former lines , and from the Center draw straight lines through both those 15. degrees , and they shall be two Hour lines more . Fór all the other Hour lines turn the Globe till 15. degrees of the Equator at a time pass through the Meridian , as before , and you will find that for every 15. degrees of the Equator that passes through the Meridian , the Colure will pass through 15. degrees of the Horizon : therefore those Hour lines must be drawn from the Center according to the succession of every 15 degrees on your Plane , Having drawn the Hour lines , you may set figures to them , beginning to number your Hour lines from one of the Diameters , marking it with XII , and the next Hour line to the left hand with I , and the next II , the next III , &c. to XII . and begin again with I , II , III , &c. till you come to the other XII , where you began : and then your Dyal is finished . See the Figure . This is an Universal Dyal , and serves in all Latitudes : therefore when you place it you must set one of the XII s downwards , and the Axis Parallel to the Axis of the World. But note , Both faces of this Dyal ought to be divided , and the Gnomon must appear on both sides like the stick in a Whirligig , which childeren use ; or else you must turn it upside down , so oft as the Sun passes the Equinoctial . PROB. III. To make an Horizontal Dyal . DIscribe a Circle on your Plane , as C B D E , and through the Center A of that Circle draw a Meridian line , as B E ; cross that line at Right angles with another line , as C D ; so shall your Circle be divided into four equal parts : Divide each of these four parts into 90. degrees ; so shall the whole be divided into 360. These 360 degrees represent the 360 degrees of the Horizon , which a Meridian line drawn through the place of the Sun runs through in every 24. Hours : The motion of which Meridian line through the degrees of the Horizon is Regular in a Parallel Sphear ; for in equal Time it moves an equal Space throughout the whole Circle , viz. it will pass through 15. degrees of the Horizon in one Hours Time , ( or which is all one ) whiles 15. degrees of the Equator passes through the Meridian ; as was shewed in the last Probleme : But in an Oblique Sphear its motion through the Horizon is Irregular , and that more or less according to the more or less Obliquity of the Sphear : For far Northwards or Southwards you may see this Meridian line pass through 40 , 50 , yea 60. degrees of the Horizon in one Hours time , viz , whiles 15. degrees of the Equator passes through the Meridian : but in an other Hours time you will scarce have 4 or 5 degrees pass through the Horizon whiles 15 degrees of the Equator passes through the Meridian . But that you may know the motion of the Sun ( represented by this Meridian line ) through the Horizon in all Latitudes ; Elevate the Pole to the Elevation of your Place , and chuse instead of a Meridian line drawn through the Place of the Sun the Vernal Colure to be your Meridian line ; both because it is most visible ; and because from thence the degrees of the Equator are begun to be numbred , so that what so ever decimal degree of the Equator you light on at the Meridian , or else where , you will find its number from that Colure already set down to your hand , without either adding to , or substracting from it . Bring this Colure therefore to the Meridian , and the Index of the Hour Circle to 12. in the Hour Circle . Then turn the Globe Westwards , and so oft as 15 degrees of the Equator passes through the Meridian , so oft you must examine what degrees of the Horizon the Vernal Colure cuts ; and those degrees and minutes so cut by the Vernal Colure must be found in the Circle C B D E , beginning your account or reckoning at B towards D , and markt with Pricks : through which Pricks you must draw lines from the Center A , and those lines shall be the Hour lines after noon . Then bring the Colure to the Meridian again to find the Fore-noon Hour-lines , and turn the Globe Eastwards , and so oft as 15 degrees of the Equator passes through the Meridian , so oft you must examine what degrees of the Horizon the Vernal Colure cuts ; and those degrees and minutes so cut by the Vernal Colure must be found in the Circle C B D E , begining your reckoning from B towards C , and markt with Pricks : through which Pricks you must draw lines from the Center A , and those lines shall be the Fore-noon Hour-lines . These Hour-lines must be markt from the Meridian line , viz. the line A B , which is the 12 a clock line towards D , with I , II , III &c. till you have numbred to the Hour of Sun set ( found by Prob. 7. of the second Book ) the longest Day , and from the Meridian line towards C with XI , X. IX , &c. till you have numbred to Sun Rising the longest Day . The Stile must be placed in the Center and Elevated so many degrees above the Plane , as the Pole is elevated above the Horizon of the Place , Example of the whole . I would make an Horizontal Dyal for Londons Latitude : Therefore I E evate the North Pole 51½ degrees above the Horizon , and bring the Vernal Colure to the Meridian , and the Index of the Hour Circle to 12 on the Hour Circle ; And turning the Globe Westwards till the Index points to 1 a clock or till 15 deg of the Equator pass through the Meridian ; I find the Colure cut the Hori in 11. 4 from the Meridian . 2 24. 15 3 38. 4 4 53. ●6 5 71. 6 6 90. These are the distances of the Hour lines from Noon till 6 at Night : and to these distances on the Plane ( counting from B towards D , ) I make pricks ; and from the Center I draw lines through these Pricks ; and these lines are the Hour lines from 12 to 6 Afternoon . But the Sun in the longest Day shines till past 8 at Night , as you may find by Prob. 48. of the second Book , therefore here wants the two Evening Hour lines ; which though they may be found after the same way I found the former , ( viz. by continuing the turning of the Globe Westwards ) yet that I may the sooner reduce my work to the Plane I Count the number of degrees between the 6 a clock line and the 5 a clock line in the Circle on the Plane ; for the same number of degrees counted from D towards E is the distance of the 7 a clock Hour line from the 6 a clock Hour line ; and the number of degrees contained between the 6 a clock Hour line and the 4 a clock Hour line is the distance of the 8 a clock Hour line from the 6 a clock Hour-line . Or I need not draw the 7 and 8 a clock Hour lines , till I have drawn the forenoon Hour lines : for then by laying the edge of a Ruler ( that will reach through the opposite side of the Plane ) to the Morning 7 and 8 a clock Hour lines , I may by the side of that Ruler draw lines from the Center through the opposite side of the Plane , and those lines shall be the 7 and 8 a clock Hour lines Afternoon . Having thus all the Afternoon Hour lines , I bring the Vernal Colure to the Meridian again ; so shall the Index again point to 12. Therefore , as before I turned the Globe Westwards , so now turning it Eastwards , till the Index points to 11 a clock , or till 15 deg . of the Equator pass through the Meridian , I find the Colure cut the Hori . in 11. 40 from the Meridian . 10 24. 15 9 38. 4 8 53. 36 7 71. 6 6 90. These are the distances of the Hour lines from Noon to 6. a clock in the Morning : and these distances I seek in the Circle of the Plain ( counting from the Noon line B towards C ) and mark them with Pricks ; through which pricks ( as before ) I draw lines from the Center to the outside the Plane : and those lines shall be the Hour lines . Or having the distance of all the Afternoon Hour-lines , I have also the distance of all the forenoon Hour lines from the Meridian ; as you may see by comparing the two former Tables . For the 1 a clock Hour line Afternoon is equidistant from the Meridian or Noon line with the 11 a clock Hour line before Noon , viz. they are both 11 degrees 40 minutes distant from the Noon line , and the 2 a clock Hour line Afternoon is from the Noon line equidistant with the 10 a clock Hour line Beforenoon ; for they are both 24. degrees 15. minutes distant from the Meridian or Noon line : and so all the other Morning Hour lines are distant from the Noon line by the same space that the same number of Afternoon Hour lines ( told from the Meridian on the contrary side the Noon line ) are distant from the Meridian . Whence it follows , that since ( as aforesaid ) the same number of Hour lines after 6 at Night , and before 6 in the Morning have the same distance from the 6 a clock line that the same number of Hour lines before 6 at Night and after 6 in the Morning have from the 6 a clock line ; and since the same number of Hour lines before Noon are equidistant from the Meridian or Noon line by the same space of degrees that the same number of Hour lines Afternoon are ; It follows ( I say ) that having found the distance of the six Hour lines either before or after Noon , you have also given the distance of all the other Hour lines . If you will have the half Hour lines placed on your Dyal you must turn the Globe till the Index points to every half Hour in the Hour Circle , as well as to the whole , and examine the degrees of the Horizon cut by the Vernal Colure , as you did for the whole Hours ; and in like manner transfer them to your Plane . Having thus drawn all the Hour lines I count from the Noon line 51½ degrees , the Elevation of the Pole here at London ; and from the Center A I draw a straight line , as A F through these 51½ degrees , for the Gnomon or Style , and prolong it to the farthest extent of the Plane : From this Gnomon or Style I let fall a Perpendicular upon the Noon line , as F G : ( this Perpendicular is called the Substile , and this Perpendicular and its Base ( which is the Noon line ) and Hypothenusa ( which is the Gnomon ) shall make a Triangle , which being erected upon the Base , so as the Substile may stand Perpendicular to the Plane , the Hypothenusa A F shall be the Gnomon , and be Parallel to the Axis of the World ; and cast a shadow upon the Hour of the Day . PROB. IIII. To make an Erect Direct South Dyal . DRaw on your Plane an Horizontal line as C A D , as was shewed in the Preface : in the middle of this line ( as at A ) discribe as on a Center the Semi-Circle C B D : from the Center A let fall a Perpendicular , which shall divide the Semi-Circle into two Quadrants each of which Quadrants you must divide into 90 degrees , Then Rectifie the Globe , Quadrant of Altitude , Colure and Hour Index ▪ thus , Elevate the Pole of the Globe to the Latitude of your Place , and screw the Quadrant of Altitude to the Zenith , Then bring the Vernal Colure to the Meridian , and the Index of the Hour Circle to the Hour of 12. in the Hour Circle ; so shall your Globe , Quadrant of Altitude , Colure and Hour Index be Rectified . A●d ●●us you must alwaies Rectifie them for the making of most sorts of Dyals by the Globe . Then to make an Erect Direct South Dyal , Bring the lower end of the Quadrant of Altitude to the West point of the Horizon ; And turn the Globe Westwards till the Index points to all the Hours Afternoon ; and examine in what numbers of degrees from the Zenith the Colare cuts the Quadrant of Altitude when the Index points to each Hour : for a line drawn from the Center A through the same number of degrees reckoned from the Perpendicular A B ( which is the 12 a clock line ) towards D on the Plane , shall be the same Hour lines the Index points at . Thus in our Latitude , viz. 51½ degrees , the Vernal Coloure being brought to the Meridian and the Index to 12 ; If you turn the Globe Westwards , till the Index points to 1 a clock , or till 15 deg . of the Equator pass through the Meridian , the Colure will cut the Quadrant of Altitude in 9. 18 counted from the Zenith . 2 19. 15 3 32. 5 4 48. 0 5 67. 4 6 90. And these are the distances of the Afternoon Hour lines ; which you must transfer to the East side of your Plane , viz , from B towards D ; and draw lines from the Center A through these distances ; and these lines shall be your Afternoon Hour lines . Note ( once for all ) when the Colure goes off that Circle you examine the Hour distances in , the Sun will shine no longer upon that Plane ; As in this example the Colure goes off the Quadrant of Altitude at 6 a clock , therefore the Sun will not shine longer then till 6 a clock upon this Plane . The Hour lines before Noon have the same distance from the Meridian that the Afternoon Hour lines have , as was shewed in the last Probleme : Only they must be drawn on the West side the Noon line , and counted from B towards C. Otherwise . You may reduce all Verticals into Horizontals ; if you Elevate the Pole of the Globe to the Complement of the Latitude of your Place , and bring the Vernal Colure to the Meridian under the Horizon , and the Index of the Hour Circle to 12 ; and turn the Globe Westwards ; for as the Index passes through every Hour on the Hour Circle , the Colure shews in the Horizon the distance of the several Afternoon Hour lines from the Meridian , or 12 a clock line , in the Circle on your Plane , numbred from B to D : and lines drawn from the Center through these distances on your Plane shall be the Afternoon Hour lines of your Dyal . Example . Londons Latitude is 51½ degrees , Its Complement to 90. is 38½ . Therefore I Elevate the Pole 38½ degrees above the Horizon , and bring the Vernal Colure to the Meridian under the Horizon , and the Index of the Hour Circle to 12 on the Hour Circle . Then Turning the Globe Westwards , till the Index of the Hour Circle points to 1 a clock , or till 15 deg . of the Equator pass through the Meridian , I find the Colure cut the Horizon in 9 18 from the Intersection of the Meridian and the Horizon : as in the former Table . 2 19 15 3 32 5 4 48 0 5 67 0 6 90 And these are the distances of the 6 Hour lines from the Merid. By this Example you may see that it is easie to reduce Verticals into Horizon●als : and Horizontals into Verticals : for this Erect Direct South Dyal is an Horizontal Dyal to those People that Inhabite 90 degrees from us , viz. in the South Latitude of 38½ degrees . Then make a Triangle , whereof the Noon line shall be Base : from it count the Complement of the Poles Elevation , viz. 38½ degrees , and through them draw the line A F , from the Center A which shall be Hypotenusa ; Then ●et fall a Perpendicular upon the Noon line A B , so is your Triangle made . If this Triangle be erected Perpendicularly upon the Base or Noon line , The Hypotenusa A F shall stand Parallel to the Axis of the World , and cast a shadow upon the Hour of the Day . PROB. V. To make an Erect Direct North Dyal . IF the Erect Direct South Dyal were turned towards the North ; and the line C A D were turned downwards , and the line marked with 7 be now marked with 5 , and the line 8 with 4 , the line 5 with 7 , and the line 4 with 8 , then have you of it a North Erect Direct Dyal . All the other Hour lines in this Dyal are useless , because the Sun in our Latitude shines on a North Face the longest Day only before 6 in the Morning , and after 6 at Night . PROB. VI. To make an Erect Direct East Dyal . THese sorts of Dyals may better be demonstrated then made by the Globe ; unless the Axis of your Globe were accessible , as in the Wyer-Globe , specified in Prob. 1. Therefore when you would make an East , or West Dyal , or a Polar Dyal . Provide a square Board , as A B C D , draw the straight line e f upon it Parallel to the sides A C , and B D. and just in the middle between them : Cross this straight line at Right Angles with another straight line , as g h , quite through the Board . Upon this Board with a little Pitch or Wax fasten the Semi-Circle of Position , so as both the Poles thereof may ly in the line g h , and the middle of the Semi-Circle marked co may ly upon the line e f , so shall i be the Center of the Semi-circle of Position : In this Center make a smal hole through the Board fit to receive a Wyer or a Nail . So may you with this Circle of Position thus fitted , and the side C D applyed to a line of Contingence elevated to the Height of the Equinoctial , draw line , from the Center through every 15 degrees of the Circle of Position , and by continuing them intersect the line of Conti●gence in the points from whence the Hour lines of an East or West Dyal is to be drawn : Example . But because in our Latitude the Sun Rises before 4. in the Morning , therefore two Hour-lines are yet wanting , viz. 5 , and 4 , which I may find either by applying the thred first to 15 , and next to 30 degrees from 0 towards g in the Semi-Circle , and so marking where it cuts the Contingent line , as before : Or else by transfering the distance of the same number of Hour lines from the 6 a clock line already drawn on the side e 〈◊〉 to the side e g , as in Prob. 2. of this Book is more fully shewed . Having thus marked out on the Contingent line the distances of each Hour ; I draw a line Parallel to the Contingent line , and draw lines from every Hour markt on the Contingent to cross the Contingent line at Right Angles and continue each line to the line Parallel to the Contingent ; and these lines shall be the Hour lines of an East Plane . To these Hour-lines I set Figures as in the Scheam may be seen . The Style D K of this Dyal ( as well as of others ) must stand Parallel to the Axis of the World : it must be also Parallel to all the Hour lines , and stand directly over the 6 a clock line , and that so high as is the distance between the Center of the Semi-Circle of Position and the point where the 6 a clock line cuts the Contingent line : Or ( which is all one ) at such a height as when it is laid flat down upon the Plane it may just reach the 3 a clock line , PROB. VII . To make an Erect Direct West Dyal . AN Erect Direct West Dyal is the same in all respects with an Erect Direct East Dyal ; Only as the East shews the Fore-noon Hours , the West shews the After-noon Hours . Thus if you should draw the East Dyal on any transparent Plane , as on Glass , Horn , or an Oyled Paper , on the one side will appear an East Dyal , and on the other a West . Only the Figures as was said before ( must be changed ) ; for that which in the East Dyal is 11 , in the West must be 1 : that which in the East Dyal is 10 , in the West must be 2 : that which in the East Dyal is 9 in the West must be 3. &c. PROB. VIII . To make a Polar Dyal . POlar Dyals are Horizontal Dyals under the Equinoctial : They are of the same kind with East and West Dyals ; Only whereas East and West Dyals have but the Hour lines of half the longest Day discribed on them , these have all the Hour lines of the whole Day ; and are marked on both sides the Noon line : as in the following Figure . The Style of this Dyal must stand over the Noon line , Parallel to the Plane ; for then it will also be Parallel to the Axis of the World : and its height above the Plane must be the distance between the Center i of the Semi-Circle and the point in the Contingent line cut by the Noon-line . But I have inserted the Figure , which alone is sufficient Instructions . PROB. IX . To make Erect South Dyals , Declining Eastwards , or Westwards . DRaw on your Plane an Horizontal line , and on it discribe a Semi-Circle , as you were taught in Prob 4. Then Rectifie the Globe , Quadrant of Altitude Colure and Hour Index ▪ as by the same Probleme : and bring the lower end of the Quadrant of Altitude to the degree of Declination from the East or West point , according is your Declination is Eastwards or Westwards ; for then the Quadrant of Altitude shall represent a Plane declining from the South E●stwards , or Westwards accordingly . Then tu●n the Globe Eastwards , till the Index of the Hour-Circle points to all the Hours before Noon , and examine in what number of degrees from the Zenith the Colure cuts the Q●●drant of Altitude , when the Index points to each Hour , For a line drawn from the Center A through the same number of degrees reckoned from the Perpendicular A B , which is the 12 a clock line towards Con the Plane , shall be the same Hour-lines the Index points at . Example . I would make an Erect Dyal declining from the South towards the East 27. degrees : The Globe , Quadrant of Altitude , Vernal Colure , and Hour Index Rectified , as before , I bring the lower end of the Quadrant of Altitude to 27. degrees counted from the East point of the Horizon towards the North : Then I turn the Globe East-wards till the Index points to 11 a clock , or till 15. deg . of the Equator pass through the Meridian , and find the Colure cut the Quadrant of Altitude in 9.43 counted from the Zenith . 10 19.0 9 25.57 8 35.10 7 45.56 6 60.15 5 79.45 And these are the distances of the Fore-noon Hour-lines , which I seek in the West side of the Plane , viz. from B towards C ; and through these distances I draw lines from the Center , and these lines shall be the Fore-noon Hour-lines . Now herein is a difference between Declining Dyals , and Direct Dyals : For having found the distances of the Hour lines for one half of the Day , be it either for Before Noon or After Noon in a Direct Dyal , you have also found the distances for the other half Day ; because , as was said Prob. 3. Equal number of Hours have equal distance from the Noon line : But in Declining Dyals it is not so : Because the Sun remaining longer upon that side of the Plane which it declines to , then it doth upon the contrary side , there will be a greater number of Hour lines upon it , and by consequence the distance of the Hour lines less then on the contrary side of the Plane . Therefore for finding the After Noon Hour lines , I turn about the Quadrant of Altitude upon the Zenith point till the lower end of it come to the degree of the Horizon opposite to that degree of Declination that the Quadrant of Altitude was placed at when I sought the Fore Noon Hour lines , viz , to 27. degrees counted ●om the West towards the South , and bring the Ver●al Colure again to the Meridian , and the Index ( as before ) to 12. Then , turning the Globe Westwards till the Index poin●s to 1 a clock , or till 15 degr . of the Equator pass through the Meridian , I find the Colure cut the Quadrant of Altitude in 11.20 counted from the Zenith . 2 26.47 3 49.20 4 75.52 And these are the distances of the After Noon Hour lines ; which dista●●●● I seek in the East side of the Plane , viz. from B towards D ( as before ) and so drawing lines from the Center A through these distances , I have all the Afternoon Hour lines also drawn on my Plane . You may note , that this Plane is capable to receive no more Hour lines After Noon then 4. for when the Colure goes off the Quadrant of Altitude , the Sun goes off these kind of Planes . To these Hour lines I set their numbers , as you may see i● the Figure . Here you may see that in Declining Dyals the Style doth not stand at the same Elevation above the Plane , that it doth in Erect Direct Dyals ; neither doth it stand over the 12 a clock line ; but swerves from it towards the Quarter of Declination . PROB. X. To make a North Erect Dyal declining Eastwards , or Westwards . AS in Prob. 5. an Erect Direct North Dyal hath the same Delineation that an Erect Direct South Dyal hath , and differs only in the placing the Figures of the Hour lines : So a North Erect Dyal that declines Eastwards , or Westwards , differs from a South Erect Dyal that Declines Eastwards , or Westwards , the same number of degrees , only in placing the Hour lines at the same distance on the contrary side of the Plane , and by transposing the Figures of 11 for 1 : 10 for 2 : 9 for 3. &c. Thus , if you draw upon Glass , Horn , or an Oyled Paper , the South Dyal Declining Eastwards , as in the foregoing Probleme , and place it to its due scituation , the back side of it shall be a North Dyal declining towards the West so many degrees as the foreside Declines towards the East ; and the only difference in it will be the Figures of the Hour lines ; as was said before . PROB. XI . To make Direct Reclining , or Inclining Dyals . DIrect Reclining or Inclining Dyals are the same with Erect Direct Dyals that are made for the Latitude of some other Places : The Latitude of which Places are either more then the Latitude of your own Place , if the Plane Recline , or less if the Plane Incline ; and that in such a proportion as the arch of Reclination or Inclination of your Plane is . Thus a Direct South Dyal Reclining 10. degrees in Londons Latitude , viz. 51½ degrees , is an Erect Direct Dyal made for the Latitude of 61½ degrees : And a Direct South Dyal Inclining 10. degrees in the Latitude 51½ degrees is an Erect Direct Dyal in the Latitude of 41½ degrees : and is to be made according to the Directions in Prob. 4. PROB. XII To make Declining Reclining , or Declining Inclining Dyals . THe distances of the Hour lines either for a Declining Reclining Plane , or a Declining Inclining Plane may most easily be found upon the Plane of the Horizon , That is ( as some Authors call it ) by the Horizontal Dyal , by changing the Circles of the Globe one into another : So as the Plane of the Horizon may serve to represent the Dyal Plane ; Yet this way not being natural , because you must admit one Circle to be another , and that in Young Learners might sometimes breed a little difficulty , Gemma Frisius , Metius , and Blaew hath prescribed a thin Brass plate to be made equal to a Semi-Circle of the Equinoctial , and divided from the middle point of it either way into 90 degrees , which may not unproperly be called a Gnomonical Semi-Circle . This Semi-Circle must be bowed close to the Body of the Globe into a Semi-Circular form , and so set to any Reclination , or Inclination , and then it will represent a Reclining or Inclining Plane : And by the motion of the Colure through the several degrees of this Semi-Circle the distances of the Hour lines may be found : Thus , The Globe , Quadrant of Altitude , Colure , and Hour Index , Rectified ; as by Prob. 4. Bring the lower end of the Quadrant of Altitude to the degree in the Horizon of the Planes Declination , if your Plane be a South Declining Recliner , and count on the Quadrant of Altitude from the Zenith downwards the number of degrees of Reclination , or Inclination , and to that number of degrees bring the middle of the Gnomonical Semi-Circle , and let the ends of ●t cut the Horizon on either side in the degrees of the Planes Azimuth , so shall the Gnomonical Semi-Circle represent a Reclining Plane . And so oft as 15. degrees of the Equator passes through the Meridian , so oft shall you enquire what degrees of the Gnomonical Semi-Circle the Colure cuts ; for so many degrees asunder must the several respective Hour lines of a Reclining Declining Plane be in a Semi-Circle divided into 180. degrees . But if your Plane be a South Declining Recliner , or a North Declining Incliner ; Bring the Quadrant of Altitude to the degree of the Horizon opposite to the degree of the Planes Declination , ( because the upper side of the Plane lies beyond the Zenith ) counted from the South point in the South Recliners , and from the North point in North Incliners . Then find the height of the Style , and place of the Substyle : thus , Keep your Gnomonical Semi-Circle in its position : But turn the Quadrant of Altitude about on the Zenith point till the lower end of it comes to the degree of the Horizon opposite to the degree it was placed at before , and turn about the Globe till the Colure cut the Quadrant of Altitude above the Horizon in the number of degrees the Plane Reclines from the Zenith ; so shall the Colure cut the Gnomonical Semi-Circle at Right Angles ; Then count the degrees contained between the middle of the Gnomonical Semi-Circle and the Colure , for that number of degrees is the distance of the Substyle from a Perpendicular line in the middle of your Plane , and must be placed Westwards of the said Perpendicular , if your Plane decline from the South East-wards ; or Eastwards , if your Plane decline from the South Westwards . Then observe how many degrees are contained between the Semi-Circle and the Pole ; for that number of degrees is the number of degrees that the Style is to be Elevated above the Substyle . Example . Here at London I would make a Dyal upon a Plane Declining from the South Eastwards 30. degrees , and Reclining from the Zenith 20. degrees ; Londons Latitude is 51½ degrees : Therefore , Having on the Plane discribed a Semi Circle , &c. as was directed Prob. 4. I Rectifie the Globe , Quadrant of Altitude , Colure , and Hour Index , as by the same Probleme ▪ and bring the lower end of the Quadrant of Altitude to 30. degrees from the North point of the Horizon towards the West , because that is the degree opposite to the degree of the Planes Declination , viz ▪ to 30 degrees from the South Eastwards , And I bring the middle of the Gnomonical Semi Circle to 20. degrees of the Quadrant of Altitude counted from the Zenith downwards towards the Horizon , and the ends of the Gnomonical Semi Circle to the degrees of Azimuth the Plane lies in in the Horizon , viz. to 30. degrees from the East point Northwards , and to 30. degrees from the West point Southwards , so shall 11. degrees 10. minutes of the Gnomonical Semi Circle be comprehended between the Quadrant of Altitude and the Brasen Meridian : These 11. degrees 10. minutes shews that the 12 a clock line is distant from the Perpendicular A B 11. degrees 10. minutes : and because the Plane Declines to the Eastwards , therefore the 12 a clock line must stand on the West side the Plane 11. degrees 10 , minutes . Then to find all the Fore Noon Hour lines , I turn the Globe East-wards till the Index points to 11 a clock , or till 15 , degr . of the Equator pass through the Meridian , and find the Colure cut the Gnomonical Semi-Circle in 15. 8 counted from the middle of the Gnomonical Semi Circle . 10 18. 56 9 22. 37 8 26. 52 7 32. 37 6 42. 5 5 62. 43 And these are the distances of the Fore Noon Hour lines ; to which distances you may set Pricks on the West side the Semi Circle of the Plane , viz. from B to C. The After Noon Hour lines are found by bringing the Colure again to the Meridian , and the Index of the Hour Circle to 12. for then turning the Globe Westwa●s till the Index points to 1 a clock , or till 15 degr . of the Equator pass throug the Meridian , I find the Colure cut the Gnomon , Semi-Circle in 5. 45 counted from the middle of the Gnomon . Semi-Circle . — — 2 2. 54 3 20. 52 4 64. 36 Having drawn the Hour-lines , I remove the Quadrant of Altitude to the degree of the Horizon opposite to the degree it was at before , viz. to 30. degrees from the South Westwards , which is so much as the Plane declines Eastwards ; But I let the Gnomonical Semi Circle stand as it did : And turning about the Globe till the Colure cut the Quadrant of Altitude in 20. degrees counted from the Horizon upwards , viz. the degrees of Reclination , I find 18. degrees 40. minutes contained between the middle of the Gnomonical Semi Circle and the Brasen Meridian , which is the distance of the Substyle from the Perpendicular ; And I find the Gnomonical Semi Circle cut the Colure in 13. degrees 49. minutes from the Pole , which is the Height that the Style must be raised over the Substyle ; Therefore I prick off in the Semi Circle on the Plane , the distance of the Substyle 18. degrees 40. minutes from the Perpendicular Westwards ; because this Plane declines Eastwards : And from the Center A , I draw through that prick the line A E , which shall be the Substyle , and from this Substyle ( either way ) I count in the Semi Circle on the Plane 13 ▪ degrees 49. minutes , and there make a Prick : Then from the Center A , I draw through that Prick the line A F , to represent the Style or Gnomon : Then I let fall the Perpendiculer F G upon the Substyle A G ; So is a Triangle made ; which if it be erected Perpendicularly upon the Substyle A G , the Style A F shall be Parallel to the Axis of the World , and cast a shadow upon the Hour of the Day . Having made this Dyal , you have made four several Dyals , whereof this is one : And his opposite , viz. North Declining Westwards 30. degrees Inclining to the Horizon 70. degrees is another . The South Declining Westwards 30. degrees Reclining from the Zenith 20. degrees is another : And his opposite , viz. North Declining Eastwards 30. degrees Inclining to the Horizon 70. degrees is the other . PROB. XIII . To make a Dyal upon a Declining Inclining Plane . THe Precepts for making these Dyals are delivered in the foregoing Probleme : Therefore we shall at first come to an Example . I would make a Dyal upon a Plane in Londons Latitude Declining from the South Westwards 25. degrees and Inclining towards the Horizon by the space of an Arch containing 14. degrees . Having first discribed on the Plane a Semi Circle , as was directed Prob. 4. I rectifie the Globe , Quadrant of Altitude , Colure , and Hour Index , as by the same Probleme , and bring the lower end of the Quadrant of Altitude to the degree of the Planes Declination , viz. to 25. degrees counted from the South Westwards , and the ends of the Gnomonical Semi Circle to the degree of Azimuth the Plane lies in , viz. to 25. degrees from the West Northwards , and the middle of the Gnomonical Semi Circle to the degree of the Planes Inclination , viz. 14. degrees counted from the Zenith downwards on the Quadrant of Altitude , Then counting the degrees of the Gnomonical Semi Circle contained between the middle of the same and the Brasen Meridian , I find 5. degrees 30. minutes : These 5. degrees 30. minutes shews the distance of the 12 a clock line from the Perpendicular ; Therefore I number in the Semi Circle discribed on the Plane , from the Perpendicular Westwards , ( Because the middle of the Gnomonical Semi Circle lies Westwards on the Globe ) from the Meridian ▪ And for finding all the Fore-Noon Hour-distances I turn the Globe East-wards till the Index points to 11 a clock , or till 15 degr . of the Equa . pass throug the Meridian , and find the Colure cut the Gnomon , Semi-Circle in 20. 5 counted from the middle of the Gnomon . Semi-Circle . 10 36. 57 9 56. 24 8 76. 31 And these are the distances of all the Fore Noon Hour lines ; to which several distances I make pricks on the West side the Semi Circle on the Plane , viz. from B to C. The After Noon Hour lines are found by bringing the Colure again to the Meridian , and the Index of the Hour Circle to 12. For then turning the Globe Westwards till the Index points to 1 a clock , or till 15. degrees of the Equator pass through the Meridian , I find the Colure cut the Gnomonical Semi-Circle in 6. 20 counted from the middle of the Gnomonical Semi Circle . 2 18. 2 3 28. 45 4 39. 56 5 52. 30 6 67. 19 7 84. 13 And these are the distances of the After Noon Hour lines , which I also prick down at their respective distances from the Perpendicular Eastwards , viz. from B towards D on the Plane ; and by drawing lines from the Center A through all the Pricks , I have all the Hour lines that this Plane will admit of . Having made this Dyal you have also four Dyals made ; as well as in the former Probleme : For this is one ▪ and its opposite viz. North declining Eastwards 25. degrees Reclining 76. degrees is another ; The South declining Eastwards 25. degrees inclining 14 ▪ degrees is another ; and its opposite , viz. North declining Westwards 25. degrees Reclining 76. degrees is another ; PROB. XIV . To find in what Place of the Earth any manner of Plane that in your Habitation is not Horizontal , shall be Horizontal . IT was said in the Preface that all manner of Planes however scituate are Parallel to some Country or other on the Earth : Therefore all manner of Planes are indeed Horizontal Planes ; and the distances of the Hour lines to be ●●scribed on them may be found as the distances of the Hour lines of the Horizontal Dyal in Prob. 3. It rests now to learn in what place of the Earth any Plane that is not Horizontal in your Habitation shall become Horizontal : And for help of your understanding herein , Take these following Rules . 1. If your Plane be Erect Direct North , or South , it shall be an Horizontal in the same Longitude at 90. degrees distance on the Meridian , ( counted from the Zenith of your Place , ) through the Equinoctial . See an Example of this in Prob. 3. where I have reduced an Erect Dyrect Dyal ▪ to an Horizontal . Thus an Erect Plane under the Pole is an Horizontal under the Equator ; and an Erect Direct in 80. degrees North Latitude is in the same Longitude an Horizontal at 10. degrees South Latitude : An Erect Direct in 70. degrees North Latitude , is in the same Longitude , an Horizontal at 20. degrees South Latitude : and so to any other degrees of Latitude ( as aforesaid ) till you come to 45. degrees Latitude ▪ where an Erect is an Horizontal , and an Horizontal an Erect ▪ Only as the Hour lines of the Horizontal ( being 〈◊〉 downwards ) are numbred from the right hand towards the left , in the Erect Direct Dyal they are numbred from the left hand towards the Right . 2. If your Pla●● be Erect Declining , it shall be an Horizontal Plane at that point on the Globe which is against the degree of Declination , found in the Horizon . But note , If your Plane declines Westwards , the Sun comes sooner to the Meridian of it , then to the Meridian of the Place where it becomes an Horizontal Plane ; and that by so many Hours or minutes as the degrees of the difference of Longitude between the two Places converted into Time amounts to . If it declines Eastwards , the Sun comes so much later to the Meridian of it : And for this Cause ( though the making this Dyal be the same with an Horizontal Dyal for another Place , yet in Respect of Time ) there will be a difference between them . Example . I would make the South Dyal Declining East 27. degrees , as in Prob. 9. by the Plane of the Horizon : First I seek in what Place of the Earth it shall become an Horizontal Plane : Thus , I Elevate the Pole of the Globe 51½ degrees above the Horizon , and bring the Vernal Colure to the Meridian , then I count from the South point in the Horizon Eastwards 27. degrees , and on the point on the Globe directly against those 27. degrees I make a prick for the Place where a Plane that declines 27. degrees from the South Eastwards at London shall be Horizontal ; or which is all one , this Declining Plane at London shall ly in the Horizon of that Prick : This Prick for distinction sake we shall hereafter call the Horizontal Place : Then by Prob. 1. of the Second Book , I examine the Latitude and Longitude of this Horizontal Place , and find Latitude 33. 40. South ; and Longitude from the Colure 33. degrees , which is the difference of Longitude between London and the Horizontal Place : which being converted into Time by allowing for every 15. degrees 1. hour of Time , gives 2 hours 12. minutes that the Sun comes sooner to the Meridian of the Horizontal Place , then to the Meridian of the Plane at London : so that when it is 12 a clock there , it will be but 9. a clock 48. minutes here ; when 12 a clock here , it will be 2 a clock 12. minutes There , &c. Having thus found in what Longitude from London and Latitude this Plane is Parallel to the Horizon , I seek the distances of the Hour-lines upon the Planes of the Horizon Thus , I Elevate the Pole of the Globe to the Height of the Pole in the Horizontal Place , viz. 33. degrees 40 , minutes , and bring the Horizontal Place on the Globe to the Meridian , and the Index of the Hour Circle to 12. Then I examine the degree of the Horizon the Colare cuts , and find it 19¾ from the South Westwards . This 19¾ degrees respresents the Meridian line of the Horizontal Place : And also the Substylar line here at London ; Therefore this 19¾ degrees I count from the Perpendicular A B of the Plane , and from the Center A draw the line A G through them ; Because from this line on the Plane all the Hour lines must be numbred , and not ( as all along hitherto ) from the Perpendicular of the Plane , Then turning the Globe East-wards till the Index of the Hour Circle points to 11 a clock , or till 15. degr . of the Equator pass through the Meridian , I find the Colure cut the Horizon in 10. 2 from the Meridian . 10 0. 45 9 6. 12 8 15. 25 7 26. 11 6 40. 30 5 60. 0 And these are the distances of the Forenoon Hour lines : which distances I transfer by pricks to the Plane . But as in Prob. 9. I sought the distances from the Perpendicular on the Plane , so now in this Case ( as was said before ) I seek them from the Substyle , and through these pricks I draw lines from the Center , as in other Dyals , and these lines shall be the Fore Noon Hour lines . To find the Afternoon Hour distances , I bring the Horizontal Place on the Globe again to the Meridian , and the Index of the Hour Circle to 12. and turning the Globe Westwards till the Index points to 1 a clock , or till 15 degr . of the Equator pass through the Meridian , I find the Colure cut the Horizon i● 31. 5 counted from the Meridian . 2 46. 32 3 68. 5 4 95. 37 And these are the distances of all the Afternoon Hour lines ; which I also transfer to the Plane , counting them from the Substyle , and draw lines from the Center A through these distances ; and these lines shall be all the Afternoon Hour lines . Then from the Substyle I count the degrees and minutes of the Latitude of the Horizontal Place , viz. 33. degrees 40. minutes , and through these degrees and minutes I draw the line A F from the Center A , for the Style : Then from the Style I let fall the Perpendicular F G upon the Substyle , so is there a Triangle made ; which if it be erected Perpendicularly upon the Substyle A G , the Style A F shall be Parallel to the Axis of the World , and cast a shadow upon the Hour of the Day . 3. If your Plane be a Direct Recliner , Seek in the Longitude of your Place the Complement to 90. of your Planes Reclination ▪ For there a Direct Recliner becomes an Horizontal Plane . 4. If your Plane be a Declining Recliner : The Globe and Quadrant of Altitude Rectified , Bring your Habitation on the Terrestrial Globe to the Meridian , and the Quadrant of Altitude to the Declination , as by the second Rule in this Probleme ; and count upwards on the Quadrant of Altitude the Reclination , and there make a prick on the Globe by the side of the Quadrant of Altitude , for at that prick on the Globe the Declining Recliner shall become an Horizontal Plane . Then examine the Latitude of that prick as by Prob. 1. of the second Book , and the difference of Longitude , as by Prob. 9. of the third Book : And convert the difference of Longitude into Time , by allowing for every 15. degrees 1. hour : Time , for every degree 4 , minutes Time , and so proportionably , so shall you know what Hours and Minutes the Sun comes sooner or later to the Meridian of your Habitation then to the Meridian of that Place where it becomes an Horizontal Plane : Sooner , if the Globe were turned Eastwards ; but Later if it were turned Westwards . Having thus found out where this Plane becomes Horizontal , make your Dyal to this Plane , as by the second Rule in this Probleme : Find also the Style as is there directed . 5. If your Plane be a Declining Incliner , The Globe and Quadrant of Altitude Rectified , Bring the Colure to the Meridian , and the Quadrant of Altitude to the degree of the Horizon opposite to the degree of the Planes Declination , and count upwards on the Quadrant of Altitude the degrees of Inclination , and make a 〈◊〉 there ; For in the 〈◊〉 of that prick ( found as by 〈◊〉 〈◊〉 , of the Second Book ) that Declining In 〈◊〉 shall become an Horizontal Plane . Then find the Latitude and difference of Longitude of this 〈◊〉 ▪ by the 〈◊〉 〈◊〉 and make a ●yal to that 〈◊〉 by the second 〈◊〉 in this Probleme . Find also the Style as therein is directed . PROB. XV. To make a Dyal on the Ceeling of a Room , where the Direct Beams of the Sun never come . FInd some convenient place in the Transum of a Window to place a smal round peece of Looking-Glass , about the bigness of a Groat , or less ; so as it may ly exactly Horizontal : The point in the middle of this Glass we will marke A , and for distinctions sake ( with Mr Palmer ) call it Nodus : Through this Nodus you must draw a Meridian line on the Floor , Thus : Hang a Plumb line in the Window exactly over Nodus , and the shadow that that Plumb line casts on the Floor just at Noon will be a Meridian line ; Or you may find a Meridian line otherwise , as by the Preface . Having drawn the Meridian line on the Floor : find a Meridian line on the Ceeling , thus : Ho●d a Plumb line to the Ceeling , over that end of the Meridian line next the Window ; If the Plumbet hang not exactly on the Meridian line on the Floor , remove your hand on the Ceeling one way or other , as you see cause till it do hang quietly just over it : and at the point where the Plumb line touches the Ceeling make a mark , as at B ; that mark B shall be directly over the Meridian line on the Floor : then remove your Plumb line to the other end of the Meridian line on the Floor , and find a point on the Ceeling directly over it , as you , did the former point , as at C , and through those two points B and C on the Ceeling strain and strike a line blackt with Smal Cole or any other Culler ( as Carpenters do , ) and that line B C on the Ceeling shall be a Meridian line , as well as that on the Floor : Then examine the Altitude of the Equinoctial , as by Prob. 6. of the Second Book you did the Meridian Altitude of the Sun ; and fasten a string just on the Nodus , and remove that string in the Meridian line on the Ceeling till it have the same Elevation in a Quadrant , that the Equinoctial hath in your Habitation ; and through the point where the string touches the Meridian line in the Ceeling shall a line be drawn at right Angles with the Meridian , to represent the Equinoctial line . Thus in our Latitude the Elevation of the Equator being 38½ degrees ; I remove the string fastned to the Nodus forwards or backwards in the Meridian line of the Ceeling , till the Plumb line of a Quadrant , when one of the sides are applyed to the string , falls upon 38½ degrees : and then I find it touch the Meridian line at D in the Ceeling : therefore at D I make a mark and through this mark strike the line D E ( as before I did the Meridian line ) to cut the Meridian line at Right Angles : This line shall be the Equinoctial line . Then I place the Center of the Semi-Circle of Position upon Nodus , and under-prop it so that the flat side of it may ly Parallel to the string when it is strained between the Nodus and the Equinoctial , and also so as the string may ly on the division of the Semi-Circle marked o , when it is help up to the Meridian line in the Ceeling : Then removing the string the space of 15. degrees in the Circle of Position to the Eastwards , and extending it to the Equator on the Ceeling , where the string touches the Equator there shall be a point through which the 1 a clock Hour-line shall be drawn : and Removing the string yet 15. degrees further to the Eastwards in the Semi-Circle of Position , and extending it also to the Equator , where it touches the Equator there shall be a point through which the 2 a clock Hour-line shall be drawn : Removing the string yet 15. degrees further to the Eastwards in the Semi-Circle of Position , and extending it to the Equator , there shall be a point through which the 3 a clock Hour-line shall be drawn : The like for all the other After-Noon Hour lines ; so oft as the string is removed through 15. degrees on the Semi-Circle of Position , so oft shall it point out the After-Noon distances in the Meridian line on the Ceeling . The scituation of the Semi-Circle of Position cannot conveniently be shewn in this Figure , unless it be drawn by the Rules of Perspective ; Neither if it were would it suit with the other demonstrations , expect they were drawn by the same Rules also ; which to do would be hard for young Learners to understand : Therefore I have left out the Semi-Circle of Position in this Figure and refer you for a demonstration thereof to the sixth Probleme ; For even as the lines drawn through every 15 , degrees of the Semi-Circle there , denote in a Contingent line the distance of any Hour line from the Meridian line , even so a line drawn through every 15. degrees of the Semi-Circle of Position posited ( as aforesaid ) point out in the Equinoctial line on the Ceeling the distance of each respective Hour line from the Meridian line , Having thus found out the points in the Equator through which the After-Noon Hour-lines are to be drawn , I may find the Fore-Noon Hour distances also the same way , viz. by bringing the string to the several 15. degrees on the West side the Semi-Circle of Position ; or else I need only measure the distances of each Hour distance found in the Equator from the Meridian line on the Ceeling ; for the same number of Hours from 12 have the same distance in the Equinoctial line on the other side the Meridian both Before and Afternoon : The 11 a clock Hour distance is the same from the Meridian line with the 1 a clock distance on the other side the Meridian , the 10 a clock distance the same with the 2 a clock distance , the 9 with the 3 , &c. And thus the distances of all the Hour lines are found out on the Equator . Thus upon the point markt for each Hour distance in the Equinoctial line on the Ceeling , I discribe the Arches I , II , III , IIII , as in the Figure , and finding the distance from the Meridian of the Hour-lines of an Horizontal Dyal to be according to the third Probleme . Thus The 1 a clock Hour-line 11.40 whose Complement 90. is 78.20 2 24.15 65.45 3 38.4 51.56 4 53.36 36.24 I measure in a Quadrant of the same Radius with those arches already drawn from the Equinoctial line for the 1 a clock Hour 78.20 2 65.45 3 51.56 4 36.24 and transfer these distances to the Arches drawn on the Ceeling : For then straight lines drawn through the mark in the Arch , and through the mark in the Equator , and prolonged both waies to a convenient length , shall be the several Hour-lines ( a foresaid ; ) And when the Sun shines upon the Glass at Nodus , its Beams shall reflect upon the Hour of the Day . PROB. XVI . To make a Dyal upon a solid Ball , or Globe , that shall shew the Hour of the Day without a Gnomon . THe Equinoctial of this Globe , or ( which is all one ) the middle line must be divided into 24 equal parts , and marked with 1 , 2 , 3 , 4 &c to 12. and then beginning again with 1 , 2 , 3 , &c. to 12. Then if you Elevate one of the Poles so many degrees above an Horizontal line as the Pole of the World is Elevated above the Horizon in your Habitation , and place one of the 12 s directly to behold the North , and the other to behold the South : when the Sun shines on it the Globe will be divided into two halfs , the one enlightened with the Sun-shine , and the other shadowed : and where the enlightned half is parted from the shadowed half , there you shall find in the Equinoctial the Hour of the Day ; and that on two places on the Ball ; because the Equinoctial is cut in two opposite points by the light of the Sun. A Dyal of this fort was made by M r John L●●k , and set up on a Composite Columne at Leaden Hall Corner in London , in the Majoralty of S r John Dethick Knight . The Figure whereof I have inserted , because it is a pretty peece of Ingenuity , and may perhaps stand some Lover of Ar● in stead , either for Imitation , or help of Invention . PROB. XVII . To make a Dyal upon a Glass Globe , whose Axis shall cast a shadow upon the Hour of the Day . FIrst divide the Equinoctial of your Globe into 24 equal parts ; and having a Semi-Circle cut out of some Brass plate , or thin Wood to the same Diameter your Globe is of , or a very little wider : Apply this Semi-Circle to the Globe , so as the upper edge of each end of the Semi Circle may touch the Poles of the Globe , and the middle of the Semi Circle may at the same edge cut through some division made in the Equinoctial : for then a line drawn by the edge of the Semi Circle thus posited shall be a Meridian line ; The same way you must draw Meridian lines through every division of the Equinoctial , and set figures to them , beginning with 1 , 2 , 3 , 4 , &c. to 12 , and then beginning again with 1 , 2 , 3 , 4 , &c. to 12 , again . This Globe being made of Glass , and having an Axis of Wyer passing through ●t from Pole to Pole , will be an Horizontal Dyal all the World over ; if its Axis be set Parallel to the Axis of the World in the same Place ; and one of the Meridians marked 12 be set so as it may directly behold the North point in Heaven , and the other the South point in Heaven ; for then the Axis of the Globe shall cast a shadow upon the Hour of the Day . And if you divide the upper half of the Glass Globe from the under half , when the Axis stands Parallel to the Axis of the World , by a Circle drawn round about the Globe , that Circle shall represent the Horizon ; and the Meridian lines drawn on the Globe shall be the Hour lines , and have in the Horizontal Circle the same distance from the 12 a clock line that the same respective Hour line was found to have , as by Prob. 3. of this Book . But because the shadow of this Axis will not be discerned through the Glass Body ; therefore you may with Water and white Lead ground together , lay a Ground on the Inside of the under half of the Glass to the Horizontal Circle ( as Looking-glass makers do their Looking Glasses with Tinfoil ) for then the shadow will appear . Such a Glass Globe Dyal hath the Lord Robert Titchborn standing in his Garden supported by Atlas . The End of the Fifth Book . The Sixth BOOK . Shewing the Practical Use of the GLOBES : Applying them to the Solution of Spherical Triangles . PRAEFACE . THe Solution of Spherical Triangles is to know the length of its Sides , and the width of its Angles . These have already by many learned Men been taught , to be performed by a Canon of Sines and Tangents ; and also by many Instruments some serving as Tables of Sines and Tangents , such as are the Sectors , Scales , the Spiral line , &c. and others serving to represent the Globe ; such as be the Mathematical Jewel , Astrolabium Catholicum , and several other Projections of the Sphear . But none hath as yet taught the Solution of Spherical Triangles by the Globe it self ; though it be the most natural , and most demonstrative way of all , and indeed ought first to be learnt before the Learner enters upon any other way . To this Authors of Trigonometry agree , for the most of them in their Books give Caution that the Learner be already sufficiently grounded in the Principles of the Globe : For those Lines or Circles which either in Tables or other Instuments your force your Imagination to conceive represents your Line or Circle in question , those Lines and Circles I say , you have Actually and Naturally discribed on the Globe , and therefore may at a single Operation , or perhaps only by a sudden inspection , have an Answer annexed , according as the nature of your Question shall require : and that more Copiously then by Tables of Sines and Tangents : For therein you find but one Question at once resolved : but by the Globe you have alwaies two resolved together . Of the Parts and Kindes of Spherical Triangles . THEOREMS . 1. ALL Spherical Triangles are made of six parts ; Three Sides , and three Angles . The Sides are joyned together at the Angles , and measured by degrees of a Great Circle , from one end to the other . The Angles are the distance of the two joyned sides : and they are also measured by an Arch of a Circle , discribed on the Angular point . If any three of these parts be known , the rest may be found . 2. All Spherical Triangles are either Right Angled , or Oblique Angled . A Right Angle contains 90. degrees : An Oblique Angle either more , or less . 3. If a Spherical Triangle have one or more Right Angles ; it is called a Right Angled Spherical Triangle . But if it have no Right Angle ; it is called an Oblique Angled Spherical Triangle . 4. If an Oblique Spherical Triangle have one Angle greater then a Right Angle : it is called an Obtuse Angled Spherical Triangle : But if it have no Angle greater , it is called an Accute Angled Spherical Triangle . 5. In Right Angled Triangles the sides including the Right Angle are called Legs : And the side opposite to the Right Angle is called Hypothenusa . Thus the sides A B and A C in the following Triangle are called Legs ; and the side B C is called Hypothenusa . 6. In a Right Angled Spherical Triangle one of the Legs are called Base ; the other Perpendicular : Thus the Leg B A is Base ; and the Leg C A Perpendicular . But the Terms may be varied : for the Base may be made Perpendicular , and the Perpendicular Base . Also One of the adjacent Angles is called the Angle at the Base ; the other the Angle at the Perpendicular : Thus the Angle B is called the Angle at the Base : the Angle C the Angle at the Perpendicular . PROB. I. The Legs of a Right Angled Spherical Triangle given ; to find the Hypothenusa , and the two other Angles . THe Base of a Right Angled Spherical Triangle shall in this following Treatise be alwayes placed on a Meridian , the Perpendicular on the Equator , the Hypothenusa on the Quadrant of Altitude , and the Angle at the Base shall be measured in an Arch of the Horizon . Elevate the Equinoctial into the Zenith , so shall the Poles of the Globe ly in the North and South points of the Horizon . Then count from the Equinoctial on the first Meridian , if you use the Terrestrial Globe ; or on the Vernal Colure , if you use the Celestial , because they are divided from the Equinoctial either way into 90. degrees ; and because from thence the degrees of the Equinoctial are begun to be numbred : Count ( I say ) from the Equinoctial the number of degrees the Base contains , and there make a prick : Then count in the Equinoctial from the first Meridian the number of degrees the Perpendicular contains , and make there a second Prick : Bring that second Prick to the Brasen Meridian , so shall the first Meridian be separated from the Brasen Meridian by the quantity of an Arch equal to the measure of the Perpendicular : Then having the Quadrant of Altitude screwed in the Zenith , turn it about till the side of it cut the Prick made in the first Meridian ; so shall the Triangle be represented on the Globe . The Base shall ly on the first Meridian between the Equinoctial and the Quadrant of Altitude , the Perpendicular in the Equinoctial between the first Meridian and the Brasen Meridian ; and the Hypothenusa on the Quadrant of Altitude between the Zenith and the first Meridian : and the number of degrees between each of these respective Arches shall be the measure of each respective Side . For the Angles ; The Right angle is known to be 90. degrees , by the second Theorem in the Preface . The measure of the Angle at the Perpendicular is numbred between the East point in the Horizon and the graduated edge of the Quadrant of Altitude : But to find the Angle at the Base you must turn the Triangle , makeing the Perpendicular Base , and the Base Perpendicular . Example . Having the two Legs given A B 79. degreee 15. minutes , and C A 23. degrees 8 minutes , I would find the measure of the Hypothenusa C B , and the Angles B C. Now , as before I counted 79. degrees 15. minutes from the Equinoctial on the first Meridian , which was the length of that Base , so now I count 23. degrees 8. minutes on the first Meridian , which is the length of this Base , and there ( as before ) I make a Prick : and as before I counted 23. degrees 8. minutes on the Equinoctial from the first Meridian , which was the length of that Perpendicular ; so now I count 79. degrees 15. minutes on the Equinoctial , which is the length of this Perpendicular ; and there I make a prick on the Equinoctial : Then I bring this Prick ( as before ) to the Brasen Meridian , so shall the first Meridian be distant ( as before ) from the Brasen Meridian so many degrees and minutes as is the length of this Perpendicular , viz. 79. degrees 15. minutes : Then Having the Quadrant of Altitude screwed to the Zenith , I turn it about till the edge of it touch the Prick made in the first Meridian at 23. degrees 8. minutes distant from the Equinoctial ; so is the Triangle Turned : And so shall the Arch of the Horizon comprehended between the Equinoctial and the Quadrant of Altitude be the measure of the Angle C in the former Triangle , ( but now made B ) 23. degrees 30. minutes : you also see again the measure of the Hypothenusa B C 80. degrees 8. minutes on the Quadrant of Altitude , counted between the Zenith and the first Meridian . PROB. II. A Leg and the Hypothenusa given , to find the Rest. EXample . The Leg given shall be C A in the former Triangle 23. degrees 8. minutes , The Hypothenusa C B 80. degrees 8. minutes . The Equinoctial and Quadrant of Altitude Rectified , as by the last Probleme ; Number the Leg C A 23. degrees 8. minutes on the Equinoctial from the first Meridian , and there make a prick ; Bring this Prick to the Brasen Meridian ; Then number on the Quadrant of Altitude the Hypothenusa B C 80. degrees 8. minutes from the Zenith towards the Horizon , and make there on the edge of the Quadrant of Altitude another prick : Then turn the Quadrant of Altitude about till the prick made on the edge of it touch the first Meridian ; so shall the Triangle be made : The arch of the Equinoctial comprehended between the first Meridian and the Brasen Meridian , shall represent A C the Perpendicular ; the arch of the Quadrant of Altitude comprehended between the Zenith and the First Meridian , shall represent B C the Hypothenusa ; and the arch of the first Meridian comprehended between the Equinoctial and the Quadrant of Altitude shall represent B A the Base ; which was one Leg sought , and is ( as you will find ) 79. degrees 15. minutes : The Angle C you will find in the Horizon 85. degrees 44. minutes : The angle A is the Right Angle 90. degrees : And to find the Angle B you must turn the Triangle , as you were directed in the former Probleme . PROB. III. The Hypothenusa and an Angle given , to find the Rest. THe Hypothenusa given shall be B C of the Triangle in Prob. 1. 80. degrees 8. minutes , The Angle given shall be C 85. degrees 44 minutes : The Globe and Quadrant of Altitude Rectified , as by Prob. 1. Count the given Angle 85. degrees 44. minutes on the Horizon from the Equinoctial , and there place the Quadrant of Altitude : Then turn about the Globe till the first Meridian touch 80. degrees 8. minutes of the Quadrant of Altitude counted from the Zenith downwards , so shall the Triangle be made on the Globe : The Arch of the Equator comprehended between the first Meridian and the Brasen Meridian shall shew the length of the Perpendicular C A 23. degrees 8. minutes ; the Arch of the first Meridian comprehended between the Equinoctial and the Quadrant of Altitude shall shew the length of the Base A B 79. degrees 15 minutes ; the Right Angle made at the Interfection of the Brasen Meridian with the Equinoctial is 90. degrees : and to find the measure of the Angle B you must turn the Triangle , as you were directed Prob. 1. PROB. IIII. A Leg and Angle adjoyning given , to find the Rest. IN the Triangle of Prob. 1. The Leg given shall be C A 23. degrees 8. minutes , the Angle adjoyning shall be C 85. degrees 44 minutes : The Globe and Quadrant of Altitude Rectified , as by Prob. 1. I turn about the Globe till the first Meridian be distant from the Brasen Meridian 23. degrees 8. minutes , the length of the Leg C A : Then I count in the Horizon from the Equinoctial 85. degrees 44. minutes , the measure of the Angle C ; so is the Triangle made on the Globe . The Arch of the first Meridian comprehended between the Quadrant of Altitude and the Equinoctial shall shew the length of the Base A B 79. degrees 15. minutes ; The Arch of the Quadrant of Altitude comprehended between the Zenith and the first Meridian shall shew the length of the Hypothenusa C B 80. degrees 8. minutes ; The Right Angle made at the Intersection of the Equinoctial and the Brasen Meridian is 90. degrees : And to find the measure of the Angle B , you must turn the Triangle , as you were directed Prob. 1. PROB. V. A Leg and the Angle opposite given , to find the Rest. IN the Triangle of Prob. 1. the Leg given shall be A B 79. degrees 15. minutes , the Angle opposite shall be C 85. degrees 44. minutes , The Globe and Quadrant of Altitude Rectified , as by Prob. 1. I bring the Quadrant of Altitude to 85. degrees 15. minutes of the Horizon , the measure of the Angle C : Then I turn the Globe till 79. degrees 15. minutes of the first Meridian ( which is the measure of the Leg A B ) touch the Quadrant of Altitude , so is the Triangle made on the Globe . The Arch of the Equinoctial comprehended between the first Meridian and the Brasen Meridian shews the length of the Leg C A 23. degrees 8. minutes ; the Arch of the Quadrant of Altitude comprehended between the Zenith and the first Meridian , shall shew the length of the Hypothenusa C B 80. degrees 8. minutes : The Right Angle made at the Intersection of the Equinoctial and the Brasen Meridian is 90. degrees : And to find the measure of the Angle B , you must turn the Triangle , as you were directed in Prob. 1 : PROB. VI. The Angle given , to find the Sides . IN this Case you must turn the Angles into Sides , making an Oblique Triangle on the Globe , whose Sides shall be equal to the given Angles : so shall the Angles of this Triangle found , be the measure of the Sides required . Example . In the Triangle of Prob. 1. The Angle A is 90. degrees , the Angle B 23. degrees 30. minutes , the Angle C. 85. degrees 44. minutes : The Globe and Quadrant of Altitude Rectified , as by Prob. 1. I set the Right Angle A 90. degrees on the Brasen Meridian , between the Pole and the Equinoctial ; For the Angle B I number downwards on the Quadrant of Altitude 23. degrees 30. minutes , which shall be the side representing that Angle : for the Angle C I number on the first Meridian from the Pole towards the Equinoctial 85. degrees 44. minutes , which shall be the side representing that Angle : Then I turn the Globe and Quadrant of Altitude till I can joyn the 23. degrees 30. minutes counted before on the Quadrant of Altitude and this 85. degrees 44. minutes counted in the first Meridian together ; So is a Triangle made on the Globe ; whose sides being equal to the Angles given , shall have its Angles equal to the sides required : Thus the Arch of the Equinoctial comprehended between the first Meridian and the Brasen Meridian shall be found 23. degrees 8. minutes , the measure of the side A C : The Arch of the Horizon contained between the nearest Pole and the Quadrant of Altitude shall be found 79. degrees 15. minutes , the measure of the side B A : And to find the Hypotenusa B C , you have now Data's enough , either to find it as by some of the former Problemes ; or else you may find it by turning the Triangle as by Prob. 1. These Cases of Right Angled Spherical Triangles may be wrought otherwaies by the Globe , If you alter its Position ; making the North or South points of the Horizon , Zenith ; or else the Poles of the World , or the Poles of the Ecliptick ; and use the Circle of Position insteed of the first Meridian or Circles of Longitude : But these Instructions together with a little Practise , are ( I judge ) sufficient ; Therefore I shall refer Varieties to the Studies of the Industrious Studient . Of Oblique Triangles . PROB. VII . The three Sides given , to find the Angles . ELevate the Pole of the Globe above the Horizon to the Complement of one of the given Sides and screw the Quadrant of Altitude in the Zenith , so shall that given Side be comprehended between the Pole and the Quadrant of Altitude ; Then count from the Pole upon the first Meridian the measure of the Second Side , and there make a prick ; Count also from the Zenith upon the Quadrant of Altitude downwards the measure of the third Side , and make there on the edge of the Quadrant of Altitude another prick ; Then turn the Globe and Quadrant of Altitude till you can joyn these two pricks together ; so shall your Triangle be made on the Globe : And then the number of degrees of the Equinoctial comprehended between the first Meridian and the Brasen Meridian shall be the measure of the Angle at the Pole : The Arch of the Horizon comprehended between the Quadrant of Altitude and the intersection of the Brasen Meridian with the Horizon on that side the Pole is elevated , shall be the measure of the second Angle : And for finding the third Angle , you must turn the Triangle , as by Prob. 1. Example . In the Triangle A B C annexed , The Side A B contains 38. degrees 30. minutes , the side B C 25. degrees , and the side A C 60. degrees ; I would measure these Angles ; I place one of these sides upon the Meridian , viz. A B 38. degrees 30 minutes , the Complement of 38. degrees 30. minutes is 51 degrees 30. minutes ; Therefore I Elevate the Pole 51. degrees 30. minutes above the Horizon , so shall the Zenith be distant from the Pole 38. degrees 30. minutes ; here I screw the Quadrant of Altitude and count downwards on it the measure of the side B C 25. degrees , and there I make a prick : Then from the Pole I count on the first Meridian 60. degrees , the measure of the side A C , and there I make another prick : Then I turn the Globe and Quadrant of Altitude backwards or forwards till these two pricks are joyned together ; so shall the Triangle A B C be made on the Globe : The arch of the Brasen Meridian comprehended between the Pole and Zenith shall represent the side A B ; the Arch of the Quadrant of Altitude comprehended between the first Meridian and the Brasen Meridian shall represent the side B C ; and the Arch of the first Meridian comprehended between the Pole and the Quadrant of Altitude shall represent the side A C ; The Pole shall represent the Angle A , the Zenith the Angle B ; and the intersection of the first Meridian with the Quadrant of Altitude shall represent the Angle C. The Angle at the Pole is measured in the Equator ; for the degrees comprehended between the first Meridian and the Brasen Meridian being 17. degrees 15. minutes shews 17. degrees 15. minutes to be the measure of the Angle A. The Angle at the Zenith is measured in the Horizon ; for the degrees comprehended between the Intersection of the Brasen Meridian with the Horizon on that side the Pole is Elevated being 142. degrees 42. minutes , shews that 142. degrees 42. minutes is the measure of the Angle B , Thus two angles are found ; the third is wanting : which I find thus , I turn the Triangle , placing either A or C in the Zenith . Example : I place A at the Zenith , which before was at the Pole ; so shall C be at the Pole , and B at the Intersection of the first Meridian and the Quadrant of Altitude , and the side A C shall be comprehended between the Pole and Zenith : The side A C contains 60. degrees ; its Complement to 90 is 30. degrees ; therefore I Elevate the Pole of the Globe 30. degrees above the Horizon ; so shall 60. degrees be in the Zenith ; therefore to 60. degrees I screw the Quadrant of Altitude and count on it downwards the measure of the other side next the Zenith , viz. 38. degrees 30. minutes ; and there I make a prick : Then from the Pole on the first Meridian I count the measure of the last side , viz. 25. degrees , and there I make another prick : Then I turn the Globe and Quadrant of Altitude ( as before ) till these two pricks joyn ; so is the Triangle altered on the Globe : For the Arch of the Brasen Meridian comprehended between the Pole and Zenith which before was 38. degrees 30. minutes , is now 60. degrees ; the Arch of the Quadrant of Altitude Comprehended between the first Meridian and the Brasen Meridian , which before was 25 degrees , is now 38. degrees 30. minutes ; and the Arch of the first Meridian comprehended between the Quadrant of Altitude and the Pole , which before was 60. degrees is now 25. degrees . Thus the Angle C being now at the Pole , its measure is found in the Equinoctial , viz. that Arch comprehended between the first Meridian and the Brasen Meridian , which is 25. degrees 24. minutes ; and the measure of the Angle A , which is now in the Zenith , having its sides , the one an Arch of the Brasen Meridian , the other an Azimuth , ( or which is all one ) an Arch of the Quadrant of Altitude , is measured in the Horizon , as all Azimuths are , and found 17. degrees 15. minutes , as before . PROB. VIII . Two Sides and the Angle contained between them given , to find the Rest. EXample . In the former Triangle I have given the sides A B , 38. degrees 30. minutes , A C , 60. degrees , and the Angle A 17. degrees 15. minutes . The Method I have hitherto used is to place the given side upon the Meridian between the Pole and Zenith ; but because the Angle at the Pole in this Example falls out so large that the Quadrant of Altitude will not reach the first Meridian ; therefore I shall use another way to work this Probleme as well . I Elevate the Pole of the Globe to the Com-plement of one of the given sides ; suppose the side A B , which being 38. degrees 30. minutes , its Complement to 90. degrees is 51. degrees 30. minutes , so shall the Zenith be distant from the Pole 38. degrees 30. minutes , the measure of the side A B : The other side is 60. degrees , this 60. degrees I count from the Pole in the first Meridian , and there I make a prick : The Angle given is 17. degrees 15. minutes ; this I count in the Equinoctial from the first Meridian , and this degree and minute in the Equinoctial I bring to the Brasen Meridian , so shall the first Meridian be separated from the Brasen Meridian 17. degrees 15. minutes : Then I screw the Quadrant of Altitude to the Zenith , and bring the side of it to the prick made in the first Meridian : so shall the Triangle be made on the Globe . Then to find the unknown side B C , I count the number of degrees on the Quadrant of Altitude comprehended between the Zenith and the first Meridian , and find 25. degrees , which is the measure of the side B C : To find the measure of the Angle B , I count the number of degrees contained between the Intersection of the Meridian with the Horizon on that side the Pole is Elevated and the Quadrant of Altitude , and find 142. degrees 42. minutes , which is the measure of the Angle B : And to find the Angle C I turn the Triangle , as in Prob. 7. PROB. IX . Two Sides and an Angle opposite to one of them given , to find the Rest. EXample . In the Triangle in Prob. 7. the Sides given are A B 38. degrees 30. minutes , and A C 60. degrees : The Angle given opposite to A C is B 142. degrees 42. minutes : I Elevate the Pole to the Complement of one of the given sides ; suppose A B , which being 38. degrees 30. minutes , its Complement to 90. degrees is 51. degrees 30. minutes ; so is the Zenith distant from the Pole 38. degrees 30. minutes : To this 38. degrees 30. minutes I screw the Quadrant of Altitude , and count in the Horizon from the Intersection of the Meridian with the Horizon on that side the Pole is Elevated the measure of the given Angle B , viz. 142 degrees 42. minutes , and to this number of degrees and minutes of the Horizon I bring the edge of the Quadrant of Altitude , then I count in the first Meridian from the Pole the measure of the side A C 60. degrees ; and there I make a prick , and turn about the Globe till that prick come to the edge of the Quadrant of Altitude , so is the Triangle made on the Globe . The degrees of the Quadrant of Altitude comprehended between the first Meridian and the Zenith being 25. degrees , is the measure of the side B C : The degrees of the Equinoctial comprehended between the first Meridian and the Brasen Meridian being 17. degrees 15. minutes , is the measure of the Angle A ; and for finding the measure of the Angle C , I turn the Triangle , as in Prob. 7. PROB. X. Two Angles and the Side comprehended between them given , to find the Rest. EXample . In the Triangle of Prob. 7. the Angles given are A 17 degrees 15. minutes , and B 142. degrees 42. minutes , the side comprehended between them is A B 38 degrees 30. minutes , I Elevate the Pole to the Complement of the side A B which being 38. degrees 30. minutes , its Complement to 90 degrees is 51. degrees 30. minutes , so is the Zenith distant from the Pole 38. degrees 30. minutes ; to this 38. degrees 30. minutes I screw the Quadrant of Altitude , and count in the Horizon from the Intersection of the Meridian with the Horizon on that side the Pole is Elevated the measure of the given Angle B , viz. 142. degrees 42. minutes , and to this number of degrees and minutes of the Horizon I bring the edge of the Quadrant of Altitude ; then I turn about the Globe till the first Meridian is distant from the Brasen Meridian 17. degrees 15. minutes of the Equinoctial , which is the measure of the other given Angle ; So shall the Triangle be made on the Globe : and the Arch of the Quadrant of Altitude comprehended between the first Meridian and the Zenith shall be the measure of the side B C 25. degrees , and the Arch of the first Meridian comprehended between the Pole and its Intersection with the Quadrant of Altitude shall be the measure of the side A C 60. degrees : The measure of the Angle C is found by turning the Triangle , as in Prob. 7. PROB. XI . Two Angles and a Side opposite to one of them given , to find the Rest. EXample . In the Triangle of Prob. 7. the Angles given are A 17. degrees 15 minutes , and B 142. degrees 42. minutes , the side given is B C 25. degrees , being the side opposite to the Angle A ; the Angle A is made at the Pole of the Globe , and measured in the Equator : Therefore I separate the first Meridian from the Brasen Meridian 17. degrees 15. minutes , so doth the Pole represent the Angle A ; the Angle B is made at the Zenith , and measured in the Horizon ; therefore I count in the Horizon 142. degrees 42. minutes , and there I make a prick , to this prick I bring the edge of the lower end of the Quadrant of Altitude , ( not minding to what degrees of the Meridian the upper end of it is placed ) Then I count from the upper end of the Quadrant of Altitude 25. degrees downwards the measure of th e side B C and there I make a prick , and keeping the lower end of the Quadrant of Altitude to the prick made in the Horizon , I slide the upper end of it forwards or backwards till the prick on the Quadrant of Altitude come to the first Meridian , so shall the Triangle be made on the Globe : Then the Arch of the Brasen Meridian comprehended between the Pole and the upper end of the Quadrant of Altitude shall be the measure of the side A B 38. degrees 30. minutes ; and the Arch of the first Meridian comprehended between the prick on the Quadrant of Altitude and the Pole shall be the measure of the side A C 60. degrees ; But the Angle C you must find by turning the Triangle ; as in Prob. 7. In the working this Probleme I would have placed the given fide B C 25. degrees upon the Brasen Meridian between the Pole and Zenith ; but then the Angle B ( being so Obtuse ) would have had that side which would be intersected by the Quadrant of Altitude ( viz. the first Meridian under the Horizon , which the Quadrant of Altitude cannot reach . PROB. XII . Three Angles given , to find the Sides . THis Triangle is taught to be resolved by M r Palmer on the Planisphear ; Book 3. Chap. 19. It is to be known ( saith he ) That if you go to the Poles of the three great Circles whereof your Triangle is made , these Poles shall be the Angular points of a second Triangle ; and the two lesser sides of this second Triangle shall be equal to the two lesser Angles of your first Triangle : the greatest side of the second Triangle shall be the supplement of the greatest Angle of the first Triangle ( that is , shall have as many degrees and minutes as the greatest Angle of the first Triangle wanted of 180. degrees ( see Pitiscus Trigonometry Lib. 1. Prop 61. This second Triangle therefore ( all whose sides are known from the Angles of the first ) you shall resolve by Prob. 7. And having by that Probleme found the Angles of this second Triangle , know that the two lesser Angles of the second Triangle shall be several and respectively equal to the two lesser sides of the first Triangle , ( and the least Angle to the least side , the middle Angle to the middle side ) and the greatest Angle of this second Triangle being subtracted out of 180. degrees , shall leave you the greatest side of your first Triangle . Example . If the Angles be given 142. degrees 42. minutes , 17. degrees 15. minutes , and 25. degrees 24. minutes ; and the sides be enquired . Draw by aim a rude Scheam of this first Triangle , writing in the Angle A 17 degrees 15. minutes , in B 142. degrees 42. minutes , in C 25. degrees 24. minutes ; supposing the sides yet unknown : then draw under this by aim also , a Scheam of the second Triangle , setting his Base Parallel with the Base of the first and making the Base of the second shorter then the Base of the first . Set also B at the Vertical Angle , and A C at the Base ; as in the first Triangle . Then say , Because A in the first Triangle is 17 , degrees 15. minutes , therefore in the second Triangle B C ( which subtendeth A ) shall be 17. degrees 15. minutes : and because C in the first Triangle is 25. degrees 24. minutes , therefore in the second Triangle the side A B which subtendeth C ) shall be 25. degrees 24. minutes ; and because B the greatest Angle in the first Triangle , is 142. degrees 42. minutes , therefore in the second Triangle the side A C ( which subtendeth B ) shall be the complement thereof to 180. degrees , viz. 37. degrees 18. minutes : Write now upon the sides of this second Triangle the quantities of the sides , so is your second Triangle ready to be resolved , as by Prob. 7. Whereby you shall find the Angles of the second Triangle , as I have expressed them in the Scheam . A 25. degrees , C 38. degrees 30. minutes , B 120. degrees . N●w lastly , I say these Angles of the second Triangle thus found , give me the sides of the first Triangle , which I seek , in this manner . In the second Triangle .   In the first Triangle . A is 25. degrees Therefore B C is 25. degrees C is 38. 30. A B 38. 30. B is 120. 00. A C 60. 00. Complement of 120. degrees to 180. And thus by all the Angles given , we have found out all the sides , which was required . Having then the Angles of your first Triangle given , and his sides now found ; you shall find his scituation on the Globe thus Place him as in Prob. 7. A B 38. degrees 30. minutes between the Pole and Zenith , A C 60. degrees in the first Meridian separated from the Brasen Meridian 17. degrees 15. minutes of the Equinoctial , B C 25. degrees on the Quadrant of Altitude , counted from the Zenith when it s lower end is applyed to the 142. degrees 42. minutes of the Horizon : you shall say , Because the East point of the Horizon is the Pole of the Arch A B , therefore at the East point of the Horizon shall stand the Angle C , which A B subtendeth : Next follow the 142. degrees 42. minutes of Azimuth which maketh B C of your Triangle to the Horizon , and from thence number in the Horizon towards the East point 37 , degrees 18. minutes , the Complement of the Angle A to 180. degrees , and number yet further 52. degrees 42. minutes beyond the East point to make up 90 , and there is the Pole of the Arch B C : Therefore there shall stand the Angle A , which B C subtendeth . Then count in the Equator from the first Meridian 90. degrees , which will end under the Horizon , and there make a prick ; for there is the Pole of the Arch or side A C. Therefore at that prick shall stand the Angle B , which A C subtendeth . Here you see your second Triangle made by the Poles of the first adjoyning to the East point of the Globe : only the side A B is wanting : To get that , make a prick upon the Globe against the 52. degres 42. minutes from the East point of the Horizon found before , to represent the Angle A : Then turn about the Globe and Qudrant of Altitude till that prick and the prick made before for the Angle B are both at once cut by the side of the Quadrant of Altitude , and you will find 25. degrees 24. minutes of the Quadrant of Altitude comprehended between the two pricks , for the measure of the side A B PROB. XIII . How to let fall a Perpendicular that shall divide any Oblique Spherical Triangle into two Right Angled Spherical Triangles . THis Probleme is much used when an Oblique Triangle having two sides and an Angle given is to be solved by the Cannon of Sines and Tangents : but by the Globe it may be solved without it , as was shewed Prob , 8 , 9. Yet because letting fall a Perperdicular is so frequent in all Authors that treat of Trigonometry , I have inserted this Probleme also . In the Oblique Triangle of the fromer Problemes there is given the sides A B 38½ degrees , and B C 25. degrees , and the Angle C 25. degrees 24. minutes ; It is required to let fall a Perpendicular as B a from the Angle B. upon the Base A C ; and to know both the measure of this Perpendicular , and the parts it divides the Base into . Therefore Elevate the Pole of the Globe above the Horizon so much as is the measure of the Angle C , which in this Example is 25. degrees 24. minutes , and bring the intersection of the first Meridian with the Equinoctial to the East point of the Horizon ; so shall the Angle at the East point of the Horizon comprehended between the Horizon and the first Meridian be equal to the Angle C : then count in the first Meridian from the East point of the Horizon the measure of the side B C 25. degrees , and having the Quadrant of Altitude screwed to the Zenith bring the graduated edge of it to these 25. degrees , so shall the Arch of the Horizon comprehended between the East point and the lower end of the Quadrant of Altitude be the number of degrees that the Perpendicular falls upon the Base , counted from the Angle C to a , which in this Example is 21¾ degrees , and the Arch of the Quadrant of Altitude comprehended between the Horizon and the first Meridian is the measure of the Perpendicular B a 11. degrees . And thus by letting fall this Perpendicular you have two Right angled Spherical Triangles made , the one B a C , wherein is found C a , 21¾ degrees , B C 25. degrees B a 11. degrees C 25. degrees 24. minutes , and a the Right Angle : There remains only the angle B unknown ; which you must find by turning the Triangle , as was taught Prob. 1. The other Right angled Spherical Triangle made , is B a A , wherein is found A a ( Complement of 21 2 / 4 degrees to 60 degrees ( the whole Base before given ) 38¼ degrees , A B 38. degrees 30. minutes , B a 11. degrees , and a the Right Angle ; which is more then enough to find the Angl● . A and B ; as was shewed in the Preface . Theorem 1. The End of the Sixth Book Here follows the Ancient STORIES of the several STARS , and CONSTELLATIONS . Shewing the Poetical Reasons why such Various Figures are placed in HEAVEN . Collected from Dr HOOD . And First , Of the Northern Constellations . 1. URSA MINOR . This Constellation hath the preheminence , because it is neerest of all the rest unto the North Pole ; And is called of the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 whereupon the Pole is called the Pole Arctick , for that it is neer unto that Constellation . It is also called Helice minor , because of the smal revolution which it maketh round about the Pole : or rather of Elice , a Town in Arcadia , wherein Calysto the great Bear , and mother to the less , was bred . It is called Cynosura , because this Constellation , though it carry the name of a Bear , yet it hath the taile of a Dog : Last of all , it is termed Phoenice , because that Thales , who first gave the name to this Constellation , was , a Phoenician : And therefore the Phoenicians being taught how to use it in their Navigations , did call it by the name of the Country wherein Thales was born . It consisteth of 7. stars , which the Latines call Septemtriones ; because by their continual motion , those seven stars do as it were wear the Heavens . The Spaniards call them all Bosina , that is , an Horn ; because they may be very well brought into that form ; whereof that which is in the end of the tail , is called the Pole-star , by reason of the neareness thereof unto the Pole of the world ▪ for it is distant ( according to the opinion of most ) from the true Pole , but 23. deg . 30. min. The Arabians call it Alrukaba : And of the Scythians it is said to be an Iron nail , and is worshipped by them as a God. The two stars that are in the sholders of the Bear , are called Guards , of the Spanish word Guardare , which is to behold ; because they are diligently to be looked unto , in regard of the singular use which they have in Navigation . The reason why this Constellation was brought into the Heavens , is diversly set down , and first in this manner : Saturn having received of the Oracle that one of his Sons should banish him out of his kingdom , determined with himselfe to kill all the men children that he should beget : whereupon he gave command to Ops his wife , being then great , that she should shew him the child so soon as ever it was born : But she bringing forth Jupiter , and being greatly delighted with his hair , gave the child unto two Nymphs of Crete , dwelling in the mount Dicte ; whereof this was one , and was called Cynosura ; the other was Helice . Jupter , after that ( according to the Oracle ) he had bereft his Father of the kingdom , in recompence of their paines and courtesie , translated them both into the Heavens , and made of them two Constellations ; the Lesser Bear , and the Greater Bear. Othersome say that it was Arcas , the son of Calysto ; and they tell the tale on this manner . Calysto a Nimph of singular beauty , daughter to Lycaon King of Arcadia , induced by the great desire she had of hunting , became a follower of the Goddess Diana . After this , Jupiter being enamored with her beauty and out of hope , by reason of her profession , to win her love in his own person , counterfeited the shape of Diana , lay with Calysto , and got her with child ; of whom was born a son , which was called Arcas . Diana , or rather Juno , being very much offended here-with , turned Calisto into a Bear. Arcas her son at the Age of fifteen , hunting in the woods by chance lighted upon his mother in the shape of a Bear : who knowing her son Arcas , stood stil , that he might come near unto her , and not be afraid : but he fearing the shape of so cruel a Beast , bent his bow of purpose to have slain her : Whereupon Jupiter to prevent the mischief , translated them both into Heaven , and of them made two several Constellations : unto the lesser Bear , there belongs but one star unformed . 2. URSA MAIOR , the Greater Bear , called also of the Greeks Arctos , and Helice , consisteth of 27. stars : Among the which , those seven that are in the hinder part and tail of the Bear , are most observed ; the Latines call them Pla●strum ; and of our men they are called Charles Wayn ; because the stars do stand in such sort , that the three which are in the tail resemble the Horses , and the other four which are in the flank of the Bear , stand ( after a manner ) like the Wheels of a Waggon , or Chariot ; and they are suposed by some to be greater then the Sun. The reason of the Translation of this Constellation into the Heaven , is at large set down in the other Constellation , and therefore needs not here to be repeated . This Constellation was first invented by Nauplius , the Father of Palamedes the Greek : and in great use among the Grecians ; and this is to be noted both in this and the former Constellation , that they never set under the Horizon , in any part of Europe : which though it fall out by reason of their scituation in the Heavens ; yet the Poets say , that it came to pass through the displeasure and hatred of Juno ; who for that she was by Calisto made a Cuckquean , and they notwithstanding ( as she took it ) in dispight of her , were translated into Heaven , requested her brother Neptune , that he should never suffer those Stars to set within his Kingdom : To which request Neptune condiscended ; so that in all Europe they never come neer unto the Sea , or touch the Horizon . If any one marvel , that ( seeing she hath the form of a Bear ) she should have a tail so long ; Imagine that Jupiter fearing to come too nigh unto her teeth , laid hold on her tail , and thereby drew her up into heaven ; so that she of her selfe being very weighty , and the distance from the Earth to the Heaven very great , there was great likelyhood that her tail must stretch . The unformed stars belonging to this Constellation are eight . 3 DRACO , the Dragon , of some named the Serpent ; of others the Snake , by the Arabians , Aben ; and by Junctinus Florentinus , Vrago ; because he windeth his tail round about the Ecliptick Pole ; it containeth 31. stars . This was the Dragon that kept the Golden Apples in the Orchard of the Hesperides , ( now thought to be the Islands of Cape de Virde ) and for his diligence and watchfulness , was afterwards translated into heaven : Yet others say that he came into Heaven by this occasion ; when Minerva withstood the Gyants fighting against the Gods ; they to terrifie her , threw at her a mighty Dragon ; but she catching him in her hands , threw him presently up into Heaven , and placed him there , as a memorial of that her resistance . Others would have it to be the Serpent Python , whom Apollo slew , after the Deluge . 4. CEPHUS , containeth in him 11. stars , and hath two unformed . This was a King of the Aethiopians , and Husband unto Cassiopeia , and father of Andromeda , whom Perseus married . He was taken up into Heaven , with his wife and daughter , for the good deeds of Perseus his son in law ; that he and his whole stock might be had in remembrance for ever . The Star which is in his right shoulder , is called by the Arabians Alderahiemin ; i. e. his right Arm. 5 BOOTES , the driver of the Oxen ( for so I suppose the name to signifie , rather then an Herdsman ; for he hath not his name because he hath the care of any Cattle , but only because he is supposed to drive Charles his Wain , which is drawn by 3. Oxen ) he is also called Arctophilax , the keeper of the Bear , as though the care of her were committed to him . This Constellation consisteth of 22 Stars . Some will have Bootes to be Areas , the Son of her who before was turned into the Great Bear ; and they tell the Tale thus : Ly●aon the Father of Calisto , receiving Jupiter into his house as a guest , took Arcas his daughters son , and cut him in pieces ; and among other Services , set him before Jupiter to be eaten : for by this means he thought to prove if his guest were a God , as he pretended to be . Jupiter perceiving this heinous fact , overthrew the table , fired the house with lightning , and turned Lycaon into a wolf : but gathering , and setting together again the limbs of the child , he commited him to a Nymph of Aetolia to be kept : Arcas afterwards coming to mans estate , and hunting in the woods , lighted at un-awares upon his mother , transformed by Juno into the shape of a bear , whom he persued into the Temple of Jupiter Lycaeus , whereunto by the law of the Arcadians , it was death for any man to come . For as much therefore as they must of likelyhood be both slain . Calysto by her son , and he by the Law ; Jupiter to avoid this mischeif , of meer pitty took them both up into heaven . Unto this Constellation belongeth but one star unformed , and it is between the legs of Bootes , and by the Grecians it is called Arcturus , because of all the stars neer the great Bear named Arctos , this star is first seen neer her tail in the evening . The Poetical invention is thus . Icarus the father of Erigone , having received of the God Bacchus a Flagon of wine , to declare how good it was for mortal men , travelled therewith into the Territories of Athens , and there began to carouse with certain shepheards : they being greatly delighted with the pleasantness of the wine , being a new kind of liquor , began to draw so hard at it , that ere they left off , they were past one and thirty ; and in the end , were fain to lay their heads to rest . But coming unto themselves again , and finding their brains scarce in good temper , they killed Icarus , thinking indeed that he had either poysoned them , or at the least-wise made their brains introxicate . Erigone was ready to die for grief , and so was Mera , her little dog . But Jupiter to allay their grief , placed her father in Heaven , between the legs of Arctophilax . 6. CORONA BOREA , the Northern garland , consisteth of eight stars ; yet Ovid saith , that it hath nine . This was the Garland that Venus gave unto Ariadne , when she was married unto Bacchus , in the Isle Naxus , after that Theseus had forsaken her : which Garland , Bacchus placed in the Heaven , as a token of his love . Novidius will have it to be the Crown of the Virgin Mary . 7. ENGONASIS : This Constellation hath the name , because it is expressed under the shape of a man kneeling upon the one knee , and is therefore by the Latines called Ingeniculum . It containeth 29. stars , and wanteth a proper name , because of the great diversity of opinions concerning the same . For some will have it to be Hercules , that mighty Conquerer , who for his 12. labours was thought worthy to be placed in the heaven . and nigh unto the Dragon whom he overcame . Others tell the tale thus : That when the Tyta●s fought against the Gods , they for fear of the Gyants , ran all unto the one side of the heaven : whereupon the Heaven was ready to have fallen , had not Hercules together with Atlas set his neck unto it , and stayed the fall : and for this desert , he was placed in the Heaven . 8 LYRA , the Harp , it containeth 10. stars ; whereof thus goeth the Fable . The River Nilus swelling above his banks , overflowed the Country of Aegypt ; after the fall whereof there were left in the fields divers kinds of living things , and amongst the rest a Tortois● ; Mercury , after the flesh thereof was consumed , the sinews still remaining , found the same , and striking it , he made it yeild a certain sound ; whereupon he made an Harp like unto it , having 3. strings and gave it unto Orpheus the son of Cassiopea . This Harp was of such excellent sound , that Trees , Stons Fowls , and wild Beasts are said to follow the sound thereof . After such time therefore that Orpheus was slain by the women of Thrace , the Muses by the good leave of Jupiter , and at the request of Apollo , placed this Harp in Heaven . Novidius will have it to be the Harp of David , whereby he pacified the evil spirit of Saul . This Constellation was afterwards called Vultur Cad●ens , the falling Grype : and Falco , the Falcon ; or Timpanum , he Timbrel . 9 OLOR , or Cygnus , the Swan , called of the Caldaeans Adigege : it hath 17. stars : of this Constellation the Poets Fable in this manner . Jupiter being overtaken with the love of Laeda , the wife of Tyndarus King of Oebalia , and knowing no honester way to accomplish his desire , procured Venus to turn her selfe into an Eagle , and himself he turned into the shape of a Swan : Flying therefore from the Eagle , as from his natural enemy , that earnestly pursued him , he lighted of purpose in the lap of Leda , and , as it were , for his more safety , crept into her bosome . The woman not knowing who it was under that shape , but holding ( as she thought ) the Swan fast in her armes , fell a sleep : In the mean while Jupiter enjoyed his pleasure ; and having obtained that he came for , betook him again unto his wings ; and in memorial of his purpose ( attained under that form ) he placed the Swan among the stars . Ovid calleth this Constellation Milvius , the Kite , and telleth the tale thus . The Earth being greatly offended with Jupiter , because he had driven Saturn his father out of his Kingdom , brought forth a monstrous Bull , which in his hinder parts was like a Serpent ; and was afterwards called the Fatal-Bull ; because the Destinies had thus decreed , that whosoever could slay him , and offer up his entrails upon an Altar , should overcome the eternal Gods. Briarens that mighty Gyant , and ancient enemy of the Gods overcame the Bull , and was ready to have offered up his entrails according to the decree of the Destinies : But Jupiter fearing the event , commanded the Fowls of the Air to snatch them away : which although to their power , they endavoured , yet there was none of them found so forward and apt to that action as the Kite , and for that cause he was accordingly rewarded with a place in Heaven . Some call this Constellation 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 that is , the Bird : others call it Vultur●● volans , the Flying Grype : It is also called Gallina , the Hen. Unto this Constellation do belong two unformed stars . 10. CASSIOPEIA , She consisteth of 13. Stars . This was the Wife of Cepheus , and mother of Andromeda , whom Perseus married , and for his sake was translated into Heaven , as some write . Others say that her beauty being singular , she waxed so proud , that she preferred her self before the Nereides , which were the Nymphs of the Sea : for which cause , unto her disgrace , and the example of all others that in pride of their hearts would advance themselves above their betters , she was placed in the Heaven with her head as it were downwards , so that in the revolution of the Heavens , she seemeth to be carried head-long . 11. PERSEUS , he hath 26. Stars . This was the Son of Jupiter , whom he in the likeness of a Golden shower begat upon Danae , the daughter of Acrisius . This Perseus coming unto mans estate , and being furnished with the Sword , Hat , and Wings of his brother Mercury , and the Shield of his sister Minerva , was sent by his foster-father Polidectes , to kill the Monster Medusa , whom he slew ; and cuting off her head , carried it away with him : But as he was hastning homeward , flying in the Air , he espied Andromeda the daughter of Cepheus and Cassiopeia , for the pride of her mother , bound with a Chain unto a Rock , by the Sea side there to be devoured by a Whale : Perseus taking notice and pitty of the case , undertook to fight with the Monster , upon condition that Andromeda might be his Wife ; to be short , he delivered Andromeda , married her , and returning homeward unto the Isle Seriphus ▪ he found there his Grand-father Acrisius , whom by mischance , and unadvisedly , he slew with a quoit : ( or as Ovid reporteth , with the terrible sight of the horrible head of Medusa , not knowing that it was his Grand-father : but afterwards understanding whom he had slain , he pined away through extream sorrow : whereupon Jupiter his Father pittying his grief , took him up into Heaven and there placed him in that form wherein he overcame Medusa , with the sword in one hand , and the head of Medusa in the other , and the Wings of Mercury at his Heels . This Constellation , because of the unluckiness thereof , is called by Astrologers Cacodemon , ( i. e. ) Unlucky , and Unfortunate . For ( as they say ) they have observed it , that whatsoever is born under this Constellation , having an evil Aspect , shall be stricken with sword , or loose his Head. Novidius saith that it is David with Goliah his head in the one hand , and his sword in the other . The unformed Stars belonging unto this Constellation , are three . 12. AURIGA , the Waggoner , or Carter : he consisteth of 14. Stars ; the Arabians call him Alaiot ; the Greeks Heniochus , i. e. a man holding a bridle in his hand , and so is he pictured . Eratostenes affirmeth him to be Ericthonious King of Athens , the son of Vulcane : who having most deformed feet , devised first the use of the Wagon or Chariot , and joyned horses together to draw the same , to the end that he sitting therein , might the better conceal his deformities . For which invention , Jupiter translated him into the Heavens . In this Constellation there are two other particular Constellations to be noted ; whereof the one consisteth but of one Star alone , which is in the left shoulder of Auriga , and is called Hircus , or Capra the Goat ; the Arabians call it Alhaioth : The other consisteth of two little Stars a little beneath the other , standing as it were in the hand of Auriga ; this Constellation is ●called Haedi , the Kids . The tale is thus ; Saturn ( as you heard before ) had received of the Oracle , that one of his sons should put him out of his Kingdom , whereupon he determined to devoure them all : Ops by stealth conveyed away Jupiter , and sent him to Melissus King of Crete , to be nourished : Melissus having two daughters , Amalthaea and Melissa , committed Jupiter unto their Nursery ; Amalthaea had a Goat that gave suck unto two Kids , so that by the milk of this Goat , she nourished Jupiter very well . To requite this her care and courtesie , Jupiter ( after he had put his Father out his Kingdom ) translated her Goat and her two Kids , into Heaven ; and in remembrance of the Nurse , the Goat is called Capra Amalthaea . Novidius saith , that when Christ was born , and his birth made manifest by the Angels unto the Shepherds , one of them brought with him for a Present , a Goat and two young Kids ; which in token of his good will , were placed in Heaven . 13. OPHIUCHUS , or SERPENTARIUS , That is , the Serpent-bearer . This Constellation hath no proper name , but is thus entituled , because he holdeth a Serpent in his hands . It containeth 24. Stars . Some say that it is Hercules , and report the tale on this manner Juno being a great enemy to Hercules , sent two snakes to kill him as he lay sleeping in his Cradle : but Hercules being a lusty Child ( for Jupiter had spent two daies in begetting him ) without much ado strangled them both : In memorial of so strange an event , Jupiter placed him in the Heavens , with a Serpent in his hands , 14. SERPENS , the Serpent of Ophiuchus , which consisteth of 18. Stars . Some say that it is one of the Serpents that should have slain Hercules in his Cradle . Novidius saith , it is the Viper that bit Paul by the hand . Others deliver the tale in these words ; Glaucus the son of Minos King of Crete , was by misfortune drowned in a Barrel of Honey : Minos his father craved the help of Aesculaptus the Physitian : and that he might be driven per ▪ force to help the child , he shut him up in a secret place , together with the dead carcass : whiles Aesculapius stood in a great maze with himself what were best to be done , upon a sudden there came a Serpent creeping towards him ; the which Serpent he slew with the staff which he had in his hand . After this there came another Serpent in , bringing in his mouth a certain herb , which he laid upon the head of the dead Serpent , whereby he restored him unto life again . Aesculapius using the same her● , wrought the same effect upon Glaucus . Whereupon ( after that ) Aesculapius ( whom some affirm to be Ophiuchus ) was placed in the Heaven , and the Serpent with him . 15. SAGITTA , or Telum ; the Arrow or Dart. This was that Arrow wherewith Hercules slew the Eagle or Grype that fed upon the Liver of Promotheus , being tyed with chains to the top of the mount Caucasus ; and in memorial of that deed , was translated into Heaven . Others will have it to be one of those Arrows which Hercules at his death gave unto Phyloctetes , upon which the Destiny of Troy did depend . The whole Constellation containeth five Stars . 16. AquILA , the Eagle , which is called Vultur Volans , the flying Grype : It hath in it 9. Stars . The Poetical reason of this Constellation , is this ; Jupiter transforming himself into the form of an Eagle , took Ganimides the Trojan Boy , whom he greatly loved , up into Heaven , and therefore in signe thereof ( because by that means he performed his purpose ) he placed the figure of the Eagle in the Heaven . There belong unto this Constellation 6. Stars ( before time ) unformed , but now brought into the Constellation of Antinous . But whereupon that name should come , I know not , except it were that some man devised it there to curry favour with the Emperour Adrian , who loved one Antinous Bithynicus so well , that he builded a Temple in his honour at Mantinea . 17. DELPHINUS , the Dolphin : It containeth 10. Stars ; yet Ovid in his second Book de Fastis , saith that it hath but nine . Neither did the ancient Astronomers attribute unto it any more , according to the number of the Muses ; because of all other Fishes , the Dolphin is said to be delighted with Musick . The tale goeth thus concerning this Constellation . When Neptune the God of the Sea greatly desired to match with Amphitrite , she being very modest and shame-faced , hid her self : whereupon he sent many messengers to seek her out , among whom , the Dolphin by his good hap , did first find her ; and perswaded her also to match with Neptune : For which his good and trusty service , Neptune placed him in the Heaven . Others say , that when Bacchus had transformed the Mariners that would have betrayed him , into Dolphins , he placed one of them in Heaven , that it might be a lesson for others to take heed how they carried any one out of his way , contrary both to his desire , and their own promise . Novidius referreth this Constellation unto the Fish which saved Jonas from drowning . 18. EQUICULUS , is the little Horse , and it consisteth of 4. Stars . This Costellation is named almost of no Writer , saving Ptolomeus , and Alphonsus , who followeth Ptolomy , and therefore no certain tale or History is delivered thereof , by what means it came into Heaven . 19. EquuS ALATHS , the Winged Horse , or Pegasus , it containeth 20. Stars . This Horse was bred of the blood of Medusa , after that Perseus had cut off her head , and was afterwards taken and tamed by Bellerophon , whiles he drank of the River Piren● by Corinth , and was used by him in the conquest of Chimera : After which exploit , Bellerophon , being weary of the earthly affaires , endevoured to fly up into Heaven : But being amazed in his flight , by looking down to the earth , he fell from his horse ; Pegasus notwithstanding continuing his course , ( as they feigne ) entred into Heaven , and there obtained a place among the other Constellations . 20. ANDROMEDA , She consisteth of 23. Stars ; but one of them is common both unto her , and Pegasus , This was the daughter of Cepheus and Cassiopeia , and the Wife of Perseus : the reason why Minerva , or Jupiter placed her in the Heavens , is before expressed . Novidius referreth this Constellation unto Alexandria the Virgin , whom S. George through the good help of his horse , delivered from the Dragon . 21. TRIANGULUM , the Triangle , called also Delt●ton , because it is like the fourth letter of the Greeks Alphabet Δ , which they call Delta ; it consisteth of four stars . They say it was placed in Heaven by Mercury , that thereby the head of the Ram might be the better known . Others say , that it was placed there in honour of the Geometricians , among whom , the Triangle is of no small importance . Others affirme , that Ceres in times past requested Jupiter that there might be placed in Heaven some Figure representing the form of Sicilie , an Island greatly beloved of Ceres , for the fruitfulnesse thereof : now this Island being triangular , ( at her request ) was represented in the Heaven under that form . Thus much concerning the Constellations of the Northern Hemisphear . Now follow the Poeical Stories of the Constellations of the Southern Hemisphear . Secondly , Of the Southern Constellations . 1. CETUS , the Wha●● , it is also called the Lion , or Bear of the Sea. This is that monstrous fish that should have devoured Andromeda , but being overcome by Perseus , was afterwards translated into Heaven by Jupiter , as well for a token of Perseus his manhood , as for the hugeness of the fish it self . This constellation consisteth of 22. Stars . 2. ORION , this hath 38. Stars . The Poetical reason of his translation into the Heaven , shall be shewn in the Scorpion , amongst the Zodietical Constellations . The Ancient Romans called this Constellation Jugala ; because it is most pestiferous unto Cattel , and as it were the very cut-throat of them . There are bright Stars in his girdle , which we commonly call our Ladies yard , or wa●d . Novidius , applying this sword of Orion unto Scripture , will have it to be the sword of Saul , afterwards called Paul , wherewith he persecuted the Members of Christ : which after his conversion was placed in Heaven . In his left shoulder there is a very bright Star , which in Latine is called Bellatrix , the Warriour , in the foeminine gender . I cannot find the reason except it be this ; that Women born under this Constellation shall have mighty tongues . The reason of the Ox-hide which he hath in his hand , may be gathered out of the next story . 3. FLUVIUS , the River ; it comprehendeth 34. Stars . It is called by some Eridanus , or Padus ; and they say that it was placed in Heaven in remembrance of Phaeton , who having set the whole World on fire by reason of misguiding of his father Phoebus his charriot , was slain by Jupiter with a thunder-bolt , and tumbling down from Heaven , fell into the River Eridanus , or Padus , which the Italians call Po. Others say that it is Nylus , and that that Figure was placed in the Heaven because of the excellency of that River , which by the Divines is called Gihon ; and is one of the Rivers of Paradice . Others call it Flumen Orionis , the flood of Orion ; and say , that it was placed there , to betoken the Off-spring from whence Orion came : for the tale is thus reported of him . Jupiter , Neptune , and Mercury , travelling upon the earth in the likeness of Men , were requested by Hyreus to take a poor lodging at his House for a Night : they being overtaken with the evening , yeilded unto his request ; Hyreus made them good cheer , killing an Ox for their better entertainment : The Gods seeing the good heart of the old man , willed him to demand what he would in recompence of his so friendly cheer . Hyreus and his Wife being old , requested the Gods to gratify them with a Son. They to fulfil his desire , called for the hide of the Ox that was slain , and having received it , they put it into the Earth , and made water into it all three together , and covering it , willed Hyreus within ten moneths after to dig it out of the Earth again ; which he did , and found therein a Man-child ; whom he called Ourion , ab Urina , of piss ; although afterwards by leaving out the second letter , he was named Orion . At such time therefore as he was placed in Heaven , this flood was joyned hard to his heels , and the Ox hide wherein the Gods did piss , was set in his left hand , in memorial of his Off-spring . 4. LEPUS , the Hare , which consisteth of 12. stars . This Constellation was placed in Heaven between the legs of Orion , to signifie the great delight in hunting which he had in his life time . But others think it was a frivolous thing , to say that so notable a fellow as Orion would trouble himself with so smal and timerous a beast as the Hare : and therefore they tell the tale thus . In times past there was not a Hare left in the Isle D●r●s : a certain youth therefore of that Island , being very desirous of that kind of beast , brought with him from another Country thereabout , an Hare great with young ; which when she had brought forth , they in time became so acceptable unto the other Countrimen , that every one almost desired to have and keep a Hare . By reason whereof , the number of them grew to be so great , within a short space after , that the whole Island became full of Hares , so that their Masters were not able to find them meat : whereupon the Hares breaking forth into the fields , devoured their Corn. Wherefore the inhabitants being bitten with hunger , joyned together with one consent , and ( though with much ado ) destroyed the Hares . Jupiter therefore placed this Constellation in the Heavens as well to express the exceeding fearfulness of the beast , as also to teach men this lesson ; that there is nothing so much to be desired in this life , but that at one time or an other it bringeth with it more grief then pleasure . Some say , that it was placed in Heaven at the request of Ganimedes , who was greatly delighted with hunting the Hare . 5. CANIS MAIOR , the Great Dog , it consisteth of 18. Stars . It is called Sirins Canis , because he causeth a mighty drought by reason of his heat . This is the Constellation that giveth the name unto the Canicular or Dog-days ; whose beginning and end is not alike in all places , but hath a difference according to the Country and Time : as in the Time of Hypocrates the Phisitian , who lived before the time of Christ 400 , years , the Canicular days began the 13. or 14. of July . In the time of Avicenna , the Spaniard , who lived in the year of our Lord 1100. the Canicular days began the 15 , 16 , or 17. of July . In our Country , they begin about S. James-tide , but we use to account them from the 6. of July , to the 17. of August ; which is the time when the Sun beginneth to come near unto , and to depart from this Costellation . Novidius will have it to be referred to Tobias Dog ; which may very well be , because he hath a tail ; Tobias Dog had one ; as a certain fellow once concluded , because it is written that Tobias his Dog fawned upon his Master , therefore it is to be noted ( said he ) that he had a tail . The Poets say , that this is the Dog whom Jupiter set to keep Europa , after that he had stolen her away , and conv●ied her into Crete , and for his good service was placed in Heaven . Others say , that it was one of Orion his Dogs . There belong unto this Constellation 11. Stars unformed . 6. CANIS MINOR ; the Lesser Dog ; this of the Greeks is called Procyon , of the Latines Ante Canis ; it containeth but two Stars . Some say , that this also was one of Orions Dogs , Others rather affirm it to be Mera , the Dog of Origone , or rather of Icarius her father , of whom mention is made in the Constellation of Bootes , and Virgo . This Dog of meer love to his Master , being slain , as is aforesaid , threw him self into the River Anygrus , but was afterward translated into Heaven with Origone . Among the Poets there is great dissention which of the two should be the Dog of Origone ; some saying one , and some the other , and therefore they do many times take the one for the other . 7. ARGO NAVIS , the Ship Argo , which comprehendeth 41. Stars ; this is the Ship wherein Jason did fetch the Golden Fleece from Colchis , which was afterward placed in Heaven as a memorial , not only because of the great Voyage , but also , because ( as some will have it ) it was the first Ship wherein any man sayled . Their reason why this Ship is not made whole is , that thereby men might be put in mind not to despair , albeit that their Ship miscarry in some part now and then . Some avouch it to be the Ark of Noe. Novidius saith it is the Ship wherein the Apostles were , when Christ appeared unto them walking on the Sea. In one of the Oars of this Ship , there is a great Star , called Canopus , or Canobus , which the Arabians called Shuel , as it were a bone-fire , because of the greatness thereof . It is not seen in Italy , nor in any Country on this side of Italy . Some say that Canobus the Master of Menelaus his Ship , was transformed into this Star. 8. HYDRA , the Hydre ; that hath 25. Stars , and two unformed . 9. CRATER , the Cup , or standing piece ; that hath seven Stars . Some say that this was the cup wherein Tagathon , that is , the chief God , mingled the stuff whereof he made the souls of Men. 10. CORVUS , the Crow ; this hath seven Stars . These 3. Constellations are to be joyned together , because they depend upon one History , which is this . Upon a time Apollo made a solemne feast to Jupiter , and wanting water to serve his turn , he delivered a cup to the Crow ( the bird wherein he chiefly delighted ) and sent him to fetch water therein : The Crow flying towards the River , espyed a Fig-tree , fell in hand with the Figs , and abode there till they were ripe : In the end , when he had fed his fill of them , and had satisfied his longing , he bethought himself of his errand , and by reason of his long delay , fearing a check , he caught up a snake in his bill , brought it to Apollo , and told him that the snake would not let him fill the Cup with water . Apollo seeing the impudency of the bird gave him this gift , that as long as the Figs were not ripe upon the Tree , so long he should never drink : and for a memorial of the silly excuse that he made , he placed both the Crow , Cup , and Snake ▪ in Heaven . 11. CENTAURUS , the Centaure , which comprehendeth 37. Stars . Some say , that this is Typhon , others call him Chiron , the Schoolmaster of those three excellent men , Hercules Achiles , and Aesculapius ; unto Hercules he read Astronomy , he trained up Achilles in Musick , and Aesculapius in Physick : and for his upright life he was turned into this Constellation . Yet Virgil calleth Sagit●arius by the name of Chiron . In the hinder feet of this Constellation , those stars are set which are called the Crosiers , appearing to the Mariners as they fail towards the South Sea , in the form of a crosse , whereupon they have their name . The four stars which are in the Garnish of the Centaures Spear , are accounted by Proclus as a peculiar Constellation , and are called by him Thyrsilochus , which was a Spear compassed about with vine leaves : but they are called by Copernicus and Clavius , and other Astronomers , the stars of his Target . It should seem that they were deceived by the old translation of Ptolome , wherein Scutum is put for Hasta , i. e. the Target , for the Spear , as it is well noted by our Countryman M. R. Record , in his Book intituled The Castle of knowledge . 12 LUPUS , the Wolf , or the beast which the Centaùre holdeth in his hand , containeth 19. stars ; the Poetical reason is this , Chiron the Centaure being a just man , was greatly given the worship of the Gods : for which thing , that it might be notified to all posterity , they placed him by this beast , which he seemeth to stick and thrust through with his Spear , ( as it were ) ready to kill for sacrifice . 13. ARA , the Alter , it is also called Lar , or Thuribulum , i. e , a Chimney with the fire , or a Censor . It consisteth of seven stars , and is affirmed of some Poets , to be the Alter whereon the Centaure was wont to offer up his sacrifice . But others tell the tale thus , When as the great Gyants called the Tytans , laboured as much as might be to pull Jupiter out of Heaven , the Gods thought it good to lay their heads together , to advise what was best to be done : Their conclusion was , that they should all with one consent joyn hands together to keep out such fellows : and that this their league might be confirmed , and throughly ratified ; they caused the Cyclops , ( which were work-men of Vulcan ) to make them an Altar : about this Altar all the Gods assembled , and there sware , that with one consent they would withstand their enemies ; afterwards , having gotten the victory , it pleased them to place this Altar in Heaven , as a memorial of their League , and a token of that good which unity doth breed . 14. CORONA AUSTRINA , the South Garland , it hath 13. Stars . Some say that it is some trifling Garland which Sagittarius was wont to wear , but he cast it away from him in jest , and therefore it was placed between his legs : others call it the Wheel of I xion , whereupon he was tormented for that great courtesy he would have offered unto Juno , thinking indeed to have gotten up her belly : but Jupiter seeing the impudency of the man , tumbled him out of Heaven ( where by the licence of the Gods he was somtime admitted as a guest ) into Hell , there to be continually tormented upon a Wheel . The Figure of which Wheel was afterwards placed in Heaven , to teach men to take heed how they be so saucie to make such courteous proffers unto other men wives . The Greeks call this Constellation by the name of Uraniscus , because of the Figure thereof : For it representeth the palate or roof of the mouth , which they call Uraniscus . 15. The last is PISCIS AUSTRINUS , or Notius , the South Fish , which comprehendeth 11. Stars besides that which is in the mouth thereof , belonging to the water , which runneth from Aquarius , and is called by the Arabians Fomahant . The reason why this Fish was placed in the Heaven , is uncertain : yet some affirm , that the daughter of Venus going into a water to wash her self , was suddenly transformed into a fish ; the which fish was afterwards translated into Heaven . The unformed Stars belonging unto this Constellation are six . Thus much concerning the Constellations of the Northern and Southern Hemisphears ; now follow the Poetical Stories of the Zodiatical Constellations . Thirdly , Of the Zodietical Constellations : 1. ARIES , the Ram , it is called by the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , it containeth in it 13. Stars , which were brought unto this Constellation by Thyestes , the son of Pelops , and brother of Atreus . This is the Ram upon which Phrixus , and Helle his sister , the children of Athamas did sit , when they fled from their step-mother Ino , over the Sea of Hellespont : which Ram was afterward for his good service , translated into Heaven by Jupiter . Others say , that it was that Ram which brought Bacchus unto the spring of water , when through drought he was likely to have perished in the desert of Lybia . Novidius will have this to be the R●m which Abraham offered up in stead of his son Isaac . The Star tha● is first in the head of the Ram , is that from whence our ●ater Astronomers do account the Longitude of all the rest , and it is distant from the head of Aries , in the tenth Sphear , 27. degrees 53. minutes . The unformed Stars belonging unto this Constellation , are five . 2. TAURUS , the Bull , which consisteth of 23. stars . This was translated into Heaven in memorial of the rape committed by Jupiter on Europa the daughter of Agenor , King of Sidon ; whom Jupiter in the likeness of a white Bull stole away , and transported into Candia . Others say , That it was 〈◊〉 the daughter of Inacus : whom Jupiter loved , and turned into the form of a Cow , to the intent that Juno comming at unawares , should not perceive what a part he had playd : Jupiter afterward in memorial of that craftie conveyance , placed that Figure in Heaven ; The reason why the Poets name not certainely whether it be a Cow or a Bull , is because it wanteth the hinder parts ; yet of the most of them it is called a Bull. In the Neck of the Bull there are certain stars standing together in a cluster , which are commonly called the seven Stars ; although there can hardly he discerned any more then six . These are reported to be the seven daughters of Atlas , called Atlan●iades , whereof six had company with the immortal Gods , but the seventh ( whose name was Merope ) being married unto Sysiphus a mortal man , did herefore withdraw and hide her self , as being ashamed that she was not so fortunate in matching her self as her sisters were . Some say , that that star which is wanting is Electra , the eldest daughter of Atlas , and that therefore it is so dim , because she could not abide to behold the destruction of Troy ; but at that time and ever since , she hid her face . The reason why they were taken up into Heaven , was , their great pittie towards their father , whose mishap they bewayled with continual tears . Others say , that whereas they had vowed perpetual virginity , and were in danger to lose it , by reason of Orion , who greatly assayled them , being overtaken , with their love ; they requested Jupiter to stand their friend ; who translated them into stars , and placed them in that part of Heaven . The Poets call them Pleiades , because when they rise with the Sun , the Mariners may commit themselves to the Sea. Others will have them to be so termed a pluendo ; because they procure rain . Others give them this name , of the Greek word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , because they be many in number . They be also called Vergiliae , because they rise with the Sun in the Spring time : likewise Athoraiae , because they stand so thick together . Our men●call them by the name of the seven Stars , or Brood Hen. The Astronomers note this as a special thing concerning these stars , that when the Moon and these stars do meet together , the eyes are not to be medled withall , or cured if they be sore : their reason is , because they be of the nature of Mars and the Moon . Moreover , there be five stars in the face of the Bull , representing the form of the Roman letter V , whereof one ( which is the greatest ) is called the Bull 's Ey . They be called Hyades , and were also the daughters of Atlas , who so long bewayled the death of Hyas their brother , slain by a Lion , that they died for sorrow , and were afterwards placed in Heaven for a memorial of that great love they bare to their brother . The ancient Romans call the Bul 's Ey , Parilicium , or Palelicium ; of Pales their goddesse ; whose feast they celebrated after the conjunction of this star and the Sun. The unformed stars belonging unto this Constellation , are eleven . 3. GEMINI , the Twins ; it consisteth of 18. stars . The Poets say they are Castor and Pollux , the sons of Leda , brethren most loving , whom therefore Jupiter translated into Heaven . Some say that the one of them is Appollo , and the other Hercules : but the most affirm the former . The unformed stars of this Constellation are seven , whereof one is called Tropus , because it is placed next before the foot of Castor . 4. CANCER , the Crab , it hath 9. Stars . This is that Crab which bit Hercules by the heele as he fought with the Serpent Hydra i● the Fen Lerna , and for his forward service , was placed in Heaven by Juno , the utter enemy of Hercules . In this Constellation , there are Stars much spoken of by the Poets ; although they be but small ; whereof one is called the Crib , other two are the two Asses , whereof one was the Asse of Bacchus , the other of Vulcan , whereon they rode to battel , when as the Gyants made war with the Gods ; with whose braying and strange noise , the Gyants were so scared upon the sudden , that they forsook the field , and fled . The Gods getting the victory , in tryumphing manner translated both the Asses , and their manger into Heaven . The unformed stars of this Constellation are four . It is called animal re●rogradum , for when the Sun cometh into his Signe , he maketh Retrogradation . 5. LEO , the Lyon ; it hath 27. Stars , this is that Lyon which Hercules overcame in the wood of Nemaea and was placed in Heaven in remembrance of so notable a deed . Novidius saith , this was one of the Lyons which were in the den into which Daniel was cast , and was therefore placed in Heaven , because of all other he was most friendly unto Daniel . In the breast of this Constellation is that notable great Star , the light whereof is such , as that therefore it is called by Astronomers 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Regulus i. e. the Victroy , or little King among the rest . The unformed Stars belonging to the Lyon are eight ; whereof three make the Constellation which is now called Coma Berenices , that is , the hair of Berenice . This Constellation was first found out and invented , by Canon the Mathematician , but described by Calimachus the Poet. The occasion of the Story was this , P●olomeus Evergetes having married his sister Berenice , was shortly after enforced to depart from her , by reason of the wars he had begun in Asia : whereupon Berenice made this vow , that if he returned home again in safety , she would offer up her hair in Venus Temple . P●olome returned safe ; and Berenice , according to her vow , cut off her hair and hung it up . After certain daies , the hair was not to be found ; whereupon Ptolome the King was greatly displeased : but Canon , to please the humor of the King , and to curry favour with him , perswaded him that Venus had conveyed the hair into Heaven . Canon attributeth seven Stars unto it , but Ptolome allotteth it but three , because the other be insensible , 6. VIRGO , the Virgin , it hath 26. Stars . This is affirmed to be Justice , which among all the Gods somtime living upon the Earth , did last of all forsake the same , because of the wickedness that began to multiply therein , and chose this place for her seat in Heaven . Others say , that it was Astraea , the daughter of Astraeus , one of the Gyants that were called Titans , who fighting against the Gods , Aftraea took their parts against her own Father , and was therefore after her death commended unto the Heavens , and made one of the 12. Signes . Others say , that it was Erigone , the daughter of Icarius , who for that her father was slain by certain drunken men , for very grief thereof did hang her self : but Jupiter taking pitty of the Virgin for her natural affection , translated her into Heaven . In her right wing there is one Star of special note , which by the Astronomers is called Vindemeator ( i. e. ) the gatherer of Graps . This was Ampelos the son of a Satyr and a Nymph , and greatly beloved of Bacchus , unto whom in token of his love , Bacchus gave a singular fair Vine , planted at the foot of an Elme , ( as the manner was in old time . ) But Ampelos in Harvest gathering Graps , and taking little heed to his footing , fell down out of the Vine , and brake his neck . Bacchus in memorial of his former affection , translated him into Heaven , and made him one of the principal Stars in this Constellation . There is another great Star in the hand of the Virgin , called of the Latines Spica , of the Greeks Stachus , of the Arabians Azimech ( i. e. ) the Ear of Corn : whereby they signify , that when the Sun cometh to this Signe , the Corn waxeth ripe . Albumazar the Arabian , and Novidius , take this Constellation for the Virgin Mary . The unformed Stars in this Constellation , are six . 7. LIBRA , the Ballance , it containeth 8 Stars . Cicero calleth it Jugum the Yoak , and here it is to be noted , that the Ancient Astronomers that first set down the number of the Constellations contained in the Zodiack , did account but eleven therein , so that the Signe which now is called Libra , was heretofore called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , that is to say , the Claws of the Scorpion , which possesseth the space of two whole Signes . But the latter Astronomers , being desirous to have 12. Signes in the Zodiack , called those eight whereof the Claws of the Scorpion do consist , by the name of Libra ; not that there was any Poetical Fiction to induce them thereto , but only moved by this reason , because the Sun joyning with this Constellation , the Day and the Night are of an equal length , and are ( as it were ) equally poyzed in a pair of Ballance . Yet ( as I remember ) some will have this to be the Ballance wherein Justice , called also Astraea , weighed the deeds of mortal men , and therein presented them unto Jupiter . It hath 9. unformed Stars appertaining unto it . 8. SCORPIO , the Scorpion ; called of the Arabians , Alatrab ; of Cicero , Nepa . It consisteth of 21 , Stars . The Fiction is thus . Orion the son of Hyreus greatly beloved of Diana , was wont to make his boast , that he was able to overcome what beast soever was bred upon the Earth : The Earth being moved with this speech brought forth the Scorpion , whereby Orion was stung to death . Jupiter thereupon ( at the request of the Earth , ) translated both the Scorpion , and Orion into Heaven ; to make it a lesson for ever for mortal men , not to trust too much unto their own strength ▪ and to the end he might signify the great enmity between them , he placed them so in the Heaven , that whensoever the one ariseth , the other setteth ; and they are never both of them seen together above the Horizon at once : Gulielmus Postellus will have it to be the Serpent which beguiled Eve in Paradise . The unformed Stars about this Scorpion are three . 9. SAGITTARIUS , the Archer . It hath thirty one Stars . Touching this Signe , there are among the Poets many and sundry opinions . Some say that it is Crocus , the son of Puphen● , that was nurse unto the Muses . This Crocus was so forward in learning of the liberal sciences , and in the practise of feats of activity , that the Muses entreated Jupiter that he might have a place in Heaven . To whose request Jupiter inclining , made him one of the 12. Signes : And to the end that he might express the excellent qualities of the Man , he made his hinder parts like unto a Horse , thereby to signify his singular knowledge in Horse-manship : and by his Bow and Arrow , he declared the sharpness of his Wit. Whereupon the Astrologers have this conceit , that he that is born under Sagittarius , shall attain to the knowledge of many Arts , and be of prompt wit , and great courage . Virgil affirmeth this to be Chiron the Centaur , who for his singular learning and Justice , was made the Master of Achilles . At which time Hercules coming to visit him ( for he had heard both of the worthiness of the School-master , and of the great hopes of the Scholler ) brought with him his quiver of Arrows dipped in the blood of the Serpent Hydra ; but Chiron being desirous to see his shafts , and not taking heed of them , being in his hand , let one of them fall upon his foot , and being greatly tormented , not only by the anguish of the poyson working in the wound , but much more because he knew himself to be immortal , and his wound not to be recovered by medicine , he was enforced to make request unto the Gods , that he might be taken out of the World , who pittying his case , took him up into Heaven , and made him one of the 12. Signes . 10. CAPRICORNUS , the Goat , it consisteth of 28. Stars . The Poets say , that this was Pan , the God of the Shepherds , of whom they faign in this manner : The Gods having war with the Gyants , gathered themselves together into Aegypt , Typhon the Gyant pursued them thither , whereby the Gods were brought into a quandary , that well was he that by changing his shape might shift for himself , Jupiter turned himself into a Ram : Apollo became a Crow : Bacchus , a Goat : Diana lurked under the form of a Cat : Juno transformed her self into a Cow : Venus into a Fish : Pan leaping into the River Nilus , turned the upper part of his body into a Goat , and the lower part into a Fish. Jupiter wondring at his strange device , would needs have that Image and Picture translated into Heaven , and made one of the 12. Signes . In that the hinder part of this Signe is like a Fish , it betokeneth that the latter part of the moneth wherein the Sun possesseth this Signe , inclineth unto Rain , 11. AQUARIUS , the Waterman . It hath 42. Stars , whereof some make the Figure of the Man : other some the Waterpot ; and some , the stream of water that runneth out of the pot . This is feigned to be Ganimedes the Trojan , the son of Oros , and Callirhoe whom Jupiter did greatly love for his excellent favour and beauty , and by the service of his Eagle carried him up into Heaven , where he made him his Cup bearer , and called him Aquarius . Others notwithstanding thinke it to be Deucallon the son of Prometheus whom the Gods translated into Heaven , in remembrance of that mighty deluge which happned in his time , whereby mankind was almost utterly taken away from the face of the earth . The unformed stars belonging unto this Signe are three . 12. PISCES , the Fishes : these , together with the line that knitteth them together , contain 24. Stars . The Poets say that Venus and Cupid her son coming upon a certain time unto the River Euphrates , and sitting upon the bank thereof , upon a sudden espied Typhon the Gyant , that mighty and fearfull enemy of the Gods coming towards them ; Upon whose sight , they being stricken with exceeding fear , lept into the River , where they were received by two Fishes , and by them saved from drowning . Venus for this good turn , translated them into Heaven . Gulielmus Postellus would have them to be the two Fishes wherewith Christ fed the 5000. men . The unformed stars of this Constellation , are four . Thus have I breifly run over the Poetical reasons of the Constellations : It remains now that I speak of the Milky way . VIA LACTEA , or Circulus Lacteus ; by the Latines so called ; and by the Greekes Galaxia ; and by the English the Milkey way . It is a broad white Circle that is seen in the Heaven , in the North Hemisphere , it beginneth at Cancer , on each side the head thereof , and passeth by Auriga , by Perseus , and Cassiopeia , the Swan ; and the head of Capricorn the tayl of Scorpio , add the feet of Centaur , Argo the Ship , and so unto the head of Cancer . Some in a sporting manner do call it Wa●ling street ; but why they call it so , I cannot tell ; except it be in regard of the narrownesse that it seemeth to have ; or else in respect of that great high way that lieth between Dover and S. Albons , which is called by our men , Watling street . Ovid saith , that it is the great Causey , and the high way that leadeth unto the Pallace of Jupiter ; but he alledgeth not the cause of the whiteness : belike he would have us imagine that it is made of white Marble . Others therefore alledge these causes : Jupiter having begotten Mercury of Mai●● the daughter of Atlas , brought the child when he was born , to the breast of Juno lying a sleepe : But Juno awaking threw the child out of her lap , and let the milke run out of her breast in such aboundance that ( spreading it self about the Heaven ) it made that Circle which we see . Others say , that it was not Mercury , but Hercules ; and that Juno did not let the milke run out of her breast ; but that Hercules suckt them so earnestly , that his mouth run over , and so this Circle was made . Others say ; that Saturn being desirous to devour his children , his wife Ops presented him with a stone wrapped in a clout , instead of his child : This stone stuck so fast in Saturn his throat as he would have swallowed it , that without doubt he had there-withall been choaked , had he not been relived by his wife , who by pressing the milke out of her breasts saved his life : the milke that missed his mouth ( whereof you must suppose some sufficient quantity ) fell on the Heavens , and running along made this Circle . Dr HOOD Commenting upon Constellations , saith ; The Stars are brought into Constellations , for Instruction sake , things cannot be taught without names : to give a name to every Star had been troublesome to the Master and for the Scholler ; for the Master to devise , and for the Scholler ; to remember : and therefore the Astronomers have reduced many Stars into one Constellation , that thereby they may tell the better where to seek them ; and being sought , how to express them . Now the Astonomers did bring them into these Figures , and not into other , being moved thereto by these three reasons : first these Figures express some properties of the Stars that are in them ; as those of the Ram to to be hot and dry ; Andromeda chained betokeneth imprisonment , the head of Medusa cut off signifieth the loss of that part : Orion with his terrible and threatning gesture , importeth tempest and terrible effects : The Serpent , the Scorpion , and the Dragon , signify poyson : The Bull insinuateth a melancholy passion : The Bear inferreth cruelty , &c. Secondly , the Stars , ( if not precisely , yet after a sort ) do represent such a Figure , and therefore that Figure was assigned them : as for example , the Crown , both North and South : the Scorpion , and the Triangle , represent the Figures which they have . The third cause was the continuance of the memory of some notable men , who either in regard of their singular pains taken in Astronomy , or in regard of some other notable deed , had well deserved of Man-kind . The first author of every particular Constellation is uncertain ; yet are they of great antiquity ; we receive them from Ptolomie , and he followed the Platonick● ; so that their antiquity is gre●a ▪ Moreover we may perce●ve them to be ancient by the Scriptures , and by the Poets . In the 38. Chapter of Job there is mention made of the Pleiades , Orion , and Aucturus , and Mazzaroth , which some interpret the 12. Signes : Job lived in the time of Abraham , as Syderocrates maketh mention in his Book de Commensurandis locorum distantiis . Now besides all this , touching the reason of the invention o● these Constellations , the Poets in setting forth those Stories , 〈◊〉 this purpose , to make men fall in love with Astronomy : When Demosthenes could not get the people of Athens to hear him in a matter of great moment , and profitable for the Common-wealth , he began to tell them a tale of a fellow that sold an Ass ; by the which tale he so brought on the Athenians , that they were both willing to hear his whole Oration , and to put in practice that whereunto he exhorted them . The like intent had the Poets in these Stories : They saw that Astronomy being for commodity singular in the life of man , was almost of all men utterly neglected : Hereupon they began to set forth that Art under these Fictions ; that thereby such as could not be perswaded by commodity , might by the Pleasure be induced to take a view of these matters , and thereby at length fall in love them . For commonly note this , that he that is ready to read the Stories , cannot content himselfe therewith , but desireth also to know the Constellation , or at leastwise some principal Star therein . FINIS . A Discourse OF THE Antiquity , Progress , AND Augmentation OF ASTRONOMIE . FIRST it seems not to be doubted , but that there was some kind of observation of Bodies Coelestial , as soon as there were Men : considering that the spectacle which the Heavens constantly present , is both so glorious , and so usefull , that men could not have eyes to see , and not fix them attentively and considerately thereupon . For , among other Apparences , when they saw the Sun dayly to change the places of its rising and setting ; at certain times of the Year : to approach neerer to the Earth in its Diurnal arch , and at others again to mount up to a height much more sublime and remote from it : and that his coming neerer to the Earth made Winter , and his remove higher made Summer : we say , when they beheld these things ; doubtless , they could not but seriously remark and consider this vicissitude , according to which they might expect the Season would be more hard , or mild , to them in this lower Region of the World. Again , so admirably various did the Moon appear , in her several shapes and dresses of light , that she could not but invite mens eyes , and engage them to frequent Speculations : specially when she assumed those various faces or apparences , at set and certain Times ; in respect whereof it came to pass , that every Nation measured their times and Seasons , by those her constant and periodical circuits ; and this , because those periods succeded much more frequently , than the Erections and Depressions of the Sun. To these , we may add that beautifull shew of the Nightly Stars , undergoing likewise their Variations , according the variety of Seasons ; and more particularly that bright star of Lucifer , rising sometimes later , sometimes earlier , and sometimes not at all before the Sun , and the like . But , what we shall principally note , is only this ; that though Mankind was long , before they came to make inquiries into the Causes of these Coelestial changes and variations , restrained to set periods : yet they observed them from the very first Age , and not only admired , but also accommodated what they observed , to the uses of their Lives and their Successors . Here it might not be fruitless , to remember , that PROMETHEUS , who was imagined to have framed the first Man , was also imagined to have given him an erected Figure , and sublime Countenance ; to the end he might the more advantageously advance his eyes to the Heavens , and contemplate the glory and motions of the Coelestial Lights . But , because this is too General , and rude a way of observation ; and it is our business to look back into those times wherein men first made such Observations of Sydereral bodies , as gave hem the hint and occasion of reducing them to Method , and founding the principles of the Art , or science of Astronomy , thereupon : we must have recourse to the monuments in Sacred Writ , for the understanding of that obscure matter . And indeed , the light we expect from Sacred Leaves , would soon be clear enough to discuss all the darkness , wherein the Original of Astronomy seems involved ; could we but from them deduce the least evidence for that which the learned Antiquarie among the Jewes , Josephus affirms of the Sons of Seth ; viz. that they invented the science of the Heavens , before the Flood , and engraved the same on two Pillars , the one of Brick , the other of Stone , that so it might be preserved in the one , in case the fury of the Deiuge to come , should demolish and deface the other : or if there remained to us any the most slender testimony of the Reason he there gives , of the so great Longevity of men in those dayes ; namely , that the duration of their lives was sufficiently long , to perfect the knowledge of Astronomy , which requires full 600 Years , at the least , to the observation of all the Varieties of Coelestial motions : Whereupon He notes , that the Great Year ( as they call it ) doth consist of six hundred common Years ; the vulgar opinion being , that the Celestial Motions do continually vary , Donec consumpto , Magnus qui dicitur , Anno , Rursus in 〈◊〉 antiquum redeant vaga sidera cursum , Qualia praeteriti steterant ab origine mundi . Again , the business might be deduced from not long after the Flood , if in Scripture we could find but the least word from whence might be argued the truth of what the same Author writes ; namely that the Egyptians were taught Astronomy , by Abraham . Probable enough it is , we confess , that Berosus and others , quoted aswell by Josephus , as Eusebius , had read some such thing in some Books of the old Rabbins : but that the same should be fetched from Holy Writ , is most improbable , therein being no mention at all of any such thing . Besides , there are pious and learned Doctors , and among them Salianus , who will not allow it to be so much as probable , that Abraham should instruct the Egyptians in Astronomy : because of the very smal time of his stay among them in Egypt . It is written indeed , that Abraham came from Ur of the Chaldeans : but not that he received Astronomy from the Chaldeans , or that he delivered it from them to the Egyptians . And therefore they conclude , that what Josephus said of Abrahams reading Astronomy in Egypt , may with more probability be imputed to his Great-grand child , Joseph . Concerning Him , therefore , we read ( in truth ) that he was singularly favourable to the Priests in Egypt , at such time , as all the rest of the people mortgaged their lands to the King , for bread , during that wofull and long Famine . For , He excepted the Lands belonging to the Priesthood , and ( as the Text saith ) assigned them certain portions out of the publick Granaries ; so that from hence may be proved ( what Aristotel tells us , from other Authority ) that amongst the Egyptians , the most ancient Nation , the Priests were exempted from labour , and left to the easy imploiment of their minds : and that this gave them occasion to invent and constitute the Mathematiques : and yet for all this , it is not written , either that Joseph taught those Egyptian Priests the Mathematiques , or that they taught them to him . And , perhaps that Favour He shewed the Priests , was an argument not only of the Respect and Veneration , born them by the King and all his people ; but also of his particular Gratitude toward them ; in that He , who had been bred up only to Sheppardry and Country imployments , and was wholy ignorant of all Arts and Sciences , at his first comming among them being afterwards advanced to the height of a Courtier , and lustre of a Favorite , had bin instructed by them in something more noble and sublime . And truely , the Divine Moses , not long after admitted into the same Court , is not delivered so much to have erudited any others , as to have been himself learned in all the Wisdom of the Egyptians . Nevertheless , considering that this Wisedom of the Egyptians , doubtless contained the Mathematiques ; and that Astronomy was ever esteemed the best and noblest part of them : this Erud●tion of Moses seems to be the most Ancient monument of the Science of the Stars , that can be found in Holy Writ . Astronomy , you see , is of great Antiquity , even upon the Records of Divinity ; and might be proved of much greater , could we but evince ( what some alleage ) that the History of Job was penn'd by Moses , as living a good while after him . Because Job there mentions Arcturus , Orion , and the Hyades , or watery Constellation : and therefore it must be , that before that time the Stars had been ranged and dispossed into certain Asterisms according to some certain method or artificial Theory then in use . But , be the time of his life never so uncertain , yet we may certainly observe from the History thereof ; that it seems Job , being an Alien to the Hebrews , derived his knowledge of God from that which in Scripture is called , Coelorum Exercitus , the Host of Heaven . Forasmuch , as the Invisible things of God are not so well learned from any visible things of Nature , or the effects of his Wisedom and Power , as from the Coelestial Orders and therefore Synesius justly calling Astronomy [ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ] a truly-venerable Science ; he saith , that it advanceth the mind to somthing of greater both Antiquity and Nobility , viz. ineffable Theology . That we may be breef , and only touch upon that sentence in the Book of Wisedom that God gave to Solomon , among other of Natural Science , to understand the Course of the Year and the Dispositions of the Stars : if any thing in Sacred Writ doth expressly prove the Antiquity of Observations Astronomical , and the founding or erecting any setled Art thereupon ; it must be that , of which the Holy Prophets complaind in their dayes ; viz. that there were Chaldaeans , who at Babylon , did contemplate the Stars , and compute the Months , that from them they might foretell things to come . For , from hence we understand , that the observation of the Motions of Heavenly bodies was a certain profest Art ; and of great Antiquity , among the Chaldeans . In the Second place , we are to revolve the Records of Ethnick Authors , to see if among them we can find the time of the Nativity of Astronomy . Look we therefore back , first , into the remains of that part of Time , which is called Obscure , or Fabulous ; because possibly enough something of truth , concerning our enquiry , may be found wrapt up in the darksome shrouds of Fables . And begin we at the most ancient of Heathen Gods , Coelus , in Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 who , as Diodorus Siculus delivers , was so named , because of his high devotion to , and delight in the observation of the Stars . This eminent person being the Father of many Sons as Ailas , Saturnus , the Titanes , and among those especially Hyperion and Japetus ; it is lawfull for us to conjecture , that led by his example , his whole family were addicted to the same Study , For seeing , that Coelus lived in Mauritania , not far from the Ocean ; and thence extended his Kingdom not only over all Africa , but also into a considerable part of Europe : it is well known that his Son Atlas , who succeded him in the same Dominions , is allowed to have given his name to the highest Mountain of that Country ; only because he had made his observations of the motions of the Heavens and Stars , from the top thereof . For , the Ancients in those dayes , as the vulgar now in ours , imagined the arch of the Heavens to be so little distant from the tops of great Mountains ; as that by how much the higher any man ascended on those hills , by so much the more clearly and distinctly might he behold Coelestial objects . To this , Diodorus , Plinie , and others add ; that Atlas was feigned to support Heaven on his Shoulders , only because He had framed a Sphear , wherein the whole Heavenly machine was strongly represented : and Clemens Alexandrinus observes , that Hercules , being both Vates and Physicus , a Prophet and Philosopher , was reported to come and relieve Atlas ( his great Uncle ) by taking the vast Burden of Heaven upon his own Shoulders ; because He succeded him in that difficult task the Study , or science of Coelestial bodies . Of Hesperus , the Sonne of Atlas , it is recorded , that while he was busy in speculating the Stars , on the top of the same mountain , he was snatched away by the violence of some disease , and could never be found : and that thereupon , the common people , in respect of his piety and justice , gave his name to the most beautifull and resplendent Star , which is also called Vesperugo , being Venus , while she is in the West . As for his Sisters , called both Atlantiades , and Pleiades ; these likewise gave their name to that glomeration of Stars , which are visible in the back of Taurus : and of one of them , named Maia , was born the Famous Mercurius , said to have brought the Science of the Stars first into Egypt . Whence Marcilius , writing of the Astronomy of the Egyptians , Saies of Mercury Tu Princeps , Authorque , sacri , Cyllenie , tanti . &c. Though we well know , that the Ethiopians , allowing the Egyptians to be no other , but one of their Colonies , sent abroad to find room to subsist in , contend ; that they recieved Astronomy from them : as first Diodorus , and after Lucian have observed . Here it is well worthy our commemoration , what Cicero saith , as of Atlas and Promotheus , so also Cepheus , a King of the Ethiopians : viz. Neither had Atlas been beleived to have sustain'd Heaven , nor Prometheus to have been chain'd on Caucasus : nor Cepheus with his Wife , Son-in Law , and Daughter , to have been Stellified : had not their Divine cognition of Coelestial bodies first occasioned the perpetuation of their Names in the disguise of Fables . To return to Saturn , another Sonne of Coelus ; He , leaving Africa , and reigning only in Italy , Sicily and Crete ; may be thought to have prosecuted his Fathers studies , no less than the former : and we have this argument for it , that the Slowest of all the Planets bears his name , to this very Day ; probably , bacause he was the first , who understood the motion and course of that Planet , which was by the Greeks called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Time , forasmuch as of all the Coelestial Circuits none was found so diuturn . And of his Sons , since Pluto addicted himself intierly to Husbandry , Neptune to Navigation ; we may conceive , that Jupiter , applying his mind to nobler cares , succeded his Father in the Study of the Heavens : as also that he chose Olympus , accounted the highest mountain , to make his observations upon : so that in process of time , he came therefore to be called Olympius ; and the name of that mountain to be transferred upon Heaven it self ; whose orders and laws He well understanding , was thereupon said to have the Dominion of Heaven . Certain it is , that the Grecians ascribed the Original of this noblest Science , partly to the Gods themselves , and partly to ancient Hero's : which Achilles Tatius seasonably alluding unto , introduceth old Aeschylus attributing to God , that He shewed the risings and settings of the Stars , and distinguish't Winter , Summer , and the other Seasons ; and Ovid Fathers the same wholly upon Jupiter . Perque Hiemes , Aestusque , & in aequales Autumnos , Et breve Ver , spatijs exegit quatuor Annum . Besides , it is in the Fiction , that Jupiter took his Father , Saturn , bound him , and precipitated him into Hell. Now this seems to intimate , that Jupiter having imposed his own name upon one of the most eminent and illustrious of the Planets , gave that of his Father to another of them , that was more remote , situate in the deepest part of the Aetherial spaces , and of the slowest progress : though all this while we are not ignorant , that those names were fixed upon those Planets a long time after : since more anciently the Planet Jupiter was called Phaeton , and that of Saturn , Phoenon . For , we may collect very neer as much from Lucian , who by Tartarus understands the immense Altitude , or Profunditie of the Aetherial Region : & so denies that Saturn was either exil'd by Jupiter into Hell , or cast into bonds ; as common heads were perswaded to beleeve . As for Hyperion ; Diodorus hath a tradition , that he being of the progeny of old Coelus , demonstrated the courses of the Sun and Moon : and therefore called the Sun , Helios , after the name of his Sonne ; and the Moon , Selene , after that of his Daughter . Last of all comes Japetus , who also was the Sonne of Coelus , but performed nothing worthy commendation in the advance of his Fathers Speculations : but Promotheus , whom he begat , was therefore imagined to have been chained on the hill Caueasus , and to have his heart perpetually torn by a hungry Eagle or Vultur ; Because ( as Servius expounds the riddle ) with restless care , and solicitude of mind , he constantly excruciated himself with observing the Stars , and studying their Ascensions and Declinations . We shall not insist upon what follows in the same Author , namely that this Prometheus was the first , who introduced Astrology to the Assyrians ( not far from Caucasus : ) it being more usefull for us now to observe , that He was imagined to have stolen Fire from Heaven , for the inanimation of Man , for no other reason , but because he infused this Heavenfetch't Knowledge into the breasts of men , and inflamed their souls with the desire and love thereof . For , as to the remainder ; for as much as Belus was the same with Jupiter , among the Assyrians , as Diodorus testifies : it is He rather , who was accounted both the most sacred of their Dieties , and the Inventor of this Sideral Science ; as Pliny affirms . It is not needfull for us here to examine many other of the ancient Traditions , accounted likewise among the Fabulous ; as , in particular , the Fable of Phaeton , which hath this Mythology , that in his life time he had made a considerable progress toward the discovery of the Suns Annual course ; but dying immaturely , he left the Theory thereof imperfect . That other of Bellerophon , whom Interpreters maintain to have been carried up to Heaven , not by a flying horse , but a studious and contemplative mind , eager in the the quest of Syderal mysteries . That of Doedalas , who indeed , by th● same towring speculations , as by the artifice of wings mounted up to the Northern part of Heaven ; while his less ingenious Sonne , Icarus , falling short in his attempt of imitating his Fathers sublime flight ( as not so well understanding the demonstrations of the reasons of his Theory ) flaggd very low in his Studies : and fell from the true and apodicticall cognition of Coelestial motions and vicissitudes : with many other the like , recounted by Lucian ; as that of Endymion , the favourite of the Moon ; of Tiresias , the Prophet , &c. Yet one thing there is , mentioned as well by Lucian , as Tatius ; which we cannot well pass by ; which falling under the account of Heroicall times , seems to come somwhat neer to that which is called Historicall . And that is the notable Centention that arose betwixt Atreus and Thyestes about supreme dominion . For when by the publike Consent and Vote of the Argives , the Kingdom was to be his of the two , who should give the most eminent testimony of Science : it came to Atreus share to be King : because , though Thyestes showed them the signe Aries , in Heaven ( for which he was honourd with a golden Ram ) yet had Aireus declared a thing more excellent : while discoursing about the variety of the Suns rising , he made it appear , that the Sun and the World ( i. e. the Starry Orb ) were not carryed the same , but quite contrary wayes ; and consequently , that that part of the Heavens which was the West or Occident of the Starry Orb , was the very rising , or Orient of the Solary . Hence that verse of Euripides , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Qui Astrorum enim contrariam ostendi viam . To the same times likewise are we to refer the Institution of the Olympick Games , by Hercules ; which after a long interruption were renewed by Iphitus . For , inasmuch as those sports were instituted for no other end ( as may be assured from Censorius ) but that their celebration might put men in mind of that Intercalation of a month and half , that was to be made constantly every fourth Year , in respect of those four times eleven , or 44. Dayes , by which the mo●ion of the Moon anticipated that of the Sun ; and the four times six hours , or one whole Day , by which the circuit of the Sun exceded 365 Dayes : manifest it is , that Hercules could not understand this , without having first exactly observed the Motions of Sun and Moon . Hither also belongs that which is reported of Orpheus , who must needs have attentively observed the seven Planets , if it be true , as Lucian averrs , that he represented their Harmony by his Seven-stringed Harp : which the Grecians thereupon designed in Heaven , by some Stars , that to this Day retain the name of Lyra. So likewise doth what Sophocles saith of Palamedes , who pointed out the several Asterisms , and particularly 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Vrsum volutam , gel●dum & occasum Canis . And lastly , what Homer recounts , that in those times were well known ( besides Bootes and the Bear , or Wain ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Pleiades , atque Hyades , roburque ipsum Orionis . We have now struggled through the Darkness of Fabulous Times , and are advanced as far as to discerne the twilight of Historicall . An here , the first thing we clearly perceive , is that the whole controversy about the Antiquity of Astronomical Observations , lies betwixt the Egyptians and the Assirians , or Babylonians . For , as to the Grecians , though some have thought they might put in also for a claim to the honour of being the Anthors of this admirable Science ; yet by the Verdict even of Plato himself , they are to lay by the presence of Competition , For , sayth He , the first who made Syderal inspections , was a Barbarian ; a more ancient Nation than ours bred those men , who first devoted their minds to that Study , in respect of the Summer-like serenity and perspicuity of the Air , such as Egypt enjoyes , and Syria , where all the Stars are , clearly visible and no Clouds or Mists to obscure the beautifull face of Heaven . And certainly , if we except what we newly mentioned , the Institution of the Olympick Games by Hercules , and the restauration of them after some Intermission , by Iphytus , which hapned about 800. Years before Christ ; and some places in the writings of Homer , and more especially of Hesiod , who lived neer upon the same time , or not long before ; we shall find that the Grecians can produce no Monuments of their Observations of the Heavens , more ancient than those of Thales , who flourisht , full 600. Years before Christ ; and who yet borrowed his knowledge of Aetherial Matters from Egypt . It being manifest therefore , that the Aegyptians , or their Priests , are the only men , that ought to be admitted to a Dispute with the Assirians or Babylonians , or their Philosophers , concerning the Antiquity of Observations ; and that their several Pleas seem equally reasonable . Truly , it is no easy matter to determine the difference , so as to place the Lawrell on their heads to whom it doth of right belong . For , albeit Josephus assignes the Honour to the Chaldaeans , and others again stand firmely for the Egyptians : yet Plato , Diodorus , Lucian , Achilles Tatius , and others alleadge such quotations for each party , as seem to have no other , but the authority of the parties themselves . Nor ought that to seem strange ; since both sides equally alleadge the convenience of their vast Companies , and the serenity of the sky ; since they both boast themselves the Original Nation and allow their Competitors to be only Colonies ; since both glory in fabulous beginnings , which we cannot trace or discusse ; and both recur to egregious falshoods about the time when their Ancestors first made Coelestiall Scrutenies . For , the Chaldaeans ( as we find on the Register of Diodorus ) affirm , that their Nation applied themselves to these Studies , from times of incredible Antiquity viz. of four hundred and three thousand Years : And the Egyptians ( as Cicero observes ) talk of Observations of four hundred thousand and seventy Years standing . Unless you shall please to consigne the Victory to the Egyptians , because they put a value only themselves by Auction . As if it were not enough for them to boast those four hundred nine thousand Years ( mentioned by Laertius ) in which from the time of V●lcan , the Sonne of Nilus , to that of Alexander of Macedon , there hapned of Eclipses of the Sun three hundred seventy three , and of the Moon eight hundred thirty two . These considerations premised , we cannot indeed deny , but the Egyptians had some Observations , some ages before Thales and other Grecians travelled among them : but , when we would enquire more precisely into the time , when those Observations first begun ; we find our selves at a loss , and brought back again into the cimmerian obsurity of Fabulous Times . Now forasmusch as , though Pliny writes , that Epigenes found no Observations among the Babylonians of above seven hundred and twenty Years antiquity , and those engraven on artificial Tyles or Slates ; and the most ancient Eclipses deduced from them , were transmitted to Ptolomy , about the same Number of Years before Christ : and that by the great Hipparchus . And to the same Time belongs what Berosus and Critodemus say , that in their Dayes , there were extant no Observations of more than four hundred and thirty Years as may be found also in Pliny : forasmuch , we say , as we have brought some considerable Monuments of Observations much elder than that time ; yet shall not concede beyond what the Chaldeans themselves profest , when they testified to Callisthenes ( who went to them upon no other errand , by the perswasion of Aristotel , as Simplicius relates ) that they had nothing of that kind among them beyond a thousand nine hundred and Three Years past : which Years seem to commense at Ninus , the Sonne of Belus , and first King of the Assyrians . It is clear , that the Antiquity of Observations ariseth to ( but not above ) one thousand and ninety Years before Alexander the Great . But , alas ! after all this great adoe , What did the Observations themselves amount to ? Why truely , for ought we can gather from all that is extant concerning them , those of the Aegyptians amounted to nothing at all : and those of the Chaldeans to very little . For the Egyptians , we confess , are said to have observed the rising of the Dog-Star , and some other , no very difficult apparences : but we have no remains delivered down to us , of that or any other particular they observed , with the exact designation of the Time , as they ought . And from the Chaldaeans we have as little , besides those Eclipses mentioned in Ptolomy . But , when I speak of the Egyptians , I except Ptolomy himself and some others , who lived and studied at Alexandria , about there hundred Years before the Nativity of our Saviour ; or after Alexander : as Timocharis , Eratosthenes , Hipparchus : for all these were either Grecians , or to be accounted among Grecians , in respect of the language they used and wrote in , rather than among the ancient Egyptians , by whose Inventions even Ptolomy himself ( one of their own Country men , without dispute ) was very little , or nothing at all assisted in his Study of Astronomy . But , what concerns aswell the Egyptians , as Chaldeans ; their Observations are to be distinguisht ( according to the division vulgarly received into ( 1. ) Astronomical , and ( 2 ) Astrological : the former relating to the Motions , Magnitudes , Distances , and proportion of the Stars ; the Latter to the Effects of them , which they conjectured were dependent on the Vertues and Influences of Heavenly Bodies , aswell in the affections of the Air , as in the actions and affairs of Mankind . For , both Nations being wonderfully prone to Supersttition , and surprised with excess of Admiration at the Eclipses of the Sun and Moon , when they first beheld them ; and observing ever now and then some Stars that moved in Courses contrary to the West , they began presently to think , that those apparences hapned not without natural Causes ; and that it remained only on Mans part , to Study how those events might come to be fore-known , which those apparences did portend . Hereupon , having attributed the most powerfull Vertue to the five wandering Stars ( as Diodorus testifieth particularly of the Chaldaeans ) as understanding them to be the Proclaimers of the will and purposes of the Gods ; because they sometimes arose , and sometimes set in various places of the Heavens ; because they varied their magnitude and colour : therefore they conceived , that they ought to adress their Studies and Disquisitions principally to these varieties . And , because they imagined , that the higher the place was , from whence they should observe these Wandering Stars , the more clearly and distinctly might they be discerned ; they builded Structures of vast altitude ; and particularly that immense Tower at Babylon , described by Herodotus , from the highest area whereof ( where stood also the Temple of Belus ) they might exactly behold and observe the rising and setting of the Stars , and other Syderal occurrences They took notice likewise , that those five Planets did keep almost the same Course , as the Sun and Moon ; and thereupon they pointed out the Zodiack , imagining that there must be some eminent vertue in that part of the Heavens , because all the Planets kept constantly to it . And this Zodiack they divided into 12. parts , or Signes ; because the Moon run it over 12. times , and the Sun only once , in one Year : and according to the number of the Dayes , during which the Sun was in passing through one Signe , they distinguished each Signe again into 30. parts , which we call Degrees . I shall not recount to you , how they would have Twelve Principal Dieties belonging to these 12. Signes , whereof each had his particular regiment over his proper Signe and Moneth dependent thereupon : nor how they substituted thirty of the fixt Stars , to assist the Planets , and called them Concelling Gods : nor how they placed 12. Stars always visible in the North , for government of the Living ; and as many more in the South , alwaies visible , for the government of the Dead , there gathered together ; with many other the like dreams and ridiculous absurdities . But the thing I think most worthy your notice , is , by what rude kind of artifice they distinguished the Zodiack into 12. Signes ; as we find it described , concerning the Chaldaeans , by Sextus Empiricus , and concerning the Egyptians , by Macrobius . The manner this . They took a vessell with a small hole in the bottom , and filling it with Water , suffered the same to distill Drop by Drop into another Vessell , placed beneath to receive it ; and this from the moment of the rising of some one Star or other , observed in one Night , untill the Moment of its rising again the next Night following . The Water fallen down into the Receiver , they divided into ●2 . equal parts , and having two other smaller vessells in readiness each of them fit to contain one twelfth part of the Water , they again poured all the Water into the upper Vessel , and strictly marking the rising of some one Star in the Zodiack , they at the same Moment gave the Water leave to distill into one of the smaller Vessells , and so soon as that was filled , observing likewise another rising Star , they put under another small Vessell ; and so alternately shifting the small vessels , they noted , if not in one Night , yet in many , the twelve Stars , by which they might discriminate the whole Zodiack into twelve equal parts . Now with what Art and exactness these Ancients measured out the Heavens , may be conjectured from this one example . I might adferr another foppery of the Chaldaeans , from the same Empiricus , who relates ; that taking it for granted , that the future fortunes of Men did depend on their particular Horoscope , or Signe rising at their Birth , when they had a mind to divine in this Kind ; Two of their wise men agreed together in the calculation of the Nativity of the Person proposed : the one stood by the Mother in Travell , the other on some high place neer at hand ; and as he that was below gave the Signe , that the Infant was then newly come into the World , the other above took care to observe the Signe , that was just then newly risen . But , it will be of more use for us to hear what Macrobius tells of the Egyptians . They , when they would know the Diameter of the Sun , had in readiness a Vessell of Stone , hollowed to the form of an Hemisphere , exactly made , with a style or Gnomen erected in the middle , and twelve Horary Lines drawn within . And on the very Day of the Equinox , observing the Moment , when the upper Limbus of the Sun first shewed it self above the Horizon ; they marked that place on the brim of the Vessel , on which the Gnomen cast its shadow . Then again marking that place on which the shadow ended , when the lower Limbus of the Suns body appeared just above the edge of the Horizon ; they measured the space or distance betwixt the two marks of the Shadowes , and found it to be the ninth part of an hour , or the hundred and eight part of the Hemisphere , and consequently the two hundred and sixteenth part of the whole Circuit : and from thence they deduced , that the Diameter of the Sun was the two hundredth and sixteenth part of its whole Orb ; ( which , in truth , is the 700th neer upon ) or did contain one Degree and an hundred Minutes ; which yet is no more than halfe a degree , or 31. Minutes , at most . To this we might super-ad , that it was the practice of elder times , to commensurate the Diameter of the Sun by an Hydrologie , or Vessel of Water ; collecting the same from part of the Water flowing down the whole Day , which had dropped until the Sun was wholly risen ; as is insinuated by Plutarch , and deduced from Capella : but Cleomedes hath at large declared , that this way of measuring by Water falling slowly and equally from Vessel to Vessel , was an Invention of the Egyptians . Now the reason , why we touch upon these particulars , was only to satisfy , that ( as we said afore ) no great matter in Astronomy was ever observed either by the Egyptians , or by the Babylonians . And , if you desire any further Argument thereof ; Pray take this . They were very far from suspecting that the Fixt Stars had any motion proper to themselves ; or that they had any Eccentricity ( excepting only that the Egyptians thought Venus and Mercury to move round about the Sun , as their center ; as is affirmed by Macrobius , and some others ) or that the Sun had any Apogaeum at all , with many other Particulars fully as considerable . Which doubtless must be the reason , why they invented no Hypotheses , by which they might regulate themselves , in making their Caluclations of the various motions of the heavenly bodies . And Peter Ramus not long since complaind , that we have not our Astronomy free from the trouble of Hypotheses ; such as the Interpreters of Aristotel themselves , and Proclus on Timaeus have recorded the Egyptians and Babylonians to have had amongst them : while , incroth , he complaind , that we had not our Astronomy as rude wild and imperfect , as theirs was . For , however some Hypotheses are more simple ( and so more easy ) than other-some : yet it is absolutely impossible , that Astronomy should consist without some or other . Hereupon , they could observe , indeed , that the Planets were one while Direct in their Progress , another while Retrogarde , and then again Stationary ; that they in their wanderings sometimes inclined towards the North , and sometimes deflected again toward the South : but all that while , they could neither comprehended the reasons of those various apparences , nor calculate them by numbers . The most they could doe , was darkly to represent those motions , by certain Hieroglyphicks , as in particular by the windings and flexures of Serpents ; and the motion of the Sun , by only a Beetle rowling his pill of dung backward : as we may read in Clemens Alexandrinus : and then came Eudoxus , who having learned that variety of motions among them , was the first who invented Hypotheses of various Orbs , for the Solution of the Phenomena . Again , they were very far from attaining the determinate places of the Fixt Stars , according to Longitude and Latitude ; or according to their Right Ascension , and Declination : so that neither could they define the true places of the Planets , by Comparation to the Fixt Stars , nor ( consequently ) designe any Observations with due exactness . And truely , this was the Cause why Hipparchus met with no Observations , either of the Egyptians or Babylonians , by which he could receive the least help or advantage , toward his composing either Hypotheses , or Tables , to represent the motions of the Five errant Stars : and Ptolomy was the first , who partly by the benefit of Observations left him by Hipparchus , and partly by those he made himself , became able to attempt such a Work ; as stands recorded in his Almagest . There were only the Eclypses , which both these Nations had set down : as observed in their Commentaries : and those only so , as that from Past , they might be able to conjecture somthing of what were to Come . Not from the motions of Sun and Mon , exactly calculated by the help of Tables ; but having learnd from common experience , that every ninetneenth Year , Eclypses did return again upon the same Day , for the most part : thereupon they endeavoured to praedict what Eclipses would happen , and the time when ; and this after they had perceived not any Anomaly in the Sun , but some certain Inequality in the Moon , which reducing to a medium , they concluded that the Moon did every Day run throug● thirteen Degrees , and a little more than one sixth part of a degree ; as Geminus delivers of the Chaldaeans . But in their predictions of Lunar Eclipses , they were somwhat more confident ; aswell because these Eclipses usually uturn , for the three Ages next succeding , within the compass of the same Dayes ; as because it is very rare , in respect of the greatness of the Earths shadow , but the Moon , either in the whole , or some part of her , more or less , falls into it : but , because ( as to Solary Eclypses ) the Moon is both so small , and hath so large a Parrallax , as that she doth not for the most part intercept the light of the Sun from the Earth ; therefore was it ( as Diodorus witnesseth specially of the Babylonians ) that they durst not determine Eclypses of the Sun to come , to any certaine time ; but if they predicted any , with limitation of time , they alwayes ( to save their credit , in case of failing ) annexed this Condition , If the Gods be not prevailed upon , by Sacrifices and Praiers , to avert them . Truth is , these Astronomers were also Priests , and it was their interest to cast in this Proviso . For , being ambitious to be reputed interpreters of the Will of the Gods to the People , and so both knowing in things to come , and skillfull in such Ceremonies , wherewith their respective Deities were most attoned and delighted : unwilling to be thought able to predict nothing , and as unwilling again to be found erring in their chief predictions , they wrapt up all in Misteries , and amused the vulgar with superstitious opinions and rites . The Egyptians , in a great part of their sacred Worship , had recourse to the Astrological Books of their Mercurius ( one of the Order of the Fixt Stars ; a second , of the Conjunction of Sun and Moon ; a third and fourth , of their rising . ) which with what ceremonious Pomp they used to carry about with them , in a kind of solemne Procession , you may find amply described by Clem. Alexandrinus . Nor is it strange that those Priests accounted so sacred and knowing , should also be estemed for Prophets . Further , you meet with no mention of the Five Errant Stars , all this while ; and the reason seems to be , because they attributed an energie of them only as they were referrable to the Inerrant or Fixt , and particularly , as they possest this or that part of some Signe in the Zodiack , and together with it had their rising , or setting . For , so much did they ascribe to the Zodiack , as that the Babylonians , and ( in imitation of them , the Persians and Indians ) thought , that each decimal of degrees , or thirds of the Signes , ( and the Egyptians came as low as to each single degree ) could not be varied in the rising , but some eminent variation most happen , especially in him , who should be borne at that time . And hereupon was it , that the Egptians made that great Circle of Gold ( described in Diodorus ) of a cubit in thickness , and three hundred sixty five cubits in circumference ( plundred at last by Cambyses ) that upon each cubits space might be inscribed each Day of the Year , 365. Dayes in the whole round , and also what Stars did rise , what set upon each Day , nay the very hour of their respective rising and setting , and what they did signifie : and whereas others used to assigne the form of some Animal or other , to each ten degrees ; they assigned one to each single degree , and so made their harsolations or conjectural predictions accordingly . For Example ; to the first degree of Aries they assigned the figure of a Man , holding a Sicle or hook in his right hand , and a Sling in his left ; to the second , a Man with a Dogs-head , his right hand stretcht forth , and a staff in his left ; and so of the rest ; then annexing the signification to each , they determined , that he , who should have the first degree of Aries for his Horoscope , should be some part of his life a Husbandman , and the rest of it a Soldier ; that he , who should be born under the second , should be contentious , quarrelsom , and envious ; and so of the rest , all which Scaliger hath fully deduced from Aben Ezra . In a Word ; what ever knowledge either the Egyptians or Chaldeans had of the Stars ; certain it is , they referred it wholly to Astronomantie , or Divination by Stars : and therefore among them there flourisht , no true and genuine Astronomy , but a spurious and false , one i. e. Astrology Divinatory , or the fraudulent Art of Fortune-telling by the Heavens . Berosus ( whom we formerly mentioned ) coming into Grece , a little after the death of Alexander , is discovered to have brought with him nothing sollid touching Astronomy , but only Judicial Astrology● ; for which , as a thing new , and strange to the people , he was highly esteemed , as Vitruvius and Pliny remark . And Eudoxus , who had returned out of Egypt before that , well knew what sort of Astrology this was ( the principal Contrivers and Founders of which are said to have been Petosires , Necepsus , Esculapius ) but he highly contenmed it as Cicero remembers , and brought home no other fruit of his tedious Travells , beside a list of some Eclipses , and the varieties of the motions of the wandering Stars , by which he first essaied to compose accommodate Hypotheses , as we have formerly hinted . Nay , Plato himself , who was Companion to Eudoxus , for thirteen Years together , in Egypt : profest : that he could attain nothing sollid and satisfactory touching those Stars , and therefore placed all his hope only in the sagacity and industry of the Grecians , such as he knew Eudoxus to be . For , having first recounted what ever he knew concerning them ; he saith , It is to beleeved that the Grecians make more perfect whatsoever they receive from Barbarians ; and therefore is it fit , we allow the same , touching the argument of which we have discoursed . Truth is , it is difficult to find out the way , how all these Apparences , so involved in obscurity may be explicated : nevertheless there is great hope that things of that sort will be better and more advantageously handled , than they were delivered to us by Barbarians . From the Egyptians and Chaldeans , therefore ( as Astronomy her self , while young and rude ) we come to the Graecians : and the most antique record of Syderal Observations to be found among them , seems to be that of Hesiod ; who in his Book of Weeks and Dayes teacheth Husbandmen the most opportune times of reaping , sowing , and other labours of Agriculture , from the rising and setting of the Pleiades , and Hyades , and Arcturus , the Dog-star , and Orion : 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Donec Pleiades , quae & Atlantiades , exoviuntur , &c. And I cannot tell , whether it were that book , or some other , that Pliny meant , when speaking of Hesiod , he sayes , Hujus quoque , nomine extat Astrologia , there is extant an Astrology of his . However , we are here to remark two things , in order to our more exact disquisition ; the First is , that the Ancient Greeks principally attended to these risings and settings , aswell that they might distinguish the several Seasons of the Year , as that they might fore-know Rain , Winds and other dispositions of the Air , usually attending those Seasons . And hereupon , Thales , Anaximander , Democritus , Euctemon , Meton , Eudoxus , and many others , composed certain Parapegmata , Tables , ( as Ephemerides , or Diaries ) in which they inscribed each Day of the Year , with the particular Stars rising or setting on each Day , and what mutations of the Air each one did portend . Such a Darapegme as these , was composed likewise by Julius Caesar himself , for the Horizon of Kome ; in allusion where to he might justly own , what Lucan said for him , Nec meus Eudoxi fastis superabitur Annus . And , him doubtless , did Ovid translate into his Fasti ; promising in the beginning , that he would sing of the Stars and Signes , that rose and again descended under the Earth . But , to keep close to the Grecians ; among them , he was held a great Astrologer , who had discovered and observed only these risings and settings here spoken of ; and so of whom that might be spoken , which Catullus said of Conon , Omnia qui magni dispexit lumina Mundi , Stellorumque ortus comperit , atque obitus . For , before the Advent of Berosus , this was the only [ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ] Praesignification or Divination by the Stars , the Grecians had among them : unless what Hesiod hints , in his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Primùm prima dies , & quarta & septima sacra , &c. where he points out , what Dayes of the Moon were accounted Lucky , and what Unlucky . The Second observable is ; that among the Grecians , and indeed among divers other Nations , beyond all Memorials of either Traditions or books , the Stars were reduced to certain Images , or Constellations , and denominated accordingly ( as their names yet shews ) as it pleased the fancies of Husbandmen , Shepheards , Matiners and the like , who used to be vigillant and gizing upon the Heavens in clear Nights . Though there have been some Constellations added of latter times , as that of the lesser Wain , by Thales , which Lacrtius and Tatius recite out of Callimachus , who also took the same elswhere , and that of Berenices Hair , removed into Heaven by Conon , as Catullus relates . Cleostratus likewise ( as we have it from Hyginus ) found out the Kidds : though , ( which Pliny moreover attributes to him , ) his invention of the Signes in the Zodiack , is so to be understood , as that he taught men through what Signes the Sun and other Planets passed . But ( that we may couch also upon this ) at first , the Grecians had only Eleven Signes in their Zodiack ; and it was long after ere they came to add the twelfth , in imitation of the Egyptians , who ( as may be collected from Servins , Marcianus , and others ) instead of the Clawes of the Scorpion , placed Libra , the place destined to Augustus , by Virgil , — Ipse tibi jam brachia contrahit ardens Scorpius . — They added the Twelfth , we say , to the end , that as the whole Compass of the Zodiack was divided into Dodecatemoria ( as they call them ) twelve equal parts , so it might consist also of twelve Signes . Albeit , being ( as it were ) necessitated to make use of such Signes , as had been brought up , rather by chance , than Art ; those 12. Signes were not exactly proportionate to the 12. Divisions of the Zodiack , but took up more space some , than others as in particular , Leo possest more room than Cancer ; Taurus than Gemini . I say , than Gemini , which though composed of Castor and Pollux ; in so little space as is allowed them , it is impossible the one should rise , when the other Sets , and both in the East : but this Empiricus interprets of the two Hemisphears . I omit to insist upon this , that all Nations had not the same Constellations : as among the Egyptians was no Bear , no Cepheus , no Dragon ; but other formes or representations , as Tatius reports ; and shall add only , that Eudoxus seems to have been the first , who partly out of the Egyptian Figures , partly out of the Grecian , furnished the whole Zodiack with Images resembling the Asterismes , ( as men had fancied , at least ) and caused them to be drawn on a Globe , or solid Sphear . For , Aratus ( upon whose Poem , intitul'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Apparences , there have been so many Commentaries set forth , as that no fewer than forty have been extant in Greek ; besides those of Cicero , Germanicus , Avienus , and other Latin Interpreters . ) did no more , but only express in verse , what Eudoxus had said before in prose , of this argument ; as Hipparchus Bythinus demonstrates . I know not , whether it would be seasonable for me , here to advertise , that it is no wonder Aratus erred so grosly in many particulars ; considering that ( as is written in his life ) he Living with Antigonus Gonata , in the quality of his Physician , and Nicander in the quality of his Astrologer ; and both were good at Poetry : Antigonus commanded the Physician to give him a tryall of his Poesie , upon an Argument in Astrology ; and the Astrologer to give another of his , upon somthing in Physick : delivering to the one , the Book of Eudoxus ; and to the other , all that was extant of Treacles , Antidotes , or Counterpoisons . So each wrote of what he did not well understand . One thing I shall not , forget ; and that is , that the Phenomena of Euclid , who lived neer about the same time , and taught at Alexandria ( as in the Memorials of Pappus ) were quite of another kind ; being indeed no other , but certain Principles of Astronomy , concerning the figure of the World , and the Circles of the Sphear , and chiefly , that of the Zodiack . But , to return back to the more primitive Greeks ; I remember I said , that Thales Melesius was accounted the First , who after old Hesiod and Homers Dayes , enquired into the Order of the Stars . And , certainly He was the Man , who among the Grecians may challenge the Palme ; as to Antiquity ; for , Apuleius calls him , ut antiquissimus , sic peritissimus Astrorum Contemplator , and Eudemus in Laertius attesteth , that this was the Opinion of most , adding moreover , that Xenophanes and Herodotus highly admired him , for that he had first predicted the Eclypses and Conversions of the Sun ; and that Heraclitus and Democritus witnesseth as much . And whereas Apuleius further subjoyns , that he found out the motions and oblique tracts of the Syderal Lights : Pliny ascribes that to Auaximander , a Disciple of Thales Milesius , ( whence he was said Rerum fores aperuisse , to have opened the Doors of Celestial matters ) and Diodorus to one Oenopides Chius : which Thales could not yet be ignorant of the Obliquity of the Zodiack , when he had written of the Solstices , and Equinoxes , and had conversed a long time with the Egyptians in their own Country , as Laertius remembers . Further , it is delivered to us , that among others , he predicted that notable Eclipse of the Sun , which hapned in the time of the warre betwixt the Meads and Lydians ; which he could not doe by any other reason , but only because , coming newly out of Egypt , he had learned , that Eclipses generally return upon the same Day after the space of nineteen Years ; and having taken notice of one , that fell out 19. Years before , he concluded that there would be one at such a time . Nor is there reason why any should think , that otherwise his whole life might be sufficient to observe all the motions of the Sun and Moon , as from thence to be able to invent all things necessary for the calculation of the times of their Several Eclipses . Moreover , it doth not appear , how by any other way , but that Helicon Cyzicenus came afterward to fore-tell that Eclipse of the Sun ( mentioned in Plutarch ) for which he was so much admired by Dyonisius , and rewarded with a Talent of Gold. Nor likewise , how Sulpitius Gallus could fore-tell that other of the Moon . which as most opportunely predicted to the Roman Army , then ready to joyne battell with the Persian , is so higly celebrated , not only by Plutarch and Pliny , but also by Valerius , Quintilian , and other Historians : for other Rule for the calculation of future Eclipses , there was none before Hipparchus , who invented Hypotheses and Tables fit for that purpose . Besides , what Laertius imputed to Anaximander , Plinius as confidently imputes to one Anaximenes , an Auditor of his : ( namely that he should be the Inventor of that Gnomon , by which the Conversions of the Sun , or the Solstices and Equinoxes , were indicated , and that he set up such a one at Lacedemon . ) Neer upon the same time was it , that Pythagoras is said to have first discoursed ( though Phavorinus , in Laertius , confers that honour upon Parmenides , ) that Lucifer and Vesper was one and the same Star of Venus , Now , whether may we conceive , that he borrowed this of the Egyptians , from whom being taught , that not only Venus , but Mercury also , were carried round about the Sun , as their Center , so that one and the same might be both Morning and Evening Star : possibly , from thence he might take the hint of his Conjecture , that the Sun was the Center of not only those two , but of the other Planets also , and consequently of the whole World : and moreover that the Earth it self , as one of the Planets , moved about the Sun ? For truely , this was an eminent and constant Tenent in his School ; as may be understood not only from Aristotle in the general , but also from Laertius in particular of Philolaus , and from Archimed of Aristarchus , both Pythagorus his Disciples : that we may not rehearse all those many passages in Plutarch , concerning this memorable particular ; nor name those , who held , that the Earth was not so much moved about the Sun as dayly turned rouud upon an Axis of its own ; as Timaeus , a Pythagorian also , who is therefore by Synesius esteemed , after Plato , the most excellent Astronomer . Furthermore , in the next Age after Thales , or neere upon , comes Cleostratus ( the same who was beleeved to have deprehended . the Signes of the Zodiack ) and he , seriously remarking that the Intercalation , which as we said , was wont to be made every fourth Year , celebrated with the Olympick Games , did indeed restore the motion of the Sun to the same Day again ; but did not restore the motion of the Moon till the eight Year , or two Olympiades , in which the intercalatory Dayes amounted to ninety Dayes , or three months : He , we say , thereupon interduced , instead of the Tetacteris , or space of four Years , the Octaeteris , or space of eight Years , which compleatly past , the New-Moons , and Full-Moons would returne again on the same Dayes . But , when in short time men had perceived , that this Institution failed them , in exactness of computation ; and that sundry wayes had bin attempted to cure this uncertainty : at length riseth up Meton , somwhat more ancient than Eudoxus ; and he demonstrateth from the New-Moons , and Full-Moons Eclyptical , that they did not return upon the same Dayes , till after full nineteen Years : and thereupon he became the Author of the Enneadecaeteris , or Period , or Cycle of 19. Years . In respect of which discovery , together with the Heliotrope , or Sun Diall he made at Athens , and some other the like Inventions , he was in eminent esteem among the Athenians . But as concerning that Period ; Callippos , familarly acquainted with Aristotle , discovering it to be too long , by the fourth part of a Day ; inferred , that from four Periods one whole Day ought to be detracted : and so erected a new Period , or Cycle of Sixty six Years , or four times nine , at the end of which one Day was to be cut off ; and this was called the Callippik Period , and remained in use for a long time together . After him succeeded Hipparchus , who detecting this Period , to be yet too long ; demonstrateth that after four Callippik Periods , or three hundred and four Years , there would remain one whole Day too much . And in truth , the experience of many succeding Ages declared , that to this detraction of Hipparchus , nine or ten Years over and above were to be expected . However , it is worthy our notice , that the Period of Meton , together with the Conection of it , applied by Callippus , was of long use in the Church under the name of the Golden-Number : though wanting the Application of Hipparchus his Correction : also , a mistake of about four Dayes , relating to the New and Full Moons , crept into the account , even from the time of the Nicene Councel ; which was one of the two main causes of the Reformation of the Kalender in the eighty second Year of the last Age. And now we have an opportunity to speak more expresly of Eudoxus , so frequently mentioned . This man , well understanding , after his return out of Egypt , that not only the Sun and Moon , but also the five Errant Stars , did keep their courses round in the Zodiack ; and so , as that aswell the Sun and Moon , as those wandering Stars did sometimes vary their latitude , or deviate from the Ecliptick Line in the midle of the Zodiack ; ( for , he thought that the Sun was also extravagant , as well as the rest ; and again , that the other Planets did not only go forward , but were also some times upon their retreat backward ; and somtimes made a hault or stood still : we say , pondering all these various motions in his mind , and casting about what might be the reasons thereof in nature ; he at last imagined to himself , that besides the Aplanes or Sphear of Fixt Stars , which being supreme , carried all the rest toward the West , there ought also to be allowed three other Sphears , as well to the Sun , as to the Moon , and four to each one of the other Errant Stars ; of which one , and that the highest , should follow the Impression of the Fixt Stars , or rather of the Primum Mobile ; the next to that should move counter to the First , or toward the East ; the third make the deviation from the Ecliptick , or midle of the Zodiack ; and the fourth , or lowest , cause in the Stars their Direction , Station and Retrogradation , and that by a certain Vibration , or Waving to and agen . So that he supposed in all , twenty seven Sphears , and all those Concentricall , that the Superior might carry on the Inferior , and these might be turned round within those . Afterwards , Callippus adjoyned two Sphears to the Sun , two to the Moon , and one a peece to Mars , Venus , and Mercury : and so made thirty three . And Aristotle , to all the Sphears , which did not follow the motion of the Aplanes , or Primum Mobile ( excepting only the Lunar Sphears ) added as many more , which he called the Revolvent ones , to the end he might conform them to the motion of the Inerrant Sphear , or Primum Mobile : and so in the whole he constituted Fifty six Sphears ; for as much , at least , as we can collect from his own context . Now all these , and even Plato himself likewise , thought that the Moon was the lowest of all the Planets ; next to her , the Sun ; and above the Sun the five wandering Stars : Nor indeed doth it appear , that Archimedes himself Living a whole Age or two after them , represented the Planets in any other , than this very order , in that so famous Sphear of his In which though Claudian tells us , that no more was represented , but only the motions of the Sun and Moon ; Percurrit proprium mentitus Signifer annum , Et simulata novo Cynthia mense redit : Yet Cicero adds other motions , when speaking of Archimedes , he saith ; when he collected together the motions of the Moon , Sun , and five wandering Stars ; he did the same as that God , who in Platoes Timaeus framed the World , that one and the same Conversion might regulate sundry motions , most different each from other in slowness and swiftness . But , Hipparchus afterwards finding , that aswell the Sun , as the Moon and the other five Stars did come somtimes neerer to the Earth , and sometimes again mounted up farther from it ; and plainly perceiving that that particular apparence could not possibly be explicated by those Sphears , that were all Concentrical to the Earth : therefore , wholly rejecting them , he resolved , that the motions of the Planets were to be accounted Eccentrick ; and though he could not himself determine each particular , he yet demonstrated the way , in which Ptolomy afterwards insisting , accomplisht the Invention . But , before wee advance further , we are to commemorate two or three Persons of note , by whose Observations both Hipparchus and Ptolomy profited very much . One was Timocharis , who , about three hundred Years before Christ , among other things relating to the Fixt Stars , observed that that Star which is called Spica Virginis , doth antecede the point of the Atumnal Equinox , by eight degrees . And with him are we to joyn Arist●ll●s , whose Observations of something about the Fixt Star ; Ptolomy made great use of , in order to his demonstrating that the Fixt Stars never change their latitude . Afterwards ( scarce in Age ) succeded Eratosthenes , who being Library-keeper to Ptolomy Evergeta the fomer , perswaded him to set up the Armillae in the Porticus of Alexandria ; which Hipparchus and Ptolomy afterwards made use of ; and himself , among other things observed , that the Obliquity of the Zodiack was of twenty three degrees , and fifty one minutes ; which account Hipparchus and Ptolomy constantly adhered to . Now that we may at length remember the great Hipparchus , who florish't neer upon an hundred and forty Years before Christ : truely , we find it no easy task to recount , how highly Astronomy was beholding to him . For , in the first place , examining that foresaid Observation of Timocharis , with some others ; albeit he could not conceive them to be in all points exact , yet because himself had found that Spica Virginis did not antecede the Equinoctial point by more than six degrees , and the other Stars in the like Proportion : he thence understood , that the Fixt Stars also were moved Eastward according to the Zodiack ; and thereupon wrote a Book of the Transgression of the Solstices & Equinoxes . And , being that in his time , as not long agoe in Tycho Brahes , there appeared a certain New Star , he therefore came to doubt ( to speak the language of Pliny concerning him ) whether the like happened often , or not ; and whether those Stars , that were thought to be fixt , had also some certain motion peculiar to themselves . Wherefore ( as the same Pliny goes on ) he attempted a task of difficulty sufficient even for the Gods themselves , namely to number the Stars for Posterity , and reduce the heavenly Lights to a rule , so that by the help of Instruments invented , the particular place of each one , together with its magnitude , might be exactly designed : and whereby men might discern , not only whether they disappeared , or newly appeared , but also whether they removed their Stations ; as likewise , whether their magnitude encreased , or diminished ; Leaving Heaven for and Inheritance for the Witts of succeding Ages , if any were found acute and industrious enough to comprehended the mysterious orders thereof . And this was the first time when the places of the Fixt Stars were observed and markt out according to Longitude and Latitude : and that Catalogue of the Fixt Stars , which he composed , is the very same , which Ptolomy afterward inserted into his Almagest . In the next place , he denoted was positions sundry Stars had in respect each of other ; whether they were posited in a right Line ; or in a triangular form ; or in quadrate or square , &c. as is manifest even from Ptolomy himself . Further , though the motions of Sun and Moon were already in some measure known ; he yet made that knowledge much more exact . For , He did not only much correct the Callippick Period , formerly spoken of , but also , having collected a long Series of Eclipses ( namely , from the time of those Babylonish ones , in the Dayes of Mardocempades , down to those observed by himself , for full six hundred Years together . ) and remarking , that neither the like Eclipses did return on the same Dayes , after the space of every nineteen Years , nor that after some recurses of ten Novennales , or ten times nine Years , any such Eclipses happened at the times supposed ; and that the cause thereof consisted both in the various Latitude of the Moon , and the anticipation of her Nodi , or Knotts , and her Eccentricicy , by reason whereof her motions to her Apogeium were found to be sometimes slower , and those to her Perigeium more speedy : therefore , we say , He comprehended and gave Reasons for all these difficulties , and composed certain Hypotheses , and according to them , certain Tables , by which he could safely and exactly calculate and predict what Eclipses were to follow , how great they were , and when . And this was it , which Pliny remembred , when having spoken of Thales , and Sulpitius Gallus , he comes to mention Hipparchus . After these ( saith He ) Hipparchus foretold the courses of both Luminaries , for six hundred Years to come ; comprehending the months , Dayes and hours of Nations , and the Scituations of Places , and turns of People : his age testifying , that he did all these great things , only as he was partaker of Natures Councels . For , it must be , that Hipparchus , besides the precise times , when such or such Eclipses were to be visible to the Horizon of Rhodes , or Alexandri● , pointed forth also some Countries , and principal Citties , together with the Designation of the Months in use among them ; as also the very Days and hours when each Eclipse would happen ; and other praedictions succeding to Rome , in the Dayes of Pliny . Again , it is well worthy our recital , that Hipparchus labouring with long desire both to constitute Hypotheses , and reduce into Tables the motions of the other Planets , or five wandering Stars ; and yet not being able to furnish himself either from the Egyptians , or from his Country men the Grecians , with any competent Observations respective to those Planets , ( for while the places of the Fixt Stars remained unknown , it was impossible any such could be made ) and again those he had himself made , were of a much shorter time , than was requisite for the establishing any thing certain and permanent in that sort : He therefore only digested such Observations as he had recorded by him , into the best order and method he could devise ; and so left them for their use and improvement , who should come after him , in case any were found capable of understanding and advancing them . And at length , by good fortune , it so fell out , that those his Observations came into the hands of Ptolomy ; who comparing them with his own , and finding them judicious and exact , thereupon first began to erect both Hypotheses , and Tables of Motions fit for those Planets : yet not without much timerousness and diffidence ; because his Observations being but few , nor of sufficient time , he durst not promise himself any certainty of his Tables for any considerable space , or number of Years . But , for more assurance let us hear his own ingenious Confession in that point . The Time ( saith He ) from whence we have the Observations of the Planets set down , is so vastly short , in comparison of the greatness of Coelestial vicissitudes , as that it renders all predictions , that are for any great number of Years to come , infirm and uncertain . And therefore I judge that Hipparchus ( that zealous lover of truth ) considering this difficulty , and withall receiving not so many true Obsertions from the Ancients , as he bequeath'd to us , undertook indeed the business of the Sun and Moon , and demonstrated that it might be performed , by equal and circular motions : yet , as for that of the Planets , those Commentaries of his , which have come into our hands , clearly shews , that he attempted it not : but collecting all his own Observations concerning them together , into one order and method , for their more commodious use , resigned them to the industry of after times ; having first demonstrated , that they were not congruous to those Hypotheses , which the Mathematicians of those Dayes made use of . And , for Others ; sure I am , that either they demonstrated nothing at all , or else only attempted the business , and left it unfinisht . But , Hipparchus being eminently knowing in all kinds of learning , conceived , that he ought not ( as others had done before him ) to attempt , what he should not be able to accomplish . So that we see , Ptolomy was the first , who from true Observations , reduced the Motions of the Planets into Hypotheses and Tables correspondent . But before we speak more particularly of him , who lived about an hundred and thirty Years after Christ ; forasmuch as in the space of time betwixt Hipparchus and Ptolomy , these studies so florisht at Alexandria , as that Julius Caesar returning thence , brought along with him that Sosigenes , by whose assistance he endeavoured the restitution of the Calendar , and so may be thought to have propagated the Study of Astronomy among the Romans : let us reflect a little upon that time , and see what care they then had of Celestial matters . In the first place , we are to lay aside the Commemoration of Sulpitius Gallus ( of whom more then once afore , as one that falls not under this account , concerning whom we may not yet forget , what Cato is induced by Cicero , saying . While we saw that Gallus dye , that familiar friend of thy Father , O Scipio , who was restless in measuring Heaven and Earth ; I say , while we saw him dying even in that Study . How often did Day oppress him , when he had set himself to observe and describe somthing in the Night ? and how often did Night oppress him , when he had begun his Speculations in the Morn ? How was he delighted , when he had a long time before predicted to us Eclipses of the Sun and Moon ? &c. For he was a man clearly singular , and in an Age when so great ignorance and neglect of good Arts tyrannized over mens minds , being himself studious and inquisitive , could not but have borrowed his skill either from Egypt or Greece , where having obtained a Series of Eclipses , and the way of deducing them through the circuit of of nineteen Years ( as we said afore ) he became able to calculate them , so as Cicero relates For , as to the rest ; how great doe you think was the ignorance and neglect , nay even contempt of studies of this nature among the Romans ? Why , truely so great , as that Virgil could not dissemble it , in the Poesy attributed to Anchisa , according to which the Romans should indeed come to rule the World ; but yet should yeeld to others , in learning to know the Stars , and describe the Heavens . — Caelique meatus Describent radio , & surgentia sidera dicent . And Cato himself is cited by Agellius to have left in writing that it was not lawfull to write what is in a Table kept by the High Preist , how often scarcity of Provision would happen , how often the light of the Sun , or Moon should be darkned : so far , saith Gellius , did Cato contemne the Science of Astronomy , and thought it useless either to know , or fore-tell the Eclipses of Sun and Moon . Furthermore , though from times as high as Numa , the Romans made several Intercalations ; yet they took all their art of that Sort , from the Greeks : and Pliny remarks , that in France , Spain and Africa , there was no one man , who could so much as tell the Rising of the Stars . Nevertheless we are not to forget , that among the Gauls was one Pythias , the Philosopher ( as Cleomedes calls him ) of Masilia , who about the time of Alexander of Macedon , found the proportion of the Gnomon to the Solsticial shadow , to be the same at Massilta , as Strabo tells us Hipparchus had observed it at Byzantium ; who first attempted the Northern Ocean , and discovered the utmost Thule , in which Cleomedes cohaerently proves the Summer Tropick to be the same with the Polar , or greatest of allwayes apparent ones : and who ( as from his Book , de Oceano , may be inferred ) was excedingly curious to find out what was the Position of Heaven , respective to the variety of Countries and Climates . But , not so soon to digress from the Romans ; Pliny delivers , that in those first times of Romes being a Common-wealth , the Invention of Dialls was very raw and imperfect : for that they had only the risings and settings named , out of twelve Tables . That after some Years , they added the Meridian , and by the indication of a certaine columne , the last hour : nor that neither , but only in clear weather , even as long as till the first Punick warre . Afterward they advanced so far , as to make one , or two Sun Dialls ; but not with lines exactly correspondent to the hours , untill about an Age after , when Q. Marcus Philippus ordered the busi ness more diligently and succesfully . And , because the hours of the Day remained yet uncertain in dark and cloudy weather , Nasica Scipio began to divide the Hours of Day and Night equally by Water distilling from Vessel to Vessel , and called it The Diall within Doores , in the Year Urbis conditae DXCV. And till then , saith Pliny , Populi Romani indiscreta lux fuit . And thus much of Hipparchus , and some Astronomers betwixt him and the Prince of them all , Ptolomy . And of him , so great is his name , all we need to say , is only , that He was the very Founder of the Art , or Science of Astronomy . For , though Hipparchus had indeed , as it were hewn out the Stones and Beams fit for so noble a Structure , and prepared good part of the Materials ; yet was it Ptolomy alone who put them into Order and Form , and by adding many admirable Inventions of his own , by infinite labour and cost , erected that so famous Building , worthily called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , the great Co-ordination , Construction , or Composition ; which consisting of no less than thirteen Books , contains all the Doctrine , that could then be advanced , concerning the Sun , Moon , and aswell the Fixt , as wandering Stars . And , albeit one Day teacheth another , and that ( as Himself had truely foretold ) there came others after him , who saw good cause for the Castigation and Correction of many things delivered in that Work : yet , in the general , the Art he had instituted , remained firm and constant , and was afterwards imbraced , not only by the Alexandrians , but also by all the Arabians , Latins and others , who devoted themselves to the service of Urania , ever since . For , that the Study of her Celestial mysteries continued in great esteem and Veneration , at Alexandria , for some Ages after his desease , may be undeniably attested , not only from hence , that ( among others ) both Theon , and Pappus , named Alexandrians , were eminent therein ; of which the one put forth eminent Commentaries upon Ptolomies Works , and the other , among sundry excellent peeces , of which his sixth Book of Mathematicall Collections is one , observed , that about four hundred Years from Christ , the Obliquity of the Ecliptick was not so great , as Erathosthenes , Hipparchus and Ptolomy had conceived : but neer upon the same we discover it to be in our Dayes : we say , that this is not the only Monument that is extant of the flourishing of Astronomy at Alexandria , long after Prolomy had given it so great a Reputation there ; but there remains another as fresh and lively , which is the memorialls of those Patriarchs of the Alexandrine Church , to whose judgement the determination of that great dispute about the true time of Easter , was thought fit to be wholly referred , aswell by the Nicene Councel , as by divers learned Bishops afterward , and by Holy Leo himself , then Pope . Now , among these Patriarchs were Theophilus , Cyrillus and Proterius , whose advice and directions were thought necessary , in regard that the Controversies raised about the Celebration of Easter , about the time of the Veneral Equinox , about the Full-Moon next following , and about constituting certain constant Rules respective to them ; could not be better composed , than by the definitive sentence of these Prelates , who Living at Alexandria , where Astronomy was in such Height , had the advantage of others , in point of knowing those things which were requisite to the finding out of the truth . But , of the Arabians , who in the Study of Astronomy succeded the Alexandrians , and translated into their own language , the Great Composition of Ptolomy , which they called Almagestum ; the First , and most worthy to be remembred , was Albategnius otherwise called Mahometes Aractensis , born of a Family of the Dynastae of Syria ; He about 800 , Years after Christ , made divers Celestial Observations , partly at Aracta , and partly at Antioch : and found , both that the Apogeium of the Sun , since the Dayes of Ptolomy , was advanced to the following Signes ; and that the Stars did regress toward the East , one degree , not in the space of a hundred Years , as Ptolomy also had designed ; but of somwhat less than seventy ; as also , that the Obliquity of the Ecliptick , according to Pappus his Theory , was less ( viz. above 23. degr . 35. minutes ) with many other particulars concerning aswell the Fixt Stars , as the Planets : whereupon he both corrected Ptolomy in many things , and composed new Tables , and wrote a Book intituled , De Scientia Stellarum . After him , within 2 or 3 Ages following , succeeded Alphraganus , Arzachel , Almeon , and other Arbians ; among whom , ( as being already tainted with that superstition which had corrupted the simplicity of Astronomy , with Astrological Fooleries ) some certain Jewes , as ambitiously affecting the glory of Divination as the others , intermixed themselves . After them , for a long time , the Worship of Urania lay neglected , nor did Astronomy receive any the least ( considerable ) advantage by Observators ; till neer about four hundred Years since , Alphonsus King of Castile and Lion , being himself also toucht with the curiosity of Astrological predictions , and discovering that the Tables aswell of Ptolomy , as Albategnius were not exactly agreeable with the Celestial motions ; set himself to the composing of new ones ; and to that purpose convocated as many Arabians and Jewes , as were eminent in those Dayes for Astronomy ; imploying them about Observations necessary to so great a Work , and comparing with them those of their Predecessors , that so they might be the more exact in the performance of their task proposed . And very memorable it is , that ( as hath been credibly reported ) He spent four hundred thousand peeces of Gold on that undertaking : a munificence truely worthy the Heroick mind of so great a Prince , and which well deserves to be had in perpetual commemoration by all lovers of Learning : but somwhat unhappily imployed , in respect the Persons set a Work were not so strict in studiously and constantly observing , as scrupulosly computing , directing their calculations not so much to what themselves and others had really observed , as to certain traditional , mysteries , or Caballistical dreams : that we may pass by their heedlesness , which Regiomontanus detecting , perceived , that they had mistaken the true places of the Fixt Stars , by very neer two whole degrees ; as accounting the numbers of Ptolomy , as if they had bin constituted by him from the beginning of the Years of Christ. Which considered , we have the less reason to wonder , if the Tables composed by them , called from the Kings name , the Alphonsine , and sometimes from the place , where they were made the Toletane Tables ( whence also He , who was President of that assembly of Astronomers , is said to have been one Isaac Chanter of the Toletun Synagogue ) have been found , ever since the time of K. Alphonsus , to disagree with the Heavens , and to require the review and castigation of some new and more faithfull hands . Thence forward Astronomy lay neglected , and almost buried in oblivion , ( only Thebitius an Arabian , and Prophalius a Jew , observed in the mean time some small matters , about the motion of the Fixt Stars , and the obliquity of the Ecliptick , ) untill about two hundred Years since , Georgius Peurhacchius , and Joh. Regiomontanus , his disciple , seemed to revive it . For , these worthy men delivered it cut of the double cloud of ignorance and vanity , which the Arabians and Jewes had raised , to the Observation of its lustre ; and kindled the Light thereof afresh in Germany : reducing Ptolomy , providing Instruments , and making not a few faithfull Observations : though they were not so happy , as to bring their designe to that perfection they hoped and had proposed to themselves ; both of them dying in the middle and flower of their Age. Animated by their example , Nicholaus Copernicus ( a Borussian born , and Canon of the Cathedral Church of Warmes , scituate neer Fruemburgh , in the same Country ) about the beginning of the last Age , seriously addressed himself to the Illustration of Astronomy ; and reviving the long neglected Systeme of the World excogitated by Pythagoras , he made many good Observations , in order to the composing of new Tables But , forasmuch as he could not determine any thing concerning the Fixt Stars , besides their Promotion Eastward , which they appeared to have made since Ptolomy's time ; he therefore composed some Canons of their motions , and those as exact as possibly he could : yet both those , and the Prutenick Tables that were built upon them , were incorrespondent to the motions of the Heavens , though less incorrespondent than the Alphonsine . Nevertheless , the man is to be highly commended , both for his sublime perspicuity , and modesty , in that foreseeing his Canons would need correction , he was wont frequently to exhort and encourage that ingenious young man , Georgius Joachimus Rheticus , deeply enamoured of the beauties of Astronomy , to apply himself principally to the Restitution of the Fixt Stars , and cheifly of those , which were in the Zodiack , or neer it , and with which the Planets might be most conveniently compared : because , without their restitution , it was impossible either to attain to the true places of the Planets , or to atcheive any thing of Moment or certainty , toward the advance of Astronomy . And then at last enters that Noble Dane , Tycho Brahe , upon the Theatre of Astronomy . Who , as by in the impulse of his Genius , being addicted to beholding and noting the Stars , even almost as soon as he saw the light of them ; was so much the more spurred on by that advice of Copernicus , published in the Works of George Joachim newly mention'd , by how much the more clearly he discerned the impossibility of determining the true and proper place of that famous New Star , ( appearing in the Constellation of Cassiopeia , from the beginning of November , in the Year M. D. LXXII . for above sixteen months together ) without the restitution of the Fixt Stars to theirs . For , He plainly perceived , that most , if not all the Errors , which had bin found in Astronomy even from its first foundation or original , took their rise chiefly from hence , that the Fixt Stars really were not in those places , in which they were supposed to be , by Observators ; But some of them were much neerer , and others again as much farther off ; and this , whether because Hipparchus in the beginning had not with due exactness consigned all the Fixt Stars to peculiar places , which indeed he had designed by the Sextant's of degrees ( and truely it is very difficult at once to invent any thing of Moment , and perfect the invention ) or whether because the Transcribers of Ptolomy , out of carelesness , or ignorance , had corrupted the Original Text in many places ; or whether the additions afterward made , in respect of the Stars progress to the following Signes , had occasioned any mistake and imperfection in that Theory ; or whether by any other unhappy cause whatever . Now , in Order to this great Work , of rectifying those fundamental Errors , it pleased Fate , that about the very same time , that truely generous and never enough commendable Prince William Landgrave of Hassia , had zealously devoted his mind and industry to the same care , of restoring the Fixt Stars to their true mansions : but yet the honour he aimed at , was decreed only for the incomparable Tycho ; who in an Heriocal bravery of Soul , had now resolved with himself to enterpise no less than the Instauration of the whole Science of Astronomy from its very fundamentals ; and so to spare neither labour , nor cost ( especially while he was so happy , as to have good part of his expences defraied by the liberal contributions of that eminent Mecenas , Frederick the II. King of Denmark , who thereby recorded his name in immortal Characters on the leaves of Fame ) that should be necessary to the making all Sorts of Observations requisite . As soon therefore as he had furnished himself with that Astronomical Colledge , or Tower for Observations , built by him in the Island of Huenna , to that purpose assigned him by the King , and furnished that Heavenly Cittadel by him called Uraniburg , with store of exquisite and magnificent Instruments Mathematical , he begun ( having provided himself of sundry learned and competent Coadjutors ) exactly to observe the Altitude of the Pole , in that place , by the Circum-polary Stars . By which understanding likewise the Altitude of the Equator , he pointed out the Equinoctial points , by the passing of the Sun through them : and attending besides to the middle parts of Taurus and Leo , he found out the Apogeium of the Sun , and the Eccentricity of it , and deduced its Course from the point of the Vernal Equinox . Moreover , from Venus , in the Day time compared with the Sun , and in the Night with the Fixt Stars ; he endeavoured to search out the right Ascensions , and Declinations of the Fixt Stars : which the Ancients had performed , but fallaciously , by using the Moon , not Venus , to that purpose . And his success was as exquisite as his care in this , that he constituted that bright Star which is in the top of Aries , and ranged the chief of those in order along the Zodiack : and then advancing to enquire or rather find out the distances of the rest aswell from them , as each from other , he defined both the right Ascensions and Declinations of all ; prescribed their several Longitudes and Latitudes , and added to the Catalogue of the Ancients about 200. other Stars , wholly by them omitted . Because the Ancients , Living in an Horizon much more Southern , had observed and set down neer upon 200. Stars , that are invisible in the Danish Horizon , which is highly Northern : and Tycho again collected about 200. more than they could discern ; and as being somwhat small , he intermixed them among others of greater magnitude . Further , having in the mean space , alwaies observed the passings of all the Planets through the Meridian , and their several distances from the cheif Fixt Stars neerest to them : he laid such sollid foundations , as by them might be exactly known not only the true places of each , but also their several Motions . So that he came very neer the heighth of his noble hopes of building the whole Theory of Astronomy a new from the very ground , and of erecting compleat and everlasting Tables for Calculation thereupon : but , alas ! prevented by an immature death , He could not accomplish his designe . It was very much , however , that He went so far , as ●o have recorded and bequeathed to Posterity such excellent Observations , by which Kepler was soon after enabled to compose an intire Theory , and make the Tables called the Rudolphine ; and by which , and others afterward contriveable , whatever can be desired in these Tables , may be fully supplied and perfected . And this among the rest deserves singular commendations , that He left us the Fixt Stars re-installed in their true mansions : wherein He alone , in few Years practice , performed and finished that prodigiously great Work , which no man , from the Dayes of Hipparchus , had either attempted , or in any measure advanced . I pass by many other admirable discoveries of his ; as that he was the first , who demonstrated all Comets to be carried freely through the Etherial Spaces ; that Refractions ought to be carefully considered and allowed for , and how ; that he perceived that the Latitude of the Moon ought to be augmented by more than a Quadrant , or fourth part , than had been conceived ; that He almost demonstrately convinced the Latitudes of the Fixt Stars to be varied ; that he excogitated an Hypothesis , which all those , who cannot allow of the Ptolomaicall , or fear to allow the Copernican , may well adhere to and defend ; with many other things , as difficult in their Invention , as excellent in their use . And observe only how vastly he transcended all that went before him , in point of exactness and certainty . As for Instruments Mathematicall , it is well known , He made such , as for the condition of their matter , for the Vastness of their magnitude , for the variety of forms , for the care of their elaboration , for the preciseness of their divisions , and for the facility in using ; as the World had never the like before . Again , so prodigious was his and his Coadjutors subtility , diligence , industry ; that whereas the Observations of Hipparchus , Ptolomy , and all others before him , had bin marked out only by the Sixth or at most by the twelfth parth of degrees ; he designed all his by the sixtieth parts of degrees , called Minutes , or Scruples , and very often also by subdivisions of Minutes . So that we may well demand what comparison can be made betwixt that gross way found out by Erastothenes , and approved and followed afterward by Hipparchus and Ptolomy , for the Observation of the Obliquity of the Zodiack ; and that most fine and exact one invented by Tycho ? His being , by a division of the Meridian into 83 , parts , and the Interval of the Tropicks deprehended to take up 11. of them , it appeared that the distance of one Tropick from the Equator , amounted to 5. of thoseparts and an half , or , by a reduction of them again to degrees , of 23. degr . 51. Min. and ⅓ : and theirs , being by an hollowed Hemispear of Stone , with a Gnomon erected in the middle , as we have formerly described it ; and to what degree of subtility and exactness this way of commensuration could arrive , the meanest Novice in Astronomy may soon judge . That Quadram likewise of Ptolomy , so much admired by ancient Authors ; Pray , How vastly short did it come of the perfection of the least that Tycho used ? And the same may be said of his Rules ; for , that those Armillae , set up by Pt●lo●y in the entrance of Alexandria had any thing in them comparable to those erected by Tycho , in his Uraniburg , cannot in the lest measure be argued from the other Instruments then in use . It is not necessary , we should here again review those machinaments , or engines , which the old Egyptians and Babylonians made use of , either in discerning the Signes of the Zodiack , or taking the Diameter of the Sun : or those , which Aristarchus and Archimedes used , for commensurating the same Diamater . Only we cannot but wonder , by the by , how Aristarchus , having aimed so neer the white of truth , in the matter of the Suns Diameter , and determining it to be the 720th . part of the Circle , or half a degree ; as is delivered by Archimed : should yet err so widely in his Book of Magnitudes and Distances , as to make the Diameter of the Moon ( which in truth ; is very neer as great as that of the Sun ) to be the 180th . part of the Circle , or 2. degr . when he called it the Fifteenth part of a Signe ; which mistake of his was long since taken notice of by Pappus . Nor is there any necessity , why we should survey those Instruments , that Albateginus , Peurbacchius , Regiomontanus , Copernicus , and other more moderne Astronomers used : considering , that besides the Rules made by Regiomontanus ( which Bernardus Waltherus , his disciple , preserved , and had recourse to , in his Observations of the Suns Altitude ) they came so short of the least of Tychoes , in point of exact reasoning , and amplitude , that they deserve rather to be perpetually forgotten , than remembred to competition . However it is seriously to be wished , that the Observations made by those incomparable Instruments of His , may ly no longer concealed from the World ( for by singular Providence , they have been hitherto preserved , as Gassendus attesteth , ïn the Life of Tycho ) but soon be brought to Light. And this aswell for sundry weighty Considerations there alleadged by Gassendus ; as for this , that not all the Stars , of which Tyeho hath given a copious Catalogue , in his Progymnasmata , may be found reduced to congruous Calculation ( in as much as they doe not exactly correspond with the Heavens ) and that various Catalogues have been pretended from the same , which are very much different each from other : for all the difficulties hereupon depending may soon be removed , and all mistakes rectified , by having recourse to the Fountain , or Original observations , which ! will clearly declare , what hath bin already corruptly deduced , and what may be at length carefully and demonstratively deduced from them . And , in the mean while , if Hipparchus his memory be so highly and ( indeed ) justly precious among learned men , for his great merrits in excogitating and framing Instruments , whereby to take the dimensions , distances , motions &c. of Heavenly bodies : certainly , that of our Tycho ought to be as highly esteemed by us and all Posterity ; since he alone , for so many Ages together was found , that durst not only imitate him in those sublime inventions ; but so imitate , as very much to exceed him . For my part , truely ; since Hipparchus may rightfully be called Atlas the Second : I shall doe but justice to name Tycho , Hercules the Second , who releived his Predecessor , long languishing and ready to faint under so prodigious a burden ; which doubtless was the Reason , why Kepler called him , the Modern Hipparchus . And thus have we in a short Relation , rehearsed to you , what we could gather together , concerning the Original , Progress , and Advance of Astronomy , from the highest of times , of which there remain any Authentick memorials , down to the decease of Tycho Brahe , the Noble and the Great . As for what Additions this excellent Science hath received , by the industry of Astronomers in this present Age , by the help of the Telescope , whose Invention may seem to have been unhappily deferred too long , as being deferred till some Years after Tychoes death : they may be easily summed up . For , all that our Dayes can justly challenge the honour of discovering , is ( 1. ) the spotts in the Sun : ( 2. ) the inequality of the superficies of the Moon : ( 3. ) Venus shifting her apparences , as doth the Moon : ( 4. ) Mercury and Jupiter , in some Proportion , doing the like : ( 5. ) Jupiter with a kind of bound about him , and guarded with four lesser Stars , as Attendants : ( 6. ) Saturn triple-bodied : ( 7. ) the Gallaxy fully beset with small Stars : and ( 8. ) divers pale assemblies of very small Stars , seeming to be only little white clouds in the Welkin ; with some other particulars lately remarked . Now , if you please to add this to the former summary : you have the whole ( though brief ) Story of Astronomy , from its very infancy to that augmented state it now hath attained to : I wish I might have said , to its Full growth and Perfection . But , alas ! that is reserved for Posterity . Notes, typically marginal, from the original text Notes for div A51553-e5650 Longitude of the Stars Latitude of the Stars The meas●res● of the severa Stars Zenith . Nadir . Azimuths , or Verticle Circles . Almicanthars , or Circles of Altitude . Amplitude . Declination . Right Ascension . Oblique Ascension . Oblique Descension . Ascensional Difference . Raise the Pole. Depress the Pole. Course . Distance . Zone . Frozen Zones . Temperate Zones . Burnt Zone . Climates . Parallels . Direct Sphear . Parallel Sphear . Oblique Sphear . Antipodes . Periaeci . Antaeci . Notes for div A51553-e15810 An Hour defined . Minutes , Seconds , and Thirds , &c. defined . Notes for div A51553-e41030 Opposite degrees and minutes of the Ecliptick possess the Cusps of opposite Houses . Notes for div A51553-e62510 Articl . I. Observation Celestial , from the beginning of the world ▪ though rude and in-artificial . Articl . II. Sacred records examined , and Moses found to b the First Astronomer there spoken of . lib. 1. Ant. c. 3. cap. 4. Epigram . de etat , Anim. Gen. 11. Gen. 47. 1. Polit. cap. and 1 Metaph. cap. 1. Act. ●7 Cap. 9. de done ad Poeon . cap. 7. Esa. 47. Articl , 3. Ethnick monuments likewise revolved ; and first those of Fabulous times : according to which Coelus is found the most ancient Astronomer : lib. 3. and after him his Senns . 1. Atlas , who taught Astromy to his Son. lib. 3. lib. 2. cap. 8. Astrom . 1. Hisperus . And Daughters , the Atlantides and Pleiades , from one of whom came Mercury . 1. Astron. lib. 3. lib. de Astrol. 5. Tusculan . 2. Saturn , who delivered the same to his Son. Jupiter . Isagog . ad Phoen. 1. Metamorph. 3. Hyperion . 4. Japetus : from whom came Prometheus , who followed the same study . in Eccles. 7. lib. 2. lib. 37 , o. 10. so did Phaeton , Doedalus , Icarus , de Astrol. in Isagog . Atreus and Thyestes . Hercules and Iphitus . cap. 18. Orpheus . de Ast●ol Palamedes . Homer . Odyss . E. Articl . 4. Secondly , those Historical times ; according to which the antiquity of Astron. Observations belongs either to the Egyptians , or Babylonians . in Epinom . 1. Antiq. 8. in Epinom . 2. lib. de Astrolog . Isagog . loc . citat . de Divi●at . in praefat . lib. 9. c. 56. in Almagest . lib. 4. cap 6. in lib. 2. de Coe lo , and comment . 46. Articl . 5. Yet neither of of them observed any thing considerable ; at to the designation of Times : but corrupted what they had observed , to the introduction of Astrology Judicial . loc . citat . lib. 1. ad Astrolog . 1. in Somn. 21. ibid. cap. 20. lib. 6. stromat . lib. 9. cap. 7. lib. 9. cap. 37. 2. de divinat . in Epinom . Articl . 6. And after them to the Grecians among whom the most ancient mention of Astron. is in Hesiod . Ex Gem Ptol. & aliis . lib. 10. lib. 1. in ●●ebns . Eb. 1. de vit . 〈◊〉 de Com. 〈◊〉 lib. 2. A 〈◊〉 . lib. 2. cap 8. in 1. Geog. l. 8. 1. Georg. 1. adven . Physic. lib. 1. in Arat. ●han● . lib. 7. and next of Thales Milesius . lib. 1. in vit . Dionys. then of Pythagoras , and his Disciples . 2. de coelo . 13. de Arenar , num . Philolaus , Aristarehus , Timaeus . de don . ad paeon. in Timaeun . After these succeeded Cleostratus . Meron . &c. Articl . 7. Eudoxus , who first discovered the necessitie of manifold Spheares . in Epigram . 2. de divinat . Prolom . lib. 1. cap. 11. Articl . 8. Hipparchus , who first observed the places of the Fixt Stars , according to Long. and Latitude . lib. 2. cap. 26. lib. 7. cap. ibid cap. 1. He also corrected the Callippick Period , and predicted future Eclipses , for 600. Years together . Almagest . lib. 9 cap 2. Articl . 9. Betwixt Hipparchus and Ptolemy , came Sosigenes , of Alexandria , by whose help Jul. Caesar endeavored the reformation of the Calendar . 6. A●nl . lib. 2. c 28. 1. Meteor 7. Pythias Massiliensis , a Gaul . and contemporary to Alex. of Maced . lib. 7. cap. 60. Quintus Marcius Philippus , &c. Nasica Scipio , Romans . Articl . 10. Prolemy , the true Founder of Astronomy in one intire structure . Who next resigned it to Theon and Pappus , both Alexandrians . and long after . to Albategnius , then to Alphraganus and other Arabians . Articl . 11. Alphonsus , K. of Castile ; who made and named the Alphonsine Tables . after whom , the Science lay neglected . till , Georg. Peurbaechius and Ioh. Regiomontanus arose , and again caltivated the same . Articl . 12. Then followed the m●st accute Nich. Coper . nicus , who revived the doctrine of Pythagoras , concerning the Earths motion . Articl . 13. And last of All , the noble Tycho Brahe , who out-did all the rest in discoveries and inventions . de Acenar . num . 
A60282	----	Natural philosophy improven by new experiments touching the mercurial weather-glass, the hygroscope, eclipsis, conjunctions of Saturn and Jupiter, by new experiments, touching the pressure of fluids, the diving-bell, and all the curiosities thereof : to which is added some new observations, and experiments, lately made of several kinds : together with a true relation of an evil spirit, which troubled a mans family for many days : lastly, there is a large discourse anent coal, coal-sinks, dipps, risings, and streeks of coal, levels running of mines, gaes, dykes, damps, and wild-fire / by G.S. Sinclair, George, d. 1696. 1683 Approx. 603 KB of XML-encoded text transcribed from 170 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2003-11 (EEBO-TCP Phase 1). A60282 Wing S3855 ESTC R15622 12279911 ocm 12279911 58658 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A60282) Transcribed from: (Early English Books Online ; image set 58658) Images scanned from microfilm: (Early English books, 1641-1700 ; 824:7) Natural philosophy improven by new experiments touching the mercurial weather-glass, the hygroscope, eclipsis, conjunctions of Saturn and Jupiter, by new experiments, touching the pressure of fluids, the diving-bell, and all the curiosities thereof : to which is added some new observations, and experiments, lately made of several kinds : together with a true relation of an evil spirit, which troubled a mans family for many days : lastly, there is a large discourse anent coal, coal-sinks, dipps, risings, and streeks of coal, levels running of mines, gaes, dykes, damps, and wild-fire / by G.S. Sinclair, George, d. 1696. [2], 8, [12], 302 p. : ill., 5 plates. ... are to be sold by Gideon Shaw ..., Edinburgh : 1683. Reproduction of original in Huntington Library. Attributed to George Sinclair. cf. BM. Table of contents: p. [6]-[8] Errata: p. 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Astronomy -- Early works to 1800. 2003-07 TCP Assigned for keying and markup 2003-08 SPi Global Keyed and coded from ProQuest page images 2003-09 Emma (Leeson) Huber Sampled and proofread 2003-09 Emma (Leeson) Huber Text and markup reviewed and edited 2003-10 pfs Batch review (QC) and XML conversion NATVRAL PHILOSOPHY Improven by NEW EXPERIMENTS . TOUCHING The Mercurial Weather-Glass , the Hygroscope , Eclipsis , Conjunctions of Saturn and Jupiter . BY NEW EXPERIMENTS , Touching the Pressure of Fluids , the Diving-Bell , and all the curiosities thereof . To which is added , Some New Observations , and Experiments , lately made of several kinds . TOGETHER , With a true RELATION of an Evil Spirit , which troubled a Mans Family for many days . LASTLY , There is a large DISCOURSE anent Coal , ●oal-sinks , Dipps , Risings , and Streeks of Coal , Levels , Running of Mines , Gals , Dykes , Damps , and Wild-fire . By G. S. Ars longa , vita brevis . Printed in the Year , 1683. And are to be sold by Gideon Schaw Bookseller , at the Sign of the Bible , in the Parliament-Closs , in Edinburgh . To the Right Honourable S r. JAMES FLEMING , Lord Provost of EDINBURGH , George Drumond , David Lindsey , Iames Nicolson , and GEORGE SINCLAR Bailiffs , Archibald Hamilton , Dean of Gild , Thomas Young , Thesaurer , William Borthwick , Deacon Conveener , and remanent Members of the Honourable Council of the said Burgh ; In all Humility offers and didicates this Philosophical Tranasaction , GEORGE SINCLAR Professor of Philosophy and Mathematicks . May it please Your Lordship , and the Honourable Senate , I Present you with a mean Oblation , less than the Widows Mite , but with a willing mind . 'T is all I can afford at present . Farre li●abit , qui non habet , thus : Who wants Frankincense , must sacrifice with Bear-meal . I have sometimes offered more to others , who were not so deserving . I still remember how kindly the Council treated me for some Years ago . when I taught the Mathematicks at Edinburgh ; and what a singular Obligation they conferred upon me after , when I was employed to search out a well , which by good Providence I lighted upon , which is now a Well-spring of Happiness to the Good-Town . I made several Observations , with a most accurate , and exact Level ; but especially one from the highest Ground in the Castle , in the Evening towards the Fountain , by the help of a Light there , on the 29. of May , 1674. which gave infallible assurance to the Magistrates , that the Source was 200. Foot higher than the Weigh-house , and great encouragement to the Council to begin the Work. It is registrate in Scripture , as one of the great Acts of Hezekiah , that he made a Cistern , and a Condu●t , and brought Water into the City of Jerusalem . This work will be extant among the Annals and Chronicles of the City , of things done from Year to Year , to all Generations , which is the glory also of the succeeding Magistrates . But your wisdom and prudence in governing the City , and composing all Differences , and setling all Matters every day so happily , is of far greater moment . This Transaction explains the Weather-Glass , and Hygroscope , which are in great esteem , even among Kings , and Princes . His Royal Highness put no small value upon that which I presented to Him. Non equidem tali me dignor honore . I now crave pardon , that I have adventured to prefix your Names to the Frontispice of this mean Pamphlet , between which , and your incomparable Merits , there is no proportion . All I can do , is to pray , that your Lordship and Council may live to be , as you are , the glory and credit of the Place , and that you may slowly , yet surely exchange at last , this Mortality with Immortal Life . This I fervently wish , while I am Your Honours most humble , and much obliged Servant , GEORGE SINCLAR . Leith , Ianuary 9. 1683. The Explanation of the Weather-Glass . I Have set down the Theory of the Weather after this manner . In the first , and upmost Station , thirty Inch and a half , above the Cistern , is Long Fair , or Most pleasant Weather , as the Poet sings , Totus & ille dies , & quin ascentur ab illo , Exactum ad mensem , pluvia ventisque carebunt . This day and all , which after it remain , F●r th●●ty day● , sha●l want both Wind and Rain . The Metal being at this height , which I rather find to be in Winter , than in Summer , the Heavens are clear : yet sometimes covered with dry and gray Clouds , but not the least appearance of Rain . Nothing for several days after , but setled calm Weather , as dry and hard Frost in Winter , with a clear Sky : sometimes the Air most pure , and clear without Frost . Here it was upon Thursday , October 26. 'T is seldom so high , because we in this Countrey have not often , a most pure , and clear Air , as in France , and other parts of the World ▪ If the Metal ascend to this Station , it is an evident token , that the Glass , is right mounted , and adjusted . I call the second Station , which is half an Inch lower , Fair , or Dry and Fair. ●ace serenato clar●m juhat emicat ax ▪ P●●gatusque nitet di●●ussis ●u●ibus ●●ther . Behold a Ray , tha● 〈◊〉 breaks forth from se●●n● Hea●en And purged Sky doth shine , all Cloud 〈◊〉 that 's been . The Quick-silver being at this Station , the Weather is good ; but not so setled , especially in the Winter-season . I have oftentimes observed a small thin showre of Rain to fall , for some Hours together , from the lowest Region of the Air , as a thick Dew or Mist , but immediatly after , the Day became Clear and Fair , the Air being under a strong disposition to be so . The third Station , half an Inch lower is Changeable , sometimes Fair , sometimes Foul , sometimes Frost , sometimes Thaw , sometimes Sleet , sometimes Snow , sometimes Wind , sometimes Calm . Nun● pluit , & clarus , nune Iupiter aethere surgit . Sometimes ●oul Jove , doth wring the Clouds for Rain , Sometimes fair Jove , appears in Heaven again . The fourth Station is Rain , or Rainy Weather ; not that it Rains always , but that there is a strong inclination in the Air , to be Rain . — Madidl● Notus evolat all● , Terribilem pleca tectus caligine vultum , Barba gravis nimbi● , can●s ●uit unda capillis . Out flyes the South , with dropping Wing● , who shrouds , His 〈◊〉 aspect in the pitchy 〈◊〉 . His white● air streams , his bea●● b●g . ●●●oln with Shor●● ▪ M●●ls bi●● hi● bro● , Rain from his boso● pu●●●es , I call the fifth Station , Much Rain , or Very Foul , as in the Summer , or Winter-time , when Rain is accompanied with strong S. W. and W. Winds . This is bad Weather indeed , both by Sea and Land. — Et den●i ●unduntur ●● aethere n●●bl ▪ Ecce cadunt ●argi , reselusia nubibu● , imbre● Inquetreom credas totum descendere coeluth . 〈◊〉 of Rain , are poured from the Heaven , Waich●●ken Phenus , and his peir●ing Beams . 〈…〉 great 〈◊〉 did fall , Some thought the Heavens to Sea , were tu●bled all . To this Station did the Mercury fall down , on Monday , November 6. and Sunday night , November 19 , being two Inch lower , than October 26. The sixth Station is Stormy , the worst of Weather in this Country . Tum mihi ●ae●ule●● , supra caput astitit imber , N●ctem Hyememque ●erens , & inhorruit und● tenebris . A purpur● showre did Canopy my head . Dark Winter came , and waves grew black indeed ▪ I have subjoyned in the last place Tempests , or Hirricanos , which do not fall out in this Country . They are lively described by the Poet. — Acvent● , velut agmine f●cto , Qua data por●●●unt , & terras turbine per●●●nt . Incubuere mari , to●●mque a sell●us im●s . Una , Eu●u●que , No●●sque en●nt , cre●erque procel●●a Africus , & vasto● volvunt ad littora fluctus ▪ Tempect●●●ine more ●urit , ton●●●●que tren●seunt . Ardua terra●um , ●●●pique & littora circum . — Winds at his mutinous ●ands Force their own way , and thunder through the strands . They take the Sea , Eurus and Notus raves , And stormy Africus from deepest c●ves . When Temp●storage , and Joves great Cannons rea● , The Mountains quake , the Plains , and every Shoar . The first Rule is , the further up the Metal goes , the Weather inclines to be the Fairer , and the further it falls down , it inclines to be the Fouler . Secondly , When it is heighest , Fair Weather is universal , when it is lowest , Foul Weather is universal . Thirdly , 'T is not so much Fair or Foul Weather actually , which influences the Quick-silver , as it is the disposition , and inclination of the Weather , to be Fair , or Foul. Note , That N. E. and E. Winds , even with Ra●n , do raise the Mercury , and keep it up sometimes beyond ordinary . And as it shews the nature of the Weather , so it foretells ; which is the great excellency of it , sometimes a day , sometimes two , sometimes three or four , before any change of Weather come . The Metal rises and falls quickly , when Fair or Foul Weather is nigh at hand . It doth not so much foretel Winds , as it is actually influenced by them , when they blow , in causing the Metal subside and fall down . 'T is said , that the Ladies and Gentle-women at London , do Apparel themselves in the Morning , by the Weather-Glass . Whatever be in this , 't is certain , that when a Man riseth in the Morning , he may know infallibly , what sort of Weather , will fall out ere Night . It is not possible to make it unerring , unless it be mounted , and set up by a skilful Hand , which few or none can do . The inclosed Weather-Glasses , are Ten Dallers , the open ones Thirty Shillings , which are as true . None from Abroad are so accurately made . Neither any such are sold , at so easie a rate . They may be transported , and carried to any part of the Country , and there set up , by my Directions . The Explanation of the Hygroscope . THis second is a curious Invention , which I call the Hygroscope . The The name is made up of two Greek words , Hygros Wet , and Scopeo to view or consider : because we know by it , the several degrees of moisture , and dryness in the Air. It is mean to look upon , being but the Awin , and Beard of a Grain of Oats . It is Twisted , and Twined by Nature , as the Lute String , or a Silk Cord is twined by Art. It is secured within a round Box , whose inside is divided into 24. equal parts . There is affixed to the top of it , a small slender Glass-Index , which goes about with the Awin , as it is altered with the moisture , or dryness of the Air. The motion is direct , or right about , following the course of the Sun , with moisture , and retrograde , or left about , with dryness . It is likewise stationary , or standing , when the Air is setled , as to wetness , or dryness . It is of all of all things , in the Universe , so far as I know , most affected and sensible of humidity and s●●city . Many curious Philosophical Questions do arise from its several Operations ▪ which would trouble Oedipus himself , to resolve . I have found the Index , from Wet Air in extremity , to Dry Air in extremity , make six Revolutions . For this cause , I have contrived a little Broad , with six Circles upon it , or rather Spirals , divided equally into 24. parts , as the inside of the Box is , by the help of which , a Man may trace the motion of it , all the Year over , most easily , whether it be Direct , or Retrograde . You will find these advantages by it . Wet Air in extremity , Dry Air in extremity , Air equally moist and dry , Wet Air , Dry Air. It discovers the least difference of Air between one Room and another . It is much influenced with Winds from the North , especially in Frost , which make it Retrograde , and with Winds from the South , which make it Direct and move right about . In a Years time , it makes several Revolutions . The motion is most sensible , for sometimes in one Night , it will alter 90. Degrees , o● the fourth part of a Circle . It not only shews the present temperament of the Air , which is a great advantage , but foretels . Nay , which is admirable , I have found it sometimes foretel Fair Weather , when it was actually Raining . It keeps a correspondence with the Weather-Glass . There is great difficulty to know what Revolution it is under , from Wet Air in extremity , or from Dry Air in extremity , for fixing the Brass-Pin in its own proper Circle . The Husk or Hool , of the Mouse-Pea , ( as we call it ) or the Wild Vetch , will make a Hygroscope , but it is somewhat dull and slow , and goes not so oft about , yet very sensible of the Wetness , and Dryness of the Air. When the Index of the Hygroscope , is altered by the Weather , it keeps not a continued motion , but sometimes moves backward , and sometimes forward ; yet at length perfects its course right about , in so many Months , and returns again in so many . Among the many difficulties which occur , this is one , What is the reason , why the Awin goes alwayes right about with Moisture , and left about with Dryness ? To say , that it is so ordered by Nature , is ridiculous . The same difficulty we find in the Shells of Snails , whose Screw , and Spiral line , goes right about , with the Sun , and in the Shells of Sea-Snails , commonly called Buckies . Some affirm , that upon the South of the Line , the Shells of these Creatures , are screwed left about , which is worthy of observation . 'T is easie to give the reason ▪ why a Lute String turns about such a way with Moisture ; because , while it was twined by the Artist , the Wheel or Spindle went such a way about , wherewith he twisted it . But who can say the like of the Awin , seing the great Artist is GOD , and Nature , whose working and manner of working is unknown to us . 〈◊〉 be asked , What way goes about the Hool of the Wild Vetch ? I answer , which is a notable Speculation ▪ The one Hool , goes right about with the Sun , by Moisture , as the Awin doth , and consequently left about , with Dryness . But the other goes right about with Dryness , and left about with Moisture , contrary to the motion of its fellow Hool . This is seen sensibly , by holding them nigh the Fire . The same holds true , in the two Hools of the Right Pea-cod . I suppose that the Hools of Brom-seed , may do the like . Another Experiment I made with the Hygroscope , in placing it , within the Receiver of the Air-pump . At the very first Exsuction of the Air , the Index moved left about most sensibly , and by the several Exsuctions , which were made one after another , it advanced , half a Circle about . It had been easie to have made it go right round once , if I had continued Pumping . Here is a Phenomenon to be salved , and well worthy the pains of a Virtuoso . But because some may think , I have spoken too much of a thing of small concern , I shall therefore say but one word or two more . That even upon the obscurest , and meanest of the Creatures , the LORD hath impress'd an Indelible Character , of His Wisdom and Skill . Though we cannot well know , for what use and end , the Oat-Grain hath an Awin , and why it is twisted , yet we must remember , that GOD , and Nature , never made any thing in vain . Do not undervalue it , because it is meanly let out ; for there is in it a Pearl of great price ; Christopherus Sturmius a German , a great Virtuoso , and famous Mathematician , makes honourable mention of it , in his Writings , which he hath taken from my A●s Nova & Magna , as he hath done many other Curiosities and published them to the World , not as his own Inventions , but as mine : which by the way , gives a notable check to my old Adversaries , who with the Bed●lls Gown about their heads , endeavour'd to make the World , in their beggarly Pamphlet believe , th●● all my Philosophical Experiments were Untruths and Lies . Sed non est remedium adversus Sycophantae mo●sum ; there is no cure or remedy against the bi●ng of Slanderers . Mr ▪ Boyl did not think so as witness his Experiments ●ouching Flame and Air. They are sold for Six Shillings . A short account of the late Comets , and of some Eclipsis . ANno 1652 , An obscure Comet appeared in the beginning of Winter , seen in the forenight , nigh to the Constellation of Taurus . It did not continue long ; yet Lilly that old Astrologer made it very prodigious . A second , far more glorious , appeared in the beginning of December , 1664. It raise before the Sun several Mornings , with a long Ray , pointing towards the West . First then , it was Cometa Barbatus , the Ray going before the Star. It had a very swift motion towards the West , inclining upward , till it came the length , to be in opposition to the Sun , on the 19. of December , where it appeared Cometa Crinitus , without a Ray. Being under a swift motion , it advanced more Westerly and upward , and was seen clearly upon Sunday night , December 25. with a long Ray , pointing towards the East , which made it Cometa Caudatus , the Train following the Star , and setting after the Sun. This made many believe , that there were two Comets . It evanished a little below the Rams-head , after it had continued from December 8. 1664 , to February 8. 1665. A third was seen , the same Year 1665 , in March , and continued till the 7. of April : A fourth was seen in the middle of April , 1677 , about 11. a Clock at Night . It continued but a short time . The fifth seen over all Europe with admiration , appeared first clearly to us , December 14. 1680. It continued till February 8. 1681. The sixth Comet , was seen Thursday Night , August 17. 1662 , in the North , about 11 a Clock at Night , in the second Foot of the Great Bear. It had a swift motion towards the West , declining from the North. It past over above the back of the Lion , and under Coma Berenices , under Arcturus , crossing Bootes forefoot , towards the Aequinoctial , and thence towards the Beam of the Ballance . Anno 1682 , Saterday night February 11 , about 11 a Clock , a prodigious Eclipse of the Moon . The total darkness , continued an Hour and a half , measured by the Pendulum Clock . The Eclipse , was not only Total , but Central , that is to say , a straight Line might have been drawn almost , from the Centre of the Moon , thorow the Centre of the Earth , to the Centre of the Sun. The Moons face was red as Blood , especially about the midle of the Eclipse . Compare it with Ioel 2 : 10. Acts 2.19 , 20. Isa. 13.10 . Ezek. 32.7 , 8. Mat. 24.29 . Luk. 21.25 . Anno 1662 , December first , all the seven Planets met in that one Sign of Sagittarius , the Archer . Anno 1663 , Friday October 9. A conjunction of Saturn and Iupiter in the 13. deg . of Sagittarius . Anno 1661 , April 23. Mercury did Eclipse the body of the Sun. This Year 1682 , a conjunction of Saturn and Iupiter in the Sign Leo , on the 23. of October , which is the fourth Conjunction , since they entered the fiery Trigon , which are Sagittarius , Leo , and Taurus . Anno 1679 , April 2. Two Suns seen in the Firmament , in the Fore-noon , in East-Lothian . Extraordinary Foul-Weather followed this Parelia . Anno 1598 , February 25. a total Eclipse of the Sun , so that the Stars were seen . It is to this day called the Dark Saterday . Anno 1652 , March 29 , in the Fore-noon , a total Ecipse of the Sun , so that the Stars were seen likewise . It is commonly called the Dark Monday . Simsines Philadelphus , a devout Man , and learned Astrologue , writes in his Book , which he published Anno 1626 , and dedicated to Frederick King of Bohemia , that there never happened , any great Change or Alteration , in any State or Kingdom , in Europe ; but what hath been accompanied , with a Conjunction of Saturn and Iupiter , under some Trigon or other . And reckoning over all the ten Principalities and Dominions , which have been in Britain , since the Year of the World 3618 , he comes at last to the Year 1603 , in which , Saturn and Iupiter , after they had returned into the Fiery Triplicity , being the seventh time from the Creation , fell in Conjunction in that Fiery Sign Sagittary , in the Month of December . Here he takes occasion , to mention King Iames , his succeeding to the Crown of England that year , of whom by the way , take this Distichon , or two Verses . Cura Del , vasemque lab●r , sapientia secii , Pax quoque , mulavit , regna quaterna Polo . Gods Care , the Ag●s Wit , Peace , Prophets Pairs , For Kingdoms fou●● in Heaven a kingdom gain● . And shews , that this , which he calls Regnum Scotorum , the Dominion of the Scots , and tenth Principality , was received , by these two superior Planets , in their Greatest Conjunction . Note , That these Conjunctions , are sometimes propitious , as this was . It was likewise favourable to the Hollanders , who were treated with a Free State Anno 1607. And concludes , with these remarkable words . Et non jam expectanda est gravior aliqua mutatio in Britannia , nisi continua Consanguinearum successio ; siquidem Periodi huic regno transierint . Nam à primo Rege Bruto usque ad presentem annum elapsi sunt anni 1978. That is , And now there is not any greater Change to be expected in Britain , but a continued Succession of the Nearest in Blood ; for truly the Periods to these Dominions are gone , and past over . Because from the first King Brutus to this present Year , there are past 1978 Years . This Brutus was the first King of the Britains , who began his Reign in the Year of the World 3618 , under the Aerial Trigon , and Conjunction of Saturn and Iupiter , in the Sign Gemini . For the better understanding , know that the twelve Signs are divided into four Triplicities , which are called by Astrologues Trigons . The first Trigon , is called the Fiery Trigon , which contains , Aries , Leo , and Sagittarius . The second is the Earthy , which contains , Taurus , Virgo , and Capricorn . The third is the A●rial , which contains , Gemini , Libra , and Aquarius . The fourth is the Watery , which contains , Cancer , Scorpius , and Pisces . If it happen , that Saturn , and Iupiter be in Conjunction this Year in Leo , there next Conjunction , will happen , twenty Years after , or truly , 19 Years , 315. Days , and 19. Hours after , in Sagittarius . From Sagittarius to Aries ▪ from Aries to Leo , and so in round till 198. Years , and 236. Days passing , they make a Transit into a New Trigon , so that the Revolution of one Trigon consumes almost 200. Year . My Author speaking of that Conjunction , which fell out Anno 1643. in Aries , says , Alicujus Imperii , vel Regni , revolutionem portendit . It betokens a change in some Empire or Kingdom in Europe , which really came to pass after , as all know . A Journal of the late great Comet under the Latitude of 55. deg . 54. m. 30. s. ON the 22. of November , 1680 , it was first seen at Plimmouth , in England , soon in the Morning . Upon the 14. of Decem. being Tuesday , it appeared first to us , in the Constellation called Antinous . This Antinous , was of the Country of Bithynia , who for his vallant deeds , was Canonized , and added to the number of the Gods , and placed in Heaven , in Capricorn , in which Sign the Sun at that time was , deg . 3. m. 39. This Comet had a Ray , which went straight up from it , about 60. Degrees in length . This Night , at 5. a Clock , it had 5. deg . of Altitude , above the Horizon . The Ray was broader , and more spread out above , than below . In the Head was a clear Star , of a whitish colour . The middle of the Ray covered the lesser Star in the Gorge of the Eagle . The Poets feign , that this was the Bird , that flew up into Heaven with Ganymedes , whom Iupiter loved so dearly ; for which good service , he placed the Bird among the Stars ▪ Wednesday , Decemb. 16 ▪ at 5. a Clock at Night , the Blazing-Star , seemed to be higher , by 3. degrees almost , and more Easterly . For this Night , the middle of the Ray eclipsed the bright Star , in the neck of the Eagle , which is the greater , and more towards the East ; but somewhat lower . The Pinion of the lowest Wing of the Swan , did terminate the extremity of the Train . On Thursday Morning following , about 5. a clock , the Ray was seen above the Horizon : at least much of it , not straight up , out sloping towards the North. At Night , December 16. about 5. a Clock , the Star had about 11. degrees of Altitude above the Horizon . At which time , the Ray had passed by , both the two forementioned Stars in the Neck of the Eagle , it being far more Easterly . It was not seen , till Sunday at Night , December 19. at which time , it was yet further up above the Horizon , the middle of the Train , covering the Constellation , called the Delphin . Neptune the god of the Sea , greatly desired , to match with Amphitrite , who being modest , and shame-faced , hid her self . After long search , he sent the Delphin , who found her out , for which good service , he placed this Fish in the Heaven . It was not seen till Decemb. 24. at which time in the Evening , it was past the Aequator , and had about 7. degrees of North Declination , and was in the 20. degree of Aquarius , not far from the Nose of Pegasus . The Night following , being Saterday , Decemb. 25. It was not seen . Sunday Decemb. 26. It was seen , at 5. a Clock , with 37. degrees of Altitude . The middle of the Ray , did cover the right Knee of Pegasus . The end did terminate in the very Zenith , between Cassiopea , and Perseus . After this the Star was not seen , till Ianuary 2. 1681. This Night the Ray , past thorow the Belly of Pegasus . Perseus did terminate the end of it . Pegasus the winged Horse , was bred of the blood of Medusa , after that Perseus had cut off her Head. Bellerophon made use of this Horse , and having performed some valiant deeds here on Earth , endeavoured to fly up to Heaven on his Back ; but being amazed by looking down to the Earth far below him , he fell from his Sadle . Pegasus , notwithstanding continuing his Journey , came at last into Heaven , and there obtained a place among the Constellations . Monday Ianuary 3. the Comet was distant from And●omeda her head , about 5 degrees , but somewhat more Westerly . Upon Tuesday Ianuary 4. the Comet , was nearer to the Head of Andromeda , but somewhat lower . Ianuary 5. being Wednesday , the Comet was within a degree and a hal● , of the Head of Andromeda , but a little lower , and more Westerly . Thursday Ianuary 6 , the Comet was higher , than the Head of Andromeda , but more Easterly . The Ray passed thorow between the two bright Stars , in the Belt of Andromeda . Perseus did terminate the end of it . This Night , the Ray was 30. degrees long . Friday Ianuary 7. it was not seen . Saterday Ianuary 8. the Head of the Comet , was within one degree , of the Star , which is in the lest Shoulder of Andromeda , but a little higher , and more Easterly . The Ray was 22. degrees extended . Sunday Ianuary 9 , the Comet was yet higher , by one degree , and more Easterly , than the foresaid Star. The bright Star in the South Foot of Andromeda , did terminate the end of the Ray. It was not seen , till Friday Ianuary 14 , on which Night , it was about mid-way between the bright Star , in the Belt of Andromeda , and the point of the Triangle , but somewhat higher to the said bright Star. Andromeda was the Daughter of Cepheus , and Casstopea , and the Wife of Perseus , who , by the favour of Minerva , was taken up into Heaven , and placed among the Constellations . Saterday Ianuary 15 , the Comet was somewhat higher , than it was the Night foregoing . Tuesday Night Ianuary 18 , it had this position with the Triangle , according to the first Figure . Thursday Night Ianuary 20 , it had this position with the Triangle , according to the second Figure . Thursday Night Ianuary 27 , it was thus placed , according to the third Figure , about one degree , and a half above the Eastmost Star in the B●se of the Triangle . The Ray was about 8. degrees in length . The end of it , was bounded with the Eastside of Medusa's Head. The Triangle was placed in Heaven , in honour of the Geometricians , among whom , the Triangle , is of no small importance . Others say , that it was placed there by Mercury , that the Head of the Ram , might be the better knowen . Saterday Night Ianuary 29 , the Comet , was in a right Line , with the first Star of Aries , and the bright Star in Medusa's Head. And in a right Line , with the West-most Star , in the Base , of the Triangle , and the Pleiades . It was the matter of 8. degrees distant from the East-most Star , in the Base of the Triangle , further up , and more Easterly . Perseus , the son of Iupiter , and Danae , kill'd the Monster Medusa , and cut off her Head. Her golden Hairs were turned into Serpents by Minerva , for polluting her Temple with Neptune . Whosoever looked on her after this , were turned into Stones . Perseus , falling into trouble of Mind , for killing accidentally , his Grand-father Acrisius , was taken up into Heaven , by his Father Iupiter , and placed there , with Medusa's Head in the one Hand , and the Sword in the other . Wednesday February 2 , the Comet was scarce discernable , yet further up in the Heavens , and more towards the East , than before . Tuesday Night , February 8. being the last time , it was seen , nothing appeared distinctly , save a small short Ray. This Night , it had 20. degrees of North Latitude , from the Ecliptick . It had 46. degrees of Longitude , from the first point of Aries . It was distant from Medusa's Head , 5. degrees . It was distant 14. degrees , from the West-most Star , in the Base of the Triangle . It was 10. deg . 30. m. from the bright Star in Andromeda's foot . It was 16. degrees , from the first Star in Aries . It was 17. deg . 30. m. from the Pleiades , or Seven Stars . It was in the 16. degree of Taurus . From December 14 , 1680. until February 8 , 1681. It had advanced , the matter of 120. degrees , in the Arch of a great Circle , following the order of the 12. Signs , from about the beginning of Capricorn , to the 16. of Taurus . This perhaps , may be lyable to the Pharisaick Censure , of some Mathematical Rabbi ; but let him first , be at as much pains , as I have been at in Observing ; and next , let him make his Observations , as accurate , and true as these are , without an Observatory , and the help , of fit , and proper Instruments . THese are to give Advertisement , to all Ingenious Persons , who have found out , any New Inventions , or made any New Observations , of things Astronomical , of things in the Sea , in the Earth , above Ground or under . In a word , whatever may be useful , for the promoting of Natural Knowledge , and Learning , and profitable to others , let them be communicated to the Author of this Transaction , a true Narration being made , he shall have them published , with accuracy , and satisfaction to himself . Printed in the Year , PraefVLsêre DVo , res anno rara , pLánetae , HeI nobIs MIserIs , IVngVntVr , In ore LeonIs . VVhen SatVrn In the heaV'ns , to IoVe CoMes near , TO THE READER . Courteous Reader , I Shall not detain thee in the entry with a long Preface , but give a short account of what is needful to be known , of the Cause , Occasion , and Matter of the following Treatise . After the publication of my last Piece , about the Weight and Pressure of the Air , I found it needful to treat of the Pressure of the Water , because of the near relation between the two : the operations , and effects of both depending almost upon the same Principles and Causes . And that there are many things , which cannot through●y be understood , of the Pressure of the Air , without the knowledge of the Pressure of the Water : therefore to make the first the more evident , I have spoken of the second : the effects and operations of Hydrostatical Experiments , being more conspicuous and sensible , then the effects and operations of the other . The Occasion was some spare time I had now and then , for making some Trials : part whereof are published here ; the rest being rather some productions of Reason , attentively exercised on that Subject ; which notwithstanding may be called Experiments , though never actually tried , nor haply can be , because of some accidental impediments : yet supposing they were , I make it evident , that such and such Phenomena would follow , whence many necessary conclusions are inferred . As for the subject matter , there are first , moe then thirty Theorems in order to the Pressure of Fluid Bodies , as Air , Water , and Mercury , which in effect are nothing else , but so many conclusions rationally deduced from various and diverse effects of Aerostatical , Hydrostatical , and Hydrargyrostatical Experiments , which for the most part , I have tried my self . There are next twenty Experiments briefly described , by their own distinct Schematisms : their Phenomena , according to the Laws of the Hydrostaticks are salved , and several new conclusions inferred . A Proposal is likewise made of a more convenient Engine for Diving . Here , several difficulties are proposed , and answered , and all the obvious Phenomena of Diving explicated . If the Lead which sinks the Ark , be judged too weighty , and big , which may render it not so tractable , and likewise hinder the Ark from going so near to the ground , as is desirable , and in some measure stop the sight , ( which troubles are ( I suppose ) incident to the Bell also ) it may be reduced to a far less weight , and quantity , and the overplus being made square and thin pieces , may line the mouth of the Ark without , between P Q and L M , according to the Figure 25 , or may be put to , or taken away at pleasure . The Bell may have likewise in stead of this troublesome Foot-board , a weighty Ring of Lead , or two , to go round about the orifice without , in form of a Girth , or Belt , which may slip off and on at pleasure , and will as conveniently sink it , as if it had a weight appended : the Foot-board then may be of any form , quantity , or weight you please . There are thirdly some Miscellany Observations , the design of which is only Philosophical . Some of them are Experiments made with the Air-pump , which I have adventured to insert here , even though the Noble Mr. Boyl hath given an account of many . But because the Engine was offered to me by the Laird of Salton , a Gentleman of a choise Spirit , I could not , but in obedience to his commands make use of it , and shew him the Product . There are also two or three observations in the close , as that of the Primum vivens in Animals : of the Aliment , and growth of plants : and of the motion of the Aliment in Trees . To all which is added a short History of Coal , which I hope will be acceptable to some ; this so needful a subject , never being treated of before by any . In it , mention is made of things common to Coal in general , as Dipps , Risings , and Streeks . Next , of Gaes , or Dykes , which prove so troublesome sometimes to the working of Coal . Thirdly , of Damps , and Wild-fire . Next , a method is taught for trying of Grounds , where never any Coal was discovered before . And lastly , the manner how Levels , or Conduits under-ground , ought to be carried on , for draining the Coal , and freeing it of Water . When this Book was first committed to the Press , I sent an intimation thereof to some of my friends , for their encouragment to it , a Practice now common , and commendable , which hath not wanted a considerable success , as witness the respect of many worthy persons , to whom I am oblidged . But there is a Generation , that rather , than they will encourage any new Invention , set themselves by all means to detract from it , and the Authors of it : so grieved are they , that ought of this kind should fall into the hands of any , but their own . And therefore , if the Author shall give but the title of New to his Invention , though never so deservedly , they fly presently in his throat , like so many Wild Catts , studying either to Ridicule his work altogether ▪ a trade that usually , the person of weakest abilities , and most empty heads , are better at , than learned men , like those Schollars , who being nimble in putting tricks , and impostures upon their Condisciples , were dolts , as to their Lesson , or else fall upon it with such snarling , and carping , as discover , neither ingenuity , nor ingeniousness , but a sore sickness , called Envy . In the Intimation , I affirmed , that the Doctrine concerning the Weight , and Pressure of the Water was New. This one word , like a spark of Fire falling accidentally among Powder , hath been the occasion of so much debate . Their ground is , because they look upon the Hydrostaticks , as a Science long ago perfected , seing Archimedes 2000 years ago hath demonstrat the Water to have a Pressure , and some others since , as Stevinus . They affirm likewise , that all the Theorems , and Experiments , that are here , are either deduceable from Archimedes , and Stevinus , or are the same with theirs . If these Gentlemen had suspended their judgment , till this Book had been published , I suspect they would not have spoken so confidently . For Archimedes his propositions , they are but few , and proven ( as Mr Boyl saith ) by no very easie demonstrations , which have more of Geometrical subtility , than usefulness in them . But these , which are here proposed , are not only useful , but evidently evicted by reason , and sensible Experiments , even to the meanest capacities . And though some of mine , may ( perhaps ) co-incide with some of his , which to me is but accidental , yet our way of procedour is toto Coelo different . His way is more Speculative : this is more Practical . His demonstrations are Geometrical : these are Physical . His propositions are but for the use of a few : these are for the use of all . His are not illustrated , and confirmed by Hydrostatical Experiments : these are . Stevinus a late Writer keeps that same method . Yet I judge it easie to let see , even in the entry , how little cogent some of his demonstrations are , without derogating from such a Learned Man. He hath indeed some Pragmatical Examples ( as he calls them ) for illustrating some of his Geometrical Propositions , anent the Pressure of the Water ; but I leave them to be considered by the judicious and understanding . Again , in this Method , I am yet as much different from others , who have written lately , as from these I have been speaking of . For , I not only treat of the Pressure of the Water , but takes in with it , the Pressure of the Air joyntly ; since to explicat sufficiently the Phenomena of the Hydrostaticks , without it , it is impossible . And yet furder , I not only counterpoise Air with Water , but Air with Mercury , and Water with Mercury ▪ by which means several mysteries , and secrets in this Art , are discovered . There are several Inventions found out of late in the Hydrostaticks , whose ●●ents and effects , cannot be clearly deduced from the grounds of Archimedes , and Stevinus , who had not that clear discovery ( for ought we know ) of the Pressure of the Air , that some now have , without which , these effects can never be sufficiently explained . And who doubts , but others afterwards , may make farder discoveries , and profit the world yet more , with their Inventions , then any have yet done . Is then the Hydrostaticks , a Science long ago perfected ? To this Pedantick Conceit , I must again oppose the judgment of Mr. Boyl , who saith moreover , that the usefulness of this part of Philosophy hath been scarce known any farder than by name , even to the generality of learned men . But let us suppose that the notion of the Pressure of the Water , is of an old date , even as old as the Flood ( for Noah surely knew , that the Pressure of the Water , would sustain the Ark ) and ( giving , but not granting ) that Archimedes 2000 years ago hath written all the Principles of the Hydrostaticks , doth this hinder any man now , from deducing new Conclusions from these old Principles ? But there is here , no such thing for neither in this , nor in my last Piece , are my Adversaries able to trace me . 'T is like the purposes would have been so much the better , if I had followed other mens foot steps : and it is like they might have been so much the worse . I doubt not , but I have lighted upon other mens thoughts in some things : and others writting on this same subject , who perhaps are my Antipodes , may fall upon mine . My Antagonists affirm , they are able to deduce all my Theorems , and the events of all my Experiments from the grounds of Archimedes and Stevinus . If they take not their word again , I hope they will do it ; for now I put them to it . And though they should , ( which I am not affraid they shall do in haste ) yet they must prove next , that these Theorems and Conclusions , so deduced , are not new , which all their Logick will not prove . But what if we do more , ( say they ) even overthrow many of all your Aerostatical and Hydrostatical Experiments , in this , and in your last Pe●ce ? I give you liberty , and for your hire , a Guiny for each Theorem , or Experiment , you are able to ransack , in either of the two Books , though they come near to an hundred . But , ye must oblige your selves ( my Maste●s ) to do it with Reason , laying aside your Sophistry and ●anina eloquentia . And this I offer , Reader , that I may reduce them , to a better humour , and encourage them to leave off flyting , and only use reason . Neither must they be like the Wasp , that only lights upon the sore place . But if they love to kindle any more fire , they will find me proof against it . If it burn them , it shall not heat me . Nevertheless , if they love to juik under deck , like Green-horns , having no courage in themselves , or confidence in their cause , they must excuse me , if at last , I write their names upon a Ticket , and bring them above deck . This is all I have to say , at present ( Reader ) and I bid thee farewell . ERRATA . Pag. 21. lin . 8. for weight read bensil . Pag. 185. lin . 24. for EH , read FH . Pag. ●35 . lin . 24. for 500. read 5000. Pag. 307. lin . 26. read promoting . Pag. 313. lin . 22. read reflection . Ibid. lin . 25. read elaborarint . Pag. 317. lin . 2. read & magna . Note , that in placing the Figures , the 12 , that should have the fourth place in the third Plate , hath the first place in the fourth . Contents of the EXPERIMENTS . THe first , second , and third Experiment , touching the rising and falling down of Water in Tubs of different sizes . Pag. 37.41.44 . The fourth is a Hydrostatical Experiment , shewing the Reason why the Mercurial Cylinder rises , and falls , in the Torricellian Experiment , as it is carried up , or down thorow the Air. pag. 46.50 The fifth , shewing the reason , why the Mercurial Cylinder rises and falls in the Baroscope , as the Pipe is reclined and erected . p. 51 The sixth , touching the suspension of Liquors in Pipes , either closs or open above , not only of Water by Water , but of Water by Air. pag. 55 , &c. The seventh , touching the Cause of the suspension , and keeping up of Water in Weather-glasses . pag. 59. The eighth , touching the reason , why a Stone weighs less in Water than in Air. pag. 71. &c. The ninth , touching the reason , why under a Water 34 foot deep , the hight of the Mercury in the Baroscope , is 58 inches . pag. 77. &c. The tenth , touching the reason , why a man gripping with his fingers the Torricellian Tub , seems to find the weight of the Liquor within , and yet finds it not . pag. 82. &c. The eleventh , touching the counterpoising of Mercury in Glass-pipes under-water , by the help of a Ballance above , adduced to prove that a heavy Body weighs as much in Water , as in Air. pag. 86. The difficulty answered , pag. 87. &c. The twelfth , touching the reason , why a Cylinder of Brass , may be suspended by a Surface of Water , before it touch the bottom , that 's 100 foot deep . pag. 101. &c. The thirteenth is , touching two plain heavy Bodies suspended under a Water 34 foot deep . pag. 109 Doctor Mores Argument against the Pressure of the Air , answered . pag. 117 The fourteenth , touching the counterpoising of Mercury with Water : of Mercury with Air and Water ; whence some notable Phenomena appear . pag. 120. &c. The fifteenth , touching an Experiment tried in a Water 72 foot deep . pag. 127. &c. The sixteenth , touching the reason , why the different wideness of Tubs , makes no alteration in the hight of the Liquors suspended in them . pag. 133. The seventeenth , a notable trial for proving the Pressure of the Water . pag. 137. &c. Mr. Boyls Experiment insufficient . pag. 146. The eighteenth , touching the Diving-Ark . pag. 153. &c. The nineteenth , touching a Siphon made to work under Water with Mercury , by the Pressure thereof , as a Siphon operats with Water , by the Pressure of the Air. p. 180. The last is for demonstrating the precise and just weight of any Pillar of Air , Water , or Mercury . p. 183. &c. Contents of the MISCELLANY OBSERVATIONS . Observation 1. Anent the killing of Animals in Coal sinks , by the power of Damps and Ill Air. pag. 197. Observ. 2. Touching the position of Iupiter , with the Stars of Gemini , Novemb. 24. 1669. p. 201. Observ. 3. For knowing the motion of the Sun , or Moon , in seconds of time . ibid. Observ. 4. Touching an Experiment made on the top of Cheviot . p. 207. Observ. 5. Touching the oval-Figure of the Sun , at his setting . p. 209. Observ. 6. Touching a considerable Thunder , with great Lightnings , in East-Lothian , in Iuly 1670. p. 210. Observ. 7. A method for finding out the true South and North Points . p. 212. Observ. 8. Touching the reason , why a dead body of a man , or beast , riseth from the ground of a Water , after it hath lien there three or four dayes . p. 216. Observ. 9. Is a second Experiment made in a Coal-sink , for knowing the power of Damps and Ill-Air . p. 217. Observ. 10. An account of Experiments tried with the Air-pump . p. 218. Observ. 11. An Experiment made , for knowing the reason , why a round heavy Body , as a Bullet of Iron , falls not off a plain Body , under motion , but lies dead . p. 224. Observ. 12. Shewing the reason why a stone demitted from the top of a Ships-Mast under Sail , falls directly upon the place it hang over . p. 226. Observ. 13. Touching the hight of the Mercury in the Baroscope , observed by D. Beal . p. 228. Observ. 14. Touching the variation of the Magnetick Needle here . p. 228. Observ. 15. Touching the Elevation of the Pole here . p. 228. Observ. 16. A second method for finding the Meridian . p. 229. Observ. 17. Touching a considerable showre of Hail , with Thunder , and Rain . ibid. Observ. 18. Touching a curious Experiment made lately in Germany , for shewing the wonderful force of the Air. p. 230. Observ. 19. Touching some proposals of new Engines for War. p. 233. Observ. 20. Touching a sad trial one Mr. Campbel suffered in his Family for many dayes from the Devil . p. 238. Observ. 21. Touching a large Horn cut off a Womans head lately . p. 248. Observ. 22. Touching the Primum vivens in Animals . ibid. Observ 23. Touching the Aliment and growth of Plants p. 252. And touching the motion of the aliment in Trees . p. 254. Observ. 24. Touching a History of Coal . p. 258. In Auctorem & Opus ENCOMIASTICON . AETher is expansi , vitrei Maris Antitalanton , Peroledos , Elasin , Fluidarum ritè videntes , Ingenio patefacta tuo , Magnalia rerum , Laudarûnt alacres Galli , Belgaeque sagaces . Aggreder is nunc Arte Novâ , trutinare profundi Corpora , submersas quondam producere Gazas , Tollere demersis ingentia pondera Cupis . Gas fracidum in Cryptis ortum Fossoribus atrox , Submisso in Fundos Aurae renovante Flabello , Propulsare doces , Lithanthracumque Cavernae Quê is foveantur Aquis , quo tendant , unde oriantur , Ordine quò circum Saxorum strata recumbant . Quòd benè coepisti Naturae cuncta foventis Munera solerti perge Illustrare Mathesi . GEORGIUS HEPBURNUS , M. D. à Monachagro . To the Reader . Reader , That thou mayest know , by one word more , how useful this part of Philosophy is , and how far from being a Science long ago perfected , take but this following proposal , lately , since my Book came to a close , communicated to me by a Friend , which , by his ●llow●nce , I have published , reserving the Answer to himself , the Author thereof . Brother , BY what you have published in your Ars Nova & Magna , and this Book , I have been led to this Invention , to beget within the Bowels of the Sea , a Power , or Force , which with great safety , and ease , shall bring up the greatest weight , that can be sunk therein : ad data quae cunque pondera demersa , in Maris visceribus Potentiam producere , quae modo securo , & facili , è fundo cujusvis altitudin's ad summum , ipsa evehat . I drew a Letter one night , sh●wing the way how this might be done , which I communicated to you , that it might have been Printed with your Book : but after second thoughts , I judged it more meet to keep it up for a time , and that it should be set forth by way of Proposal only at the first , by Your Brother , Mr. Iohn Sinclar . O miston , May 20. 1682. This New Invention , though Hydrostatical , is tru●y Mechanical , there being here a ●ondus and a Potentia , whose operations depends upon Mechanical Principles . But in several respects it is far more admirable , than the most part of the Mechanical Engines , which are look'd upon as stupendious . Many things , almost incredible , are reported of Archimedes , which he admirably brought about , by his Mechanical Powers ; but I am confident , that by this Invention , as great a weight may be lifted , if not greater , as the Power of any Mechanical Faculty can be able to move . I know , the greatest conceivable weight , may be demonstrat , to be moved by the least conceivable Power , as the Earth , by the force of a mans hand . But how is it possible to contrive Artificially , an Engine for that purpose , which will do that by Art , which the demonstration makes evident by reason ? It was thought a great enterprize , when Pope Sixtus the fifth , transported an Obelisk , which had been long since dedicated to the memory of Iulius Cesar , from the left side of the Vatican , to a more eminent place , 100 foot distant ; but to raise a Ship of 1000 Tun intirely , nay , a weight 100 times greater , is surely a far greater enterprize . This Invention is so much the more admirable , that not only by it , any supposed weight may be lifted , but from any deepness . Though this ( perhaps ) cannot be done Mechanically , because of some Physical , or Moral impediment , yet according to the Laws of the Hydrostaticks it can be demonstrat , and made evident by reason . And if this be , then surely , when the Weight is determinat , as the burdens of all Ships are , and the deepness known to be within so many fathoms , this Invention cannot but be successful . Though the strength of Mechanical Inventions , may be multiplied , beyond the bounds of our Imagination , whereby the greatest Weight , may be moved , by the least Power ; yet the Wisdom of God , hath thought it fit , so to confine that knowledge , that it cannot teach , how both of them , can move with the same quickness and speed . For , if that were , the very works of Nature might be overturned . Therefore , it is observable , that when a great Weight is moved by a small Power , the motion of the one , is as much slower than the motion of the other , as the Weight of the one , exceeds the Force of the other . If it were possible Mechanically to move the Earth with the Force of a mans hand , the motion thereof would be as much slower , than the motion of the hand , as the Weight of the one , exceeds the Force of the other , which is a great disadvantage . And as the Weight and Power do thus differ , as to swiftness , and slowness in motion , so also , as to Space . For , by how much the Power is in it self less , than the Weight , by so much will the bounds or Space , the Weight moves thorow , be less than the Space , the Power goes thorow . If it were possible ( keeping the same instance ) to move the Earth with a mans hand , the Space thorow which it passeth , would differ as much from the Space the hand goes thorow , as the one exceeds the other ; which is another disadvantage . It may be thought , that if this Invention depend upon Mechanical Principles , it may be obnoxious to these abatements . I answer , though there be in it a Pondus , and a Potentia , a Weight , and a Power , this moving the other , yet it will evidently appear from Experience , that the motion of the one , is as swift as the motion of the other , and that the one moves as much Space and bounds in the same time , as the other , which is a great advantage . In this , it excells all the Mechanical Powers , and Faculties , that have ever yet been invented and practised . If any think , that such a device cannot be effectuat , without a considerable expence . I answer , the expence is so small , that I am ashamed to mention it . The method and manner of doing this , is most easie likewise . Neither ought this to be a ground , why any man should contemn it ; since the most useful Inventions ordinarily are performed with the greatest facility . As it commends this part of Philosophy to all ingenious Spirits , as most pleasant , and most profitable , so it gives a check to the ignorant , who look upon it as a Science long ago perfected . In praise of the AUTHOR , and his WORK . 1. WHilst Infant-Art no further did pretend Then to flat notions , and a bare desi●e ; What by small toyl we now do comprehend , Our Predecessors only did admire . 2. Now fruitful Reason , arm'd with powerful Art , Uncovers Nature to each knowing eye : Our Author to the World doth here impart What was before esteem'd a mystery . 3. The various motions of that Element , Whose liquid form gives birth to much debate ; By demonstration he doth represent , Unfolding th'intrigues of that subtil state . 4. The Waters Course , and Sourse , from whence they flow , By him to th'sense so clearly are display'd ▪ Their current Weight , and Measure now we know , 'T is no more secret , but an open Trade . W. C. Hydrostatical THEOREMS , Containing some useful Principles in order to that excellent Doctrine , anent the wonderful Weight , Force , and Pressure of the Water in its own Element . THEOREM I. In all Fluids , besides the first and visible Horizontal surface , there are many moe imaginary , yet real . Figure 1. FOR the better understanding the following Experiments , it is needful to premit the subsequent Theorems ; the first whereof is , that in all Fluid bodies , such as Air , Water , and Mercury , or any other liquid , there is besides the first and visible surface , innumerable moe imaginary , under that first , yet real , as may be seen from the following Schematism , which represents a Vessel full of Water , where besides the first surface ABCD , there is a second EFGH , and a third IKLM , and so downward , till you come to the bottom . This holds true , not only in Water , but in Air also , or in any other Fluid body whatsoever . I call the under-surfaces imaginary , not because they are not real ; for true and real effects are performed by them ; but because they are not actually distinguished amongst themselves , but only by the Intellect . THEOREM II. In all Fluids , as it is needful to conceive Horizontal Plains , so it is needful to conceive Perpendicular Pillars , cutting these Plains at right Angles . Figure 1. THis Proposition is likewise needful for understanding the following Doctrine , anent the Pressure of the Water : for in it , as in all Fluids , though there be not Columes or Pillars actually divided , reaching from the top to the bottom , yet there are innumerable imaginary , which do as really produce effects by their pressure , as if they were actually distinguished . These imaginary Pillars are represented in the first Schematism , one whereof is AEINOPQ , the other BFKRT , and so forth . THEOREM III. There is a twofold Ballance , one Natural , another Artificial . BY the Artificial Ballance , I understand that which the Mechanicks call Libra , which Merchants commonly use . By the Natural Ballance ( which for distinctions cause I so nominat ) I mean , v. g. a Siphon , or crooked Pipe , wherein water naturally ascends or descends , as high or low in the one Leg , as in the other , still keeping an evenness , or likeness of weight . THEOREM IV. Fluid bodies counterpoise one another in the Ballance of Nature , according to their Altitude only . THis Theorem will appear afterwards most evident , while we pass through the several Experiments ; and it is of special use for explicating sundry difficulties that commonly occur in the Hydrostaticks . The meaning of it is shortly this : while two Cylinders of Water are in the opposite Scales of the Natural Ballance , they do not counter poise one another according to their thickness : for though the one Pillar of Water be ten times thicker , then the other , and consequently heavier , yet is it not able to press up the other , that 's more slender , and so lighter , beyond its own hight : and therefore they weigh only according to their Altitudes . THEOREM V. In all Fluids there is a Pressure . Figure 1. THis is true not only of the Elements of Air , and Water , while they are out of their own place ( as they speak ) but while they are in it . For Air and Water , being naturally indued with weight , the second foot cannot be under the first , unless it sustain it : if this be , it must necessarily be prest with its burden . So this Water being naturally a heavy body , the foot I cannot be under E , unless it sustain it , and be prest with the burden of it ; the foot N , being burdened with them both . From this Pressure , which is in Air , ariseth a certain sort of force , and power , which may be called Bensil , by vertue whereof , a little quantity of Air , can expand and spread out it self , to a very large quantity , and may by extrinsick force be reduced to that small quantity again . Though this expansive faculty be evident in Air , yet it is scarcely discernable in Water , unless it be in very deep parts , near the bottom , where the Pressure is great . This Pressure is not of the same Degree in all the parts , but is increased and augmented , according to the deepness of the Air and Water ▪ for the Air upon the tops of Mountains , and high places , is thought to be of a less Pressure , then in Valleys : and Water is of a less Pressure , ten or twelve foot from the top , then twenty or thirty . So is the Water N , under a far less Pressure , then the Water , P or Q. THEOREM VI. The pressure of Fluids is on every side . Figure 1. THe meaning is , that Air and Water presseth not only downward , but upward , not to the right hand only , but to the left also , and every way . So the foot of water K , not only presseth down the foot R , but presseth up the foot F , yea presseth the foot I , and the foot L , with the same weight . And the first imaginary surface , is as much prest up , by the water IKLM , as it is prest down by the water EFGH . Upon this account it is , that when a Sphere , or Glob is suspended in the midle of Water , or Air , all the points of their surfaces are uniformly prest . After this manner , are our bodies prest with the invironing Air , and the man that dives , with the ambient and invironing Water . THEOREM VII . All the parts of a Fluid in the same Horizontal Line , are equally prest . Figure I. THe meaning is , that the foot I , is no more prest , then the foot K : neither is the foot L , more burdened , then the foot M. The reason is , because each of these feet , sustains the same weight : for EFGH are all of them , of the same burden : therefore all the parts of a Fluid in the same Horizontal surface , are prest most equally . This holds true in Air , and Mercury , or in any other Liquid also . THEOREM VIII . The Pressure of Fluids seem to be according to Arithmetical Progression . Figure I. THe meaning is , that if the first foot of Water , have one Degree of Pressure in it , the second must have only two , and the third must have only three , and so forth , which appears from the Schematism : for the first foot E , having one Degree of weight , and the second foot I , having of its self as much , and sustaining E , it must have two Degrees , and no more . So the foot N , sustaining two Degrees of Pressure from I and E , must have the weight only of three Degrees , O of four , P of five . It 's evident also from Experience , for while by the Pressure of Water , Mercury is suspended in a glass tub , we find , that as the first fourteen inches of Water , sustains one inch of Mercury , so the second fourteen inches sustains but two , and the third , but three . But if the Pressure were according to Geometrical progression , the third foot of Water ought to sustain four inches of Mercury , the fourth , eight ; the fifth , sixteen , &c. which is contrary to Experience . THEOREM IX . In all Fluids there is a twofold weight , one Sensible , the other Insensible . THe first is common to all heavy bodies , which we find in Water , while we lift a Vessel full of it from the ground . The Insensible weight of Water , and Air , or of any other Fluid , can scarcely be discerned by the senses , though it be as real , as the former , because the Pressure is uniform . By vertue of the second , bodies naturally lighter than Water , are driven from the bottom to the top , as Cork . So , a man falling into a deep Water , goes presently to the bottom , and instantly comes up again . Here is a natural effect , which cannot want a natural cause ; and this can be nothing else , but the Pressure of the Water , by vertue whereof he comes up , and yet he finds nothing driving him up , or pulling him up . Therefore , there is in all Fluid bodies , an Insensible weight , as there is one Sensible ; seing the man that ( perhaps ) weighs seventeen Stone , is driven up fifteen or sixteen fathom by it . And it must be very considerable , and exceed the weight of the man , seing it is able to overcome such a weight . So are vapours and smoke driven upward by the Insensible weight of the Air , and by that same weight , do the Clouds swim above us . THEOREM X. The Insensible weight of Fluids , is only found by sense , when the Pressure is not uniform . FOr understanding of this Proposition , I must suppose somethings that are possible , but not practicable . Put the case then , while a man opens his hand , the Air below were removed , he would scarce be able to sustain the weight of the Air , that rests upon the Palm above : or if the Air above were annihilated , he would not be able to bear down the weight that presseth upward . Or , while a Diver is in the bottom of the Sea , if it were possible to free any one part of his body from the Pressure of the Water , suppose his right arm , I doubt not , but the blood would spring out in abundance from his finger-ends : for the arm being free , and the other parts extreamly prest , the blood of necessity must be driven from the shoulder downward , with force , which cannot be without considerable pain . It is evident also , from the application of the Cuppin-glass , which being duely applied to a mans skin , causeth the Air to press unequally , the parts without , being more prest than the parts within , in which case the unequal Pressure causeth the pain , and so is found by sense . THEOREM XI . A Cylinder of Water , or of any other Fluid body , loseth of its weight , according to its reclination from a Perpendicular position , towards an Horizontal or levell scituation . FOr understanding of this , consider that while a Pipe full of Water stands perpendicular , the lowest foot sustains the whole weight of the Water above it : but no sooner you begin to recline the Pipe from that Position , but assoon the Pressure upon the lowest foot grows less ; So that if the lowest foot , in a perpendicular position , sustained the burden of ten feet , it cannot sustain above five or six , when it is half reclined . A certain evidence whereof is this , the more a Cylinder of Water is reclined towards the Horizon , or Level , it takes the shorter Cylinder of Water to counterpoise it , as is evident in Siphons . For , though the one Leg , be sixteen inches long , and the other but six ; yet a Cylinder of Water six inches long , will counterpoise a Cylinder of sixteen . But this cannot be , unless an alteration be made in the Pressure . For , how is it possible , that a Cylinder of Water can sometimes be in aequilibrio with a lesser , and sometimes with a greater weight , unless the Weight , and Pressure of it , be sometimes more , and sometimes less ? When I say a Cylinder of Water loseth of its weight by reclination , it is to be understood only of the Insensible Weight : for the Sensible Weight is unchangeable , seing it is alwayes a Pillar of so many inches , or feet . Now the true reason , why the Pressure upon the lowest foot grows less , is this ; the more the Pipe is reclined , the more weight of the Cylinder rests upon the sides of the Pipe within ; by which means , the lowest foot is eased of the burthen , and is altogether eased , when once the Pipe lyes Horizontal . THEOREM XII . All motion in Fluids , is from the unequal Pressure of the Horizontal surface . Figure 1. FOr understanding this , I must distinguish a twofold motion in Fluids ; one common , another proper , by vertue of the first , they incline , as all other heavy bodies , to be at the center of the Earth . It is evident in the motion of Rivers , which descend from the higher places to the valleys , even by vertue of that tendency they have to be at the center . By vertue of the second , they incline to move every way ; not only downward , but upward , hither and thither . This sort of motion is peculiar , and proper only to Fluids ; and it is that which is spoken of in this Theorem . I say then , that all motion in Fluids , is from the unequal Pressure of the Horizontal surface . For put the case A , were more prest then B , e. g. with a stone , then surely as the part A descends , the other part B will ascend , and so will C and D rise higher too . Suppose next , the part A were fred of the Pressure of the Air , then surely in the same instant of time , would the part A ascend , and the parts BCD descend . As this Proposition is true in order to the first and visible surface ABCD , so it is true in order to the imaginary surface IKLM ; for put the case the space I , were filled with a body naturally heavier then Water , as lead or stone , then behoved that part of the surface to yeeld , it being more prest , then the part of the same surface K. Or if the space K were filled with a body naturally lighter then water , as Cork , then ought the water R to ascend , it being less prest , then the water N or S. THEOREM XIII . A body naturally heavier then Water , descends ; and a body naturally lighter , ascends . Figure 1. FOr understanding of this , let us suppose the quadrat space E , to be filled with a piece of Lead or Iron . I say then it must go down to I ; and the reason is , because the quadrat foot of Water I , is more pressed then the quadrat foot of Water K. To illustrat this , let us suppose that each quadrat foot of this Water weighs a pound , and that the heavy body existing in E , weighs two pound . If this be , the foot of Water I , must yeeld , seeing it is more prest then K : upon the same account must the Water N yeeld , and give way to the Stone , seeing it is more prest then R. For according to the twelfth Theorem , There cannot be unequal Pressure upon a surface , unless motion follow . For understanding the second part , let us suppose the space R , to be filled with a piece of Cork , that is specifically or naturally lighter then Water . I say then , it must ascend to the top B ; and the reason is , because the quadrat foot of Water K , is more prest upward , then the quadrat foot of Water I , or L is : but this cannot be in Fluid bodies , unless motion follow thereupon . I say , it is more prest up , because R being lighter then N , or S , it must press with greater force upon K , then S can do upon L , or N upon I. It is still to be remembred , That Fluids presseth with as much strength upward , as downward , according to the sixth Theorem ; and that an Horizontal surface doth as really suffer unequal Pressure from below , as from above . THEOREM XIV . Bodies naturally lighter then Water , swim upon the surface and top . Figure 1. THe reason of this Proposition must be taken from the nature of an equipondium , or equal weight . For without doubt , there is a counter-ballance between the Pressure of the Water , and the weight of the body that swims . To make this probable , let us suppose there were a piece of Timber in form of a Cube , six inches thick every way , without weight . In this case , the under-surface of that four-squar'd body , being applied to the surface of the Water A , would ly closs upon it , as one plain Table lyes upon the face of another , without any pressure : and it being void of weight , the part of the surface A , would be no more burdened , then the next part B adjacent , whence no motion would follow . Here is no equipondium , or counter-ballance . Secondly , let us suppose the said body to acquire two ounces of weight , then it follows , that it must subside , and sink two inches below the surface ABCD ; and that so far , till it come by vertue of its new acquired weight , to a counter-ballance with the Pressure of the Water . Which Pressure is nothing else , but as much force or weight , as is equivalent to the weight of Water , that is thrust out of its own place , by the subsiding and sinking of that body , two inches . Thirdly , let us suppose the same body to acquire other two ounces of weight , then must it subside other two inches . Lastly , let us suppose that it acquires six ounces of weight , then it follows that the whole body sinks , so far , I mean , till its upmost surface be in an Horizontal line with the surface of the Water ABCD. Here it swims also , because the weight of it becomes just the weight of so much Water , as it hath put out of its own place . I say , it must swim , because if the Water I , was able to sustain the Water E , which is put from its own place , surely it must be able to sustain that body also , that did thrust it from its own place , seing both are of the same weight , namely six ounces . In this case , the body immerged , and the water wherein it is drowned , become of the same weight specifically , seing bulk for bulk is of the same weight . To make this body specifically , or naturally heavier then Water , and consequently to sink to the bottom , nothing is required , but to suppose that it acquires one ounce more of weight ; which done , it presently goes down , I , being more burdened then K. Note by the way , a twofold weight in heavy bodies , one individual , the other specifick , and that two bodies agreeing in individual weight , may differ in specifick weight . So a pound of Lead , and a pound of Cork , agree individually , because they are both 16. ounces : but they differ specifically , because the one is naturally heavier then the other . THEOREM XV. No Body that flots above Water , even though its upper surface be level with the surface of the Water , can ever be made to swim between the top and the bottom . Figure 1. FOr clearing this Proposition , let us suppose F to be a four-square piece of Timber , of the same specifick and natural weight with Water , and consequently its upper surface to be level with the surface of the Water ABCD. I say then , if it be prest down to R , it shall arise thence , and never rest till it be where it was , namely in F. The reason seems to be this , because the four-squar'd body of Water R , is really heavier , then the four-squar'd piece of Timber F. If this be true , it follows of necessity , that it must ascend : for if the Timber existing in R , be lighter then the Water R , the Water T must be less prest , then the Water O , or the Water V ; whence ( according to the twelfth Theorem ) motion must follow . Again , if the Timber R , existing in the Water R , be lighter then the same Water is , then must the Water K , be more prest up then the Water I , or L ; whence yet , according to the same Theorem , motion must follow . If it be said , that the Timber F , is of the same weight with the Water R , because , it being equal in weight with the Water F , which it hath thrust out of its own place , it must also be equal in weight to the Water R , seeing F and R being of the same dimensions , are of the same weight . There is no way to answer this difficulty , unless I say the four-squar'd body of water R , is really and truly heavier then the four-squar'd body of Water F. The reason seems to be , because the Water R , is under a greater Pressure , then the Water F ; and by vertue of this greater Pressure , there are really moe parts of Water in it , then in F ; therefore it must be heavier . Even as there are far moe parts of Air , in one cubick foot near the Earth , then in six or seven near the Atmosphere . Hence it is , that a pint of Water taken from the bottom of the Sea , fourty fathom deep , will be heavier , I mean in a ballance , then a pint taken from the surface . Take notice , that when the vessel is once full at the bottom , the orifice must be closely stopped , till it come to the top : otherwise the parts that are compressed at the bottom , namely by the weight of the superiour parts , relaxes themselves , before they come to the top . THEOREM XVI . It is not impossible for a body to be suspended between the surface and the bottom . Figure 1. FOr understanding this , suppose F to be a four-square piece of Timber , which though it will not rest but at the surface , ABCD , yet may be made to go down of its own accord , and rest at T , namely , by making it so much heavier , as the Water T is heavier then the Water F. To know this difference , which is not very practicable ; the Cube of Water T , must be brought from its own place , under the same degree of Pressure it hath , and put into the Scale of a Ballance , and weighed with the Cube of Water F , put into the other Scale . Now if the Water T , be half an ounce heavier , then the Water F , then to make the Timber F hing in T , it must be made half an ounce heavier . There seems to be reason for it also ; for if a Cube of Timber resting in the space T , be just the weight of the Water T , the imaginary surface OTV , is no more prest , then if T were Water , and so it cannot go downward : neither can it go upward , seing the under part of the Water R , is no more prest up by the Timber T , then if the space T were filled with Water . If it be said , according to this reasoning , a Stone may be suspended in a deep Water , between the top and the bottom , which is absurd . I answer , such a thing may happen in a very deep Water : For put the case a Cube of Lead twelve inches every way , were to go down twelve thousand fathom , it is probable , it would be suspended before it came to the ground . For coming to an imaginary surface far down , where the Pressure is great , a Cube of Water twelve inches thick there , may be as heavy ( even specifically ) as the Cube of Lead is , though the Lead be ten times heavier specifically , then any foot of VVater at the top . If Water suffer compression of parts , by the superiour burden ; it is more then probable , that the second foot of Water burdened with the first , hath moe parts in it , then are in the first , and the third moe , then in the second , and so forth ; and consequently , that the second is heavier , then the first , and the third heavier , then the second . Now , if this be , why may not that foot of Water , that hath sixty thousand foot above it , by vertue of this burden , be so comprest , that in it may be as many parts , as may counter-ballance a Cube of Lead twelve inches every way ? If then , that imaginary surface , that is sixty thousand foot deep , be able to sustain the said foot of VVater , which perhaps weighs twenty pound , why may it not likewise sustain the Lead , that is both of the same dimensions with it , and weight ? Hence it is , that the Clouds do swim in the Air , by vertue of a counter-ballance : And we see , which confirms this Doctrine , that the thinnest and lightest are alwayes farthest up ; and the thickest and blackest , are alwayes farthest down . THEOREM XVII . The lower the parts of a Fluid are , they are the heavier , though all of them be of equal quantity and dimensions . Figure 1. THis follows from the former , which may appear a Paradox , yet it seems to be true : for though the Water Q at the bottom , be of the same dimensions with the Water E at the top , yet it is really heavier , which happens ( as I said ) from the superiour Pressure . It is clear also from this , namely the Cube of Timber E , which swims upon the surface , being thrust down to Q , comes up to the top again , which could not be , unless the Water Q , were heavier then the Water E. I suppose the Water E , and the Timber E , to be exactly of the same sp●cifick weight , and consequently the surface of the Timber , to ly Horizontal with BCD . Now the reason , why the Timber ascends from Q to E , is no other then this , namely that the one Water is heavier then the other ; for the under part of the Water P , being more prest up with the Timber existing in Q , then with the Water Q it self , it must yeeld and give way to the ascent : for if the Cube of Timber existing in Q , were as heavy as the Water Q it self , it would no more press upon P , or endeavour to be up , then the Water Q does . THEOREM XVIII . A heavy body weighs less in Water , then in Air. Figure 1. THis is easily proven from experience ; for after you have weighed a stone in the Air , and finds it two pound , and an half , take it , and suspend it by a threed knit to the scale of a ballance ; and let it down into the Water , and you shall find it half a pound lighter . The question then is , why doth it lose half a pound of its weight ? I answer , the stone becomes half a pound lighter , because the surface of Water on which it rests , sustains half a pound of it : For put the case a stone were resting in R , that weighed two pound and an half in the Air , it behoved to weigh but two pound in this Water ; because the Water T sustains half a pound of it . For if this Water T be able to sustain the Water R , that weighs half a pound , it must be also able to sustain half a pound of the stone , seing half a pound of stone is no heavier , then half a pound of Water . Note , that when a heavy body is weighed in Water , it becomes so much lighter exactly , as is the weight of the Water it thrusts out of its own place . THEOREM XIX . A heavy body weighs less nigh the bottom of the Water , then nigh the top thereof . Figure 1. FOr clearing this proposition , I must suppose from the 17. Theorem , that the lower the parts of Water be , they are the heavier , though all of them be of equal dimensions . If then the lowest foot Q be heavier , that is , have moe parts in it , then the foot N , it of necessity follows , that a stone suspended in Q , must be lighter then while it is suspended in N or I. Because , if a stone be lighter in Water then in Air , as is said , even by as much , as is the weight of the bulk of Water , that the bulk of the stone expells , then surely it must be lighter in the one , then in the other place ; because suspended in Q , it expells moe parts of Water , then while it is suspended in N or I. For example , let us suppose the Water N , to weigh eight ounces , and the Water Q to weigh nine , then must the stone suspended in Q , weigh less by an ounce , then suspended in N , seeing as much is deduced from the weight of the stone , as is the weight of the Water it expells : but so it is , that it thrusts nine ounces of Water out of its own place in Q , and but eight in N or I ; therefore it must be one ounce lighter in the one place , then in the other . This may be tried , with a nice , and accurat ballance , which will bring us to the knowledge of this , namely how much the foot of Water Q is heavier , then the Water N or O. THEOREM XX. One part of a Fluid , cannot be under compression , unless all the parts next adjacent , be under the same degree of Pressure . Figure 1. THis proposition may be proven by many instances : for when the Air of a Wind-gun , is reduced to less quantity by the Rammer , all the parts are most exactly of the same Bensil . So is it in a Bladder full of wind . It 's true , not only in order to this artificial Pressure , but in order to the natural Pressure , and Bensil of the Air likewise . For the Air within a parlour , hath all its parts , under the same degree of natural compression : so is it with the parts of the Air , that are without , and immediatly under the weight of the Atmosphere . It s evident also in the parts of Water : for the foot of Water R , cannot be under Pressure , unless the Water S , and N , be under the same degree of it . Though this be true of Fluids , while all the parts lye in the same Horizontal surface , yet to speak strictly , it will not hold true of the parts scituated under divers surfaces ; for without question , the foot of VVater T , must be under four degrees of Pressure , if the VVater R , be under three . And if the Air in the lowest story of a building , be under six degrees of Bensil , the Air in the highest story must be under five . If a man would distinguish Metaphysically , and subtilly , he will find a difference of this kind , not only between the first , and second fathom of Air , nearest to the Earth , but between the first , and second foot ; yea , between the first and second inch , and less ; much more in Water , as to sense . However it be , yet the Theorem holds true ; for we find no difference sensible , between the compression of Air in this room ; and the compression of Air in the next room above it , no not with the Baroscope , or Torricellian Experiment , that discerns such differences accurately . I judge it likewise to be true , in order to the next adjacent parts of Fluids of different kinds ; for while a surface of Mercury , is burdened with a Pillar of Water , or a surface of Water , with a Pillar of Air , whatever degree of weight and Pressure , is in the lowest parts of these Pillars , the same is communicated entirely , to the surfaces , that sustains them . So then , there is as much force and power , in the surface of any Water , as there is Weight and Pressure , in the lowest foot of any Pillar of Air , that rests upon it : otherwise , the surface of Water would never be able to support the said Pillar : for a surface of six degrees of force , can never be able to sustain a a Pillar of Air , of eight , or ten degrees of weight . THEOREM XXI . The Pressure of Fluids , may be as much in the least part , as in the whole . Figure 1. THis Theorem may seem hard , yet it can be made manifest , by many instances : for albeit the quantity of Air , that fills a Parlour , be little in respect of the whole Element , yet surely , there is as much Pressure in it , as in the whole ; because Experience shews , that the Mercurial Cylinder in the Baroscope , will be as well sustained in a Chamber , as without , and under the whole Atmosphere directly ; which could not be , unless the small portion of Air , that 's in this Parlour , had as much Pressure in it , as in the whole Element . Besides this , it will be found in a far less quantity : for though the Baroscope were inclosed , and imprisoned so closs , within a small Vessel , that the Air within , could have no communion with the Air without , yet the Pressure of that very small quantity , will sustain 29. inches of Mercury , and this will come to pass , even though the whole Element of Air were annihilated . This Proposition is likewise evident in order to the Pressure of the Water : for put the case , the Baroscope , whose Mercurial Cylinder is 29. inches , by the Pressure of the Air ; were sent down to the bottom of a Sea 34. foot deep , within a Vessel , as a Hogs-head , and there exactly inclosed , that the VVater within , could have no commerce with the VVater without , yet as well , after this shutting up , as before , other 29. inches would be sustained , by the Pressure of this imprisoned VVater , which proves evidently , that there is as much Pressure in one Hogs-head full of VVater , at the bottom of the Sea , as in the whole Element of VVater , above , or about : for an Element of VVater never so spacious , if it exceed not 34. foot in deepness , can sustain no more Mercury , then 29. inches by its Pressure . Yea , though the Vessel with the Baroscope , and imprisoned VVater in it , were brought above to the free Air , yet will the VVater retain the same Pressure , and will de facto sustain 29. inches of Mercury , provided the Vessel be kept closs . It is therefore evident , that as much Pressure may be in one small quantity of VVater , as in the whole Element , or Ocean . 'T is to be observed , that this Theorem is to be understood chiefly of the lower parts of Fluids ; seing there cannot be so much Pressure in the VVater P , as in the VVater Q ; for in effect , there is as much Pressure in the VVater Q , as is in the whole VVater above it , or about it . From this Theorem , we see evidently , that the Pressure , and Bensil of a Fluid , is not to be measured , according to its bulk , and quantity , seing there is as much Bensil in one foot , nay , in one inch of Air , as is in the whole Element , and as strong a Pressure in one foot of VVater , or less , as there is in the whole Ocean : therefore the greatest quantity of Air , hath not alwayes the greatest Bensil , neither the greatest quantity of VVater , the greatest Pressure . But this will appear more evident afterwards . THEOREM XXII . The Pressure , and Bensil of a Fluid , is a thing , really distinct from the natural weight of a Fluid . Figure 1. THis may be easily conceived ; for as in solid bodies , the Bensil , and natural weight , are two distinct things , so is it in Air , and Water , or in any other Fluid . The weight of a Bow , is one thing , and the natural weight of it , is another . The weight of the Spring of a Watch , and the Bensil of it , are two distinct things . The weight ( perhaps ) will not exceed two ounces : but the Bensil ( may be ) will be equivalent to two pound . Though these may illustrate , yet they do not convince : therefore I shall adduce a reason , and it 's this . The natural weight of a Fluid is less , or more , as the quantity is less or more ▪ but it is not so with the Pressure , because there may be as much Pressure in a small quantity , as in a great , as is evident from the last Theorem , therefore they may be different . The first part of the Argument is manifest , because there is more weight in a gallon of Water , then in a pint . A second reason is , because a Fluid may lose of its pressure , without losing of its weight . This is evident from the Schematism , for if you take away the four foot of Water EFGH , and consequently make the four Pillars shorter , the foot of Water Q becomes of less Pressure , but not of less Weight , seeing the quantity still remains the same : at least , the loss of weight is not comparable , to the loss of Pressure . I say , it becomes of less Pressure , because there is a less burden above it . Thirdly , the Pressure and Bensil may be intended , and made stronger , without any alteration in the weight : so is the Bensil of Air , within a Bladder , made stronger by heat , without any alteration , in the weight of it . Likewise , the Pressure of the foot of Water Q , may be made stronger , by making these four pillars higher , without any alteration , at least considerable , in the weight ; for it still remains a foot of water , whatever be the hight of the pillars above it . Lastly , the weight of a Fluid is essential to it , but the Pressure is only accidental ; because it is only generated , and begotten in the inferiour parts , by the weight of the superiour , which weight may be taken away . THEOREM XXIII . Though the Bensil of a Fluid , be not the same thing formally with the weight , yet are they the same effectively . THis proposition is true in order to many other things , besides Fluids : for we see that the Sun , and Fire , are formally different , yet they may be the same effectively ; because the same effects , that are done by the heat of the Sun , may be done by the heat of the Fire . So the same effects , that are produced by the weight of a Fluid , may be done by the Pressure , and Bensill of it . Thus , the Mercurial Cylinder in the Torricellian Experiment , may be either sustained by the Bensil of the Air , or the weight of it . By the Bensil , as when no more Air , is admitted to rest upon the stagnant Mercury , then three or four inches , the rest being secluded , by stopping the orifice of the Vessel . By the weight of it , as when an intire Pillar of Air , from the top of the Atmosphere , rests upon the face of the stagnant Quicksilver . It is also evident in a Clock , which may be made to move , either by a weight of Lead , or by the force , and power of a Steel Spring . THEOREM XXIV . The surfaces of Waters , are able to sustain any weight whatsoever , provided that weight press equally , and uniformly . Figure 1. THis is evident , because the imaginary surface of VVater OTVX , doth really support the whole sixteen Cubes of VVater above it , yea , though they were sixteen thousand , And the reason is , because they press most equally , and uniformly . VVhat I affirm of the imaginary surface , the same I affirm , of the first and visible . For let a plain body of lead , never so heavy , be laid upon the top of the VVater ABCD , yet will it support it , and keep it from sinking , provided it press uniformly all the parts of that surface . It is clear also , from the subsequent Theorem . THEOREM XXV . The surfaces of all Waters whatsoever , support as much weight from the Air , as if they had the weight of thirty four foot of Water above them , or twenty nine inches of Quick-silver pressing them . THis Proposition is evident from this , that the Pressure of the Air , is able to raise above the surface of any Water , a Pillar of Water thirty four foot high . For , put the case there were a Pump fourty foot high , erected among stagnant Water , and a Sucker in it , for extracting the internal Air , a man will find , that the Water will climb up in it four and thirty foot ; which Phoenomenon could never happen , unless the surface of the stagnant Water , among which the end of the Pump is drowned , were as much prest with the Air , as if it had a burden of Water upon it thirty four foot high . The second part is also evident , because if a man drown the end of a long Pipe , in a Vessel with stagnant Quick-silver , and remove the Air that 's within the Pipe by a Sucker , or more easily by the help of the Air-pump , he will find the Liquor to rise twenty nine inches , above the surface below , which thing could never come to pass , unless the Pressure of the Air , upon the surfaces of all Bodies , were equivalent to the Pressure and weight of twenty nine inches of Quick-silver . THEOREM XXVI . All Fluid Bodies have a sphere of Activity , to which they are able to press up themselves , or another Fluid , and no further , which is less or more , according to the altitude of that pressing Fluid . Figure 2. FOr understanding this Proposition , let us imagine GHCD to be a Vessel , in whose bottom , there are five inches of Mercury EFCD . Next , that above the stagnant Mercury , there are thirty four foot of Water resting , namely ABEF . Lastly , that upon the surface of the said Water , there is resting the Element of Air GHAB , whose top GH , I reckon to be about six thousand fathom above AB . Besides these , let us imagine , that there are here three Pipes , open at both ends , the first whereof CAG , having it 's lower orifice C , drowned among the stagnant Mercury EFCD , goeth so high , that the upper orifice goeth above the top of the Air GH . The second , whose lower orifice I , is only drowned among the Water ABEF , reaches to the top of the Air likewise . The third , whose open end K , is above the surface of the VVater ANB , and hanging in the open Air , goeth likewise above the Atmosphere . These things being supposed , we see that no Fluid can , by its own proper weight , press any part of it self , higher then it 's own surface , seing the stagnant Mercury EFCD , cannot press it self within the Pipe CG , higher then E. Neither can the VVater ABEF , press it self higher within the Pipe IL , then the point N. Lastly , neither can the Air GHAB , press it self within the Pipe KM , higher then M ▪ But when one Fluid presseth upon another , as the VVater ABEF , upon the Mercury EFCD , then doth the said Mercury ascend higher than it 's own surface , namely from E to O , which point is the highest , to which the thirty four foot of VVater ABEF , can raise the Mercury , which altitude , is twenty nine inches above the surface EIF . But if a second Fluid be super-added , as the whole Air GHAB , then must the Mercury , according to that new Pressure , rise by proportion ; so rises the Mercury from O to P , other twenty nine inches . By this same additional weight of Air , the Water rises thirty four foot in the Pipe IL , namely from N to R. Now , I say , the outmost and highest point , to which the Element of Air GHAB can raise the Mercury , is from O to P ; for by the Pressure of the Water ABEF , it rises from E to O. And the highest point , to which the said Air can raise the VVater , is from N to R. The reasons of these determinate altitudes , must be sought for , from the altitudes of the incumbing and pressing Fluids : for as these are less or more , so is the altitude of the Mercury , and of the VVater within the Pipes more or less . The hight therefore of the Mercury EO , is twenty nine inches , because the deepness of the pressing water ABEF is thirty four foot . And the hight of the VVater NR , is thirty four foot , because the hight of the Air GH , above AB , is six thousand fathom , or thereabout . And for the same reason , is the Mercury OP twenty nine inches . THEOREM XXVII . A lighter Fluid , is able to press with as great burden , as a heavier . Figure 2. THis Proposition is true , not only of VVater in respect of Mercury , but of Air in respect of them both : for albeit Air be a thousand times lighter then VVater , yet may it have as great a Pressure with it , as VVater ; as is evident from this second Schematism , where by the Pressure of the outward Air GHAB , twenty nine inches of Mercury OP are supported , as well as the twenty nine inches EO , by the Pressure of the VVater ABEF . So doth the same Air , sustain the thirty four foot of VVater NR , which are really as heavy , as the twenty nine inches of Mercury OP . Now , if the weight of the Atmosphere , be equivalent to the weight of thirty four foot of Water , or of twenty nine inches of Mercury , 't is no wonder to see Water press with as great weight as Mercury ; which is likewise clear from this same Figure , where by the Pressure of the Water ABEF , twenty nine inches of Mercury EO are suspended , as truly as the Mercury CE , within the lower end of the Pipe , is supported by the outward invironing Mercury . The reasons of these Phenomena , are taken from the altitudes of the pressing Fluids : for though a Body were never so light , yet multiplication of parts makes multiplication of weight ; which multiplication of parts in Fluids , must be according to altitude : for multiplication of parts according to thickness and breadth will not do it . Observe here , that if as much Air , as fills the Tub between N and L , were put into the scale of a Ballance , it would exactly counterpoise the thirty four foot of Water NR , poured into the other scale . Item , that as much Water as will fill the Tub between E and A , is just the weight of the Mercury EO . Lastly , that as much Air as will fill the Pipe , between O and G , is just the weight of the Mercury OP . THEOREM XXVIII . The Pressure of Fluids , doth not diminish , while you subtract from their thickness , but only , when you subtract from their altitude . Figure 1. FOr understanding this , let us look upon the first Schematism , where there are four Pillars of Water . Now I say , though you cut off the three Columes of Water , upon the right side , yet there shall remain as much Pressure , in the quadrat foot of VVater Q , as was , while these were intire . But if you cut off from the top , the VVater EFGH , then presently an alteration follows , not only in the lowest parts , nigh to the bottom , but through all the intermediat parts : for not only the VVater Q loseth a degree of its Pressure , but the VVaters P and O suffer the same loss . This Theorem holds true likewise in order to the Element of Air. For if by Divine Providence , the Air should become less in Altitude , than it is ; then surely , the Bensil of the ambient Air , that we breath in and out , should be by proportion weakned also . And contrariwise , if the Altitude became more , then stronger should the Bensil be here , with us , in the lowest parts : both which would be hurtful to creatures , that live by breathing . For if the Altitude of the Air , were far more then it is , our bodies would be under a far greater Pressure , which surely would be very hurtful . And upon the other hand , if the Altitude of the Air , were far less then it is , we should be at a greater loss ; for then , by reason of the weak Bensil , we would breath indeed , but with great difficulty . THEOREM XXIX . A thicker Pillar of a Fluid , is not able to press up a slenderer , unless there be an unequal Pressure . Figure 3. FOr understanding this , let us suppose this third Schematism to represent a vessel with VVater in it , as high as AB , among which is thrust down to the bottom , the Pipe GH , open at both ends . I say then , the two thicker Pillars of Air EA , and FB , pressing upon the surface of the VVater AB , are not able to press up the Water HI , or the slender Pillar of Air IG within the Pipe , the one higher then I , the other higher then G. If it be said , they are heavier , because they are thicker . I answer , they are truly heavier , for the Pillar of Air FB apart , will be thrice as heavy , as the slender Pillar of Air IG . But , if you reckon the Pillar of Air EA , upon the left hand , both together , will be six times heavier , then the Air IG : yet are they not able , either severally , or con●unctly , to press up the Water HI , higher then I , or the Air IG , higher then G. For solving this difficulty , I must say conform to the fourth Theorem , that Fluid Bodies , counterpoiseth one another , not according to their thickness , and breadth , but according to their altitude only : therefore , seing the slender Pillar of Air IG , is as high , as either FB , or EA , it cannot be prest up by them . For by vertue of this equal hight , all the three press equally and uniformly , upon the surface of Water AB ; and therefore according to the twelfth Theorem , there can be no motion . But if so be , the Pillar FB , were higher then the Pillar IG , then surely would the Water HI , be prest up ; for in such a case , there is an unequal Pressure . Or if the Pillar IG , were higher then the Pillar FB , then surely would the Water IH be prest down , there being again an unequal Pressure : the Water within the Pipe , being more burdened then the Water about the Pipe. In a word , there 's no more difficulty here , then if the Pipe were taken away : in which case , there would be but one Pillar of Air , resting upon the surface of Water AB . If it be said , the Pipe being thrust down , makes of one Pillar , three distinct ones , and consequently a formal counter-ballance , or mutual sustentation . Be it so , yet because all these press uniformly , there can be no motion . THEOREM XXX . Fluids press not only according to perpendicular Lines , but according to crooked Lines . Figure 4. FOr proving this Proposition , let us suppose ABCD , to be a large Vessel full of VVater , as high as ANB , and a little Vessel lying within it , near to the bottom , closs above at M , but with an open orifice downward , as G , and having other two passages going in to it , upon the right , and left side , as EO , and FP . Now , I say , the Pressure of this VVater , is not only from N to M , in a Straight line downwards , but from E to O , and from F to P , by crooked lines . Nay , put the case this Vessel had no passage in to it , but by a Labyrinth , or entry full of intricate windings , yet the Pressure will be communicated , thorow all these , even to the middle of it : and which is more , the VVater H or I , within the Vessel , would be under the same degree of Pressure , with the VVater E or L , without , or with the VVater K or F. And which is strange , let us suppose both the entries E and F stopped , and nothing remaining open , but the hole G , which I judge no wider , then may admit the hair of ones head ▪ yet thorow that smal hole , shall the Pressure be communicated , to the parts of the Water within , in as high a degree , as if the upper part of the Vessel EML , were cut off , to let the Pressure come down directly . What is true Fig. 1. Pag. ● Fig. 2. Pag. 25 Fig. 3 Pag. 29 Fig. 4 Pag. 3● in order to Water , the same is true in order to Air , or Mercury , or any other Fluid . For , though a house were built never so closs , without door , or window , yet if there remain but one smal hole in it , the Pressure of the whole Atmosphere , shall be transmitted thorow that entrie , and shall reduce the Air within the house , to as high a degree of Bensil , as the Air without . THEOREM XXXI . The Pressure , and Bensil of a Fluid , that 's in the Lowest foot , is equivalent to the weight of the whole Pillar above . Figure 5. FOr understanding this Proposition , let us suppose EF to be the lowest foot of a Pillar of Air , cut off from the rest , and inclosed in the Vessel EF , six inches in Diameter , or wideness , and twelve inches high . Now I say , the Bensil and Pressure , that 's in that one foot of Air , is exactly of as great force and power , as is the weight of the whole Pillar of Air , from which it was cut off . Let AB be that Pillar of Air , which I suppose is six inches thick , and six thousand fathom high . Take it , and weight it in a Ballance , and say it weighs 500 pound , yet the Pressure , and Bensil , that 's in the Air EF , is of as much force : and if the one be of strength by its weight , to move , v. g. a great Clock , the other by its Bensil , will be of as much . This proposition is true also in order to Water . For put the case EF , were the lowest of 34 foot of Water : in it will be found as much Pressure , and force , as will be equivalent to the weight of the whole thirty three foot , from which it was cut off . But here occurreth a difficulty ; for if the Pressure , and Bensil of the foot of Air EF , be equivalent to the weight of the whole Pillar of Air AB , which weighs 500 pound , then must the slender Pillar of Air CD , that 's but two inches in diameter , be as heavy weighed in a ballance , as the thicker Pillar AB , which is absurd . I prove the connexion of the two parts of the Argument thus : as the Bensil of the Air GH , is to the Bensil of the Air EF , so is the weight of the Pillar CD , to the weight of the Pillar AB : but so it is , that the Bensil of the Air GH , is equal in degree to the Bensil of the Air EF , according to the Theorem 21. Where it 's said , that the Pressure of Fluids may be as much , in the least part , as in the whole : therefore the Pillar CD , and the Pillar AB , must be of equal weight , when both are weighed together in the opposite scales of a Ballance , which is false , seing the one is far thicker , and so heavier then the other . There 's no way to answer this objection , but by granting the Air GH , and EF , to be equal in Bensil , and yet the two Pillars unequal in weight , because according to the 22 Theorem , the Bensil of a Fluid is one thing , and the natural weight is another . THEOREM XXXII . In all Fluids there is a Pondus and a Potentia , a weight and a power , counterpoising one another , as in the Staticks . THat part of the Mathematicks , which is called Staticks , is nothing else , but the Art of weighing heavy Bodies ; in which , two things are commonly distinguished , viz. the pondus and the potentia , the weight and the power . 'T is evident , while two things are counterpoising one another in the opposite scales of a Ballance , as Lead and Gold , the one being the pondus , the other the potentia . The same two are as truly found in the Hydrostaticks : for while the Mercurial Cylinder is suspended in the Torricellian Experiment , by the weight of the Air , the one is really the pondus , the other the potentia . Or while into a Siphon , with the two orifices upward , Water is poured , there arises a counterpoise , the Water of the one Leg counter-ballancing the Water of the other ; this taking the name of a pondus , the other the name of a potentia . 'T is evident also , while a surface of Water , sustains a Pillar of Water , this being the pondus , that the potentia : Or , while a surface of Water sustains a Pillar of Air , the Pillar of Air being the pondus , and the surface of Water the potentia . Or , while a surface of Quick-silver sustains a Pillar of Water or Air ; the surface is the power , and either of the two is the pondus , or weight , as you please . THEOREM XXXIII . Fluid Bodies can never cease from motion , so long as the pondus exceeds the potentia , or the potentia the pondus . THis is a sure Principle in the Hydrostaticks , which will appear most evident ; while we pass thorow the subsequent Experiments , I shall only now make it appear by one instance , though afterwards by a hundred . In the Torricellian Experiment , lately mentioned , 't is observed , that though the Pipe were never so long , that 's filled with Mercury , yet the Liquor subsides , and falls down alwayes till it come twenty nine inches above the surface of the stagnant Mercury below . The reason whereof is truly this , so long as the Mercury is higher then the said point , as long doth the pondus of it exceed the potentia of the Air ; therefore the motion of it downward can never cease , till at last by falling down , and becoming shorter , it becomes lighter , in which instant of time , the motion ends , both of them being now in equipondio , or in evenness of weight . THEOREM XXXIV . When two Fluids of different kinds are in aequilibrio together , the height of the one Cylinder is in proportion to the height of the other , as the natural weight of the one is to the natural weight of the other . FOr understanding this Theorem , we must consider , that when two Cylinders of the same kind , as one of Water with Water , or as one of Mercury with Mercury , are counterpoising one another , both are of the same altitude , because both are of the same natural weight . But when the two are of different kinds , as a Cylinder of Air with Mercury , or as a Cylinder of Air with Water , or as a Cylinder of Water with Mercury , then it will be found , that by what proportion , the one Liquor is naturally heavier or lighter , then the othe● ▪ by that same proportion , is the one Cylinder higher or lower then the other . For example , because Air is reckoned 14000 times lighter then Quick-silver , therefore the Pillar of Air that counterpoiseth the Pillar of Quick-silver in the Torricellian Experiment , is 14000 times higher . The one is 29 inches , and therefore the other is 406000 inches : which will amount to 33833 foot , or about 6766 fathom , counting five foot to a fathom . And because Air is counted 1000 times lighter then Water , therefore the Pillar of Air that sustains the Pillar of Water is 1000 times higher . The hight of Water by the Pressure of the Air is 34 foot , and therefore the hight of the Air is a thousand times 34 foot . And because Water is reckoned 14 times lighter than Mercury , therefore you will find , even by experience , that the Pillar of Water , that counterpoises the Pillar of Mercury , is 14 times higher . For if the Mercury be ten inches , the Water will be exactly 140. If it be 29 inches , the Water will be thirty four foot . The reason is evident , because if one inch of Mercury be as heavy naturally as 14 inches of Water , it follows of necessity , that for making of a counterpoise , to every inch of Mercury , there must be 14 of Water , and these in altitude , each one above another . Hydrostatical EXPERIMENTS , For demonstrating the wonderful Weight , Force , and Pressure of the Water in its own Element . EXPERIMENT I. Figure 6. IN explicating the Phenomena of the Hydrostaticks , and in collecting speculative , or practical conclusions from them , I purpose to make choise of the plainest , and most easie Experiments , especially in the entry , that this knowledge , that 's not very common , and yet very useful , may be communicated to the meanest capacities . For , if at the first , any mystical , or abstruse Experiments , should be proposed with intricate descriptions , they would soon discourage , and at last hinder the ingenuous Reader from making progress . For , if a man do not take up distinctly , the Experiment it self first , he shall never be able to comprehend next the Phenomena , nor at last see the inferences of the conclusions . Next , though some of the trials may seem obvious , yet they afford excellent Phenomena , by which many profound secrets of Nature are discovered . And if that be , 't is no matter what kind they be of . Then , the grand design here , is not to multiply bare , and naked Experiments ; for that 's a work to no purpose , for it 's like a foundation without a superstructure : but the intention is , not only to describe such and such things , but to build such and such Theorems upon them , and to infer such and such conclusions , as shall make a stately building , and give a man in a short time a full view of this excellent Doctrine . For the first Experiment then , prepare a Vessel of any quantity , as ABCD , near half full of Water , whose surface is MH . Prepare also two Glass-pipes , the one wider , the other narrower , open at both ends , which must be thrust down below the Water , first stopping the two upper orifices E and F. This done , open the said orifices , and you shall see the Water ascend in the wider to G , and in the narrower to H. Now , the question is , What 's the reason , why the Water did not ascend , the orifices E and F , being stopped , and why it ascends , they being opened ? To the fi●st part I answer , the Water cannot ascend , because the imaginary surface of Water LK is equally and uniformly prest : for with what weight the outward Water ML , and HK press the said surface , with the same weight , doth the Air within the two Pipes press it . To the second part I answer , the Water ascends , because the same surface ( the orifices E and F being opened ) is unequally prest : for the outward Water ML , and HK , press it more , then the Air within the Pipes do . The difficulty only is , why it is equally prest , the orifices E and F being stopped , and why it is unequally prest , the said orifices being once opened . To unloose the knot , I must shew the reason , why the Air within the Pipes , press the surface LK , with as great a burden , as the outward Water press it . For understanding this , you must know , that when the orifice I is thrust down below the Water , there ariseth a sort of debate between the lower parts of the Water , and the Air within the Pipes , the Water striving to be in at I , and the Air striving to keep it out : but because the Water is the stronger party , it enters the orifice I , and causeth the Air retire a little up , one fourth part , or sixth part of an inch , above I , and no more , which is a real compression it suffers . For the orifice E being stopped , hinders any more compression , than what is said ; in which instant of time the debate ends , the Air no more yeelding , and the Water no more urging ; by which means the Air having obtained a degree of Bensil , more then ordinary , by the Pressure of that little quantity of Water , that comes in at I , presseth the part of the imaginary surface , it rests upon , with as great weight , as the outward Water presseth the parts it rests upon . But when the orifice E is opened , the outward water ML , and HK , press the imaginary surface LK more , than the Air within the Pipe can do . And the reason is , because by opening the orifice above , the internal Air , that suffered a degree of Bensil more then ordinary , presently is freed , and consequently becomes of less force , and weight ; which the Water finding , that hath a little entered the orifice I , instantly ascends to G , it being less pressed , then the Water without the Pipe. Now the reason , why it ascends no higher then G , is taken from the equal Pressure of the Body that rests upon the surface MGH : For , assoon as it comes that length , all the parts of the horizontal Plain of Water , is uniformly prest with the incumbing Air , both within the Pipe , and without the Pipe. The Water in going up , cannot halt mid-way between I and G , for then there should be an unequal Pressure in Fluids without motion , which is impossible ; for the Water is still stronger then the Air , till once it climb up to G. From this Experiment we see first , that in Water there is a Pressure and Force ; because having opened the orifice E , which is only causa per accidens of this motion , the Water is prest up from I to G. We see secondly , that Fluid Bodies , can never cease from motion , till there be an equal Pressure among the parts , which is evident from the ascent of the Water from I to G , which cannot halt in any part between I and G , because of an unequal Pressure , till it once climb up to G. We see thirdly , that Fluid Bodies do not sustain , or counterpoise one another according to their thickness and breadth , but only according to their altitude ; because there is not here any proportion between the slender Pillar of Water HK within the Pipe , and the outward Water that sustains it , I means as to the thickness ; therefore 't is no matter , whither the Glass Tubs be wider or narrower , that are used in counterpoising Fluid bodies one with another . And this is the true reason , why 't is no matter , whither the Tub of the Baroscope be a wide one , or a narrow one , seing the Air doth not counterpoise the Mercury , according to thickness , that 's to say , neither the thickness of the ambient Air that sustains , nor the thickness of the Mercury that is sustained , are to be considered ; but only their altitudes . 'T is true , the element of Air is fourteen thousand times higher , then the Mercurial Cylinder , yet there is a certain and true proportion kept between their heights ; so that if the element of Air , should by divine providence become higher or lower , the height of the Mercury would alter accordingly . EXPERIMENT . II. Figure 6. TAke out of the Water , the wide Pipe EGI , and stopping the orifice I , pour in Water above at E , till the Tub be compleatly full . Having done this , thrust down the stopped orifice I to the bottom of the Vessel , and there open it , then shall you see the Water fall down from E to G , and there halt . The reason is taken from unequal Pressure ; for the Tub being full of Water from E to I , that part of the imaginary surface , upon which the Pillar of Water rests , is more burdened than any other part of it , namely more then L or K ; therefore seing one part is more burdened than another , the Cylinder of Water that causeth the burden , must so far fall down , till all the parts be alike prest , in which instant of time , the motion ceaseth . This leads us to a clear discovery of the reason , why in the Baroscope , the Mercury falls from the top of the Tub of any height , alwayes to the twentieth and ninth inch , above the stagnant Quick-silver . For example , fill the Pipe NQ , which is sixty inches high with Mercury , and opening the orifice Q , the Liquor shall fall out , and fall down from N , till it rest at R , which is twenty nine inch above the open orifice Q. The reason is the same , namely unequal Pressure , seing one part of the imaginary surface of Air XS , upon which the Cylinder of Mercury stands , is more burthened then the other next adjacent : therefore , so long and so far must the Mercury subside and fall down , till the part Q , upon which the Basis of the Pillar rests , be no more burthened , than the rest of the parts ; in which instant of time , the motion ceaseth , and there happeneth an equal ballance , between the Silver within the Tub , and the Air without . If it be said , I see a clear reason , why the outward Water ML , ought to sustain the inward GI , but cannot see , why the outward Air TZS and VRX , ought to sustain the inward Mercury RX : neither do I see a reason , why it should halt at R , as the Water rests at G. I answer , though sense cannot perceive the one , as evidently as the other , yet the one is as sure as the other . For taking up the reason why it halts at R , 29 inches above X , you must remember , from the 25 Theorem , that the Pressure of the Air upon Bodies , is equivalent to the weight of 34 foot of VVater perpendicularly , or 29 inches of Quick-silver . The Pillars of Air then TZS , and VRX , being as heavy each one of them , as two Pillars of Mercury , each one of them 29 inches high , it follows of necessity , that the Mercury within the Tub , must be as high as R. 'T is no wonder to see the Silver halt at R , provided RX , and ZS , were two bulks of Mercury , environing the Pipe , as the outward VVater environs the wider and narrower Pipe. Neither ought any to wonder , when the Silver falls down , and rests at R , nothing environing the Pipe but Air , seing the Pressure of the Air is equivalent to the weight of 29 inches of Quick-silver . This Experiment is easily made : take therefore a slender Glass-pipe of any length , beyond 30 inches , open at both ends ; but the lower end Q , must be drawn so small by a flame of a Lamp , that the entry may be no wider , than may admit the point of a small needle , or the hair of ones head . Then stopping the said orifice , pour in Mercury above at the orifice N , till the Pipe be compleatly full . Next , close the said orifice with wet Paper , and the pulp of your finger ; and opening the lower orifice , you shall find , ( which is very delightful to behold ) the Mercury spring out , like unto a small silver threed , and falling down from the top N , shall rest at R , the motion ceasing at the narrow orifice Q. This shews evidently , that there is not need alwayes of stagnant Mercury , for trying the Torricellian Experiment ; but only when the mouth of the Pipe below is wide : for being narrow , the silver runs slowly out , and consequently subsides slowly above , and coming down slowly to R , there rests . But when the mouth is wide below , the silver falls down so quickly , that it goes beyond R , before it can recover it self , which recovery would never be , unless there were stagnant Mercury to run up again . From what is said , we see first , that when one part of a surface of Water or Air , is more burthened than another , the burthened part presently yeelds , till it be no more burthened than the other . This is clear from the falling down of the Water from E to G , which cannot be supported by the part I , because more burthened than the rest . We see secondly , that the element of Air , rests upon the surfaces of all bodies with a considerable weight ; otherwise it could not sustain the Water , before it fall down from E to G : for if it did not rest upon the surface MH , with weight , the Water could never be suspended ; seing the application of the finger to the orifice E , is only the accidental cause of this sustentation . We see thirdly , that according to the difference of natural weight , between two Fluids , so is the proportion of altitudes between two of their Cylinders : therefore Air being reckoned 14000 times lighter then Mercury , it followes that the Cylinder of Mercury sustained by the Air , must be 14000 times lower and shorter , than the Cylinder of Air that sustaines it ; which appears from this experiment to be true , seeing by the Pressure of the Air , which is thought to be about 7000 fathom high , 29 inches of Mercury is supported between R and X. In a word , if Air be naturally 14000 times lighter than Mercury , which is very probable ; then must the altitude of it , commonly called the Atmosphere , be fourteen thousand times , nine and twenty inches , that is 406000 , or of feet 33833. EXPERIMENT III. Figure 6. WHile the outward , and inward Water are of the same altitude , withdraw the inward Air EG by suction , or by any other device you think fit , and you will find the Water rise as high as E , which I suppose to be 34 foot above MGH . The same Phenomenon happens , in taking the Air out of the narrow Pipe FK . The reason is still unequal Pressure ; for in removing the Air , that 's within the Pipe , the part of the surface M , and the part H , remaines burthened , while the part G is freed of its burden : therefore this part of the surface , being liberated of its burden , that came down through the Pipe , instantly rises , and climbs up as far , as the outward Air resting upon M and H , can raise it , which is to E 34 foot : for the Pressure of the Air upon the surfaces of all Waters , according to the 25 Theorem , being equivalent to the weight of 34 foot of Water , must raise the said Water in the Pipe 34 foot . You do not wonder , why it rises from I to G , as in the first experiment ; no more ought you to wonder , why it rises from G to E , seing the weight of the Air , doth the same thing , that 34 foot of Water resting upon the surface MH , would do . From this experiment we see first , that the Pressure of the Air , is the proper cause of the motion of Water , up thorow Pumps and Siphons , or any other instrument , that 's used in Water-works of that kind ; for if the weight of the Air , resting upon the surface MH be the cause , why the Water climbs up from G to E , the same must be the cause , why the stagnant Water followes the Sucker of the Pump , while it 's pulled up . And the same is the cause , why Water ascends the Leg of a Siphon , and is the cause , why motion continues after suction is ended . We see secondly , that every Pressing Fluid hath a Sphere of activity , to which it is able to raise the Fluid , that is pressed . This is evident in this experiment , because the Pressure of the Air resting upon MH , is able to raise the Water , the hight of E in the wide Pipe , and the hight of F in the narrow , and no further , even though the said Pipes were far longer : and this altitude and highest point is precisely 34 foot between Air and Water . We see thirdly , that 't is all one matter , whether Pumps and Siphons be wider or narrower , whether the tub of the Baroscope be , wherein the Mercury is suspended , of a large Diameter , or of a lesser Diameter . This is also evident from the same experiment ; seing there is no more difficulty in causing the Water ascend the wide Pipe , than in causing it ascend the narrow one . And the reason is , because the pressing Fluid repects not the pressed Fluid , according to its thickness and breadth ; but only according to its altitude . Therefore'its as easie for the Air , to press up Water through a Pump four foot in Diameter , as to press it up through a Pump , but one foot in Diameter . EXPERIMENT IV. Figure 7. THis Schematism represents a large Vessel full of Water , whose first and visible surface is DEHK . The second , that 's imaginary is , LI , six foot below it . The third of the same kind , is MG , six foot lower . The fourth , is NFO , six foot yet lower . The last , and lowest , is ABC . There are here also four Tubs , or rather one Tub under four divers positions , with both ends open . After this Tub DA is thrust below the Water , till it ascend , as high as D in it , lift it up between your fingers , till it have the position of the second Pipe EF , and then you shall see , as the orifice of the Pipe ascends , the Cylinder of Water fall out by little and little , until it be no longer than EF. Again , lift it further up , till it have the position of the Pipe HG , then shall you find the Cylinder of Water become yet shorter . Lastly , if it be scituated , as the Pipe KI , the internal Water becomes no longer than KI . The reasons of these Phenomena are the same ; namely unequal Pressure ; for the Orifice A being lifted up as high as F , it comes to the imaginary surface NO , which is not under so much Pressure , as the other is ; therefore one part of it being more burdened , than another , namely the part upon which the Cylinder of Water rests , it presently yeelds , and suffers the Cylinder to become shorter , and lighter , till it become no heavier , then is proportionable to its own strength . To make this reason more evident , it is to be noted , that no surface of Water is able to support a Cylinder higher then its own deepness , that is to say , if a surface be 40 foot deep , it is able to sustain a Cylinder 40 foot high , and no more : therefore the surface NO , being but 18 foot deep , it cannot sustain a Cylinder 24 foot long : for if that were , then the Potentia , should be inferiour to the Pondus , which is impossible in the Hydrostaticks . In effect , it were no less absurdity , then to say , 18 ounces are able to counterballance 24. For a second trial , lift up the same Pipe higher , till it acquire the position of the Tub GH ; in this case , the Cylinder of Water within it , becomes yet shorter , even no longer , than GH . The reason is the same , namely unequal Pressure ; for when a Cylinder of Water 18 foot high , comes to rest upon this surface , that is but 12 foot deep , it makes one part of it more burdened then another ; therefore the part that is more prest , presently yeelds , and suffers the Cylinder to fall down , till the Pondus of it , become equal to its own Potentia . For the last trial , lift up the Tub , till it acquire the position of the Pipe KI : in this case , the Water within it becomes no longer then KI , the surface LI , that is but six foot deep , not being able to sustain a Cylinder 12 foot high . From this Experiment we see first , that in all Fluid Bodies there is a Pressure , which is more or less , according to the deepness of that Fluid ; this is evident from the four several surfaces ; there being more Pressure and force in the lowest ABC , then in the next NO ; and more in this , then in the surface MG ; and more in this , then in LI. We see secondly , that in all Fluids , there is a Pondus and a Potentia ; which two are alwayes of equal force , and strength ; the Potentia is clear and evident in the surface , by supporting the Pillar ; which Pillar is nothing else , but the Pondus supported . And that they are alwayes of equal strength , is most evident also ; for when you endeavour to make the Pondus unequal to the Potentia , in making a surface 18 foot deep , to support a Pillar 24 foot high , they of their own accord become equal ; the Pillar becoming shorter , and suitable to the strength of the surface that sustains it . We see thirdly , that 't is impossible for one part of the same Horizontal surface , to be more burdened then another : for when you endeavour to do it , by setting a longer Pillar upon it , the part burdened instantly yeelds , till it be no more prest , then the next part to it . We see fourthly , that the inequality , that is between the Pondus and the Potentia in Fluids , is the proper cause of the motion of Fluids . For when you endeavour to make a surface 30 foot deep , sustain a Pillar 40 foot high , this inequality is the true cause , why the Pillar subsides , and falls down , and why the surface yeelds , and gives way to it . And this inequality is the true cause , why the motion of Water thorow Siphons continues . For understanding this , you must conceive a Siphon , to be nothing else , but a crooked Pipe with two legs , the one drowned among Water , the other hanging in the open Air. The use of it is , for conveying Wine or Water from one Vessel to another , which is easily done by suction . Now after suction is ended , the motion of the Water continues , till the surface become lower , then the orifice out of which it runs . The true reason then , why the Water flows out , is the inequality between the Potentia of the Air , and the Pondus of the VVater ; the Pondus being stronger then the Potentia . For in Air as in VVater , we must conceive Horizontal surfaces ; and these surfaces to be endowed with Pressure and force , as are the surfaces of VVater . Now when the leg of a Siphon is hanging in the Air , it must rest upon one surface or another , and consequently the VVater in it , must rest upon the same surface . If the Potentia of the surface be stronger , then the Pondus of the VVater ; the VVater is driven backward , which alwayes comes to pass , when the orifice is higher , then the surface of the VVater of the Vessel , among which the other leg is drowned . If the Potentia of the surface of that Air , be of equal power and strength , with the Pondus of the VVater , the VVater goeth neither backward , nor forward , but stands in equilibrio : this happens , when the orifice is neither higher , nor lower , than the surface of the VVater in the Vessel . But if the Potentia of the surface of the Air be weaker , than the Pondus of the VVater ; in this case , the Air yeelds , and suffers the VVater to run out , even as a surface 30 foot deep , yeelds to a Pillar of VVater 40 foot high . The same inequality is the reason , why VVater climbs up the Pump ; why VVater climbs up a Pipe , when a man sucks with his mouth . Before suction , the Potentia that 's in the surface of VVater , among which the end of the Pipe is drowned , is of equal force with the Pondus of the Pillar of Air , that comes down thorow the Pipe , or Pump ; but assoon as a man begins to suck , the said Pillar of Air becomes lighter ; and the VVater finding this , presently ascends . The same is the reason , why the Mercury falls down to 29 inches in the Baroscope , and no further : for as long as the Pondus of the Pillar of Mercury , exceeds the Potentia of the surface of Air , so long doth the motion continue ; and when both are become equal in force , the motion ceaseth . VVhen the Glass-tub is 40 inches long , and filled with Mercury , and inverted after the common manner , you are endeavouring as it were , to cause a surface 29 inches deep , sustain a Pillar 40 inches high , which is utterly impossible in Fluids . It is judged by many a wonder to see the deflux of the Mercury in the Baroscope ; but in effect , there 's no more cause of admiration in it , than to see the Cylinder of Water grow shorter , by lifting the Pipe up from one surface to another . From this Experiment , we see the true reason , why the Mercurial Cylinder of the Baroscope becomes shorter and shorter , according as a man climbs up a mountain with it . For at the root of the hill , the surface of Air , that sustains the Pillar of Mercury , is of greater force , than the surface at the middle part : and this is stronger than any surface at the top . The Pipe therefore being carried up from one surface to another , the Mercury in it , must subside , and full down , even as the Water falls down , and becomes shorter , by lifting the Pipe from the surface ABCD to the surface NO . And as the whole VVater would fall down , if the orifice I , were lifted above the surface DEHK , so i● the Baroscope could be carried so high , till it came above the top of the Air , the whole Mercurial Cylinder would surely fall down . And as by thrusting down the said Pipe to the bottom of the Vessel again , as the Pipe DA , the VVater ascends in it ; so by bringing down the Baroscope to the earth again , the whole 19 inches would rise again . EXPERIMENT V. Figure 8. FIll the Vessel ADGH with VVater to the brim . Next , thrust down the open orifice of the Tub DA , to the bottom , and you shall see the VVater ascend in it , as high as D , according to the first experiment . When this is done , recline the said Pipe , till it ly as BE , and you shall find the Pipe , compleatly full of VVater . Next , erect the same Tub again as DA , and you shall see the Cylinder of VVater fall down , and become shorter , as at first . For salving this Phenomenon , and such like , I must suppose this VVater to be 50 inches deep , and the Tub IA , and BE 90 inches long : and the said Tub in reclining , to describe the quadrant of a Circle FEG . Now the question is , why there being but 50 inches of Water in the Tub , while erected , there should be 60 in it , when it is reclined ? Secondly , why there should be 90 inches of Water in the Tub BE , and but 50 in it , when it stands Perpendicular , as DA ? If you reply , because there are 90 inches in recta linea between the point B , and the point E , and but 50 between A and D. But this will not answer the case ; because , if you stop the orifice E , with the pulp of your Finger , before it be erected , you will find the Tub remain full of VVater , even while it stands Perpendicular ; and fall down , when the orifice is opened . Or , while the Tub stands Perpendicular , stop the orifice I , and recline it as BE : yet no more Water will be found in it , than 50 inches : but by unstopping the said orifice , the VVater climbs up from R to E , and becomes 90 inches . Now , what 's the reason , why it runs up from R to E , and why it falls down from I to D ? I answer then , the VVater must run up from R to E , because of the inequality , that 's between the Pondus of the Cylinder BR , and the Potentia of the surface of VVater ABC , that supports the said Cylinder . For understanding this , know , while the Tub is erected , there is a perfect equality , between the weight of the Pillar AD , and the force or Power of the surface that sustains it , seing a surface 50 inches deep , supports a Pillar 50 inches high . But assoon as the Tub is reclined , there arises ane inequality between the saids two parties , the Pondus of the Cylinder becoming now less than before . If you say the quantity of the VVater is the same , namely 50 inches , in the reclined Tub , as well as in the Perpendicular . I grant the quantity is the same , but the weight is become less . Now the reason , why the same individual VVater , is not so heavy as before , is this ; there are 40 ounces of it , supported by the sides of the Tub within ; which were not , while the Tub was erected : for in this position , the whole weight of the Cylinder rests upon the surface : but while the Tub is reclined , the said surface is eased , and freed of 40 ounces of it ; this 40 , resting and leaning upon the sides of the Pipe within . The surface then , finding the said Cylinder lighter now than before , instantly drives it up from R to E , 40 inches . And likewise , when the reclined Pipe is made Perpendicular , the Water falls down from I to D , because of the inequality , that 's between the Pondus of the Pillar , and the Potentia of the surface ; this surface 50 inches deep , not being able to support a Pillar 90 inches high , for if this were , then one part , should be more burthened than another , which is impossible . It is to be observed , that by how much the more , the Tub is reclined from a Perpendicular , towards the horizontal surface ABC , by so much the more growes the inequality , between the Pondus and the Potentia , and that according to a certaine proportion Hence is it , that the Tub being reclined from 60 degrees to 50 , there arises a greater inequality between the Pondus of the Cylinder , and the Potentia of the surface , than while it is reclined from 70 to 60 : and more yet in moving from 50 to 40 , than in moving from 60 to 50 , and so downward , till it be horizontal , in which position , the whole Pondus is lost . And contrariwise , while the Pipe is elevated , the Pondus begins to grow ; and growes more , being lifted up from 10 to 20 , than from 1 to 10 : and yet more in travelling from 20 to 30 , than from 10 to 20 , and so upwards , till it be Perpendicular , in which position , the Cylinder regaines the whole Pondus and weight , it had . This proportion is easily known , for it s nothing else , but the proportion of Versed Sines upon the line FB ; for according to what measure , these unequal divisions become wider , and wider from 90 to 1 , according to the same proportion does the Pondus of the Cylinder become less and less : and contrariwise , according to what proportion the said divisions become more and more narrow from 1 to 90 , according to the same measure and rate , does the Pondus of the Cylinder become greater and greater . From this experiment we see first , that two Cylinders of Fluid bodies , differing much in quantity , may be of the same weight : because though the Cylinder BE 90 inches long , be far more in quantity , than the Cylinder DA , that 's but 50 , yet both of them are of the same weight , in respect of the surface that sustaines them . If it be said , the one is really heavier , than the other , notwithstanding of all this . I answer , it is so indeed , in respect of the Libra , or Artificial Ballance , that we commonly use in weighing of things : but it is not so in respect of this Natural Ballance , if I may so speak , wherein Fluid bodies are onely weighed after this manner . We see secondly a clear ground for setting down the ninth Theorem , namely , that in all Fluid bodies a twofold weight may be distinguished , one Sensible , another Insensible : because the Sensible weight of the Cylinder of Water BE , remaines still the same , even though it should be reclined to G ; for take it out , and weigh it in a Ballance , it will be as heavy the one way as the other . But it is not so with the Insensible weight ; seeing the Tub begins no sooner to recline , but assoon it begins to diminish , and grows less . This Insensible weight is nothing else , but the sensible weight considered after another manner . For look upon the weight of the Pillar of Water BE , as it weighs in a pair of Scales , it is then Sensible , and weighs so many ounces , and cannot be more or less : but look upon it in reference to the Potentia of the surface , that sustains it , it is then Insensible as to us : for though a man should put his hand below the Water , and endeavour to find the weight of the said Pillar , yet he shall not find it , though that part of the surface upon which it rests , doth really ( if I may so speak ) find the weight of it . And as it is Insensible , so is it sometimes more , and sometimes less , according as the Tub is elevated , or reclined : now these two being put together , gives a very probable ground for this distinction . We see thirdly , that the Pondus or weight of Fluids , doth not only press according to Perpendicular lines , but according to lines falling obliquely upon the imaginary surface ; so doth the weight of the Pillar of Water BE , press the surface ABC . We see fourthly , that Fluid Bodies , do counterpoise one another , according to Altitude only : for put the case , the Pipe BE , were ten times wider then it is , yet will the surface sustain the Water in it , provided the Pipe keep still the same position of Altitude , namely 50 degrees : the reason seems to be this ; for if the Base of the Pillar become more in Diameter , it necessarily requires a larger part of the surface to rest upon ; which larger part is really stronger than the lesser part , as will be shewed afterwards . From this Experiment we see lastly , an evident reason , why the Mercurial Cylinder in the Baroscope runs up , and fills the empty space , when the Pipe is reclined , and why it runs down , when the Tub is erected again . In effect , the reason is the same , namely , an inequality between the Pondus of the Quick-silver , and the Potentia of the surface of the Air : for when the Tub begins to recline , the Pondus begins to rest upon the side of the Tub within ; by which means the Potentia of the surface finding the burden less , instantly thrusts up the stagnant Mercury to supply that loss , seing two Fluids cannot counterpoise one another , unless they be in aequilibrio . And contrariwise , assoon as the Tub begins to be erected , the Pondus of the Mercury begins to grow , and so overcomes the Potentia of the surface , till by falling down it can do no more . EXPERIMENT VI. Figure 9. THis Schematism represents a Vessel full o● Water , whose first and visible surface is HIK ; the second , which is imaginary , is EFG : the third , ABCD. Fig. 5 Pag. 32 Fig. 6 Pag. 37 Fig. 7 Pag. 46 Fig. 8 Pag. 55 Besides these three in Water , conceive a fourth in the Air , above the Water , namely LMN . Upon this aërial surface , rests the orifice M , of the Tub TM , open above . Upon the surface EFG , is standing the mouth F , of the Pipe SF . And upon the surface ABCD , stands the Pipe RB , open at both ends . After the orifice B is drowned below the VVater , you will find the Liquor rise from B to H. Then close with the pulp of your Finger the mouth R , and lift the Pipe so far up , till it have the Position of the Pipe SF ; and you shall see the VVater hing in it between F and O. Lastly , bring the said orifice compleatly above the VVater , till it have the position of the Tub TM ; yet shall the VVater still hing in it , as MP . The first question is , what sustains the VVater IO ; for the part FI , is sustained by the ambient VVater ? I answer , it cannot be the pulp of the Finger closing the orifice S ; for though , by taking away the Finger , the VVater OI falls down , and by putting to the Finger , it is keeped up , yet this proves not the pulp of the Finger to be the principal , and immediat cause . I say then , the VVater OI is suspended by the weight of the incumbing Air , resting upon the surface HIK . For understanding this , consider , as I said before , 25. Theorem , that the Pressure of the Air upon all Bodies , is just equivalent to the weight of 34. foot of VVater . Hence then is it , that if the Air be able to sustain a Pillar of VVater , 34 foot high , it must be able to sustain the short Pillar OI , that exceeds not four foot . The second question is , whether the part F , be equally burthened with the part E , or G ; for it would seem not , seing the VVater OIF , is but four foot high ; whilest upon E or G is resting , not only more then a foot of VVater to the top HIK , but the whole weight of the Atmosphere upon the said top is resting , which is equivalent to the burden of 34 foot of VVater . I answer , there 's more to be considered , than that four foot of VVater , which in it self is but of small burden , therefore to this we must add the weight of the Air between O and S , within the Pipe ( remember that the orifice S is stopped with the pulp of the Finger ) which in effect will be as heavy as 31 foot of VVater . Put the case then , F , to be one foot below the first surface HIK , and the VVater OI to be three foot , then ought the Air OS , to have the weight of 31 foot , because the surface EFG is able to support a Pillar of 35 foot . This I prove , because the part E , de facto , sustains 35 foot , because the Air above is equivalent to 34 foot of it , and there is a foot of VVater between it and the top , namely between E and H. The third question is , how it comes to pass , that the Water still remains in the Pipe , after the orifice M is brought above the surface of the Water ; for there is here no stagnant Water guarding it , as guards the orifice F. I answer , that the base M , of this Pillar of Water PM , as really rests upon the horizontal surface of this Air LMN , as a Cylinder of Brass or Timber rests upon a plain Marble Table , and after the same manner . Remember that the orifice T is stopped all this time , with the pulp of the Finger . If it be said , that the part M , is more burdened then the part N , seing it sustains four foot of Water , which the part N supports not , and the Air PT within the Pipe also , which is of as much Bensil and Pressure , as the Air NY is of . For clearing of this difficulty , consider , that the Pillar PM is shorter now than before ; for the orifice M coming up from D , some inches of Water falls out , as will be found by experience . Suppose then , that of four foot , six inches fall out ; if this be , then the inclosed Air between P and T , must be six inches longer , if this be , then of necessity the Bensil of it must be proportionably remitted and slackened : whence follows by Metaphysical necessity , that it cannot burden the Water PM , with as much weight as it had , and consequently the surface of Air cannot be so much burdened . It must then be no more bu●dened with them both together , than it is with the single Pillar of Air YN . If then the Water PM , be three foot and an half , the weight of the enclosed Air TP , must be exactly the weight of thirty foot of Water and an half . From this experiment , we see first the Pressure of the Air , for by it the Water OI is suspended , and by the same pressure is the Water PM suspended . We see secondly , that in Air , there is a power of dilating it self , and that this dilatation never happens , without a relaxation of the Bensil . We see thirdly , that one Fluid cannot sustain another , unless the Potentia of the one , be equal to the Pondus of the other , as is clear from the Aërial surface , that cannot sustain the whole four foot of Water , but suffers six inches of it to fall out , that the Pondus of the rest , and the Air above it , may become equal to its own Potentia . We see fourthly , that Fluid Bodies have not only a power of pressing downward , but of pressing upward likewise : as is clear from the Water OI , that 's suspended by the Air pressing down the surface of Water HIK . It presseth upward also , while it supports the Water PM . This Experiment also answers a case , namely , whether or not , it is alwayes needful to guard the orifice of the Tub of the Baroscope with stagnant Quick-silver ? I say then , it is not alwayes needful , provided the orifice be of a narrow diameter ; for experience tells , that while it is such , the Mercury will subside , and halt at 29 inches above the orifice , though no stagnant Mercury be to guard . In making this trial , the orifice must be no wider , than may admit the point of a needle . Or suppose it to have the wideness of a Tobacco-pipe , yet will the Mercury be suspended , though the end be not drowned among stagnant Quick-silver , even as the Water PM , is kept up without stagnant Water about it . For trial of this , you must first let the end of the Pipe , be put down among stagnant Mercury , and after the Cylinder is fallen down to its own proper altitude , lift up the Pipe slowly , till the orifice come above the surface , and you will find , provided you do not shake the Pipe , the Cylinder to be suspended after the same manner , immediatly by the Air , as the Water PM is . EXPERIMENT VII . Figure 10 , 11. TAke a Vessel of any quantity , such as ABCDE , and fill it with VVater . And a Glass-pipe , such as GFD , of 15 or 20 inches long , of any wideness , closs above , and open below . Before you drown the open end among the VVater , hold the Glass before the fire , till it be pretty hot , and having put it down , you will see the VVater begin to creep up till it come to F , where it halts . The question now is , what 's the reason , why the VVater creeps up after this manner , 10 or 12 inches above the surface AB ? I answer , the heat having ra●ified the Air within , and by this means , having expelled much of it , and the Air now contracting it self again with cold , the VVater ascends , being prest up with the weight of the incumbing Air , resting upon the surface of Water AB . There is here surely an inequality between a Pondus and a Potentia , that must be the cause of this motion . I judge then the inequality to consist between the weight of the Air within the Pipe , and the surface of Water CDE . To explicate this , I must suppose the Pipe to be thrust down cold ; in this case , little or no Water can enter the orifice D. And the reason is , because the Pondus of the Air within the Glass , is equal to the Potentia of the surface CDE . But when the Pipe is thrust down hot , much of the Air having been expelled by the heat , and now beginning to be contracted by cold , the Pondus of the Air becomes unequal to the Potentia of the surface , and therefore this , being the stronger party , drives up the Air within the Glass , till by this ascent , the Pondus of the Air GF , and the Pondus of the Water FD together , become equal to the Potentia of the surface CDE , that sustains them . For a second trial ; bring a hot coal neat to the side of the Glass , between G and F , and you will find the Water to creep down from F toward the surface AB ; and if it continue any space , it will drive down the whole Water , and thrust it out at D. To explicate this , I must suppose that heat , by rarifying the Air within the Glass , intends and increaseth the Bensil of it , and the Bensil being now made stronger , there must arise an inequality between the Pondus of the said Air , and the Potentia of the surface CDE ; the Air then , being the stronger party , causeth the surface to yeeld . By comparing this Experiment with the former , we see a great difference between the dilatation of Air , of its own accord , and by constraint . For while it is willingly expanded , the Bensil begins to grow slack , and remiss , and loseth by degrees of its strength ; even as the Spring of a Watch by the motion of the Wheels , becomes remiss . But when the dilatation is made by heat , and the Air compelled to expand and open it self , the Bensil becomes the stronger , and the Pressure the greater . Notwithstanding , though the Bensil of this inclosed Air GF , may be made stronger by heat , to the expulsion of the Water FD , yet if this rarefaction continue any time , the Bensil becomes dull and slack . And the reason is , because Air cannot be expanded and opened to any quantity ; an inch cannot be dilated and opened to an hundred , or to a thousand : neither can the Bensil of it be intended , and increase to any degree , v.g. from one to 20 , 30 , or 100. And therefore , as the expansion grows , the Bensil must at length slacken . But if so be the Air were inclosed , as in a bladder knit about the neck with a string , then the more heat , the more Bensil : for in this case there is a growth of Pressure , without dilatation . And sometimes the Bensil may be so intended with the heat , that the sides of the bladder will burst asunder . From this Experiment we see first a confirmation of the 21 Theorem , namely , that there may be as much Bensil and Pressure , in the smallest quantity of a Fluid , as in the greatest ; as is clear from the Bensil of the Air GF , which in effect counterpoiseth the weight of the whole Atmosphere , resting upon the surface of Water AB . We see secondly , that when the pondus , and the potentia of two Fluids , are in equilibrio , or of equal strength , a very small addition to either of them , will cast the ballance . For if a man should but breath softly upon the side of the Glass between G and F , or lay his warm hand to it , the said Air will presently dilate it self , and by becoming thus stronger , thrust down the Water , and so overcome the potentia of the surface . We see thirdly a confirmation of the sixth Theorem , namely , that the Pressure of Fluids is on every side ; as is clear from the inclosed Air GF , that not only presseth down the Water FD , but with as great force presseth up the top of the Glass within , and presseth upon all the sides of it within , with the same force . This Experiment also , leads us to the knowledge of two things : First , of the reason , why with cold the Water ascends in the common Weather-glasses ; and why in hot weather the Water descends . Secondly , from this Experiment we may learn to know , when the Air is under a greater Pressure , and when under a lesser : because when the Air becomes heavier , as in fair weather , the Water creeps up in some measure , it may be two or three inches ; when there is no alteration as to heat and cold : and in foul weather , or in great winds , when the Air is really lighter , the said Water creeps down as much . If it be asked , how shall I know , whether it be the cold of the Air , or heaviness of the Air , that causeth the Water to ascend ; and whether it be the heat of the Air , or the lightness of the Air , that causeth the Water to descend ? I have proposed this question of purpose , to let you see a mistake . Many believe , that the ascent and descent of Water in common Weather-glasses , is allanerly from the heat and coldness of the Air ; and therefore they conclude a cold day to be , because the Water is far up : whereas the Water hath ascended since the last night , by reason of a greater weight in the Air , which alwayes is , when the weather is dry , and calm , though there hath been no alteration of heat to cold . If it be asked , how come we to the knowledge of this , that the pressure and weight of the Element of Air , is sometimes less , and sometimes more ? I answer , this secret o Nature , was never discovered , till the invention of the Torricellian Experiment , otherwise called the Baroscope . For after the falling down of the Quick-silver to 29 inches ▪ if you suffer it to stand thus in your Parlour or Chamber , according as the Pressure , and weight of the Element of Air , becomes more or less , so will the Altitude of the Mercury become less or more , and vary sometimes above 29 inches , and sometimes below . This alteration is very sensible , which is sometimes the tenth part of an inch , sometimes the sixth , and sometimes the third , according as the weight of the Air is less or more . From December to February , I found the alteration become less and more from 30 inches to 28 , which will be three fingers breadth . The common Weather-glasses then are fallacious , and deceitful , unless they be so contrived , that the Pressure of the Air cannot affect them , which is easily done by sealing them Hermetically , and in stead of common Water , to put in Spiritus Vini rectificatissimus , or the most excellent Spirit of Wine , and strongest that can be made . It may be here inquired , whether or not , Mercury would ascend in this Glass , as the Water does ? I answer it would ; because the ascent depends only upon the Pressure of the Air , incumbing upon the stagnant Liquor in the Vessell , that 's able to drive up Mercury as well as Water . It may be inquired secondly , how far Mercury will ascend , and how far Water will creep up ? I answer , Mercury can ascend no higher in a Tub , than 29 inches ; and Water no higher , than 34 foot ; and this onely happens , when there is no Air above the tops of the Cylinders to hinder their ascents . But when there is Air , as GF above the liquor , it can go no higher , than the point to which the cold is able to contract the inclosed Air , which is in this Glass , the point F. It may be inquired thirdly , which is the greater difficulty , whether or not Mercury , will rise as easily in a Tub as Water ; for seeing , it s 14 times heavier , it seemes the Air should have greater difficulty to press it up , than to press up Water ? I answer , 't is greater difficulty for the Air to press up 20 inches of Mercury , than to press up 20 inches of Water ; yet it s no greater difficulty , for the Air to press up 20 inches of Mercury , than to press up 23 foot of Water , because the burden and weight is the same . It may be inquired fourthly , whether or not , it be as easie for the Air , to press up a thick and gross Cylinder of Water , as to press up a thin and slender one ? For example , whether is it as easie for the Air to press up a Cylinder of Water 10 inches in Diameter , and 10 foot high , as it is to press up one , two inches in diameter , and 10 foot high ? I answer , there is no more difficulty in the one , than in the other : and the reason is , because Fluid bodies do not counterpoise one another according to their thickness , but only according to their altitude , according to the fourth Theorem . Therefore seeing the slender Cylinder is as high as the grosser , it must be no more difficult to the Air , to press up the one then the other . There is one difficulty yet remaining , which is truely the greatest of all ; namely what 's the reason , why its more difficult to the Air , to press up 20 inches of Mercury , than to press up 20 inches of Water : or more difficult to the Air , to press up 20 inches of Mercury , than to press up 10 ? I answer , this comes to pass , because the Air is more burthened with 20 inches of Mercury , than with 10. Now , if this be , then surely it must be more hard to the Air , to do the one , than to do the other : even as it is more hard ; for a man , to lift up from the ground , 20 pound of iron , than to lift up 10 or 15. The case may be better illustrated after this manner . Suppose a man standing on the ground , with a rope in his hand , coming down from a Pulley above , drawing up a weight to the top of the house : put the case likewise , the weight be a stone of 20 pound , and the weight of it , to increase successively , as it is pulled up . Now its easie for the man to pull up the stone the first fathom ; because it is but 20 pound weight : but the stone becoming 40 pound in the second fathom , and 60 in the third , and 80 in the fourth and so forth , untill it become 1000 , he will find the greater difficulty , the longer he pulls . 'T is just so with Air , or Water , raising Mercury in a Tub ; for as the Cylinder of the Mercury grows higher by rising , so it becomes heavier , and consequently the imaginary surface , upon which the Base of the Pillar rests , is more and more burdened , and so becomes less and less able to press it up . This leads us to a clear discovery of the reason , why 't is more difficult by suction , to pull up Mercury in a Pipe , than to pull up Water ; and more hard to suck up ten foot of Water , then to suck up five . For trial of this , which is soon done , take a slender Glass-pipe 30 or 40 inches long , open at both ends , and drown the one end among Quick-silver , and put your mouth to the other , and having sucked , you will find greater difficulty to pull up thorow the Pipe 15 inches of Mercury , than to pull up 10 , or 8 ; and far greater difficulty to suck up 20 , than to pull up 15. It may be objected , that if a man had strength sufficient in his Lungs , to suck out the whole Air of the Pipe , thirty inches of Mercury would come as easily up , as three , which seemes to prove , that the difficulty of the Mercurie's up-coming , depends not upon the weakness of the Air , but upon the weakness of the Lungs , and want of strength to suck . I answer , though a man were able to suck out the whole Air of the Pipe , yet 30 inches , will never ascend so easily , as ten , nor ten so easily as three ; and that for the reasons already given . But why is it then , ( say you ) that the stronger the suction be , the higher the Mercury ascends in the Pipe ? I answer , the suction serves for no use , but to remove the impediment , that hinders the Mercury from coming up , which is nothing else , but the Air within the Pipe. Now , the more of this Air that 's taken away by suction , ( the stronger the suction is , the more Air is taken away ) the farder up comes the Mercury . But why ought there to be difficulty in the suction of Mercury , to the altitude of 15 or 20 inches , more than in the suction of Water to that altitude ? I answer , when I suck Water up thorow a Pipe , the suction of the Air above it , is easie ; because the ascending Water helpes much to drive it up to the mouth , the outward Air driving up both . But the suction is difficult in Mercury , because the ascending liquor , does not help so much , to drive up the Air to the mouth , as the Water does . And the reason is , because the Air , being more burdened with 15 inches of Mercury , than with 15 inches of Water , cannot so easily drive up the one as the other , and so Mercury cannot so easily drive up the Air of the Pipe to the mouth , as Water does . In a word , according to the difference of specifick weight , between Water and Mercury , so is the difficulty of suction ; therefore , because Mercury is 14 times heavier than Water , there is 14 times more difficulty , to pull up the one , than the other . Note , that suction is not taken here strict●y , as contradistinguished from pulsion ; but in a large sense , as it may comprehend it . To proceed a little further , let us suppose the Pillar of Mercury ( see the 11. Figure ) GH , that 's raised by the surface of Air FG , to be 29 inches , and every inch to weigh one ounce . Secondly , that the said surface has 29 degrees of power or force in it : for in all counterpoises the Pondus and the Potentia are equal ; therefore , if the Mercury be 29 inches , the Potentia of the surface must have 29 degrees of strength or force in it , to counterballance the Pondus . These things being supposed , which are evident , let us imagine the surface of Air , to raise the Mercury one inch above FG. In this case , the surface is weaker than it was ; which I prove evidently , because it is now but able to raise 28 of Mercury . Imagine next , the said surface to have raised the Mercury two inches above FG , then it follows , that it must be yet weaker , because it 's now but able to raise 27 inches : for by supporting two ounce of the Pondus , it loseth two degrees of it's own Potentia . In raising three inches of Mercury , it is three degrees weaker ; and in raising four , it is four degrees weaker , and so forth ; therefore , having raised 28 inches , there is but one degree of force remaining in the surface . And when it hath raised the whole , namely 29 , it is no more able , and can no more press . For confirmation , put the case that the surface of Air FG , were as able , and had as much Pressure in it , after it hath raised 29 inches of Mercury , as it is after the raising of 10 ; then it follows of necessity , that after the raising of 20 , it shall raise 19 moe , which is impossible , seing the greatest altitude is 29. It follows of necessity , ( I say ) because after the raising of 10 , it is able to raise 19 moe : therefore if it be as able after 20 , as after 10 , it must raise 19 after 20. Yea , if it be as able after 20 as 10 , it must be as able after 29 as 10. If this be , then it may raise other 29 , and a third 29 , and so in infinitum . Therefore , I conclude , that when two Fluid Bodies are in equilibrio one with another ; or when the pondus is equal to the potentia , none of them doth actually press upon another , at least the su●face hath lost all its Power and Pressure , which is also evident in the Pillar . For understanding this , let us suppose ACB ( Figure 11. ) to be a Pipe 58 inches long , and full of Mercury , and every inch of it to weigh one ounce . Now , when the orifice D is opened , there is here as great an inequality , between the pondus and the potentia of the surface of Air EB , on which it rests , as was between the surface FG , and the pondus of Mercury HG . For as FG had 29 degrees of power to raise GH , so the Pillar AB has 29 ounce of weight , to overcome the surface EB . And as the surface FG , became one degree weaker , by raising one inch of the Mercury HG , and two degrees weaker , by raising two inches , and so forward , till it lost all its Pressure ; so the Pillar , by falling down one inch , loseth one ounce of the weight ; by falling down two , it loseth two ounce , and so forward , till by falling down from A to C , it loseth all its Weight and Pressure . But here occurreth a difficulty ; for if the surface FG , hath lost all its Pressure , by raising the Mercury from G to H ; and if the Pillar CB , hath lost all its Pressure , by falling down from A to C ; it follows , that when a Pillar of a Fluid , and a surface of a Fluid are in equal termes , or b●ought to an equipondium , there is no Pressure in them at all . For answer , consider first , that in all counterpoises , there a●e necessarily two things , the movens and the motum , the thing that moves , and the thing that is moved . Secondly , you must consider the motum , to have a pondus or weight in it , and the movens to have a potentia , or power , wherewith it moves that weight . Thirdly , that as the thing that moves , hath a power or force in it self , whereby it moves , so the thing that is moved hath a power or force in it self , whereby it resists the motion . Fourthly , that sometimes the resistance of the thing moved , may exceed the power of the movent , as when a Quarrier with a Leaver , endeavours to prize up a stone too heavy for him : or the power of the movent , may exceed the resistance of the weight ; or both may be of equal power . Consider fifthly , that as the pondus of the thing moved , begins to grow more and more , so the power of the movent decreaseth proportionably ; not absolutely , as heat is extinguished in Water by the cold Air , when it is removed from the Fire , but respectively . For example , when a man holds a ballance in his hand , with six pound in the one scale , and but one pound in the other , if you add another pound , the weight grows more , and the power and force of the opposite scale grows less proportionably ; not absolutely , for it still remains six pound , but respectively : that 's to say , six pound is less in respect of four , than in respect of five ; or the resistance of six pound is less , two counterpoising it , than being counterpoised by one . When a third is added , the weight grows yet more , and consequently the resistance of the opposite scale becomes yet less , till by adding the sixth and last pound , you augment and encrease the pondus to that same degree of strength , that the resistance of the opposite scale is of . From these considerations , I say , the surface of Air FG , hath not lost all its Pressure absolutely , by raising the Mercury from G to H , but only respectively , because it still retains 29 degrees of force in it self . I say respectively , because when the Mercury is raised ten inches , the power of the Air which is of 29 degrees of force , is less in respect of ten ounce , then in respect of five ; or the power of 29 degrees of force is less , being counterpoised by ten ounce , than being counterpoised only by five . And when it is raised 20 , it is yet less in this respect , than in respect of ten . And when it has raised the Mercury to the greatest altitude H , it may be said to have lost all its Pressure , seing it is not able , by vertue of a counterpoise , to do any more . Even as six pound in this scale , may be said to have lost all its resistance and weight , by putting in the other scale , first one pound , next two pound , and then three pound , till the last be put in , at which time it hath no more resistance . Though this be , yet it still remains six pound . Even so , the Air FG still remains of the same force and power , while it suspends the Mercury GH , that it was of before . Likewise , the Pillar AB , cannot be said to have lost all its pressure absolutely , by falling down from A to C , but only respectively , because the said Pillar CB , is still 29 ounce weight . I say respectively , because in falling down ten inches , or in losing ten ounce , the weight that 's now but 48 , is less , in respect of 29 , than while it was 58. It is yet less , when it hath fallen down other ten , because being now but 38 , it must be yet less in respect of 29 , than 48. And when it hath fallen down to C 29 , it may be said to have lost all its weight , because it can do no more , having respectively lost all its Pressure . From what is said , we see a clear ground to distinguish in Fluids a pondus and a potentia . Secondly , that the potentia may sometimes exceed the pondus , and contrariwise the pondus may exceed the potentia . Thirdly , that inequality of weight , between the pondus and the potentia , is the cause of motion of Fluids . Fourthly , that the motion never ceaseth , till the pondus and the potentia become of equal force . This conclusion is not so universal as the rest , because the motion may sometimes cease , before this be . For example , when the Air is pressing Mercury up thorow a Tub shorter then 29 inches , the motion ends before there be a perfect counterpoise ; for 20 or 15 inches of Mercury , can never counterballance the force and power of the Air. In such a case then , there is an unequal Pressure , the Air pressing the Mercury more , than the Mercury doth the Air. EXPERIMENT VIII . Figure 12. TAke the Vessel ABCD , and fill it with Water , as high as HI . Take next a Cylinder of stone FG , and drowning the half of it among the Water , suspend it with a chord to the beam NO , with a ring at E. Now in this case , though the stone do not touch the bottom of the Vessel , yet the Water becomes heavier , than before . For discovering the true reason of this , I suppose fi●st , the weight of the Water , before the stone be drowned , to be 40 pound . I suppose next , that after the stone is drowned , the said Water to weigh 50 pound . And lastly , the stone to weigh 60 pound . I say then , the Water must be 10 pound heavier than before , because it supports 10 pound of the stone . 'T is certain the beam is less burdened by 10 pound than before . If this be , then surely the Water must sustain it . It were great temerity and rashness , to averr that neither the Beam , nor the Water sustains it , which is really to say , it is sustained by nothing . It cannot be said without ignorance , that 10 pound of the stone is evanished , and turned into a Chimera . If it be said , how can such a Fluid Body as Water , be able to support any part of the weight of the stone , that is such a heavy Body ? I answer , there is here no difficulty , for if the imaginary surface KL , upon which the 10 pound of the stone rests , be able to sustain 10 pound of Water ( I suppose the stone taken away , and the place of it filled with Water ) then surely it must also be able to sustain 10 pound of the heaviest metal ; seing ten pound of Lead , or Gold , or Stone , is no heavier than 10 pound of VVater . If some say , this rather seems to be the reason , why the Water becomes heavier , after the stone is drowned , because it possesseth the place of as much Water , as would weigh 10 pound ; not ( as was said ) because the VVater supports 10 pound of it . Therefore it may be judged , and thought , that if the space that the stone occupies , were filled with Air , or some light Body , without sensible weight , the VVater would become heavier than before . For example , if in stead of the stone , there were placed a bladder full of wind , within the VVater , and tied to the bottom with a string , that the surface might swell from HI to AB , the VVater of the Vessel would become as much heavier than before , as is the bulk of VVater , equal to the quantity of the bladder . Therefore , the VVater becomes heavier , not because it supports any part of the stone , but because the stone occupies as much room and space , as would contain 10 pound of VVater : for by this means the drowned stone raiseth the VVater from HI to AB ; and so the Cylinders AC , and BD , being higher , press with greater weight upon the bottom CD , even with as much more weight , as if the space that the stone occupies were filled with VVater . For answer to this , we shall make this following Experiment . Take the Vessel MPVX , and fill it with VVater to QR . Next , take a large bladder WY full of wind , and tying the neck with a threed , thrust it below the Water , and fasten it to the bottom , with a string , to the Ring Z. This done , the Water swells , and rises from QR , to MP . Now , if it be true , that the Water in the Vessel becomes heavier , not because it supports 10 pound weight of the stone , but because the stone occupies the room of 10 pound of Water ; then it ought to follow , that after the bladder is tyed below the Water , the said Water should become heavier , than before , even by three pound ; for I suppose a bulk of Water , equal to the bulk of the bladder , to weigh as much . And the reason is , because ( as you say ) the quantity of the bladder WY , makes the water swell from QR to MP , by which means the Pillars of Water MV , and PX becomes higher , and so presseth with greater weight upon the bottom VX . For clearing this difficulty , I say , when a bladder is thus below the VVater , tyed to the bottom , the VVater becomes not three pound heavier : for when you place the Vessel with the VVater and bladder , in the Scale of a Ballance , the said VVater weighs no more , than if it wanted the bladder : therefore the VVater becomes not heavier , because the stone possesseth the room of 10 pound of Water , but because the Water sustains 10 pound of the stone . Now the reason , why the bladder makes not the water heavier , though it raise it from QR to MP , is this ; because though verily there be a greater Pressure then before , even upon the bottom of the Vessel , yet because moe parts are not added , the natural weight cannot be augmented , which essentially depends upon the addition of these parts . If it be replyed , the Experiment of the bladder is to no purpose , because it being knit to the bottom , pulls up the Vessel , with as great force , as the growth of the Pressure bears it down , and so the Bladder cannot make the Water heavier . But , if so be , it were possible , that the Bladder could remaine within the middle of the Water , without being knit to the bottom , and consequently without pulling up the Vessel , then surely the Pillars of Water MV , and PX , being higher , would press with greater weight upon the bottom , and so make the Vessel , and the Water weigh more in the ballance : for 't is to be supposed , that during all this time , this Vessel with the Water , is in one scale , and a great weight of stone or lead , in the other . So would the Water ABCD become heavier likewise , provided the space and room , that the stone fills among the Water , remained intire , after the stone is taken away : because that room and empty space remaining , would keep the surface , as high as AB , by which means , the Pillars AC and BD , being higher , would press with greater weight upon the bottom , and cause the Water weigh more in the ballance . I answer , though by some extraordinary power , the bladder could remain below the water , of its own accord , as it were , and though the space and room , by that same power , which is left by the stone , were keeped empty , yet shall they never be able to make the Water heavier . As to the reason , that 's brought , I answer , the rising and swelling of the Pillars , will make indeed a greater Pressure upon the bottom of the Vessel , but because this Pressure may be produced , and generated without the addition of new parts , therefore , it can never make the Water heavier : for if this were true , then it would follow , that the more a body is comprest , it should be the heavier , which is contrary to sense , and experience . This Pressure is like unto Bensil , that cannot weigh in a ballance , though the thing bended do weigh ; as a Bow that weighs so many pounds , but the Bensil of it weighs nothing : Next , will any man think , that a Cub of Water six foot high , and six foot thick , will weigh more in a ballance , then it did , after it is turned into a long square Pillar 216 inches high ? I grant , there is near 60 times a greater Pressure , upon the bottom of the Vessel , yet because this Pressure is generated , without the addition of new parts , it cannot make the Water heavier . Moreover , it is mechanically possible to keep the VVater STVX , under that same degree of Pressure it hath , though the rest above were taken away : if this be , then it ought to be as heavy , as the whole , seing it still Presses the bottom , with that same degree of Pressure , it had from the whole : but what is more absurd , than to say , one part of VVater , is as heavy , as the whole ? e. g. a pint as heavy as a gallon . If it be said , the Pressure , and the weight , are but one thing , at least effectively , which is sufficient to the purpose in hand , as is clear from the Theorem 23. I answer , they are but one thing indeed , in order to the Ballance of Nature , but they are neither formally , nor effectively the same thing in order to the Libra or Artificial Ballance , whereof we are now treating . I shall conclude with this ; while the Vessel with the VVater , is thus placed in the Scale of the Ballance , and in equilibrio , with the opposite Scale , cut the string that tyes the bladder to the bottom , and when it comes above , you will find the VVater , just of the same weight it was of : for though the surface MP , by taking out the bladder , settle down to QR , yet there 's no alteration made in the weight . From this I gather , that if the swelling of the VVater should make it heavier , then the subsiding and falling down of it , ought to make it lighter . From these Experiments we gather first , that in VVater there is a Pressure , because it sustains 10 pound of the stone FG. Secondly , that whatever heavy body is weighed in Water , it loseth just as much of its weight , as the bulk of Water weighs , it puts out of its place . This is evident , because the stone is 10 pound lighter in VVater , than in the Air , because the VVater that would fill the room of the stone , is just of that weight . VVe see thirdly , that the Pressure of VVater , and the natural weight of it , are two things really distinct ; because the Pressure may be augmented , without any increment of the natural weight . VVe see fourthly , that the Pressure , or Bensil of a Fluid , cannot affect the Scale of a Ballance , but only the natural weight . VVe see fifthly , that a body naturally heavier than Water , weighs in Water , because the stone FG , makes the Water about it , 10 pound heavier . If it be inquired , whether bodies , that are naturally lighter , will weigh in Water ? I answer , if they be of any sensible weight , they weigh , as well as the other . For this cause , I except Air. For though they were never so light , in respect of Water , yet if they have any considerable gravity with them , they will make the Water heavier , they are among . Put the case the Body were a Cube of Timber of six inches , weighing sixteen ounces , and that a Cube of Water of that quantity , weighed 112 ounces . Here 's a great inequality , between their natural weights : yet if that piece of Timber , were made to exist in the middle of Water , as the Bladder doth , it would make it 16 ounces heavier . The reason is this ; these 16 ounces are either supported by a surface of Water , or they support themselves . This last is impossible . If the VVater support them , then must they make the said VVater 16 ounces heavier . Note , that though a Body naturally lighter then VVater , as Cork , may be said to weigh in Water , that 's to say , to make it heavier , in which sense VVater weighs in Water , because if you add a pint to a gallon , it makes it heavier ; yet if you take a piece of Cork , and knit it to the Scale of a Ballance , by a threed , the Cork hanging among the VVater , the Scale hanging above in the Air , it will not weigh in Water ; because in this sense , no Body weighs in Water , but that which is naturally heavier then VVater , as Lead , or Stone . In this sense , VVater doth not weigh in Water , as will be seen in the 17 Experiment . EXPERIMENT IX . Figure 13. Take a Glass-pipe 70 inches long or there-about , and of any wideness , having the upper end H , hermetically sealed , the lower end C compleatly open , and fill it with Mercury , and cause a Diver carry it down to the ground of the sea MN , where I suppose is standing the Vessel ABDE with stagnant Mercury , and drown the end below the surface AB . This being done , the Mercury falls from the upper end H , to the point G , and there halts ; the space HG being empty . For understanding this Experiment , I shall propose several questions , and answere them . First , what 's the reason , why the Mercury subsides , and sinks down from H to G ? I answer , as formerly in the like cases , inequality of weight between the Pondus of the impending Quick-silver , and the Potentia of the surface , of the stagnant Quick-silver DCE . For while the Tub is compleatly full , the weight is so great , that the surface DCE , is not able to sustain it , therefore it must fall down , seing motion necessarily followes in Fluids , upon inequality of weight . It may be inquired secondly , why it halts at G , 58 inches from AB , and comes no further down ? I answer it halts at G , because when it hath fallen down to that point , there happens equality of weight , between the suspended Pillar , and the foresaid surface : for whatever weight the said Pillar is of , the surface on which it rests , is of the same . In a word , the Pondus of the one , and the Potentia of the other are now equal . For understanding this , consider according to the 25 Theorem , that the weight of the Element of Air , upon the surfaces of waters , is equivalent to the burden of 34 foot of water , therefore the first and visible surface of this Water LIK , is really as much prest , with the burden of the Atmosphere , as if it had 34 foot of Water upon it . Consider next , that between the said surface , and the ground MN , are 34 foot of Water indeed . Consider thirdly , that a Pillar of Water 34 foot high , is exactly of the same weight , with a Pillar of Mercury 29 inches high ▪ for if Water be 14 times lighter than Mercury , then they cannot be of equal weight , unless the one be 14 times higher than the other . Now , supposing the weight of the Air upon the surface LIK , to be equivalent to 34 foot of Water , or ( which is the same thing ) to 29 inches of Mercury , the surface of the stagnant Mercury AB , must be as much burdened with the incumbing Water , and the Air together , as if it had really resting upon it , a Pillar of Mercury 58 inches high . If this be , then it follows by necessity , that there must be an equality of weight , between the pondus of the Mercury in the Tub , and the potentia of the surface DCE ; Or ( which is all one thing ) that the part C , on which the Pillar rests , is no more burdened , than the part D or E. For if 34 foot of Water , and 34 foot of VVater , be equivalent for weight , to 58 inches of Mercury , then must the part D and E , be as much burdened with the said weight , as the part C is burdened with the Pillar within the Tub , seing both are of the same height : therefore the power , and force of the imaginary surface of the stagnant Mercury DCE , is of the same strength , with the weight of the Pillar GFB . And this lets us see the reason , why the whole 70 inches cannot be suspended ; for if the outward Pressure that 's upon AB , be but equivalent to the Pressure of 58 , it can never make the surface DCE able to support 70. To make it evident ( if any doubt ) that the Mercury is suspended by the weight of the Water , and the weight of the Air superadded , let a Diver bring up this Engine to the top of the Water , and he will find the one half to have fallen down , namely from G to F , the other half FB remaining . And if it were possible , to convey this Experiment to the top of the Air , the Bearer would see , the remaining half to fall down likewise , and become level with AB ; for where no Pressure of Air is , there can be no Mercury suspended . This falling down , is not all at once , but by degrees , and keeps a proportion with the Pressure of the Air , that grows less and less , from the ground to the top . From this Experiment we see first , the great Pressure and weight , the Elements of Air and Water are under , seing this Water , that 's but 34 foot deep , sustains the Mercury between G and F , 29 inches , as much between F and E , being kept up by the Pressure of the Air. We see secondly , that this Pressure is according to Arithmetical Progression , as 1 , 2 , 3 , 4 , 5. because in going down the first 14 inches , the Mercury rises one inch ; in going down the second 14 inches , it rises two ; in going down the third 14 inches , it rises three , and so forward . We see thirdly , though a VVater were 100 fathom deep , yea 1000 , yet the Pressure of the Air above is found at the bottom : for supposing this Experiment were 100 fathom deep , yet would the Air from above have influence upon it , to sustain so many inches of the Mercurial Cylinder . A Diver then , 10 or 15 fathom under the VVater , must be burdened with the weight of the Air , as well as with the weight of the VVater , so must the Fishes , though never so deep . We see fourthly , that the parts of a Fluid cannot cease from motion , so long as there is an inequality of weight between the pondus and the potentia . This is clear from the falling down of the Mercury from H to G. And assoon as equality of weight happens , the motion ends . This is clear from the Mercurie's halting at G. Fifthly , that in Mercury , as well as in Water , or Air , surfaces may be distinguished , and that these surfaces , are endowed with a Potentia or power , begotten in them by superior and extrinsick weight . This is clear from the imaginary surface DCE , that 's made powerful to support 58 inches of Mercury in the Tub , and that by the weight and Pressure of the Air resting upon AB . Sixthly , that , as two Fluids differ in specifick and natural weight , so they differ in altitude , when they counterpoise one another . This is clear from the disproportion that 's between the altitude of the Mercury suspended , and the height of the Water , and Air suspending . GF then is 29 inches , and the deepness of the Water from K to N is 34 foot , because Water is naturally 14 times lighter than Mercury . FB is likewise 29 inches , and the hight of the Air , that rests upon the surface of Water is six or seven thousand fathom high ; because Air is 14000 times naturally lighter than Mercury . Seventhly , that Fluid Bodies counterpoise one another , not according to their thickness and breadth , but only according to their altitude . This is evident ; for though this Tub were never so wide or narrow , yet the altitude of the Mercury is unchangeable . Hence it is , that the thickest Pillar of Water in the Ocean , is not able to suspend more Mercury , than the slenderest , I mean as to altitude . And hence it is , that the smallest Cylinder of Mercury , no thicker than a silk threed , is able to counterpoise a Pillar of Water , of any thickness whatsoever . We may conclude lastly , that when a Diver is 20 fathom under the Water , he is under as much burden , as if he were under 14 or 15 foot of Quick-silver . Suppose a man lying on his belly , within a large Vessel , and 14 or 15 foot of Mercury poured in upon him , surely it may be thought , that such a burden were insupportable . But put the case , the Diver were down 40 fathom , then must the burden be doubled . This follows , because if a Pillar of Water 34 foot high , with the weight of the Air superadded , be as heavy , as 58 inches of Mercury , then surely a Pillar 20 fathom high , or 100 foot , must be as heavy as 170 inches , which is more than 14 foot . EXPERIMENT X. Figure 14. AGainst the former Experiment , there occurres some difficulties , which must be answered . As first , if it be the Pressure of the Water , that sustains the Mercury in the Tub ( see the 13. Figure ) then the weight of the said Mercury ought not to be found , while the Tub is poised between a mans Fingers . But so it is , that when a Diver grips the Tub about the middle , and raises it a little from the bottom of the Vessel , he not only finds the weight of the Tub it self , but the weight also of the 58 inches of Mercury that 's within it . But this ought not to be , if the said Mercury , be sustained by the outward Water . In a word , it ought not to be found , because the said Pillar of Mercury , as really stands , and rests upon the imaginary surface DCE , as a Cylinder of Brass or Stone , rests upon a plain Table of Timber or Stone . If then , it be supported by the said surface , why ought I to find the weight of it , when I lift up the Pipe a little from the bottom of the Vessel ? For clearing this difficulty , consider , that when the Mercury falls down from H to G , it leaves a sort of vacuity behind it , wherein there is neither Air nor Water . Consider secondly , that for this cause , there happens an unequal Pressure ; the top of the Tub without , being burdened with the Pillar of Water IH , which actually presseth it down , and nothing within between G and H , that may counterballance that downward Pressure . These things being considered , I answer to the difficulty and say , it is not the weight of the suspended Mercury that I find , but the weight of the Pillar of Water IH , that rests upon on the top of the Tub. If it be said , the Pressure of a Fluid is insensible , and cannot be found . I answer , it 's true , when the Pressure is equal and uniform , but not when the Pressure is unequal , as here . If it be asked , how comes it to pass , that the Pillar of Water IH , is exactly the weight of the 58 inches of Mercury ? I answer , besides the said Pillar , there is another of Air , that rests upon the top of it , which two together are exactly the weight of the suspended Mercury ; IH being of the same weight with the Mercury GF , and the foresaid Pillar of Air , being of the same weight with the Mercury FB . To make it more evident , remember that one inch of Mercury , is exactly the weight of 14 inches of Water ; and that one inch of Mercury , is of the same weight with 14000 inches of Air. If this be , then must the Pillar of VVater IH , that 's 34 foot high , and of the same thickness with the 29 inches of Mercury GF , be of the same weight with it , seing 29 inches are to be found 14 times in 34 foot . For the same reason , is the Pillar of Air , namely SI , that rests upon the top of the Pillar of VVater IH , of the same weight with the 29 inches of Mercury FB . For after a just reckoning , you will find , that 29 inches will be found 14000 times in the Pillar of Air , that rests upon the Pillar IH . Or in a word , the hight of the Air is 14000 times , 29 inches . But here occurrs another difficulty . Let us suppose there were a Tub six foot high , one inch wide , having the sides , 3 inches thick . Imagine likewise the said Tub to be under the water 34 foot , with 58 inches of Mercury in it , as is represented in this 14 Figure . This being supposed , the Pillar of Water EAFCGD , must be far heavier , than the 58 inches of Mercury HB . The reason is clear , because the said Pillar , is not only 34 foot high , but as thick , as the Diameter of the Tub , whose sides are three inches thick . I answer , the whole weight of that Water EAFCGD is not found , while a man poises the Tub between his fingers , but only the weight of the part GA , which is exactly the weight of the Mercury HB . But here occurrs the great question , namely , why I find only the weight of the Water GA , and nothing of the weight of the Water , CE , or DE ? I answer , I cannot find the Pressure of the Water CE , because it is counterpoised with the upward Pressure of the Water IK . And for the same reason , I cannot find the weight of the Water DF , because it is counterpoised by LM ; but because there is nothing between H and A , to counterpoise the downward Pressure of the Water GA , therefore I find that . If it be objected , that the Water IK , cannot counterpoise the Water CE , because the one is farder down than the other , and consequently under a greater Pressure , than the other . I answer , though IK be stronger than CE , yet a compensation is made by the weight of the Tub. For understanding this , let us suppose the Water CE , and DF , to press downward with the weight of six pound , and the Water KI , and LM , to press upward with the weight of ten pound , there being four pound in difference . Suppose next , the Tub to weigh in the Air ten pound , and in the Water only six pound . If this be , then according to the eighth Experiment , and eighteenth Theorem , four pound weight of the Tub must rest upon the surface IL. And if this be , then must the Water IK , and LM , be four pound weaker with the Tub , than without it , and must only have six pound of upward Pressure . Fig. 9 Pag. 5● Fig. 10 Fig. 1● Pag. 7● Fig. 13 Pag. 81 Fig. 14 Pag. 86 EXPERIMENT XI . Figure 15. AMZC is a Water 15 foot deep . AB a Glass-tub 14 inches long , and full of Mercury . BC a Pillar of Water 13 foot , 10 inches high , thorow whose middle goes a string to the scale of the Ballance K , existing in the Air. DE is a Tub full of Mercury 28 inches long , with a Pillar of Water above it EF , 12 foot and eight inches . GH a Tub 42 inches long , with a Pillar of Water above it HI , 11 foot and six inches high . And lastly , ADGSM an imaginary surface , 15 foot deep . This Experiment is brought hither , to demonstrate that a heavy Body , weighs as much in Water , as in Air , which is point-blank to the common received opinion , and destructive of the 18 Theorem . To evince this , I must suppose the 14 inches of Mercury in the Tub AB to weigh 14 ounce ; and the 28 inches of Mercury DE , to weigh 28 ounce ; the 42 inches GH to weigh ( I mean in the Air ) 42 ounce . Now I say , to make a just equipondium between the two Scales K and L , there must be 14 ounce put into the Scale L. If after this manner you weigh the Tub and Mercury DE , 28 ounces will be required in the Scale L , and 42 , if you weigh the Tub and Mercury GH . For proving this Doctrine , I must appeal to Experience , which will not fail in this . If you reply , and say , upon supposition the Tub and Mercury GH , were a solid piece of brass , or iron thus suspended in the Water , ought it not to weigh less here than in the Air , even as much less , as is the weight of the quantity of Water , it puts out of its place : why then should not the Pipe HG , with the Mercury in it , do the same , seing there is no apparent difference between them , as to this ? But to leave this , which will appear afterwards , and to let the Reader see the truth of the 18 Theorem , I affirm , 't is not the weight of the 14 ounces of Mercury AB , that burdens the scale of the Ballance K , and that makes a counterpoise with the 14 ounces of Stone , or Lead , that 's in the scale L. What then is it , you say ? I answer , 't is 14 ounces of the Pillar of Water BC that does this . Neither doth the weight of the 28 ounces of Mercury DE burden the Ballance , but only 28 ounces of the Water EF. Neither doth the Ballance support the weight of the 42 ounces of Mercury GH , but it is only burdened with 42 ounces of the Water HI . The reason is most evident , because according to the Principles of the Hydrostaticks already laid down , the Cylinder of Mercury AB , within the Tub AB , rests immediatly upon the imaginary surface of the Water ADG , and therefore cannot burden the scale in any wise . The same is true of the other two Cylinders of Mercury . But in this I find small difficulty . The greater is , how to make it out , that the scale K , supports 14 ounces of the Water BC , and 28 of the Water EF , and 42 of the Water HI . To make this seem probable , consider first , as was noted , that this VVater is 15 foot deep , and consequently the Pillar of VVater BC , 13 foot 10 inches . The VVater EF 12 foot eight inches . And HI , 11 foot and a half . Consider secondly , though this be true , yet we must count the Pillar of VVater ZM 49 foot high . The reason is evident , because the Pressure of the Air , upon the surface of all Waters ( according to the 25 Theorem ) is equivalent to 34 foot of Water : this then being added to 15 , makes 49 , and by this reckoning the Water BC is 47 foot ten inches : the Water EF 46 foot eight inches : And lastly , the Water HI 45 foot six inches . Thirdly , for easie counting , I must suppose the whole Cylinder ZM to weigh 42 ounces , every 14 inches one ounce : and consequently the Water BC to weigh 41 ounces ; the Water EF to weigh 40 ounces ; the Water HI 39 ounces . Note , that in Physical demonstrations , 't is not needful to use Mathematical strictness in counting ; and so leaving out fractions , we shall onely use round numbers ▪ Consider fourthly , that in all Fluids , as hath been frequently marked , there is a pondus and potentia , the Water BC being the pondus , and the Mercury AB the potentia , the one striving to press down the Tub , the other striving to press it up . Consider fifthly , that by how much the more a Body suspended in a Fluid is pressed up , by so much the less the weight that presseth it down is found : and contrariwise , by how much the less it is pressed up , by so much the more the Pressure above is found . Consider sixthly , the less that a surface of Water is burdened , the more able it is counterballance the opposite Pressure , and the more it is burdened , it is the less able . Consider seventhly , that the Mercury AB , ( which is evident in all Fluids ) not only presseth downward , and burdens the surface ADG , but also presseth upward , and therefore actually endeavours to thrust up the Tub ; and so it is , that the Tub is pressed between two , namely between the Water CB , and the Mercury within it . Now from these considerations I say , the scale K , must support , and bear up 14 ounce of the Water BC : for seing the Mercury is supported by the surface of VVater on which it rests , it cannot by any means burden the ballance with its weight ; and seing it actually presseth up the Tub , ( according to the seventh consideration ) it must so much the more counterpoise ( according to the sixth ) the opposite Pressure of the VVater BC , and consequently diminish the weight of it : so that the Ballance cannot support the whole , but a part . For according to what degrees of force , the Mercury presseth up the Tub with , according to the same , must the Pressure upon the top of the Tub be diminished , and so if the Mercury press up the Tub with the force of 27 ounce , the VVater BC must press it down with 14 ounce only , and so the Cylinder BC , that weighs really 41 ounce , must press the top of this Tub only with 14 , which 14 ounce really counterpoiseth , the 14 ounce of Stone in the Scale L. But how is it made out , that the Mercury AB , presseth up with 27 ounce ? For understanding this , remember , that the VVater is 49 foot high , taking in the Pressure of the Air , and that a VVater of that deepness is able to support 41 inches of Mercury , every inch weighing one ounce . For if 14 of Water , be able to support one of Mercury , 49 foot , or 567 inches , must support 41. If then , the part of the surface A , be able to weigh 41 , it must have of upward Pressure 27 ounces , seing it's counterpoised de facto only with 14. Take notice , that in the Hydrostaticks , the word pressing , or weighing , as really and truly signifies a weighing up , as a weighing down , seing it is no less essential to Fluid Bodies to move upward , than downward , and that with equal force , and weight . According to this reasoning , the Ballance supports 28 ounces of the Water EF , ( Imagine the second Tub to be suspended as the first ) seing the Cylinder of Mercury DE , presseth up the Tub only with the weight of 12 ounce , which 28 ounce , really counterpoiseth the 28 ounce of Stone in the Scale L. But why doth the Mercury AB press up with 27 ounce , and the Mercury DE with 12 ? For answer , remember , ( according to the sixth consideration ) the shorter a Cylinder of Mercury is , the surface upon which it rests , is the stronger , and more able to press it up ; and contrariwise , the longer it is , the surface is the more unable and weak : therefore AB being shorter , and lighter than DE , the surface of Water must press it up with greater force : so that if the said surface AM , be able to press up the Mercury AB with 27 ounce , it must press up the Mercury DE only with 12 ounce . According to this rule , if the Mercury AB were 15 inches high , it would press up only with 26 ounce , if it were 16 , with 25 : if 17 , with 24 : if 18 , with 23 , and so forward . This leads us to a clear discovery of all the secrets here : for if the Mercury AB , thrust up the Pipe , with the weight of 27 ounce , then must the Scale K , be eased of so much weight , and so much must be subtracted from L. Now let us imagine the Pipe AB , to be empty both of Air , Water , and Mercury : in this case 41 ounce must be in the Scale L , to counterpoise it , seing the whole Cylinder BC , that weighs so much , does now really counterpoise it . Let us imagine next , these 14 inches of Mercury to rise , and fill the Tub AB : in this case , there happens a great alteration ; because the rising of them , are really equivalent to the subtracting of 27 ounce from the Scale L ; and the reason is , because by so rising and filling the Tub , they thrust up the said Tub , and by this means easeth the Scale K , of so much weight . Now this Scale being eased , you must of necessity take out from L 27 ounce for making a new counterpoise . And lastly , the Scale K must support the whole weight of the Water HI , which is 39 ounce , nothing remaining to counterballance this downward Pressure , and consequently to ease the Ballance . How then is it counterpoised ? For clearing this , you must remember that this Water , that 's really 15 foot deep , must be reckoned ( as I said ) 49 , because of the Pressure of the Air upon the top , that 's equivalent to 34. If then it be so , it cannot raise Mercury higher in a Tub than 42 inches ; the one being 14 times heavier than the other : so that if 14 inches of Water , cannot raise Mercury higher than one inch , 49 foot cannot raise it higher , than 42 inches : for as 14 inches , are to one inch ; so is 49 foot to three foot and an half , which is 42 inches . Now I say , the whole weight of the Water HI , rests upon the top of the Tub , and so presseth down the Scale K , to which you must imagine this Tub , knit by a string , as the former was , nothing remaining to counterpoise this downward Pressure : for the top of the Mercurial Cylinder being raised as high within the Pipe , as the surface of Water DGS , is able to raise it , the said top can impress no force upon the Tub within , to thrust it up , and so to ease the Scale K. For example , when a man erects upon his hand a Cylinder of Timber , or any such like thing , which is the outmost he can support , he will not be able to impress any impulse , upon the seiling of a room above his head ; but if so be , in stead of that taken away , there be one lighter erected , which he is able to command , he can easily thrust up the seiling at his pleasure . Just so it is here ; for the 42 inches of Mercury , being the outmost , that the surface of Water DGS is able to bear , it cannot impress any impulse therewith upon the top of the Tub within : but easily can the Cylinder DE impress an impulse , and more easily the Cylinder AB , seing they are lighter , and so more powerful . To evidence this a little more , let us imagine two things , first , the Tub GH to be empty , as if vacuity were in it . In this case the top of the Tub ought to bear the whole burden of the Water , and consequently the Ballance to bear it also : because there is not a potentia within the Tub , to counterpoise this pondus . Next , let us imagine the Tub to be only full of Water : according to this supposition , the Ballance cannot be in the least part burdened ; because the Water within the Pipe , presseth it up with as much force , as the Water IH presseth it down : and if any thing should burden the Ballance , it would be only the weight of the Pipe , that 's not considerable . From what is demonstrated , we see first , that though this Experiment would seem to prove at the first , that a heavy Body weighs as much in the Water , as it doth in the Air , because the whole weight of the Mercury AB is found in the scale L , yet 't is not so , because the 14 ounce of Stone L , doth not counterpoise any of the Mercury AB , but 14 ounce of the Pillar of Water BC. Secondly , there 's here a clear ground , for asserting a pondus and a potentia in Fluids ; because this Tub AB , is prest down with the VVater BC , and prest up with the Mercury within it . Thirdly , there 's here a clear ground for asserting the Pressure of VVater , even in its own place ; because the Water BC , counterpoises by it's weight , the 14 ounce of Stone L. Fourthly , we see an excellent way for finding the weight of any Cylinder of Water ; for whatever be the weight of the Mercury in the Tub , the Cylinder of Water , that rests upon the top , will be of the same weight exactly ; this is evident in comparing the weight of the Mercury GH , with the weight of the Water HI . Fifthly , that whatever be the height , and weight of a Pillar of Water , yet the Ballance can sustain no more of it , than the just weight of the Mercury : this is also evident , because the scale of the Ballance , supports no more of the weight of the Water BC , than the just weight of the Mercury AB . We see sixthly , the further down a Pipe with Mercury goes through Water , the greater is the Pressure it makes upon the top of the Tub within : for put the case , this were 100 foot deep , the Mercury GH , that wants all upward Pressure now , would press up the Tub with 40 ounce : the Mercury DE with 55 , and the Mercury AB with 70. We see seventhly , the shorter a Cylinder of Mercury be , it is the stronger in pressing ; and longer it be , it is the weaker ; for there 's more strength in AB , than in DE. We see eighthly , that the strength decayes , and grows , according to Arithmetical progression , as 1 , 2 , 3 , 4 ; because if you make the Cylinder GH 41 , that 's now 42 , it presseth up with one ounce . Make it 40 inches , it will press up with two ounces of weight . Make it 39 , it presseth up with three . And contrariwise , make the Cylinder DE 29 inches , that 's now but 28 , it will press up with 11 ounce only . ( VVith 28 it presseth up with 12. ) Make it 30 inches high , it will press up with 10. If it be 31 inches , it presseth up with nine , and so forward . Lastly , make the Cylinder AB 15 inches , that 's now but 14 , it presseth up with 26 ( with 14 , it presseth up with 27 ) make it 16 , it presseth up with 25 ; make it 17 , it presseth up with 24. We see ninthly , that in Fluids , we may make a distinction between a sustentation , and an equipondium . 'T is evident here , because there 's a perfect equipondium between the 42 inches of Mercury GH , and the outward Water that 's 49 foot deep . But 't is not so , between the said Water , and the Mercury DE ; because the said Water is able to raise the said Mercury 14 inches higher : therefore the Water only sustains the Mercury DE , but counterballances the Mercury GH . We see tenthly , that the pondus of the pillar of Water BC is counterpoised by two distinct powers really . The one is the 14 ounce of Stone in the scale L , the other is the 14 inches of Mercury AB , that as really thrusts up the Water , as the scale K pulls it up , by vertue of the opposite weight . Eleventhly , take away the Stone L , and you will find the Pipe with the Mercury AB sink down : this happens , not because the surface of Water on which it rests is not able to sustain it , but because the 14 ounce of the Water BC , that was supported by the Stone , doth now press it down . Twelfthly , the more a Body is unequally pressed by a Fluid , the more of the weight of that Fluid is sensible ; and the more equally a Body is pressed , the less sensible is the weight of that Fluid : this is evident , because there 's a greater weight of the VVater HI found in the Ballance ( it takes 42 ounce to counterpoise it ) than of the VVater EF , which is counterpoised with 28 ounce : and the reason is , because the top of the Tub H , supports the whole 39 ounce of VVater HI , the Mercury within the Tub , not being able in the least to counterpoise it , or thrust it up . But because the Tub DE , is more equally pressed ( the VVater EF presseth down with 40 , and the Mercury DE presseth up with 12 ) therefore less weight of the VVater EF burdens the Ballance , only 28 ounce . Hence it is , that because the Tub AB , is more equally pressed , than either DE or GH , there 's less of the weight of the VVater BC , found in the Ballance , only 14 ounce . Thirteenthly , if in the instant of time , while the Tubs are thus suspended in the VVater , the Pressure of the Air above were taken away , and annihilated ; then first , the 42 inches of Mercury GH would fall down , to about 13 inches . Secondly , the 28 inches of Mercury DE , would fall down to as many . And lastly , the 14 AB , would sink down to the same height . The reason is , because the Pressure of the Air being equivalent to 34 foot of VVater , no more would remain but 15 foot , which is the real height , according to ZM . But 15 foot of Water , cannot sustain moe inches of Mercury than about 13. And consequently , first , 14 ounce of Stone in the Ballance , would counterpoise the whole Water BC. The reason is , because the Water BC is but of 14 ounce ; and the Mercury AB , being but 13 inches high , could impress no impulse upon the top of the Tub within , that 's 14 inches high . Secondly , 13 ounce of Stone in the Scale L , would counterpoise the whole Water EF , seing EF is but 13 ounce . Thirdly , the same weight ( one ounce being deduced ) would counterpoise the Water HI , because in this case , it weighs but 12 ounce , To proceed a little further , imagine the Pipe GH to be suspended by the ballance , as the Pipe AB is ; and then a little hole opened in the top H , to suffer the Water to come in , till the Mercury subside 14 inches , namely from Q to O ( imagine this Tub to be the other ) and then stop it . The reason why the VVater rusheth in , and presseth down the Mercury , is the force and Pressure of it : for the said VVater , finding the Cylinder in equilibrio with the outward VVater , presently by its own weight , casts the scales , which is easily done , seeing the surface GSM supports as much burden as it can . But that which is more considerable is this ; after the subsiding of the Mercury from Q to O ; the equilibrium that was between the scale of the ballance , and the VVater QR is destroyed : for whereas 42 ounces were required before ; 29 will now do it . For understanding the reason of this , consider that between Q and O , are 14 inches of VVater rushed in , which are equivalent to one inch of Mercury . Next , according to former reasonings , the ballance must support 29 ounces of the VVater QR ; because in this case , the top of the Pipe within , is pressed up with the weight of 13 ounces ; which in effect , diminisheth as much of the downward Pressure of the VVater RQ , which before had the burden of 39 ounces . But why is the Tub prest up with 13 ounces ? I answer , because the Mercury , that before was 42 inches , is now but 28 ▪ or having the 14 inches of Water QO above it , it is 29 , therefore being shorter , the surface GSM is the more able to Press it up , even with as much more force , as it is in inches shorter . In the second place , let in as much Water more , as will depress the Mercury other 14 inches , namely from O to P. In this case , 16 ounce of stone will make an equipondium ; because , the 14 inches of Mercury PS , and the 28 inches of Water POQ , being a far lighter burden by 26 , than the 4● inches of Mercury , the surface GSM must be far abler to press them up now , than before : and therefore , must diminish as much of the downward Pressure of the VVater QR , that burdens the Ballance , as themselves wants of weight : seing then , the whole Cylinder of Mercury , and Water together , are but equivalent for weight to 16 inches of Mercury , the top of the Tub within , must be prest up with 26 ounce ; and therefore they by their upward Pressure , must diminish 26 ounce of the weight of the Water RQ , that weighs 39. Lastly , let in so much VVater , as will depress the last 14 inches PS ; and you will find no more weight required in the Ballance to make an equipondium , than counterpoiseth the simple weight of the Tub , which is not considerable . The reason is , because , the part S , of the surface GSM , being liberated of the burden of Mercury , and sustaining only the VVater within the Tub , instead of it , this surface presseth up the VVater within the Tub , and consequently the top of it , with as great force , and w●ight , as the top of the Tub without is depressed , with the outward VVater RQ : therefore , 39 ounce depressing the Tub , and 39 ounce pressing it up , the Ballance must be freed of the whole weight of VVater RQ . If it be objected , that the 42 inches of VVater QS , are equivalent in weight to three inches of Mercury ; therefore the part of the surface S , being burdened with this , cannot press up , with as great force , as the VVater RQ presseth down . For answer , consider , that the part S , is able to support 42 ounce of VVater , and next , that the VVater RQ weighs but 39. Then I say , seing the 42 inches of VVater within the Tub , weighs only three ounce , the part S , that 's burdened therewith , being able to support 42 , it must press up with the weight of 39 , and so counterballance the VVater RQ . If it be inquired , whether or not , would the 14 inches of Mercury AB fall down , a small hole being made in the top of the Tub at B ? I answer , they would . If it be objected , that these 14 inches of Mercury , are not in equilibrio , with the Pressure of the ambient Water , as the Mercury GH , and therefore they cannot be so easily depressed by the Water , that comes in at the said hole . I answer , they must all fall down , and as easily , as the other , and that because of inequality of weight between the Potentia of the surface of VVater , and the Pondus . It 's certain , the part A of the surface , cannot support more weight of any kind , than 42 ounce ; but when a hole is opened in B , and the VVater comes in , 't is then burdened with the weight of 14 ounce of Mercury , and with the weight of 41 ounce of VVater ; so much the VVater BC weighs , which is 55 ounce : but a surface that hath only the Potentia of 42 , can never support a Pondus of 55 , no not of 43. It may be objected thus : Put the case a Cylinder of Gold , or Brass were suspended in this VVater ; as the Pipe and Mercury GH are suspended by the Ballance , would not the Ballance support the whole weight of it , without supporting any part of the weight of the VVater IH , that rests upon the top of it . I answer , there 's a great difference between the two ; because a Cylinder of Gold or Brass , suffers both the upward and downward Pressure of the VVater ; but the Mercury GH , suffers only the upward Pressure , being freed of the downward , by the top of the Tub. From this Experiment of letting in the VVater upon the top of the Mercury , we see first , that when two Fluids are in equilibrio one with another , a very small weight will cast and turn the Scales , because , if the sixth part of an inch of VVater come in at Q , it presently alters the hight of the Mercury from 42 inches to less . Secondly , 't is impossible for a surface of Water , to support more weight , than its own proper burden ; because the part S , cannot support more , no not a grain , than 42 ounce . VVe see thirdly , that it is as impossible for a surface of VVater , to support less , than its own burden ; because whatever loss of weight the Pillar of Mercury SQ suffers , by the ingress of the VVater QO , it s made up again by the same VVater . If it be objected , that the 14 inches of VVater QO , are not so heavy by far , as the 14 inches of Mercury , that fell down . I answer , its true , yet the part S , is as much burdened as before , because what is wanting in weight , it s made up , and compensed by Pressure . VVe see fourthly , that the Pressure of a Fluid is a thing really distinct from the natural weight , according to the 22 Theorem : because though the 14 inches of Water QO , are not so heavy naturally as the 14 inches of Mercury that fell down , yet the Pressure of them upon the surface S , is as much . We see fifthly , that 14 inches of Water , that 's a body fourteen times lighter than Mercury , may have as much weight with them , as 14 ounce of Mercury . We see sixthly , that a Cylinder of Mercury cannot be suspended in Air , or in Water unless it be guarded with a Tub , to preserve it from the downward Pressure of that Air or Water : for by opening an hole in Q , the Mercury subsides . We see seventhly , that 't is impossible for two Fluids to suspend one another mutually , unless there be a sort of equipondium between them ; because no sooner you destroy the equipondium , between the 42 inches of Mercury QS , and the part of the surface S , by the ingress of the Water QO , but assoon there ariseth a new one . We see eighthly ( as we noted before ) the nearer a Body comes to be equally pressed with a Fluid , the less is the Pressure of that Fluid sensible : because less weight is required in the Ballance , to counterpoise the Pressure , and weight of the Water RQ , after the ingress of the Water QOP , than after the ingress of the Water QO . We see ninthly , that when a Body is equally , and uniformly pressed with a Fluid , the Pressure is insensible ; because , after the Water hath thrust down all the Mercury from Q to S , there 's no more weight at all of the Water RQ found in the Ballance . We see tenthly , that not only in Water , the Pressure of Water may be found , but out of it , namely in the Air ; as is clear from the Ballance , that supports the Pressure of the Water RQ . We see eleventhly , a ground to distinguish between the natural Ballance , and the artificial Ballance . The artificial Ballance , is the Ballance KL : the natural , is the Pipe QS . We see twelfthly , that they keep a correspondence between themselves , or some Analogy : for by what proportion the Water thrusts down the Mercury , by that same proportion the pondus L , of the Ballance is lessened : and by what proportion the Mercury rises in the Pipe , by that same , is the weight L augmented in the Scale . We may subjoyn lastly , that the easiest way of explicating the Phenomena of Nature , is not always the best , and truest . For some may think , it were far easier to say , that the Ballance supports the Mercury AB , or DE , and not any part of the Water BC , or EF. But such a way would be false , and absurd , and contrary to all the former Doctrine . EXPERIMENT XII . Figure 16. THis Schematism represents a Water 100 foot deep , whose first and visible surface is IHK . And LM is the ground of it . CD is a piece of brass 30 inches high , and 12 inches in diameter , suspended upon the imaginary surface of Water ANB , which is distant from the top IHK , 25 foot . This Brass cannot go farder down , when demitted from H ; because it 's keeped up , by the Force and Pressure of the surface of Water ANB , which I prove thus . The part B sustains de facto , a Pillar of Water KB 1400 pound weight : therefore the part N is able to sustain as much . I suppose here , the said piece of Brass to weigh 1400 pound . The Water KB is 1400 pound , because its a Pillar 25 foot high , and 12 inches thick , for one cubical foot weighs 56 pound Trois . The connexion of the argument is evident , because it is as easie for a surface of Water , to sustain a solid Body , as to sustain a Fluid Body : therefore , if the part B , support the Fluid Pillar KB , the part N must be able to support likewise the solid Pillar CD , which is of the same weight . If it be objected , that the part N , sustains besides the Brass CD , a Pillar of Water EF 22 foot high , and a half , which two will weigh 2260 pound . I answer , upon supposition , that neither Water nor Air succeeded , the space EF being void of both , the Brass would be suspended with the force and power of the Water N. And though this cannot be made practicable , yet the Theory of it may conduce much for explicating the secrets and mysteries of the Hydrostaticks . But why ought the Brass to be suspended at 25 foot from the top ? I answer , because the potentia of the surface ANB , is equal to the pondus of the Brass . To evidence this , consider that Brass is a Body naturally heavier then Water , I shall suppose ten times , that 's to say , one inch of Brass will counterpoise ten inches of Water . If this inequality be , then must this Pillar of Brass go so much farder down , than the first surface IHK , as the one is heavier in specie , or naturally , than the other : therefore it must sink 25 foot exactly ; seing a piece of Brass 30 inches high , requires 400 inches of Water , or 25 foot to counterpoise it : for if one inch of Brass require ten inches of Water , then surely 30 inches must require 300. Yet it is no matter , what the thickness be , provided it be no higher than 30 inches . To advance some farder , let us make a second supposition , namely , while the Brass is thus suspended upon the surface ANB , suppose the Air to come down , and fill up the imaginary space EF , then must the Brass be thrust down as far as the surface OP , that 's 34 foot below the surface AND , and 59 from the top . The reason of it is this , because the weight of the Air superadded , is equivalent to the Pressure of a Pillar of Mercury 29 inches high , and 12 inches thick : therefore the Brass being burdened with this , it must go so farder down , till it meet with a surface , whose potentia is equal in weight , to the pondus of both , which is precisely 59 foot from the top : for if one inch of Mercury require 14 of Water , then 29 inches must require 405 inches , or 34 foot . In a word , it must go as far down , as that surface , that sustains a Pillar of Water , that would counterpoise in a Ballance , the Brass CD , and a Pillar of Mercury 29 inches high , and 12 inches thick , both which weighs 3290 pound . From what is said , we see first , that of two heavy bodies differing in weight , the lighter may go further down than the heavier . This is clear , because a slender Cylinder of Gold , in form of an Arrow , half an inch thick , and 28 inches long , weighing 28 pound ( 't is no matter , though the just weight of it be not determined ) will go down 35 foot in Water , before it meet with a surface , whose potentia is equal in weight to its own pondus ; for if Gold be 15 times heavier naturally than Water , then the said Cylinder must go down before it rest , 420 inches , or 35 foot . But a piece of Gold 12 inches long , and six inches thick , that perhaps will weigh 208 pound , will sink no further than 15 foot . And the reason is , because , if one inch of Gold require 15 of VVater to counterpoise it , then 12 must only require 180 , or 15 foot . Note , that both the bodies must go down Perpendicularly , and not as it were Horizontally , with their sides downmost : for if they go down after this manner , they cannot sink so far . The reason of this is also evident , because a heavy body goes so far down , and no further , till it hath thrust as much Water out of its place , as will counterpoise it self in a Ballance . That 's to say , if an heavy body weigh 100 pound , it must go no further down , than after it hath thrust out 100 pound of Water . But so it is , that a piece of Gold , in form of an Arrow , going down side-wise , or with the two ends parallel to the Horizon , will thrust as much Water out of its place , as will be the weight of it self , before it can go down 15 or 16 inches from the top : because for every inch it goes down side-wise , it expells 28 inches of Water . In going down two inches , it expells 56. In going down three inches , it expells 84 , and so forward , till it go down 15 inches , where it expells 420 inches : but 420 inches amounts to 35 foot . Now , take a Cylinder of Water 35 foot high , and just the thickness of the Cylinder of Gold , which I supposed to be of half an inch , and put them in a ballance , and you will find the one just the weight of the other . Neither can the piece of Gold go so far down as before , if it go down side-wise ; because for every six inches it is drowned , it expells a bulk of Water 12 inches long , and six inches thick ; therefore it must be suspended , before it go beyond 90 inches , or seven foot and an half : now , if six inches give one foot , 90 inches will give 15 foot : but 15 of Water in hight , and six inches thick , is the just weight of it in a ballance , viz. 208 pound . We see secondly , the broader and larger the surface of a Fluid be , 't is the more able and strong to support an heavy burden : therefore the part of a surface of Water six inches square every way , will carry a far greater weight , than a part four inches square . Though a surface of Water 34 or 35 foot deep , be not able to sustain a Cylinder of Gold. if it exceed 28 or 29 inches in hight , yet take a Cylinder of Gold , 10 foot high , and reduce it , by making it thicker , to the hight of 20 inches , a surface of Water little more than 24 foot deep will sustain it . Or reduce a Cylinder 10 foot high , which requires a surface more than 100 foot deep , to a Cylinder six inches high , a surface little more than seven foot deep will support it . We see thirdly , the reason why bodies that are broad and large , move slowlier through Air and VVater , than bodies that are more thin , and slender , though both be of the same weight in a ballance . For example , 20 pound of Lead , long and slender like an Arrow , will go sooner to the ground of a deep VVater , than a piece of Lead of the same weight , in form of a Platter or Bason . The reason is , because as the body is broader , so it takes a broader part of a surface , which broader part is stronger and abler , than a narrower part , and so makes the greater resistance . The same is the reason , why a Bullet six inches in Diameter , moves slowlier thorow the Air , shot from a Cannon , than a Bullet one inch in Diameter . For the same reason , Ships of seven or eight hundred Tun , move far slowlier thorow the Air , and Water , than Vessels of less burden . Item , large and big Fowls , as Eagles , move slowlier , than small Birds , as Swallows . Yea , of Fowls of the same quantity , one may move quicklier than another , as is evident in long-wing'd Hawks , as Falcons , that by the sharpness of their Wings , move far more space in half an hour , than Kites , or Gose-Hawks , whose wings are rounder . We see fourthly , that there 's no body how heavy soever , but it may be supported by the surface of a Fluid , either in Air or in VVater . I grant , the strongest surface of Air , that can be had , is not able to support more weight , than a Cylinder of Gold 28 inches high : yet though it were as large , and broad , as a Mill-stone , if it do not exceed the said hight , the Air is able to sustain it . For the same cause , if it were possible to free a Mill-stone of the Air , that rests upon it , the Air below would lift it from the ground , and carry it up many fathoms , even till it came to a surface , equal in power to the weight of the Stone . Or , if a large Mill-stone were demitted from the top of the Atmosphere , towards the Earth , it could hardly touch the ground , being detained by the way , by a surface counterpoising it . Or if it did touch , through the swiftness of the motion , it would surely , as it were , rebound , and be carried up again . It is alwayes to be remembred , that in such trials , the Air is supposed not to follow , or to be united , after the Stone passeth thorow . Now if the Air be able to do this , far more the VVater , that 's a body a thousand times heavier . We see fifthly the reason , why heavy bodies move so easily thorow Air , and Water , namely because the parts that were divided , by the body that is moved , are presently reunited , and closed again , by which means it is driven forward , the Pressure upon the back , being as much as the Pressure before . If this were not , no body whatsoever would be able to move it self one foot forward . For example , if , when a man hath advanced one step forward , the Air did not close again upon his back , the force of the Air upon his belly and breast , would not only stop him , but violently thrust him backward . We see sixthly , the reason , why the same body descends with more difficulty thorow Water , than Air , because a surface of Water is far stronger , than a surface of Air. We see seventhly , that a heavy body is never suspended by a surface of Water , or Air , in going down , till once it hath displaced , as much Water or Air , as will counterpoise it self in a ballance . This is clear from the Brass CD , that goes alwayes down , till it expell its own weight of Water . For this cause , if a Mill-stone were demitted , or sent down from the top of the Air , and never rested , till it came within 40 fathom of the Earth , then so much Air , as is expelled by the descent , is the just weight of the stone . We see eighthly , the heavier a body be naturally , than Water , it goes the further down , and the lighter it is , it sinks the less . For if CD were of Gold , it would go further down , than being of Brass or Iron : and if CD were a stone , that 's lighter in specie than Brass , it would not go so far down . This lets us know the reason , why thicker , blacker , and heavier clouds comes nearer to the Earth , than thinner , whiter , and lighter . VVe see ninthly , that the Pressure of the Air is determinable , even in its heighest degree , and seemes to be the same in all places of the world ; but the Pressure of the Water is not so . The reason of the first part is , because the Element of Air seems to be of the same hight in all places , and therefore we may know its outmost Pressure , which is just equivalent to the weight of 28 or 29 inches of Gold , or Mercury . But because the deepness of the Sea is variable , therefore the Pressure is variable likewise . Yet if the exact deepness , of the deepest place were known , it were as easie to determine the greatest Pressure of it , as to determine the greatest Pressure of the Air. We see tenthly , that a very small weight added or subtracted in height , will change and alter the counterpoise of a Fluid . Because if you lay but one ounce upon the top of the brass at F , it presently subsides accordingly : or take one ounce from it , and it rises . But though never so much weight be added to it , or subtracted from it in thickness , no alteration follows . Therefore , though this piece of Brass CD , that 's now but 12 inches in thickness , were made 24 , by which means the weight would be tripled and more , yet the same surface ANB would sustain it : yet , add to it in altitude , but one inch , and presently it sinks down proportionably . This evidently discovers the reason , why it s as easie for the Air , to support a Cylinder of Mercury 3 inches thick , as to support a Cylinder half an inch thick : and why it cannot support more in height than 29 inches , and why it cannot support less . Now the reason , why a thicker Pillar , is as easily suspended , as a thinner , is this , because if a Pillar of Mercury be thicker , and consequently heavier , than i● takes a broader , and consequently a stronger surface of Air to ●est upon : if it be but slender , and so but light , then it takes a lesser part of a surface to bear it up , and consequently a weake● ; by which means the Pondus of the one , is alwayes proportionable to the Potentia of the other . Is it not as easie for a Pillar of stone , 6 foot in Diameter , to support another six foot in Diameter ; as it is for a Pillar one foot in Diameter , to support a Pillar one foot in Diameter ? But as a Pillar one foot in Diameter , cannot support a Pillar 6 foot in Diameter , neither can a surface of Air , one inch in Diameter , support a Pillar of Mercury 6 inches in Diameter . But why should a larger part of a surface be stronger than a narrower part ? I answer , the one is stronger than the other , for that same reason , why a thicker Cylinder is heavier than a thinner : for what I call strength in a surface , it s nothing else but weight , and what I call weight in a Cylinder , it s nothing else but strength . The same thing hath two names , because the pillar of a Fluid presseth down , and the surface supports : therefore , in the one it s called pondus , in the other potentia . As when two scales are in equilibrio , either this , or that may be called the pondus , or either this , or that , may be called the potentia . Now I say , if a part of a surface four inches broad , have as much weight or force in it , as a Pillar of Mercury four inches thick ; then surely , a part of a surface eight inches broad , must have as much weight and force in it , as a Pillar of Mercury eight inches thick . But why ought a surface to succumb , when the Pillar grows in hight , and not to fail when it grows only in breadth ? Ans. VVhen it grows in breadth , the pondus never exceeds the potentia ; but when it becomes higher , then it becomes heavier . That 's to say , when a Pillar grows broader , there 's not one part of the surface that sustains it , more burdened than another ; seing the part eight inches broad , is no more prest with a Pillar eight inches thick ; than the part four inches broad , is prest with a Pillar four inches thick : as eight ounce of Lead in this Scale , is no more counterpoised with eight ounce in the other Scale , than four ounce in this Scale , is counterpoised with four in the other . But when a Cylinder grows in hight , the pondus exceeds the potentia ; one part of a surface being more burdened than another . We see eleventhly , that in a large surface of a Fluid , wherein are many parts ; each part is able to sustain its own proper burden . So a part eight inches in Diameter supports a Pillar eight inches thick ; and a part four inches , supports a Cylinder four inches thick ; but cannot support a Pillar six inches thick . But this seems rather to slow from the disproportion of Magnitudes , seing a circular plain 4 inches in diameter , cannot receive a Base of a Pillar 6 inches in diameter . But this is certain from the very nature of Fluids , that in a deep VVater , wherein may be distinguished 100 , or 1000 different surfaces , each one is able to support his own burden , and no more . EXPERIMENT XIII . Figure 17 , 18 , 19. FOr making this Experiment , take two plain Bodies of Brass , or Marble well polished . Make them of any quantity ; but for this present use , let each of them be four inches broad square wise . Upon the back part , let each one have an handle about six inches long , of the same metal , formed with the plain it self , in the founding ( if they be of Brass ) as is represented in this Schematism . When they are thus prepared , anoint their inner-sides with Oyl or Water , and having thrust the one face alongst upon the other , with all the strength you have , till all the four edges agree , two whereof are represented by AB , and CD , you will find them cleave so closs together , as if they were but one Body . The effect is this , that ordinary strength will not pull them asunder ; and that under a surface of Water , a stronger pull is required than in the Air. That we may deduce some Hydrostatical conclusions from this Experiment , let us suppose these two plain Bodies to be united in the middle of the VVater IKPQ , that 's 34 foot deep , and suspended by a beam or long tree TV existing in the Air , near the top of the VVater , by a chord SE passing between the middle of the beam , and the end of the handle at E. Suppose next a great weight of Lead R , 350 pound , to be appended to the end of the handle at H , of the under plain Body CDNO . This done , I affirm , that the beam TV , neither sustains the under plain Body CDNOGH , nor the 350 pound weight of Lead R , that hangs down from the handle GH . If it be objected , that the beam supports the upper plain Body ABLMFE ; therefore it must bear the weight also of the under plain CDNOGH , with the weight R ; seing they are both united together , and cleave so closs , as if they were but one Body . I answer , it supports the one unquestionably , but not the other . To explicate this Hydrostatical Mystery , I must aver three things ; first , that the inferior plain is supported by the upward Pressure of the lower VVater PQNO . Secondly , that the burden which the beam sustains , is not the weight of the under plain , but the weight of the 34 foot of Water IKLM . Thirdly , that this weight is exactly the weight of the inferior plain , and Lead R. But is it not more easie to say , that the beam supports both the plains ? I answer , if I say so , I can neither affirm truth , nor speak consequentially , But may it not be said , that the inferior plain is supported both by the beam , and the lower water PQNO ? I answer , this is impossible ; because one and the same weight , cannot be supported totally , by two distinct supporters . For making these assertions evident , I must suppose the superior Water IKLM to be 34 foot deep , and to weigh , if it were put into a ballance , 400 pound : and which is unquestionable , that the said Water rests upon the back of the superior plain LM . I suppose secondly , that the lower Water PQNO weighs as much , and thrusts up the inferior plain with as great weight , as the superior plain is prest down with , by the superior Water . This is evident from former Experiments . And lastly , I suppose each plain to weigh two pound , and the weight of Lead R 350. It is to be observed here , that no mistake may arise in the calculation afterwards , that though it be said , this 34 foot of Water weighs 400 pound , yet in it self it weighs but 200 : but considering the Pressure of the Air upon IK , which is as much , it may be truly said to weigh 400. These things being premitted , I say the weight that the beam TV sustains , is not the weight of the inferior plain , and the Lead R , but 352 pound of the superior VVater IKLM , and consequently , that the inferior plain is supported by the lower VVater PQNO . The reason is , because the lower VVater presseth up with the weight of 48 pound . It is in it self 400 pound : but being burdened with 352 , it cannot thrust up with more weight than 48. Now , it pressing up with 48 , must ease the beam of 48 , and counterpoise so much of the superior VVater , and consequently the beam must support only 352 pound of it . But put the case ( you say ) the weight R , were 130 pound , 160 pound , or 180 pound , would the beam be less or more burdened with the superior Water ? I answer , if R be 130 pound , then the beam supports only 132 pound of the superior Water ; for if the inferior be only burdened with 130 , the weight of R , and with two the weight of the inferior plain , then must it press up with 368 , and by this means , must ease the beam of so much , it sustaining 132 pound only . According to this compting , when the Lead R weighs 160 pound , the beam supports only 238 pound of the superior Water . If it weigh 180 pound , it sustains 218. And if the weight R were taken away , the beam supports no more of the superior VVater than two pound . To proceed a little further ; imagine the two Plains to be drawn up 17 foot nearer the first surface IK , namely as high as ZW . This done , the union breaks up , and they presently fall asunder . The reason is , because the surface ZW is not able to support 352 pound , but only 300 , which I prove thus . If 68 foot sustain 400 , then 51 foot must sustain 300. I say 68 , and not 34 , because as was noted , the Pressure of the Air upon the surface IK , is equivalent to other 34 foot : and therefore though the deepness of this VVater , between IK and LM be but 34 foot really , yet it is 68 foot virtually , and in effect . Imagine secondly the surface IK to subside 17 foot , namely to ZW . In this case the union is broken also , and the lower Plain falls from the upper . The reason of this , is the same with the former ; because by what proportion you diminish the hight of the superior VVater , by that same proportion you diminish the upward Pressure of the lower VVater . Therefore , if you subtract from the superior VVater 17 foot , that weighs 100 pound , you subtract likewise 100 pound from the inferior VVater , and consequently , you make it press up only with 300 , but 300 is not able to counterpoise 352. Let us suppose thirdly , the superior Plain , and the superior Water to be annihilated ; then I say , the Pressure and force of the under Water would thrust up the inferior Plain and the weight R about eight foot higher then XY and there suspend them . The reason is , because the surface XY , being able to sustain 400 , and being burdened only with 352 , must have the weight of 48. Now the upper Plain being taken away , and the upper Water also , and the empty space of both remaining , the said weight of 48 pound , must carry the under Plain as high as is said . Let us suppose fourthly , the Pressure of the Element of Air , that rests upon IK , to be taken away , then must the two Plain bodies be disunited , the inferior falling from the superior . The reason is , because in this case , the superior Water would have but the weight of 200 pound , and consequently the inferior , would press up only with as much : but 200 is not able to counterpoise 352. From what is said we see first , that in all Fluids there is an upward Pressure , as well as a downward ; and that the one is alwayes of equal force to the other : because the inferior Plain is pressed up with as great force , as the superior Plain is pressed down with . We see secondly , that in Fluids , there is a Pondus and a Potentia . The Potentia here is the inferior Water , and the Pondus is the superior . Or , the 350 pound of Lead R , may be called the Pondus , which counterpoiseth the Potentia of the surface of VVater XY . We see thirdly , that though the Pressure of a Fluid , be not the same thing with the natural weight , yet it is equivalent to it : because the 352 pound of Lead R , is sustained by the Pressure of the inferior VVater , which could not be , unless they were virtually the same . We see fourthly , that there may be as much Pressure in one foot of Water , as there is weight in 100 , or in 1000 foot , or in 1000 fathom , For put the case , these two plain bodies were suspended , 100 fathom below the surface of the sea , and within a foot or two of the ground , as much weight would be required to pull them asunder , as is the weight of a Pillar of Water 100 fathom high , and 4 inches thick every way , which will be more then 3000 pound weight , besides the weight of the Air above , that will weigh 200 pound . This could not be , unless there were as much Pressure in the lowest foot of this Water , that 's 100 fathom deep , as there is weight in the whole Pillar above . We see fifthly , the more the potentia of a surface is burdened , the more sensible is the pondus : because the heavier you make the Lead R , that burdens the inferior Water , the more weight of the superior Water rests upon the Beam. We see sixthly , the more unequally a body is pressed , the more the Pressure is sensible . For understanding this , consider that the under-face of the superior Plain , is more and less pressed , according to the more and less weight the Lead R is of : for put the case , the inferior Plain were taken away , the face of the superior Plain , would be equally prest with the back of it . But when the inferior Plain is united to it , the Pressure of the Water is kept off ; by which means the back is prest more than the face . Now , as the inferior Plain becomes heavier and heavier , by making the weight R more and more weighty , the less and less is the face of the superior Plain prest up . Hence it is , that as this inequality of Pressure becomes greater and greater ; so the weight of the superior Water , affects the Beam more and more . Or , if the superior Plain were a sensible body , as Animals are , it would find the back of it more and more burdened , according as the weight R , becomes heavier and heavier . We see seventhly , that Water weighs in Water : because all the weight the Beam supports , is the burden of the superior VVater , and not the burden of the inferior Plain , or of the weight R. It supports the weight also of the superior Plain , but this is not considerable . This is only to be understood , when the Pressure is unequal ; for if the upper Plain were as much prest up , as it 's prest down , the weight of the superior VVater would not be found by the Beam. We see eighthly , that the higher a surface be , it is the weaker ; and the lower it be , it is the stronger : because when the two plain bodies are pulled up , 17 foot , they fall asunder . We see ninthly , the vanity of the common opinion , that maintains two plain bodies to cleave closs together for fear of vacuity ; and that neither Humane nor Angelick strength is able to break this union , without the rupture and fracture of them both . It may be enquired , upon supposition , that the inferior plain had four holes cut thorow the middle , square-wise , as ABCD in the 18 Figure , what Phenomena would follow ? Before I answer , consider that this Figure represents the inner face of the Brass-plate CDNO , of the 17 Figure , which as was supposed , is four inches from side to side , and consequently contains 16 square inches . Now , imagine the under plain CDNO , while it is united to the uppermost , to have four square inches cutted out of it , as ABCD. These things being rightly conceived , and understood , I say , when the said holes are cutted thorow the beam TV , that now sustains 350 pound , shall by this means , only sustain 250 pound . To make this evident , consider that the under plain ( as was said ) contains 16 square inches . Next , that the top of the inferior Water upon which the plain rests , contains as many , and that every inch of the Water weighs 25 pound , seing the whole , as was supposed before , weighs 400 pound . Now , I say , the beam must support only 250 pound of the Water IKLM ; because , these holes being made , the top of the inferior Water comes through them , and presseth up the face of the superior plain with 100 pound , and so easeth the beam of so much . I affirm next , that though the inferior Water NOPQ be in it self 400 pound , and consequently able to support the inferior plain , with the weight R , albeit they weighed so much , yet the said holes being cut out , it is not able to support more burden than 300. The reason is , because of 16 parts that did actually bear up before , there are only 12 now that sustains . And every one of these twelve , being but able to support 25 pound , it necessarily follows , that the greatest weight they are able to sustain , is 300 pound . I affirm thirdly , that if a fifth hole were cut through , the under plain would fall from the upper ; because in this case , the inferior Water is not able to support 350 pound as before , seing of 16 parts , there are five wanting , and eleven remaining , cannot support more weight than 275 pound . Moe questions of this kind might be proposed ; as first , what would come to pass , if the the upper plain had as many holes cut through it , answering to the four of the nether ▪ Secondly , what would folow , if the nether plain were intire , and four bored through the upper ? But I shall supersede , and leave these to be gathered by the judicious Reader . From this Experiment we see first , that the broader and larger a surface of a Fluid be , it 's the more able to sustain a burden , and the narrower it be , 't is the less able . Secondly , that each part of a surface , is able to sustain so much weight , and no more , and no less . Before I put a close to this Experiment , it will be needful to answer an objection , proposed by Doctor More in his Antidote against Atheism , against the Pressure of the Air , which in effect militats , by parity of reason , against the Pressure of the VVater likewise . He argues thus . If the Air were indowed with so much Pressure , as is commonly affirmed , then it ought to compress , squeez , or strain together , any soft body that it environs , as , v. g. Butter . Put the case then , there were a piece of Butter , four inches broad every way , and one inch thick , containing 16 square inches , upon every side ; as may be represented by the Figure 19. In this case , there is a far greater Pressure , upon the two faces , than upon the four edges ; and therefore , it ought to be comprest , and strained together , to the thinness of a sheet of Paper . For answer , let us suppose the piece of Butter , to be 30 or 40 foot below the surface of a Water , where it ought to suffer far more Pressure , than above in the Air. Next , that it lies Horizontal , with one face upward , and the other downward . Thirdly , that the upper face supports a Pillar of Water 200 pound weight , and consequently , that the under face is prest up with as much . And lastly , that every edge is burdened with 50. It may be represented , with the help of the fancy , in the 19 Figure , where AB is a piece of Butter four inches square , and one inch thick . Only take notice , that nothing here is represented to the sight , save one of the four edges , namely AB ; the other three , and the two faces being left to the fancy : Yet , the upper face may be represented by FHKM , and the under by NOPQ . These things being rightly understood , it is wondered , why the two great and heavy Pillars of Water , the one EGILFHKM , that presseth downward , and the other NOPQRSTV , that presseth upward , do not strain together the sides of the Butter ; seing the Pressure of the Water BC , and the Pressure of the Water DA , are far inferior to them for strength , even by as much difference , as four exceeds one . Though this objection seem somewhat , yet it is really nothing , which I make evident after this manner . First , I grant that the upper face FHKM is burdened , with 200 pound , and the nether face NOPQ with as much . Secondly , that the edge B , is only burdened , with 50 pound , as is the edge A. The other two edges , sustains each one , as much . Secondly , though this be , yet I affirm the two sides to be no more burdened , than the edges : that 's to say , the Pressure upon the sides , is equal to the Pressure upon the edges , which I prove thus . The Pressure upon the part M , is equal to the Pressure upon the part K , but the Pressure upon the edge B , is equal to the Pressure upon the part M : therefore the Pressure upon B , is equal to the Pressure upon K. The major Proposition is evident , because the Pillar of Water LM , is of the same weight , with the Pillar of Water IK . The Minor is also evident , because , the Pillar BC , is of the same weight , with the Pillar LM . Now , if the Pressure upon the edge B , be equal to the Pressure upon M and K , it must be likewise equal to the Pressure upon H and F. If this be , then the edge of the Butter B , must be no more prest , than the side FHKM : therefore the Water BC , can no more yeeld to the VVater EFGHIKLM , and suffer the Butter to be squeezed out at B , than the VVater LM , can yeeld to the VVater EFGHIK , and suffer the Butter to be squeezed out at M. If any man shall insist and say , that the upper face bears the weight of four Pillars , which weighs 400 pound ; but the edge B is only burdened with 50 : therefore 50 ought to yeeld to 400. I answer , according to the 29 Theorem , namely , that a thicker Pillar of a Fluid is not able to press , or move a slenderer , unless there be an unequal Pressure , therefore the thick Pillar , that presseth the face , cannot move the slender Pillar , that presseth the edge : but there is here no unequal Pressure , seing the Water XYZV , is of the same hight with the four Pillars that rests upon the face of the Butter . I grant , if the said Water were not so high , as the other is , by the one half ; then surely the Butter would be squeezed out at B ; because the shorter a Pillar be , the less Pressure is in the surface under it ; therefore , there must be less Pressure , according to that supposition in the Water BC , then now is . Or put the case , the Pillar IK were shorter then GH , or LM , the same effect would follow , namely , a squeezing out of the Butter from K. Or , let us suppose the Pillar IK , to be higher than GH or LM . In such a case , the weight of the said Pillar would press through the Butter . From what is said , we shall only inferr this conclusion , that equality of hight between Pillars of a Fluid makes equal Pressure , and inequality of hight makes unequal Pressure . Therefore 't is no matter , whether they be gross or small , thick or slender , provided they be all of the same Altitude . Fig. 12 Pag. 81 Fig. 15 Pag. 100 Fig. 16 Pag. 109 Fig. 17 Pag. 119 EXPERIMENT XIV . Figure 20. THis Schematism represents a Vessel full of Water 8 foot deep . EF is a Glass-Pipe , open at both ends , about 9 foot high , and one inch in Diameter . ABCD is a Vessel of Glass , or of any other metal , thorow whose orifice above , the said Pipe comes down . BHI is a Pipe going out from the said Vessel , crooked with a right angle at H , that the orifice I may look upwards . That some Hydrostatical conclusions may be inferred from this Experiment , fill the lower Vessel ABCD with Quick-silver almost ; then pour in as much Water above it , as will fill the space ABH , leaving from H to I full of Air. Next , thrust down the orifice of the Pipe E , below the said Water and Mercury , till it rest upon the bottom CD . Lastly , stop well with cement the passage of the lower Vessel , through which the Pipe came down , that neither Air nor Water may go out , or come in . These things being done , let down this Engine to the bottom of the large Vessel , which , as was noted , is full of VVater from MN to KL , 8 foot , and you will find the Mercury to rise in the Pipe from AB to G , 6 inches , and more . The reason is , because there is a Pillar of VVater KI , that enters the orifice I , and presseth down the Air , from I to P , 3 inches , which before was 6. This Air being so burdened ; instantly presseth forward the VVater HBA : and this pressing the surface of the stagnant Mercury AB , causes the liquor run up the Pipe from AB to G , 6 inches : The reason , why it riseth 6 inches , is this : between the surface of the stagnant Mercury AB , and the top of the Water LOK , are 84 inches . Now Water being 14 times naturally lighter then Mercury , there must be 14 inches of Water , required for sustaining one inch of Mercury , and consequently 84 , for supporting 6. For a second trial , lift up the whole Engine to the top of the Water , and you will find the 6 inches of Mercury BG sink down , and become no higher within the Pipe , than the surface of the stagnant Mercury AB without . The reason is , because by coming up above the Water , the Pressure of the Water KI , is taken away from the orifice I , by which means the comprest Air HP , extending it self to I , liberats the Water ABH of the Pressure it had , and this freeth the Mercury of its Pressure , and so the 6 inches falls down . For a third trial , stop closely the orifice I , and let all down as before . In this case , you will find no ascent of Mercury from B to G : because the Water KI cannot have access to thrust down the Air from I to P , as formerly . For a fourth , open the said orifice I , while the Engine is below the Water , and you will find the Mercury rise from B to G : because the Pillar of Water KI , hath now access to press . For a fifth trial , stop the orifice I , and bring up all to the top , and you will find the six inches of Mercury BG suspended , as if the Engine were under the Water . The reason is , because the stopping of the orifice , keeps the inclosed Air PH , under the same degree of Pressure it obtained from the Water KI . For a sixth proof , open the same orifice I , while the Engine is above the Water , and you will find the six inches of Mercury fall down , because the imprisoned Air HP , obtains now its liberty ; and expanding it self from H to I , eases the Water BH of the burden it was under . For a seventh , pour in 14 inches of Water at the orifice F , till it rest upon the top of the Mercury at G , and you will find one inch fall down . Pour in as much , and two inches falls down . In a word , pour in as much Water , as will fill the Pipe to O , and you will find the whole six inches fall down . The reason is , because the Water KI , is not able to sustain , both the six inches of Mercury and the Water , that 's poured in ; any one of them being able and sufficient to counterpoise it , For an eighth trial , empty the Pipe of the said Water , and after the Mercury is ascended from AB to G , as formerly , suck out the whole Air between G and F , and you will find the Mercury to rise from G to R 29 inches . The reason of this is evident from the Pillar of Air SK , that rests upon the top of the Pillar of Water KI : for by sucking out the said Air , you take away the pondus or weight , that counterpoised the weight of the Pillar SK , therefore it finding its counterpoise removed , presently causeth the Water KI , to enter farder within the crooked Pipe , till it hath prest up the liquor to R. For a ninth trial , take the six inches of Mercury BG , and put them into the scale of a ballance ; then take as much Water , as will fill the Tub between AB and O , and put it into the other scale , and you will find a most exact counterballance between them . The reason is , because if the Water KH , or a Pillar of that hight , be able to raise and counterpoise the Mercury BG ; then must as much Water , as fills the Pipe betwen B and O , be the just weight of it . The reason of this consequence is , because these two Waters are of the same weight : therefore , if the one be the just weight of it , the other must be so too . If it be said , that the Water , that fills the Pipe between B and O , is far thicker , then the Water KH ; therefore they cannot be both of one weight . I answer , equality of altitude , in this Ballance of Nature , is equality of weight : therefore , seing the one Water , is as high as the other , they must be both of one weight . If it be said , that a Pillar of Water between K and H , cannot counterpoise the six inches of Mercury BG , both being put into a ballance : and the reason is , because the one is thicker than the other . I answer , this only proves that two Pillars differing in weight in the Libra or Artificial Ballance , may be of one weight in the Natural Ballance : because in the Artificial Ballance , bodies counterpoise one another , according to all their dimensions , but in the Natural Ballance , such as this Engine is , Fluids counterpoise one another , according to their altitude only . From the first trial , we conclude first , that Water even in its own place gravitats and weighs , because this Water by its Pressure , de facto thrusts up 6 inches of Mercury . We see in the next place , that the Pressure of a Fluid , is as easily communicated Horizontally , as Perpendicularly ; because the Pressure runs alongst from H to B. We see thirdly , that Fluids , may have as much Pressure begotten in them , even while they are environed about closely with solid bodies , whereby the superior Pressure , immediatly and directly by perpendicular lines is keeped off , as if they were immediatly under the Pressure : because the Mercury ABCD , is as much burdened with the Pressure , that comes from H , as if the upper part of the Vessel AB , were open to let in the superior Pressure , by perpendicular lines . The Air then under the roof of a house , is under as great a Bensil and Pressure , as the Air without , that 's directly under the Pressure of the Atmosphere . VVe see fourthly , that the Pressure of a Fluid , may be as easily communicated thorow the parts of Heterogeneous Fluids , as thorow the parts of Homogeneous ; because the Pressure of the VVater KI , is as easily communicated thorow the Air PH , thorow the Water HB , and thorow the stagnant Mercury BD to the orifice E , as if nothing interveened but VVater . VVe see fifthly , that Mercury can suffer a Pressure , as well as VVater or Air ; because the six inches cannot rise from B to G , unless the stagnant Mercury ABCD were compressed , even in all the parts of it . From the second trial , we see , that there cannot be a Pondus in a Fluid , unless there be a Potentia , to counterpoise it : for when you take away the Water RI , by lifting up the Engine to the top of the Water , the Mercury BG presently falls down . From the third trial , we conclude , that the Pressure of a Fluid , cannot be communicated thorow solid Bodies : for when the Engine is drowned below the Water , with the orifice I , stopped , no ascent of Mercury follows . We conclude from the fourth trial , that it is impossible for two Fluids to counterpoise one another , unless they be in Equilibrio ; because the Water KI cannot sustain the Mercury BG , unless it be of the same weight . From the fifth , we conclude , that a Fluid may be keeped under the same degree of compression , after the superior weight that begat it , is taken away : for after the Engine is brought above the Water , with the orifice I stopped , the Mercury BG is still suspended , even by vertue of the Pressure , that 's in the stagnant Mercury . This tells us , that a sphere of glass full of Air , may retain its Bensil , even though the whole Element of Air , that begat it , were destroyed . From the sixth we gather , that a Fluid cannot abide under Pressure , when the burden is taken away that begat it , or that keeped it under Pressure : for by opening the orifice I , the Air PH extends it self : and so are the VVater , and Mercury within the Vessel freed of their Pressure likewise . We gather from the seventh trial , that in the Ballance of Nature , one Scale cannot be more burdened then another ; or that two Fluids cannot counterpoise one another , unless they be in equilibrio : for when you pour in 14 inches of Water , upon the top of the Mercury at G , they thrust down one inch , that there may be a just equipondium , between them , and the opposite weight KI . We gather from the eighth trial , which was observed before ; first , that there cannot be a Potentia in a Fluid , unless there be a Pondus to counterpoise it : for when you suck out the Air GO , which was the Pondus , that counterpoised the Air SK , this presently in stead of it , raiseth 29 inches of Mercury from G to R. We see secondly , that one pillar of Air can counterpoise another , Fluids of diverse kinds interveening : because the Air SK , counterpoises the Air within the Pipe GO , the VVater KP first interveening ; the Air PH next interveening , and the stagnant , and suspended Mercury interveening also . We see thirdly from this eighth trial , that the Pressure of the Atmosphere , may be communicated thorow diverse kinds of Fluids , without the least diminution of its weight : because the weight of the Pillar of Air SK , is communicated , and sent down thorow the Water KI , thorow the Air PH , thorow the VVater HB , thorow the stagnant Mercury BD , and up thorow the suspended Mercury BG , till it suspend the 29 inches between G and R , which is the just counterballance of it . We see moreover , that Fluids counterpoise one another , according to altitude only , and not according to thickness and breadth ; by comparing the Water KI , that 's but half an inch thick , to the Mercury BG , that 's a whole inch thick . We see from the last trial , that when a Fluid is necessitated , to counterpoise a Fluid of another kind , in stead of a Fluid of its own kind , it sustains no more of it , than what is the just weight of the Fluid of its own kind , because the VVater KI , being under a necessity to counterpoise the Mercury BG , in stead of so much VVater as would fill the Tub , it sustains no more of it , than the just weight of so much VVater , as is said . We see secondly , that when two Fluids of divers kinds , do counterpoise one another , that which is heaviest in speciè , hath alwayes the shortest Cylinder . Next , that the difference between their altitudes , is most exactly according to the difference between their natural weights , therefore BG is 14 times lower than BO ; because Mercury is 14 times heavier than VVater . We see moreover , that though two Cylinders of a Fluid , can counterpoise one another in the Natural Ballance , such as this Engine is , yet they will not do it in the Artificial Ballance : because though BG counterpoise KI in this Ballance , yet in a pair of Scales , the Mercury will be as heavy again as the VVater . We see lastly , that notwithstanding of this , yet such a thing may be ; for if the orifice I , were made as wide as the orifice F , that the Cylinder KI might be equal to the Mercury BG in thickness , then surely the one would counterpoise the other in the Libra or Artificial Ballance . EXPERIMENT XV. Figure 21. THis Schematism represents a Water 72 foot deep , as CDAB , together with a crooked Pipe of glass INH , the one half whereof is IP , 56 inches high , and one inch wide , the other half is PNRH , of a far narrower diameter , with an orifice H. There is also an orifice at L , with a neck , about which is knit a small chord ML , for letting down this Engine to the bottom of the VVater AB . For trials cause , fill the wide glass with Mercury from P to K , and you will find it rise in the narrow Pipe , as high as the orifice H. This being done , close hermetically , or with good cement the orifice L ; then by help of this chord , let all go down from the surface CD , till it be exactly 17 foot from the top , and you will find the Mercury thrust down in the narrow Pipe , from H to R , 14 inches and an half . Let it down next , as much , and the Mercury will be yet further thrust down , namely from R to N , the part HRN being full of Water . For understanding the reason of this , consider that between N and E , are 34 foot : for so high is the slender Pillar of Water , that comes from the top , and entring the orifice H , comes down thorow the Pipe to N. Consider next , that between the said Pillar of Water , and the Mercury NPK , there is a counterpoise : but this counterpoise cannot be , unless the Pillar of Water be 34 foot high , seing between N and K are 29 inches of Mercury ; for each inch thereof requires 14 of Water . Upon this account it is , that when the glass is 17 foot drowned , 14 inches and an half are thrust down from H to R. If it be objected , that the Pressure and Bensil of the inclosed Air IK ; is equivalent to the weight of other 29 inches ; and therefore the Pillar of Water EHRN , must be 68 foot high , before a counterpoise can happen . I answer , 't is true that 's said , but you do not consider , that there is a Pillar of Air FE , resting upon the top of the Pillar of Water , that makes a compensation exactly . To speak then truely and really , the 29 inches of Mercury NPK , have the weight of 58 inches ; and the 34 foot of Water EHRN , have the weight of 68 foot . For a third trial , let down the glass 6 foot further , and you will find the Water pierce up thorow the thick Cylinder of Mercury PK , and rest upon the top K. The only difficulty is to determine , how much will spring up before the motion of it cease ? 'T is evident , that the Water will ascend , because coming to the Base of a thick and gross Cylinder , that it cannot intirely lift , it must pierce thorow it , seing the force of such a Pillar of Water , is now much stronger , than the Mercury : for in effect , the glass being drowned 6 foot further , the Pillar that comes down thorow the slender Pipe , hath the just weight of 34 inches of Mercury : but 29 cannot resist 34 : therefore the Water not being able to lift it , by reason of the disproportion that 's between the thickness of the one , and the slenderness of the other , it must pierce up thorow it . For clearing this difficulty , consider , that this glass cannot go down from one imaginary surface to another , v. g. from 34 foot , where it was , till it come to 40 , where it now stands , but there must be an alteration in the equipondium , seing by going down , the Pillar of Water EHRN grows h●gher , and consequently heavier ; and therefore , some VVater must pierce up thorow the Mercury , for making a counterpoise ; for 't is impossible for two Fluids to counterpoise one another , unless they be in equilibrio . Consider secondly , that after the Water is come to the top of the Mercury at K , it will find difficulty to find a room for it self , seing the space between S and I is full of Air. Notwithstanding of this , it must ascend . I say then , after the glass is gone down from 34 , to 40 foot , there will be about four inches of VVater above K , which have reduced the 29 inches of Air KI , to ●5 , SI . If it be asked , between what two things is the equipondium now ? I answer , the first was at R , between EHR , and RNPK . The second was at R , between NRHE , and NPK . The third is now at S , between the 25 inches of inclosed Air IS , as one Antagonist , and the four inches of Water SK , with the 29 inches of Mercury KP , and the Water PNRHE , as the other . To make a fourth equipondium , sink the Glass other six foot , till it be 46 foot from the top CD , then must some more VVater spring up thorow the Mercury ; this of necessity must be , seing the Cylinder of VVater NRHE , is six foot higher , and so far heavier , than it was : if this be , then must the 25 inches of Air IS , be reduced to less quantity ; seing 'tis impossible , for one Fluid to become heavier , unless its opposite and antagonist become heavier too , for an equipondiums sake . Note , that the Air IS , will not lose other four inches , with this six foot of VVater , as it did with the former . The reason is , because , if for every six foot the Glass goeth down , the Air were comprest four inches , it were easie at last to reduce it to nothing : for if six reduce it to four , and 12 to eight , 38 ought to reduce it to no inches , which is impossible . Therefore I judge it must suffer compression , by a certain proportion , as we see upon a Scale , the divisions of Artificial or Natural Sines grow less and less , there being more space between 1 and 2 , than between 2 and 3 ; more between 2 and 3 , than between 3 and 4 , and so upward till you come to 90. Therefore the second six foot , must reduce the 25 inches , not to 21 , but to 23 circiter , and so forth . By the which means , though the Glass should go down in infinitum , yet the Air shall never be reduced to nothing , and there shall still some small quantity of VVater come up . Or in such a case , the Air may be so comprest , that it can be no more , all the disseminate vacuities being expelled . But suppose this to be at 1000 fathom , then at 1500 , where the Pressure is stronger , there can be no equipondium , which is absurd , for where the pondus becomes stronger , the potentia ought to grow stronger likewise . I answer , the motion of condensation ceaseth indeed ; but there still remains a potentia , or rather in such a case , a perfect resistentia , whereby the Air is able to resist the greatest weight imaginable , before it can be reduced to nothing , or suffer a penetration of parts , that 's to say , two parts to be in one space . From the explication of these Phenomena we conclude first , that in Water there is a considerable Pressure , seing in letting down the Glass 17 foot , the Mercury is prest down from H to R , and from R to N , in going down other 17 foot . Secondly , that 29 inches of Mercury are as heavy as 34 foot of VVater : because the Mercury KPN makes a just equipondium with the VVater EHRN . Thirdly , that Fluids not only of the same kind , but of different kinds , do counterpoise one another according to altitude , and not according to thickness ; because though the Mercury KPN be far thicker , than the VVater EH , yet they counterballance one another , because a proportion is kept according to their altitudes . Fourthly , that a Fluid naturally lighter , may move a Fluid naturally heavier , and thrust it out of its own place , because the Water coming in at H , thrusts down the Mercury to R , and from R to N , and so forth . Fifthly , that of two Fluids unequal in strength , debating together , the weaker of necessity must yeeld to the stronger , though the weaker be far heavier naturally than the stronger , as is evident in the Mercury , that yeelds to the Water . Sixthly , that it is impossible for two Fluids , so long as they are unequal in strength , to cease from motion , till they come to an equipondium ; because the Water alwayes springs up thorow the Mercury , till an equal Ballance happen . Seventhly , that one Fluid of this kind , can counterpoise another Fluid of the same kind , though there be divers Fluids interveening : because the Air FE , counterpoiseth the Air IK , or IS , notwithstanding of Water and Mercury interveening . Eighthly , that there may be as much Pressure in one inch of a Fluid , as in a million ; because the 29 inches of Air IS , have as much Bensil in them , as is in the whole Pillar of Air EF , that goeth up from the top of the VVater , to the top of the Atmosphere . Ninthly , that when one Fluid is under Pressure , the next must be under the same degree of Pressure , though they be not of the same kind , but of different sorts ; because the Air IS , the Water SK , and Mercury KP , are surely under the same degree of Pressure ; otherwise the motion could not end . Tenthly , that when two Fluids of divers kinds do press one another , that which is naturally lighter , ascends alwayes to the higher place , and the heavier to the lowest : because the Air IS , is above the Water SK , and the Water SK is above the Mercury . Note , that this is not universal , but only happens when the lighter Cylinder , is slenderer than the other , for if the Mercury KP , were no thicker than the Water PNRH , this would raise it intirely . Eleventhly , that the compression of Air to less space , is not according to Arithmetical progression , 1 , 2 , 3 , 4 , 5 , but according to some other proportion , which may be called Uniform-difform . Note here , that though this be true of the Air , while it is comprest from a more quantity to a less , as here , or in a Wind-Gun ; yet it is not true of the Pressure of the Element of Air , which is more and more from the top of the Atmosphere to the Earth , according to Arithmetical Progression , as in Water . We see lastly , that the heaviest of Fluids , such as Mercury , press upward , as well as downward ; because the top of the Mercury K , thrusts up the Water KS , as well as it thrusts down the Water PNRH . It may be enquired here , how far this Glass would go down , before the 29 inches of Air IK were reduced to one inch ? I answer , its hard to determine ; but it seems it ought to go down more than 300 fathom . In this case , there would be 28 inches of Water above K. Let us suppose the orifice H to be stopped at that deepness , and the Glass brought above the Water ; then , when the said orifice is opened in the Air , you will find the whole VVater PNRH thrust out : and not only this , but the whole Mercury PK , spring out at the orifice H likewise , except a little that remains between N and H : the reason is , because the 29 inches of Air , being reduced to one , would be under a very great Bensil ; therefore the weight being taken away that begat it , of its own accord , it would expand it self to its old dimensions ; which it could not do , unless both the 28 inches of VVater , that 's supposed to be above K , and the Mercury KP were thrust out of their places . EXPERIMENT XVI . Figure 22. THis Schematism represents a vessel full of VVater 84 inches deep , namely from LN the first surface , to MR the bottom . From M to R in breadth are 20 inches . There are here also two Glass-Pipes open at both ends ; the one , two inches wide , the other half an inch wide . Both of them are 85 inches long . XYO is a surface of stagnant Mercury , among which the two ends of the Pipes are drowned . EC is a Pillar of Mercury six inches in height , and so is GD , both of them raised to that altitude , by the Pressure of the Water upon the surface XYO . The Pillar ECA is supported by , and rests upon , the imaginary Pillar AP. And so is the Pillar GDB , supported by the Pillar BQ . There are three things that occurres here from this operation of nature to be enquired after . First , why ought the Mercury to rise in the two Tubs , after the Vessel is filled with Water ? Secondly , why rather six inches , then seven or eight ? Thirdly , what 's the reason , why it rises as high in the wide Tub , as in the narrow ? I answer , the Mercury rises from C to E , and from D to G , by the Pressure of the Water , that rests upon the surface XYO . Before that the Water is poured into the Vessel , there is here a m●st equal and uniform Pressure upon the surface XYO , both without and within the Tub , namely from the Air that rests upon it . But no sooner is the Water poured in , but as soon the Pressure becomes unequal ; the parts of the surface without the Tub , being more burdened , then the parts C and D within . Therefore , the part that 's less prest , must rise and climb up , till the Pressure become equal : for it 's impossible that a Fluid can cease from motion , so long as there is inequality of weight between the pondus and the potentia . If any doubt , let him pierce the side of the Vessel , and when the whole Water is run out , he will find EC and GD to have fallen down , which clearly proves the climbing up of the Mercury , to depend upon the in-pouring of the Water . For understanding the reason of the second , remember that Mercury ( as we have often noted ) is counted 14 times heavier then Water ; therefore EC must be six inches , seing XYO is prest with the altitude of 84 inches of Water . It would be judged no marvel , to see the Mercury rise from C to E , and from D to G , provided the face of the stagnant Mercury were as high as ZF . No more strange it is , to see the two Mercuries rise , with the Pressure of the Water ; for in effect and really , the said Water is the just weight of as much Mercury as would fill between XO and ZF . For understanding the third , remember ( as was noted before ) that Fluid Bodies counterpoise one another , only according to altitude : therefore 't is no matter , whether the Tubs be wide or narrow . If it be enquired , how can one and the same Water , counterpoise two Fluids of different weights ? To say , that Fluids counterpoise one another according to altitude , doth not clear the difficulty ; for it still remains to be asked , why they counterpoise one another after this manner ? Therefore it seems , that if the Water raise the Mercury from C to E in the wide Pipe , it must raise it in the narrow one from D to K. For answer , consider first , that as there are here two Pillars of Mercury CE , and DG within the two Tubs , so there are here also two Pillars of Mercury AP and BQ , under the two orifices , upon which the said two Pillars stand , and rest . Consider secondly , that the Potentia or force of the Pillar AP , is just equal to the Pondus of the Pillar ECA : Item , that the Potentia of the Pillar BQ , is equal to the Pondus GDB . Thirdly , that the Potentia of AP ▪ is most exactly equal to the Potentia of BQ ; and the reason is , because their tops A and B , are parts of the same horizontal surface . I say then , if AP be equal to ECA , and BQ equal to GDB , and AP , and BQ , equal among themselves , then must ECA be equal to GDB . The same Water then , doth not counterpoise two Bodies of different weight . I grant ECA to be far heavier , than GDB , while they are weighed in a pair of scales , but the one is not heavier than the other , as they are weighed in this ballance of nature . From what is said , we see first , that in VVater there is a Pressure , and a considerable weight . This is evident from the rising of the Mercury . VVe see secondly , that Fluids counterpoise one another , only according to Altitude . Thirdly , that when a lighter Fluid presseth up a heavier , there is no more prest up of it , than is the just weight of the pressing Fluid , because the Mercury EC , is just the weight of the VVater that presseth upon XYO . That 's to say , the part of the surface C , is no more prest with the Mercury EC , than the part X , is prest with the VVater LZX . Fourthly , if Mercury were 28 times heavier than VVater , only three inches would be prest up : if it were but seven times heavier , the altitude would be at S , 12 inches above C. Fifthly , it 's as easie for a large part of a surface , to sustain a large Pillar , as 't is for a narrow part , to sustain a narrower Pillar : because AP sustains ECA , as easily , as BQ sustains GDB . Sixthly , that in Fluids there is a pondus and a potentia : as is clear from the potentia of AP , that sustains the pondus of ECA . The VVater likewise that sustains , hath a potentia , and the Mercury EC is the pondus of it . Seventhly , that there is alwayes equality of weight between the pondus and the potentia . So is the potentia of AP , equal to the pondus ECA . Eighthly , that the pondus begets the potentia . So the weight of the VVater , begets the potentia that's in AP. For make this VVater deeper , and you augment the potentia of AP. If you subtract from it , the potentia of AP grows less by proportion . Or the weight of ECA , may be said to beget the potentia of AP. To proceed a little further , let us suppose the Air HE to be removed . In this case , the Mercury rises 29 inches higher than E , or 35 above C ; even as high as S. In the narrow Tub it will climb up to K , if you take away the Air IG . This comes to pass , by vertue of the Pressure of the Atmosphere , that rests upon LN . From this we gather ninthly , that there is a counterpoise between the Air HE , and the weight of the Air that rests upon LN ; and that a slender Pillar of Air , is able to counterpoise a thicker : for HE is far narrower than LN . Tenthly , that the Pressure of the Air , can be communicated thorow divers kinds of Fluids ; because the weight that rests upon LN , is sent down thorow the VVater LZX , and down thorow the stagnant Mercury , and thrusts up the Liquor from A to S , 35 inches . Eleventhly , that a lighter Fluid may be made to press with greater burden , than a Fluid naturally heavier ; because the weight of the Air upon LN , raises 29 inches of Mercury , but the VVater raises only six . VVe see twelfthly , that Fluids have a sphere of activity , to which they are able to press up themselves , or Fluids of different kinds : because fi●st , the stagnant Mercury can raise it self no higher within the Pipe , than it is without . Next , the 84 inches of Water , can raise the Mercury no higher than E. Lastly , the weight of the Atmosphere , can raise the Mercury no higher than S , 29 inches above E. For another trial , take out from among the Water , the two Pipes , and stopping closely the two under orifices , fill them with Mercury to the brim . Then thrust them down as before , and open the said two orifices , while they are below the surface XYO , and you will find the whole Cylinder fall down from H to E , and there halt : and the whole Cylinder in the narrow Pipe falls down from I to G. Or , if you please , before this be done , stop closely the orifice H , and the orifice I , and you will find the Mercury go no further down than S , by opening the orifice A ; and no further down than K , by opening the orifice B. This leads us to a clear discovery of the reason , why the Mercury subsides , and sinks down from the top of the Tub in the Baroscope , to the 29th inch , whatever the diameter of the Pipe be . And this lets us see , that the Mercurial Cylinder is suspended by the Air , after the same manner , that the Mercury EC is suspended after : and that there is no more difficulty in the one , than in the other . EXPERIMENT XVII . Figure 23 , 24. Fig. 18 Pag. 116 Fig. 19 Pag. 119 Fig. 20 Pag. 126 Fig. 21 Pag. 132 Fig. 22 Pag. 137 There are here several Phenomena to be considered . First , that the Water creeps in at the orifice G , and fills the under part of the Glass from M to K. Secondly , that not one particle of Air comes out , all the time the VVater is in going in . Thirdly , that this Air is comprest from M to K , nine inches . Lastly , that the ingress of the Water , is according to unequal proportion : because while the Glass passeth from A to B , more VVater creeps in at G , and fills the bottom , then in passing from B to C. And more in going down from B to G , than in going down from C to D , as is clear from the unequal divisions 1 , 2 , 3 , 4 , 5 , 6 , For understanding the reason of the first , remember that in this deep Water , there is a Pressure , and that this Pressure grows , as the VVater grows in deepness . It is then by vertue of this , that the VVater creeps in , and fills the bottom of the Vessel : for in effect , every part being under a burden , and being therefore desirous to liberat themselves from it , they take occasion to thrust in themselves , finding , as it were , more ease here , than without , the Air within the Glass , being under less Pressure , than the VVater without . The second Phenomenon is caused by the straitness and narrowness of the hole G : for this entry being no wider , than the thickness of a Sack-Needle , the Air cannot go out , while the VVater is coming in ; that is , the passage is so strait , that the one cannot go by the other . This leads us to the reason of the third , for if not one particle of Air go out , all the while the Glass is in going down , then surely , the VVater filling between M and K , must compress the Air , and reduce it from twelve inches to three . But the greater difficulty is , why the ingress of the VVater is according to unequal proportion . For understanding this , consider , that this inequality , is not caused by any unequal Pressure that 's in the VVater ; for if this were true , then there ought to be less Pressure in the surface F , than in the surface E , and less in E , than in D , which is false and absurd . This inequality then , must flow from the nature of the Air it self , that naturally suffers compression after such a manner . 'T is evident from the compression of Air in Wind-guns ; for less force is required to compress the fi●st span , than to compress the second : or contrariwise , more strength is required , to compress the third span , than the second ; more to compress the fourth , than the third , and so forth . 'T is evident in all bodies endowed with Bensil , as in the Spring of a Watch , that requires more strength to bend it . in the end , than in the beginning . For a second trial , pull up from the bottom of the Water the Glass LIH , and when it comes above , you will find nothing in it . The reason is , because the Vessel being open between T and S , the whole VVater IH , falls down by degrees ; but in effect , is really thrust out , by the strong Bensil of the comprest Air IL , that now expands it self , when it finds the Glass go up thorow the VVater , whose Pressure is less , and less from the bottom to the top ▪ but the contrary effect follows , when the other Glass is pulled up ; namely , the VVater remains within the Glass , and the Air above it , is thrust out by degrees , as the Glass comes nearer to the top . For understanding the reason of this , consider first , that while the orifice G , is level with the lowest surface , where it now is ; that 's supposed to be 30 fathom deep , there is a real counterpoise between the inclosed Air GK , and the ambient VVater without : for with what force the one strives to be in , with the same force the other endeavours to be out ; and because they are in equal terms , therefore the one cannot yeeld to the other . If you please to give the victory to the VVater , then let the Glass go further down ▪ but if you desire the Air to overcome , then must the Glass be pulled up . Pull it then up from the place it is in , till it come to F , and you will find a considerable quantity of Air come out at G , and after 2 or 3 minuts of time , emerge and come to the top A , in form of round Bells , or Bubbles . The deepness and groseness of the Water thorow which the Bubbles come , makes their motion so slow . The reason of this eruption , must be less Pressure of Water in the surface F , than in the lowest G , from whence the Glass came . Suppose then , the lowest to have six degrees of Pressure , F to have five , E to have four , D three , C two , and B to have one : and supposing the inclosed Air KG , to be equal in force to the Pressure of the lowest fathom , it must then have six degrees of Bensil in it . Put the case then , that with six degrees of Bensil , it come to the surface F , that hath but five , it must surely break forth , and overcome the force and power of that surface : for 't is impossible that two Fluids can be unequal in force and power , but the strongest must overcome , and the weakest yeeld : therefore , when the orifice comes to F , the Air being stronger than the Water , breaks forth ; and as long doth this eruption continue , as inequality of power continues between the one and the other . In pulling up the Glass from F to E , other five fathom , more Air comes out . The reason is the same , namely less Pressure in E than in F : therefore , when the inclosed Air , that hath five degrees of Bensil , comes to E , that hath but four , it must overcome , and so long must it be victorious , till by expanding it self , it be reduced to the Bensil of four . In pulling up the Glass from E to D , more Air yet breaks out , because a surface of three degrees of Pressure , is not able to resist four degrees of Bensil . In passing from D to C , more Air comes yet out for the same reason , till in going up to the top , where there is no Pressure , no more Air breaks out . 'T is to be observed first , that the motion of the Air up thorow the Water is but slow , the medium being thick , and gross . Secondly , that if the Glass be pulled up quickly , from one surface to another , or contrariwise , let down quickly , it presently breaks in pieces . This comes to pass through the strong Bensil of the inclosed Air , that must have time to expand it self , otherwise it breaks out at the nearest : for it being of six degrees of Bensil , and coming quickly to a surface of five , there happens an unequal Pressure , the sides of the Glass being thrust out , with greater force , than they are thrust in with . But if so be , the Glass move slowly up , the inclosed Air gets time to thrust it self out by degrees , so that whatever surface the Glass comes to , there is little difference between the Pressure of the Water , and the Bensil of the Air. The reason why the Glass breaks in pieces , while it goes quickly down , is likewayes unequal Pressure upon the sides : for in passing quickly from a surface of five degrees , to a surface of six , the sides are prest in with greater force , than they are prest out with , and the reason is , because through the straitness of the hole G , the Water cannot win in soon enough , to make as much Pressure within , as there is without . 'T is to be observed thirdly ; that if the orifice G be stopped , before that the Glass be sent down , it will not go beyond three or four fathom , when it shall be broken in peices ; though the motion were never so slow : and this comes to pass , through the strong Pressure of the Water . Fourthly , the stronger the Glass be in the sides , it goes the further down without breaking : therefore a round Glass Bottle , will sink 20 or 30 fathom , before that it be broken with the Pressure of the Water . If a Vessel of iron were sent down , it ought to go much further . An empty Cask , or Hogshead , will not sink beyond seven or eight fathom , without breaking , or busting ; yet a Bladder full of wind , knit about the neck with a Pack-Threed , will go down 100 fathom , yea 1000 without bursting . It may be here inquired , what sort of proportion is keeped by the unequal ingress of the Water ? I answer , it may be known after this manner . Let first down the Glass one fathom , and having pulled it up again , measure the deepness of the Water in the bottom , of it . Next , having poured out that Water , let it down two fathom , and pulling it up , measure the deepness , which you will find more , than afore . Do after this manner , the third time , and the fourth time , till you come to the lowest fathom , and you will find the true proportion . From what is said we see first , that in Water there is a Pressure , because through the force and power of this Water , the 12 inches of Air that filled the Glass , are reduced to three . Secondly , that this Pressure growes , as the Water growes in deepness : because there is more Pressure in B , than in A , more in C , than in B ; and so downward . Thirdly , that when Air is comprest , by some extrinseck weight , the Bensil is intended , and grows stronger by unequal proportion , as is clear from the unequal divisions , 1 , 2 , 2 , 4 , 5 , 6. Fourthly , two Fluids cannot cease from motion , so long as the potentia of the one , is unequal to the pondus of the other : this is evident from the Water 's creeping in at G , all the while the Glass is in going down ; and from the Air 's coming out , all the while the Glass is in coming up . Fifthly , that no sooner two Fluids come to equality of weight , but as soon the motion ends : because , if the Glass halt at D , E or F , in the going down , upon which follows a counterpoise , then doth the creeping in of the Water cease . Sixthly , there may be as much Pressure in a small quantity of a Fluid , as in the greatest : because there is as much Bensil in the small portion of Air , included between K and G , as there is of Pressure , and weight , in this whole Water , that 's 30 fathom deep . Seventhly , that the Pressure of a Fluid , is a thing really distinct , from the natural weight : this is evident from the Pressure of the inclosed Air GK , that 's more and less , as the Pressure of the Water KM , is more and less , but the natural weight is still the same , seing the same quantity remains . Eighthly , one part of a Fluid , cannot be under Pressure , but the next adjacent , must be under the same degree of Pressure : this is also clear , because what ever degree of bensil the included Air KG is under , the Water KM is under the same . Therefore , when the one is under six , as in the lowest fathom , the other is under six likewise . And when the one is under five degrees of Pressure , as in the surface F , the other is under as much . Ninthly , Bensil and Pressure are equivalent to weight : because the Water KM , is as much burdened with the Bensil of that small portion of Air above it , as if it had a Pillar of Water 30 fathom high upon it . Tenthly , that the Pressure of Fluids , is most uniform and equal , and that two Fluids of different kinds , may press as uniformly , as if they were but one : this is evident from the sides of the Glass , that are not broken in pieces , by the strong Bensil of the inclosed Air , and heavy Pressure of the inclosed Water ; and this happens because the Pressure without , is as strong as the Pressure within . We see lastly , that Water does not weigh in Water , because when a man lets down this Glass by the chord , to the lowest surface , he finds not the weight of the Water KM , that 's within the Glass , but only the weight of the Lead Q. 'T is certain , he finds not the weight of the Water IH ; because it rests not upon the Glass within , but is sustained by ' its own surface , the mouth of the Glass being downward , and open . When I say Water does not weigh in Water ; the meaning is not , that Water wants weight or Pressure in it , but that this weight and Pressure is not found , as the weight and Pressure of other bodies are found , while they are weighed in Water . For example , a piece of Lead or Gold , hung in the Water by a string , the other end being fastened to a Ballance in the Air , gravitats , and weighs down the Scale ; and the reason is , because Lead and Gold , are naturally and specifically heavier than VVater ; but a piece of Metal of the same specifick weight with Water , or VVater it self , cannot gravitat in VVater , or weigh down the Scale of a Ballance ; and the reason is , because the surface of Water upon which they rest , bears them up with as great weight and force , as they press down with . If it be said , that the Water KM , rests upon the bottom of the Glass within ; and therefore , if the man above , find the weight of the Glass , he must find the weight of the Water within it . I answer , the consequence is bad , because the weight of the Water within , is sustained , and counterpoised by the weight of the Water without , whereupon the bottom of the Glass rests . That 's to say , as there is a Pillar of Water KM within the Glass , that presseth down the bottom , so there is a Pillar of Water without the Glass , whereupon the bottom of the Glass rests , and which bears up both . But the greater difficulty is this , the further down the Glass goes , it grows the heavier , because of more and more Water , that creeps in at G. Now 't is certain , the weight Q grows not heavier , therefore it must be the Water within the Glass , that makes the increase of the weight ; and therefore Water must still weigh in VVater . If this argument had any strength in it , it would prove the weight of the VVater IH to gravitat and weigh likewise ; because the further down this glass goes , it grows the heavier , because of more , and more Water , that creeps up from H to I. Now 't is certain , the weight of Lead B grows not heavier . Behold , the difficulty is the same in both , and yet it were rashness to affirm the Water IH to be found by a mans hand , when he pulls up the Glass with a string , seing it is sustained by its own surface , and not by any part of the Glass . Though this might suffice for an answer , yet because the contrary is mantained by some , and that with a new Experiment to prove it , I shall be at some more pains to vindicat the truth of what I have said . This new Experiment to prove that Water weighs in Water , I found in a Philosophical Transaction , of August 16. Anno 1669. Numb . 50 , the Invention whereof is attributed by the publisher , to that honorable and worthy Person Mr. Boyl , whose conclusions and trials , I never much called in question , but finding this opposite , and contrary to what I have demonstrated , I shall crave liberty to say , amicus Socrates , amicus Plato , sed magis amica veritas ; and shall therefore examine it as briefly as may be . The words of the Publisher are as follows . The Author of this Invention is the Noble Robert Boyl ; who was pleased to comply with our desires , of communicating it in English to the curious in England , as by inserting the same in the Latine Translation of his Hydrostatical Paradoxes , he hath gratified the Ingenious abroad . And it will doubtless be the more welcome , for as much as no body , we know of , hath so much as attempted to determine , how much Water may weigh in Water ; and possibly , if such a Problem had been proposed , it would have been judged impracticable . The Method or Expedient , he made use of , to perform it , as near as he could , may easily be learned by the ensuing accompt of a Trial or two , he made for that purpose , which among his Notes he caused to be registred in the following words . A Glass-bubble of about the bigness of a Pullets egg , was purposely blown at the flame of a Lamp , with a somewhat long stem turned up at the end , that it might the more conveniently be broken off . This Bubble being well heated to rarify the Air , and thereby drive out a good part of it , was nimbly sealed at the end , and by the help of the Figure of the stem , was by a convenient Weight of Lead depressed under Water , the Lead and Glass being tyed by a string to a Scale of a good Ballance , in whose other there was put so much weight , as sufficed to counterpoise the Bubble , as it hung freely in the midst of the Water . Then with a long Iron Forceps , I carefully broke off the seal'd end of the Bubble under Water , so as no Bubble of Air appear'd to emerge or escape through the Water , but the Liquor by the weight of the Atmosphere , sprung into the un-replenish'd part of the Glass-Bubble , and fill'd the whole cavity about half full ; and presently , as I foretold , the Bubble subsided , and made the Scale 't was fastned to , preponderate so much , that there needed 4 drachms , and 38 grains to reduce the Ballance to an equilibrium . Then taking out the Bubble with the Water in it , we did , by the help of a flame of a Candle , warily applyed , drive out the Water ( which otherwise is not easily excluded at a very narrow stem ) into a Glass counterpoised before ; and we found it , as we expected , to weigh about four drachms and 30 grains , besides some little that remained in the Egg , and some small matter that might have been rarified into vapors , which added to the piece of Glass that was broken off under Water and lost there , might very well amount to 7 or 8 grains . By which it appears not only , that Water hath some weight in Water , but that it weighs very near , or altogether as much in Water , as the self same portion of Liquor would weigh in the Air. The same day we repeated the Experiment with another sealed Bubble , larger then the former ( being as big as a great Hens-egg ) and having broken this under Water , it grew heavier by 7. drachms and 34 grains ; and having taken out the Bubble , and driven out the Water into a counterpois'd Glass , we found the transvasated Liquor to amount to the same weight , abating 6 or 7 grains , which it might well have lost upon such accompts , as have been newly mentioned . Thus he . Figure 24. THe design then of this Experiment is to prove that Water weighs in Water ; but , it seems , there is here a very great mistake , which I shall make out after this manner . For which cause , let this Schematism 24 represent the Experiment already described . The Glass-bubble then is EPFR . The stem is HC : the weight that sinks the Glass is B. The surface of Water under which it is drowned , is AD. The Ballance to which the Glass is knit by a string is NO . And lastly EFR is the Water that came in , and filled the half of the Bubble . Now I say , it is not the weight of the Water EFR , that turnes the Scales above , and makes an alteration in the Ballance , but ' its only the weight of the Lead B , that does it . For evincing this , consider that all heavy bodies , are either lighter in specie than Water ; as cork , or of the same specifick weight with it , as some Wood is , or last●y heavier in specie than Water , as Lead or Gold. Now 't is certain , that bodies of the first sort cannot weigh in Water , and the reason is , because they being naturally lighter , their whole weight is supported by the Water , and therefore not one part of them , can be born up by a Ballance above . A piece of Cork that weighs 12 ounces in the Air , weighs nothing in Water , because as soon as it toucheth the surface , the whole weight of it is supported , and therefore cannot affect the Ballance above . But bodies of the third sort , as is clear from experience and reason , does really weigh in Water : And the reason is , because they being naturally heavier than water , their whole weight cannot be supported by it , and therefore some part of them must burden the Ballance , to which the body is knit . A piece of Lead , that weighs 12 ounces in the Air , will not lose above 2 ounces , when ' its weighed in Water ; or may be less . But here there is no difficulty . The question then is , in order to bodies of the same specifick weight with Water , as some Wood is , or as Water is . I say of such also , that they cannot weigh in Water ; and the reason is , because they being ●ust of the same weight , must have their whole weight supported by it ; even as one foot of Water , supports the whole weight of the foot above it . It may be evidenced after this manner . Take a piece of Wood , that 's lighter in specie than Water , and add weight to it by degrees , till it become of the same weight with Water . Knit it with a string to a Ballance , ond weigh it in Water , and you will find the whole weight supported by the Water . And the reason is , because , being left to it self , it can go no further down , than till the upper part of it , be level with the surface of the Water . Now , the whole weight being thus supported , not one ounce of it can burden the Ballance . In a word , the Ballance can never be burdened , unless the body that 's knit to it , have an inclination to go to the ground , when left to it self , which a body of the same weight with Water can never have . I conclude then , if a body of the same weight with Water , cannot weigh in Water , neither can Water weigh in Water , seing Water is of the same weight with Water . And Therefore the Water EFR , that 's now within the Bubble , cannot in anywise burden the Ballance above ; but must be supported wholly by the Water IKGH , upon which the bottom of the Glass rests . If it be said , that the Glass it self is supported by the Ballance , because ' it s heavier in specie than Water ; therefore the VVater within that rests upon the sides of it , must be supported likewise by it . I answer , the whole weight of the Glass is not supported , by the Ballance , but only a part ; the VVater IKGH supporting the other part . And this part is just as much as is the weight of VVater , that 's expelled by the Glass . Now , if the said VVater support so much of the Glass , because it is the just weight of so much VVater , why should it not also , support the VVater within the Glass ? Seing the VVater within the Glass , is just the weight of as much VVater , as will fill the space EFR . I come in the next place to shew , that it is the weight of the Lead B that turns the Scales , when the VVater comes in at C , and fills the half of the sphere . For understanding this , let us suppose first , the weight that 's in the Scale O to weigh six ounces . Secondly , that the Glass takes 12 ounces to sink it compleatly under the surface AD. Thirdly , the weight B to be 18 ounces ; namely for this cause , first , that 12 of it may sink the Glass ; next , that the other six may counterpoise the six in the Scale O. Lastly , that the VVater within the Glass weighs six ounces . I abstract from the weight of the Glass it self , which is not considerable , seing the most part of it , is suppo●ted by the VVater , and not by the Ballance . Now , I say , 't is six ounces of the weight B that makes this alteration , and turnes the Scales . For if 12 ounces sink the Glass below the VVater , when ' its full of Air , and no Water in it , then surely six are sufficient to sink it , when it is half full . And the reason is , because there is a less Potentia or force in six inches of Air , by the one half , to counterpoise a weight of 12 ounces , than in 12 inches of Air. Therefore this Air , being reduced from 12 inches to six , it must take only six ounces to sink it . If this be , then the other six ounces that now wants a party to counterpoise them , must burden the Ballance , and be supported by the Scale : and therefore , to make a new equipondium again , you must make the weight O 12 ounces , by adding six to it , that it may counterpoise 12 of B , the other six being counterpoised by the Air EPF . Let us suppose next , this Glass to be compleatly full of VVater , and the whole Air expelled . In this case the Scale O , must have 18 ounces in it , for making a new equipondium . The reason is , because there being no Air in the Glass to counterpoise any part of B , the whole weight of it must be sustained by the Ballance , and therefore in the Scale O , there must be 18. Now , I enquire , whether these 18 ounces , are the equipondium of the VVater within the Glass , or of the weight of Lead B ? 'T is impossible it can counterpoise them both , seing the VVater is now 12 , and B 18. It must then either be the counterballance of the Water , or the counterballance of the Lead . It cannot be the first , because 12 cannot be in equipondio with 18 , It must then be the second . Or if these 18 ounces in the Scale O , be the counterpoise of the Water within the Glass , I enquire what sustains the weight of the Lead B ? The weight of it , cannot be sustained by the Water , because 't is a body naturally heavier than Water , it must therefore be sustained by the Ballance , I conclude then , that Water cannot weigh in Water . If it be objected , that this conclusion seems to contradict , and oppose the Pressure of the Water , that 's been hitherto confirmed with so many Experiments . I answer , the Pressure of the Water is one thing , and Water to weigh in Water is another . The first is , when one Pillar of Water counterpoises another , or when a Pillar of Water counterpoises a Pillar of Mercury , or is counterpoised by a Pillar of Air , all which is in order to the Natural Ballance , wherein bodies weigh only according to altitude . The second is , when VVater is not counterpoised by VVater , or by Mercury , or by Air , or by any other Fluid ; but when ' its weighed by a piece of Lead or stone in an Artificial Ballance , for knowing how many ounces or pounds it is of , as if a man should endeavour to weigh the Water EFR by help of the Ballance above , which in effect is impossible . EXPERIMENT XVIII . Figure 25. MAke a Wooden Ark after this following manner . The Planks must be of Oak , an inch thick . The height 40 inches . The breadth 36. Closs on all sides , and above , and open below . And because the form is four-square , there must be four Standarts of Timber , in each corner one , to which the Planks must be nailed . Four likewise upon the top , crossing the other four at right angles , to which the cover must be joyned . The sides must be plained , and the edges both plained and gripped in all the parts , that the joynings m●y be closs . Upon the top fasten a strong Iron Ring , as at N , through which must be fastned a Rope , of so many foot or fathom . And because the use of this Engine is for Diving under the Water , it must therefore be all covered over with Pitch within and without , especially in the couplings . And because this Instrument cannot sink of its own accord , it must have a great weight of Lead appended to it , for that cause , whereupon the Divers feet must stand , while he is in going down . The precise quantity and weight of it cannot be determined ; because it depends upon the quantity of the Ark , which if large , requires a great weight : if of a lesser size , requires a lesser weight . But whatever the dimensions of the Ark may be , the weight of the Leaden-foot-stool can easily be found out by trial . This Invention then , is for Diving , a most excellent Art , for lifting up of Guns , Ships , or any other things , that are drowned below the Water . And it is in imitation of the Diving bell , already found out , and made use of with success . It is called a Bell , because of the form , that represents a Church-bell indeed , being round , wide below , and narrower in the top : only , the matter is of Lead . It seems , it is of this mettal , first , because Lead is weighty , and will therefore easily sink : secondly , because it 's easily founded , and will by this means , being of one piece , be free of rifts , and leaks : thirdly , it being of Lead , will be of a considerable strength for resisting the force of the VVater , that ordinarily breaks in pieces Vessels that are weak . I cannot well d●vine and guess the reason , why first it is round , and next narrower above , than below , unless , because its more easily founded after this way , than after another . This device here described is named a Diving Ark ; first , because it is of Timber , and next , because it saves a man from being overwhelmed with the Waters . I prescribe it of Wood , because of less trouble , and expence in making of it . 'T is four square , because it contains under this Figure , far more Air , than if it were round ; even as much more , as a square Vessel 30 inches wide , contains more than a round Vessel 30 inches wide . Now , the more Air , that 's in the Vessel , the easier is the respiration , and the longer time is the man able to abide under the VVater , which two things are of great advantage to this Art. For if by a guess we reckon , how much more Air is in the one , than in the other , we will find in the Ark , as before it is described , 30 square foot of Air , but in the Bell , though it be 36 inches wide , as well above , as below , yet little more than 23 will be found , which is a considerable difference . But far less must be in it , seing it's narrower above , than below . Besides this advantage , there are others very useful : for being of Wood , it 's more tractable . Next , several Knags of Iron may be fastened conveniently to the sides within , to which a man fastning his hands , may keep his body fixed and sure in going down , and coming up . Moreover , if a man were in hazard to be confounded with fear , or lose the right exercise of his senses , and so be in danger of falling out of the Ark ; or if his feet should slide off the foot-stool , and his hands fail him too , a chord knit to one of those , and fastened about his wast or middle , might bring him up , though he were dead . Then , it s far easier to cut out a window or two in the sides of it , not very large , but little , as K and I , whereby , they being covered with Glass , a man may see at a distance , what 's upon the right hand , and what 's upon the left , and what is before . This device is of excellent use , for through the want of it , the Diver sees no more , but what is just below him , which sometimes , when he is near the ground , will not exceed the compass of a large Miln-wheel . But if so be , three holes be cut thorow , one on every hand , and one before , he may see as much bounds , and all things in it , as if he were not inclosed , and invironed with a cover . A little schelf likewise may be fixed upon the one side or the other , for holding a Compass with a Magnetical Needle , for knowing how such and such a thing lies in the ground of the Sea. In one of the corners may hing a little bottle with some excellent spirits , for refreshing the stomach , under VVater . Many moe advantages I might name , this Engine being of Timber , but shall forbear ; leaving the collection of them to the ingenious Reader , and proceeds to answer some objections , that may be made against it . First , if this Engine be made of Wood , it will not sink so easily , as being made of Lead . I answer , this difficulty is soon overcome , namely by making the Foot-stool the heavier : therefore how light soever it be , a weight may be found to counterpoise it in the VVater , If it be judged too light in Timber , it may be lined with Lead , especially without . Secondly , if it be of VVood , there must be couplings and joynings in it , and so rifts and leaks in it , through which the VVater may come . I answer , there is less difficulty here , than in the former ; because the joynts may be made so closs in all the parts , and may be so covered over with pitch , or with some such like matter , that it may defie either Water to come in , or Air to go out . Thirdly , if it be made of VVood , it will be in hazard of breaking by the force of the VVater : for oft times its found , that the strongest Hogshead will burst asunder by the Pressure of it , if they go but down 7 or 8 fathom . I answer , this objection flows from the ignorance of the nature of Fluid bodies . If so be then , that a man knew , that the Pressure of VVater is uniform , most equal , and presseth upon all the parts of a body within it alike , no such scruple would occurre . I say then , the Ark , though no thicker in the sides , than a thin sawen dale , will go down , in spight of all the Pressure that 's in the VVater , not only 10 , but 20 , or 30 fathom , without all hazard . And the reason is , because what Pressure soever is without , to press in the sides , the same degree of Pressure is within to press them out . By this means , there is not one part of the VVater , how deep soever , to which the Ark may come down , but there will be found as much force in the Air within , as will counterballance the whole weight without , as will be infallibly demonstrated afterwards . This answers a fourth objection , namely if holes be cut out in the sides of the Ark , in stead of windows , the force of the VVater will break the Glasses in pieces , that covers them . There is here no hazard , though the said windows were 12 inches in Diameter : but it s not needful they be so large . It 's sufficient , if they be 2 inches wide : for a mans eye near to a hole , 2 inches wide , will see a great way about him . There 's a necessity the Glasses be joyned in with cement , that Water may not have access to come in , or Air to go out . In such a case ther 's no hazard , that the Pressure of the VVater , will break through the windows , or break the Glasses ; because the Pressure of the Air within , being of the same force with the strength of the VVater without , the Glasses are keeped intire . It may be enquired , what hazard would follow , upon supposition a small hole were pierced in the head of the Ark above , when it is going down ? I answer , ther 's not so much hazard , as a man would think ; provided the hole be not wide , but narrow . If it be wide , not only the VVater comes in , but the Air goes out , the one thrusting it self by the other . If the hole be no wider , than the point of a bodkin is in thickness ; ther 's no danger at all : for by reason of the strait passage ; the one cannot thrust it self by the other , and therefore neither the VVater can come in , nor the Air go out . And this comes to pass , by reason , that the Air within , is as strong as the Water is without . Now , if they be both of the same strength and force , why ought the Air rather to go out , then the Water to come in ; or the Water rather to come in , then the Air to go out ? I am confident , though the hole were as wide , as a man might thrust in his little finger , yet no irruption of Water , or eruption of Air would follow . This demonstrats clearly , that though a small rift , or leak should happen in the Ark , yet no hazard or danger would follow thereupon . If it be inquired , whither the greatest hazard is from the ingress of the Water , or from the egress of the Air ? I answer , ther 's no danger from the coming in of the Water from above ; because as it comes in , it falls down , and so mingles with the rest below . But if the Air should go out , the Ark fills presently full of Water , and drowns the man that is in it . The next thing considerable in this Diving Instrument , is the foot-stool of Lead CD , that 's not only useful for a man to set his feet upon , when he dives ; but especially for sinking of the Ark. For this being made of Timber ; and full of Air , cannot of ' its own accord go down , unless it be pulled , and forced by some weight . It may either be broad and round , or square : if square , a large foot over from side to side , or 16 inches will determine the breadth . By this means , it will happen to be pretty thick , seing a great quantity of Lead is required . In each corner , there must be a hole , for four chords , by which it is appended to the mouth of the Ark. Between it , and the roof within , must be the height of a man and more . The weight of it , cannot be well determined without trial ; seing it depends upon the dimensions of the Ark. First then try , how much weight , will bring the top EFGH level with the surface of the Water . When this is found , add a little more weight till it begin to sink , and this will surely take it to the ground , though it were 40 fathom . 'T is to be observed , that when the top EF is level with the surface , there is here a just counterpoise , namely between the Lead foot-stool on the one part , as a pondus , and the Ark on the other part , as a potentia ; for with what force the Ark endeavours to pull up the Lead ; with the same force strives the Lead to pull down the Ark. Hence it is , that as a small weight will turn a pair of Scales , when they are in equilibrio ; so a small weight added to the foot-stool will sink the Ark. Though it may seem difficult to determine the just weight of the foot-stool , without trial as I said , yet I purpose to essay it . For this cause consider that there is no Vessel of VVood almost , if it be once full of Water , but the orifice of it will ly level with the surface of the VVater , wherein it sweems . This proposition is so evident from experience , that it needs no confirmation . From this I gather , that as much weight of Lead or Stone will bring the top of the Ark EFGH , level with the surface of the VVater , as is the weight of the Water , that fills it . If you suppose then the Ark to be 36 inches broad , and 40 inches high , it must contain 30 cubique foot of Water . Now , supposing each square foot of this Water to weigh 56 pound , 30 foot must weigh 1680 pound . This is gathered from trial and experience , for after exact search , I found a cubique foot of Water , in bulk about 16 pints of our measure , to weigh 56 pound . Take then a piece of Lead of that weight , and you will find it make a just counterpoise with the Ark. If any be desirous to know the quantity of it . I answer , if lead be 13 times naturally heavier then Water , you will find that a piece of Lead about 16 inches every way will do it . If it be objected , that when a mans body is within the Ark , the weight of the foot-stool must be less , even as much less , as is the weight of the man , whom I suppose to weigh 224 pound , or 14 stone . I answer , the whole weight of the man is not to be deduced from the foot-stool , but the one half only , and the reason is , because a mans body being of the same specifick and natural weight with Water , it cannot preponderat or weigh in VVater , because magnitudes only naturally heavier then VVater weigh in VVater , as Lead , or Stone ; therefore seing the one half of the man is within the Ark , and the other without among the Water , that part only must weigh , that 's invironed with Air. This may seem a plausible answer , and might do much to satisfy these , that are not very inquisitive , yet , being examined , it will be found unsufficient . Therefore , I say , there 's not one part of the mans body , that weighs within the Ark , or makes it heavier . Yet , I affirm , that when the mans body is within the Ark , a less weight will sink it , then when his body is out of it , even as much less than before , as is the just weight of the one half of the man. For example , if 1680 pound be the just counterpoise of it without the Man , then after the Man is in it , it will take only 1568 pound to counterballance it , supposing the one half of the man to weigh 112 pound , or seven stone : yet it is not the weight of the man that makes this difference . For understanding what 's the cause of this alteration , consider , that when a mans body is within the Ark , there is less Air in it , then while his body is out of it , even as much less in quantity , as the bulk of the parts are , that are within . If this be , then must the Ark become heavier , not because the mans body makes it heavier , but because there is less Air , in the Ark , then before , and therefore , there arises an inequality between the weight of the foot-stool and the weight , or rather lightness of the Ark. For if 1680 pound of Lead , was the just counterballance of it , when it had 30 cubique foot of Air within it , it must exceed , when there is less Air in it . But there occures , here two difficulties , the first is , what 's the reason , why as much weight must be deduced from the foot-stool , as is the the precise weight of the one half of the man ? Secondly , how shall we come to the true knowledge of that weight ; that is , to know distinctly how many pounds or ounces it is of ? For answer , let us suppose , that the one half of the man , is just as heavy , as so much Water equal in bulk to his own half . This may be granted without scruple , seing a mans body is judged to be of the same specifick , and natural weight with Water : and though there should be some small difference , yet it will not make , or produce any insufficiency in the argument , for these demonstrations , are not Mathematical but Physical . Therefore , as much Water in bulk , as is equal to that part of the man , that is within the Ark , must be as heavy , as the half of the man. Now supposing the half of the man , to weigh 112 pound , and consequently that Water , to weigh as much , I affirm the said Water to contain 3456 cubique inches : but 3456 cubique inches , makes exactly two cubique feet , which I gather thus . Seven pound of Water requires 216 cubique inches , because a Cube of six inches , weighs exactly seven pound , therefore according to the rule of proportion , 112 pound will require 3456 inches , which amounts to two cubique foot . The Ark then by receiving the one half of the mans body , loseth two cubique foot of Air , therefore if 30 foot of Air , require 1680 pound weight of Lead to counterpoise it , 28 foot of Air , must require only 1568 pound : therefore to make a new counterballance , you must deduce 112 pound from the foot-stool . This answers both the difficulties . If it be said , that the foot-stool weighs less in VVater than in Air , therefore it must be heavier , then 1680 pound . I answer , 't is needful to abstract from that difference , till the just calculation be once made , and that being now done , I say , that a Cube of Lead 16 inches weighing 1680 pound , ( If Lead be 13 times heavier than VVater , ) will lose about 130 pound . The reason is evident , because a heavy body weighs as much less in VVater than in Air , as is the weight of the Water it expells . But so it is , that a Cube of Lead of 16 inches expells a Cube of VVater 16 inches : But a Cube of VVater 16 inches weighs 130 pound , which I gather thus . 216 inches , or a Cube of six inches , weighs seven pound , therefore 4032 inches , must weigh 130 pound . For if 216 give 7 , 4032 must give 130. But to return . Though there be small difficulty to let it down and to sink it 20 or 30 fathom , yet there is no small difficulty to pull it up again . And the reason is this , because the further down it goes , the Air within , is the more contracted , and thrust up , by the Pressure of the Water , towards the roof . By this means , though near the top of the Water , there was little difference between the weight of the Lead and the Ark ; yet 9 or 10 fathom down , the difference is great , the weight of the one , far exceeding the weight of the other , and therefore there must be greater difficulty to pull it up from 10 fathom , than from 5 : and yet more difficulty from 20 than from 10. However , yet 't is observable that , as the Ark in going down , becomes heavier and heavier , so in coming up , it growes lighter and lighter : therefore less strength is required , in pulling it up from the tenth to the fifth fathom , than from the fifteenth , to the tenth : the reason is , because in coming up , the Air within expands it self , and fills more space in the Ark , which in effect makes it lighter , and more able to overcome the weight of the Lead . To make these things more evident , let us suppose , that when the Ark is down 18 or 20 fathom , the Air to be contracted by the force of the Water , from LM to PQ 12 inches . Next , that the weight of the foot-stool is 1680 pound . Now , if this weight was the just counterpoise of the Ark , at the top of the Water , then surely it must far exceed it now , when it 's 20 fathom down , because the Air that was 30 foot , is now reduced to 21. Count then , and you will find , that if 30 require 1680 , 21 will only require 1176 : therefore the weight of the Lead , will exceed the weight of the Ark , at 20 fathom deep , by 504 pound . This will be yet more evident , if we consider , that while the top of the Ark EFGH , is level with the surface above , the VVater thrust out of ' its own place by this bulk , is just the weight of both Lead and Ark. But when ' its down 20 fathom , and the Air reduced from LM to PQ , there cannot be so much VVater expelled now as before , seing the space LMPQ is full of VVater . Now , I say , the Lead at 20 fathom , must be exactly so much heavier than the Ark , as is the weight of the said VVater LMPQ , which in effect will be 504. pound : for ' its a square body , 36 inches in thickness and 12 in deepness . The weight of the rope is likewise to be considered , that lets down the Ark : for the longer it be , and more of it goes out , it 's the heavier , and more troublesome to pull up . There is no way to cure this difficulty , but by finding out a way , how to keep a just counterpoise between the Lead and the Ark , all the time it is in going down . If the Air within did not contract it self , no difference would happen : but this is impossible , so long as the Water is under a Pressure . The expedient then must be found out another way , namely by kniting a small rope to the iron ring N , in length with the other , to which at certain distances , relating to the fathoms the Ark goes down , must be fastned empty little Vessels of Wood , or bladders , which by their lightness , may compense the decrement and decreasing of the Air. First then , let down the Ark three fathom , and see how much it is heavier than before : and as you find the difference , so fasten to R one Bladder , or two , till the Ark be brought near to a counterpoise . Secondly , let it go down other three fathom , and observe that difference also , and accordingly fasten to T as many , as will reduce the two to a counterpoise again . Do after this manner , till it sink 15 or 20 fathom . 'T is to be observed , that the further down the Ark goes , the difference is the less : therefore less addition will serve : and the reason is , because there is less Air contracted , in passing between the fifth and the tenth fathom ; than in passing from the first to the fifth . The proportion of contraction is represented by the unequal divisions within the mouth of the Ark , as 1.2.3.4 . In a word , by what proportion the decrement of the Air is , by that same proportion must the addition be , upon the rope SN . Suppose then , the Air to be diminished four inches , in going down four fathom , which will be 5184 square inches , or three square foot , then surely as much Air must be added to the rope SN , by bladders . In going down as far , let us suppose three inches to be contracted ; then less will suffice . Though it cannot be determined without trial , how much Air is contracted in three fathom , and how much in six , and how much in nine ; yet this is sure , that the decreasing is according to unequal divisions , that 's to say , less in six than in four , less in 8 , than in six , and less in 10 , than in 8 , and so downward : and that this is the rule , namely according to what quantity , the Air within the Ark is contracted , according to that same measure , must the addition of Air be to the rope . If it be said , that Bladders full of wind , cannot go down thorow the VVater without bursting . I answer , 't is a mistake , because their sides being pliable , and not stiff like the sides of a Timber Vessel , they yeeld , and therfore cannot burst . It 's observable that when a bladder goes far down , the sides becomes flaccid and slagging . In this case , the Air , that before , had the forme of the Bladder , and was somewhat ovall , must now become perfectly globular , and round : for 't is sure , that the dimensions of it are altered by the Pressure of the VVater , namely from more quantity to less : if this be , then the form must be round , seing the Pressure of the Water is most uniform ; even as drops of VVater , or Rain from a house side are round upon this account . This second way , may be thought upon also . Make the Leaden foot-stool that sinks the Ark , not of one piece , but of many , that so , when the Air within it , begins to be contracted by degrees , in going down , a proportionable weight may be subtracted , for keeping a just counterpoise , all the while of the descent . Or because the greatest trouble is in bringing of it up , let the Diver , when once he is at the bottom , subtract so much weight from the foot-stool , as he thinks will go near to make a counterpoise , at that deepness . For example , if the weight of the foot-stool be 40 pound heavier than the Ark , then let him subtract 30 or 36 , which may ly , and rest upon the ground , till it be drawen up , at a convenient time , by a chord . By his means it will be easie to move the Ark , from one place to another . Next , there shall be little or no difficulty to pull it up . Nay , upon supposition , the rope were broken , by which it was let down , yet if the Diver please , he may come up without any mans help . And this is most easily done , namely by subtracting as much weight , as will make the Ark the stronger party . 'T is to be observed , that when you are at the bottom , and if you make the Lead but one pound lighter than the Ark , it will surely come up , and cannot stop by the way . The reason is , because a very small weight will turn the Scales , between two bodies , thus weighing in VVater . Next , the further the Ark comes up , it becomes the lighter , because the Air within it , expands it self the more . But leaving this , let us come to explicat the reason , why the contraction of the Air is not uniform , but rather difform . For if in going down three fathom , three inches be contracted , there will not be other three contracted in going down the second three , but less : and yet less in going down the third three . Two things then are to be explicated here . First , why there is a contraction . Next , why it is after such a manner . As for the first ; the contraction is caused by the Pressure of the Water , which gradually increaseth from the top to the bottom ; as is clear from the last Experiment : therefore , there being a greater Pressure in a surface six fathom deep , than in a surface three fathom deep , the Air within the Ark , must be more contracted in passing between the third and sixth , than in passing between the first and third . When I say more contracted , the meaning is , that more quantity is contracted to less , whereby the Bensil of it is more intended ; or that the Air is more bended . As for the second , we must remember from the last Experiment , that the cause of this , is not from the VVater , as if forsooth the Pressure of it , were according to unequal proportion , but from the Air it self , whose kind and nature it is , to suffer compression after such a way . 'T is evident in Wind-guns , whose second span of Air is comprest with greater difficulty , than the first : and the third with greater difficulty , than the second . 'T is so with all bodies endowed with Bensil : for ay the longer you bend , you find the greater difficulty . As there is a great disadvantage to the man that Dives , from the contraction of the Air , so there is a great advantage to him , from this manner and way of contraction ; for if it were uniform , according to the Pressure of the Water , then if three fathom comprest three inches , six fathom ought to compresse six inches , nine fathom nine inches , and so forward , till by going down , either the whole Air , should be comprest to no inches , or else very little should remain for respiration . The next thing to be taken notice of , is that all the while , during the down going of the Ark , there is still equality of weight , between the Pondus of the Water , and the Potentia of the Air , for with what degree of weight , the Water presseth up the Air , with the same degree of force and power , doeth the Air press down the Water . If this were not , it would be impossible for a man to go down ; because of pain . For when one part of a mans body , is less prest than another , there ariseth a considerable pain , which sometimes is intolerable , as is evident from the application of Ventoso-glasses . This equality of weight , is the true reason , why respiration is so easie . Yet 't is to be observed , that a man cannot breath so easily in the Ark , under the Water , as above in the Air ; not because there is any inequality , between the weight of the VVater , and the force of the Air ; but only because the quantity of it is little . For when a man sucks in as much Air , as fills his lungs , the quantity must be diminished : if this be , the Water must ascend by proportion , though insensibly . When a man thrusts out the same Air again , the quantity is increased ; if this be , then the Water must subside a little ; both which cannot be , without difficulty , seing there is a sort of ebbing and flowing both of the Air and of the Water , in every respiration . But it rather seems ( you say ) that this difficulty flowes from the strong , extraordinary bensil , that the Air is under . I answer , as long as the pressure of a Fluid is uniform , though in a high degree , yet there can be no trouble in respiration ; because with what force soever , it is driven in upon the lungs , with the same force it is driven out again : therefore , though the Air we live in , were as much again bended as it is , yet ( as is probable ) we would find no more difficulty in breathing than now . There is one thing makes breathing easie under the Water , in the Ark , namely this ; when a man sucks in the Air to his lungs , his breast and belly goes out , and so fills the space deserted by the Air , that goes in . This makes the ebbing and flowing far less . From this equality of weight between the pressure of the VVater , and the pressure of the Air , we see good ground to say , that though the Ark , were no thicker in the sides , than a thin sawed dale , yet there would be no hazard of breaking . I am confident , though it were no stronger in the sides , than a wine-glass , that 's soon broken ; yet it might go down 40 fathom without hazard , or danger of bursting . This affords good ground likewise to make windows in the Ark covered with glass : for if the Pressure be uniform , and equal , its impossible they can be broken . The VVater cannot thrust them inward , because the Pressure of the Air , is as able to thrust them outward . It 's certain , the more Air be in the Ark , the more easie is respiration : therefore it s more easie to breath , when the Ark is but down 5 fathom , than when it is down 10 or 15. It 's probable a man might live within the Ark , it being 40 inches deep , and 36 inches wide , at the deepness of ten fathom , near two houres ; whereas if it were round , and narrow above in form of a Bell , he could not continue an hour . It were very easie to try how long other creatures might live in it , for example dogs , and such like , or fowls , as hens , pheasants or doves . They might easily be inclosed from coming out ; for though the whole mouth of the Ark were shut up , except as much passage , as would receive a mans fist , yet it will operate , as well that way , as the other . And there , a little door might be made to open , and shut at pleasure . 'T is observed , that by long tarrying under the Water in the Bell , the Air becomes gross and misty , which hinders a man from seing about him . The cause of this , are vapors that come from the stomach , lungs and other parts of the body , especially from the stomach , when the ventricle is full of meat . It 's not fit then , that a man about to dive , should eat too much , or drink too much , especially such liquors as Sack or Brandy , that beget many fumes and vapors . If a man were necessitated to tarry a pretty while below , fresh Air might be sent down from above , in bottles or bladders , even as much as might fill up the place deserted by the contracted Air. 'T is observed by some , that have been under the VVater , that their eares have been so troubled , that for a long time , they have found difficulty to hear distinctly . The reason of this must be from the great Pressure , the tympanum hath suffered from the imprisoned Air of the Bell. The Organ of hearing is soon troubled , especially when a man is near to a great gun , when it 's fired . And surely , when a man is but 34 foot down , the Air within the Ark , will be of double Bensil : put the case the man go down 68 foot , or 13 or 14 fathom , the Bensil is tripled : that 's to say , if the Air above have five degrees of Pressure in it , the Air of the Bell , at 68 foot deep , will have 15 degrees of Pressure ; therefore the tympanum of the ear that 's but a small and thin membran , must be sore distressed ; that is overbended , and prest inward ; even as , while a man sets upon a drum head a great weight , v. g. a Bullet of Lead or Iron , of 20 or 30 pound , the skin by this , suffers an extraordinary Pressure , whereby it is in hazard to be rent . 'T is probable , if a man should go very far down , the tympanum might be in hazard of breaking , or being rent in two pieces , there being a greater Pressure upon the one side from the Air without , than upon the other side , from the internal Air within , which is thought to be within the tympanum . There remains another Phenomenon to be explicated , and it 's this : the further up the Ark comes from the ground of the Water , towards the top , the Water within it , subsides and settles down more and more , towards the mouth . The reason of it is , because the further up , the Pressure of the Water is the less ; and therefore the contracted Air gets liberty to expand , and dilate it self , and so thrusts down the Water from PQ to LM . In a word , by what proportion the Air is contracted in going down , by that same proportion it dilates , and opens it self in coming up . This lets us see , as there is disadvantage in going down , from the contraction of the Air , so there is advantage in coming up , from the dilatation of it . Some think , that the coldness of the Water is the cause , why the Air is contracted in the Ark , such are those , who deny the Pressure of it . But this fancy is easily refuted ; because in asserting this , they must maintain , the further down , the cold is the greater . If this be , then far more Air must be contracted , in going down from 10 to 15 fathom , than in passing from 5 to 10 ; seing as they say , the further down , the cold is the greater ; and therefore the contraction of the Air must be the greater ; that 's to say , there must be more quantity of Air contracted in the one space , than in the other . But so it is , that the further down , the contraction is the less . They judge likewise the coldness of the Water to be the cause , why the sides of empty Vessels are broken in going down . But if this be , then a strong Vessel should go no further down than a weak Vessel ; seing cold can pierce thorow the sides of the one , as well as thorow the sides of the other . And why is it , that a bladder full of wind will go down 40 or 50 fathom without bursting , yea 100 , and yet a stone-bottle or glass-bottle , cannot go beyond 20 or 30 ? If cold have in it , that power to break the sides of a strong bottle , it must be far more able to burst the sides of a thin Bladder . This difference is clearly explicated from the Pressure of the Water ; but I defy any man to shew the difference from the coldness of it . 'T is to be observed , that in all such Experiments of sinking of Vessels , as Hogs-heads , Barrels , and Bottles , they must be closs on all sides . Therefore , if a man desire to know , how far down a Glass-bottle is able to go without bursting , he must stop the mouth of it exactly , with a piece of wood , and cement . In setting down the dimensions of the Ark , I have restricted them to 40 inches high , and 36 inches wide . But if any man be desirous to enlarge them , or make them less , he may do it . Only 't is to be observed , that the larger the Ark be , the Foot-stool that sinks it , must be the heavier . Yet it hath this advantage , that it contains much Air , which is the great perfection of it . One of a lesser size hath this advantage , that it 's more tractable , and easier to let down , and to be pull'd up . But these things are best known from Experience , or if a man please , he may calculate . As the Ark is a most useful device for profit , so 't is excellent for pleasure , and recreation , if a man were disposed to see the ground and channels of deep VVaters , or were inclined to find out Hydrostatical conclusions , a knowledge very profitable , and which few have attained to . Though it seem somewhat difficult to enter the Ark , and go down below the Water , yet a little use will expell all fear . Then , a man may go down with less hazard , and fear in the Ark , then in the Bell , because he may conveniently fasten his hands , to each side of the Ark , if need were . He may conveniently sit , as in a Chair , all the time of down going , and up-coming , by fixing a little seat in it : he may have windows to look out at : his body may be so fixed , that there needs be no fear of falling out . If a man were desirous to make Hydrostatical conclusions , by Diving under the VVater , the dimensions of the Ark might be enlarged , so that it might conveniently cover a mans whole body , by which means , having much Air in it , a Diver might continue under Water half a day , if need were . Let us suppose then , the hight of it to be 8 foot , and the breadth 3 foot , or more . In such a case , a man might continue under the VVater many hours ; and yet not one part of his body wet : for if the Ark be 8 foot high , and the man 5 foot in stature , at the deepness of 10 fathom , the Water can scarce rise 3 foot in it . But why may not a man come up every half hour , when he finds difficulty to tarry down in a little Ark ? I answer , he may ; but it 's trouble and pains to pull him up , and let him down so frequently . And it may so happen , that through want of Air in a small Ark , he be necessitated to come up before he end his work . And leaving the work imperfect , he may find difficulty in the second down going , to find sometimes the place where he was , or the thing he was about to lift , v. g. a chest of Gold. If it be said , that a great weight of Stone or Lead is required to sink an Ark 8 foot high , which will amount to 4032 pound weight . I answer , 't is so indeed : but here is the advantage ; when it is once below the Surface , there 's little more trouble , then with an Ark of lesser dimensions ; because of the equipondium that's between it , and the weight , that sinks it . In such a Vessel many trials might be made . As first , that of the Torricellian-Experiment , which is nothing else , but a Glass-Tub so many inches long , with a Mercurial Cylinder in it of 29 inches high , that 's supposed to be kept up at that hight by the Pressure of the Air. If this were taken down about 34 foot , 't is very probable the Mercury would rise other 29 inches . The reason is , because the Air within the Ark , that presseth upon the Surface of the stagnant Mercury , must be under as much pressure again , as the Air above ; but the Air above , is able to support 29 ; therefore this Air must sustain 58. The reason why the Bensil is exactly doubled is this , 34 foot of Water hath exactly as much Pressure in it , as the whole element of Air ; therefore , the Air within the Ark , being 34 foot down , must not only have in it the Pressure of the Air above , but the Pressure of the Water likewise : this necessarily follows , because when two Fluids touch , or are contiguous to other , the one cannot be under five degrees of Pressure , unless the other be under as many . According to this reasoning , if the Ark go down 68 foot , the Mercury will rise from 58 to 87. If to 102 , it rises 116. This reckoning is founded upon this , namely that Water is 14 times lighter than Mercury ; and therefore one inch of Mercury requires 14 of Water to support it in a Tub , and therefore , before Water is able to raise 29 inches of it , the Pipe must be 34 foot deep . For a second trial , blow a Bladder as full of wind as it can hold , and having knit the neck about with a Pack-threed , place it in the Ark , and you will find the sides , that hath been stifly bended become flaccid and feeble , as if the one half of the Wind had gone out , and this will come to pass , before the Ark can go down eight or nine fathom . The strong bensil of the Air within the Ark is the cause of this : for as the Ark goes down , the Air grows stronger , and so at length becomes of that power and force , that it easily overcomes the force and Bensil of the Air of the Bladder , and reducing it to less room , causes the sides become flagging . In this case , the said Air , that was oval , and had the form of the Bladder , must become round in form of a Globe , because of the uniform Pressure , that it suffers from the Air of the Ark. When once the Ark is down 14 or 15 fathom , take the same bladder , and blow it stiff with Wind , and knit the neck as afore . And you will find that in the up-coming , the sides of it will burst asunder with a noise . When the Bladder is thus full of Wind , 't is supposed , that there is a sort of counterpoise between it , and the Air of the Ark. But as the Ark ascends , the Air of it , becomes weaker and weaker , while in the mean time , the Air of the Bladder suffers no relaxation ; therefore , when the Ark comes near the surface , there arises a great disproportion between the one Air and the other , as to strength , and therefore the Air of the Bladder being the strongest , rents the sides in pieces , and comes out with a noise . Or , blow it but half full of wind , and you will find before , the Ark come near to the top , the said Bladder to be bended to the full . For a third trial , take a Glass , such as they use in Caves , for preserving of Brandy , and stopping the mouth closely , take it down with you in the Ark ; and you will see , the sides of it break in pieces , before you go down four or five fathom . The strong Bensil of the ambient Air , is the cause of this . If you take it down with the orifice open , no hurt shall befal it . Or if you stop the orifice in the up-coming , you will find the same hurt come to it . But here is the difference , in the first bursting , the sides are prest inward , by the ambient Air ; in the second , the sides are prest outward , by the Air within the Glass . For a fourth trial , take a round Glass-bottle , pretty strong in the sides , and when it is down with you in the Ark 14 or 15 fathom , stop the mouth of it exactly , and when it comes above , you will find a considerable quantity of Wind come out of it , when the orifice is opened . This evidently demonstrats , that the Air within the Ark , 12 , 13 , or 14 fathom down , is under a far stronger Bensil then the Air above . For a fifth trial , let a man apply to his skin a cold Cupping-Glass , when he enters the Ark ; and he will find such a swelling arise within it , as when it is applied hot by a Chyrurgion . This tumor begins to rise , assoon as the Ark begins to go down . The reason is evident from unequal Pressure , the parts within the Glass being less prest , than the parts without . For a sixth trial , take a common Weather-Glass , and Place it in the Ark , and in the going down , you will see the liquor cre●p up in it , by degrees , as the Ark goes down , as if some extraordinary cold , were the cause of it . And as the Ark comes up by degrees , the said liquor creeps down by degrees . The cause of this Phenomenon is not cold , as some might judge , but the strong Bensil of the Air within the Ark , that so presseth upon the surface of the stagnant Water , that it drives it up . If you take with you , a Weather-Glass , hermetically sealled , no such thing will follow ; because the outward Pressure is keeped off . 'T is not then cold , that 's the cause , but weight . By the way take notice , that all common Weather-Glases are fallacious and deceitful ; because the motion of the Water in them , is not only caused by heat , but by the weight of the Air , which sometimes is more , and sometimes less , as frequently I have observed , and as hath been observed by others . This difference is found , by the alteration of the altitude of the Mercurial cylinder , in the Baroscope , which is more and less , as the Pressure of the Air changeth . In fair weather , and before it comes , the Mercury creeps up . In foul and rainy weather , and a pretty while , before it fall out , it creeps down . Because in fair weather , the weight of the Air is more , than in rainy and dirty weather . December , 13. 1669. I found the altitude 29 inches , and nine ten parts of an inch : at this time the heavens were covered with dry and thick clouds , and no rain followed . March 26. 1670. I found the altitude no more , than 27 inches , and nine ten parts , at which time , there was a strong Wind with rain . Between these two termes of altitude , I have found the Mercury move near a twelve moneth . 'T is a most sure prognosticator , for if after rain , you find the Mercury creep up in the morning , you may be sure , all the day following will be fair , notwithstanding that the heavens threateneth otherwayes . If after fair weather , the Mercury subside , and fall down a little , you may be sure of rain within a short time , though no appearance be , in the present . It falls down likewise , when winds do blow . What the true cause is , why there is such an alteration in the Pressure of the Air , before foul weather , and fair , and in the time of it , it is not easie to determine . But we proceed . Trial likewise might be made , by firing a great piece of Ordnance above , whether the report would be heard below the Water or not ? This would determine the question , whether Water be a fit medium for conveying sound as Air is . Item , whether or not , the Sea water be fresher at the bottom , than near the top , which is affirmed by some . Item , whether sounds be as distinct in such a small portion of Air , as they are above . This might be tried with a Bell of a Watch. If need were , a little chamber Bell might be hung within the Ark , and a small chord might pass up from it , through the cover , whereby the persons above , might by so many tingles , speak such and such words to the Diver . I have demonstrated before , that though there were a little narrow hole made in the cover above , yet neither Air would go out , nor Water come in . If a man were curious , he might have a window not only in the sides , but in the roof above , covered with a piece of pure thin Glass , thorow which he might look up , after he is down two or three fathom , and see whether there appeared any alteration in the dimensions of the body of Sun or not , or seemed nearer . We now come to infer some Hydrostatical conclusions , as from former Experiments . We see then first , that in Water there is a pressure ; namely from the strong Bensil of the Air within the Ark , that groweth stronger , and stronger , as the Water groweth deeper , and deeper . We see next , that the pressure of the VVater hath an increment : because the further down the Ark goeth , the Air is the more bended . Thirdly , two Fluids cannot be contiguous one to another , unless both of them be under the same degree of pressure : because the Air of the Ark , and the Water that creepeth up within the mouth of it , are perpetually under the same degree of power , and force , whatever the deepness be . Fourthly , that in Fluids the pressure is uniform ; because the Air of the Ark , and the Water without , press most equally , one against the other . Fifthly , the more that the Air is bended , it is the more difficult to bend it ; and consequently , that the diminution of the quantity , is according to unequal proportion . Sixthly , that when the Ark is down 34 foot , the Bensil of the Air is doubled : and tripled , when it s down 68 foot : because the pressure of 34 foot of VVater , is as much as the whole pressure , that 's from the Atmosphere . If it be enquired , how much weight rests upon the palm of a mans hand , when the Ark is down about 68 foot ? I answer , the pressure of the Water upon a mans hand , at that deepness with the pressure of the Air above , will be equivalent to the weight of a pillar of Mercury 87 inches high , and three inches thick , which will exceed in real weight 200 pound . If so much rest upon the palm , how much must rest upon the rest of the parts of the body ? Let us suppose then , the quantity of the palm , to be found in a mans skin , 200 times , then must he suffer as much pressure , and actually support as much burden , as will amount to 40000 pound weight . Seventhly , our bodies may be under a huge pressure , and yet that burden not perceptible ; as is evident from the Diver , who findeth little or no weight , while he is under the Water . Or if there be any Pressure found , it 's not comparable to that , which really is . Eighthly , when a man is 14 or 15 fathom down , at every inspiration and expiration , his breast and belly must lift up the weight of 1800 pound : because , if the whole burden be 40000 , the weight that rests upon the breast , and belly , will be about 1800. Ninthly , that between every inspiration , and expiration , there happens a perfect counterpoise , namely by the Air , that goeth into the lungs , and the outward Air of the Ark : for if the Pressure of the one , were more , than the Pressure of the other , there could be no motion of the lungs . Tenthly , when a man draweth his breath , the Air cometh not in by suction , but by pulsion . For this cause , though the VVind-pipe were stopped , yet a man might live by having a hole in his side , going into the lungs . Lastly , that there is no such thing as suction properly ; and therefore the motion of all Fluid bodies , is caused by Pressure and weight . The motion of the blood then thorow the heart , is driven , and not sucted . Infants properly do not suck , but have the milk squeezed into their mouth . 'T is evident from the sucking-glass that some women use for milking their own breasts : for by help of this , the Air that guardeth the head of the Pap is removed , and so the Air , that presseth the parts about , and without , squeezes out the milk . Fig. 25 Pag. 179 EXPERIMENT XIX . Figure 26. THis Figure represents a deep Water , whose first and visible surface , is FG. The imaginary surface , is ELC , 34 foot below it . ADB is a Siphon , working below this VVater with Mercury . AEL is a Vessel with stagnant Mercury , among which the orifice A is drowned , the other orifice B existing among the Water ▪ DM is the hight of the Siphon above the line of level , which I suppose is 58 inches . For making it work , stop the two orifices closely , and pour in as much Mercury at a hole made at D , as will fill both the legs . Then stopping the said hole , open the two orifices A and B , and you will find the liquor run as long out at B , as there is any almost in the vessel AEL . For evincing this , which is the only difficulty , consider , that if this Siphon , were filled with Water , and made to work only with Air , ( as is clear from daily experience ) the liquor would run out constantly at B. Because there is here an unequal Pressure ; the surface of Air NB , being more burdened , than the surface ELC , but where unequal Pressure is in Fluids ( according to the 12th Theorem ) motion must follow , I prove the surface NB to be more burdened , than the surface ELC , because the Water BD , is heavier than the Water LD , as is evident to the eye . The Air B therefore , sustaining far more weight , than the Air EL , must cede and yeeld . Next , there is here a pondus and a potentia , the pondus is the VVater LD ; the potentia by which it is counterpoised , is the Water BD ; but these are unequal , BD being heavier , than LD ; therefore according to the 33 Theorem , these two Fluids cannot cease from motion . If it be said , that the surface NB is stronger , than the surface ELC , seing it is lower . I answer , the difference is so unsensible , that they may be judged but one . Now , I say , if this Siphon work in Air , with Water , it must likewise , work in Water with Mercury . Therefore , this Siphon being 34 foot below the first sur●ace FG , the liquor must run out constantly at B. Because , there is here , an unequal Pressure , the surface of VVater NB , be●ng more burdened , than the surface ELC. Though there be more weight in NB , than in ELC , because it is lower , yet because the difference is not so much , as is between the weight of BD , and the weight of LD , it proves nothing . Note here , that so long as D , is within 58 inches of EL C , this Siphon will work . The reason is , because the Pressure of 34 foot of VVater , with the Pressure of the Air , upon FG , are able to raise Mercury exactly 58 inches . But if D exceed that hight , no Art will make the liquor run out at B. Note secondly , that this Siphon will operate with Air and VVater , though the top D were 34 foot above M ; and the reason is , because the Pressure of the Air , is able to raise a pillar of Water to that hight . Note thirdly , that if there were an orifice opened at C , upon the level line ELC , the two Waters would become of the same weight , the one not being able to move the other . If you bore a hole at R , the liquor ascends from R to D , and goeth down from D to A , and so the motion ends . But , if the leg AD were six times wider , than BD , the liquor would not run out at B. I shall answer this in the close . From this Experiment we see first , that the motion of Fluid Bodies up thorow Pumps , and Siphons is not for shuning vacuity , but because they are prest up violently . We see next , that when the Pressure is uniform , there is no motion in Fluids ; but assoon , as one part is more prest , than another , motion begins : because , this Siphon will not operate , if the orifice be made in C ; but if so be , it be in D , then the motion begins ; because there is here an unequal Pressure , which was not in the other . We see thirdly , that Fluids have a determinate Sphere of activity , to which they are able to press , and no further : because this Water , is not able to press Mercury higher than 58 inches . So the Air cannot raise Water higher than 34 foot . If this Water were 68 foot deep , the Sphere of it's activity would be 116 inches . We see fourthly , that in Fluids there is a Pondus and a Potentia ; and that the inequality of weight between the two , is the only cause of motion . We see fifthly , that as long as this inequality of weight continues , as long continues the motion , because , as long as BD , is heavier than LD , the motion perseveres . We see sixthly , the possibility of a perpetual motion in Fluids ; because the liquor runs perpetually out at B. If it be said , the motion ends , when the stagnant Mercury AEL faileth . I answer , this stop is only accidental , and not essentially from the nature of Fluids . If it be enquired , whether or not , would the Mercury run out at B , upon supposition , the shank LD were twice as wide , as the shank BD ? I answer it would . If it be said that the one is far heavier than the other , namely LD than DB. I answer , weight in Fluids is not counted according to thickness , but according to altitude . EXPERIMENT XX. Figure 27. THis last is for demonstrating the precise and just weight of any Pillar of Air , Water , Mercury , or of any other Fluid body , if some of their dimensions , be but once knowen . AB then is a square Pipe 12 foot high , and six inches in wideness , full of Water , resting upon the surface of Air AC . And EG is a square Pipe 12 foot high , and 12 inches wide , full of VVater , resting upon the surface of Air EF. None needs to doubt , but the two Waters , will be suspended after this manner , even though the orifices A and E were downward , especially if they be guarded with Water , but the demonstrations , will be the more evident , that wee suppose the two Pillars of Water to be suspended as they are . From this Experiment I say first , that the Pillar of Air CD is 168 pound weight , at least ; which I prove thus . The VVater AB is 168 pound : therefore the Air CD , must be as much . I prove the Antecedent , because it 's a Pillar of VVater 12 foot high , and six inches thick : but every half cubical foot of VVater , that containes 216 inches , weighs seven pound : therefore seing the Pillar is 12 foot , it must contain 24 half feet ; but 24 times 7 is 168. The only difficulty is to prove the Connexion , which I do thus , from the seventh Theor. all the parts of a Fluid in the same Horizontal line , are equally prest , but so it is , that the part A , and the part C , are in the same horizontal surface ; therefore the part A , and the part C , are equally prest . But if the part A , and the part C , be equally prest , the Pillar of Air CD , must be as heavy , as the Pillar of VVater AB . I say secondly , that the Pillar of Air FH , weighs 672 pound , I prove it thus . The Water EG weighs 672 pound ; therefore the Air FH , weighs as much . The Antecedent is clear , because EG , is a square Pillar of VVater 12 foot high , and 12 inches thick ; but every cubical foot of VVater weighs 56 pound : but 12 times 56 , is 672. I prove the connexion , as before . All the parts of an horizontal surface , are equally prest ; therefore the part F , must sustain as much burden , as the part E. To proceed a little further , let us suppose the Pipe AB to be 34 foot high , and the Pipe EG to be as much . I assert then thirdly , the Pillar of Air CD to weigh 476 pound , which I prove as before . All the parts of the same surface , are burdened with the like weight , but the part A sustains 476 pound , therefore the part C must support as much . The Connexion is evident , and the Antecedent is so too , because the VVater AB being 34 foot high , and six inches thick , must weigh 476 pound : for , if 216 inches , weigh seven pound , 14688 inches , must weigh 476 pound . I assert fourthly , the Pillar of Air FH to weigh 1904 pound , which I demonstrat by the former Medium . All the parts of a Fluid that ly in the same horizontal surface , are equally prest ; but so it is , that E and F , do so ly ; therefore F must be as much burdened as E ▪ the Water therefore EG , weighing 1904 pound , the Air FH , must weigh as much . For if 216 inches of Water weigh seven pound , 58752 inches ( for so many are in the Water EG ) must weigh 1904 pound . Let us suppose secondly , the Tub AB to be only 29 inches high , and the Tub EG , of the same hight , and that six inches wide , and this 12 inches wide . I affirm then fifthly , the Air CD to weigh yet 476 pound , and the Air FH , to weigh 1904 pound . Because the Pillar of Mercury AB , weighs 476 pound , and the Pillar of Mercury EG , weighs 1904 pound : therefore , if AB be 476 , CD must be as much . And if EG be 1904 ; FH , must be of the same weight . I prove the Mercury AB to weigh about 476 pound , though it be but 29 inches high ; because it is 14 times heavier then Water . For the same cause , doth the Mercury EG weigh about 1904 pound . I say about , because 34 foot , containes 29 inches , more than 14 times . Let it be supposed thirdly , the Pipe EG , ( being 34 foot high , ) to have the one half of it IG , full of Air , and the other half EK full of VVater , I affirm then sixthly , the part E , and the part F , to be yet equally burdened . That 's to say , the VVater EK , that 's now but 17 foot , makes as great a Pressure upon E , as when it was 34 foot . The reason of this , is surely the Pressure of the Air IG , that bears down the Water KE , with the weight of 952 pound , the half of 1904 pound . If it be said according to the Theorem 21 , that there is as much Pressure and weight in the least part of a Fluid , as in the whole ; therefore the Air IG , must be as heavy as EH . I answer IG , is not so heavy as FH , because the Water EK impending in the lower part of the Tub , hath occasioned the Air IG , to expand it self so many inches , by which means , it loseth so many degrees of it's Bensil . If you remove the Water EK , then will the Air IG , be as heavy , as FH ; because EK being Air , it reduceth IG to that same degree of Bensil with it self ; but when the Air E is burdened with the Water EK , it cannot make the Air IG , of that same weight with it self . Let us suppose fourthly , that only eight foot and an half of Water , are in the Tub , namely between E and N. I say then seventhly , that the part E , is as much burdened with it , as when the Pipe was full ; because the 25 foot , and an half of Air NG , is exactly as heavy , as the 25. foot and an half of the Water that 's gone . I prove it thus . The Air E hath the weight of 1904 pound in it self , seing the weight of the surface , is alwayes equal to the weight of the Pillar , but being burdened with the VVater EN , that weighs 476 pound , it cannot press up with more weight then with 1428 pound : and therefore the top of the Water N , must press upon the under part of the Air , that 's contiguous with it , with 1428. If this be , the Air NG , must press down with as much , seing according to the 20 Theorem , it is impossible , that one part of a Fluid , can be under Pressure , unless the next adjacent part , be under the same degree of Pressure . Therefore I conclude , that the 25 foot and an half of Air NG , is as heavy , as the 25 foot and an half of the Water that 's gone . This makes it evident also , that when the Pipe is half full of VVater , as EK , the Air IG , hath the weight of 952 pound . Because E being in it self 1904 , but being burdened with EK 952 , it cannot make the top of the Water K , press upon I with more weight than 952 ; and therefore ( by the 20 Theorem , ) the Air GI , must weigh 952 likewise . I affirm eighthly , that , when the Pipe is full of Water ▪ from E to G , if a man poise it in his hand , he doth not find the weight of the Water EG . And the reason is , because it 's sustained by the part of the surface E. But if the Air E sustain it , my hand cannot sustain it . I find then only the weight of the Tub , but not the weight of the VVater within it . I say ninthly , that when I poise the said Tub , I find the whole weight of the Pillar of Air LM , which is exactly 1904 pound . I prove it thus . The pondus of a Fluid is then only found , when there is not a potentia to counterpoise it , or at least , when the potentia is inferior to the pondus : but there is here no potentia , counterpoising the pondus of the Air LM . Therefore , I must find the weight of it , when I lift up the Tub. The major proposition is clear from the tenth Theorem . It 's evident also , from common experience ; for while a ballance is hanging upon a nail , with six pound in the one scale , and nothing in the other , you will find the whole burden , if you press up that one scale with the palm of your hand . But if so be , there were six pound in the opposite scale , you will not find the first six ; and the reason is , because it is in equilibrio with other six . 'T is just so here , I must find the weight of the Air LM , while I poise the Tub , because it wants a weight to counterballance it . I prove the minor proposition thus . If any thing counterballance the Air LM , it must either be the Air below , namely the part E ; or the Water EG : but neither of the twain can do it . Not the Air E , because it hath as great a burden upon it , as it is able to support , namely the Water EG , that weighs 1904 pound . And for this cause , not the VVater it self , seing all the force it can have to counterballance LM , is from the surface of Air E ; but this is in equilibrio with it already . I said that the Air LM , was exactly 1904 pound weight . This also is evident , because it is just of these same dimensions , with the Air FH . If it be said , the Air LM must be thicker ; seing it's equal to the Tub without ; but the Air FH , is only equal to the Tub within . I answer , it is so indeed ; but here is a solution to the difficulty . I do not find the whole weight of the Air LM , but only as much of it , as is equal to FH . Suppose the Tub to be 12 inches within , from side to side , and 16 without , from side to side . I say then , I find only the burden of so much Air , as answers to the cavity of the Tub , because the rest of these inches , are counterpoised , by as much below , namely by the Air , that environs the orifice E : for it 's supposed , that if the Tub be two inches thick above , it must be as thick in the lips . So that the whole Tub , is not unequally prest , but only so much of it within upon the top , as answers to the cavity . Tenthly , that when the Pipe is but half full of VVater , namely from E to K , I find only 952 pound of the Air LM , though before I found 1904. The reason is , because the one half of it is now counterpoised by the Air IG , and therefore the weight of it becomes insensible . 'T is clear from the sixth assertion , that the Air IG , presseth down with 952 ; therefore it must press up with as much , seing according to the sixth Theorem , the Pressure of a Fluid is on every side . Eleventhly , that when there is only eight foot of VVater and a half in the Tub , namely between E and N , I find only 476 pound of the Air LM . Because in this case , the Air NG counterpoiseth 1428 pound of it . For if the said Air , burden the Water NE , with 1428 pound , as is clear from the seventh assertion , it must likewise press up the Tub with as much , and so counterpoise as much of the Air LM . Twelfthly , that when there is nothing within the Pipe but Air , the whole weight of the Air LM becomes insensible to me . The reason is evident , because it is wholly counterpoised by the Air within the Pipe. I affirm thirteenthly , that the VVater EG , is in equilibrio with the Water AB : that 's to say 1904 pound , is in equilibrio with 476 pound . I prove it evidently , by the first medium ; all the parts of an Horizontal surface , are equally prest ; therefore the part A , sustains no more burden , then the part E , therefore AB , is as heavy as EG , and consequently , the Air CD , must be as heavy , as the Air FH . Lest this proposition may seem to contradict what is already said , I must distinguish a twofold Ballance , according to the third Theorem , one Natural , another Artificial . In the Artificial Ballance , where magnitudes do weigh according to all their dimensions , viz. Longitude , Latitude , and Profundity , the Water AB , and the Water EG , are not in equilibrio together , seing the one is 1428 pound heavier than the other . But in the Ballance of Nature , such as these Pipes are , all the four makes an equipondium together ; because they do not weigh here , according to their thickness , but only according to their altitude . Therefore seing AB is as high as EG , and seing CD is as high as FH , they must all be of the same weight . From the first assertion I infer , that one and the same Fluid , even in the Ballance of Nature , may sometimes be in equilibrio with a lesser weight , and sometimes with a greater , because the Air CD , that weighs really 476 pound , is in equilibrio with the Water AB , that weighs but 168. This is , when AB is supposed to be only 12 foot high . It 's likewise in equilibrio with it , when it s 34 foot high . But how can AB , that 's 12 foot high , press A , with as much weight , as when it s 34 foot high ? I answer by a similitude , when a Cylinder of Wood 12 foot high stands upon a Table , it may burden it as much , as if it were a Cylinder 34 foot high . For , supposing it to be thrust in , between it , and v. g. the ceiling of the room above , it must press down with more weight , then if it were not thrust in . So , this Cylinder of Water AB , that 's but 12 foot high , being prest between the surface A , and the top of the Tub within , must burden A , as much , as if it were 34 foot high ; for being of this hight , it only stands upon the surface , without pressing up the top of the Tub. I infer from the second assertion , that each Pillar in a Fluid hath a determinate weight . This is evident from the determinate weight of AB , that weighs first 168 pound , being 12 foot high , and 467 pound , being 34 foot high , and so of the rest . I infer secondly , that the thicker , and grosser a Pillar of a Fluid be , it is the heavier , ( even in the Artificial Ballance ) and contrariwise , the more slender and thinner it be , it is the lighter . This is evident from the Water AB , six inches thick , that weighs 476 pound , and from the Water EG , 12 inches thick , that weighs 1904 pound . So doth the Pillar of Air CD , weigh less , then the Pillar FH . Here is ground for knowing the certain and determinate weight of a Pillar , in any sort of a Fluid whatsoever . As to Air , its clear and evident , that a four-square Pillar thereof , 12 inches every way , weighs 1904. That 's to say , if it were possible , to take the Pillar of Air FH , in its whole length , from the surface of the earth , to the top of the Atmosphere , and pour it into the Scale of a Ballance , it would be exactly the weight of 1904 pound . Here is a secret : though that same Pillar of Air , were no longer , than 6 or 10 foot , yet the Pressure of it , upon the body , it rests upon , is equivalent to 1904 pound . If this be , ( you say ) what is the weight of Air , that rests upon this Table , that 's 36 inches square ? I answer , it must be as heavy , as a Pillar of Water 34 foot high , and 36 inches thick , which will , by just reckoning , amount to 17136 pound , or to 1071 stone weight . It may be inquired next , what 's the weight of the Air , that burdens the pavement of this parlour , that 's 16 foot square ? I answer 487424 pound . Because it is exactly the weight of a bulk of Water 34 foot high , and 16 foot thick . 'T is to be remembred , that though the Pressure of it , be so much , yet being poured into the scale of a Ballance , it will not weigh so much : for not only as much as fills the room must be taken , but as much as passeth from the pavement to the top of the Atmosphere . According to this method 't is easie to determine the weight of any Pillar of Air whatsoever , provided a man but once know the thickness of it , both the wayes , e. g. there 's a planum 12 inches long , and six inches broad , upon which rests a Pillar of Air. The weight of it then is , just the burden of a magnitude of Water 34 foot in hight , 12 inches in length , and six inches in breadth . Though the weight of any Pillar of Air may be known , by knowing only the dimensions of it , in breadth and length ; yet the weight of a Pillar of Water cannot be known , unless all the three common dimensions of it , be first known . The reason is this , the Pillars of Air , are all of the same hight , but the Pillars of Water in the Ocean , are of different hights : therefore , not only must they be known , secundum longitudinem , & latitudinem , in length and breadth , but secundum profunditatem , that is , according to deepness . 'T is easie to know then , what each particular Pillar weighs . First then , try how much weight is in a cubical foot of Water , and having found this to be v. g. 56 pound , you may determine , that a Pillar of Water 34 foot high , and 12 inches thick , weighs 1904 pound . A Pillar 34 foot high , and six inches thick weighs 476 pound . Note , that in a Cube of Water six inches thick , there are 216 inches , which weighs seven pound . In a Pillar 12 inches thick , and 20 fathom , or 100 foot high , you will find 5600 pound weight . In one , of the same thickness , but 200 fathom high , there are 56000 , fifty six thousand pound weight . In a Pillar three foot square , and 20 fathom deep , there are 50400 , fifty thousand , and four hundred pound weight . Make it 200 fathom high with that thickness , and it will weigh 504000 , five hundred and four thousand pound . But , if according to the Theorem 25 , you consider ▪ the weight of the Air above , it will weigh 521136 , five hundred , twenty and one thousand , one hundred thirty and six pound . A Pillar 12 foot square , and 300 fathom deep , weighs 12096000 , twelve million , ninety and six thousand pound , Lastly suppose there were a bulk of Water 500 fathom deep , and 500 fathom thick , such a magnitude would weigh 8750000000. eight thousand seven hundred , and fifty million of pounds . But if the Pressure of the Air , that rests upon a surface of Water 500 fathom in breadth and length , be taken in , that weighs 119000000 , a hundred and nineteen million of pounds , the total , that the bottom of the sea sustains , must be 8940000000 , eight thousand , nine hundred and fourty million of pounds ▪ or 558750000 five hundred fifty and eight million , seven hundred , and fifty thousand stone weight . I infer from the fifth assertion , that the lightest of Fluids may be brought to an equilibrium with the heaviest . For though Mercury be 14000 times heavier than Air , yet the part of the surface A , is no more prest with the Mercury AB , then the part C is prest with the Air CD . Secondly , that 29 inches of Mercury , are of the same weight with 34 foot of Water . Thirdly , the heavier a Fluid be naturally , it hath the less altitude in the Natural Ballance ; and contrariwise , the lighter it be , it hath the more altitude . This is clear from the Mercury , that 's 29 inches , the Water that 's 34 foot , and the Air , that 's counted 6867 fathom . I infer from the sixth assertion , that two Fluids of different gravities , may make an equilibrium with a third of the same kind . Because the 27 foot of Air IG , and the 17 foot of Water EK , are in equilibrio with the Air FH . I infer secondly , that 17 foot of Air , may be as heavy as 17 foot of Water , because the Air IG , is exactly as heavy , as the Water EK . I infer thirdly , that the Bensil of a Fluid , is a thing really distinct , from the Natural weight of it : because the Pressure of the Air IG , is 952 pound ; but the natural weight of it will not exceed , if it were weighed in a Ballance , two or three ounces . I infer fourthly , that Air cannot suffer dilatation , but it must lose of it's Pressure . Because the Air IG , that ought to weigh 1904 pound , weighs only 952. For understanding this , you must know , that when a Pipe is about half full of Air , and half full of Water , and inverted , so much of the Water falls out , and consequently so many inches doth the Air above it , expand it self . So to make this Pipe that 's 34 foot high , half full of Air and half full of Water , you must pour in about 19 foot of Water , and the 15 foot of Air that 's in it besides , will , when the Pipe is inverted , go up and expand it self to 17 foot , two foot of Water falling out . I infer from the seventh assertion , that when there are two Fluids of different gravities , and weights counterpoising a third , by what proportion the one grows lighter , by that same proportion the other becomes heavier . For , when the VVater EK , that weighs 952 pound , becomes EN , that weighs 476 , the Air above it , that weighed 952 , becomes now 1428 pound . I infer from the eighth , that the pondus of a Fluid , cannot be counterpoised , by two distinct powers . Because the 34 foot of Water EG , cannot be both sustained , by the part of the surface of Air E , and my hand . I infer from the ninth , that the Pressure and weight of a Fluid , may be found , even in its own Element , by sense . Because in poising of the Tub , I find the weight of the Air LM . I infer secondly , that the weight of a Fluid is only found in its own Element , when there is not a potentia to counterpoise the pondus of it , because I find only the weight of the Air LM , because it wants a potentia to counterpoise it . I infer thirdly , that it is very possible even in the Artificial Ballance , to weigh a Fluid in its own Element , and to know the precise weight of it , to a grain . For this cause , take a small chord , and fasten therewith the top of the Pipe G , to the Scale of a Ballance , and the Lead or Stone that makes the counterpoise in the opposite Scale , is the just weight of the Air LM . I infer from the tenth , that by how much the nearer , the potentia of a Fluid , comes to the pondus , by so much the less , is the pondus found , or is sensible . This is clear , because I find less of the weight of the Air LM , it being counterpoised with the Air IG , than before . This follows likewise from the eleventh assertion . I infer from the twelfth , that when the pondus of a Fluid , is counterpoised , by an equal potentia , it becomes altogether insensible . I infer from the last , that two Fluids differing in weight , according to the Libra or Artificial Ballance , may agree in weight , according to the Natural Ballance . I infer secondly , that Fluids in the Ballance of Nature , do not counterpoise one another according to their thickness , but only according to their altitude . Fig. ●● Pag. 1●4 Fig. 24 Pag. 152 Fig. 26. Pag. 182 Fig. 27 Pag. 196 AN ACCOMPT OF Miscellany OBSERVATIONS , Lately made , by the Author of the foregoing EXPERIMENTS . OBSERVATION I. IN May 1669 , there was need of a new Sink , on the east side of Tranent , for winning of Coals . But while the Coal-hewers were in digging down , and had come the deepness of 13 or 14 fathom , they were stopped from working by Damps , or ill Air , that flowed out plentifully from the sides of the sink , wherein there were a great number of Cutters , or rifts , out of which that ill Air came . To try the nature and power of Damps , I took a dog , and fastned him in a bucket , with a small roap , that he might not leap over , and when he had gone down 7 or 8 fathom , he presently begins to howl , and cry pitifully , as if he had been beaten sore with a rod , and a little after , he begins to stagger , and his feet failing him , he falls down , as one overtaken with the Epilepsy , and in going down to the bottom , his eyes turning in his head , they appeared very shining and clear like two large bright Diamonds . Fearing , that the Damp should have killed him out of hand , he was instantly pulled up from the bottom , where he had not tarried 15 seconds of time . And when the bucket had come to the mouth of the sink , he was pulled out , and laid upon the ground , to get fresh Air. When he had lien a while as dead , he begins at last to gape , and gasp , and make some respirations , as if he had been rather expiring , than recovering . Next , he began to stir and move his feet , and after , to raise himself upon his knees , his head staggering and wavering from side to side . After a minut or two , he was able to stand upon his feet , but so weakly , that he was not in capacity to walk or run . Yet at last , being much refreshed , he escaped from us , and ran home , but slowly . In the afternoon , the same Experiment was repeated , with another dog , whose case was the same in all things . But after he was perfectly recovered , for a further trial , we let him down the second time , and suffered him to tarry in the bottom of the sink , about the space of three minuts : but when he was pulled up , and taken out , we found no symptomes of life in him ; and so after half an hour and more , his body began to swell , which ordinarily befalls such , who are killed after this manner . After this , we sent down in the Bucket , a little Chicken , which , when it came near the Damp , presently slapped with the wings , and falling down , turned over and over for a pretty while , as if it had been taken with a vertigo , or giddiness . But by drawing up the Bucket in haste , and bringing the Bird to the fresh Air , it recovered . In the evening , we let down a lighted Candle , but it was soon extinguished , when it came near mid-sink ; for here , rather than in the bottom , was the strongest Damp. Lastly , we let down by a chord , a Brand-iron , with burning Coals , whose flame was soon put out , and after a little while , we perceived the red Coals to be extinguished by degrees ; yet not totally , because , as the Coal-hewers observed , the power of the Damp was not so strong , as before . These Damps then have their ebbings and flowings , which seem to depend upon the weather , or rather upon the situation of the winds , and their force . For 't is observed , that a high South-west wind causeth ill Air in this place ; and that , by reason of much wast ground , that lies upon the South , and South-west hand of this Sink , whence are conveyed under ground by secret passages , which are nothing else but so many rifts and openings , commonly called by the Coal-hewers , Cutters , corrupted and rotten Air , full of sulphurious stems . The reason why these passages are open , and replenished with nothing , but corrupted Air , is this , the Water , that 's ordinarily called the Blood of the Coal , being withdrawn with subterraneous Gutters ( commonly called Levels ) that are digged , and wrought under ground , sometimes a very long way , for drying of the Mines , and the veins of the earth being now empty , there succeeds Air ; which Air , by process of time , and long standing , rots , and contracts a sulphurious quality , which causeth sudden death . Now , when the wind is high , and strong from the South or South-west , that sulphurious Air is driven through the ground ▪ and coming to Sinks and Mines , where men are working , presently infects the place , and hinders the work . 'T is often observed , that the wind and Air under ground , keep a correspondence in their motion , with the wind above ground : and therefore , when the wind is in such a point above , 't is found , that the motion of the Air below runs such a way , and the contrary way , when the wind above ground , is in the opposite point . When there is a free passage between the bottom of the two Sinks , you may observe the wind come down through the one , and running alongst under the ground , rise up thorow the other , even as Water runs thorow a Siphon . For this cause , when the Coal-hewers have done with such a Sink , they do not use to stop it , or close it up , but leaves it standing open , that the Air under ground may be kept under a perpetual motion and stirring , which to them is a great advantage . 'T is very strange to see sometimes , how much Air , and how fresh it will be , even at a very great distance , namely four or five hundred pace , from the mouth of the Sink . This could never be , unless there were a considerable Pressure and weight in it , whereby it is driven forward , thorow so many Labyrinths . And even in the utmost room , where the Coal-hewers are working , the Pressure is as great , as it is above ground , which is found by the Torricellian Experiment . In such a case , the Air cannot press down thorow the Earth and Metalls , therefore the Mercury must be suspended , not by a Pillar from the Atmosphere , but by the Bensil of it . Nay , put the case , that the whole Element of Air were destroyed , and this remaining , yet would it be able to support 29 inches . To shut up this discourse , it is observed by the Coal-hewers , that when there is ill Air in a Sink , a man may perceive distinctly , what is lying in the bottom , so clear and transparent is the Air of it : but when the Damp is gone , the Medium is not so clear . In temperat and cold weather , the Damps are not so frequent . From this Sink , in soft winds , or in Northerly winds , or when it blows from East or North-east , the Damps are driven away . OBSERVATION II. JUpiter upon Wednesday night , at eleven a clock , being 24 of November , 1669 , had the following position with the stars of Gemini . He was so near to the Star C , that to appearance , the points of his rayes did touch it . This Star by looking upon the material Glob , is fixed in the very Zodiack , and in the 13 degree of Cancer , and is the very navel of the following Twine . The Star A is Castor . The Star B is Pollux . The star D , is fixed in the forefoot of the following Twine . From this place he moved , with a retrograde motion , till he came to the 5 of Cancer , about the 20 of February , 1670 , and from that time became Direct in his motion , and so upon the 27 of March , 1670 at 9 a clock , he was in a right line with Canis minor , and the brightest Star in Auriga , and was in a right line with the eastmost shoulder of Orion , and Castor in Gemini , or with that Star , when South-west , that 's highest , and West-most . OBSERVATION III. IT is written in the History of the Royal Society , that such a member of it , whose name I have forgotten , hath found out , among many other curious inventions , this , namely a way for knowing the motion of the Sun in seconds of time : but is not pleased to reveal the manner how . Because such a device may be usefull in Astronomy , and likewise for adjusting the Pendulum Clock , I shall therefore briefly shew , the manner and way how such a thing may be done , as I have tried it my self . I took an Optick Tub , about 12 foot long , only with two Convex-glasses in it , and did so place it in a dark room , by putting the one end , in which was the Object-glass , without the window , and keeping the other within , that I caused the beams of the Sun shine thorow it , which were received upon a white wall four or five foot from the Tub. This image , which was perfectly round , and splendid , did move alongst the wall very quickly , so that in a minut of time , it did advance seven inches and a half , which will be the eight part of an inch in a second , a motion very sensible . Now , this beam that came thorow the Tub , and lighted upon the wall , would not have moved one inch in a minut , if it had wanted the two Glasses ; for as they magnify , and seem to bring nearer the Object , so they quicken the motion of it . In a word , by what proportion the Object is made more , by that same proportion is the motion quickned . 'T is to be observed , that the longer the Tub be , the motion is the swifter : for as the longest Tub doth ordinarily most magnify the object ; so doth it most quicken the motion . Next , the farther distant the white wall is from the end of the Tub , the larger is the image ; and contrariwise , the nearer it be , it is the less . Thirdly , the farther the wall be from the end of the Tub , the circumference of the image is the more confused , and the nearer it be , it is the more distinct . Fourthly , the darker the room be , it is so much the better . Lastly , this trial may be made with ordinary Prospects , of a foot , two foot , or three foot long , which will really do the thing , but not so sensibly , unless the glasses be very good . As to the use of this device in Astronomy , I shall not say much . But shall only mention what it may serve for in order to the Pendulum Clock . For this cause , let a man choise a convenient room , with a window to the South , wherein this Tub may be so fixed , that it may ly just , or very near to the true meridian , and may move vertically upon an axil-tree , because of the Suns declination every day . Then at a certain distance from the end of it , fix and settle a large board of timber , smooth , and well plained , and well whited , for receiving the image . In the middle of this board , draw a circle with Charcoal , equal in diameter to the circle of the image . Now , this being done , you will find that assoon as the west side of the Sun , begins to come near to the Meridian , the image begins to appear upon the board , like the segment of a circle , and grows larger , and larger , till it become perfectly round . Now in the very instant of time , wherein the image , and the circle are united , set the wheels of your Clock a going , from the hour , minut , and second of XII . To morrow , or 3 or 4 dayes after , when you desire to make an examination , wait on about 12 a clock , when the Sun is coming to the Meridian , and you will find what the difference is . If the Clock go slow , observe , assoon as the image is united with the circle ( which you will perceive in a second of time ) the variation , that 's to say , how many seconds interveens between that second , wherein the union fell , and that second , that closes XII hours in the Clock . If it go fast , observe how many seconds passes from that second , that ends XII hours , and that wherein the image of the Sun is united with the circle , which if you do , you will know exactly , what the difference is , even to a second . But without this , you will find great difficulty to know the variation in 15 or 20 seconds , especially in a common Dial. But here , you will see distinctly the image of the Sun move every second of time , the eighth part , or the sixth part , or the fourth part of an inch , according to the length of your Tub , and goodness of your glasses . 'T is to be observed , that in adjusting the Pendulum Clock , respect must be had to the table of Equation of dayes , commonly known in Astronomy . For if this be not , it is impossible to make it go right , and that because all the natural dayes of the year , are not equal among themselves : that 's to say , the time that 's spent by the Suns motion from the Meridian this day , to the same Meridian , the next day , is not equal , but is more or less , than the time spent betwixt Meridian and Meridian , a third or fourth day after . For instance , the Sun this day being 11 of Iuly , comes sooner to the Meridian by three seconds of time , than he came yesterday . Within 9 or 10 dayes , ( suppose the 22 of Iuly ) he will be longer in coming to the Meridian by 4 seconds , than upon the 21. This difference I grant , in short time is not sensible , yet once in the year , it will amount to more than half an hour . This inequality of dayes arises from two-causes . First , from the Suns eccentricity , whereby he moves slowlier in one part of the Zodiack , than in another : for in Summer when he is furthest from the Earth , he goes slowlier back in the Ecliptick , than in Winter , when he is nearer to it . The second cause , which is truly the far greater , is this , because in the diurnal motion of the Sun , equal parts of the Aequator , does not answer to equal parts of the Zodiack . Hence it followes , that if the natural dayes be not equal among themselves , the hours must be unequal also : but this is not considerable . By help of such a Tub placed in a dark room , it is easie , when the Sun is under Eclipse , to enumerat distinctly the digits eclipsed . Likewise , if you take out the object Glass , and cover a hole in the window board with it , you shall see distinctly upon a white wall , the species and true representations of all objects without . And by comparing the quantity of the object without , with the quantity of it within , you may know the distance of it from the window , though it were many miles . For as the one quantity , is to the other , so is the distance between the Glass and the object on the wall , to the distance between the Glass and the object without . It may be inquired whether or not , the retrograde , as well as the diurnal motion of any of the Planets , may be discerned , in minuts or seconds , by the help of a long Telescope ? In answer to this , we must suppose the Planets only to have a retrograde motion , and consequently to move slowly from West to East , Saturn once in 29 years , or 30 , to run about the Zodiack ; Iupiter in 12 , Mars in 2 years , the Sun in one year , Venus and Mercury in less time , and lastly the Moon in a moneth . Now I say , it is impossible by the longest Tub , that the greatest Artist can make , to discern the motion of the inferior Planets , far less the motion of the superior , either in Minuts or in Seconds , and that by reason of the great tardity , and slowness of the motion . Notwithstanding of this , I am induced to think , that the retrograde motion of the Moon might be discerned , at least in Minuts . For evincing of this , let us suppose which is true , that the Sun runs from East to West half a degree in two Minuts of time , seing in an hour he runs 15 degrees . Next , that the Moon goes about the Zodiack in 27 dayes and 7 hours , namely from that same point , to that point again , and consequently runs back every day 13 degrees and about 10 Minuts . By this account , she must retrograde half a degree , and about 2 minuts of a degree every hour . The Sun then runs half a degree in two Minuts , and the Moon half a degree in 60 Minuts ; therefore the Moon must be 30 times slower in her retrograde motion , than the Sun is in his diurnal motion . Let us suppose next , as I observed with a Tub 12 foot long , that the image of the Sun runs the eighth part of an inch every second , and consequently , seven inches and an half , in a Minut : then must the image of the Moon with that same Telescope , run the thirtieth part of seven inches and a half in a Minut , seing she runs 30 times slowlier ; therefore in every Minut of time she must advance the fourth part of an inch , which will be very sensible . Though we grant , that the Moon hath no retrograde motion properly , yet by comparing the diurnal Motion of the Moon , that 's slower , to the diurnal motion of the Sun , that 's swifter , we shall really find the thing it self . Therefore in the time of a Solar Eclipse , this retrograde motion is conspicuous , which by an ordinary Telescope may be discerned in Minuts . Assoon then as the East side of the Moon , begins to enter upon the West side of the Sun ( the greater the Eclipse be , it is the better ) observe , and you will find the one image , which will be black , cover the other by degrees , that 's splendid , and run in every minut of time , the fourth part of an inch of the Suns diameter , provided alwayes , that the Sun run the eighth part of an inch in a second . OBSERVATION IV : UPon Tuesday the 19. of Iuly 1670 , the following Experiment was made . In the middle Marches between Scotland and England , there is a long tract of Hills , that run from Flowdon , many miles South and South-west , amongst the which , the Mountain Cheviot is famous beyond , and conspicuous above all the rest for altitude , from whose top a man may discern with one turning of his eye , the whole Sea-coast from New-castle to Berwick , much of Northumberland , and very many Leagues into the great German Ocean : the whole Mers and Teviotdale , from the foot of Tweed , to very near the head of it : Lauderdale , and Lammer-moor , and Pentland hills above Edinburgh . The North side of this Mountain is pretty steep , yet easie to climb , either with men or horse . The top is spacious , large and broad , and all covered with a Flow-moss , which runs very many miles South . When a man rides over it , it rises and falls . 'T is easie to thrust a Lance over the head in it . The sides of this Hill abounds with excellent Well-springs , which are the original of several Torrents , amongst the which Colledge-Water is famous , upon which , not a mile from the foot of this Mountain is White-hall . The adjacent Hills are for the most part green , and excellent for the pasturage of Cattel . Not many years ago , the whole Valleys near the foot of Cheviot , were Forrests abounding with Wild-Deer . Upon the highest part of this Mountain was erected the Torricellian Experiment for weighing of the Air , where we found the altitude of the Mercurial Cylinder 27 inches and an half . The Air was dry and clear , and no wind . In our Valley-Countreys , near to the Sea-Coast , in such Weather , we find the altitude 29 inches and an half . When this difference was found , care was taken to seal up closly with Bee-wax , mixed with Turpentine , the orifice of the Vessel , that contained the stagnant Mercury , and thorow which the end of the Pipe went down . This being done with as great exactness as could be , it was carried to the foot of the Mountain in a Frame of Wood , made on purpose , and there opening the mouth of the Vessel , we found the Mercury to rise an inch and a quarter higher than it was . The reason of this strange Phenomenon must be this , namely a greater Pressure of the Air at the foot of the Hill , than upon the top : even as there is a greater Pressure of Water in a surface 40 fathom deep , than in a surface 20 fathom deep . 'T is not to be doubted ▪ but if the root of the Mountain had been as low as the Sea Coast , or as the surface of Tweed at Kelso , the Mercurial Cylinder would have been higher . This way of observing , seems to be better than the common : for while the Baroscope is carried up and down the Hill , without stopping the orifice of the Vessel , that contains the stagnant Mercury , the Cylinder makes such reciprocations , by the agitation of a mans body , that sometimes abundance of Air is seen to ascend up thorow the Pipe , which in effect makes the Cylinder shorter than it ought to be . But if so be , the end of the Pipe be immerged among Quick-silver , contained in a Glass with a narrow orifice , so that it may be stopped compleatly , you will find no reciprocations at all . And to make all things the more sure , the Glass may be filled up either with Mercury , or with Water above the Mercury ; by which means the Cylinder in the down-coming , or in the up-going shall remain immoveable . Besides the stopping of the orifice of the said Glass , you may have a wider Vessel , that may receive the same Glass into it , and it being full of Water , may so cover the sealed orifice , that there shall be no hazard of any Air coming in . Or this Experiment may be first tried at the root of the Hill , and having stopped compleatly the mouth of the Vessel , the whole Engine may be carried up to the top , where you will find the Mercury subside and fall down so much ; namely after the said orifice is opened : for as the stopping of the orifice at the root of the Hill , is the cause , why that same degree of Pressure remains in the stagnant Liquor ; so the opening of it upon the top of the Hill , is the cause why it becomes less . This Experiment lets us see , that the Pressure of the Air seems to be as the Pressure of the Water , namely the further down the greater ; and the further up the less : and therefore , as by coming up to the top of the Water , there is no more Pressure , so by coming up to the top of the Air , there is no more weight in it ; which in effect sayes , that the Air hath a determinat hight , as the Water hath . From this Experiment we cannot learn the determinat hight of the Air , because the definit hight of the Mountain is not known . I know there are some , who think that the Air is indefinitly extended , as if forsooth , the Firmament of fixed Stars were the limits of it , but I suppose it is hard to make it out . OBSERVATION V. JUne 5. 1670. I observed the Sun within 3 minuts of setting , to have a perfect oval figure , the two ends lying level with the Horizon . His colour was not red as ordinarily , but bright and clear , as if he had been in the Meridian : neither was the Sky red , but clear also . And by the help of the Pendulum Clock , I have observed his body to be longer in setting than it ought , by eight minuts , and sometimes by ten , and his Diameter longer in going out of sight than it ought , by two , and sometimes by three minuts . The reason of these Phenomena , must be the Refraction unquestionably . OBSERVATION VI. UPon Saturday evening the 30 of Iuly 1670 , and the night following , till about two a Clock in the Sabbath morning , there fell out a considerable rain , with great thunder , and many lightnings . About Sun-set , the convocation of black clouds appeared first towards the Horizon in the South-west , with several lightnings ; and the wind blowing from that point , carried the clouds and rain over Mid and East-Lothian , towards the Firth and Sea-coast . About 9 a clock , the whole Heavens almost were covered with dark clouds , yet the rain was not very great , neither were the thunder claps frequent , but every fifth or sixth second of time , a large and great lightning brake out . But before the thunder crack was heard , which happened every fourth o● fifth minut , the lightning was so terrible for greatness , and brightness , that it might have bred astonishment . And because the night was very dark , and the lightning very splendid , a man might have perceived houses and corn-fields at a great distance . And if any had resolved to catch it , in the breaking out , it did so dazle the eyes , that for half a minut , he was not able to see any thing about him . Sometimes the lightning that went before the thunder , brake forth from the clouds , like a long spout of fire , or rather like a long flame raised high , with a Smiths Bellow● , but did not continue long in sight . Such an one above the Fi●th was seen to spout downward upon the Sea. Sometimes there appeared from the one end of the cloud to the other , an hiatus , or wide opening , all full of fire , in form of a long surrow , or branch of a River , not straight , but crooked . I suppose the breadth of it , in it self , would have been twenty pace and more , and the length of it five or six hundred pace : the duration of it , would have been about a second of time . Sometimes a man might have perceived the nether side of the cloud , before the crack came , all speckled with streams of fire , here and there , like the side of an Hill , where Moor-burn is , which brake forth into a lightning . But there was one , after which followed a terrible thunder crack , which far exceeded all the rest , for quantity and splendor . It brake out from the cloud , being shot from North to South , in form of fire from a great Cannon , but in so great quantity , as if a Gun ten foot wide , with 500 pound weight of Powder in it , had been fired . And surely the lightning behoved to be far greater in it self , seeing it appeared so great , at so great a distance . It did not evanish in an instant , like the fire of a Gun , but continued about a second and an half ; by reason ( it seems ) that it could not break out all at once . This did so dazle the sight , that for half a minut almost , nothing was seen , but like a white mist flying before the eyes . The whole Countrey about was seen distinctly . All these great lightnings were seen a considerable time , before the crack was heard . Sometimes 30 seconds numbered by the Pendulum Clock interveened , namely when the thunder was at a distance , about 7 or 8 miles . Sometimes 15 or 16 only interveened . But when the thunder was just above our head , no moe passed , than 7 or 8 , which seems to demonstrat , that these thick black clouds , out of which the thunder breaks , are not a Scottish mile from the earth , when they are directly above us . 'T is observable , that in all lightnings , and thunderings , there is no smoke to be seen , which seems to evince , that the matter whereof they are generated , must be most pure , and subtil . Who knows , but this Countrey , that abounds with Coal , may occasion more thunder and lightnings , than other places , namely by sending up sulphurious exhalations to the middle region of the Air , wherewith the Coal-mines abound . OBSERVATION VII . THis is a method for finding out the true South and North Points , which are in effect very difficult to know . Take therefore four pieces of Timber , each one of them five foot long , and about six inches thick , square-wise . Sharpen their ends , and fix them so in the ground , that they may stand Perpendicular , and as near to South and North , by a Magnetick Needle , as may be . The place would be free of Trees , or of any such impediment , that it may have a free prospect of the Heavens . As for their distance one from another , let the two North-most , and the South-most be two foot asunder : let the two East-most , and two West-most , be but one foot , making as they stand , an oblong quadrangle . For keeping them equidistant above , as well as below , take four bars of Wood , about three inches broad , and one inch thick , and nail them round about upon the four sides , on each side one , so that being nailed on Horizontally , they may make right angles , with the tops of the standards above . There are then for distinctions cause , the North-bar , and the South-bar , that runs East and West , and the East-bar , and the West-bar , that runs South and North , There is here no difficulty in the thing it self , but only in the fancy to conceive it . Besides these four , there must be other four of the same form and fashion , nailed on arder down about the middle of the four standards . Take next some small Brass Wyre strings , such as are used in Virginals , and fix one from the middle of the South-bar , that 's upmost , to the middle of the South-bar just under it . Fix it so , that it may be exactly Perpendicular , which may be done , with a great weight of Lead . Take a second Wyre string , and hang it plumb from the West end of the North-bar , and another from the East end of the same Bar , I mean the Bar that 's nearest to the top . These three strings so fixed , will go near to make an equilateral triangle . Now because the device is for finding out the Meridian by the Stars in the night time , not by any indifferently , but by these that are nearest to the Pole , therefore observe in Iuly and August , when the Guard-stars in the evening begin to come down towards the West , and keeping closs one eye , bring the other somewhat near to the South-most string , and order your sight so , that this string , and the West-most string upon the North side , may catch the foremost Guard-star in the down-coming , when it is furthest West , and there fix it . When the same Star is turning up towards the East , catch it by the South-most string , and the East-most string on the North side , and your work is done , if so be , you divide exactly , between the East-most and West-most , and there hang a fourth string , which with the string upon the South-side , gives you the true South and North. For better understanding , note first , that , when the Guard-stars are coming down , or going up , the Altitude varies quickly , but the Azimuth , or motion from East to West , will not vary sometimes sensibly in two hours almost , which is a great advantage in this case . But when you find out the Meridian with a Plain , and a Perpendicular Stilus , by the shadow of the Sun , if it be not when he is about East and West , the Azimuth alters more than the Altitude , wh●ch is a great disadvantage . Now its certain , the slower the motion be from East to West of any Star , it is the easier to observe , and it is the more sure way . Note secondly , that special care must be had , to cause the strings hang Perpendicular . Note thirdly , that before you begin your Observations , the South-most string must be made immoveable , but the East-most , and West-most , on the other side , must not be so , because as the Stars in going about move from East to West , so must the said two strings be left at liberty , to move a little hither and thither , till the Observations be ended . Note fourthly , that assoon as you perceive sensibly , the foremost Guard-star to decline towards the West , then you must begin to observe , which is nothing else , but to fix your eye so , that the South-most and West-most string , may cover the said Star. And because in coming down , it goes West , therefore , let the West-most string move towards the left hand by degrees , following the Star to its utmost , till it be covered by them both . Follow the same method , in observing the same Star in going up towards the East . Note fifthly , that when you make the two strings cover the Star , that which is nearest to the eye , will appear transparent , and of a larger size , so that you may perceive distinctly thorow it , not only the Star it self , but the other string also , which is a great advantage . This is evident to any , who holds a bended silk threed between their eye and a Star in the night time ; for when you direct your sight to the Star , the string appears like the small string of a Virginal when it trembles . Note sixthly , that in observing in a dark night , you must have a Cut-throat , that by the light of the candle you may perceive the strings . Some other things might be noted , but you will find them better by experience , than they can be exprest here . I named Iuly and August in the evening for observing the Guard-stars , when they are West-most , but there are several other seasons , when this may be done as conveniently . They are East-most in the latter end of October , and beginning of November about 5 or 6 a clock in the morning . If a man were desirous to make this observation quickly , I suppose he might in the end of October , find the said stars West-most in the evening , and East-most the next morning . Besides the Guard-stars , a man may make use of the Polar-star ; for as it goes higher , and lower than the true Pole , by 2 degrees and 26 minuts , so it goes as much to the East , and as much to the West , once in 24 hours . In the end of Iuly , you will find the Polar-star East-most , about 9 a clock at night , and in the end of Ianuary West-most at 9 a clock . Note , that every month , the fixed stars come sooner to the same place by two hours : therefore in the end of August the Polar-star must be West , at 7 a clock at night , and East at 7 a clock in the morning . When the Meridian is found out after this manner , there is no Star or Planet can pass it , but you may know exactly when , be it never so high , or never so low . For there is nothing to be done , but to wait , till the South-most and North-most string cover the body of the Star. If it be the Sun , hold up a white Paper , behind the two strings , and when their shadows do co-incide , and are united , then is his Center in the Meridian . If the Sun do not shine clear , as when he is under mist , or a thin cloud , you may exactly take him up in the Meridian , with the two strings . This Frame will serve as well , to know when any of the North Stars comes South , or North , and consequently when they are highest , and when they are lowest : for being fixed in an open place of the Orchard , there 's no Celestial Body can pass the Meridian , either on the one side , or the other , but it may be catched , what ever the Altitude be , and that most easily . OBSERVATION VIII . THere hath been much inquiry made by some anent the reason , why the dead body of a man or beast , riseth from the ground of a Water , after it hath been there three or four days . But though many have endeavoured to solve the question , yet the difficulty remains ; and in effect it cannot be answered , without the knowledge of the foregoing Doctrine , anent the nature of fluid Bodies . To find out the reason then of this Phenomenon , consider , that all Bodies , are either naturally heavier then Water , as Stone and Lead , or naturally lighter , as Wood and Timber . If they be heavier , they sink : if they be lighter , they swim . Now I say , a mans body immediatly after he is drowned , his belly being full of Water , must go to the ground , because in this case , it will be found specifically or naturally heavier then Water . That 's to say , a mans body , will be heavier , than as much Water , as is the bulk of a mans body . For pleasing the fancy , imagine a Statue to be composed of Water , with all the true dimensions of the person that 's dead , so that the one shall answer most exactly to all the dimensions of the other . In this case , if you counterpoise them in a Ballance , the real body , that 's made up of flesh , blood , and bones , shall weigh down the other . But after this dead body hath lien a short time among the Water , it presently begins to swell , which is caused by the fermentation of the humors of the blood , which goeth before putrefaction , and after three or four dayes swells so great , that in effect , it becomes naturally lighter than Water , and therefore riseth . That is to say , take that body , that is now swelled , and as much bulk of Water , as will be the precise quantity of it , and having counterpoised them in a Ballance , you will find the Water heavier than the body . OBSERVATION IX . UPon Thursday the 25 of August 1670 , the following Experiment was made in a new Coal-sink , on the West side of Tranent . When the Coal-hewers had digged down about 6 or 7 fathom , they were interrupted sometimes with ill Air : therefore to know the power and force of the Damp , we let down within the Bucket a Dog. When he had gone down about 4 fathom , or middle Sink , we found little or no alteration in him , save only that he opened his mouth , and had some difficulty in breathing , which we perceived evidently : for no sooner he was pulled up to the top , where the good Air was , but he left off his gaping . We let him down next to the bottom , where he tarried a pretty while , but no more change we found in him than before . After this we let down a great quantity of Whins , well kindled with a bold flame , but they no sooner came to the middle of the sink , but the flame was in an instant extinguished : and no sooner was the Bucket pulled up , but they took fire again . This was 5 or 6 times tried , with the same success . If we compare this Observation with the first , we will find , that all Damps are not of the same power and force ; but that some are stronger , and kills men and beasts in an instant : and that others are less efficacious , and more feeble , and doth not so much hurt , and that men may hazard to go down into a Sink , where ill Air is , even though fire be sometimes extinguished . We see next , that these Damps doth not alwayes infect the whole Air of a Coal-pit , but only a certain quantity : for sometimes it is found in the bottom , sometimes in the middle . And we see lastly , that they are not alwayes of long continuance : for it is found , that though the Air be ill in the morning , yet it may be good ere night ; and totally evanished ere the next day . We may add , as was noted in the first Observation , that these Damps depend much upon the scituation of the winds , seing in strong Southerly winds , they are frequently in these places . OBSERVATION X. OF these many excellent devices , that have been found out of late , the Air-pump is one , first invented in Germany , and afterwards much perfected in England by that Honourable Person Mr Boyl , who for his pains , and industry in making Experiments therewith , deserves the thanks of all learned persons . Several trials hath been made of late by it , some whereof , are as follows . I took a slender Glass-tub about 40 inches long , closs above , and open below , and filled it with VVater . I next inverted it , and set the orifice of it , just upon the mouth of the Brass-pipe , that bends upward thorow the board , whereon the Receiver useth to stand , and cemented them together . At the first exsuction , the whole VVater in the Pipe fell down , and ran thorow the Brass-conduit to the Pump . Having for a short while stopped the passage , and thrust down the Sucker , I next opened it again , and the Pump being full of VVater , it was driven with a considerable force up thorow the Pipe ; yet was it not compleatly fill'd as before , by reason of some Air , that I saw in the top . After this was done , with pleasure five or six times , I opened the Stop-cock more quickly , than I had used , but the VVater , by this means , was so furiously driven up thorow the Tub , that in effect , it broke the end of it , that was Hermetically sealed ; and the piece that flew off , did hit the seiling so smartly , that it rebounded a very far way . From this we see the reason , why VVater falls not down from Vessels that have narrow necks , though they be inverted , because it 's kept in by the force and power of the environing Air. 'T is observable , that though this Pipe had been 30 foot high , yet the whole VVater in it would have subsided , and fallen down , with one exsuction . The next trial was with the help of a small Receiver , which in effect was a real Cupping-glass . This had a hole made in the bottom of it , and was cemented to the Brass-plate , and the mouth of it looking upward , had a lid for covering of it . I took next the lately mentioned Glass-pipe , and filled it with good Brandy , and having drowned the end of it among stagnant Brandy , I set the Vessel wherein it was within the Receiver , the Pipe coming up thorow the lid , and having cemented it closly , I made the first exsuction , and found no descent of the Liquor from the top of the Tub. At the second , it fell down about an inch . At the third , it fell down four or five . But here appeared a great multitude of small Bubbles of Air , like broken VVater , near the top of the Pipe within . And besides this Phenomenon , there ascended from the stagnant Liquor up thorow the Pipe , an infinit number of small Bubbles , no bigger than Pin-heads , for a very large time . VVith a fourth exsuction , it fell down within two or three inches of the stagnant Brandy . And thinking to make the one level with the other , I made a fifth ; but here appeared a strang effect , namely , not only the whole Brandy in the Pipe subsided , and was mingled with the stagnant Brandy , but at this exsuction , there came a great quantity of Air from the mouth of the Pipe , and rose up thorow the stagnant Liquor in Bubbles . Having made another exsuction , there came yet more Air out , and so copiously , that I thought there had been some seak in the Tub , through which the outward Air had entered ; but knowing the contrary , I continued Pumping a very long time , till I found less and less come out , and at length , after near 30 exsuctions it ceased . This Air to appearance , was so much as might have filled twenty Tubs , every one of them as large , as the Tub it came out of . And surely all of it came out from among the small quantity of Brandy that filled the Pipe , and that environed the mouth of it , I mean the stagnant Brandy , both which would not have been eight spoonful . After this I opened the Stop-cock leasurely to let in the Air to the Receiver ; then did the Brandy climb up the Pipe slowly , till it came near to the top , and there made some little halt , by reason of half an inch of Air that appeared there . But more and more Air coming into the Receiver , that half inch in the top of the Pipe , did so diminish , that it appeared no bigger than the point of a Pin , and was scarcely discernable to the eyes . What a strange and wonderful faculty of dilatation and contraction must be in the Air , seing that which presently had filled the whole Tub , that was 40 inches long , and the sixth part of an inch wide , was contracted to as little room , as the point of a Needle . And by making some new exsuctions , that small Atome of Air did so dilate it self again , that it filled the same Tub , and not only that , but , as formerly , it bubbled out from the mouth of the Pipe several times . 'T is to be observed , that though at the first falling down of the Brandy , it appeared like broken Water , near the top of the Pipe within , yet no such thing was seen the second time it fell down ; the reason is , because by the first exsuctions , it was well exhausted of its aërial particles . Once or twice I found , after the Brandy within the Pipe was well freed of Air , that no exsuctions could make it move from the top of the Tub ; and observed a round Bubble of Air to march up , which when once it came to the top , did separate the one from the other . If this hold good , it seems to prove , that neither Mercury , nor any other Liquor would fall down in Pipes , unless there were Air lurking amongst the parts to fill up the deserted space . From this Experiment we learn , that no person can well apprehend or conceive , how far , and to what bounds the smallest part of Air is able to expand it self . And it proves evidently , that when the Receiver is as much emptied as it can be , by the Art of man , yet it is full of Air compleatly . The third trial was after this manner : I set within the Receiver a little Glass half full of Brandy , and the lid being cemented on , I began to pump , but there appeared no alteration at the first exsuction . At the second , I perceived a great company of very small Bubbles , that for a long time ascended from the body of it , and came to the surface . At the third , they were so frequent , and great , that the Brandy appeared to seeth and boil , and by reason of the great ebullitions , much of it ran over the lips of the Glass , and fell into the bottom of the Receiver . This boiling continued for the space of 7 or 8 exsuctions , and by process of time , the Bubbles grew fewer and fewer , and when about 30 or 40 exsuctions were made , no more appeared . With this same sort of Brandy , I filled the fore-named Pipe , and set it within the Receiver , the mouth of the Tub being guarded with the same sort of Liquor . When it began to subside , there appeared no Bubbles near the top as before : the rea●on seems to be , because the Brandy was well exhausted from its aërial particles . For a fourth trial , I filled the same Tub with Ale , that was only 5 or 6 dayes old , and drowning the end of it among stagnant Ale of the same kind , I began to Pump , and found , that assoon as the Liquor began to subside , from the top of the Pipe , the whole Ale within the Pipe , almost turned into Air , and Froth , and so many large Bubbles came up from the stagnant Liquor , that I thought the whole was converted into Air. It was most pleasant to behold their several forms and shapes , their order and motion . This same Tub being filled with sweet milk , I found very few Bubbles in it , when by the exsuctions , it began to subside . I likewise took a little Glass-viol , and fill'd the half of it full with common Ale , and set it within the Receiver . At the first exsuction , Bubbles of Air began to rise out of it . At the second and third , they did so multiply , that they fill'd the other half of the Glass , and ran over , as a Pot doth when it boileth . And before I could exhaust all the Air out of it , moe than 20 exsuctions passed . For a fifth trial , I filled the often mentioned Pipe with Fountain-water , and when it began to subside by Pumping , I found it leave much Air behind it . But all the exsuctions I made , could not make the Water of the Pipe go so low , as the stagnant Water , by which impediment , I could Pump no Air out of the Pipe , as I did , while I made use of Brandy . This tells us , that either there is not so much Air lurking among Water , as among Brandy , or that the Air among this , hath a more expansive faculty in it , than the Air that lurks among Water . If any think , that it is not true and real Air , which comes from the Brandy , but rather the Spirits of it , which evaporats . I answer , if a man tast this Brandy that 's exhausted of its aërial particles , he will find it as strong , as before , which could not be , if the Spirits were gone , For a sixth trial , I took a Frog and inclosed her within the Receiver . But all the exsuctions I was able to make , could not so much as trouble her . Only , when the Receiver was exhausted , I perceived her sides to swell very big , and when the Stop-cock was turned , to let in the Air again , her sides clapped closs together . I observed likewise , when the Air was pretty well Pumped out , that the Frog had no respirations , or if there were any , they were very insensible . The next day , after she had been prisoner in the Receiver 24 hours , I began again to Pump , and after several exsuctions , her sides swell'd pretty great , and I perceived her open her mouth wide , and somewhat like a Bag endeavouring to come out , which surely hath been some of her noble parts , striving to dilate themselves , the body being freed of all Pressure from the ambient Air. OBSERVATION XI . TAke a slender chord , about 4 or 5 yards in length , and fasten the middle of it to the seiling of a Room with a nail , so that the two ends of it may hang down equally . Take next a piece of Wood , two or three foot long , two inches broad , and one inch thick , and boring an hole in each end of it , put through the two ends of the chord , and fasten them with knots ; but so , that the piece of Wood may ly Horizontal , and be in a manner a Pendulum to swing from the one end of the Chamber to the other . Take next a Bullet of Lead or Iron , about 20 or 24 ounces , and lay it upon the said piece of Wood : but because it cannot well ly , without falling off , therefore nail upon the ends , and the sides of the Timber , four pieces of Sticks , on each end one , and on each side one , as Ledgets , for keeping the Bullet from falling off . All things being thus ordered , draw up the piece of Wood towards the one side of the Room , by which means losing its horizontal position , it will ly declining-wise , like the roof of an house . In this position , lay the Iron Bullet in the upmost end of it , and then let them both pass from your fingers , the one end of the Wood going foremost , and you will find it swing towards the other side of the house , and return again , as a Pendulum . This motion , if the Wood be well guided in its vibrations , will last perpetually , because in its moving down , the Bullet is hurled from the one end of the Wood , to the other , and hits it so smartly , that it begets in it , an impulse , whereby it is carried farder up , than it would be , without it . By this means , the vibrations get not liberty to diminish , but all of them are kept of the same length . In the second vibration , the same Bullet is hurled back again to the other end , and hiting it with all its weight , creats a second impulse , wherewith the Wood is carried , as far up as the point it was first demitted from . Though this may seem a pretty device to please the fancy , that 's many times deceived , while things are presented to it , by way of speculation , yet upon tryal and experience , there will be found , an unspeakeable difficulty : and it 's such an one , that a man would not readily think upon . I said , that when the Wood was let go , and was in passing down , the Bullet in it , would hurl down , and hit the oppsite end , and beget an impulse ; but there is no such thing , for verily , though the Bullet be laid upon a very declining plain Board , whereupon no man could imagine a round body could ly , yet all the time the Board is in swinging , from the one side of the Chamber , to the other , and consequently , sometimes under an horizontal , and somtimes under an declining position , the Bullet lies dead in the place , where you first placed it . This Observation is not so much for a perpetual motion , as for finding out the reason of this pretty Phenomenon , namely , what 's the cause , why the Bullet , that cannot ly upon a reclining Board , while it 's without motion , shall now ly upon it , while it 's under motion ? What is more difficult , and nice , to ly upon any thing , that declines from a levell , than Quick-silver ; yet lay never so much of it upon this Board , while it is swinging , it shall ly dead , and without motion . But no sooner you stop the motion of the wood , but assoon , the Bullet , or the Quick-silver , is hurled , either this way , or that way . OBSERVATION XII . I Find it mentioned by some learned persons , that when a Ship is under Sail , if a stone be demitted from the top of the Mast , it will move down in a line parallel with it , and fall at the root . Some might think , it ought not to fall directly above the place it hang over , but rather some distance behind , seing the Ship hath advanced so much bounds , in the time , wherein the stone is coming down . Likewise , while a Ship is under Sail , let a man throw up a stone never so high , and never so perpendicular , as to his apprehension , yet it will fall down directly upon his head again , notwithstanding that the Ship hath run ( perhaps ) her own length in the time , while the stone was ascending and descending . This experiment I find to hold true , which may be easily tryed , especially when a man is carried in a Boat upon smooth Water , drawn by a horse , as is done in some places abroad . Let him therefore throw up a little Stone , or any heavy Body , and he will find it descend just upon his head , notwithstanding that the Horse that draggs the Boat , be under a gallop , and by this means hath advanced ten or twelve paces in the time . Or while the Boat is thus running , let a man throw a stone towards the brink of the VVater ; in this case he shall not hit the place he aimed at , but some other place more forward . This lets us see , that when a Gun is fired in a Ship under Sail , the Bullet cannot hit the place it was directed to . Neither can a man riding with a full Career , and shooting a Pistol , hit the person he aims at , but must surely miss him , notwithstanding , that though in the very instant of time wherein he fires , the mouth of the Pistol was most justly directed . For remedy whereof , allowance must be granted in the aiming at the mark . VVhile a man throws up a stone in a Ship under Sail , it must receive two distinct impulses , one from the hand , whereby it is carried upward , the other from the Ship , whereby it is carried forward . By this means , the stone in going up , and coming down , cannot describe a perpendicular , but a crooked Line , either a Parabola , or a Line very like unto it . Neither can it describe a perpendicular Line , in coming down from the top of the Mast , though in appearance it seem to do so , but a crooked one , which in effect must be the half of that , which it describes in going up , and coming down . For this same cause , a stone thrown horizontally , or towards the brink of the VVater , must describe a crooked Line also . And a Pistol Bullet shot , while a man is riding at a full Carreer , must describe a Line of the same kind . Note , that a man walking from the Stern of a Ship to the Head , walks a longer way , than in walking from the Head to the Stern . Secondly , a man may walk from the Head to the Stern , and yet not change his place . 'T is observable , that a man under board , will not perceive whether the Ship be sailing , or not , and cannot know when her Head goes about . And it is strange , that when a man is inclosed in a Hogs-head , though he have light with him , yet let him be never so oft whirled about , he shall not know , whether he be going about , or not . OBSERVATION XIII . I Found in a Philosophical transaction lately Printed , that Decemb. 13. 1669 , one Doctor Beal found the Mercury in the Baroscope , never to be so high , as it was then . That same very day , I found the hight of it 29 inches , and nine ten parts , which I never observed before . And though the day here was dark , and the Heavens cove●ed with Clouds , yet no rain for many dayes followed , but much dryness , and fair weather . On Saturday night , March 26 , 1670 , I found the altitude no more than 27 , and nine ten parts . This night was exceeding windy , with a great rain . On February 1. 1671. I found the altitude 30 inches , and the Heavens most clear . But in the most part of May following , I have found the hight but 27 inches , and five ten parts , in which time there was abundance of rain . OBSERVATION XIV . NOvember 7. 1670. I made exact trial , with the Magnetick Needle for knowing the variation , and I found it vary from the North , three degrees and a half , towards the West . Hevelius writes from Dantzick to the Royal Society at London , Iuly 5. 1670 , that it varies with him seven degrees twenty minuts , west . OBSERVATION XV. DEcember . 17. 1669 , I observed with a large Quadrant , half 9 a clock at night , the formost Guard-star , when it was in the Meridian , and lowest , to have 41 degrees 22 minuts of altitude . And on Ianuary 7. 1670 at 7 a clock in the morning , I found it , when it was in the Meridian , and highest , to have 70 degrees , 27 minuts Hence I conclude the elevation of the Pole here to be 55 degrees , 54 minuts , 30 seconds : and consequently as much at Edinburgh ; because both the places are upon one and the same Parallel . OBSERVATION XVI . FOr finding the true Meridian , follow this method . In some convenient place fix two Wyre strings with weights at them , that they may hang perpendicular . Then in the night time , observe , when the fourth star of the Plough begins to come near to the lowest part of the Meridian , at which time you will find the Polar star highest . Then , so order the two strings , by moving them hither , and thither , till both of them cover both the said Stars , then shall they in that position give you the true South and North. This observation is the product of the seventh . OBSERVATION XVII . THere fell out in Mid and East-Lothian , on Thursday May 11 , 1671 , in the afternoon , a considerable shour of hail , with thunder and rain . It came from the South-west , with a great blast of wind , and ran alongs from Picts-land-hills North-east , towards the Sea-coast . The hail were big in several places , as Musquet Ball , and many of them rather oval than round . Some persons suffered great loss of their young Pease ; others of their Glass Windows . Eight or ten days before , there was a considerable heat , and dry VVeather . For 20 dayes after , cold Easterly winds , with rain every day , but especially , in the end of the Moneth , extraordinary rain and mist. This is so much the more to be observed , because in this Countrey , seldom such extraordinary hail falls out . This year the Agues and Trembling Fevers have been most frequent , and to many deadly . OBSERVATION XVIII . I Did hear lately of a curious Experiment in Germany , made by a Person of note , which I shall briefly in this Observation , let the Reader understand . And though I have heard since , that it is now published in Print , yet I hope it will not be impertinent to mention it here , especially for their cause , who cannot conveniently come to the knowledge of such things . And for this reason also , that I may explicat the Phenomena thereof , from the foregoing doctrine , and demonstrat particularly the true cause of that admirable effect , that 's seen in it , which I desiderat in the publisher . The Auctor then takes two Vessels of Brass , each one of them in form of half a sphere , of a pretty large size . Nothing can more fitly represent them for form and quantity , than two Bee-skeps . Only , each of them , hath a strong Ring of Brass upon the Center without : and they are so contrived by the Artist , that their orifices agree most exactly , so that when they are united , they represent an intire Sphere almost . In one of the sides , there 's a hole , and a Brass Spigot in it , through which the whole Air within , is exsucted , and drawn out , namely by the help of the Air-pump . And , when by several exsuctions the Vessels are made empty , the Stop-cock is turned about , by which means , no Air can come in . And , they remaining empty , are taken from the Pump , and do cleave so fast together , that though a number of lusty fellows , 12 on each side , do pull vigorously , by help of ropes fastned to the Rings , yet are they not able to pull them asunder . And because this will not do it , he yokes in 12 Coach Horses , six on every side , yet are they not sufficient , though they pull contrariwise to other , to make a separation . But to let the Spectators see , that they may be pulled asunder , he yokes in 9 or 10 on every side , and then after much whipping , and sweating , they pull the one from the other . The cause of this admirable effect , is not the fear of vacuity , as some do fancy , for if that were , all the Horses in Germany would not pull them asunder , no not the strength of Angels . It must then be some extrinsick weight and force , that keeps them together , which can be nothing else , but the weight of the invironing Air. Because , no sooner a force is applied , that 's more powerful , than the weight of the Air , but assoon they come asunder . And so neither six men , nor six horses on each side are able to do it : but nine or ten on each side makes a separation . For understanding the true cause of this Phenomenon , we must consider that the Vessels are 18 inches in diameter . If this be , then according to the last Experiment , there are two Pillars of Air , each one of them as heavy as a Pillar of Mercury 18 inches thick , and 29 inches long , by which they are united . Or , each Pillar of Air , is as heavy , as a Pillar o● Water 34 foot high , and 18 inches in diameter . For finding the weight of it in pounds , and consequently , the weight of each Pillar of Air , by which the two Vessels are united , follow this method . First , multiply 9 the semidiameter of the Pillar , by 54 the circumference , and this gives you 486 , the half whereof is the bounds of the Area , namely 243. And because 34 foot contains 408 inches , I multiply 408 by 243 , the product whereof is 99144 ; so many square inches are in a Pillar of Water 34 foot high , and 18 inches thick . Now seing there are 1728 inches in a cubical foot , I divide the number 99144 , by this number , and I find 57 square foot of Water , and more . And because every square foot weighs 56 pound Trois , I multiply 56 by the number 57 , and the product is 3192 pound , which is the just weight of a Pillar of Water 34 foot high , and 18 inches in diameter , and which is the just weight also of each Pillar of Air , by which the two Vessels are kept together , which will be more weight than seven Hogs-heads full of Water . This is easily known ; for seing a quart of our measure weighs seven pound , ( or to speak strictly six pound fourteen ounces , seing the Standard-jug of Striviling contains three pound seven ounces of Water ) a gallon must weigh 28 pound : but 16 times 28 , is 448. A Puncheon then full of Water , weighs 448 pound . If then you divide 3192 by 448 , you will find more than 7. The 9 horses then upon this side have 3192 pound weight to draw , or 199 stone , or the weight of seven Hogs-heads full of Water . The other 9 horses upon the other side , have as much to pull . 'T is no wonder then to see so much difficulty and pains to make a separation . It is observed , that before the Air be exsucted and drawn out of the two Vessels , one man is able to pull them asunder with his hands only . Nay , which is more , if he but blow into them , as a man doth into a Bladder , he will separat them . The reason is , because the Air within , is of as great force , as the Air without . 'T is observable next , that the larger the Vessels be in diameter , the more strength is required to pull the one from the other . Upon supposition then , they were 4 foot wide , I verily believe 30 yoke of oxen , upon every side , would hardly disjoyn them ; because the weight of each Pillar of Air , would be no less , than 22844 pound , which would take 63 strong horses to overcome the force of it . To pull the one Vessel therefore from the other , there must be 126 horses , that is , 63 on every side . OBSERVATION XIX . THough this Observation may seem useless , because the Proposals , that are mentioned in it , cannot be made out , and brought to pass , the Author having died , before he had encouragment to prosecute them : yet for these following reasons , I have adventured to insert it here . First , that others , may either be minded to find out ( if possible ) his inventions , or set a work to find out somethings , that may be as useful . Next , because , he was one of this same Nation , and a great Master of the Mathematicks , not only in the Speculative , but in the Practical part chiefly , and admirable for invention . And for this cause principally I have presumed to mention his designs , and proposals , which were found among his Notes , after his death , which are here insert , as they were written with his own hand , and offered to the publick , not only at home , but abroad to strangers . There have been men in all ages famous , for some one Art and Science beyond others , as Apelles for Painting , Hippocrates for Medicine , Demosthenes for Oratry , but who have been more famous in their time than some persons for their profound knowledge in Astronomy , Geometry , and the other parts of the Mathematicks . What an admirable person was Archimedes for his divine knowledge , both in the Speculative , and Practical part . Yet , it was not his speculations simply , though excellent , that did so much commend him , as his Inventions , and admirable Engines for peace and war , as is clear from the Romane Histories , and others . I confess the Students of these Arts , are not so much in request now , at least amongst some , and that knowledge is not so much esteemed ; and the reason may be ; because some who profess themselves great Masters , study nothing but the pure speculations , which sometimes are to small purpose , others before knowing the same , unless for perfecting of the mind , and giving to a man some private satisfaction . But such things will never commend a man so much as the practical part , and new Invention will do . 'T is surely a small business for one to do nothing , but to nibble at some petty Demonstration . But when such speculations are joyned with invention and practice , for the profit , and use of men , among whom they live , then are they far more to be commended . And if this be not , such knowledge is of small advantage to themselves or others . Many of the Ancient , and late Astronomers have been , and are famous for practice , as witness the indefatigable pains they have been at in making their Observations . What hath so highly commended Merchiston over all Europe , as his inventions , especially his Logarithmes ? And if all be true , that 's reported ( which I am apt to believe ) he might have been more renowned , for his many excellent Engines , which though useful , yet because hurtful to mankind , he buried with himself . I am confident , if the Author of these proposals had had time to have prosecuted them , he would have been celebrated in the Catalogue of the most famous Mathematicians of his time . But leaving this , I shall give you them in his own words : but first his Apology . These bold proposals will need perhaps an apology to such , to whom the causes , and circumstances are unknown . Let it suffice , that the Proposer finding himself between two extreams , either to leave unprosecuted this affair , for fear of being mistaken by some , as impudent , or to commit himself openly to the charitable judgement of others , who will suspend their censure , till they have seen what his endeavours will produce . He hath rather chosen this last , especially considering , that his silence could not answer to his duty , which he owes to his Countreys service , seing the following Engines may be so useful to it . A deduction of the fabrick , causes , and occasions of these new Engines , that set the Inventer a-work , would take a long time to discourse upon . This Paper therefore is only destined for a short informat●on of their use , the rest , which could not here be insert without impertinency , may be supplied afterwards ( if need be ) either by a discourse , or by a particular demonstration . The Proposer then is of opinion , ( if self-love of his own Inventions do not blind his Judgement ) that these paradoxes may be truly affirmed . That if it shall please His Majesty to arm with these new Arms , and Engines , 5000 Foot , or fewer , this small number shall be Masters of the Fields in France , Germany , Spain , or where else it shall please His Majesty , however encountered by the most powerful Army of Horse or Foot , armed with ordinary Arms , of Pistol , Carabine , Pike , Musquet , which Europe can bring to the Fields . The cause of this admirable effect , is in the quality of these new Arms , by which , the whole Horsemen and Footmen of the enemy are rendred useless , and unservicable ; neither can they do any offence to these , who are so armed . The Musquetteers , who can only serve against these Machins , shall be put to such disadvantage , as it is impossible they can stand , the least time , in the common way of service with the Musquet , it not being able to make one shot for twenty , which shall be made from these new Engines . These new Arms , have this advantage likewise , that these who are so armed , can by no force of Horse or Foot be broken , or put to disorder . The Souldiers are also by them put to a necessity of keeping together , and fighting , and by them , they are so Baricado'd , and strongly defended , that if they leave them not , they cannot be exposed to danger . This contributes much to good Discipline , when the Souldiers shall by necessity be tied to his duty , and fear , which otherwise makes him run away , shall here for his safety make him stand . These new Arms are useful , as well in Marching , as in Combating , for with them , we may march securely two in front , through the straitest passages , and be able to force with them any advantage a strait passage can give to an enemy . Besides , for a long hasty march , where Victuals cannot be well carried , the Souldiers are able with these Arms to carry their own provision for eight dayes , with more facility , then they can now carry one dayes provision . To lodge in the open fields , these Arms shall need no Intrenching , for they sufficiently both Arm and Baricade the Souldiers . And as they are useful in Service , so are they a great deal cheaper than the ordinary Arms. For although with 5 thousand men so armed , the service of 100000 armed with common Arms may be done , yet the whole price of them will not amount to that which will be required for arming 20500 Corrassiers , as may be particularly deduced , from the particular prices of the Arms , and Engines fitted for the service of 5000 men . The Proposer doth offer to shew , that these Arms will not surmount 40000 pound Sterling . The Artillery will amount to 4500 , and the payments of this number of men so armed , yearly to 70000 pound . Yet all these are taken in so large a latitude of reckoning , as the sum of Arms , Artillery , and payments , will not be much above 130000 pound Sterling . The Arms from which this effect is promised , are new Engines , with which one man is able to do the service of a great many Musquetteers . And those are of two sorts , either to be used upon a small Wagon for Footmen , or on a greater for a Horse , with either of which , one hand is able to make the fire of 100 Musquetteers , and so much better , by how much it is more regularly , and fitly done for execution and offence . The new Cannon shall have the like advantage above the old , both for easie carriage , being lighter , and for greater execution , shooting six , nine , or twelve Bullets for one . These Arms give not only this advantage at Land in the field , but also in Ships , and places of defence . These nine following propositions he likewise offered to make good , First , With one shot of Cannon , to do the execution of five shot of the same Cannon , in the common way of Battery . Secondly , to disable any Ship or Galley with one shot of Cannon . Thirdly , to fire any combustible matter with the shot of a Cannon . Fourthly , to make an Machin or Engine for transporting an Army , which may be carried without the incommodity thereof . Fifthly , to make a flotting Fortress for defence of Rivers , and prohibition of Passages . Sixthly , to make a Mortar that hath a directory Stell upon the Carriage . Seventhly , to make Petards of divers forms , that shall be able to do twice as much execution , as those that contain as much Powder . Eighthly , to make small Petards of great effect . Lastly , to make Bridges , and Scaling Ladders of easie Carriage . OBSERVATION XX. THese Observations being Miscellany , require not a formal connexion between themselves , and therefore 't is no matter what method I keep in setting them down . And though this may seem not so pertinent , as others , yet because the design of it is only Philosophical , and for advancing the Historical part of Learning in order to Spirits , upon which the Scientifical part doth so much depend , I have presumed to insert it here , considering also that there are some , who have adventured to deny their existence , and being ; which from such a History as this , may be more than probably evicted . I find likewise , that several Writers have remarked such strange accidents , and have transmitted them to posterity , which may serve for good use . The subject-matter then of this Observation , is a true and short account of a remarkable trial , wherewith the Family of one Gilbert Compbel , by Profession a Weaver in the old Paroch of Glenluce in Galloway , was exercised . Though the matter be well known to several persons at that time , and since too ; yet there are others , eighteen years interveening , to whom ( perhaps ) such a relation will not be unacceptable , who have either not as yet heard of it , or at least , have not gotten the true information , which is here set down , as it was Written , at the desire of a special Friend , by Gilbert Campbel's own Son , who knew exactly the matter , and all the circumstances , whose words are as follows . It happened in October 1654 , that after one Alexander Agnew , a bold and sturdy Beggar , who afterwards was hanged at Dumfreis for blasphemy , had threatned hurt to the Family , because he had not gotten such an alms as he required : the said Gilbert was oftentimes hindered in the exercise of his Calling , all his Working-Instruments being some of them broken , some of them cutted , and yet could not know by what means this hurt was done ; which piece of trouble did continue , till about the middle of November , at which time the Devil came with new and extraordinary assaults , by throwing of Stones in at Doors and Windows , and down thorow the Chimney-head , which were of great quantity , and thrown with great force , yet by Gods good providence , there was not one person of the Family hurt , or suffered dammage thereby . This piece of new and sore trouble , did necessitat Mr. Campbel to reveal that to the Minister of the Paroch , and to some other Neighbours and Friends , which hitherto he had endured secretly . Yet notwithstanding of this , his trouble was enlarged ; for not long after , he found oftentimes his Warp and Threeds cut , as with a pair of Sizzers , and the Reed broken : and not only this , but their apparel cut after the same manner , even while they were wearing them , their Coats , Bonnets , Hose , Shooes , but could not discern how , or by what mean. Only it pleased God to preserve their persons , that the least harm was not done . Yet , in the night time , they wanted liberty to sleep , something coming , and pulling their Bed-cloaths and Linnings off them , and leaving their bodies naked . Next , their Chests , and Trunks were opened , and all things in them strawed here and there . Likewise , the parts of the Working Instruments , that had escaped , were carried away , and hid in holes and bores of the house , where hardly they could be found again . Nay , what-ever piece of Cloath , or Houshold-stuff , was in any part of the house , it was carried away , and so cut and abused , that the Good-man was necessitated with all haste and speed , to remove , and to transport the rest to a Neighbours house , and he himself compelled to quite the exercise of his Calling , whereby only he maintained his Family . Yet , he resolved to remain in the house for a season . During which time , some persons about , not very judicious , counselled him to send his children out of the Family , here and there , to try whom the trouble did most follow , assuring him , that this trouble was not against all the Family , but against some one person , or other in it , whom he too willingly obeyed . Yet , for the space of four or five dayes after , there were no remarkable assaults , as before . The Minister hearing thereof , shewed him the evil of such a course , and assured him , that if he repented not , and called back his children , he might not expect that his trouble would end in a right way . The children that were nigh by , being called home , no trouble followed , till one of his sons , called Thomas , that was farrest off , came home . Then did the Devil begin afresh ; for upon the Lords Day following , in the afternoon , the house was set on fire , but by his providence , and the help of some people , going home from Sermon , the fire was extinguished , and the house saved , not much loss being done . And the Monday after , being spent in privat Prayer and Fasting , the house was again set on fire upon the Tuesday about nine a Clock in the morning , yet by providence , and the help of Neighbours , it was saved , before any harm was done . Mr. Campbel , being thus wearied , and vexed , both in the day , and in the night time , went to the Minister , desiring him , to let his son Thomas abide with him for a time , who condescended , but withal assured him , that he would find himself deceived , and so it came to pass : for , notwithstanding that the child was without the family , yet were they , that remained in it , sore troubled both in the day time , and in the night season , so that they were forced to wake till mid-night , and sometimes all the night over . During which time , the persons within the Family , suffered many losses , as the cutting of their Cloaths , the throwing of Peits , the pulling down of Turff , and Feal from the Roof , and Walls of the House , and the stealing of their Apparel , and the pricking of their flesh and skin with Pins . The Presbytery having conveened at the place , for a solemn Humiliation , perswaded Gilbert Campbel to call back his Son Thomas , notwithstanding of whatsoever hazard might follow . The Boy returning home , affirmed that he heard a voice speak to him , forbidding him to enter within the house , or into any other place where his Fathers Calling was exercised . Yet he entered , but was sore abused , till he was forced to return to the Ministers house again . Upon Monday the 12 of February , the rest of the Family began to hear a voice speak to them , but could not well know from whence it came . Yet , from evening till midnight , too much vain discourse was kept up with the Devil , and many idle and impertinent questions proposed , without that due fear of God , that should have been upon their Spirits , under so rare and extraordinary a trial . The Minister hearing of this , went to the house upon the Tuesday , being accompanied with some Gentle-men , who after Prayer was ended , heard a voice speaking out of the ground , from under a bed , in the proper Countrey Dialect , saying , Would ye know the Witches of Glenluce ? I will tell you them ; and so related four or five persons names , that went under an evil report . The said Gilbert informed the company , That one of them was dead long ago . The Devil answered , and said , It is true , she is dead long ago , yet her spirit is living with us in the world . The Minister replied , saying , ( though it was not convenient to speak to such a person ) . The Lord rebuke thee Satan , and put thee to silence ; we are not to receive any information from thee , whatsoever fame any persons go under . Thou art but seeking to seduce this Family : for Satans Kingdom is not divided against it self . After which all went to Prayer again , which being ended ( for during the time of Prayer no trouble was made ) the Devil with many threatnings boasted and terrified the Lad Thomas , who had come back that day with the Minister , that if he did not depart out of the house , he would set all on fire . The Minister answered , and said , The Lord will preserve the House , and the Boy too , seing he is one of the Family , and hath Gods warrand to tarry in it . The Devil answered , He shall not get liberty to stay : he was once put out already , and shall not abide here , though I should pursue him to the end of the world . The Minister replied , The Lord will stop thy malice against him . And then they all prayed again , which being ended , the Devil said , Give me a Spade and a Shovel , and depart from the house for seven dayes , and I shall make a grave , and ly down in it , and shall trouble you no more . The Good-man answered , Not so much as a Straw shall be given thee , through Gods assistance , even though that would do it . The Minister also added , God shall remove thee in due time . The Devil answered , I will not remove for you , I have my Commission from Christ to tarry , and vex this Family . The Minister answered , A permission thou hast indeed , but God will stop it in due time . The Devil replied , I have ( Mes. Iohn ) a Commission , that ( perhaps ) will last longer than your own . After which , the Minister and the Gentlemen arose , and went to the place where the voice seemed to come from , to try if they could find any thing . And after diligent search , nothing being found , the Gentlemen began to say , We think this voice speaks out of the children , for some of them were in their beds . The Devil answered , You lie , God shall judge you for your lying , and I and my Father will come and fetch you to hell , with Warlock-theeves ; and so the Devil discharged the Gentlemen to speak any , saying , Let him speak that hath a Commission ( meaning the Minister ) for he is the Servant of God. The Gentlemen returning back with the Minister , they sat down near to the place whence the voice seemed to come from , and he opening his mouth , spake to them , after this manner . The Lord will rebuke this Spirit , in his own time , and cast it out . The Devil answering , said , It is written in the 9 of Mark , the Disciples could not cast him out . The Minister replied , What the Disciples could not do , yet the Lord having hightned the Parents faith , for his own glory did cast him out , and so shall he thee . The Devil replied , It is written in the 4 of Luke , And he departed , and left him for a season . The Minister said , The Lord in the dayes of his humiliation , not only got the victory over Satan , in that assault in the wilderness , but when he came again , his success was no better , for it is written , Joh. 14. Behold the Prince of this world cometh , and hath nothing in me ; and being now in glory , he will fulfill his promise , and God shall bruise Satan under your feet shortly , Rom. 16. The Devil answered , It is written , Mat. 25. There were ten Virgins , five wise , and five foolish ; and the Bridegroom came : The foolish Virgins had no Oyl in their Lamps , and they went unto the wise to seek Oyl ; and the wise said , Go and buy for your selves : and while they went , the Bridegroom came , and entered in , and the door was shut , and the foolish Virgins were sent to hells fire . The Minister answered , The Lord knows the sincerity of his servants , and though there be sin and folly in us here , yet there is a fountain opened to the house of David for sin and for uncleanness , and when he hath washed us there , and pardoned all our sins , for his Names sake , he will cast the unclean spirit out of the land . The Devil answered and said , That place of Scripture is written in the 13 of Zechariah , In that day I will cause the Prophets , and the unclean spirit , pass out of the land ; but afterwards it is written , I will smite the Shepherd , and the Sheep shall be scattered . The Minister answered and said , Well are we , that our blessed Shepherd was smitten , and thereby hath bruised thy head ; and albeit in the hour of his sufferings , his Disciples forsook him , Mat. 26. yet now having ascended on high , he sits in glory , and is preserving , gathering in , and turning his hand upon his little ones , and will save his poor ones in this Family from thy malice . The Minister returning back a little , and standing upon the floor , the Devil said , I knew not these Scriptures , till my Father taught me them . I am an evil Spirit , and Satan is my Father , and I am come to vex this house ; and presently there appeared a naked hand , and an arm , from the elbow down , beating upon the floor , till the house did shake again ; and also the Devil uttered a most fearful and loud cry , saying , Come up Father , come up : I will send my father among you . See , there he is behind your backs . The Minister said , I saw indeed an hand , and an arm , when the stroak was given , and heard . The Devil said to him , Saw you that ? It was not my hand , it was my fathers ; my hand is more black in the loof . Would you see me ? Put out the candle then , and I shall come butt the house among you like fire-balls . After which all went to Prayer , during which time , it did no harm , neither at any other time when God was worshipped . When Prayer was ended , the Devil answered and said , Mes John , if the Good-mans sons prayers at the Colledge of Glasgow , did not prevail more with God , than yours , my father and I had wrought a mischief here ere now . To which one of the Gentlemen replied , though a check had been given him before , Well well , I see you confess there is a God , and that prayer prevails with him , and therefore we must pray to God , and will commit the event to him . To which the Devil replied , Yea Sir , you speak of prayer , with your broad lipped Hat ( for the Gentleman had lately gotten a new Hat in the fashion with broad lips ) I 'le bring a pair of Shears from my father , that shall clip the lips of it a little . The night now being far spent , it was thought sit every one should withdraw to his own home . Then did the Devil cry out fearfully , Let not the Minister go home , I shall burn the house if he go ; and many other wayes did he threaten . And after the Minister was gone forth , the Good-man being instant with him to tarry , whereupon he returned , all the rest of the company going home . Then said the Devil to the Minister , You have done my bidding . Not thine , answered he , but in obedience to God , have I returned to bear this man company , whom thou dost afflict . Then did the Minister call upon the Name of God , and when Prayer was ended , he discharged Mr. Campbel , and all the persons of the Family , from opening their mouth , in one word to the evil spirit , and when it spake , that they should only kneel down , and speak to God. The Devil then roared mightily , and cryed out , What ? Will ye not speak to me ? I shall burn the house , I shall strike the bairns , and do all manner of mischief . But after that time , no answer was made to it , and so for a long time no speech was heard . After this , the said Gilbert suffered much loss , and had many sad nights , not two nights in one week free ; and thus it continued till April . From April to Iuly , he had some respite , and ease . But after , he was molested with new assaults : and even their Victuals were so abused , that the Family was in hazard of starving ; and that which they did eat , gave them not the ordinary satisfaction they were wont to find . In this sore and sad affliction , Mr. Campbel resolved to make his address to the Synod of Presbyters , for advice and counsel what to do , which was appointed to conveen in October 1655 , namely whether to forsake the house and place , or not ? The Synod by their Committee , appointed to meet at Glenluce in Feb. 1656 , thought fit , that a solemn Humiliation should be kept thorow all the bounds of the Synod , and amongst other causes , to request God in behalf of that poor afflicted Family , which being carefully done , the event was , through the Prayers of his People , that his trouble grew less till April , and from April to August , he was altogether free . About which time , the Devil began with new assaults , and taking the ready meat that was in the house , did sometimes hide it in holes by the door-posts , and at other times did hide it under the beds , and sometimes among the Bed-cloaths , and under the Linnings ; and at last , did carry it quite away , till nothing was left there , save Bread and Water to live by . After this , he exercised his malice and cruelty against all the persons of the Family , in wearying them in the night time , with stirring and moving thorow the house , so that they had no rest for noise , which continued all the moneth of August after this manner . After which time , the Devil grew yet worse , and began with terrible roarings , and terrifying voices , so that no person could sleep in the house , in the night time , and sometimes did vex them with casting of stones , striking them with staves on their beds in the night time : and upon the 18 of September , about midnight , he cried out with a loud voice , I shall burn the house ; and about three or four nights after , he set one of the beds on fire ; which was soon extinguished , without any prejudice , except the bed it self : and so he continued to vex them . OBSERVATION XXI . I Need not make any apology for inserting this Observation , even though it be well known upon the matter in this place . But because the thing is extraordinary , and that there are many who have not so much as heard of it , I have therefore presumed to mention it here . The matter is shortly this . There 's a certain Woman , named Mistris Low , who had a real and true Horn , growing upon the right side of her Head , three inches above her right Ear. The length of it is eleven inches , and two inches about . The form is crooked spirally . It is convex on the outer side , and somewhat guttered in the inner side . It is hard and solid , and all very near of the same greatness . It is not hollow within , as horns are ordinarily , but full , yet it seems to be spongious as a Cane is . It was seven years in growing , and was cut off in May 1671 , by Mr. Temple , an expert Chirurgeon here at Edinburgh . OBSERVATION XXII . THis Observation is for finding the Primum vivens in Animals . Albeit I doubt not but the red Spirit , or Blood , in most Terrestrial Animals , is the first product of the Primigenial juice , and therefore not improperly named the true Callidum Innatum of these Creatures , by the Noble and Ingenious Harvey , in his Book de Generatione . Neither do I scruple to yeeld , that the Heart , and appendent Vessels , are the first formed , and perfected parts in the hotter kind of Animals : yet I am confident to affirm , that in many of the colder , and moister kinds of Aquaticks , if not in all , neither the redness and heat of the Vital Spirits , nor the formation of the Heart , Liver , &c. are previously requisite , to the structure and existence of the other parts ; seing the light of life , which at first inhabited the clear and Cristalin radical moisture , before the formation of any particular part , doth alwayes move in every living creature , according to their particular exigency , without any absolute dependency upon any one part , or member ( excepting singular conditions , wherein they may be stated ) as to its substance , light , and motion : there being in some Animals a simple undulation , in others a slow creeping , but in the more perfect , an impetuous running , or rather flying of the Vital Spirits , necessarily required for illumination and vivification of the whole . For confirmation , I shall give you this singular Experiment . About the middle of March , the sperm of Frogs ( according to the number of Prolifick Eggs therein contained ) sends forth a multitude of small round Creatures , covered with a black , and moveable Frock , which about the end of March , and beginning of April , by the Gyrations of a Tail behind , like a Rudder , do slowly move their bodies in the Water . At this time having opened severals of them , I found nothing ( apparent to the naked eye ) but a clear th●n Membran , under the fore-named black Frock , within which were contained a clear Water , and some small Fibres like Intestines , and in the fore-part a small orifice like a mouth . About the middle of April , its motion is more vigorous , and the Tripes within are most evident , lying in a very fine circular order , but as yet , there is no Vestige of Heart , Blood , or Liver , &c. About the middle of May , the feet formed like small threeds , appear thorow the black Coat : within the Breast , the Heart is then visible , of a white and Fibrous substance , the Liver is white , and the Gall therein easily discerned . But ( which is the head of this Experiment ) the Vital Spirit , in form of a clear and pure Water , is manifestly received by the Nervous Heart , and by the contraction thereof transmitted to all the Body , thorow white transparent Vessels , which being full of this Liquor , do represent the Lymphatick , rather than the Sanguiferous Veins . Last of all do the Pneumatick Vesicles ( which in this Amphibium supply the place of the Lungs ) arise in the Breast , after whose production , the Lympid and Crystalin Liquor , while the Heart is turgid therewith , seems to be red and fiery , but in the other Vessels , it is of a faint pale colour , untill ( about , or near the end of Iune ) the Frock being cast off , and a perfect Frog formed , the whole Vessels are full of Blood , or a red substance very thin , and clear : the Liver , and Pneumatick Vesicles , &c. become red , and Rosy ; so that the Blood in this Amphibium ( which in the more perfect Animals is first compleat ) seems to be the last part in attaining its perfection . That Salmonds , and great Trouts have an aqueous liquor which runs thorow their Arteries , and Veins , before their Blood attain the true consistency , and saturat tincture I am certain : whether it hold in many others , I suspect , but dar not affirm . Hence it may be ( if mens observations , were frequent in all kind of Anatomical inspections , in several Embryo's of every species ) it would be found evident , that the Blood in all these , called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 hath its immediat original from a simple homogeneous , and uniform liquor , and doth by gradual and frequent influences of the vital ferment of the heart , receive at length the full tincture , essence , and subsistence requisite for vivification , and illumination of the whole members . Whether this Experiment doth not sufficiently impugn the universality of the hearts first living , the original of the Gall from the fervour , and ebullition of the Blood , the production of the Blood by the Liver , and many other ancient errors , let any judge , who will but take pains to make and compare Harveys trials de ovo , with this of the Porwigl or Gyrinus , ab ovo . Yea , if the aqueous liquor , be not one with the vital Spirit , and subsequent Blood , then my eyes , and taste are altogether erroneous . Moreover , it were to be wished , that Physitians would not simply stand upon the Galenick suppositions of the four alledged Components of the Blood , nor any such , or equivalent fancies of the latter Chymists ; but that they would seriously examine the first original , and rise thereof from the Primigenial juice , or liquamen , the progress , and perfection of its tinctures , how many renovations , or new tinctures it is capable of ; the vast difference between the Blood of old and young Animals , ( though , it may be , they are both univocal substances , while in their integrity within the Vessels ) with the specifick discriminations , not only of that of any one Aquatick , from any Volatil , or Terrestrial , but likewise of any one Species living in the same Element , with these that enjoy the same Aliments , but of a different Species . And lastly , the variety of particular constitutions , and singular properties of individual Animals , radicated in the fountain of life , or first original of the Blood. If these things , and many more , were truly inquired after ( though the Cook be sometimes necessitated to throw away some of the Broth with the Scum ) I doubt not but the Neoterick Invention of Transfusion of Blood , would prove altogether ridiculous , and the ancient mistake of too much Profusion of this treasure by Phlebotomy , might suffer some reasonable checks from infallible Experience , and sound reasons , not here to be mentioned . There are truths in Natural Philosophy , which ( I doubt not ) but sound reason and experience will convince the vain world of in due time . OBSERVATION XXIII . THis Observation is concerning the aliment and growth of Plants . The inquisitive wits of this , and the last age , having rejected the old opinion of the earths nourishing of Plants , or being converted into their aliment , have made many laudable Experiments for finding out the materials , and means of their growth , and vegetation , such as Sir Francis Bacon's Observe of Germination , Helmonts of a Willow , and the Noble Mr. Boyl's of a Gourd , &c. For though a Tree be cut down , and the root thereof wax old in the earth , and the stock die in the ground , yet through the sent of Water , it will bud , as Iob speaketh , Chap. 14.7 , 8 , 9. I shall add a short remark of a Willow growing without earth . Upon the 13 of April 1662 , I set a top branch of the Peach-leaf'd Willow in a Glass-viol , among 12 ounces of pure Spring Water , with three small buds upon the top thereof , scarce yet discernable . The first ten or twelve dayes , little white specks appeared upon the sides of the Willow , like small drops of Quick-silver , or like the first Bubbles that arise upon the fermentation of Ale or Wine , but no consumption of the Water all this time . Indeed the Gemms , which stood three inches above the Water , did visibly swell about the twelfth day . About the fifteenth day , I perceived small white roots within the Water , upon several places of the Plant , and observed the Liquor grow somewhat thick , and decay in bulk considerably . Having perceived this , I took another Glass of the same bigness , with that wherein the Willow grew , and having filled both top-full with Spring Water , I observed clearly the consumption of the Water wherein the Plant stood , to be so great , that during May , Iune , and a great part of Iuly , every week ( at least ) an ounce and an half , or two ounces of it were insensibly spent : whereas the other Water , standing by in an open Vessel of the same size , made not waste of one spoonful in a whole moneth . About the middle of August , the Water turned very thick , and green , like that whereon Duck-weed useth to grow , and the fair white roots were all obscured from the sight , although the Vessel by the multitude of roots was not capable of the third part of Water it received at first . At this time the branches were advanced to half the bigness , and a much greater length , than the whole stock , at its first planting ; and the leaves of as fresh a verdure , as any Willow in the fields . Thus , having observed , that a tree of four ounces weight , could in three moneths time , and little more , consume insensibly , seven or eight times its own weight of pure Water , without the warm preservation of the earth , and by its own proper digestion , to thicken the remnant of the Water , that it might serve for lorication of the tender fibres of the roots , I took the Glass , the Tree , and all , and threw them over a Window , supposing it needless to recruit the Water any more , and judging it impossible without the warm guard of the earth , that the naked Tree could be preserved in Winter : yet it had the good fortune to fall among some thick Herbs in the corner of a little Garden , where ( after it had lien all Winter ) it was found , and brought back to me , the branches fairly budding in April , the whole Tree fresh and green , yet very little Water was left in the Glass , by reason , as I judged , it had fallen upon its side . Then I endeavoured to keep Water about it , but the Stock filling the neck of the Viol , and the Roots the whole body thereof , the starved Plant died in May , after it had lived a whole year without earth . From this it would seem , that this kind of Tree , ( and it may be , many moe ) doth dissipat insensibly six times more Liquor , than it doth assimilat , and by consequence , that a great quantity of moisture is necessary for maintainance of great Woods . Neither is there any way so advantagious for draining moist ground , where there are no living Springs , as that of planting abundance of Timber , which will best agree with that kind of soyl : for by this means , what was formerly noisome , and superfluous , is now converted partly into the useful aliment of the Timber , and partly sent abroad in insensible exhalations , which ( according to the nature of the emitting Plants ) prove either very noisome , or wholsome to the Neighbour-Inhabitants . Great care therefore would be had in the choise of such Trees , as are to be planted in such moist ground , as are near to mens dwellings , or places of concurse . They are not fools , who prefer Firs , and Lime-trees in their Avenues to Oak and Elme . Let the effects of the Atomical exhalations of Alder and Oak upon fine Linnen , and white Skins be more particularly noticed . Having spoken somewhat of the aliment and growth of Plants , I shall in the next place give a short hint at the motion of their aliment , especially of Trees . That the alimentary juice of Plants , is much thinner , than that of Animals , no man , I suppose , will deny , seing that is conveyed thorow the trunck , or body of the Plants , by inperceptible pores ; but this ( for the most part ) is sent thorow all the members , through patent and manifest Vessels . But how the nourishing , and vital juice in Plants doth move , and by what passages , hath not yet been made known , by any that I have seen . I made once a few Observations , for trying of the motion of the aliment of Trees , which bred in me this conjecture . The nutritive juice of Trees is transmitted both to the roots and branches , through the heart , or pitch , and woody pores of the Timber , and when it is come to the extream parts , it returns again from the tops of the roots and branches , between the bark and timber , into these forenamed interior passages , and so back to the extremities again , and that continually , so long as the life remains . And because the substance of that skin , or bark , which invests the fibres of the root , is more open and porous , than that which is upon the outward branches : therefore it seems , that so much as is superadded to the stock of the former aliment , from the earth , is conveyed to the heart and pitch , by means of , and together with , that part of the retrograd juice , which returns from nourishing , and enlivening the timber of the root-branches , ( for it is an easie Experiment , to make the top of any Tree become root , by laying it down ) and receives the impressions of the life of the Tree , common to the whole mass of alimentary juice , like the I hyll in Animals mixed with the blood of the Veni-cave , before it come to the heart . This motion is not to be thought alwayes alike swift , or of equal celerity : for the vital juice of the Tree becomes so thick and oleagenous in the Winter , that the motion thereof to the outward , is scarce discernable ( though the preparation of the Gemmes , both for leaves and flowers , are observed by the curious , and can be distinguished , even in the coldest seasons ) and the returns inward are in so small quantities , that they are rather like vapours , than liquid juice . Indeed , some Trees , when their root-branches are cut ( even in Winter ) will yeeld no small quantity of an acid liquor , which by addition of the recent Leffas from the earth , smells evidently of the Matrix , from which it did proceed . Moreover , the passages especially from the branches to the Trunk , are so straitned and contracted , that the bark cleaveth to the Timber , as every Wood-man knows . But so soon as the warm Spring hath attenuated the ever-flowing juice in the whole Tree , then doth it become turgid , and more aqueous over all : the passages , and channels both in the trunk , and among the tunicles , and particular skinnes , are so palpably filled with this vital juice , that having no sufficient place to be comprehended in , it putteth forth new growths both in the top , and in the root , which may be easily seen to have more pitch than wood , and to be sealed on the extremity , with the vestiges of a future Gemm ; that by the former , they may the more freely receive the vital influences from within , and by the latter , may be secured from the depredation of the external Air. To prove the motion ad extra , or to the extremities of the branches ; take the branch of any ordinary Tree , about the bigness of a mans wrist ; make it bare near the body of the Tree of all bark , and subjacent tunicles ( for every Tree according to its kind , hath moe or fewer skins , which serve for Veins , within the strong outmost Cortex ) at least for the breadth of a span , or two hand-breadth . Then tye up the place , so excorticated with a compost , made of horse-dung mixed with earth ; let it stand so from May , till November . Then cut off the branch , a little above the Compost , near the body of the Tree , and you shall find it living and fresh , like the rest of the branches : yea , small roots shall evidently appear to have come forth under the Compost near the bark , but not under the bared place . This branch in many kind of Trees being planted , will hold , though not in all . I say then , seing the foresaid bough is nourished from May till November , it is necessary , that it receive nutriment from the body of the Tree , by the internal porosities thereof : for the bark being discontinued by excortication , can send nothing upward towards the top of the bough ; and if it received nothing from the root , it would wither in a few dayes . Yea , leave the discovered part naked , but for a few dayes , and of necessity the branch dieth , the aliment thereof being exhausted by the Air , before it can reach the extremities of the bough . That the Vital Balsome of the Tree returns from the extremities by the internal bark , and inward superfice of the external , together with the smooth outward part of the trunck , although the necessity of both timber and bark in all Incisions , and Inoculations , might perswade the judicious , and the visible course of the juice of the Sycamor in February , and of the Birch in March , upon the cutting of any small branch , might convince any curious beholder ; yet the knot or callus , that is made upon grafted Trees , will better inform the ignorant : for this knot being alwayes upon the shoulder , or root of the Graff , and never upon the top of the Stock , doth evince clearly , that it is made by restagnation , of the descending , and not of the ascending juice : otherwise , why doth it not swell the top of the Stock , as well as the root of the Graff ? Or why doth it not extuberat in any other place of the Graff ? These are accidental varices , which can hardly be shunned in Imping , seing the top of the Stock ( except when it is very young and succulent ) doth not receive so kindly , as it ought , the retrograd sap , although all that is sent out to the Graff must ascend thorow the pores of the Stock . Hence many times a considerable part of the Stock is mortified , because although abundance of aliment ascends to the head or top thereof , yet no more of it goes to the branches , but what is bestowed upon the Graff , a great part of the rest being exhaled by the Air ( especially in big Stocks ) and consequently , the place defrauded of its nourishment : no other wayes than when the motion of the vital sap faileth , either in the whole , or in part , a total decay or particular mortification of some part necessarily follows , as in the Stemms of annual Plants , and mortified tops of the Ectrapelous branches ( that I may so call them ) of Willows , Plumbs , &c. we may observe every Autumn . OBSERVATION XXIV . Sir , I Was not a little surprised , at the receit of yours , when I had considered your desire in it , being prest with two difficulties , which seemed equally hard to evite . The one , to give you my judgement in a matter wherein I have been so little conversant my self , and have had the steps of no other to follow , never one having hitherto touched that subject in writting ; I mean of Coals , and other Minerals of that nature , their Course , and other things relating thereunto ; the observation whereof ( I grant ) wants not its own pleasure , and usefulness . The other , to refuse the desire of a friend , when importuned , to whom I owe my self , by many obligations . This last having prevailed , hath determined me to assay the overcoming of the first . And though I am confident , what account I can give you , shall give but very little satisfaction : yet I adventure to offer it , such as it is , very freely in the following discourse , wherein you are not to expect , that I will meddle with some questions , thereanent , which might be more curious , and pleasant , then profitable , or satisfying , such as , if Coal , and Free-stone , which keep one course , and have the same accidental qualities , have been created in the beginning , in their perfection , as wee now find them , and since that time only preserved , as they were created for the use of men , to whom all sublunary things were made subservient ? Or , if they have been but produced gradually , as they speak of Gold , and other Minerals , by the influence of the Sun , in the bowels of the Earth ? And if their production be of that nature , out of what matter they are formed ? These things being above my reach , I shall leave their inquiry , to those that are knowing in the secrets of Nature , and shall therefore give you a narration , of what either I have observed of these things , which occurr in the Winning of Coal in my own experience , or by conversing with others of more experience than my self , in doing whereof , I shall follow this Method . First , I shall speak of these things that are common to all Coal , wherein they all agree , and which are , as it were , essential to all , and of there differences , which are but accidental , and gradual sometimes , and yet are abundantly conspicuous , and causeth different effects in the working ; as their Dipps and Rise , and Streek , for so are they termed . Secondly , of some things , which are but accidental to Coal , and yet so ordinary , that scarcely any is found without them , in lesser or greater degrees ; such are Gae's , and Dykes , that alter the natural Course of the Metalls , very incident to every Coal , though in some less frequent , conform to the nature and kind of the ground , where the Coal is . Thirdly , I shall speak something of Damps , and of their different causes , and effects : of Wild-fire , and other such like things , which are met with in the working of Coal . And lastly , of the best way for trying grounds to find Coal , where never any hath been hitherto discovered : of carrying on of Levels , for draining the water of Coal and making it workable . It is to be cosidered , that all Free-stone , though of different natures , hath the same course , with the Coal , that ly either above them , or below them , except it be accidentally , interrupted : therefore , whatsoever is spoken of the one , is applicable to the other . And so we find in Digging or Sinking , that after the Clay is past , which keeps no course , all Metals , as Stone , and Tilles ( which are Seems of black Stone , and participat much of the nature of Coal ) ly one above another , and keep a regular Course ; wherein the three things most remarkable are their Dipp , and Rise , and their Streek , as it is termed . The Dipp , and Rise , are nothing but a declining of the whole body of the Metalls . And this general holds , that all of them from their Center rises , till they be at the very surface of the Earth ; some only at a foot or two foot , some at an ells distance from the surface , which is here termed a Cropping : and whether Coal or Stone , the nearer they come to the surface , the softer they become , till at last they are converted , if it be a Stone , to a very Sand , and if Coal , to a Dross , which will not burn . This declining or Dipping , of the Coal , is sometimes greater , and sensible , sometimes lesser , and almost insensible . There being some , that if you consider the declination , it will not be found one foot in ten ; some one foot in twenty , or one in thirty . Whereas in others it will be one foot in three , or one in five . And sometimes it hath its Course from the Center of the Earth , almost in a perpendicular to the surface , it cutting it , near to a right Angle . The first sort , they term Flate-broad-coal , in regard of the plainness , and evenness of its Course . The next , they call Hinging-coal . The last is called Edge-Coal . The first is the most profitable , in regard , that it 's long before the Coal-hewers can reach the Cropp , and consequently the more of it is workable . The second and third sort , are sometimes of their own nature , more firm , and fitter for burning , but less of them can be reached in working . The Course of all the three is most perceptible in the three following Schematisms . Figure 1. 2 3 In all the three Figures , the point B is the Cropp of the Coal . The Line BC is the body of the Coal declining or the Dipp from the Cropp . AC is the perpendicular , falling from the Horizontal Line , whereby the true declination or Dipp of the Coal is found . So that after you have found your Coal at B , you must set down your Sink at the point A. In the Flat-broad-Coal , which we suppose only to decline , three fathoms in sixty ; the Sink , that answers to the perpendicular AC , will be of deepness three fathoms . If the distance BA , be supposed to be 120 fathoms alongst the Grass , or surface , then will the deepness of the Sink be six fathom , and so forth . In the second , if the Coal be supposed to decline one fathom in three , the Sink AC , being set down at the same distance from the Cropp B , with the former , it will prove thirty fathom deep . If the said distance be doubled , it becomes sixty fathom deep , and so forth . In the third , keeping that same distance alongst the surface , you shall not encounter the Coal with a Perpendicular Sink , because of its great declination , and therefore through want of Air , and other difficulties , you cannot dig so deep , as is necessary to that effect , except the Sink should be made to decline , as doth the Line AD. All these Dipps are to be seen in several places of Lothian . The first is most conspicuous in the Earl of Wintons ground at Tranent , where the Coal , and other Metals are extraordinary flat and even . The second is within the said Lordship of Tranent , in a piece of ground , called Wester-Fauside . The third in Lonhead of Laswaid , which pertains to Sir Iohn Nicolson of Nicolson : and in many other places , one may see very different declinations , who is curious to observe them . From this general position of the Dipp , and Cropp of all free Metals , there is one consequent , which is no uncouth Observation , namely that these Metals rising from their Dipp to a Cropp , every one of them riseth in their proper course , if none of these things whereof we shall treat hereafter interveen , and make an alteration , that is the Coal or Stone , which is lowest , comes farrest out in its Cropp●ng , which is easily understood by the subsequent Schematism . Figure 4. Wherein the Line AM represents the surface of the Earth . CD . EF. GH . IK . LM , are so many several Metals , lying in course one above another . Suppose CD were a Stone , and the Roof of the Coal EF ( for so they term the Stone , immediatly next above the Coal ) and GH , IK , were other two Stones , interveening between the Coals EF , and LM , then if the Cropp of the uppermost Coal be found at F , the Crop of the Stone above it , must be found back , at the point D , and the Cropp of the Coal under it , which is LM , must be found at M. And this distance of Cropp is proportioned by the length of the perpendicular between them , and the quantity of their declination . For , the more even and flat a Coal is in its course , and other Metals , above and below , the farder doth the Cropp of the lowest Coal advance before the Cropp of the uppermost . For illustration whereof , let us suppose in two several grounds , two Coals , between which , there is an equal distance of perpendicular . And suppose the Metals in the one ground to decline at 13 to 24 , the other at 13 to 16 , then will the distance between the Cropps in the two grounds be very considerable , as may be represented by the two following Figures . Figure 5. 6. Suppose then , that DI , is of equal length in both Triangles , which is the perpendicular , between the two Coals : yet DF in the fifth Figure , is much longer than DF in the 6. And the reason is evident , because the Angle DIF , in the 5 , is greater then the Angle DIF in the 6 : and therefore the Base DF , which is subtended by the greater Angle in the 5 , must be greater then the Base DF , which is subtended by the lesser Angle in the 6 , which Euclide proves in his 24. Proposition of his first Book , and is demonstrat by Proclus in the Scholium to the 4 th Proposition of the same Book . By this is made to appear the profitableness of a Flat-Coal , beyond a Hinging-Coal , which was touched before , in regard that having the Sinks of equal deepness in both , there is much more of the Flater-Coal to be wrought , before it Cropp out , then of the Hinging , as there is a difference between the Lines DF in the first and second Figure , or between the Lines IF , in the same . If it be enquired , if in rising grounds , where there is a considerable ascent above ground , the Coal keeps a proportion in its Rising and Dipping with the ascent and descent of the ground above ? I answer , there is no certain and constant proportion kept , whatever sometimes may happen . For I have observed some Coals upon grounds of a considerable ascent , and their Dipp run quite contrary to the descent of the Hill : and others have had a quite contrary course to that , and have declined , or dipped with the declination of the ground above ▪ But in the Streek ( whereof I shall speak a little hereafter ) there is more proportion ordinarily to be remarked . There remains only one Question about the Dipps , and Risings of Coals , which I shall a little consider , having encountered different judgements anent it , in conversing with persons , who had experience in Coal , viz. whether Coal and other Metals , after they have declined such a length from their Cropp , suppose from West to East , take another course , and rise to the same point , to which formerly they dipped ? Figure 7. As if the Coal dipped from A , which is the Cropp , to B , which should be the Center of that Body ; and after that rise to C ? Or if it should continue its declination thorow B to D , which is Antipodes to us ? I shall not offer to determine in a matter wherein there can be so little certainty attained , but shall give my opinion , which is founded upon the experience I have had , and Observations I have had occasion to make on that Head. And first , I find in all these Coals , wherein no contrary Cropp or Rising could be visible , there are invincible obstructions ; as either , they have been near the Sea , and have dipped that way ; and so if they took any contrary course , the cropping behoved to be in the deeps , and so no access to trace them . Or next , they have dipped towards the foot of a Mountain , and so the ground above rising the same way which they declined ; their course could not be pursued , till a contrary rising should be discerned . Or thirdly , they have encountered some Gae , or Dyke , which hath cut them off , before they came to their full dipp , and thus their course was obstructed . Now , those that have been acquainted with no other Coals but such , I think it not strange , if it be hard to perswade them of those things they have not seen . But besides all those kinds , I have seen others , whose contrary rising and dipping have either been visible to the eye , or demonstrable by reason . For example , I have entered under ground , as it were at the point C , at the very Grass-cropp , and have gone following the dipp of that Coal to the point B , at which the course hath altered , and carried me out at the Grass at A , which are two contrary points of the Compass . And that alteration of course was not occasioned by any Gae , or trouble , which sometimes have that effect , the ground being very clean , and good Metals , keeping their course most regularly . There are other instances for confirming my experience , in fields , which are so large , that 't is impossible to work the Coal so far to the Dipp , it falling deep , and so wants Level for conveying water from it , or wants Air , for following it to such a deepness , as to overtake its Center , where it takes a contrary course , and yet the contrary Cropp hath been wrought in several places , which is evident to be a part of the same body , with the other , both by the nature of the Coal it self , by the Metals lying above it , and the Coals below it , all which keeping the same Course , except when they encounter troubles , which are incident to some parcels of ground , more than to others . The greatest field I know wherein this is conspicuous , is in Mid-lothian where is to be found , the cropping of a Coal of a considerable thickness , which is termed their great-seam , or Main-coal , and the other Coals lying below it , which may be traced in the order following . At Preston-Grange these Coals are found dipping to the N W , and rising to the SE , which have been wrought up to Wallifoo●d : from that along by the foot of Fauside Hill , the dipp lying in the Lands of Inneresk , which marches therewith on the North. From thence it runs through the ground of Carberry , every one of these grounds from Preston-Grange , Giving Levell to another . From thence , through a part of the Lands of Smeaton , and next through a piece of ground belonging to the Family of Buccleugh , called Condon : and through West-houses , which belongs to the Earl of Lothian , and at Cockpen , and Stobhill , from thence runs through to Carington-Mill ; all which is a course , which in Streek lyes near to SW , and NW , and will be in length about eight miles . From thence , the course of the Coal turns , and is found in the Barony of Carington , White-hill Ramsay , Gilmerton , and from thence taking its Dipp , quite contrary to what it had before , the other Dipping N and NW , or NE , according to the turn of the Streek , it Dipps there S , SE , &c. and from Gilmerton , it is found at Burntstone , a piece of ground belonging to the Earl of Lauderdale : and from thence at the Magdalen Pans , where the turn of the cropp being within the Sea , is not seen , till it be found at Preston-Grange , where we began to remark its course . The parcel of ground , under which this great body of Coal lyes , is of a considerable extent , it being eight miles in length , and five or six in breadth ; in regard whereof many other Coals are found lying above the great Coal , the cropps whereof doth not come near the Cropp of it , by a considerable distance . Though this instance alone , may sufficiently convince , yet I shall not be unwilling to give another . The parcel of ground , in which this Coal is found , is not of so great an extent , as the other , and therefore its course may be the more easily traced . For the greatest part , it belongs to the Earl of Winton , and lyes within the Lordship of Tranent , whose contrary Cropps , are most conspicuous . This great Coal , which is 10 , or 12 foot thick ( beginning at the head of the Toun of Tranent ) where it hath been wrought , runs SW towards the march of the Lands of Elphingston , belonging to the Lord Register , and continues in that same course , till it come near to the house , and for the most part dipping to the SE. And near the house , the Cropp is turned downward towards the march between Elphingston and Ormiston , where the dipp is contrary to the former . And from Elphingston-mains , it takes its course almost round , through the Lands of Panston , and returns to the Toun of Tranent where it began , which body of Coal will be in length two miles , and in some places , as much in breadth . Now , I leave it to the judgement of any person , if there be not more reason to perswade , that this should be the natural course of these Minerals , where such pregnable instances , to evince it , are found ; then to conclude the contrary from these Coals , the course whereof cannot be followed , because of the invincible impediments , I mentioned before . However , I leave every one to be determined , by his own opinion , and shall be satisfied to injoy my own , till these of more experience convince me of the contrary . There are some other things farder to be remarked about the Dipp , and Rise of Coals , which ( possibly ) every one hath not seen , they being so very rare , and therefore are not fit here to be passed without being considered . One is , of a Coal , which having that contrary Dipp and Rise , ( whereof I have been speaking ) in one of the cropps , hath not come out to the Grass , and terminat ; but after it hath risen a considerable way in its contrary course , in stead of Cropping out , hath taken a Dipp towards the same point , to which it dipped first , and so having dipped to the Center of its course , it hath risen again , and cropped to the contrary point , as is to be seen in this eight Figure . Figure 8. Where AB is the surface of the Earth . The point B is the Cropp of a Coal dipping from NW , to the SE. From C it takes its rise , and course to a contrary Cropp , towards the point F , where the dead Cropp ought to be found . But in stead of going that length , it takes another course from the point E , dipping SE towards D , from which it takes its rise , and continues it to the point A , where it terminats , and where the dead Cropp is found . I grant , that it meets with a trouble , or Gae , at the point E , which seems to be the cause , why its natural course is changed . But it s very extraordinary to see such an effect . But of this afterwards , in its own place . There is yet another thing to be remarked , in the dipps , and risings of Coals , which is this . In the most part of Coals , that have their course from dipp to cropp , without the intervention of a dyke or gae , the declination is straight down , from the horizontal line drawn from the point of the cropp , to the fardest point of the dipp . That is , the Coal declining from that point in a right line , makes with the horizontal line , a right lined angle , angulus rectilineus , though in some the angle is more acute , and in others less , as is to be seen in the first , and second figures , where AB being the horizontal Line , and B the cropp , BC is the body of the Coal declining , which meeting with AB in the point B , constitutes a right lined angle , and where ABC in the second figure , is a greater angle , then ABC in the first . Yet I have seen a Coal , the body whereof from the dipp , or fardest point of declination , had its rise towards the cropp very insensibly , it being Flatt , and then began to be more sensible , till at last coming near to the surface of the Earth , it takes in a sudden such a rise , that from declining one foot of 12 or 14 , it declines now one foot of three , as may be made evident from this following Figure . Figure 9. Where AB is the Line drawn from the extream points of the Cropp , right horizontal . The body of the Coal rising insensibly , is DC . But assoon as it comes to C , it riseth with a great ascent till it Cropp out at A. Here you see , that in stead of one side of a Triangle , which the course of other Coals in their rising , or in their declination makes ; this Coal in rising makes two sides , namely DC , and CA , the Figure DBCA being quadrilateral . The Coal of this course was really wrought , and is yet visible in its waste , where there is found no Gae or Dyke to make this alteration . These are the chief things that I have thought worthy of Observation in the Dipps , and Risings of Coals , and therefore I come now to touch a little the other part of their course , which is commonly termed the Streek of a Coal . To make intelligible to those , who are not experimentally , acquainted with Coal , this term , or what the Streek is , we must lay this foundation , that the Coal is a Physical Body , and so hath its three principal dimensions , which do constitute it so , viz , Longitude , Latitude , and Profundity . It s Latitude , is that part contained between its extream lines , which is measurable by its surface , to which its dipping and rising , though alwayes incident , yet is but accidental . It s Profundity is to be measured by the distance , between the two surfaces , immediatly next to it , above and below : which are termed in Coallery its Roof and Pavement , because of the resemblance they have to the Roof , and Pavement of a house . The Longitude is nothing else but what is termed by the Coal-hewers , the Streek . For if you imagine a Line drawn along the extream points of the Rise , or Cropp of the Coal , that is properly the Streek of the Coal . There are but few things to be remarked , as to this part of Coal : only first to find how it lyes , to what points of the Compass it moves . For knowing whereof , there is this general Rule , that , having found your Dipp and Rise , to what ever Points that Course is directed , the Streek is to the quite contrary . For supposing a Coal Dipp SE , the two points , that respect the Dipp and Rise , must be SE , and NW , being the points opposite one to another . Then it must needs follow , that the Streek must run SW , and NE , which two courses divides the Compass , at right Angles . And therefore , where a Coal is found to have contrary Dipps , and Risings , they declining sometimes to all the Points of the Compass ( whereof there hath been given two notable instances before ) it must needs follow , that there be also contrary Streeks , and so the Streek of a Body of Coal is sometimes found to describe a round figure , though not perfectly circular , and somtimes a multangular figure . For it cannot be supposed that the Streek makes alwayes a right Line , between the two points , from which it is reckoned . For example , between the Laird of Preston-grange his house at Preston-pans , and the Stob-hill , there are the Streeks of several Coals , lying one above another , which will be of length , about seven or eight miles , lying near upon SW , and NE ; yet the Cropps of the said Coals ( their dipp , and rise , being NW , and SE ) are sometimes farder advanced towards the SE , sometimes farder back towards the NW , by the difference of a mile , and this generally occasioned by the encounter of a Dyke or Gae , whereof hereafter . The same question , that occured in the Coals dipping towards a Hill , on rising above ground , comes to be inquired into here ; viz. If a Coal encountering amascent , or Brae above ground in its Streek , rises also with the ground , and keeps its ascent ? I answer , I have found it so in all the Coals I have ever seen of that nature . GOD in his providence , having so ordered it , that thereby it may be the more useful , in regard more thereof may be wrought by one Level or Aquaeduct , by which the Water is conveyed away , as afterwards will be observed in speaking to Levels . For confirmation whereof , I shall bring instances both of Coals , that declines towards the Hill , and of others that declines with the same dipp , the Hill hath it self . In the Coals of Bonhard , Grange , Kinglassy , and Kinneil , which keep all one general course ; the ascent above ground is from the Sea , ( which lyes North ) towards the South , or thereabout ; the Coal dipps or declines towards the NW , and so consequently rises to the SE. The Streek of these Coals , is from the NE to SW , which slops alongs the Hill , and comes up to the top thereof to the Westward of the House of Bonhard . Now , in sinking in that ground , if an equal proportion be kept , in all the Sinks from the Cropp , and a just allowance given for the different Rising above ground , the Sinks will be near of an equal deepness along all the Streek . So that a Sink upon the same Coal near to the Sea , which is the NE point of the Streek , at equal distance from the Cropp , will be as deep as a Sink upon the top of the Hill , being the SW point of the Streek at the same distance from the Cropp , allowing alwayes the different rise above ground , and excepting some particular troubles falling in upon the Metals of one Sink , and not of another , and so making them dipp more , which will occasion a difference of the deepness . The same is also found in the Coals of Dysart , and Weems . As also in that great body of Coal before mentioned , between Preston-grange and Stobhill , the declination whereof is to the NE , which is also the course of the descent above ground . Another instance is from the Coals within the Lordship of Tranent , the dipp whereof is of another course , being contrary to the descent of the Hill , viz. the Coal dipping to the SE , and consequently the Streek running SW , and NE , where the same is to be observed that was seen in the other , anent the equality of the deepness of Sinks along the Streek , with the same allowances , and exceptions before mentioned . Some have been of opinion that Streeks of Coals ly generally South and North , or to some of the points near to these two Cardinal ones , between South and SW , and North and NE , as South and by West , and North and by East , &c. To which general I cannot agree , in regard of wh●● I have before made evidently appear , viz. that some Coals have their croppings towards all the points of the Compass , and the Streeks being regulated by the Cropps , they must necessarily be judged to have their courses proportioned to theirs : so that if a Coal dipp to the true North , and rise to the South , the Streek must be East , and West . However , I acknowledge two things , for confirming that opinion . First , that of all the Coals I ever have seen , where these contrary dipps and risings , could not be traced , and made visible , the Streek hath inclined to those points of South and North. But I must also confess , that they are but few I have seen , in respect of what I have not seen , and so if any others experience , who have seen more , contradict mine , I shall willingly yeeld , and not be tenacious . Next , in these Coals , which I instanced , that have their Cropp to all the Points , and consequently their Streeks , and in others of the same nature , which I have seen , and not instanced , I found that part of the Streek , which lyes towards these Cardinal points , to be the greatest , being double , or triple to the other Sreeks in length . So that when the Streek , that lyes either along the one Cropp , or the other , towards the SW , and NE , will be seven miles in length , that lying SE , and NW , will be but four , and sometimes less . And this is all the account I can give , of that part of Coal , called the Streek . The second thing I promised to speak of , was of some things , which are but accidental to Coals , and yet so ordinary , that hardly are any found without them in lesser , or greater degree , such are Gae's , and Dykes , which alters their natural course , and they being the occasion of so much Trouble , in the working of Coal , and following its course , the Coal-hewers call them ordinarily by that name Trouble . This Trouble or Gae then , is a Body of Metal falling in upon the course of the Coal , or Free-stone , obstructing , or altering their kindly and natural course , keeping no regular course it self , and being of nature alwayes different from the Metal , whose course it interrupts . And these Gae's differ also among themselves , in their nature , and in their course they keep : or more properly in the way wherein they encounter other Metalls , and in their effects . In their nature , for some of them consists of an impregnable Whin-Rock , or Flinty-Stone , thorow which it is almost impossible to work : and if there be a necessity to cut them thorow , it is done at a vast expence , and takes a long time , and must be cut open to the surface of the earth , it being impossible to Mine it under ground . Some of them are again of Stone , like a Free-stone , but seems rather an abortive of nature , they having no rule in their course , by which a man can follow them , nor can their stone be useful . In their encountering of Coals , or Free-stone , sometimes they encounter them in the Dip , and sometimes in the Streek , and sometimes between the two . These that are met with in following the Dipp of the Coal , ly along the Streek thereof . For example , if the Coal Dipp SE , the Gae lies NE , and SW . These that are encountered in the Streek , lyes to the Dipp and Rise : so the Coal Streeking NE , and SW , the Gae is found to ly SE , and NW . Others of them , lyes between Streek and Dipp , that is to some point between the two : as the Streek being SW , and NE , and the Dipp and Rise SE , and NW , there may be a Gae found lying WSW , and ENE . Now , when I speak of a Gae's lying to such Points of the Compass , this doth not contradict what was said before , that they had no regular course themselves . My meaning being , that though they have a certain length , lying between two points , and a thickness between two Metalls , yet by the Metal of the Gae it self , it is impossible to know its course , as it is in other Metalls of Coal or Free-stone , whose courses are discernable at the first view . Their effects are different , as their nature and course are different : only they agree in these two generals . First , that all of them renders that part of the Coal , that comes nearest to them , unprofitable and useless , though some less , and some more , they being unfit for burning . And it is remarked , that these Gaes that consists of Whin-rock , renders the Coal next to it , as if it were already burnt , being so dried , that it moulders in handling it . In others , the Coal is not altogether so ill , and yet its nature is altered , from what it is at a distance from the Gae . The next general is , that all of them alters the natural course of the Coal in less or more , some of them making it Dipp much more then its ordinary course , which they call Down-gaes : Some again making their rise much more than their course , which they call Up-gaes . Others making an alteration as to the Streek , causing it go out beyond its ordinary bounds , as we observed before in that great Streek of Coal between Preston-Grange and Stobhill . Now it is to be considered , that when in working of a Coal , whether to the Dipp , or Rise , or Streek , one of these Gaes is encountered with , the Coal is quite cut off , and as it were terminat : so that you see nothing where the Coal should be , but either a Stone , or Clay , or rotten Till , or some such thing . And the practique of Coallery is to trace the course of the Coal through that , till you overtake it in the other side . And before any thing be said to that part , you must notice , that some Gaes are of greater force than others , and their influence upon the course of other Metalls greater , whence you shall see a threefold effect . One is , that by some great Gaes , which a Coal meets with , it is quite cut off , so that in the other side thereof , there is not a vestige of that Coal , or of any other Metal that was above it , or below it , to be seen . And if there be any other Coal , as sometimes there are , they are quite different from them of the other side . I said by some , because there is one instance to the contrary , which is somewhat singular . In the Earl of Winton's ground at Cockeny , there is found a course of Coals and Free-stone , dipping to the SE in the Links ; and upon the full-sea-mark , there is a tract or course of Whin●rocks lying E and W , underneath which these Coals and Stones comes thorow without alteration of course , and are found within the Sea-mark , with the same Dipp and Rise upon the North side , they had upon the South side of the said Rocks : and yet the Coal is encountered upon the South hand by a Gae under ground , through which it passeth , not without a considerable alteration . The greatest of these Gaes , that I know , is that which takes its beginning , that we see on Land , at the Harbour of the Pans , called Achisons-Haven , which hath been cut by Preston-Grange , for Level to his Coal , and goes from that to Seton , which may be traced above ground , almost the whole way ; and hath been cut at Seton●a ▪ for serving the Level of that Coal now wrought at Tr●nent . From thence it passeth through the fields of Long-Niddry , a place pertaining to the Earl of Winton , and through the Coats , which pertains to the Earl of Hadington , till it joyn with Pancreck-hills , a tract of Rocky-Mountains , from whence it is traceable to Linton-bridges , where it is v●sible in the Water , the Water of Tyn falling over it , and making a Lin , which they call Linton-Lin ; from thence to the East-sea . And it is known by Sea-men , that it keeps a course thorow the Firth from Achisons-haven , ( whence we reckoned its beginning upon Land ) towards the West and NW , it being found to the Southward of Inch-keith , and before Leith , where stands a Beacon , and so can be traced to the North Shore . The second effect of Gaes , is to cut off the Coal quite , as to a part of the field , so that in the other side , having pierced the Gae , you shall not find the Coal , and possibly not within a quarter of a mile of the Gae , which cuts it off , and at that place shall only find the Cropp and the Body Dipping , as it did before it was cut off ; and if you shall measure between that side of the Gae , where you lost your Coal ( I suppose the Coal then being 24 fathom from the Grass ) to the place where the Coal in the other side of the Gae shall be found at the same deepness , it will be near 500 paces . For making this more intelligible , let us suppose a Coal Dipping SE , and in working to the Dipp , there is a Gae encountered with ( This was really done in a piece of ground I know , and so it is no meer supposition ) at which Gae the Coal is cut off ; for finding whereof the Gae is pierced , and nothing found in the other side , viz. in the SE side of the Gae , but at more than 100 paces distant , the Crop of a Coal , which lyes under the Coal , that was lost , was found , after which it was easie to find the other . Now , that it was the same Coal , that was lost , upon the North side of the Gae , is not only evident , by the kind of Coal , and all the Metals above , and below keeping the same course , but by this , that the Gae wearing out towards the West , the two parts of the Coal that was separated by it , joynes themselves again , and continues in one body , as they were before separation . The last effect of the Gae is , that it doth not quite cut off the Coal from the other side of it , but makes an alteration in the course , either in the Dipp , or in the Rise , or Streek , as was before noted : so that in meeting with one of these Gaes , having considered its nature , and pierced it , the Coal will be found in the other side , immediatly touching the Gae , but with an alteration of course . Now , in these two last effects , since the Coal is not totally cut off , it will be worth the inquiry , to find the surest way of recovering the Coal after it is lost . Therefore , where the Coal is not cut off , by a considerable distance , and having pierced the Gae , it is not to be found in the other side , you are to consider well the nature of the Metals you find approach to the Gae , and if they be such , whether Stone , or Coal , as you know to ly under the Coal that you have lost , then you may be sure the Coal is to be found above in its course , which is to be traced by the Dipp of the Metals you find . As sometimes I have seen , when a Coal hath been cut off by a Gae , happly there is another Coal under it 12 fathom , after the Gae hath been pierced , and the lost Coal not coming near to it in the other side , that hath been found there , by which it was certainly concluded , that the uppermost Coal behoved to be there also , though a little back , conform to its course . But , if the Metals or Coals , under the lost Coal , hath not been known , then you are to take notice of the Dipp and Rise of these Metals , you find on the other side of the Gae , which you have pierced , and making that your rule , range back over the Metals , conform to the direction to be given afterwards , and you shall find the Cropp of the Coal you want , and after which you were inquiring . Where the Coal is not quite cut off by the Gae , but hath its course only altered , you are to consider , in searching for it , before you pierce your Gae , that which the Coal-hewers term the Vise , or some of them the Weyse of the Gae , which in effect is nothing else , but a dark vestige of the Dipp or Rise , that the body which now constitutes the Gae , should have had naturally , if it had been perfected ; which when it tends downward , then must the Gae be put over that way , and in the other side shall the Coal be found , and Down , as they term it ; that is , the Dipp which it had naturally , augmented . And , if the Vise be Up , the same way must be taken for piercing the Gae , and the Coal will be found Up , that is , its Rise augmented . But these things cannot be made so intelligible , as by seeing , there being many things in the alteration of the course of Metals very curious , and worthy of Observation : as when a Coal is cast down out of its natural course by a Gae , and so made sometimes under-Level , it riseth as much to another hand , and the Cropps go so much farder out , which still makes the Level useful , the use whereof would have been judged lost by the down-casting . Sometimes a Coal made to have four contrary courses , as is evident from the eighth Figure , where there being a Gae at E , makes it take such another course , in stead of coming out to the grass . Sometimes , before the Metals overtake the Gae , they are made to ly like a Bowe ; one instance whereof is visible above ground in some Metals lying between Bruntiland and Kinghorn , at a place called the Miln-stone , where there is a small Coal with Free-stone above it , all Dipping to the S E , and Rising to the N W. Upon the Rise they meet with a gae , which is a great Whin-rock . In their course to the grass , before they touch the said Rock , they take a contrary course , and dipps into it , and are there quite cut off . The manner whereof is to be seen in this tenth Figure following . Figure 10. Where AB is the Rock : EF the Coal : CD the Free-stone . Now , whereas they should have risen towards A , they turn at D , and dipps into the Rock , which any may observe in passing that way . Many other such motions are observable , which I pass , and leaves them to the observation of the curious . The third thing I promised to speak of , was of Damps , and as they are termed by the Coal-hewers , Ill Air. These do deserve a more accurat inquiry into their kinds , their causes , and effects ; then I am capable to make , there being many things in them very con●iderable , and worthy of a narrow search : therefore following the course I have hither to observed , I shall shew my own Observations thereof , and leave the more curious search to the spirits fitted for that purpose . This Damp then makes an obstruction of respiration in Men , or other living Creatures , in Subterraneous spaces , as Caves , Coal-rooms , Levels , Sinks , and such like ; which obstruction proceeds principally from two causes , both which goes under the name of Ill Air , among the vulgar . The first is the corruption , or putrefaction of the Air , whereof there are two sorts ; one is in places where hath been fire kindled , which burns the Coal under ground , the smoke whereof , being full of Sulphur , and other Bituminous matter , and not having free passage to come above ground , filleth all the waste Rooms under ground , and infects the Air so , that the smell of it , even at a distance , is intolerable , and amongst it no living Creature is able to breath . Of this there are examples in Dysert in Fife , and Fauside in East-Lothian . This was kindled on design by a Fellow , who for his pains was hanged in the place , and hath burnt these 50 years , and more , the fire whereof is sometimes seen near the grass , with abundance of smoke , as it runs from one place to another . The second , where the Air is corrupted without the mixture of smoke , or any other gross corrupting body , which is the most considerable of all Damps , and hath the strangest effects , in killing Animals in an instant , and so hath been alwayes most prejudicial in the works , where it is found , many persons having thereby lost their lives , without access to cry but once Gods mercy , to some instances whereof I have been witness . I shall not offer to determine about the cause of this Damp , but shall give an account of somethings I have observed about it , which when duely pondered , may haply lay a foundation , at least of a probable conjecture , whence it may proceed . This kind of Damp then , and Ill Air , is never found in Coal , or other Metals , where there is Water to be found ; I mean , whence the Water hath not been drawn away by a Level , or Aquae-duct : as in Coals , where there is a necessity to lave the Water from place to place , or to pump it along the ascent or rise of the Coal , to the bottom of the Sink , from which it is drawn out above ground , this Ill Air is not found . Nor is found frequently , if at all , in these Coals where the Water is drawn from the Coal by a Level , or Aquae-duct under ground , till it come of its own accord to the bottom of a Sink , which is in place of a Cistern , out of which it is forced also above ground , and differs only from the other , that the Water runs here of its own accord by a descent to the Sink , which is termed a drawing Sink : in the other it must be forced by the Rise of the Coal , because happly , a Sink upon the Dipp would be of such a deepness , that no force could draw it up in a perpendicular . But this kind of Damp is found ordinarily in these Coals from which the Water is drawn by a Level , the beginning or mouth whereof is above ground , and carried along by a right Line under ground , till it overtake the Coal , which it is to d●y : so that the Water which comes from the Coal , runs without being forced , and is sometimes so considerable , that it makes Mills go , without any other addition , as is to be seen in the Earl of Wintons Lands of Seton , where four Mills goes with the Water that comes from under ground , out of the Coal ; which kind of Levels are only found where the Coal lyes in a Field , which hath a considerable Rise , or ascent above ground ; there being a necessity to make use of the other two wayes spoken of , for drying the Coal , when the Field in which it lyes is a Plain . Further , of these Coals , which are dryed by the Free-level ( for so they term the Level that runs unforced ) there are some to which this kind of Damp is more incident , than to others . The cause of which difference is found to be , the solidity and clossness of the Metals , whether of Coal or Stone , wherein some exceeds another . There being some , that are full of rifts , or empty spaces ( I mean empty of any part of the same body where they are ) which will sometimes serve , to convey a considerable quantity of Water in place of an aquae-duct or level ▪ which spaces are termed by the vulgar , Cutters , which sometimes proves very profitable in the ground where they are found , both in regard of the use they serve for , in stead of Level , and for rendring the Metals wherein they are found , more easie to work , in making them yeeld easily to the force of the wedge and leaver . Other Metals there are , wherein few of these Cutters are to be found , and if water be to be conveyed through them , there is a necessity of cutting a passage through them for that effect . Now , this Damp , whereof we speak is sound most frequently , and most violent in the first sort of Metals , viz. in these which are full of Cutters or Rifts , which gives some ground to this conjecture of its cause . These Spaces which are found in Coal , or other Metals , as Stone or Till , before the Coal begin to be dryed by a Level , are full of water , which is still in motion , as are all subterraneous springs , whereof some are more violent , some more slow , conform to the passage they have to the fountains above ground , where they discharge themselves . Now , for drying these Coals , and rendring them workable , there is a necessity to cut a passage , thorow which that water discharges it self quickly , it being large , and admitting a great quantity at once , by vertue whereof ; a great field is drained at once , and the Sourse not being able to furnish so much water , as the Conduit is able to convey , these Spaces in the body of the Metals , being emptied of Water , must needs be filled with Air , which Air having little contact and commerce , with the great body of Air above ground , and so hath little or no motion , corrupts in these places , and thereby becomes poisonable , so that when any Animal is necessitat to draw it , and respire by it , it choaks them on a sudden , just as standing Water , which being without motion corrupts , and becomes poisonable , though haply not in so great a degree as the Air : the Air , being a body much finer and purer , than Water , that holding good in it , corruptio optimi pessima . This is much confirmed by what is before asserted , that in the Coals , whence the Water is drawn , and they drained , but not by free-course , but by Force , as Pumping , and drawing by buckets , these Damps are seldom or never found : because the passage of the Water being forced , it does not so suddenly dry the Metals , as the other , whereby there is alwayes left in these Spaces some Water , which being it self in motion , keeps the Air also in motion with it , and thereby the Air is kept from corruption , at least in such a degree , as it is in the other . Hence we find , that in these kinds of Coals , the Rooms under-ground are alwayes wet , or for the most part they are so : whereas in the other , there will be no Water found to wash a mans hands : and sometimes the Coal through want of Water , becomes so dry , that it cannot be wrought in great pieces , as others , but crushes in the very working , and when wrought , is rendered useless , and will not at all burn . This puts me in mind of a very pleasant conception of a worthy and learned Person , Doctor George Hepburn of Monk-ridge , with whom I had occasion one day to discourse on this Subject . He is of opinion that the Water is the Mother of the Coal , whereby it is preserved fresh , and incorrupted , and that when the Water is drawn off , and this Damp follows , it is not the Air , which succeeds in place of the Water , and is corrupted for want of motion , that occasions it . But as we see , when the corruption of a Liquor within a Vessel , when the Mother is gone , corrupts the Vessel it self , and occasions an ill savour or taste in the Vessel ; so that the Coal being corrupted by the want of its Mother , the Water ; corrupts the Air in the subterraneous Spaces , as in Coal-Mines , Sinks , Caves , and other such like . He had likewise another pleasant conception about the generation of Coal , judging it to be formed gradually out of another Metal , as of Till , by the help of Water , of which he himself may perhaps give an account . And though I be not of his opinion in that matter , yet I must acknowledge , I was taken with it , and shall be glad to see a more full account of it from him , than he had access to do in the short conference we had . The effects of this Damp are first , it hinders the burning of all combustible matter , as Candle , Coal , Pitch , Sulphur , &c. so that if you take a Torch lighted , and let it down to a Sink , where the Ill Air is prevalent in the time , it shall straight extinguish it . Or take a Coal , which is burning , and let it down , it shall not only extinguish the Flame , but shall make the Coal in an instant dead , and as cold as never heat had been in it . But the most dangerous effect is , its killing of living Creatures , whereby many persons have been suddenly killed . Some in going down to a Sink , where it hath been powerful , have fallen out of the Rope , and perished . Others have been choaked , and yet have gotten out by the help of others in a sudden , and have remained a considerable time without the least appearance of life , but yet have at last recovered . Yet it hath been observed , that some of these persons that have been so struck with the Damp , and recovered , have had alwayes some lightness of Brain thereafter , and never so settled as formerly . This I know to have happened to one , whom I have seen so , many times thereafter . What hath been its effects on some Animals , whereof you have made Experiment , I leave to the account you have given . One thing I shall only mention , which to me seems somewhat strange , that notwithstanding these Damps are so effectual , and causeth so suddenly the death of Animals , yet the Ratts , which are in some of these places , where the Damps are most violent , are not reached by them . For sometimes , when they are so powerful , that nothing that lives can enter under ground , without sudden death , yet they continue there , and are not found to diminish , even where they have no access to escape , by coming above ground . Or if it should be imagined , they removed to some other place of the ground , where the Damp is not , how is it , they are not as quickly choaked with it , as Dogs are , and other Animals , which at the first encounter are killed ? If it be inquired , how comes it to pass , that in these Fields of Coals , which are dryed fully ( as was said ) and to which these Damps are incident , because of corrupted Air that remains within the Body of the Coal , or other Metals , how comes it to pass ( I say ) that they are but sometimes incident , and are not alwayes found ? For clearing this , it is certain , that even in the grounds , where these Damps are most frequent , for the reasons above mentioned , yet they are only powerful when the Wind blows from such a certain Point , as some Chimneys , that do only smoke , when the Wind is in such an Airth . This is so generally , and well known , that the Work-men observe it , and when they find the Wind in such a Point , whence they fear the Damp , they will not enter under ground , till trial be made of the Air , which they do in Sinks , by first letting down a lighted Candle , or some burning Coals : which if they do not burn , then there is no access to enter . Secondly , the wind in which this Ill Air is most noxious , and hurtful , blows from that Point , where the Field of Coal lyes , that 's not yet wrought , which seems somewhat strange , and yet when duely considered , it will appear abundantly consonant to reason . An example of this is to be found in the Coal of Tranent and Elphingston , the Streek whereof goes to the rise of the Hill above ground , from NE to SW , as hath been formerly observed . So that the beginning of their Level , is at the NE point of the Streek , from which the Coal hath been wrought up along the Streek towards the SW , the Wastes lying all towards the NE. Yet when the Wind blows from NE , or N , or almost from any other Point of the Compass , they are not troubled with this Damp. But if it blow from SW , and blow hard , they are in hazard to encounter it . And though the Damp is not alwayes found when that Wind blows ( whereof there may be some particular cause ) yet it is never observed in another Wind , whether it blow less or more : the reason whereof may probably be , that the Wind blowing from other Points , as from N , or NE , hath more access to enter the Wastes under ground , and move the Air that is in them , towards the face of the unwrought Coal , whence is supposed to proceed the corrupted Air , that lurks in the Rifts and Cutters thereof , ( from which the Water is drawn away , ) and occasions the Damp. Now this Air being moved by the force of the Wind , keeps the corrupt Air from coming out , it being stronger then the other . Whereas , upon the contrary , while the Wind blows from SW , it entering the empty Rooms , drives the Air under ground from the face of the unwrought Coal , down towards the old wastes , which have their course from the beginning of the Level . By which means , the Air , that is corrupted within the bowels ( to speak so ) of the Coal , comes out to the Wastes , without resistance , it being certain , that Fluid Bodies , as Water , and Air , inclines to move towards that place , where they meet with the least resistance . Hence is it , that the more direct the Wind be , in blowing against the face of the unwrought Coal , as is the Wind from NE , the Ill Air is the more repelled and driven back , but the more oblique it be , as are the Winds from these Points , that are nearest to SW , the Air is not so good and free : which difference is known by the burning of Candles , they burning with greater difficulty in these Winds , than in others , which blow from these Points nearest to N , and NE. Some are of opinion , this Ill Air ( in those places we have been speaking of ) comes from the great Wastes , that ly above the un-wrought Coal , and by strong SW Winds is driven thorow the Cutters thereof . Or the Wind blowing from that Point , and coming thorow these Cutters , brings the corrupted Air alongs with it , even as , after a showr of Rain , a spait of Water comes , and carries alongs with it , both the foul Water and the clean , it meets with . Though this may be probable , which seems to be your own opinion , yet the other seems to be more probable . The other sort of Damp , is that which they call want of Air ; and though the term be not altogether proper ( there being no space without some Air ) yet there is a want of Air , which is sufficient for respiration of Animals , or for the burning of fire . This is ordinarily found in the running of Mines under ground , for conveying of Water from Coal , or other Metals , or in the waste Rooms of Coals , where the Sinks are very deep , and to evite the charge thereof , there is some necessity to work as far under ground for winning of Coal , as is possible , without new Sinks . The cause seems to be , that the Air under ground , in such cases , wants communication with the Air above ground , because it is found , that by giving more communication , the evil is cured . Whence comes the necessity of Air-holes in Levels , which are so many Sinks set down , for no other use , but for giving Air to the Workers ▪ Some are of opinion , that this defect might be supplied by the blowing of Bellows , from above ground , through a Stroop of Leather , or of some other thing , which must run along to the end of the Level , for keeping the Air there in motion . But I have not yet heard , that it hath been made practicable . The effects of this Damp are not so dangerous , as these of the other . 'T is true , it will kill Animals , and extinguish burning Coals and Candles , but not so suddenly as the former ; and so people are not so readily surprized by it . The other seems to kill by some poisonous quality : in this Animals dies for want of sufficient Air for respiration . Therefore in advancing in a Coal Room , or Level where this is , you shall see the flame of the Candle grow less and less by degrees , till at last it be totally extinguished , and the person entering , shall find the difficulty of breathing grow greater , as he advanceth forward , till at last he cannot breath at all . Hence it is , that few or none are killed by this kind of Damp , and all its prejudice is , that it renders the work more chargeable , when there is a necessity to remove it . For that , which they call Wild-fire , it being a thing not incident , but to very few Coals , is less known , than any of the rest of the accidents that follows Coals . The account I have heard of it , is , that in some Coals , which naturally are full of Oil , and that are ( as they call them ) fa●t Co●ls , there is a certain Fire , which is as a Meteor , and I judge , that from its resemblance to Ignis fatuus , which the Vulgar termeth Wild-fire , it hath the same name . It seems to be composed of some fatt oily vapour , that goeth out of the Coal , the Pores thereof being once opened , which is kindled after the same manner , as those fires above ground are , which are most ordinarily found in fatt , and marrish ground . Of this fire it is reported , that in the day time , while the Work men , are working in the Coal-roomes , it comes to no height , though it be sometimes seen in little holes of the Coal-wall , shining like kindled sulphure , but without force : but when the Work-men are once removed , and have stayed out all night , it gathers to such a strength , that at its first encountering with fire , which the Coal-hewers are necessit●te to have , by taking in of light , it breaks out with such a violence , that it kills any person , it finds in its way . The reason , why it is without this force , while the Work-men are in the place , seems to be this , that they working with such violence , and motion as they do , do certainly move the Air considerably , it being contained in so narrow a place , as a Coal-room . And this Air being violented by motion , moves that oily vapour , whereof the fire is formed , so that it gets not liberty to unit it self , being dissipated by the motion of the Air. But so soon , as the Air is still , and quiet , after the Work-men are gone home , it units it self , and gathers force , and therefore , so soon , as it meets with fire , which is more forcible , than the flame that is kindled in it , it rarifieth ; the sulphurious parts being kindled , and forceth it self out , as powder out of a Gun. For it hath been observed , that if any person stay in the Coal-sink while it breaks within the Coal-room , they are in danger of being killed . The ordinary way by which the hurt of it is prevented , is by a person that enters , before the Work-men , who being covered with wet sack-cloath , when he comes near the Coal-wall , where the Fire is feared , he creepeth on his belly , with a long Poll before him , with a lighted candle on the end thereof , with whose flame the Wild-fire meeting , breaketh with violence , and running alongs the roof , goeth out with a noise , at the mouth of the Sink , the person that gave fire , having escaped , by creeping on the ground , and keeping his face close to it , till it be over-passed , which is in a moment . The place , where this was most known , was in a Coal be-west Leith , in a piece of Land called Werdy , which for want of Level , and the violence of that Fire , the Owners were forced to abandon . I come now to the last part , which I promised to speak of , namely of the best way for trying of grounds , to find Coal , where never any hath hitherto been discovered , and of carrying on of Levels , for draining the Water of Coals and making it workable . As to the first part , there are but three wayes . First by sinking , which is most chargeable , in regard , that in such grounds , where the Metals are all intire , Water abounds , and this doth not only bring the Master under a necessity of great expence for drawing the Water , but also rendereth it impossible to get sinked to any deepness , which may suffice , for giving an account of all the Metals to be found , within the field , that may be rendred workable . There was a second way invented to supply this defect , which is by boaring , with an instrument made of several Rods of Iron , which boareth thorow the Metals , and tryes them . This way in my opinion , is worse then the former . For first , if the Coal ly deep , in the place where you try by boaring , it becomes almost as tedious , and expensive , as sinking , the drawing of the Rodes , consuming so much time , in regard it must be frequently done . Next , in boaring , suppose the nature of the Metals , be found , yet thereby their course can never be known , till they be sinked , which is one of the things most considerable in the search of a Coal , because thereby is known , whether it be workable , with advantage or not , and whether it be possible to draw Water from it by a Level , or otherwise . Lastly , this way leaves the Master at an uncertainty ( notwithstanding the Coal had been found ) of its goodness , as to its nature , and as to its thickness . As to its goodness , because all that is found of the Coal , by this boaring instrument , is some small dross , which remains after the washing of the thing that 's brought up in the wumble , by which none can judge of its goodness , or badness . As to its thickness , because it is impossible to discern exactly , when the boaring-instrument hath passed the Coal : all the rule for trying thereof , being the kind of Metal that is brought up in the wumble . Now , I have known in my experience a Coal boared , which the B●arer by that rule hath judged four foot in thickness , yet when it came to be sinked , hath not proven one . The reason whereof , is obvious , because the boaring-irons , being long , and weighty in lifting them up , and down , they break the Coal , already pierced ; and this falling down among the Metals , they are piercing , and being found in the wumble with them ( especially when the Metal under the Coal , is a black Till ) gives g●ound to imagine , that all that time , they have been peircing a Coal , and so consequently , the Coal must be of such a thickness . The last , and best way of trial , is that which is termed an ranging over the Metals . For doing whereof , this method , is to be observed . Suppose there be any place within in the ground to be searched , where the course of Metals can be seen , as in the banks of a River , or Rivolet , or Sea-banks , when the place is near the Sea , then consideration must be had how far the lowest of these Metals , can go before they Crop out to the Grass , which will be known by observing the Dipp or declination of the Metals , and the Rise of the ground above , whereof a just allowance must be given , and having digged before the said Crop , you shall certainly find , the Metal , that is next under it , and if that prove not Coal , keeping the former proportion , you must advance , and digg before its Crop , and so shall you find , the next Metal under it , and so still , till you have tried your ground , and found the Crops of all your Metals within it . But if there be no Water-banks , or such like , to give you the first view , of the course of your Metals , then must you sink first at random , and having once past the Clay , you will readily overtake some Metals , whereby you will know the course of the rest , and having once found the Dipp and Rise , you must follow the method of ranging already prescribed , except the ground so to be tried , contains not within it self the Crops of the Metals , the body whereof lies in it , whether of Coal , or Stone , in that case , there is no way to try , but by sinking , or boaring . The way of ranging is conspicuous in the following figure . Figure 11. The piece of ground to be tried , is PN , where there are several Seams of Metals , that Cropps out at the Points KLMN . Suppose the lowest to be the Coal , viz. IN , for which you are to make trial . You Digg first at K , without the Cropp of the Seam FK , and you dig till you find the other Seam of Stone GL , at the Point C. Following the Rule before given , you advance before its cropp , and diggs at L , and finds the other Seam of Stone HM , at the point D : from which you also advance , and diggs before its cropp , at the point M , and finds your Coal at the point E. But , if by advancing over the cropps of these Metals , which comes out from under one another , you find no Coal ; then you are to range backward , for the cropps of Metals lying above these , where haply the Coal may be , as at O , and P. This in my opinion , is the most certain and exact way of trying Fields for Coal , or any other Metal of that nature , and least chargeable of all others . The second of this last part , I promised to speak of , was in order to Levels , or Coal-Mines , which are nothing else , but Conduits or Gutters made under ground , for conveying of the Water from the Coal , and so rendering it workable . It seems that a very little time before this , that way of Mineing under ground hath not been fallen upon . For there are to be found Coals wasted in their Cropps only ; for conveying the Water whereof , they have made a Conduit , or Level , which hath been open to the Surface , like a great Ditch , some whereof have been ten or twelve fathom in their deepness . The beginning of the Level ( to keep the term used ) must alwayes be at the lowest part of the Field , where the Coal lyes to be dryed . Some whereof , by the rising of the ground , and the Streek of the Coal rising that way ( as we shew before ) gives the advantage of a Free Level , that is , when the Water comes above ground of its own accord , without being forced by drawing . In others , there is a necessity of Engines to draw the Water from the lowest part of the Level , and bring it above ground ; which Engines are of several sorts . As when men draw with ordinary Buckets , or when there is a horse-work , or water-work , and that either by a Chain with Plates , and a Pump , or with a Chain and Buckets ; all which are very common , especially those we have in Scotland , they being capable to draw but a very small draught , making only use of one Sink for that effect . But there are to be seen in the North of England , in Bishoprick , Water-works , by which Water is drawn above 40 fathom in perpendicular , but not all in one Sink . The manner whereof is thus , there being a Sink from the end of their Level , to the surface of the earth , where their Works are going , 40 fathom deep , which must dry the Coal-Sinks at 60 or 70 , which ly above the Banks of the River , where the Water-works are scituated , there is first one 40 fathom deep from the Grass . Another in a right Line from that , of 24. Another of 12 ; upon all which there are Water-works . In the first Sink the Water is drawn from the bottom 12 fathom , and thence conveyed into a Level or Mine , which carries it away to the second Sink . By the second Work , the Water is drawn out of the second Sink 14 fathom , from the bottom , and set in by a Level to the third Sink , which being only 12 fathom deep , the Water-work sets it above ground . The form of the Engine is after this manner . In the first Sink there is an Outter-wheel moved , as other Milns are , by the Water of the River : upon the end of the Axle-tree of which Wheel , there is a Ragg-wheel , turning vertically , as doth the Outer-wheel . This Ragg-wheel by a Nutt , or Trinle turns another , which moves horizontally , the Axle-tree whereof goes right down in the Sink , and may be is 8 or 10 fathom ; at the end whereof there is another Ragg , which by a Nutt turns another Wheel , which goes vertically as the first Ragg , and causeth another Wheel with a long Axle-tree turn as the first , and so down till it come to the Wheel , which turns the Axle-tree , by which the Chain is drawn . The second Sink , hath such another Engine , but not so many Wheels , in regard it is not so deep . The third , hath only one single Wheel , whereby the Water is drawn above ground . The most curious of these Engines , that are to be seen , are at Ravensworth near to Newcastle , which belongs to Sir Thomas Liddel , a most ingenious Gentleman , who , for procuring a Fall of Water , which may serve the Wheels of all the three Sinks , hath erected the first work upon Pillars like a Wind-Mill , pretty high above ground , from which the Water falling , makes the second go closs above ground . And to make the Water fall to the third , the whole Wheel is made go within the surface of the ground , which terminats at a River under the Works , which Mine is of a considerable length . Where Water cannot be had to make such Works go , they use Horse-works , but not with so good success , being more chargeable , and not having so much force and power , as the Water-works . But I am of opinion , that Wind-works might serve well , where Water cannot be had ; and when no Wind should happen to blow , the same Works might be supplied by Horse : and that the Wind , when it blows but ordinarily , hath as much force , as so much Water , which is made use of for turning such Wheels , is to me unquestionable . For I have seen in Holland , a Wind-Mill , that by the motion of the Outter-wheel , caused seven pair of Mill-stones to go at once , besides another motion for bringing the Victual from the ground , four or five Stories high , to be Grund . And several Saw-Mills , which besides six or seven great Saws , they caused go , did by another motion bring up from the Water great Trees like Ship-Masts , to be sawen , and placed them right against the Saw ; all which could not be but of greater weight , than 10 or 12 fathom of Chain with Buckets , or Plates for drawing of Water . But to return , for the right making of a Level , the true hight of the ground , where the Coal lyes must be first taken , that it may be known , how much of the field can be drained by it ; which must be done , either with a Quadrant , or with an Instrument made express . Then care must be taken , to take the lowest part for the mouth of the Level , that the field can afford , and from that it must be carried in a straight line towards that part of the field , where the Coal is thought to be encountered by the Mine . In working whereof , two things are in a special manner to be reguarded . First , that the Level be wrought without ascent , or descent : the best way for trying this , being by the surface of the Water passing through it , which ought to be as little moving , as can be : for the loss of one foot of Level , which the ground gives , is a loss of a considerable parcel of Coal to be digged , especially if it be state . If there occur any Metals , which are impregnable , in the course of the Level , so that it is impossible , to follow so straight a line , in regard the Mine must be wrought over the top of that stone , which is unworkable , in that case , there is but one of two to serve the loss of Level ; either the Coal rises in Streek towards which the Mine is carried , and if that be , then after that stone is past , the Level must be carried , as low , as it was before it encountered the same , and the course of the Water shall not be obstructed , because the sourse , viz. the Coal from whence the Water comes , rising higher than the Stone , the Water shall easily pass over that hight . Hence it is , that we see in some Coals , that have been wrought , at the lowest point of their Streek by a drawing-sink , and the Streek rising from that point , the Water that hath come off the Coal , being in its Sourse higher , than the mouth of that drawing-sink , hath made it to over-run , and serve to discharge all the Water , that comes therefrom . But , if the Mine be run to a Coal , that after it hath overtaken it , rises no higher in Streek , than the Mine it self , the Water that comes from it , will not pass over any hight in its way , but will be unquestionably stopped . Therefore , in case such an impediment could not be removed , as many times such Metals will fall in , which are unworkable in a direct line , the use of a Siphon might be tried , which would unquestionably supply the loss of about 32 foot of Level , this being the hight in Perpendicular , to which the Pressure of the Air , is able to raise Water up thorow a Siphon . The next thing to be observed in carrying on of Levels , are the Air-holes , for which there is a necessity indispensable . In setting down whereof , care must be had , that they be not directly upon the Mine , lest rubbish falling thorow from above ground , should stop , and obstruct the same , and so obstruct the course of the Water ; and therefore it 's better they be set down at a side , their only use being to communicate fresh Air to the Work-men , which if it could be otherwise supplied ( as I think it not utterly impossible ) would render the charge of the Coal-works a great deal more easy . Other things might be spoken to of Levels , as that some run with the course of Metals , they pass thorow ; and that some run against that course ; and of bringing Level from the Dip of an upper-Coal , which hath a Level of its own , to dry a Coal lying under it , which cannot be otherwise done . But these things being common and obvious to any , who have but the smallest skill and experience , I shall forbear . This confused account , your importunity hath drawen from me , for which if your Book suffer censure , which I grant it may do , as to this part of it , you are to blame your self , and so I rest and am , &c. FINIS . 
A15364	----	A discourse concerning a new world & another planet in 2 bookes. Discovery of a world in the moone Wilkins, John, 1614-1672. 1640 Approx. 563 KB of XML-encoded text transcribed from 261 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2004-05 (EEBO-TCP Phase 1). A15364 STC 25641 ESTC S119973 99855177 99855177 20652 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A15364) Transcribed from: (Early English Books Online ; image set 20652) Images scanned from microfilm: (Early English books, 1475-1640 ; 1016:20) A discourse concerning a new world & another planet in 2 bookes. Discovery of a world in the moone Wilkins, John, 1614-1672. Marshall, William, fl. 1617-1650, engraver. [10], 242, [6]; [14], 246, [2] p. : ill. (woodcuts, metal cut) Printed [by John Norton and R. Hearne] for Iohn Maynard, & are to be sold at the George, in Fleetstreet neare St. Dunstans Church, [London] : 1640. By John Wilkins. An expanded edition of: The discovery of a world in the moone. The general title page is engraved and signed: W. Marshall, sculpsit. "The first book· The discovery of a new world .. The third impression. Corrected and enlarged .. Printed by Iohn Norton" and "A discourse concerning a nevv planet .. Printed by R[ichard]. H[earne]." each have separate dated letterpress title page, pagination, and register. Richard Hearne's name from STC. ² P7 is a cancel (printed as 2a8). The cancellandum lacks the engraving on the verso. The final leaves to part 1 are [1] errata and [2-3] "The propositions that are proved in this discourse", signed "R2" (some copies signed "aa") and "aa2" respectively. With a final errata leaf. Reproduction of the original in the Henry E. Huntington Library and Art Gallery. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. 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Printed for Iohn Maynard , & are to be sold at the George , in Fleetstreet neare St. Dunstans Church . 1640. THE FIRST BOOK . THE DISCOVERY OF A NEW WORLD OR , A Discourse tending to prove , that 't is probable there may be another habitable World in the Moone . With a Discourse concerning the possibility of a Passage thither . The third impression . Corrected and enlarged . Quid tibi inquis ista proderunt ? Si nihil aliud , hoc certè , sciam omnia hic angusta esse . Seneca praef . ad I lib. Nat. Quest. LONDON : Printed by IOHN NORTON for IOHN MAYNARD , and are to be sold at the George in Fleetstreet , neere St. Dunstons Church . 1640. To the Reader . IF amongst thy leisure houres , thou canst spare any for the perusal of this discourse , and dost looke to find somewhat in it which may serve for thy information and benefit : let me then advise thee to come unto it with an equall minde , not swayed by prejudice , but indifferently resolved to assent unto that truth which upon deliberation shall seeme most probable unto thy reason , and then I doubt not , but either thou wilt agree with mee in this assertion , or at least not think it to be as farre from truth , as it is from common opinion . Two cautions there are which I would willingly admonish thee of in the beginning . 1. That thou shouldst not here looke to find any exact , accurate Treatise , since this discourse was but the fruit of some lighter studies , and those too hudled up in a short time , being first thought of and finished in the space of some few weekes , and therefore you cannot in reason expect , that it should be so polished , as perhaps , the subject would require , or the leisure of the Author might have done it . 2. To remember that I promise only probable arguments for the proofe of this opinion , and therefore you must not looke that every consequence should be of an undeniable dependance , or that the truth of each argument should bee measured by its necessity . I grant that some Astronomical appearances may possibly be solved otherwise than here they are . But the thing I aime at is this , that probably they may so be solved , as I have here set them downe : Which , if it be granted ( as I think it must ) then I doubt not , but the indifferent Reader will find some satisfaction in the maine thing that is to be proved . Many ancient Philosophers of the better note , have formerly defended this assertion , which I have here laid downe ; and it were to be wished , that some of us would more apply our endeavours unto the examination of these old opinions , which though they have for a long time lien neglected by others , yet in them may you find many truths well worthy your paines and observation . T is a false conceit for us to thinke , that amongst the ancient varietie and search of opinions , the best hath still prevailed . Time ( saith the learned Verulam ) seemes to be of the nature of a river or streame , which carrieth down to us that which is light or blown up , but sinketh that which is weighty and solid . It is my desire that by the occasion of this discourse , I may raise up some more active spirit to a search after other hidden and unknowne truths . Since it must needes be a great impediment unto the growth of sciences , for men still so to plod on upon beaten principles , as to be afraid of entertaining any thing that may seeme to contradict them . An unwillingnesse to take such things into examination , is one of those errours of learning in these times observed by the judicious Verulam . Questionlesse , there are many secret truths , which the ancients have passed over , that are yet left to make some of our age famous for their discovery . If by this occasion I may provoke any Reader to an attempt of this nature , I shall think my selfe happy , and this worke successefull . Farewell . The first Book . That the Moone may be a World. The first Proposition , by way of Preface . That the strangenesse of this opinion is no sufficient reason why it should be rejected , because other certaine truths have beene formerly esteemed ridiculous , and great absurdities entertained by common consent . THere is an earnestnesse and hungering after noveltie , which doth still adhere unto all our natures , and it is part of that primitive image , that wide extent and infinite capacity at first created in the heart of man. For this , since its depravation in Adam , perceiving it felfe altogether emptied of any good , doth now catch after every new thing , conceiving that possibly it may finde satisfaction among some of its fellow creatures . But our enemie the devill ( who strives still to pervert our gifts , and beat us with our owne weapons ) hath so contriv'd it , that any truth doth now seeme distastefull for that very reason , for which errour is entertain'd .. Novelty . For let but some upstart heresie be set abroach , and presently there are some out of a curious humour ; others , as if they watched an occasion of singularity , will take it up for canonicall , and make it part of their creede and profession ; whereas solitary truth cannot any where find so ready entertainment ; but the same Novelty which is esteemed the commendation of errour , and makes that acceptable , is counted the fault of truth , and causes that to be rejected . How did the incredulous World gaze at Columbus , when hee promised to discover another part of the earth , and he could not for a long time , by his confidence , or arguments , induce any of the Christian Princes , either to assent unto his opinion , or goe to the charges of an experiment ? Now if he , who had such good grounds for his assertion , could finde no better entertainement among the wiser sort , and upper end of the World ; 't is not likely then that this opinion which I now deliver , shall receive any thing from the men of these dayes , especially our vulgar wits , but misbeliefe or derision . It hath alwayes beene the unhappinesse of new truths in Philosophy , to be derided by those that are ignorant of the causes of things , and rejected by others , whose perversenesse ties them to the contrary opinion , men whose envious pride will not allow any new thing for truth , which they themselves were not the first inventors of . So that I may justly expect to be accused of a pragmaticall ignorance , & bold ostentation ; especially since for this opinion Xenophanes , a man whose authority was able to adde some credit to his assertion , could not escape the like censure from others . For Natales Comes speaking of that Philosopher , and this his opinion , saith thus , Nonulli ne nihil scisse videantur , aliqua nova monstra in Philosophiam introducunt , ut alicujus rei inventores fuisse appareant . Some there are who lest they might seeme to know nothing , will bring up monstrous absurdities in Philosophy , that so afterward they may be famed for the invention of somewhat . The same Author doth also in another place accuse Anaxagoras of folly for the same opinion . Est enim non ignobilis gradus stultitiae , vel si nescias quid dicas , tamen velle de rebus propositis hanc vel illam partem stabilire . 'T is none of the worst kindes of folly , boldly to affirme one side or other , when a man knowes not what to say . If these men were thus censur'd , I may justly then expect to be derided by most , and to be beleeved by few or none ; especially since this opinion seemes to carry in it so much strangenesse , and contradiction to the generall consent of others . But how ever , I am resolved that this shall not be any discouragement , since I know that it is not common opinion that can either adde or detract from the truth . For , 1. Other truths have beene formerly esteemed altogether as ridiculous as this can be . 2. Grosse absurdities have beene entertained by generall opinion . I shall give an instance of each , that so I may the better prepare the Reader to consider things without a prejudice , when hee shall see that the common opposition against this which I affirme , cannot any way derogate from its truth . 1. Other truths have beene formerly accounted as ridiculous as this . I shall specifie that of the Antipodes , which have beene denied , and laught at by many wise men and great Schollers , such as were Herodotus , Chrysostome , Austine , Lactantius , the venerable Bede , Lucretius the Poet , Procopius , and the voluminous Abulensis , together with all those Fathers or other Authors who denied the roundnesse of the heavens . Herodotus counted it so horrible an absurdity , that hee could not forbeare laughing to think of it . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . I cannot choose but laugh , ( saith he ) to see so many men venture to describe the earths compasse , relating those things that are without all sense , as that the Sea flowes about the World , and that the earth it selfe is round as an Orbe . But this great ignorance is not so much to be admired in him , as in those learneder men of later times , when all Sciences began to flourish in the World. Such were St. Chrysostome , who in his 14 Homily upon the Epistle to the Hebrewes , dos make a chalenge to any man that shall dare to defend that the heavens are round , and not rather as a tent . Thus likewise St. Austine , who censures that relation of the Antipodes to be an incredible fable ; and with him agrees the eloquent Lactantius , Quid illi qui esse contrarios vestigiis nostris Antipodes putant ? num aliquid loquuntur ? aut est quispiam tam ineptus , qui credat esse homines , quorum vestigia sunt superiora quàm capita ? aut ibi quae apud nos jacent inversapendere ? fruges & arbores deorsum versus crescere , pluvias & nives , & grandinem sursum versus cadere in terram ? & miratur aliquis hortos pensiles inter septem mira narrari , quum Philosophi , & agros & maria , & urbes & montes pensiles faciunt , &c. What ( saith he ) are they that think there are Antipodes , such as walk with their feet against ours ? doe they speake any likelihood ? or is there any one so foolish as to beleeve that there are men whose heeles are higher than their heads ? that things which with us doe lie on the ground , doe hang there ? that the Plants and Trees grow downwards , that the haile , and raine , and snow fall upwards to the earth ? and doe we admire the hanging Orchards amongst the seven wonders , whereas here the Philosophers have made the Field and Seas , the Cities & mountains hanging ? What shall we think ( saith hee in Plutarch ) that men doe cling to that place like wormes , or hang by their clawes as Cats ? or if we suppose a man a little beyond the Center , to be digging with a spade , is it likely ( as it must be according to this opinion ) that the earth which hee loosened , should of it selfe ascend upwards ? or else suppose two men with their middles about the Center , the feet of the one being placed where the head of the other is , and so two other men crosse them , yet all these men thus situated according to this opinion should stand upright , and many other such grosse consequences would follow ( saith he ) which a false imagination is not able to fancie as possible . Vpon which considerations , Bede also denies the being of any Antipodes , Neque enim Antipodarum ullatenus est Fabulis accommodandus assensus , Nor should we any longer assent to the Fable of Antipodes . So also Lucretius the Poet speaking of the same subject , sayes , Sed vanus stolidis haec omnia finxerit error . That some idle fancie faigned these for fooles to beleeve . Of this opinion was Procopius Gazaeus , but hee was perswaded to it by another kinde of reason ; for hee thought that all the earth under us was sunk in the water , according to the saying of the Psalmist , He hath founded the earth upon the Seas ; and therefore hee accounted it not inhabited by any . Nay , Tostatus a man of later yeares and generall learning , doth also confidently deny that there are any such Antipodes , though the reason which hee urges for it , be not so absurd as the former ; For the Apostles , saith hee , travelled through the whole habitable world , but they never passed the Equinoctiall ; and if you answer that they are said to goe through all the earth , because they went through all the knowne world ; he replies , that this is not sufficient , since Christ would have all men to be saved , and come to the knowledge of his truth , and therefore 't is requisite that they should have travelled thither also , if there had beene any Inhabitants ; especially since hee did expresly command them to goe and teach all nations , and preach the Gospell through the whole world , and therefore hee thinks that as there are no men , so neither are there seas , or rivers , or any other conveniencie for habitation . 'T is commonly related of one Virgilius , that hee was excommunicated and condemned for a Heretique by Zachary Bishop of Rome , because hee was not of the same opinion . But Baronius sayes , it was because hee thought there was another habitable world within ours . How ever , you may well enough discerne in these examples how confident many of these great Schollars were in so grosse an errour , how unlikely , what an incredible thing it seemed to them , that there should be any Antipodes ; and yet now this truth is as certaine and plain , as sense or demonstration can make it . This then which I now deliver , is not to be rejected , though it may seeme to contradict the common opinion . 2. Grosse absurdities have beene entertained by generall consent . I might instance in many remarkable examples , but I will onely speake of the supposed labour of the Moone in her eclipses , because this is neerest to the chiefe matter in hand , and was received as a common opinion amongst many of the Ancients , In so much that from hence they stiled eclipses by the name of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 passions , or in the phrase of the Poets , Solis lunaeque labores . And therefore Plutarch speaking of a Lunary eclipse , relates , that at such times 't was a custome amongst the Romans ( the most civill and learned people in the world ) to sound brasse Instruments , and hold great torches toward the heaven . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . For by this meanes they supposed the Moone was much eased in her labours ; and therefore Ovid calls such loud Instruments the auxiliaries or helps of the Moone , Cum frustra resonant aera auxiliaria Lunae . And therefore the Satyrist too , describing a loud Scold , sayes , She was able to make noise enough to deliver the labouring Moone . Vna laboranti poterit succurrere Lunae . Now the reason of all this their ceremonie , was , because they feared the world would fall asleepe , when one of its eyes began to wink , and therefore they would doe what they could by loud sounds to rouse it from its drowsinesse , and keepe it awake : by bright torches , to bestow that light upon it which it began to lose . Some of them thought hereby to keepe the Moone in her orbe , whereas otherwise shee would have fallen downe upon the earth , and the world would have lost one of its lights ; for the credulous people beleeved , that Inchanters and Witches could bring the Moone downe , which made Virgil say , Cantus & è coelo possunt deducere Lunam . And those Wizards knowing the times of her eclipses , would then threaten to shew their skill , by pulling her out of her orbe . So that when the silly multitude saw that shee began to looke red , they presently feared they should lose the benefit of her light , and therefore made a great noise that shee might not heare the sound of those Charmes , which would otherwise bring her downe ; and this is rendred for a reason of this custome by Pliny and Propertius : Cantus & è curru lunam deducere tentant , Et facerent , si non aera repulsa sonent . Plutarch gives another reason of it , and he sayes , 't is because they would hasten the Moone out of the dark shade wherein she was involv'd , that so shee might bring away the soules of those Saints that inhabit within her , which cry out by reason they are then deprived of their wonted happinesse , and cannot heare the Musick of the Spheares , but are forced to behold the torments , and wailing of those damned soules which are represented to them as they are tortured in the region of the ayre . But whether this or what ever else was the meaning of this superstition , yet certainly 't was a very ridiculous custome , and bewrayed a great ignorance of those ancient times ; especially since it was not only received by the vulgar , such as were men of lesse note and learning , but beleeved also by the more famous and wiser sort , such as were those great Poets , Stesichorus and Pindar . And not onely amongst the more sottish Heathens , who might account that Planet to be one of their gods ; but the Primitive Christians also were in this kind guilty , which made Saint Ambrose so tartly to rebuke those of his time , when he said , Tum turbatur carminibus Globus Lunae , quando calicibus turbantur & oculì . When your heads are troubled with cups , then you think the Moone to be troubled with charmes . And for this reason also did Maximus a Bishop , write a Homily against it , wherein hee shewed the absurdity of that foolish superstition . I remember that Ludovicus Vives relates a more ridiculous story of a people that imprisoned an Asse for drinking up the Moone , whose image appearing in the water , was covered with a cloud as the Asse was drinking , for which the poore beast was afterward brought to the barre to receive a sentence according to his deserts , where the grave Senate being set to examine the matter , one of the Counsell ( perhaps wiser than the rest ) rises up , and out of his deepe judgement thinks it not fit that their Towne should lose its Moone , but that rather the Asse should be cut up and that taken out of him ; which sentence being approved by the rest of those Politicians , as the subtillest way for the conclusion of the matter , was accordingly performed . But whether this tale were true or no , I will not question ; however , there is absurdity enough in that former custome of the Ancients , that may confirme the truth to be proved , and plainely declare the insufficiencie of common opinion to adde true worth or estimation unto any thing . So that from that which I have said may be gathered thus much . 1. That a new truth may seeme absurd and impossible not onely to the vulgar , but to those also who are otherwise wise men and excellent Schollars ; and hence it will follow that every new thing which seemes to oppose common principles is not presently to be rejected , but rather to be pry'd into with a diligent enquiry , since there are many things which are yet hid from us , and reserv'd for future discoverie . 2. That it is not the commonnesse of an opinion that can priviledge it for a truth ; the wrong way is sometime a well beaten path , whereas the right way ( especially to hidden truths ) may be lesse trodden and more obscure . True indeed , the strangenesse of this opinion will detract much from its credit ; but yet wee should know that nothing is in it selfe strange , since every naturall effect has an equall dependance upon its cause , and with the like necessity doth follow from it ; so that 't is our ignorance which makes things appeare so ; and hence it comes to passe that many more evident truths seeme incredible to such who know not the causes of things : you may as soone perswade some Country Peasants that the Moone is made of greene Cheese ( as wee say ) as that 't is bigger than his Cart-wheele , since both seeme equally to contradict his sight , and he has not reason enough to leade him farther than his senses . Nay suppose ( saith Plutarch ) a Philosopher should be educated in such a secret place , where hee might not see either Sea or River , and afterwards should be brought out where one might shew him the great Ocean , telling him the quality of that water , that it is brackish salt and not potable , and yet there were many vast creatures of all forms living in it , which make use of the water as wee doe of the ayre , questionlesse hee would laugh at all this as being monstrous lies , and fables , without any colour of truth . Just so will this truth which I now deliver , appeare unto others ; because we never dreamt of any such matter as a World in the Moone ; because the state of that place hath as yet beene vailed from our knowledge , therefore we can scarcely assent to any such matter . Things are very hardly received which are altogether strange to our thoughts and our senses . The soule may with lesse difficulty be brought to beleeve any absurdity , when as it has formerly beene acquainted with some colours and probabilities for it ; but when a new , and an unheard of truth shall come before it , though it have good grounds and reasons , yet the understanding is afraid of it as a stranger , and dares not admit it into his beleefe , without a great deale of reluctancie and triall . And besides , things that are not manifested to the senses , are not assented unto without some labour of minde , some travaile and discourse of the understanding ; and many lazie soules had rather quietly repose themselves in an easie errour , than take paines to search out the truth . The strangenesse then of this opinion which I now deliver , will be a great hinderance to its beliefe , but this is not to be respected by reason it cannot be helped . I have stood the longer in the Preface , because that prejudice which the meere title of the booke may beget , cannot easily be removed without a great deale of preparation , and I could not tell otherwise how to rectifie the thoughts of the Reader for an impartiall survey of the following discourse . I must needs confesse , though I had often thought with my selfe that it was possible there might be a world in the Moone , yet it seemed such an uncouth opinion that I never durst discover it , for feare of being counted singular , and ridiculous ; but afterward having read Plutarch , Galileus , Keplar , with some others , and finding many of mine owne thoughts confirmed by such strong authority , I then concluded that it was not onely possible there might be , but probable that there was another habitable world in that Planet . In the prosecuting of this assertion , I shall first endeavour to cleare the way from such doubts as may hinder the speed or ease of farther progresse ; and because the suppositions imply'd in this opinion , may seeme to contradict the principles of reason or faith , it will be requisite that I first remove this scruple , shewing the conformity of them to both these , and proving those truths that may make way for the rest , which I shall labour to performe in the second , third , fourth , and fifth Chapters , and then proceede to confirme such Propositions , which doe more directly belong to the maine point in hand . Proposition 2. That a plurality of worlds doth not contradict any principle of reason or faith . T Is reported of Aristotle , that when he saw the Books of Moses , hee commended them for such a majestick stile as might become a God , but withall hee censured that manner of writing to be very unfitting for a Philosopher ; because there was nothing proved in them , but matters were delivered as if they would rather command than perswade beliefe . And 't is observed that hee sets downe nothing himselfe , but hee confirmes it by the strongest reasons that may be found , there being scarce an argument of force for any subject in Philosophy , which may not be picked out of his Writings ; and therefore 't is likely if there were in reason a necessity of one onely world , that hee would have found out some such necessary proofe as might confirme it : Especially since hee labours for it so much in two whole Chapters . But now all the arguments which hee himselfe urges in this subject , are very weake , and farre enough from having in them any convincing power . Therefore 't is likely that a plurality of worlds doth not contradict any principle of reason . However , I will set downe the two chiefe of his arguments from his owne works , and from them you may guesse the force of the other . The first is this , since every heavie body doth naturally tend downwards , and every light body upwards , what a hudling and confusion must there be if there were two places for gravity , and two places for lightnesse : for it is probable that the earth of that other world would fall down to this Center , and so mutually the ayre and fire here ascend to those Regions in the other , which must needs much derogate from the providence of nature , and cause a great disorder in his works . But ratio haec est minimè firma , ( saith Zanchy ) And if you well consider the nature of gravity , you will plainely see there is no ground to feare any such confusion ; for heavinesse is nothing else but such a quality as causes a propension in its subject to tend downwards towards its owne Center ; so that for some of that earth to come hither , would not be said a fall but an ascension , since it moved from its own place , and this would be impossible ( saith Ruvio ) because against nature , and therefore no more to be feared than the falling of the Heavens . If you reply that then according to this , there must be more Centers of gravity than one ; I answer . 'T is very probable there are , nor can we well conceive , what any piece of the Moon would doe being severed from the rest in the free and open ayre , but only returne unto it againe . Another argument hee had from his Master Plato , that there is but one world , because there is but one first mover , God. Infirma etiam est haec ratio ( saith Zanchy ) and we may justly deny the consequence , since a plurality of worlds doth not take away the unity of the first mover . Vt enim forma substantialis , sic primum efficiens apparentem solummodo multiplicitatem induìt per signatam materiam ( saith a Country-man of ours . ) As the substantiall forme , so the efficient cause hath only an appearing multiplicity from its particular matter . You may see this point more largely handled , and these Arguments more fully answered by Plutarch in his booke ( why Oracles are silent ) and Iacob Carpentarius in his comment on Alcinous . But our opposites the Interpreters themselves , ( who too often doe jurare in verba magistri ) will grant that there is not any strength in these consequences , and certainly then such weake arguments could not covince that wise Philosopher , who in his other opinions was wont to be swayed by the strength and power of reason : wherefore I should rather think that he had some by-respect , which made him first assent to this opinion , and afterwards strive to prove it . Perhaps it was because hee feared to displease his scholler Alexander , of whom 't is related that he wept to heare a disputation of another world , since he had not then attained the Monarchy of this ; his restlesse wide heart would have esteemed this Globe of Earth not big enough for him , if there had beene another , which made the Satyrist say of him , Aestuat infoelix angusto limite mundi . That he did vex himselfe and sweat in his desires , as being pend up in a narrow roome , when hee was confin'd but to one world . Before , he thought to seat himselfe next the Gods ; but now , when hee had done his best , hee must be content with some equall , or perhaps superiour Kings . It may be , that Aristotle was moved to this opinion , that hee might thereby take from Alexander the occasion of this feare and discontent ; or else , perhaps , Aristotle himselfe was as loth to hold the possibility of a world which he could not discover , as Alexander was to heare of one which he could not conquer . 'T is likely that some such by-respect moved him to this opinion , since the arguments hee urges for it , are confest by his zealous followers and commentators , to be very fleight and frivolous , and they themselves grant , what I am now to prove , that there is not any evidence in the light of naturall reason , which can sufficiently manifest that there is but one world . But however some may object , would it not be inconvenient and dangerous to admit of such opinions that doe destroy those principles of Aristotle , which all the world hath so long followed ? This question is much controverted by some of the Romish Divines ; Campanella hath writ a Treatise in defence of it , in whom you may see many things worth the reading and notice . To it I answer , that this position in Philosophy , doth not bring any inconvenience to the rest , since 't is not Aristotle , but truth that should be the rule of our opinions , and if they be not both found together , we may say to him , as hee said to his Master Plato , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Though Plato were his friend , yet hee would rather adhere to truth than him . I must needs grant , that wee are all much beholden to the industry of the ancient Philosophers , and more especially to Aristotle , for the greater part of our learning ; but yet 't is not ingratitude to speak against him , when hee opposeth truth ; for then many of the Fathers would be very guilty , especially Iustin , who hath writ a Treatise purposely against him . But suppose this opinion were false , yet 't is not against the faith , and so it may serve for the better confirmation of that which is true ; the sparks of errour , being forc'd out by opposition , as the sparks of fire by the striking of the flint and steele . But suppose too that it were hereticall , and against the faith , yet may it be admitted with the same priviledge as Aristotle , from whom many more dangerous opinions have proceeded : as that the world is eternall , that God cannot have while to looke after these inferiour things , that after death there is no reward or punishment , and such like blasphemies , which strike directly at the fundamentals of our Religion . So that it is justly to be wondred why some should be so superstitious in these dayes , as to stick closer unto him , than unto Scripture , as if his Philosophy were the onely foundation of all divine truths . Vpon these grounds both St. Vincentius and Serafinus de firmo ( as I have seene them quoted ) think that Aristotle was the violl of Gods wrath , which was powred out upon the waters of wisedom by the third Angel ; But for my part , I think the world is much beholden to him for all its sciences . But yet 't were a shame for these later ages to rest our selves meerely upon the labours of our Fore-fathers , as if they had informed us of all things to be knowne ; and when we are set upon their shoulders , not to see further than they themselves did . 'T were a superstitious , a lazie opinion to think Aristotles works the bounds and limits of all humane invention , beyond which there could be no possibility of reaching . Certainly there are yet many things left to discovery , and it cannot be any inconvenience for us , to maintaine a new truth , or rectifie an ancient errour . But the position ( say some ) is directly against Scripture , for 1. Moses tels us but of one world , and his History of the Creation had been very imperfect , if God had made another . 2. Saint Iohn speaking of Gods works , says hee made the world , in the singular number , and therefore there is but one : 't is the argument of Aquinas , and he thinks that none will oppose it , but such who with Democritus esteeme some blinde chance , and not any wise providence to be the framer of all things . 3. The opinion of more worlds has in ancient times beene accounted a heresie , and Baronius affirmes that for this very reason Virgilius was cast out of his Bishoprick , and excommunicated from the Church . 4. A fourth argument there is urged by Aquinas ; if there be more worlds than one , then they must either be of the same , or of a diverse nature ; but they are not of the same kinde ; for this were needlesse , and would argue an improvidence , since one would have no more perfection than the other ; not of divers kindes , for then one of them could not be called the world or universe , since it did not containe universall perfection . I have cited this argument , because it is so much stood upon by Iulius Caesar la Galla , one that has purposely writ a Treatise against this opinion which I now deliver ; but the Dilemma is so blunt that it cannot cut on either side , and the consequences so weake that I dare trust them without an answer ; And ( by the way ) you may see this later Author in that place , where hee endeavours to prove a necessity of one world , doth leave the chiefe matter in hand , and take much needlesse paines to dispute against Democritus , who thought that the world was made by the casuall concourse of atoms in a great vacuum . It should seeme that either his cause or his skill was weake , or else he would have ventured upon a stronger adversary . These arguments which I have set downe , are the chiefest which I have met with against this subject , and yet the best of these hath not force enough to endanger the truth that I have delivered . Vnto the two first it may be answered , that the negative authority of Scripture is not prevalent in those things which are not the fundamentals of Religion . But you 'le reply , though it doe not necessarily conclude , yet 't is probable if there had beene another world , wee should have had some notice of it in Scripture . I answer , 't is as probable that the Scripture should have informed us of the planets , they being very remarkable parts of the Creation ; and yet neither Moses , nor Iob , nor the Psalmes ( the places most frequent in Astronomicall observations ) nor any other Scripture mention any of them but the Sunne and Moone . Because the difference betwixt them and the other starres , was knowne onely to those who were learned men , and had skill in Astronomie . As for that expression in Iob 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the starres of the morning , it is in the plurall number , and therefore cannot properly be applied to Venus . And for that in Isaiah 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , 't is confessed to be a word of obscure interpretation , and therefore is but by guesse translated in that sence . It being a true and common rule , that Hebraei reisideralis minime curiosi coelestium nominum penuriâ laborant . The Jewes being but little skilled in Astronomie , their language dos want proper expressions for the heavenly bodies , and therefore they are faine sometimes to attribute the same name unto divers constellations . Now if the Holy Ghost had intended to reveale unto us any naturall secrets , certainly hee would never have omitted the mention of the planets , Quorum motu nihilest quod de Conditoris sapientiâ testatur evidentius apud eos qui capiunt . Which doe so evidently set forth the wisedome of the Creator . And therefore you must know that 't is besides the scope of the old Testament or the new , to discover any thing unto us concerning the secrets of Philosophy ; 't is not his intent in the new Testament , since wee cannot conceive how it might any way belong either to the Historical , exegeticall , or propheticall parts of it : nor is it his intent in the old Testament , as is well observed by our Countrey-man Master WRIGHT . Non Mosis aut Prophetarum institutum fuisse videtur Mathematicas aliquas aut Physicas subtilitates promulgare , sed ad vulgi captum & loquendi morem , quemadmodum nutrices infantulis solent , sese accommodare . 'T is not the endeavour of Moses or the Prophets to discover any Mathematicall or Philosophicall subtilties , but rather to accommodate themselves to vulgar capacities , and ordinary speech , as nurses are wont to use their Infants . True indeed , Moses is there to handle the History of the Creation . But 't is certaine ( saith Calvin ) that his purpose is to treat only of the visible forme of the world , and those parts of it which might be most easily understood by the ignorant and ruder sort of people , and therefore we are not thence to expect the discovery of any naturall secret . Artes reconditas aliunde discat qui volet ; hic spiritus Dei omnes simul sine exceptione docere voluit . As for more hidden Arts , they must be looked for else-where ; the Holy Ghost did here intend to instruct all without exception . And therefore 't is observed , that Moses does not any where meddle with such matters as were very hard to be conceived ; for being to informe the common people as well as others , he does it after a vulgar way , as it is commonly noted , declaring the originall chiefely of those things which are obvious to the sense , and being silent of other things which then could not well be apprehended . And therefore Pererius proposing the question , why the Creation of plants & herbs is mentioned , but not of mettalls and mineralls ? Answers . Quia istarum rerum generatio est vulgo occulta & ignota . Because these things are not so commonly knowne as the other ; and hee adds , Moses non omnia , sed manifesta omnibus enarranda suscepit . Moses did not intend to relate unto us the beginnings of all things , but those onely which were most evident unto all men . And therefore too , Aquinas observes that hee writes nothing of the ayre , because that being invisible , the people knew not whether there were any such body or no. And for this very reason , St. Ierom also thinks that there is nothing exprest concerning the Creation of Angels , because the rude and ignorant vulgar were not so capable of apprehending their natures . And yet notwithstanding , these are as remarkable parts of the Creation , and as fit to be knowne as another world . And therefore the Holy Ghost too uses such vulgar expressions , which set things forth rather as they appeare , than as they are , as when he calls the Moone one of the greater lights , whereas 't is the least that wee can see in the whole heavens . So afterwards speaking of the great raine which drowned the world ; hee sayes , The windowes of heaven were opened , because it seemed to come with that violence , as if it were poured out from windowes in the Firmament . And in reference to this , a drowth is described in sundry other * places by the heavens being shut up . So that the phrases which the Holy Ghost uses concerning these things , are not to be understood in a literall sense ; but rather as vulgar expressions ; and this rule is set down by Saint Austin , where speaking concerning that in the Psalm , who stretched the earth upon the waters , he notes that when the words of Scripture shall seeme to contradict common sense or experience , there are they to be understood in a qualified sence , and not according to the letter . And 't is observed , that for want of this rule , some of the Ancients have fastned strange absurdities upon the words of the Scripture . So Saint Ambrose esteemed it a heresie to think that the Sunne and Starres were not very hot , as being against the words of Scripture , Psalm . 19. 6. where the Psalmist sayes , that there is nothing that is hid from the heat of the Sunne . So others there are that would prove the heavens not to be round , out of that place , Psal. 104. 2. Hee stretched out the heavens like a curtaine . So Procopius also was of opinion , that the earth was founded upon the waters ; nay , hee made it part of his faith , proving it out of Psal. 24. 2. He hath founded the earth upon the seas , and established it upon the floods . These and such like absurdities have followed , when men looke for the grounds of Philosophy in the words of Scripture . So that , from what hath beene said , I may conclude that the silence of Scripture concerning any other world , is not sufficient argument to prove that there is none . Thus for the two first arguments . Vnto the third , I may answer , that this very example is quoted by others , to shew the ignorance of those primitive times , who did sometimes condemne what they did not understand , and have often censur'd the lawfull and undoubted parts of Mathematicks for hereticall , because they themselves could not perceive a reason of it . And therefore their practise in this particular , is no sufficient testimonie against us . But lastly , I answer to all the above named objections , that the terme ( World ) may be taken in a double sense , more generally for the whole Vniuerse , as it implies in it the elementarie and aethereall bodies , the starres and the earth . Secondly , more particularly for an inferiour World consisting of elements . Now the maine drift of all these arguments , is to confute a plurality of Worlds in the first sense , and if there were any such , it might , perhaps , seem strange , that Moses , or St. Iohn should either not know , or not mention its creation . And Virgilius was condemned for this opinion , because hee held quòd sit alius mundus sub terrâ , aliusque Sol & Luna , ( as Baronius ) that within our globe of earth , there was another world , another Sunne and Moone , and so he might seeme to exclude this from the number of the other creatures . But now there is no such danger in this opinion , which is here delivered , since this World is said to be in the Moone , whose creation is particularly exprest . So that in the first sense I yeeld , that there is but one world , which is all that the arguments doe prove ; but understand it in the second sense , and so I affirme there may be more , nor doe any of the above named objections prove the contrary . Neither can this opinion derogate from the divine Wisedom ( as Aquinas thinks ) but rather advance it , shewing a compendium of providence , that could make the same body a world , and a Moone ; a world for habitation , and a Moone for the use of others , and the ornament of the whole frame of Nature . For as the members of the body serve not onely for the preservation of themselves , but for the use and convenience of the whole , as the hand protects the head as well as saves it selfe ; so is it in the parts of the Vniverse , where each one may serve as well for the conservation of that which is within it , as the help of others without it . Mersennus a late Jesuite , proposing the question whether or no the opinion of more worlds than one , be hereticall and against the faith ? He answers it negatively , because it does not contradict any expresse place of Scripture , or determination of the Church . And though ( saith he ) it seemes to be a rash opinion , as being against the consent of the Fathers ; yet if this controversie be chiefly Philosophicall , then their authorities are not of such weight . Vnto this it may be added , that the consent of the Fathers is prevalent onely in such points as were first controverted amongst them , and then generally decided one way , and not in such other particulars as never fell under their examination and dispute . I have now in some measure , shewed that a plurality of worlds does not contradict any principle of reason or place of Scripture , and so cleared the first part of that supposition which is implied in the opinion . It may next be enquired , whether 't is possible there may be a globe of elements in that which wee call the aethereall parts of the Vniverse ; for if this ( as it is according to the common opinion ) be priviledged from any change or corruption , it will be in vain then to imagine any element there ; and if we will have another world , we must then seeke out some other place for its situation . The third Proposition therefore shall be this . Proposition 3. That the heavens doe not consist of any such pure matter , which can priviledge them from the like change and corruption , as these inferiour bodies are liable unto . IT hath beene often questioned amongst the ancient Fathers & Philosophers , what kinde of matter that should be of which the heavens are framed . Some think that they consist of a fifth substance distinct from the foure elements , as Aristotle holds , and with him some of the late Schoolemen , whose subtill braines could not be content to attribute to those vast glorious bodies but commonmaterialls , and therefore they themselves had rather take pains to preferre them to some extraordinary nature ; whereas notwithstanding , all the arguments they could invent , were not able to convince a necessity of any such matter , as is confest by their owne * side . It were much to be desired , that these men had not in other cases , as well as this , multiplied things without necessity , and as if there had not beene enough to be knowne in the secrets of nature , have spunne out new subjects from their own braines , to finde more work for future ages ; I shall not mention their arguments , since 't is already confest , that they are none of them of any necessary consequence ; and besides , you may see them set downe in any of the books de Coelo . But it is the generall consent of the Fathers , and the opinion of Lombard , that the heavens consist of the same matter with these sublunary bodies . St. Ambrose is so confident of it , that he esteemes the contrary a heresie . True indeed , they differ much among themselves , s●me thinking them to be made of fire , others of water , and others of both ; but herein they generally agree , that they are all framed of some element or other . Which Dionysius Carthusianus collects from that place in Genesis , where the heavens are mentioned in their creation , as divided onely in distance from the elementary bodies , & not as being made of any new matter . To this purpose others cite the derivation of the Hebrew word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , quasi 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ibi & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 aquae or quasi 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ignis & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 aquae . Because they are framed out of these elements . But concerning this , you may see sundry discourses more at large in Ludovicus Molina , Eusebius Nirembergius , with divers others . The venerable Bede thought the Planets to consist of all the foure elements ; and 't is likely that the other parts are of an aereous substance , as will be shewed afterward ; however , I cannot now stand to recite the arguments for either ; I have onely urged these Authorities to countervaile Aristotle , and the Schoolemen , and the better to make way for a proofe of their corruptibility . The next thing then to be enquired after , is , whether they be of a corruptible nature , not whether they can be destroyed by God ; for this , Scripture puts out of doubt . Nor whether or no in a long time they would weare away and grow worse ; for from any such feare they have beene lately priviledged . But whether they are capable of such changes and vicissitudes , as this inferiour world is lyable unto ? The two chief opinions concerning this , have both erred in some extremity , the one side going so farre from the other , that they have both gone beyond the right , whilst Aristotle hath opposed the truth , as well as the Stoicks . Some of the Ancients have thought , that the heavenly bodies have stood in need of nourishment from the elements , by which they were continually fed , & so had divers alterations by reason of their food ; this is fathered on Heraclitus , followed by that great Naturalist Pliny , & in generall attributed to all the Stoicks . You may see Seneca expresly to this purpose iu these words . Ex illâ alimenta omnibus animalibus , omnibus satis , omnibus stellis dividuntur ; hinc profertur quo sustineantur tot Sidera tam exercitata , tam avida , per diem , noctémque , ut in opere , ita in pastu . Speaking of the earth , he sayes , from thence it is that nourishment is divided to all the living creatures , the Plants and the Starres ; hence were sustained so many constellations , so laborious , so greedy , both day and night , as well in their feeding as working . Thus also Lucan sings , Necnon Oceano pasci Phoebúmque polumque Credimus . Vnto these Ptolomie also that learned Egyptian seemed to agree , when hee affirmes that the body of the Moone is moister , and cooler than any of the other Planets , by reason of the earthly vapours that are exhaled unto it . You see these Ancients thought the Heavens to be so farre from this imagined incorruptibility , that rather like the weakest bodies they stood in need of some continuall nourishment , without which they could not subsist . But Aristotle and his followers were so farre from this , that they thought those glorious bodies could not containe within them any such principles as might make them lyable to the least change or corruption ; and their chiefe reason was , because we could not in so long a space discerne any alteration amongst them ; But unto this I answer . 1. Supposing wee could not , yet would it not hence follow that there were none , as hee himselfe in effect doth confesse in another place ; for speaking concerning our knowledge of the Heavens , he sayes , 't is very imperfect and difficult , by reason of the vast distance of those bodies from us , and because the changes which may happen unto them , are not either bigge enough , or frequent enough to fall within the apprehension and observation of our senses ; no wonder then if he himselfe be deceived in his assertions concerning these particulars . But yet , in this hee implies , that if a man were nearer to these heavenly bodies , hee would be a fitter Judge to decide this controversie than himselfe . Now it s our advantage , that by the help of Galileus his glasse , wee are advanced nearer unto them , and the heavens are made more present to us than they were before . However , as it is with us where there be many vicissitudes and successions of things , though the earth abideth for ever : So likewise may it be amongst the planets , in which though there should be divers alterations , yet they themselves may still continue of the same quantity and light . 2. Though wee could not by our senses see such alterations , yet our reason might perhaps sufficiently convince us of them . Nor can wee well conceive how the Sunne should reflect against the Moone , and yet not produce some alteration of heat . Diogenes the Philosopher was hence perswaded , that those scorching heats had burnt the Moone into the forme of a Pumice-stone . 3. I answer , that there have beene some alterations observed there ; witnesse those comets which have beene seene above the Moone . As also those spots or clouds that encompasse the body of the Sun , amongst which , there is a frequent succession by a corruption of the old , and a generation of new . So that though Aristotles consequence were sufficient , whē he proved that the heavens were not corruptible , because there have not any changes beene discovered in them ; yet this by the same reason must be as prevalent , that the Heavens are corruptible , because there have beene so many alterations observed there ; But of these , together with a farther confirmation of this proposition , I shall have occasion to speak afterwards ; In the meane space , I will referre the Reader to that work of Sheiner , a late Jesuite which he titles his Rosa Vrsina , where hee may see this point concerning the corruptibility of the Heavens largely handled , and sufficiently confirmed . There are some other things , on which I might here take an occasion to enlarge my selfe ; but because they are directly handled by many others , and doe not immediatly belong to the chiefe matter in hand , I shall therefore referre the Reader to their Authors , and omit any large proofe of them my selfe , as desiring all possible brevity . 1. The first is this : That there are no solid Orbes . If there be a habitable world in the Moone ( which I now affirme ) it must follow , that her Orbe is not solid as Aristotle supposed ; and if not hers , why any of the other . I rather think that they are all of a fluid ( perhaps aereous ) substance . Saint Ambrose , and Saint Basil did endeavour to prove this out of that place in I say , where they are compared to smoak , as they are both quoted by Rhodiginus . Eusebius Nicembergius doth likewise from that place confute the solidity and incorruptibility of the Heavens , and cites for the same interpretation the authority of Eustachius of Antioch ; and Saint Austin , I am sure , in one place seemes to assent unto this opinion , though hee does often in his other works contradict it . If you esteeme the testimony of the ancient Fathers , to be of any great force or consequence in a Philosophicall dispute , you may see them to this purpose in Sixtus Senensis lib. 5. Biblioth . annot . 14. The chiefe reasons , that are commonly urged for the confirmation of it , are briefly these three . 1 From the altitude of divers comets , which have beene observed to be above the planets , thorough whose Orbs ( if they had beene solid ) there would not have beene any passage . To these may be added those lesser planets lately discovered about Iupiter and Saturne , for which Astronomers have not yet framed any Orbs. 2 From that uncertainty of all Astronomicall observations , which will follow upon the supposition of such solid spheres . For then we should never discerne any Starre but by a multitude of refractions , and so consequently wee could not possibly finde their true situations either in respect of us , or in regard of one another : Since what ever the eye discernes by a refracted beame , it apprehends to be in some other place than wherein it is . But now this would be such an inconvenience , as would quite subvert the grounds & whole Art of Astronomy , and therefore is by no meanes to be admitted . Vnto this it is commonly answered , that all those Orbs are equally diaphanous , though nor of a continued quantity . Wee reply , that supposing they were , yet this cannot hinder them from being the causes of refraction , which is produced as well by the diversity of superficies , as the different perspicuity of bodies . Two glasses put together , will cause a divers refraction from another single one that is but of equall thicknesse and perspicuity . 3 From the different height of the same planet at severall times . For if according to the usuall Hypothesis , there should be such distinct , solid Orbs , then it would be impossible that the planets should intrench upon one anothers Orbs , or that two of them at severall times should be above one another , which notwithstanding hath bin proved to be so by later experience . Tycho hath observed , that Venus is somtimes nearer to us than the Sunne or Mercury , and somtimes farther off than both ; which appearances Regiomontanus himselfe does acknowledge , and withall , does confesse that they cannot be reconciled to the common Hypothesis . But for your better satisfaction herein , I shall referre you to the above named Scheiner , in his Rosa Vrsina , in whom you may see both authorities and reason , very largely and distinctly set downe for this opinion . For the better confirmation of which hee adjoynes also some authenticall Epistles of Fredericus Caesius Lynceus , a Noble Prince , written to Bellarmine , containing divers reasons to the same purpose . You may also see the same truth set downe by Iohannes Pena , in his Preface to Euclids Opticks , and Christoph. Rothmannus , both who thought the Firmament to be onely ayre : and though the noble Tycho doe dispute against them , yet he himselfe holds Quod propius ad veritatis penetralia accedit haec opinio , quàm Aristotelica vulgariter approbata , quae coelum pluribus realibus atque imperviis orbibus citra rem replevit . That this opinion comes neerer to the truth , than that common one of Aristotle which hath to no purpose filled the Heavens with such reall and impervious Orbs. 2. There is no element of fire , which must be held with this opinion here delivered ; for if wee suppose a world in the Moone , then it will follow , that the sphere of fire , either is not there where 't is usually placed in the concavity of his Orbe , or else that there is no such thing at all , which is most probable , since there are not any such solid Orbs , that by their swift motion might heat and enkindle the adjoyning ayre , which is imagined to be the reason of that element . The arguments that are commonly urged to this purpose , are these . 1 That which was before alledged concerning the refractions which will be caused by a different medium . For if the matter of the heavens be of one thicknesse , and the element of fire another , and the upper Region of ayre distinct from both these , and the lower Region severall from all the rest , there will then be such a multiplicity of refractions , as must necessarily destroy the certainty of all Astronomicall observations . All which inconveniences might be avoyded by supposing ( as wee doe ) that there is onely one Orbe of vaporous ayre which encompasses our earth , all the rest being Aethereall and of the same perspicuity . 2 The situation of this element does no way agree with Aristotles own principles , or that common providence of nature , which wee may discerne in ordinary matters . For if the heavens be without all elementary qualities , as is usually supposed , then it would be a very incongruous thing for the element of fire to be placed immediatly next unto it : Since the heat of this is the most powerfull and vigorous quality that is amongst all the rest ; And Nature in her other works , does not joyne extreames , but by something of a middle disposition . So in the very frame of our bodies , the bones which are of a hard substance , and the flesh of a soft , are not joyned together but by the intercession of membranes and grissels , such as being of a middle nature may fitly come betwixt . 3 'T is not conceiveable for what use or benefit there should be any such element in that place , and certaine it is that Nature does not doe any thing in vaine . 4 Betwixt two extreams there can be but one Medium , and therefore betweene those two opposite elements of earth and water , it may seeme more convenient to place onely the ayre , which shall partake of middle qualities different from both . 5 Fire does not seeme so properly and directly to be opposed to any thing as Ice , and if the one be not an element , why should the other ? If you object that the fire which we commonly use , does alwayes tend upwards . I answer , This cannot prove that there is a naturall place for such an element , since our adversaries themselves doe grant that culinary and elementary fire are of different kinds . The one does burne , shine , and corrupt its subject ; the other disagrees from it in all these respects . And therefore from the ascent of the one , wee cannot properly inferre the being or situation of the other . But for your farther satisfaction herein , you may peruse Cardan , Iohannes Pena that learned Frenchman , the noble Tycho , with divers others who have purposely handled this proposition . 3. I might adde a third , viz. that there is no Musick of the spheares ; for if they be not solid , how can their motion cause any such sound as is conceived ? I doe the rather meddle with this , because Plutarch speakes as if a man might very conveniently heare that harmony , if he were an inhabitant in the Moone . But I guesse that hee said this out of incogitancy , and did not well consider those necessary consequences which depended upon his opinion . However , the world would have no great losse in being deprived of this Musick , unlesse at somtimes we had the priviledge to heare it : Then indeed Philo the Jew thinks it would save us the charges of dyet , and wee might live at an easie rate by feeding at the eare only , and receiving no other nourishment ; and for this very reason ( sayes he ) was Moses enabled to tarry forty dayes and forty nights in the Mount without eating any thing , because hee there heard the melody of the Heavens . — Risum teneatis . I know this Musick hath had great Patrons , both sacred & prophane Authors , such as Ambrose , Bede , Boetius , Anselme , Plato , Cicero , and others ; but because it is not now , I think , affirmed by any , I shall not therefore bestow either paines or time in arguing against it . It may suffice that I have onely named these three last , and for the two more necessary , have referred the Reader to others for satisfaction . I shall in the next place proceed to the nature of the Moones body , to know whether that be capable of any such conditions , as may make it possible to be inhabited , and what those qualities are wherein it more neerely agrees with our earth . Proposition 4. That the Moone is a solid , compacted , opacous body . I Shall not need to stand long in the proofe of this Proposition , since it is a truth already agreed on by the generall consent of the most and the best Philosophers . 1 It is solid , in opposition to fluid , as is the ayre ; for how otherwise could it beat back the light which it receives from the Sunne ? But here it may be questioned , whether or no the Moone bestow her light upon us by the reflection of the Sun-beames from the superficies of her body , or else by her owne illumination ? Some there are who affirme this latter part . So a Averroes , b Caelius Rhodiginus , c Iulius Caesar , &c. And their reason is , because this light is discerned in many places , whereas those bodies which give light by reflexion , can there only be perceived where the angle of reflexion is equall to the angle of incidence , and this is only in one place ; as in a looking-glasse , those beams which are reflected from it , cannot be perceived in every place where you may see the glasse , but onely there where your eye is placed on the same line whereon the beames are reflected . But to this I answer , That the argument will not hold of such bodies whose superficies is full of unequall parts and gibbosities as the Moone is . Wherfore it is as wel the more probable as the more common opinion , that her light proceeds frō both these causes , from reflexion & illumination ; nor doth it herein differ from our earth , since that also hath some light by illumination : for how otherwise would the parts about us in a Sunne-shine day appeare so bright , when as the rayes of reflexion cannot enter into our eye ? For the better illustration of this , we may consider the several wayes wherby divers bodies are enlightned . Either as water by admitting the beams into its substance ; or as ayre and thin clouds , by transmitting the rayes quite thorow their bodies ; or as those things that are of an opacous nature and smooth superficies , which reflect the light only in one place ; or else as those things which are of an opacous nature and rugged superficies , which by a kind of circumfluous reflexion , are at the same time discernable in many places , as our Earth and the Moone . 2. It is compact , and not a spungie and porous substance ▪ But this is denied by a Diogenes , b Vitellio , and c Reinoldus , and some others , who held the Moone to be of the same kind of nature as a Pumice stone ; & this , say they , is the reason why in the Suns eclipses there appeares within her a duskish ruddy colour , because the Sun beames being refracted in passing through the pores of her body , must necessarily be represented under such a colour . But I reply , if this be the cause of her rednesse , then why doth shee not appeare under the same forme when shee is about a Sextile Aspect , and the darkned part of her body is discernable ? for then also doe the same rayes passe through her , and therefore in all likelyhood should produce the same effect ; and notwithstanding those beames are then diverted from us , that they cannot enter into our eyes by a straight line , yet must the colour still remaine visible in her body . And besides , according to this opinion , the spots would not alwayes be the same , but divers as the various distance of the Sunne requires . Againe , if the Sun beames did passe through her , why then hath she not a taile ( saith Scaliger ) as the Comets ? why doth she appeare in such an exact round ? and not rather attended with a long flame , since it is meerely this penetration of the Sunne beames , that is usually attributed to be the cause of beards in blazing starres . 3. It is opacous , transparent or diaphanous like Crystall or glasse , as Empedocles thought , who held the Moon to be a globe of pure congealed ayre , like haile inclosed in a spheare of fire ; for then , 1. Why does shee not alwayes appeare in the full ? since the light is dispersed through all her body ? 2. How can the interposition of her body so darken the Sunne , or cause such great eclipses as have turned day into night , that have discovered the starres , and frighted the birds with such a suddaine darknesse , that they fell downe upon the earth , as it is related in divers Histories . And therefore Herodotus telling of an eclipse which fell in Xerxes time , describes it thus : 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . The Sun leaving his wonted seat in the heavens , vanished away : all which argues such a great darknesse , as could not have beene , if her body had beene perspicuous . Yet some there are who interpret all these relations to be hyberbolicall expressions ; and the noble Tycho thinks it naturally impossible that any eclipse should cause such darknesse , because the body of the Moone can never totally cover the Sunne . However , in this he is singular , all other Astronomers ( if I may beleeve Keplar ) being on the contrarie opinion , by reason the Diameter of the Moone does for the most part appeare bigger to us than the Diameter of the Sunne . But here Iulius Caesar once more , puts in to hinder our passage . The Moone ( saith he ) is not altogether opacous , because 't is still of the same nature with the heavens which are incapable of totall opacity : and his reason is , because perspicuity is an inseparable accident of those purer bodies ; and this hee thinks must necessarily be granted ; for he stops there , and proves no further ; but to this I shall deferre an answer , till hee hath made up his argument . Wee may frequently see , that her body does so eclipse the Sunne , as our Earth doth the Moone . And besides , the mountains that are observed there , doe cast a dark shadow behind them , as shall be shewed afterwards . Since then the like interposition of them both , doth produce the like effect , they must necessarily be of the like natures , that is , alike opacous , which is the thing to be shewed ; and this was the reason ( as the Interpreters guesse ) why Aristotle affirmed the Moone to be of the Earths nature , because of their agreement in opacity , whereas all the other elements save that , are in some measure perspicuous . But , the greatest difference which may seeme to make our Earth altogether unlike the Moone , is , because the one is a bright body , and hath light of its owne , and the other a grosse dark body which cannot shine at all . 'T is requisite therefore that in the next place I cleare this doubt , and shew that the Moone hath no more light of her owne than our Earth . Proposition 5. That the Moone hath not any light of her owne . T Was the fancie of some of the Jewes , and more especially of Rabbi Simeon , that the Moone was nothing else but a contracted Sunne , and that both those planets at their first creation , were equall both in light and quantity . For , because God did then call them both great lights , therefore they inferred that they must be both equall in bignesse . But a while after ( as the tradition goes ) the ambitious Moone put up her complaint to God against the Sunne , shewing that it was not fit there should be two such great lights in the heavens ; a Monarchie would best become the place of order and harmony . Vpon this , God commanded her to contract her selfe into a narrower compasse ; but shee being much discontented hereat , replies , What! because I have spoken that which is reason and equity , must I therefore be diminished ? This sentence could not chuse but much trouble her ; and for this reason was shee in great distresse and griefe for a long space ; but that her sorrow might be some way pacified , God bid her be of good cheere , because her priviledges and Charter should be greater than the Sunnes ; he should appeare in the day time onely , shee both in the day and night ; but her melancholy being not satisfied with this , shee replied againe , That , that alas was no benefit ; for in the day time shee should be either not seene , or not noted . Wherefore , God to comfort her up , promised , that his people the Israelites should celebrate all their feasts and holy dayes by a computation of her moneths ; but this being not able to content her , shee has looked very melancholy ever since ; however , she hath still reserved much light of her owne . Others there were , that did think the Moone to be a round globe ; the one halfe of whose body was of a bright substance , the other halfe being dark ; and the divers conversions of those sides towards our eyes , caused the variety of her appearances : of this opinion was Berosus , as hee is cited by a Vitruvius ; and b St. Austin thought it was probable enough . But this fancie is almost equally absurd with the former , and both of them sound rather like fables , than Philosophicall truths . You may commonly see how this latter does contradict frequent and easie experience ; for 't is observed , that that spot which is perceived about her middle when shee is in the encrease , may be discern'd in the same place when she is in the full : whence it must follow , that the same part which was before darkned , is after inlightened , and that the one part is not alwayes dark , and the other light of it selfe . But enough of this , I would be loth to make an enemy , that I may afterwards overcome him , or bestow time in proving that which is already granted ; I suppose now , that neither of them hath any patrons , and therefore need no confutation . 'T is agreed upon by all sides , that this Planet receives most of her light from the Sunne ; but the cheife controversie is , whether or no shee hath any of her owne ? The greater multitude affirme this . Cardan amongst the rest , is very confident of it , and hee thinks that if any of us were in the Moone at the time of her greatest eclipse , Lunam aspiceremus non secus ac innumeris cereis splendidissimis accensis , atque in eas oculis defixis caecutiremus ; Wee should perceive so great a brightnesse of her owne , that would blinde us with the meere sight , and when she is enlightened by the Sun , then no Eagles eye ( if there were any there ) is able to look upon her . This Cardan sayes , and hee doth but say it , without bringing any proofe for its confirmation . However , I will set downe the arguments that are usually urged for this opinion , and they are taken either from Scripture , or reason ; from Scripture is urged that place , 1 Cor. 15. where it is said , There is one glory of the Sunne , and another glory of the Moone . Vlysses Albergettus urges that in Math. 24. 29. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , The Moon shall not give her light : therefore ( sayes he ) shee hath some of her owne . But to these we may easily answer , that the glory and light there spoken of , may be said to be hers , though it be derived , as you may see in many other instances . The arguments from reason are taken either . 1. From that light which is discerned in her , when there is a totall eclipse of her owne body , or of the Sunne . 2. From the light which is discerned in the darker part of her body , when shee is but a little distant from the Sunne . 1. For when there are any totall eclipses , there appeares in her body a great rednesse , and many times light enough to cause a remarkable shade , as common experience doth sufficiently manifest : but this cannot come from the Sun , since at such times either the earth or her own body shades her from the Sun-beames ; therfore it must proceed from her owne light . 2. Two or three dayes after the new Moone , we may perceive light in her whole body , whereas the rayes of the Sun reflect but upon a small part of that which is visible ; therefore 't is likely that there is some light of her owne . In answering to these objections , I shall first shew , that this light cannot be her owne , and then declare that which is the true reason of it . That it is not her owne , appeares . 1 Because then she would alwayes retaine it , but shee has beene sometimes altogether invisible , when as notwithwanding some of the fixed Starres of the fourth or fifth magnitude might easily have been discerned close by her , As it was in the yeare 1620. 2 This may appeare likewise from the variety of it at divers times ; for 't is commonly observed that sometimes 't is of a brighter , sometimes of a darker appearance , now redder , and at another time of a more duskish colour . The observation of this variety in divers eclipses , you may see set downe by Keplar and many others . But now this could not be , if that light were her owne , that being constantly the same , and without any reason of such an alteration : So that thus I may argue . If there were any light proper to the Moone , then would that Planet appeare brightest when she is eclipsed in her Perige being neerest to the earth , and so consequently more obscure and duskish when shee is in her Apoge or farthest from it ; the reason is , because the neerer any enlightned body comes to the sight , by so much the more strong are the species and the better perceived . This sequell is granted by some of our adversaries , and they are the very words of noble Tycho , Si Luna genuino gauderet lumine , utique cum in umbra terrae esset , illud non amitteret , sed eò evidentiùs exereret ; omne enim lumen in tenebris , plus splendet cum alio majore fulgore non praepeditur . If the Moone had any light of her own , then would she not lose it in the earths shadow , but rather shine more clearely ; since every light appeares greater in the dark , when it is not hindered by a more perspicuous brightnesse . But now the event falls out cleane contrary , ( as observation doth manifest , and our opposites themselves doe grant ) the Moone appearing with a more reddish and cleare light when she is eclipsed , being in her Apoge or farthest distance , and a more blackish iron colour when shee is in her Perige or nearest to us , therefore she hath not any light of her owne . Nor may wee think that the earths shadow can cloud the proper light of the Moone from appearing , or take away any thing from her inherent brightnesse ; for this were to think a shadow to be a body , an opinion altogether misbecomming a Philosopher , as Tycho grants in the fore-cited place , Nec umbra terrae corporeum quid est , aut densa aliqua substantia , ut Lunae lumen obtenebrare possit , atque id visui nostro praeripere , sed est quaedam privatio luminis solaris , ob interpositum opacum corpus terrae . Nor is the earths shadow any corporall thing , or thick substance , that it can cloud the Moones brightnesse , or take it away from our sight ; but it is a meere privation of the Sunnes light by reason of the interposition of the earths opacous body . 3 If she had any light of her owne , then that would in it selfe be either such a ruddy brightnesse as appeares in the eclipses , or else such a leaden duskish light as wee see in the darker parts of her body , when shee is a little past the conjunction . ( That it must be one of these may follow from the opposite arguments ) but it is neither of these , therefore shee hath none of her owne . 1 'T is not such a ruddy light as appeares in eclipses ; for then why can we not see the like rednesse , when wee may discerne the obscurer parts of the Moone ? You will say , perhaps , that then the neerenesse of that greater light takes away that appearance . I reply , this cannot be ; for then why does Mars shine with his wonted rednesse , when hee is neere the Moone ? or why cannot her greater brightnesse make him appeare white as the other Planets ? nor can there be any reason given why that greater light should represent her body under a false colour . 2. 'T is not such a duskish leaden light , as we see in the darker part of her body , when shee is about a sextile Aspect distant from the Sunne ; for then why does shee appeare red in the eclipses , since meere shade cannot cause such variety ? for 't is the nature of darknesse by its opposition , rather to make things appeare of a more white and cleare brightnesse than they are in themselves . Or if it be the shade , yet those parts of the Moone are then in the shade of her body , and therefore in reason should have the like rednesse . Since then neither of these lights are hers , it followes that she hath none of her owne . Nor is this a singular opinion , but it hath had many learned Patrons ; such was Macrobius , who being for this quoted of Rhodiginus , hee calls him vir reconditissimae scientiae , a man who knew more than ordinary Philosophers , thus commending the opinion in the credit of the Author . To him assents the venerable Bede , upon whom the glosse hath this comparison . As the Looking-glasse represents not any image within it selfe unlesse it receive some from without ; so the Moone hath not any light , but what is bestowed by the Sunne . To these agreed a Albertus Magnus , b Scaliger , c Maeslin , Keplar , and more especially d Mulapertius , whose words are more pat to the purpose than others , and therefore I shall set them down as you may finde them in his Preface to his Treatise concerning the Austriaca sydera ; Luna , Venus , & Mercurius , terrestris & humidae sunt substantiae , ideoque de suo non lucere , sicut nec terra . The Moone , Venus , and Mercury ( saith he ) are of an earthly and moyst substance , and therefore have no more light of their owne , then the earth hath . Nay , some there are , who think , ( though without ground ) that all the other Starres doe receive that light , whereby they appeare visible to us , from the Sunne : so Ptolomie , a Isidore Hispalensis , b Albertus Magnus , and c Bede ; much more then must the Moone shine with a borrowed light . But enough of this . I have now sufficiently shewed what at the first I promised , that this light is not proper to the Moone . It remaines in the next place , that I tell you the true reason of it . And here , I think 't is probable that the light which appeares in the Moone at the eclipses , is nothing else but the second species of the Sunnes rayes which passe through the shadow unto her body : and from a mixture of this second light with the shadow , arises that rednesse which at such times appeares unto us . I may call it Lumen crepusculinum , the Aurora of the Moon , or such a kinde of blushing light , that the Sunne causes when he is neere his rising , when he bestowes some small light upon the thicker vapours . Thus we see commonly the Sunne being in the Horizon , and the reflexion growing weak , how his beames make the waters appeare very red . The Moabites in Iehorams time , when they rose early in the morning , and beheld the waters afarre off , mistooke them for blood . Et causa hujus est quia radius solaris in Aurora contrahit quandam rubedinem , propter vapores combustos manentes circa superficiem terrae , per quos radij transeunt , & ideo cum repercutiantur in aqua ad oculos nostros , trahunt secum eundem ruborem , & faciunt apparere locū aquarum , in quo est repercussio , esse rubrum , saith Tostatus . The reason is , because of his rayes , which being in the lower vapours , those doe convay an imperfect mixed light upon the waters . Thus the Moone being in the earths shadow , and the Sunne beames which are round about it , not being able to come directly unto her body , yet some second rayes there are , which passing through the shadow , make her appeare in that ruddy colour : So that shee must appeare brightest when shee is eclipsed , being in her Apoge or greatest distance from us , because then the cone of the earths shadow is lesse , and the refraction is made through a narrower medium . So on the contrary , shee must be represented under a more dark and obscure forme when she is eclipsed , being in her Perige or neerest to the earth , because then shee is involved in a greater shadow , or bigger part of the cone , and so the refraction passing through a greater medium , the light must needs be weaker which doth proceed from it . If you ask now , what the reason may be of that light which wee discerne in the darker part of the new Moone ? I answer , 't is reflected from our earth , which returnes as great a brightnesse to that Planet , as it receives from it . This I shall have occasion to prove afterward . I have now done with these propositions which were set downe to cleare the passage , and confirme the suppositions implied in the opinion ; I shall in the next place proceed to a more direct treating of the chiefe matter in hand . Proposition 6. That there is a World in the Moone , hath beene the direct opinion of many ancient with some moderne Mathematicians , and may probably be deduced from the tenents of others . SInce this opinion may be suspected of singularity , I shall therefore first confirme it by sufficient authority of divers Authors , both ancient and moderne , that so I may the better cleare it from the prejudice either of an upstart fancie , or an absolute errour . This is by some attributed to Orpheus , one of the most ancient Greek Poets . Who speaking of the Moone , sayes thus , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , That it hath many mountaines , and cities , and houses in it . To him assented Anaxagoras , Democritus , and Heraclides , all who , thought it to have firme solid ground , like to our earth , containing in it many large fields , champion grounds , and divers Inhabitants . Of this opinion likewise was Xenophanes , as he is cited for it by Lactantius ; though that Father ( perhaps ) did mistake his meaning whilst hee relates it thus Dixit Xenophanes , intra concavum Lunae esse aliam terram , & ibi aliud genus hominum simili modo vivere sicut nos in hac terra , &c. As if hee had conceived the Moone to be a great hollow body , in the midst of whose concavity , there should be another globe of sea and land , inhabited by men , as our earth is . Whereas it seemes to be more likely by the relation of others , that this Philosophers opinion is to be understood in the same sence , as it is here to be proved . True indeed , the Father condemnes this assertion as an equall absurdity to that of Anaxagoras , who affirmed the snow to be black : but no wonder , for in the very next Chapter it is that hee does so much deride the opinion of those who thought there were Antipodes . So that his ignorance in that particular may perhaps disable him from being a competent Judge in any other the like point of Philosophy . Vnto these agreed Pythagoras , who thought that our earth was but one of the Planets which moved round about the Sun , ( as Aristotle relates it of him ) and the Pythagoreans in generall did affirme that the Moone also was terrestriall , & that she was inhabited as this lower world ; That those living creatures and plants which are in her , exceed any of the like kind with us in the same proportion , as their dayes are longer than ours : viz. by 15 times . This Pythagoras was esteemed by all , of a most divine wit , as appeares especially by his valuation amongst the Romans , who being commanded by the Oracle to erect a statue to the wisest Graecian , the Senate determined Pythagoras to be meant , preferring him in their judgements before the divine Socrates , whom their Gods pronounc'd the wisest . Some think him a Iew by birth ; but most agree that hee was much conversant amongst the learneder sort and Priests of that Nation , by whom hee was informed of many secrets , and ( perhaps ) this opinion which he vented afterwards in Greece , where he was much opposed by Aristotle in some worded disputations , but never confuted by any solid reason . To this opinion of Pythagoras did Plato also assent , when he considered that there was the like eclipse made by the earth ; and this , that it had no light of its owne , that it was so full of spots . And therefore wee may often reade in him and his followers , of an aetherea terra , and lunares populi , An aethereall earth , & inhabiters in the Moon ; but afterwards this was mixed with many ridiculous fancies : For some of them considering the mysteries implied in the number 3 , concluded that there must necessarily be a Trinity of worlds , whereof the first is this of ours ; the second in the Moon , whose element of water is represented by the spheare of Mercury , the ayre by Venus , and the fire by the Sunne . And that the whole Vniverse might the better end in earth as it began , they have contrived it , that Mars shall be a spheare of the fire , Iupiter of ayre , Saturne of water ; and above all these , the Elysian fields , spacious and pleasant places appointed for the habitation of those unspotted soules , that either never were imprisoned in , or else now have freed themselves from any commerce with the body . Scaliger speaking of this Platonick fancy , quae in tres trientes mundum quasi assem divisit , thinks 't is confutation enough , to say , 't is Plato's . However , for the first part of this assertion , it was assented unto by many others , and by reason of the grosnesse and inequality of this planet , 't was frequently called quasi terra coelestis , as being esteemed the sediment and more imperfect part of those purer bodies ; you may see this proved by Plutarch , in that delightfull work which he properly made for the confirmation of this particular . With him agreed Alcinous and Plotinus , later Writers . Thus Lucian also in his discourse of a journey to the Moon , where though hee does speake many things out of mirth & in a jesting manner : yet in the beginning of it he does intimate that it did contain some serious truths concerning the real frame of the Vniverse . The Cardinall Cusanus and Iornandus Brunus , held a particular world in every Starre , and therefore one of them defining our earth , he sayes , it is stella quaedam nobilis , quae lunam & calorem & influentiam habet aliam , & diversam ab omnibus aliis stellis ; A noble Starre having a distinct light , heat , & influence frō all the rest . Vnto this Nichol. Hill , a Country man of ours , was enclined , whē he said Astrea terrae natura probabilis est : That 't is probable the earth hath a starry nature . But the opinion which I have here delivered , was more directly proved by a Maeslin , b Keplar , and c Galilaeus , each of them late Writers , and famous men for their singular skill in Astronomy . Keplar calls this World by the name of Levania from the Hebrew word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 which signifies the Moon , and our earth by the name of Volva à volvendo , because it does by reason of its diurnall revolution appeare unto them constantly to turne round , and therefore hee stiles those who live in that Hemisphere which is towards us , by the title of Subvolvani , because they enjoy the sight of this earth ; and the others Privolvani , quia sunt privati conspectu volvae , because they are deprived of this priviledge . But Iulius Caesar , whom I have above quoted , speaking of their testimony whom I cite for this opinion , viz. Keplar and Galilaeus , affirmes that to his knowledge they did but jest in those things which they write concerning this , and as for any such world , he assuredly knowes they never so much as dreamt of it . But I had rather beleeve their owne words , than his pretended knowledge . 'T is true indeed , in some things they doe but trifle , but for the maine scope of those discourses , 't is as manifest they seriously meant it , as any indifferent Reader may easily discerne ; As for Galilaeus , 't is evident that hee did set downe his owne judgement and opinion in these things ; otherwise sure Campanella ( a man as well acquainted with his opinion , and perhaps his person as Caesar was ) would never have writ an Apologie for him . And besides 't is very likely if it had beene but a jest , Galilaeus would never have suffered so much for it as report saith afterwards he did . And as for Keplar , I will onely referre the Reader to his owne words as they are set downe in the Preface to the fourth book of his Epitome , where his purpose is to make an Apologie for the strangenesse of those truths that he was there to deliver , amongst which there are divers things to this purpose concerning the nature of the Moone . Hee professes that he did not publish them either out of a humor of contradiction , or a desire of vaine-glory , or in a jesting way , to make himselfe or others merry , but after a considerate and solemne manner for the discovery of the truth . Now as for the knowledge which Caesar pretends to the contrary , you may guesse what it was by his strange confidence in other assertions , and his boldnesse in them may well derogate from his credit in this . For speaking of Ptolome's Hypothesis , hee pronounces this verdict , Impossibile est excentricorum & epicyclorum positio , nec aliquis est ex Mathematicis adeo stultus qui veram illam existimet . The position of Excentrickes and Epicycles is altogether impossible , nor is there any Mathematician such a foole as to think it true . I should guesse hee could not have knowledge enough to maintaine any other Hypothesis , who was so ignorant in Mathematicks as to deny that any good Author held this . For I would faine know whether there were never any that thought the Heavens to be solid bodies , and that there were such kindes of motion as is by those fained Orbs supplied ; if so , Caesar la Galla was much mistaken . I think his assertions are equally true , that Galilaeus and Keplar did not hold this , and that there were none which ever held that other . Thus much for the testimony of those who were directly of this opinion . But , in my following discourse I shall most insist on the observation of Galilaeus , the inventor of that famous Perspective , whereby we may discern the Heavens hard by us ; whereby those things which others have formerly guest at , are manifested to the eye , and plainely discovered beyond exception or doubt ; of which admirable invention , these latter Ages of the world may justly boast , and for this expect to be celebrated by posterity . 'T is related of Eudoxus , that hee wished himselfe burnt with Phaeton , so hee might stand over the Sunne to contemplate its nature ; had hee lived in these dayes , he might have enjoyed his wish at an easier rate , and scaling the heavens by this glasse , might plainely have discerned what hee so much desired . Keplar considering those strange discoveries which this Perspective had made , could not choose but cry out in a 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and rapture of admiration , O multiscium & quovis sceptro pretiosius perspicillum ! an qui te dextrâ tenet , ille non dominus constituatur operum Dei ? And Iohannes Fabricius an elegant Writer , speaking of the same glasse , and for this invention preferring our age before those former times of greater ignorance , sayes thus ; Adeo sumus superiores veteribus , ut quam illi carminis magici pronunciatu demissam representâsse putantur , nos non tantum innocenter demittamus , sed etiam familiari quodam intuitu ejus quasi conditionem intueamur . So much are wee above the Ancients , that whereas they were faine by their Magicall charmes to represent the Moones approach , we cannot onely bring her lower with a greater innocence , but may also with a more familiar view behold her condition . And because you shall have no occasion to question the truth of those experiments , which I shall afterwards urge from it ; I will therefore set downe the testimony of an enemie , and such a witnesse hath alwayes beene accounted prevalent : you may see it in the above-named Caesar la Galla , whose words are these : Mercurium caduceum gestantem , coelestia nunciare , & mortuorum animas ab inferis revocare sapiens finxit antiquitas . Galilaeum verò novum Iovis interpretem Telescopio caduceo instructum Sydera aperire , & veterum Philosophorum manes ad superos revocare solers nostra aetas videt & admiratur . Wise antiquity fabled Mercury carrying a rod in his hand to relate newes from Heaven , and call back the soules of the dead ; but it hath beene the happinesse of our industrious Age to see and admire Galilaeus the new Embassadour of the Gods furnished with his Perspective to unfold the nature of the Starres , and awaken the ghosts of the ancient Philosophers . So worthily & highly did these men esteeme of this excellent invention . Now , if you would know what might be done by this glasse , in the sight of such things as were neerer at hand , the same Author will tell you , when he sayes , that by it those things which could scarce at all be discerned by the eye at the distance of a mile and a half , might plainly and distinctly be perceived for 16 Italian miles , & that as they were really in thēselves , without any transposition or falsifying at all . So that what the ancient Poets were faine to put in a Fable , our more happy Age hath found out in a truth , and wee may discerne as farre with these eyes which Galilaeus hath bestowed upon us , as Lynceus could with those which the Poets attributed unto him . But if you yet doubt whether all these observations were true , the same Author may confirme you , when hee sayes they were shewed Non uni aut alteri , sed quamplurimis , neque gregariis hominibus , sed praecipuis atque disciplinis omnibus , necnon Mathematicis & Opticis praeceptis optimè instructis sedulâ ac diligenti inspectione . Not to one or two , but to very many , and those not ordinary men , but to those who were well vers'd in Mathematicks and Opticks , and that not with a meere glance , but with a sedulous and diligent inspection . And least any scruple might remaine unanswered , or you might think the men who beheld all this though they might be skilfull , yet they came with credulous minds , and so were more easie to be deluded : Hee adds that it was shewed Viris qui ad experimenta haec contradicendi animo accesserant . To such as were come with a great deale of prejudice , and an intent of contradiction . Thus you may see the certainty of those experiments which were taken by this glasse . I have spoken the more concerning it , because I shall borrow many things in my farther discourse , from thsoe discoveries which were made by it . I have now cited such Authors both ancient and moderne , who have directly maintained the same opinion . I told you likewise in the Proposition that it might probably be deduced from the tenents of others : such were Aristarchus , Philolaeus , and Copernicus , with many other later Writers who assented to their hypothesis ; so Ioach. Rhelicus , David Origanus Lansbergius , Guil. Gilbert , and ( if I may beleeve Campanella ) Innumeri alij Angli & Galli , Very many others , both English and French , all who affirmed our Earth to be one of the Planets , and the Sunne to be the Center of all , about which the heavenly bodies did move . And how horrid soever this may seeme at the first , yet is it likely enough to be true , nor is there any maxime or observation in Opticks ( saith Pena ) that can disprove it . Now if our earth were one of the Planets ( as it is according to them ) then why may not another of the Planets be an earth ? Thus have I shewed you the truth of this Proposition . Before I proceed farther , 't is requisite that I enforme the Reader , what method I shall follow in the proving of this chiefe assertion , that there is a World in the Moone . The order by which I shall be guided , will be that which Aristotle uses in his book De mundo ( if that book were his . ) First , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 of those chiefe parts which are in it ; not the elementary and aethereall ( as hee doth there ) since this doth not belong to the present question , but of the Sea and Land , &c. Secondly , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , of those things which are extrinsecall to it , as the seasons , meteors , and inhabitants . Proposition 7. That those spots and brighter parts which by our sight may be distinguished in the Moone , doe shew the difference betwixt the Sea and Land in that other World. FOr the cleare proofe of this Proposition , I shall first reckon up and refute the opinions of others concerning the matter and forme of those spots , and then shew the greater probability of this present assertion , and how agreeable it is to that truth , which is most commonly received ; As for the opinions of other concerning these , they have beene very many ; I will only reckon up those which are common and remarkable . Some there are that think those spots doe not arise from any deformity of the parts , but a deceit of the eye , which cannot at such a distance discerne an equall light in that Planet ; but these doe but only say it , and shew not any reason for the proofe of their opinion : Others think that there are some bodies betwixt the Sunne and Moone , which keeping off the light in some parts , doe by their shadow produce these spots which we there discerne . Others would have them to be the figure of the seas or mountaines here below , represented there as in a looking-glasse . But none of those fancies can be true , because the spots are still the same , and not varied according to the difference of places ; and besides , Cardan thinks it is impossible that any image should be conveyed so farre as there to be represented unto us at such a distance . But 't is commonly related of Pythagoras , that he by writing what he pleased in a glasse , by the reflexion of the same species , would make those letters to appeare in the circle of the Moone , where they should be legible by any other , who might at that time be some miles distant from him . a Agrippa affirmes this to be possible , and the way of performing it not unknowne to himselfe , with some others in his time . It may be , that Bishop Godwine did by the like meanes perform those strange conclusions , which he professes in his Nuncius inanimatus , where he pretends , that he can inform his friends of what he pleases , though they be an hundred miles distant , forte etiam , vel milliare millesimum , ( they are his owne words ) and , perhaps , a thousand , and all this in a little space , quicker than the Sunne can move . Now , what conveyance there should be , for so speedy a passage , I cannot conceive , unlesse it be carried with the light , than which wee know not any thing quicker ; But of this only by the way ; however , whether those images can be represented so or not , yet certaine it is , those spots are not such representations . Some think that when God had at first created too much earth to make a perfect globe , not knowing well where to bestow the rest , hee placed it in the Moone , which ever since hath so darkned it in some parts ; but the impiety of this is sufficient confutation , since it so much detracts from the divine power and wisedome . The a Stoicks held that Planet to be mixed of fire and ayre , and in their opinion , the variety of its composition caused her spots : Being not ashamed to stile the same body a Goddesse , calling it Diana , Minerva , &c. and yet affirme it be an impure mixture of flame , and smoke , and fuliginous ayre . — But this Planet cannot consist of fire ( saith Plutarch ) because there is not any fewell to maintaine it . And the Poets have therefore fained Vulcan to be lame , because hee can no more subsist without wood or other fewell than a lame man without a staffe . Anaxagoras thought all the starres to be of an earthly nature , mixed with some fire ; and as for the Sunne , he affirmed it to be nothing else but a fiery stone ; for which later opinion , the Athenians sentenc'd him to death ; those zealous Idolaters counting it a great blasphemy to make their God a stone , whereas notwithstanding , they were so senslesse in their adoration of Idols , as to make a stone their God. This Anaxagoras affirmed the Moone to be more terrestriall than the other Planets , but of a greater purity than anything here below , and the spots he thought were nothing else , but some cloudy parts , intermingled with the light which belonged to that Planet ; but I have above destroyed the supposition on which this fancy is grounded . Plinie thinks they arise from some drossie stuffe , mixed with that moysture which the Moone attracts unto her selfe ; but he was of their opinion who thought the starres were nourished by some earthly vapours , which you may commonly see refuted in the Commentators on the books de Coelo . Vitellio & Reinoldus affirme the spots to be the thicker parts of the Moone , into which the Sunne cannot infuse much light ; and this ( say they ) is the reason why in the Sunnes eclipses the spots and brighter parts are still in som measure distinguished , because the Sun beames are not able so well to penetrate through those thicker , as they may through the thinner parts of that Planet . Of this opinion also was Caesar la Galla , whose words are these ; The Moone doth there appeare clearest , where she is transpicuous , not onely through the superficies , but the substance also , and there shee seemes spotted , where her body is most opacous . The ground of this his assertion was , because hee thought the Moone did receive and bestow her light by illumination onely , and not at all by reflexion , but this , together with the supposed penetration of the Sun-beames , and the perspicuity of the Moones body I have above answered and refuted . The more common and generall opinion is , that the spots are the thinner parts of the Moone , which are lesse able to reflect the beames that they receive from the Sunne , and this is most aggreeable to reason ; for if the starres are therefore brightest , because they are thicker and more solid than their orbes , then it will follow , that those parts of the Moone which have lesse light , have also lesse thicknesse . It was the providence of nature ( say some ) that so contrived that planet to have these spots within it , for since that is neerest to those lower bodies which are so full of deformity , 't is requisite that it should in some measure agree with them , and as in this inferiour world , the higher bodies are the most compleat , so also in the heavens perfection is ascended unto by degrees , and the Moone being the lowest , must be the least pure , and therefore Philo the Jew interpreting Iacobs dreame concerning the ladder , doth in an allegory shew , how that in the fabricke of the world , all things grow perfecter as they grow higher , and this is the reason ( saith he ) why the Moone doth not consist of any pure simple matter , but is mixed with aire , which shewes so darkely within her body . But this cannot be a sufficient reason ; for though it were true that nature did frame every thing perfecter as it was higher , yet is it as true that nature frames every thing fully perfect for that office to which shee intends it . Now , had she intended the Moone meerely to reflect the Sunne-beames and give light , the spots then had not so much argued her providence , as her unskilfulnesse and oversight , as if in the haste of her worke shee could not tell how to make that body exactly fit for that office to which shee intended it . T is likely then that she had some other end which moved her to produce this variety , and this in all probability was her intent to make it a fit body for habitation with the same conveniences of sea and land , as this inferiour world doth partake of . For since the Moone is such a vast , such a solid and opacous body , like our earth ( as was above proved ) why may it not be probable , that those thinner and thicker parts appearing in her , doe shew the difference betwixt the sea and land in that other world ? and Galilaeus doubts not , but that if our earth were visible at the same distance , there would be the like appearance of it . If wee consider the Moone as another habitable earth , then the appearances of it will be altogether exact , and beautifull , and may argue unto us that it is fully accomplished for all those ends to which Providence did appoint it . But consider it barely as a starre or light , and then there will appeare in it much imperfection and deformitie , as being of an impure darke substance , and so unfit for the office of that nature . As for the forme of those spots , some of the vulgar thinke they represent a man , and the Poëts guesse t is the boy Endymion , whose company shee loves so well , that shee carries him with her , others will have it onely to be the face of a man as the Moone is usually pictured , but Albertus thinkes rather , that it represents a Lyon with his taile towards the East , and his head the West , and * some others have thought it to be very much like a Fox , and certainly 't is , as much like a Lyon as that in the Zodiake , or as Vrsa major is like a Beare . I should guesse that it represents one of these as well as another , and any thing else as well as any of these , since 't is but a strong imagination , which fancies such images as schoole-boyes usually doe in the markes of a wall , whereas there is not any such similitude in the spots themselves , which rather like our Sea , in respect of the land , appeares under a rugged and confused figure , and doth not represent any distinct image , so that both in respect of the matter , and the forme it may be probable enough , that those spots and brighter parts may shew the the distinction betwixt the Sea and Land in that other world . Proposition 8. The spots represent the Sea , and the brighter parts the Land. WHen I first compared the nature of our earth and water with those appearances in the Moone ; I concluded contrary to the proposition , that the brighter parts represented the water , and the spots the land ; of this opinion likewise was Keplar at the first . But my second thoughts , and the reading of others , have now convinced me ( as after he was ) of the truth of that proposition which I have now set downe . Before I come to the confirmation of it , I shall mention those scruples which at first made mee doubt the truth of this opinion . 1. It may be objected , 't is probable , if there bee any such sea and land as ours , that it beares some proportion and similitude with ours : but now this proposition takes away all likenesse betwixt them . For whereas the superficies of our earth is but the third part of the whole surface in the globe , two parts being overspread with the water ( as Scaliger observes ) yet here , according to this opinion , the Sea should be lesse than the land , since there is not so much of the bespotted , as there is of the enlightened parts , wherefore 't is probable , that there is no such thing at all , or else that the brighter parts are the Sea. 2. The water , by reason of the smoothnesse of its superficies , seemes better able to reflect the Sun-beames than the earth , which in most places is so full of ruggednesse of grasse and trees , and such like impediments of reflexion ; and besides , common experience shewes , that the water shines with a greater & more glorious brightnesse than the earth ; therfore it should seeme that the spots are the earth , and the brighter parts the water . But to the first it may be answered . 1. There is no great probability in this consequence , that because 't is so with us , therefore it must be so with the parts of the Moone , for since there is such a difference betwixt them in divers other respects , they may not perhaps agree in this . 2. That assertion of Scaliger is not by all granted for a truth . Fromondus with others thinke that the superficies of the Sea and Land in so much of the world as is already discovered , is equall and of the same extension . 3. The Orbe of thicke and vaporous aire which incōpasses the Moone , makes the brighter parts of that Planet appeare bigger than in themselves they are ; as I shall shew afterwards . To the second it may be answered , that , that though the water be of a smooth superficies , and so may seeme most fit to reverberate the light , yet because 't is of a perspicuous nature , therefore the beames must sinke into it , and cannot so strongly and clearely be reflected . Sicut in speculo ubi plumbum abrasum fuerit , ( saith Cardan ) as in Looking-glasses where part of the lead is razed off , and nothing left behind to reverberate the image , the species must there passe through and not back againe ; so it is where the beames penetrate and sinke into the substance of the body , there cannot be such an immediate and strong reflexion , as when they are beate back from the superficies , and therefore the Sunne causes a greater heate by farre upon the Land than upon the water . Now as for that experiment where it is sayd , that the waters have a greater brightnesse than the Land : I answer , 't is true onely there where they represent the image of the Sunne or some bright cloud , and not in other places , especially if wee looke upon them at any great distance , as is very plaine by common observation . And 't is certaine that from any high mountaine the land dos appeare a great deale brighter than any lake or river . This may yet be farther illustrated by the similitude of a looking glasse hanging upon a wall in the Sun-shine , where , if the eye be not placed in the just line of reflexion from the glasse , t is manifest that the wall will bee of a brighter appearance than the glasse . True indeed in the line of reflexion , the light of the glasse is equall almost unto that which comes immediately from the Sunne it selfe ; but now this is onely in one particular place and so is not like that brightnesse which wee discerne in the Moone , because this dos appeare equally in severall situations , like that of the wall which doe seeme bright as well from every place as from any one . And therefore the ruffnesse of the wall , or ( as it is in the objection ) the ruggednesse of our earth is so farre from being an hinderance of such a reflexion as there is from the Moone , that it is rather required as a necessary condition unto it . We may conceive that in every rough body there are , as it were innumerable superficies , disposed unto an innumerable diversitie of inclinations . Ita ut nullus sit locus , ad quem non pertingant plurimi radii reflexi a plurimis superficieculis , per omnem corporis scabri radiis luminosis percussi superficiem dispersis . So that there is not any place unto which there are not some beams reflected from these diverse superficies , in the severall parts of such a rugged body . But yet ( as I said before ) the earth dos receive a great part of its light by illumination , as wel as by reflexion . So that notwithstanding those doubts , yet this proposition may remaine true , that the spots may be the Sea , and the brighter parts the Land. Of this opinion was Plutarch : unto him assented Keplar and Galilaeus , whose words are these , Si quis veterum Pythagoreorum sententiam exuscitare velit , lunam scilicet esse quasi tellurem alteram , ejus pars lucidior terrenam superficiem , obscurior verò aqueam magis congruè repraesentet . Mihi autem dubium fuit nunquam terrestris globi à longè conspecti , atque a radiis solaribus perfusi , terream superficiem clariorem , obscuriorem vero aqueam sese in conspectum daturam . If any man have a mind to renue the opinion of the Phythagoreans , that the Moone is another earth , then her brighter parts may fitly represent the earths superficies , and the darker part the water : and for my part , I never doubted but that our earthly globe being shined upon by the Sunne , and beheld at a great distance , the Land would appeare brightest , and the Sea more obscurely . The reasons may be . 1. That which I urged about the foregoing chapter , because the water is the thinner part , and therefore must give lesse light . Since the Starres and Planets , by reason of their brightnesse , are usually concluded to bee the thicker parts of their orbe . 2. Water is in it selfe of a blacker colour ( saith Aristotle ) and therefore more remote from light than the earth . Any parts of the ground being moistned with raine , dos looke much more darkely than when it is dry . 3. 'T is observed that the secondary light of the Moone ( which afterwards is proved to proceede from our earth ) is sensibly brighter unto us , for two or three dayes before the conjunjunction , in the morning when she appeares Eastward , than about the same time after the conjunction , when shee is seene in the West . The reason of which must be this , because that part of the earth which is opposite to the Moone in the East , has more land in it than Sea. Whereas on the contrary , the Moone when she is in the West , is shined upon by that part of our earth where there is more Sea than Land , from whence it will follow with good probabilitie that the earth dos cast a greater light than the water . 4. Because observation tels us , that the spotted parts are alwayes smooth and equall , having every where an equality of light when once they are enlightned by the Sunne , whereas the brighter parts are full of rugged gibbosities and mountaines , having many shades in them , as I shall shew more at large afterwards . That in this Planet there must bee Seas , Campanella indeavours to prove out of Scripture interpreting the waters above the Firmament spoken in Genesis , to bee meant of the Sea in this world . For ( saith he ) 't is not likely that there are any such waters above the Orbes to moderate that heate which they receive from their swift motion ( as some of the Fathers think . ) Nor did Moses meane the Angels which may be called spirituall waters , as Origen and Austin would have it , for both these are rejected by the generall consent : Nor could he meane any waters in the second region , as most Commentators interpret it . For first there is nothing but vapours , which though they are afterwards turned into water , yet while they remayne there , they are onely the matter of that element , which may as well bee fire or earth or ayre . 2 Those vapours are not above the expansum but in it . So that hee thinkes there is no other way to salve all , but by making the Planets severall worlds with Sea and Land , with such Rivers & Springs as we have here below : Especially since Esdras speakes of the springs above the Firmament . But I cannot agree with him in this , nor doe I thinke that any such thing can bee proved out of Scripture . Before I proceede to the next position , I shall first answer some doubts which might be made against the generalitie of this truth , whereby it may seeme impossible that there should be either Sea or Land in the Moone ; for since she moves so swiftly as Astronomers observe , why then does there nothing fall from her , or why doth she not shake something out by the celerity of her revolution ? I answer , you must know that the inclination of every heavy body to its proper Center , doth sufficiently tie it unto its place ; so that suppose any thing were separated , yet must it necessarily returne againe . And there is no more danger of their falling into our world than there is feare of our falling into the Moone . But yet there are many fabulous relations of such things as have dropped thence . There is a tale of the Nemean Lyon that Hercules slew , which first rushing among the heards out of his unknowne den in the Mountaine of Cytheron in Boeotia , the credulous people thought hee was sent from their Goddesse the Moone . And if a whirlewinde did chance to snatch any thing up , and afterwards raine it downe againe , the ignorant multitude were apt to believe that it dropt from Heaven . Thus Avicenna relates the story of a Calfe which fell downe in a storme , the beholders thinking it a Moone-calfe , and that it fell thence . So Cardan travelling upon the Apennine Moūtaines , a sudden blast tooke off his hat , which if it had been carryed farre , he thinks the peasants who had perceived it to fall , would have sworne it had rained hats . After some such manner , many of our prodigies come to passe , and the people are willing to believe any thing , which they may relate to others as a very strange and wonderfull event . I doubt not but the Trojan Palladium , the Romane Minerva , and our Ladies Church at Loretto , with many sacred reliques preserved by the Papists might drop from the Moone as well as any of these . But it may be againe objected , suppose there were a bullet shot up in that world , would not the Moone runne away from it , before it could fall downe , since the motion of her body ( being every day round our earth ) is farre swifter than the other , and so the bullet must be left behind , and at length fall downe to us ? To this I answer , 1. If a bullet could bee shot so far till it came to the circumference of those things which belong to our center , then it would fall downe to us . 2. Though there were some heavie body a great height in that ayre , yet would the motion of its center belong by an attractive vertue still hold it within its convenient distance , so that whether their earth moved or stood still , yet would the same violence cast a body from it equally far . That I may the plainer expresse my meaning , I will set downe this Diagramme . Suppose this earth were A , which was to move in the circle C D. and let the bullet be supposed at B. within its proper verge ; I say , whether this earth did stand still or move swiftly towards D , yet the bullet would still keepe at the same distance by reason of that Magnetick vertue of the center ( if I may so speake ) whereby all things within its spheare are attracted with it . So that the violence to the bullet , being nothing else but that whereby 't is removed from its center , therefore an equall violence can carry a body from its proper place , but at an equall distance , whether or no this earth where its center is , dos stand still or move . The impartiall Reader may finde sufficient satisfaction for this and such other arguments as may be urged against the motion of that earth , in the writings of Copernicus and his followers , unto whom for brevities sake I will referre them . Proposition 9. That there are high Mountaines , deepe Vallies , and spacious Plaines in the body of the Moone . THough there are some , who think Mountaines to be a deformitie to the earth , as if they were either beate up by the Flood , or else cast up like so many heaps of rubbish left at the Creation ; yet if well considered , they will bee found as much to conduce to the beauty and conveniency of the universe , as any of the other parts . Nature ( saith Pliny ) purposely framed them for many excellent uses : partly to tame the violence of greater Rivers ; to strengthen certaine joynts within the veines and bowels of the earth , to break the force of the Seas inundation , and for the safety of the earths inhabitants , whether beasts or men . That they make much for the protection of beasts , the Psalmist testifies , The highest hils are a refuge for the wild goates , and the rocks for conies . The Kingly Prophet had likewise learned the safety of these by his owne experience , when he also was faine to make a mountaine his refuge from the fury of his Master Saul , who persecuted him in the wildernesse . True indeed , such places as these keepe their neighbours poore , as being most barren , but yet they preserve them safe , as being most strong ; witnesse our unconquered Wales and Scotland , whose greatest protection hath beene the naturall strength of their Countrey , so fortified with Mountaines , that these have alwayes beene unto them sure retraites from the violence and oppression of others . Wherfore a good Author doth rightly call them natures bulwarks , cast up at God Almighties owne charges , the scornes and curbes of victorious armies ; which made the Barbarians in Curtius so confident of their owne safety , when they were once retired to an inaccessible mountaine , that when Alexanders Legate had brought them to a parley , and perswading them to yeeld , told them of his masters victories , what Seas and Wildernesses he had passed ; they replied , that all that might be , but could Alexander fly too ? Over the Seas hee might have ships , and over the land horses , but hee must have wings before hee could get up thither . Such safety did those barbarous nations conceive in the mountaines whereunto they were retired . Certainly then such usefull parts were not the effect of mans sin , or produced by the Worlds curse , the Flood , but rather at the first created by the goodnesse and providence of the Almightie . This truth is usually concluded from these and the like arguments . 1. Because the Scripture it selfe , in the description of that generall deluge , tells us , it overflowed the highest mountaines . 2. Because Moses who writ long after the Flood , dos yet give the same description of places and rivers , as they had before ; which could not well have been if this had made so strange an alteration . 3. 'T is evident that the trees did stand as before . For otherwise Noah could not so well have concluded , that the waters were abated , from this reason , because the Dove brought an Olive leafe in her mouth , when she was sent forth the second time : whereas had the trees been rooted up , she might have taken it the first time , from one of them as it was floating on the top of the waters . Now if the motion of the water was not so violent as to subvert the trees , much lesse was it able to cast up such vast heapes as the mountaines . 4. When the Scripture doth set forth unto us the power and immensisitie of God by the varietie or usefulnesse of the creatures which hee hath made , amongst the rest it doth often mention the mountaines . Psal. 104. 8. item . 148. 9. Isai. 40. 12. And therefore 't is probable they were created at the first . Unto this I might adde that in other places Divine Wisdome in shewing of its owne antiquitie , saith that he was From the beginning , before the earth or the mountains were brought forth . 5. If we may trust the relations of Antiquitie , there were many monuments left undefaced after the Flood . So that if I intend to prove that the Moone is such a habitable world as this is ; 't is requisite that I shew it to have the same conveniences of habitation as this hath ; and here if some Rabbi or Chymick were to handle the point , they would first prove it out of Scripture , from that place in Moses his blessing , where hee speakes of the ancient mountaines and lasting hills , Deut. 33. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 for having immediately before mentioned those blessings which should happen unto Ioseph by the influence of the Moone , he does presently exegetically iterate them in blessing him with the chiefe things of the ancient mountaines and lasting hills ; you may also see the same expression used in Iacobs blessing of Ioseph . But however we may deale pro or con in Philosophy , yet we must not bee too bold with divine truths , or bring Scripture to patronize any fancy of our owne , though , perhaps , it be a truth . I am not of their mind who think it a good course to confirme Philosophicall secrets from the letter of the Scripture , or by abusing some obscure text in it . Mee thinks it savors too much of that Melancholly humor of the Chymicks , who , aiming in all their studies at the making of gold , doe perswade themselves , that the most learned and subtile of the antient Authors , in all their obscure places doe meane some such sence as may make to their purpose . And hence it is that they derive such strange mysteries from the fables of the Poëts , and can tell you what great secret it was that antiquitie did hide under the fiction of Iupiter being turned into a shower of gold : of Mercuries being made the interpreter of th● gods : of the Moones descending to the earth for the love of Endymion : with such ridiculous interpretations of these and the like fables , which any reasonable considering man cannot conceive to proceed from any but such as are distracted . No lesse fantasticall in this kind are the Jewish Rabbies , amongst whom is not any opinion , whether in nature or policy , whether true or false , but some of them , by a Cabalisticall interpretation can father it upon a darke place of Scripture , or ( if need bee ) upon a text that is cleane contrary . There being not any absurditie so grosse and incredible , for which these abusers of the text , will not find out an argument . Whereas , 't is the more naturall way , and should be observed in all controversies , to apply unto every thing , the proper proofes of it ; and when wee deale with Philosophicall truths , to keepe our selves within the bounds of humane reason and authority . But this by the way . For the better proofe of this proposition , I might here cite the testimony of Diodorus , who thought the Moone to bee full of rugged places , velut terrestribus tumulis superciliosam ; but hee erred much in some circumstances of this opinion , especially where he sayes , there is an Iland amongst the Hyperboreans , wherein those hills may to the eye bee plainly discovered ; and for this reason * Caelius calls him a fabulous Writer . But you may see more expresse authority for the proofe of this in the opinions of Anaxagoras and Democritus , who held that this Planet was full of champion ▪ grounds , mountains and vallies . And this seemed likewise probable unto Augustinus Nifus , whose words are these : Forsitan non est remotum dicere lunae partes esse diversas , veluti sunt partes terrae , quarum aliae sunt vallosae , aliae montosae , ex quarum differentia effici potest facies illa lunae ; nec est rationi dissonum , nam luna est corpus imperfectè Sphaericum , cum sit corpus ab ultimo coelo elongatum , ut supra dixit Aristoteles . Perhaps , it would not be amisse to say that the parts of the Moone were divers , as the parts of this earth , whereof some are vallies , and some mountaines , from the difference of which , some spots in the Moone may proceed ; nor is this against reason ; for that Planet cannot be perfecty sphericall , since 't is so remote a body from the first orbe , as Aristotle had said before . You may see this truth assented unto by Blancanus the Jesuit , and by him confirmed with divers reasons . Keplar hath observed in the Moones eclipses , that the division of her inlightned part from the shaded , was made by a crooked unequall line , of which there cannot bee any probable cause conceived , unlesse it did arise from the ruggednes of that Planet ; for it cannot at all be produc'd from the shade of any mountaines here upon earth , because these would bee so lessened before they could reach so high in a conicall shadow , that they would not be at all sensible unto us ( as might easily bee demonstrated ) nor can it be conceived what reason of this difference there should be in the Sun. Wherefore there being no other body that hath any thing to doe in eclipses , we must necessarily conclude , that it is caused by a variety of parts in the Moone it selfe , and what can these be but its gibbosi●●ties ? Now if you should aske a reason why there should bee such a multitude of these in that Planet , the same Keplar shall jest you out an answer . Supposing ( saith hee ) that those inhabitants are bigger than any of us in the same proportion , as their dayes are longer than ours , viz. by fifteen times it may be , for want of stones to erect such vast houses as were requisite for their bodies , they are faine to digge great and round hollowes in the earth , where they may both procure water for their thirst , and turning about with the shade , may avoid those great heats which otherwise they would be liable unto ; or if you will give Caesar la Galla leave to guesse in the same manner , he would rather thinke that those thirsty nations cast up so many and so great heaps of earth in digging of their wine cellars ; but this onely by the way . I shall next produce the eye-witnesse of Galilaeus , on which I most of all depend for the proofe of this Proposition , when he beheld the new Moone through his perspective , it appeared to him under a rugged and spotted figure , seeming to have the darker and enlightned parts divided by a tortuous line , having some parcels of light at a good distance from the other ; and this difference is so remarkable , that you may easily perceive it through one of those ordinary perspectives , which are commonly sold amongst us ; but for your better apprehending of what I deliver , I will set downe the Figure as I find it in Galilaeus . Suppose A B C D to represent the appearance of the Moones body being in a sextile , you may see some brighter parts separated at a pretty distance from the other , which can be nothing else but a reflexion of the Sun beames upon some parts that are higher than the rest , and those obscure gibbosities which stand out towards the enlightened parts , must be such hollow and deepe places whereto the rayes cannot reach . But when the Moone is got farther off from the Sunne , and come to that fulnesse as this line B D doth represent her under , then doe these parts also receive an equall light , excepting onely that difference which doth appeare betwixt their sea & land . And if you doe consider how any rugged body would appeare being enlightned , you would easily conceive that it must necessarily seeme under some such gibbous unequall forme , as the Moone is here represented . Now for the infallibility of these appearances , I shall referre the reader to that which hath been said in the sixth Proposition . But Caesar la Galla affirmes , that all these appearances may consist with a plaine superficies , if wee suppose the parts of the body to be some of them Diaphanous , and some Opacous ; and if you object that the light which is convayd to any diaphanous part in a plaine superficies , must bee by a continued line , whereas here there appeare many brighter parts among the obscure at some distance from the rest . To this he answers , it may arise from some secret conveyances and channels within her body , that doe consist of a more diaphanous matter , which being covered over with an opacous superficies , the light passing through them may break out a great way off ; whereas the other parts betwixt , may still remaine darke . Just as the River Arethusa in Sicily which runnes under ground for a great way , and afterwards breaks out againe . But because this is one of the chiefest fancies , whereby hee thinks hee hath fully answered the argument of this opinion ; I will therefore set downe his answer in his owne words , least the Reader might suspect more in them than I have expressed . Non est impossibile coecos ductus diaphani & perspicui corporis , sed opacâ superficie protendi , usque in diaphanam aliquam ex profundo in superficiem emergentem partem , per quos ductus lume nlongo postmodum interstitio erumpat , &c. But I reply , if the superficies betwixt these two enlightened parts remaine darke because of its opacity , then would it alwayes be darke , and the Sunne could not make it partake of light more than it could of perspicuity : But this contradicts all experience , as you may see in Galilaeus , who affirmes that when the Sunne comes neerer to his opposition , then , that which is betwixt them both , is enlightned as well as either . Nay , this opposes his owne eye-witnesse , for he confesses himselfe that he saw this by the glasse . Hee had said before , that he came to see those strange sights discovered by Galilaeus his glasse , with an intent of contradiction , and you may reade that confirmed in the weaknesse of this answer , which rather bewrayes an obstinate , than a perswaded will ; for otherwise sure he would never have undertooke to have destroyed such certaine proofes with so groundlesse a fancy . That instance of Galilaeus , would have beene a better evasion had this Author been acquainted with it ; who might then have compared the Moone to that which wee call mother of pearle , which though it bee most exactly polished in the superficies of it ; yet will seeme unto the eye as if there were divers swellings and risings in its severall parts . But yet , this neither would not well have shifted the experiment of the perspective . For these rugged parts doe not only appeare upon one side of the Moone , but as the Sunne dos turne about in divers places , so doe they also cast their shadow . When the Moone is in her increase , then doe they cast their shadowes to the East . When she is in the decrease , and the Sunne on the other side of her , then likewise may we discover these brighter parts casting their shadowes Westward . Whereas in the full Moone there are none of all these to be seene . But it may be objected , that 't is almost impossible , and altogether unlikely , that in the Moone there should bee any mountaines so high , as those observations make them . For doe but suppose according to the common principles , that the Moones diameter unto the Earths , is very neere to the proportion of 2 to 7. Suppose withall that the Earths diameter containes about 7000. Italian miles , and the Moones 2000 ( as is commonly granted . ) Now Galilaeus hath observed , that some parts have beene enlightned , when they were the twentieth part of the diameter distant from the common terme of illumination . From whence , it must necessarily follow that there may bee some Mountaines in the Moone , so high , that they are able to cast a shadow a 100 miles off . An opinion that sounds like a prodigie or a fiction ; wherefore 't is likely that either those appearances are caused by somewhat else besides mountaines , or else those are fallible observations , from whence may follow such improbable , inconceiveable consequences . But to this I answer : 1. You must consider the height of the Mountaines is but very little , if you compare them to the length of their shadowes . Sir Walter Rawleigh observes that the Mount Athos now called Lacas , cast its shadow 300 furlongs , which is above 37 miles ; and yet that Mount is none of the highest . Nay Solinus ( whom I should rather believe in this kinde ) affirmes that this Mountaine gives his shadow quite over the Sea , from Macedon to the I le of Lemnos , which is 700 furlongs or 84 miles , and yet according to the common reckoning it doth scarce reach 4 miles upwards , in its perpendicular height . 2. I affirme that there are very high Mountaines in the Moone . Keplar and Galilaeus thinke that they are higher than any which are upon our earth . But I am not of their opinion in this ; because I suppose they goe upon a false ground , whilst they conceive that the highest mountaine upon the earth is not above a mile perpendicular . Whereas 't is the common opinion and found true enough by observation , that Olympus , Atlus , Tauras and Emus , with many others , are much above this height . Tenariffa in the Canary Ilands , is commonly related to bee above 8 miles perpendicular , and bout this height ( say some ) is the mount Perjacaca in America . * Sir Walter Rawleigh seemes to thinke , that the highest of these is neere 30 miles upright : nay , Aristotle speaking of Caucasus in Asia , affirmes it to bee visible for 560 miles , as some interpreters finde by computation ; from which it will follow , that it was 78 miles perpendicularly high , as you may see confirmed by Iacobus Mazonius , and out of him in Blancanus the Jesuite . But this deviates from the truth more in excesse , than the other doth in defect . However , though these in the Moone are not so high as some amongst us ; yet certaine it is they are of a great height , and some of them at the least foure miles perpendicular . This I shall prove from the observation of Galilaeus , whose glasse can shew to the senses a proofe beyond exception ; and certainly that man must needs be of a most timerous faith who dares not believe his own eye . By that perspective you may plainly discerne some enlightned parts ( which are the mountaines ) to bee distant from the other about the twentieth part of the diameter . From whence it will follow , that those mountaines must necessarily be at the least foure Italian miles in height . For let B D E F be the body of the Moone , A B C will be a ray or beame of the Sunne , which enlightens a mountaine at A , and B is the point of contingency ; the distance betwixt A and B , must bee supposed to bee the twentieth part of the diameter , which is an 100 miles , for so far are some enlightened parts severed from the common terme of illumination . Now the aggregate of the quadrate from A B a hundred , and B G a 1000 will be 1010000 ; unto which the quadrate arising from A G must be equall ; according to the 47 proposition in the first booke of elements . Therfore the whole line A G is somewhat more than 104 , and the distance betwixt H A must be above 4 miles , which was the thing to be proved . But it may be againe objected , if there be such rugged parts , and so high mountaines , why then cannot we discerne them at this distance ? why doth the Moone appeare unto us so exactly round , and not rather as a wheele with teeth ? I answer , by reason of too great a distance ; for if the whole body appeare to our eye so little , then those parts which beare so small a proportion to the whole , will not at all bee sensible . But it may be replied , if there were any such remarkeable hils , why does not the limbe of the Moone appeare like a wheele with teeth , to those who looke upon it through the great perspective , on whose witnesse you so much depend ? or what reason is there that shee appeares as exactly round through it , as shee doth to the bare eye ? certainely then , either there is no such thing as you imagine , or else the glasse failes much in this discovery . To this I shall answer out of Galilaeus . 1. You must know that there is not meerely one ranke of mountaines , about the edge of the Moone , but divers orders , one mountaine behind another , and so there is somewhat to hinder those void spaces which otherwise , perhaps , might appeare . Now , where there be many hils , the ground seemes even to a man that can see the tops of all . Thus when the sea rages , and many vast waves are lifted up , yet all may appeare plaine enough to one that stands at the shore . So where there are so many hils , the inequality will bee lesse remarkable , if it be discerned at a distance . 2. Though there be mountains in that part which apeares unto us to be the limbe of the Moone , as well as in any other place , yet the bright vapors hide their appearance : for there is an orbe of thicke vaporous aire that doth immediatly compasse the body of the Moone ; which though it have not so great opacity , as to terminate the sight , yet being once enlightened by the Sunne , it doth represent the body of the Moone under a greater forme , and hinders our sight , from a distinct view of her true circumference . But of this in the next Chapter . 3. Keplar hath observed , that in the solary Eclipses , when the rays may passe thorough this vaporous ayre , there are some gibbosities to be discerned in the limbe of the Moone . I have now sufficiently proved , that there are hills in the Moone , and hence it may seeme likely that there is also a world ; for since providence hath some speciall end in all its works , certainly then these mountaines were not produced in vaine ; and what more probable meaning can wee conceive there should be , than to make that place convenient for habitation ? Proposition 10. That there is an Atmo-sphaera , or an orbe of grosse , vaporous aire , immediately encompassing the body of the Moone . AS that part of our aire which is neerest to the earth , is of a thicker substance than the other , by reason 't is alwayes mixed with some vapours , which are continually exhaled into it . So is it equally requisite , that if there be a world in the Moone , that the aire about that , should be alike qualified with ours . Now , that there is such an orbe of grosse aire , was first of all ( for ought I can reade ) observed by Meslin , afterwards assented unto by Keplar and Galilaeus , and since by Baptista Cisacus , Sheiner with others , all of them confirming it by the same arguments which I shall onely cite , and then leave this Proposition . 1. 'T is not improbable that there should be a sphere of grosser aire about the Moone ; because 't is observed , that there are such kind of evaporations which proceed from the Sun it selfe . For there are discovered divers moveable spots , like clouds , that doe encompasse his body : which those Authors , who have been most frequently versed in these kind of experiments and studies , doe conclude to be nothing else but evaporations from it . The probabilitie and truth of which observations may also bee inferred from some other appearances . As , 1. It hath been observed that the Sunne hath sometimes for the space of foure days together , appeared as dull and ruddy almost as the Moone in her Ecclipses ; In so much that the Starrs have been seene at midday . Nay , he hath been constantly darkned for almost a whole yeare , and never shined , but with a kind of heavy and duskish light , so that there was scarse heate enough to ripen the fruits . As it was about the time when Caesar was killed . Which was recorded by some of the Poëts . Thus Virgil , speaking of the Sunne . Ille etiam extincto miseratus Caesare Romam , Cum caput obscurâ nitidum ferrugine texit , Impiaque aeternam timueruut saecula noctem . He pittying Romé when as great Caesar dyde , His head within a mourning vaile did hide . And thus the wicked guilty world did fright , With doubtfull feares of an eternall night . Ovid likewise speaking of his death — Solis quoque tristis imago Lurida sollicitis praebebat lumina terris . — The Suns sad image then Did yeeld a lowring light to fearefull men . Now these appearances could not arise from any lower vapor . For then 1. They would not have been so universall as they were , being seene through all Europe ; or else 2. that vapor must have covered the starres as well as the Sunne , which yet notwithstanding were then plainly discerned in the day time . You may see this argument illustrated in another the like case . Chap. 12. Hence then it will follow , that this fuliginous matter , which did thus obscure the Sunne , must needs bee very neere his body ; and if so , then , what can we more probably guesse it to be , than evaporations from it ? 2. 'T is observed , that in the Suns totall Ecclipses , when there is no part of his body discernable , yet there dos not always follow so great a darknesse , as might bee expected from his totall absence . Now 't is probable , that the reason is , because these thicker vapors , being enlightned by his beames , doe convey some light unto us , notwithstanding the interposition of the Moone betwixt his body and our earth . 3. This likewise is by some guest to be the reason of the crepusculum or that light which wee have before the Suns rising . Now , if there be such evaporations from the Sunne , much more then from the moone , which does consist of a more grosse and impure substance . The other arguments are taken from severall observations in the Moon herselfe , and doe more directly tend to the proofe of this proposition . 2. 'T is observed , that so much of the Moone as is enlightned , is alwayes part of a bigger circle , than that which is darker . The frequent experience of others hath proved this , and an easie observation may quickly confirme it . But now this cannot proceede from any other cause so probable , as from this orbe of aire ; especially when we consider how that Planet shining with a borrowed light , doth not send forth any such rayes as may make her appearance bigger than her body . 3. When the Moone being halfe enlightned , begins to cover any Starre , if the Starre bee towards the obscurer part , then may it by the perspective be discerned , to bee neerer unto the center of the moone , than the outward circumference of the enlightned part . But the moone being in the full ; then dos it seeme to receive these starres , within its limbe . 4. Though the Moone doe sometime appeare the first day of her change when so much as appeares enlightned , cannot be above the 80 part of her diameter , yet then will the hornes seeme at least to be of a fingers breadth in extension . Which could not bee , unlesse the ayre about it were illuminated . 5. 'T is observed in the Solary ecclipses , that there is sometimes a great trepidation about the body of the Moone , from which wee may likewise argue an Atmo-sphaera , since we cannot well conceive what so probable a cause there should be of such an appearance as this , Quod radii Solares à vaporibus Lunam ambientibus fuerint intercis● , that the Sunne-beames were broken and refracted by the vapours that encompassed the Moone . 6. I may adde the like argument taken from another observation which will be easily tried and granted . When the Sunne is eclipsed , we discerne the Moone as shee is in her owne naturall bignesse ; but then she appeares somewhat lesse than when she is in the full , though she be in the same place of her supposed excentrick and epicycle ; and therfore Tycho hath calculated a Table for the Diameter of the divers new Moones . But now there is no reason so probable , to salve this appearance , as to place an orbe of thicker aire , neere the body of that Planet , which may bee enlightned by the reflected beames , and through which the direct rayes may easily penetrate . But some may object , that this will not consist with that which was before delivered , where I said , that the thinnest parts had least light . If this were true , how comes it to passe then , that this aire should bee as right as any of the others parts , when as t is the thinnest of all ? I answer , if the light be received by reflection only , then the thickest body hath most , because it is best able to beate backe the rayes ; but if the light be received by illumination ( especially if there be an opacous body behinde , which may double the beames by reflexion ) as it is here , then I deny not but a thinne body may retaine much light ; and perhaps , some of those appearances , which wee take for fiery comets , are nothing else but a bright cloud enlightned ; So that probable it is , there may be such aire without the Moone ; & hence it comes to passe , that the greater spots are only visible towards her middle parts , and none neere the circumference ; not but that there are some as well in those parts as elsewhere , but they are not there perceiveable , by reason of those brighter vapours which hide them . Proposition 11. That as their world is our Moone , so our world is their Moone . I Have already handled the first thing that I promised , according to the Method which Aristotle uses in his Book de Mundo , and shew'd you the necessary parts that belong to this world in the Moone . In the next place 't is requisite that I proceed to those things which are extrinsecall unto it , as the Seasons , the Meteors , and the Inhabitants . 1. Of the Seasons ; And if there be such a world in the Moone , 't is requisite then that their seasons should bee some way correspondent unto ours , that they should have Winter and Summer , night and day , as we have . Now that in this Planet there is some similitude of Winter and Summer , is affirmed by Aristotle himselfe , since there is one hemispheare that hath alwayes heate and light , and the other that hath darknesse and cold . True indeed , their dayes and yeares are always of one and the same length ( unlesse we make one of their yeares to be 19 of ours , in which space all the Starres doe arise after the same order . ) But t is so with us also under the Poles , and therefore that great difference is not sufficient to make it altogether unlike ours ; nor can we expect that every thing there should be in the same manner as it is here below , as if nature had no way but one to bring about her purposes . We have no reason then to thinke it necessary that both these worlds should be altogether alike , but it may suffice if they be correspondent in something only . However , it may bee questioned whether it doth not seeme to bee against the wisedome of Providence , to make the night of so great a length , when they have such a long time unfit for worke ? I answer , no ; since t is so , and more with us also under the poles ; and besides , the generall length of their night is somewhat abated in the bignesse of their Moone which is our earth . For this returnes as great a light unto that Planet , as it receives from it . But for the better proofe of this , I shall first free the way from such opinions as might otherwise hinder the speed of a clearer progresse . Plutarch one of the chiefe patrons of this world in the Moone , doth directly contradict this proposition ; affirming , that those who live there , may discerne our world , as the dreggs and sediment of all other creatures , appearing to them through clouds and foggy mists , and that altogether devoid of light , being base and unmoveable , so that they might well imagine the darke place of damnation to bee here situate , and that they onely were the inhabiters of the world , as being in the midst betwixt Heaven and Hell. To this I may answer , 't is probable that Plutarch spake this inconsiderately , and without a reason ; which makes him likewise fall into another absurditie , when hee says our earth would appeare immoveable ; whereas questionlesse , though it did not , yet would it seeme to move , and theirs to stand still , as the Land doth to a man in a Shippe ; according to that of the Poët : Provehimur portu , terraeque urbesque recedunt . And I doubt not but that ingenuous Author would easily have recanted , if hee had beene but acquainted with those experiences which men of latter times have found out , for the confirmation of this truth . 2. Unto him assents Macrobius , whose words are these ; Terra accepto solis lumine clarescit tantummodò , non relucet . The earth is by the Sunne-beames made bright , but not able to enlighten any thing so farre . And his reason is , because this being of a thick and grosse matter , the light is terminated in its superficies , and cannot penetrate into the substance ; whereas the Moone doth therefore seeme so bright to us , because it receives the beames within it selfe . But the weaknesse of this assertion , may bee easily manifest by a common experience ; for polished steele ( whose opacity will not give any admittance to the rayes ) reflects a stronger heate than glasse , and so consequently a greater light . 3. 'T is the generall consent of Philosophers , that the reflection of the Sunne-beames from the earth doth not reach much above halfe a mile high , where they terminate the first region , so that to affirme they might ascend to the Moone , were to say , there were but one region of aire , which contradicts the proved and received opinion . Unto this it may be answered : That it is indeed the common consent , that the reflexion of the Sunne-beames reach onely to the second region ; but yet some there are , and those too , Philosophers of good note , who thought otherwise . Thus Plotinus is cited by Caelius , Si concipias te in sublimi quopiam mundi loco , unde oculis subjiciatur terrae moles aquis circumfusa , & solis syderumque radiis illustrata , non aliam profecto visam iri probabile est , quam qualis modo visatur lunaris globi species . If you conceive your selfe to bee in some such high place , where you might discerne the whole Globe of the earth and water , when it was enlightned by the Sunnes rayes , 't is probable it would then appeare to you in the same shape as the Moone doth now unto us . So Paulus Foscarinus . Terra nihil aliud est quàm altera Luna , vel Stella , talisque nobis appareret , si ex convenienti elongatione eminus conspiciretur , in ipsaque observari possent eaedem aspectuum varietates , quae in Lunâ apparent . The earth is nothing else but another Moone or Starre , and would appeare so unto us if it were beheld at a convenient distance with the same changes and varieties as there are in the Moon . Thus also Carolus Malapertius , whose words are these , Terra haec nostra , si in luna constituti essemus , splendida prorsus quasi non ignobilis planeta , nobis appareret . If wee were placed in the Moone , and from thence beheld this our earth , it would appeare unto us very bright , like one of the nobler Planets . Unto these doth Fromondus assent , when he sayes , Credo equidem quod si oculus quispiam in orbe lunari foret , globum terrae & aquae instar ingentis syderis à sole illustrem conspiceret . I believe that this globe of earth and water would appeare like some great Star to any one , who should looke upon it from the Moone . Now this could not bee , nor could it shine so remarkably , unlesse the beames of light were reflected from it . And therefore the same Fromondus expresly holds , that the first region of ayre is there terminated , where the heate caused by reflexion begins to languish , whereas the beames themselves doe passe a great way further . The chiefe argument which doth most plainely manifest this truth , is taken from a common observation which may bee easily tryed . If you behold the Moone a little before or after the conjunction , when she is in a sextile with the Sunne , you may discerne not onely the part which is enlightned , but the rest also to have in it a kind of a duskish light ; but if you chuse out such a situation , where some house or chimney ( being some 70 or 80 paces distant from you ) may hide from your eye the enlightned hornes , you may then discerne a greater and more remarkable shining in those parts unto which the Sunne beames cannot reach ; nay there is so great a light , that by the helpe of a good perspective you may discerne its spots . In so much that Blancanus the Jesuite speaking of it , sayes , Haec experientia ita me aliquando fefellit , ut in hunc fulgorem casu ac repente incidens , existimarim novo quodam miraculo tempore adolescentis lunae factum esse plenilunium . This experiment did once so deceive mee , that happening upon the sight of this brightnesse upon a sudden , I thought that by some new miracle the Moone had beene got into her full a little after her change . But now this light is not proper to the Moone ; it doth not proceed from the rayes of the Sunne which doth penetrate her body , nor is it caused by any other of the Planets and Starres . Therefore it must necessarily follow , that it comes from the earth . The two first of these I have already proved , and as for the last , it is confidently affirmed by Caelius , Quod si in disquisitionem evocet quis , an lunari syderi lucem foenerent planetae item alii , asseveranter astruendum non foenerare . If any should aske whether the other Planets lend any light to the Moone ? I answer , they doe not . True indeed , the noble Tycho discussing the reason of this light attributes it to the Planet Venus ; and I grant that this may convey some light to the Moone ; but that it is not the cause of this whereof wee now discourse , is of it selfe sufficiently plaine , because Venus is sometimes over the Moone , when as shee cannot convey any light to that part which is turned from her . It doth not proceed from the fixed starres ; for then it would retaine the same light in ecclipses , whereas the light at such times is more ruddy and dull . Then also the light of the Moone would not be greater or lesser , according to its distance from the edge of the earths shadow , since it did at all times equally participate this light of the starres . In briefe , this is neither proper to the Moone , nor does it proceed from any penetration of the Suns rays , or the shining of Venus , or the other Planets , or the fixed starrs . Now because there is no other body in the whole Universe , save the earth , it remaines that this light must necessarily be caused by that , which with a just gratitude repaies to the Moone such illumination as it receives from her . And as loving friends equally participate of the same joy and griefe , so doe these mutually partake of the same light from the Sunne , and the same darkenesse from the eclipses , being allo severally helped by one another in their greatest wants : For when the Moone is in conjunction with the Sun , & her upper part receives all the light , then her lower Hemispheare ( which would otherwise be altogether darke ) is enlightened by the reflexion of the Sunne-beames from the earth . When these two Planets are in opposition , then that part of the earth which could not receive any light from the Sunne-beames , is most enlightened by the Moone , being then in her full ; and as shee doth most illuminate the earth when the Sunne-beames cannot , so the gratefull earth returnes to her as great ( nay greater ) light when shee most wants it ; so that alwayes that visible part of the Moone which receives nothing from the Sunne , is enlightened by the earth , as is proved by Galilaeus , with many more arguments , in that Treatise which he calls Systema mundi . True indeed , when the Moone comes to a quartile , then you can neither discerne this light , nor yet the darker part of her body , and that for a double reason . 1. Because the neerer it comes to the full , the lesse light dos it receive from the earth , whose illumination dos always decrease in the same proportion as the Moone dos increase . 2. Because of the exuperancy of the light in the other parts . Quippe illustratum medium speciem recipit valentiorem , the clearer brightnesse involves the weaker , it being with the species of sight , as it is with those of sound ; and as the greater noise drowns the lesse , so the brighter object hides that which is more obscure . But as they do always in their mutuall vicissitudes participate of one anothers light ; so also doe they partake of the same defects and darknings ; for when our Moone is eclipsed , then is their Sunne darkned ; and when our Sun is eclipsed , thē is their Moon deprived of its light , as you may see affirmed by Meslin . Quod si terram nobis ex alto liceret intueri , quemadmodum deficientem lunam ex longinquo spectare possumus , videremus tempore eclipsis solis terrae aliquam partem lumine solis deficere , eodem planè modo sicut ex opposito luna deficit . If we might behold this globe of earth at the same distance , as we doe the Moon in her defect , wee might discerne some part of it darkened in the Sunnes eclipses , just so as the Moone is in hers . For as our Moone is eclipsed by the interposition of our earth , so is their Moone eclipsed by the interposition of theirs . The manner of this mutuall illumination betwixt these two you may plainly discerne in this Figure following . Where A represents the Sunne , B the Earth , and C the Moone ; Now suppose the Moone C to be in a sextile of increase , when there is onely one small part of her body enlightened , then the earth B will have such a part of its visible Hemispheare darkned , as is proportionable to that part of the Moone which is enlightened ; and as for so much of the Moone , as the Sun-beames cannot reach unto , it receives light from a proportionall part of the earth which shines upon it , as you may plainly perceive by the Figure . You see then that agreement and similitude which there is betwixt our earth and the Moone . Now the greatest difference which makes them unlike , is this , that the Moone enlightens our earth round about , whereas our earth gives light onely to that Hemispheare of the Moone which is visible unto us , as may be certainly gathered from the constant appearance of the same spots , which could not thus come to passe , if the Moone had such a diurnall motion about its owne axis as perhaps our earth hath . And though some suppose her to move in an epicycle , yet this doth not so turne her body round , that wee may discerne both Hemispheares ; for according to that hypothesis ( say they ) the motion of her eccentrick doth turne her face towards us , as much as the other doth from us . But now , if any question what they doe for a Moone who live in the upper part of her body ? I answer , the solving of this , is the most uncertaine and difficult thing that I know of , concerning this whole matter . But yet unto mee this seemes a probable conjecture . That the upper Hemispheare of the Moone doth receive a sufficient light from those Planets about it ; and amongst these , Venus ( it may bee ) bestowes a more especiall brightnesse , since Galilaeus hath plainly discerned that she suffers the same increases and decreases ; as the Moone hath , and 't is probable that this may bee perceived there , without the help of a glasse , because they are farre neerer it than wee . When Venus ( saith Keplar ) lies downe in the Perige or lower part of her supposed Epicycle , then is she in conjunction with her husband the Sunne , from whom after shee hath departed for the space of ten moneths , shee gets plenum uterum , and is in the full . But you 'll reply , though Venus may bestow some light when she is over the Moone , and in conjunction , yet being in opposition , she is not visible to them , and what shall they then doe for light ? I answer , then they have none ; nor doth this make so great a difference betwixt those two Hemispheares , as there is with us , betwixt the places under the poles , and the line . And besides , 't is considerable , that there are two kinde of Planets . 1. Primarie , such whose proper circles doe encompasse the body of the Sunne , whereof there are six . Saturne , Iupiter , Mars , Ceres or the Earth , Venus , Mercury . As in the Frontispice . 2. Secondary , such whose proper circles are not about the Sunne , but some of the other primarie Planets . Thus are there two about Saturne , foure about Iupiter , and thus likewise dos the Moone encompasse our earth . Now t is probable that these lesser , secondary Planets , are not so accommodated with all conveniences of habitation , as the others that are more principall . But it may seeme a very difficult thing to conceive , how so grosse and darke a body as our earth , should yeeld such a cleere light as proceeds from the Moone ; and therefore the Cardinall de Cusa ( who thinks every Starre to be a severall wo●ld ) is of opinion that the light of the Sunne is not able to make them appeare so bright ; but the reason of their shining is , because wee behold them at a great distance through their regions of fire which doe set a shining lustre upon those bodies that of themselves are darke . Vnde si quis esset extra regionem ignis , terra ista in circumferentia suae regionis per medium ignis lucida stella appareret . So that if a man were beyond the region of fire , this earth would appeare through that , as a bright Starre . But if this were the onely reason , then would the Moone be freed from such increases and decreases as shee is now lyable unto . Keplar thinks that our earth receives that light whereby it shines , from the Sunne , but this ( saith he ) is not such an intended cleare brightnes as the Moon is capable of , and therefore he guesses , that the earth there , is of a more chokie soyle , like the I le of Crete , and so is better able to reflect a stronger light , whereas our earth must supply this intention with the quantity of its body . But this I conceive to bee a needlesse conjecture , since our earth , if all things were well considered , will bee found able enough to reflect as great a light . For 1. Consider its opacity ; if you marke these sublunary things , you shall perceive that amongst them , those that are most perspicuous , are not so well able to reverberate the Sunne-beames , as the thicker bodies . The rayes passe singly through a diaphanous matter , but in an opacous substance they are doubled in their returne , and multiplyed by reflexion . Now if the moone and the other Planets can shine so cleerely by beating backe the Sunne-beames , why may not the earth also shine as well , which agrees with them in the cause of this brightnesse their opacity ? 2. Consider what a cleare light we may discerne reflected from the earth in the middest of Summer , and withall conceive how much greater that must bee which is under the line , where the rayes are more directly and strongly reverberated . 3. 'T is considerable that though the Moon dos in the night time seeme to be of so cleere a brightnesse , yet when wee looke upon it in the day , it appeares like some little whitish cloud : Not but that at both times , she is of an equall light in her selfe . The reason of this difference is , because in the night wee looke upon it through a darke and obscure medium , there being no other enlightned body , whose brightnesse may abate from this : Whereas in the day time , the whole heavens round about it , are of an equall clearenesse , and so make it to appeare with a weaker light . Now because wee cannot see how the enlightned parts of our earth doe looke in the night , therefore in comparing it with the Moone , wee must not consider her , as she is beheld through the advantage of a darke medium , but as she seemes in the day-time : Now , in any cleere Sun-shine-day , our earth does appeare as bright as the Moone , which at the same time does seeme like some duskish cloud ( as any little observation may easily manifest . ) Therefore we need not doubt but that the earth is as well able to give light , as the Moone . To this , it may be added that those very clouds , which in the day-time seeme to be of an equall light to the moone , doe in the evening become as darke as our earth ; and as for those of them , which are looked upon at any great distance , they are often mistaken for the mountaines . 4. T is considerable , that though the moone seeme to bee of so great a brightnesse in the night , by reason of its neerenesse unto those severall shadowes which it casts , yet is it of it selfe weaker than that part of twilight , which usually wee have for halfe an houre after Sunne-set , because wee cannot till after that time discerne any shadow to be made by it . 5. Consider the great distance at which we behold the Planets , for this must needs adde much to their shining ; and therefore Cusanus ( in the above cited place ) thinks that if a man were in the Sunne , that Planet would not appeare so bright to him , as now it doth to us , because then his eye could discerne but little , whereas here , we may comprehend the beames as they are contracted in a narrow body . Keplar beholding the earth from a high mountaine when it was enlightned by the Sunne , confesses that it appeared unto him of an incredible brightnes , whereas then he could onely see some small parts of it ; but how much brighter would it have appeared if hee might in a direct line behold the whole globe of earth and these rayes gathered together ? So that if we consider that great light which the earth receives from the Sunne in the Summer , and then suppose wee were in the Moone , where wee might see the whole earth hanging in those vast spaces , where there is nothing to terminate the sight , but those beames which are there contracted into a little compasse ; I say , if we doe well consider this , wee may easily conceive that our earth appeares as bright to those other inhabitants in the Moone , as theirs doth to us . But here it may bee objected , that with us , for many days in the yeare , the heavens are so overclowded , that wee cannot see the Sunne at all , and for the most part , in our brightest dayes , there are many scattered clouds which shade the earth in sundry places ; so that in this respect , it must needs be unlike the Moon and will not be able to yeeld so cleare , unintermitted a light , as it receives from that planet . To this I answer . 1. As for those lesser brighter clouds which for the most part are scattered up and down in the clearest days , these can be no reason why our earth should be of a darker appearāce , because these clouds being neere unto the earth , and so not distinguishable at so great a distance from it , and likewise being illuminated on their back parts by the Sunne that shines upon them , must seeme as bright to those in the Moone , as if the beames were immediately reflected from our earth . 2. When these clouds that are interposed , are of any large extension or great opacity , as it is in extraordinary lasting and great rains , then there must be some discernable alteration in the light of our earth ; But yet this dos not make it to differ from the Moone : since it is so also with that Planet , as is shewed in the later part of the next chapter . Proposition . 12. That t is probable there may be such Meteors belonging to that world in the Moone , as there are with us . PLutarch discussing this point , affirmes that it is not necessary there should be the same meanes of growth and fructifying in both these worlds , since nature might in her policy finde out more wayes than one how to bring about the same effect . But however , he thinks it is probable that the Moone her selfe sendeth forth warme winds , and by the swiftnesse of her motion there should breathe out a sweet and comfortable ayre , pleasant dewes , and gentle moisture , which might serve for refreshing and nourishment of the inhabitants and plants in that other world . But since they have all things alike with us , as sea and land , and vaporous ayre encompassing both , I should rather therefore thinke that nature there should use the same way of producing meteors as shee doth with us ( and not by a motion as Plutarch supposes : ) because shee doth not love to vary from her usuall operations without some extraordinary impediment , but still keepes her beaten path unlesse shee bee driven thence . One argument whereby I shall manifest this truth , may bee taken from those new Stars which have appeared in divers ages of the world , and by their paralax have been discerned to have been above the Moone , such as was that in Cassiopeia , that in Sagittarius , with many others betwixt the Planets . Hipparchus in his time tooke especiall notice of such as these , and therefore fancied out such cōstellations in which to place the Starrs , shewing how many there were in every asterisme , that so afterwards , posterity might know whether there were any new Starre produced , or any old one missing . Now the nature of these Comets may probably manifest , that in this other world there are other meteors also ; for these in all likelyhood are nothing else but such evaporations caused by the Sunne from the bodies of the Planets . I shall prove this by shewing the improbabilities and inconveniences of any other opinion . For the better pursuite of this 't is in the first place requisite , that I deale with our chiefe adversary , Caesar la Galla , who doth most directly oppose that truth which is here to be proved . Hee endeavouring to confirme the incorruptibility of the Heavens , and being there to satisfie the argument which is taken from these Comets , He answers it thus : Aut argumentum desumptum ex paralaxi , non est efficax , aut si est efficax , eorum instrumentorum usum decipere , vel ratione astri , vel medii , vel distantiae , aut ergo erat in suprema parte aeris , aut si in coelo , tum forsan factum erat ex reflectione radiorum Saturni & Iovis , qui tunc in conjunctione fuerant . Either the argument from the paralax is not efficacious , or if it bee , yet the use of the instruments might deceive , either in regard of the star , or the medium , or the distance , and so this comet might be in the upper regions of the ayre ; or if it were in the heavens , there it might be produced by the reflexion of the rayes from Saturne and Iupiter , who were then in conjunction . You see what shifts hee is driven to , how he runnes up and downe to many starting holes , that he may find some shelter , and in stead of the strength of reason , he answers with a multitude of words , thinking ( as the Proverbe is ) that hee may use haile , when hee hath no thunder . Nihil turpius ( saith * Seneca ) dubio & incerto , pedem modo referente , modo producente . What can there be more unseemely in one that should bee a faire disputant , than to be now here , now there , and so uncertaine , that one cannot tell where to find him ? Hee thinks that there are not Comets in the heavens , because there may bee many other reasons of such appearances ; but what he knowes not ; perhaps ( hee sayes ) that argument from the paralax is not sufficient , or if it be , then there may bee some deceit in the observation . To this I may safely say , that he may justly bee accounted a weake Mathematician who mistrusts the strength of this argument ; nor can hee know much in Astronomy , who understands not the paralax , which is a foundation of that Science ; and I am sure that hee is a timerous man , who dares not believe the frequent experience of his senses , or trust to a demonstration . True indeed , I grant 't is possible , that the eye , the medium , and the distance may all deceive the beholder ; but I would have him shew which of all these was likely to cause an error in this observation ? Meerely to say they might be deceived , is no sufficient answer ; for by this I might confute the positions of all Astronomers , and affirme the starres are hard by us , because 't is possible they may bee deceived in their observing distance . But I forbeare any further reply ; my opinion is of that Treatise , that either it was set forth purposely to tempt a confutation , that hee might see the opinion of Galilaeus confirmed by others , or else it was invented with as much haste and negligence as it was printed , there being in it almost as many faults as lines . Others thinke that these are not any new Comets , but some ancient starres that were there before , which now shine with that unusuall brightnesle , by reason of the interposition of such vapors , which doe multiply their light ; and so the alteration will be here only , and not in the heavens . Thus Aristotle thought the appearance of the milkie way was produced . For hee held that there were many little starres , which by their influence did constantly attract such a vapour towards that place of heaven , so that it alwayes appeared white . Now by the same reason may a brighter vapor bee the cause of these appearances . But how probable soever this opinion may seeme , yet if well considered , you shall finde it to bee altogether absurd and impossible : for , 1. These starres were never seene there before , and t is not likely that a vapour being hard by us , can so multiply that light which could not before be at all discerned . 2. This supposed vapour cannot be either contracted into a narrow compasse , or dilated into a broad : 1. it could not bee within a little space , for then that starre would not appeare with the same multiplied light to those in other climates . 2. it cannot be a dilated vapour , for then other starres which were discerned through the same vapour , would seeme as bigge as that ; this argument is the same in effect with that of the paralax , as you may see in this Figure . Suppose A B to be a Hemispheare of one earth , C D to be the upper part of the highest region , in which there might be either a contracted vapour , as G , or else a dilated one , as H I. Suppose E F likewise to represent halfe the heavens , wherein was this appearing Comet at K. Now I say , that a contracted vapour , as G , could not cause this appearance , because an inhabitant at M could not discerne the same starre with this brightnesse , but perhaps another at L , betwixt which the vapour is directly interposed . Nor could it be caused by a dilated vapour , as H I , because then all the starres that were discerned through it , would bee perceived with the same brightnesse . 'T is necessary therfore that the cause of this appearance should be in the heavens . And this is granted by the most & best Astronomers . But , say some , this doth not argue any naturall alteration in those purer bodies , since t is probable that the concourse of many little vagabond starres , by the union of their beames may cause so great a light . Of this opinion were Anaxagoras and Zeno amongst the ancient , and Baptista Cisatus , Blancanus , with others amongst our moderne Astronomers . For , say they , when there happens to be a concourse of some few starres , then doe many other flie unto them from all the parts of heaven like so many Bees unto their King. But 1. 't is not likely that amongst those which wee count the fixed starres , there should be any such uncertaine motions , that they can wander from all parts of the heavens , as if Nature had neglected them , or forgot to appoint them a determinate course . 2. If there be such a conflux of these , as of Bees to their King , then what reason is there , that they doe not still tarry with it , that so the Comet may not bee dissolved ? But enough of this . You may commonly see it confuted by many other arguments . Others there are , who affirme these to bee some new created starres , produced by an extraordinary supernaturall power . I answer , true indeed , t is possible they might be so , but however , t is not likely they were so , since such appearances may be salved some other way ; wherfore to fly unto a miracle for such things , were a great injury to nature , and to derogate from her skill ; an indignity much mis-becoming a man who professes himselfe to be a Philosopher . Miraculum ( saith one ) est ignorantiae Asylum , a miracle often serves for the receptacle of a lazy ignorance ; which any industrious Spirit would be ashamed of , if being but an idle way to shift off the labour of any further search . But here 's the misery of it , we first tye our selves unto Aristotles principles , and then conclude that nothing could contradict them , but a miracle ; whereas 't would be much better for the Common-wealth of learning , if wee would ground our principles rather upon the frequent experiences of our owne , than the bare authority of others . Some there are who thinke , that these Comets are nothing else , but exhalations from our earth , carryed up into the higher parts of the Heaven . So Peno , Rothmannus & Galilaeus . But this is not possible , since by computation 't is found , that one of them is above 300 times bigger than the whole Globe of Land and Water . Others therefore have thought that they did proceed from the body of the Sunne , and that that Planet only is Cometarum officinae , unde tanquam emissarii & exploratores emitterentur , brevi ad solem redituri : The shop or forge of Comets from whence they were sent , like so many spies , that they might in some short space returne againe . But this cannot be , since if so much matter had proceeded from him alone , it would have made a sensible diminution in his body . The Noble Tycho therefore thinks that they consist of some such fluider parts of the Heaven , as the milky way is framed of , which being condenst together , yet not attaining to the consistency of a Starre , is in some space of time rarifyed againe into its wonted nature . But this is not likely ; because the appearance of the milky way dos not arise from some fluider parts of the heaven ( as he supposes ) but from the light of many lesser starrs which are thereabouts . And therefore it is usually thus described . Via lactea nihil aliud est quàm innumerabiles stellarum fixarum greges qui confuso & pallenti lumine tractum illum inalbant . The milky way is nothing else but the pale and confused light of many leser starres , whereby some parts of the heaven are made to appeare white . And beside , what likely cause can we conceive of this condensation , unlesse there bee such qualities there , as there are in our ayre , and then why may not the Planets have the like qualities as our earth ? and if so , then 't is more probable that they are made by the ordinary way of nature , as they are with us , and consist of such exhalations from the bodies of the Planets , as being very much rarified , may bee drawne up , through the orbe of grosse vaporous ayre that incompasses them . Nor is this a singular opinion ; but it seemed most likely to Camillus Gloriosus . Th. Campanella , Fromondus , with some others . But if you aske , whither shall all these exhalations returne ? I answer every one into his own Planet . If it be againe objected , that then there will be so many centers of gravity , and each severall Planet will be a distinct world ; I reply , wee have not like probabilitie concerning the rest ; but yet , perhaps all of them are so , except the Sunne , though Cusanus and some others think there is one also ; and later times have discovered some lesser clouds moving round about him . But as for Saturne , he hath two Moones on each side . Iupiter hath foure , that incircle him with their motion . Which are likwise ecclipsed by the interposition of his body , as the Moone is by our earth . Venus is observed to increase and decrease as the Moone . And this perhaps hath been noted by former ages , as may be guest by that relation of Saint Austin out of Varro . Mars , and all the rest , derive their light from the Sunne . Concerning Mercury , there hath been little or no observation , because for the most part , hee lies hid under the Sunne-beames , and seldome appeares by himselfe . But when he dos , yet the compasse of his body is so little , and his light of so cleare a brightnesse , by reason of his neerenesse to the Sunne , that the perspective cannot make the same discoveries upon him , as from the rest . So that if you consider their quantity , their opacity , or these others discoveries , you shall finde it probable enough , that each of them may bee a severall world . Especially , since every one of them is allotted to a severall orbe , and not altogether in one , as the fixed starres seeme to bee . But this would bee too much for to vent at the first : the chiefe thing at which I now ayme in this discourse , is to prove that there may bee one in the Moone . It hath been before confirmed , that there was a spheare of thick vaporous ayre encompassing the Moone , as the first and second regions doe this earth . I have now shewed , that thence such exhalations may proceed as doe produce the Comets : now from hence it may probably follow , that there may be winde also and raine , with such other Meteors as are common amongst us . This consequence is so dependant , that Fromondus dares not deny it , though hee would ( as he confesses himselfe ; ) for if the Sunne be able to exhale from them such fumes as may cause Comets , why not then such as may cause winds , and why not such also as may cause raine , since I have above shewed , that there is Sea and Land , as with us ? Now , raine seemes to be more especially requisite for them , since it may allay the heate and scorchings of the Sunne , when hee is over their heads . And nature hath thus provided for those in Peru , with the other inhabitants under the line . But if there bee such great , and frequent alterations in the Heavens , why cannot we discerne them ? I answer : 1. There may be such , and wee not able to perceive them , because of the weaknesse of our eye , and the distance of those places from us ; they are the words of Fienus ( as they are quoted by Fromondus in the above cited place ) Possunt maximae permutationes in coelo fieri , etiamsi a nobis non conspiciantur ; hoc visus nostri debilitas & immensa coeli distantia faciunt . And unto him assents Fromondus himselfe , when a little after he sayes , Si in sphaeris planetarum degeremus , plurima forsan coelestium nebularum vellera toto aethere passim dispersa videremus , quorum species jam evanescit nimiâ spatii intercapedine . If we did live in the spheares of the Planets , we might there perhaps discerne many great clouds dispersed through the whole Heavens , which are not now visible by reason of this great distance . 2. Maeslin and Keplar affirme , that they have seene some of these alterations . The words of Maeslin are these ( as I find them cited . ) In eclipsi Lunari vespere Dominicae Palmarum Anni 1605. in corpore Lunae versus Boream , nigricans quaedam macula conspecta fuit , obscurior caetero toto corpore , quod candentis ferri figuram repraesentabat ; dixisses nubila in multam regionem extensa pluviis & tempestuosis imbribus gravida , cujusmodi ab excelsorum montium jugis in humiliorae convallium loca videre non rarò contingit . In that lunary eclipse which happened in the even of Palme-sunday , in the yeere 1605 , there was a certaine blackish spot discerned in the Northerly part of the Moone , being darker than any other place of her body , and representing the colour of red hot iron ; You might conjecture that it was some dilated cloud , being pregnant with showers ; for thus doe such lower clouds appeare from the tops of high mountaines . And a little before this passage , the same Author speaking of that vaporous ayre about the Moone , tells us . Quod circumfluus ille splendor diversis temporibus apparet limpidior plus minusve . That it dos at divers times appeare of a different clearnesse , sometimes more , and sometimes lesse ; which he guesses to arise from the clouds and vapors that are in it . Unto this I may adde another testimony of Bapt. Cisatus , as he is quoted by Nicrembergius , grounded upon an observation taken 23 yeeres after this of Maeslin , and writ to this Euseb. Nicremberg . in a letter by that diligent & judicious Astronomer . The words of it runne thus ; Et quidem in eclipsi nupera solari quae fuit ipso die natali Christi , observavi clarè in luna soli supposita , quidpiam quod valde probat id ipsum quod Cometae quoque & maculae solares urgent , nempe coelum non esse à tenuitate & variationibus aeris exemptum ; nam circa lunam adverti esse sphaeram seu orbem quendam vaporosum , non secus atque circum terram , adeoque sicut ex terra in aliquam usque sphaeram vapores & exhalationes expirant , it a quoque ex luna . In that solary eclipse which happened on Christmas day , when the Moone was just under the Sun , I plainly discerned that in her , which may clearely confirme what the Comets and Suns spots doe seeme to prove , viz. that the heavens are not so solid , nor freed from those changes which our aire is liable unto ; for , about the Moon I perceived such an orbe , or vaporous aire , as that is which doth encompasse our earth ; and as vapours and exhalations are raised from our earth into this aire , so are they also from the Moone . You see what probable grounds , and plaine testimonies I have brought for the confirmation of this Proposition : many other things in this behalfe might bee spoken , which for brevity sake I now omit , and passe unto the next . Proposition 13. That t is probable there may be inhabitants in this other World , but of what kinde they are , is uncertaine . I Have already handled the Seasons , and Meteors belonging to this new World : t is requisite that in the next place I should come unto the third thing which I promised , and say somewhat of the inhabitants ; Concerning whom there might bee many difficult questions raised ; as ; whether that place bee more inconvenient for habitation than our World ( as Keplar thinks ; ) whether they are the seed of Adam ; whether they are there in a blessed estate , or else what meanes there may be for their salvation ? with many other such uncertaine enquiries , which I shall willingly omit , leaving it to their examination who have more leisure and learning for the search of such particulars . Being for mine owne part content only to set downe such notes belonging unto these , which I have observed in other Writers . Cum tot a illa regio nobis ignota sit , remanent inhabitatores illi ignoti penitus ( saith Cusanus ) since wee know not the regions of that place , we must be altogether ignorant of the inhabitants . There hath not yet beene any such discovery concerning these , upon which we may build a certainty , or good probability : well may wee guesse at them , & that too very doubtfully , but wee can know nothing ; for , if wee doe hardly guesse aright at things which bee upon earth , if with labour wee doe find the things that are at hand , how then can wee search out those things that are in heaven ? What a little is that which wee know , in respect of those many matters contained within this great Universe ? This whole globe of earth and water , though it seeme to us to bee of a large extent , yet it beares not so great a proportion unto the whole frame of Nature , as a small sand doth unto it ; and what can such little creatures as we , discerne , who are tied to this point of earth ? or what can they in the Moone know of us ? If we understand any thing ( saith Esdras ) t is nothing but that which is upon the earth ; and hee that dwelleth above in the heavens , may onely understand the things that are above in the height of the heavens . So that 't were a very needelesse thing for us to search after any particulars ; however , we may guesse in the generall that there are some inhabitants in that Planet : for why else did providence furnish that place with all such conveniences of habitation as have beene above declared ? But you will say , perhaps ; is there not too great and intolerable a heate , since the Sunne is in their Zenith every moneth , and doth tarry there so long before he leaves it ? I answer , 1. This may , perhaps , be remedied ( as it is under the line ) by the frequency of mid-day showers , which may cloud their Sunne , and coole their earth . 2. The equality of their nights doth much temper the scorching of the day ; and the extreme cold that comes from the one , requires some space before it can bee dispelled by the other , so that the heat spending a great while before it can have the victory , hath not afterwards much time to rage in . Wherfore notwithstanding this doubt , yet that place may remaine habitable . And this was the opinion of the Cardinal de Cusa , when speaking of this Planet , he sayes , Hic locus Mundi est habitatio hominum & animalium atque vegetabilium . This part of the world is inhabited by men , & beasts , and plants . To him assented Campanella ; but he cannot determine whether they were men or rather some other kinde of creatures . If they were men , then he thinks they could not be infected with Adams sinne ; yet perhaps , they had some of their owne , which might make them liable to the same misery with us , out of which , it may bee , they were delivered by the same means as we , the death of Christ ; and thus he thinks that place of the Ephesians may be interpreted , where the Apostle sayes , God gathered all things together in Christ , both which are in earth , and which are in the heavens : So also that of the same Apostle to the Colossians , where he sayes , that it pleased the Father to reconcile all things unto himselfe by Christ , whether they be things in earth , or things in heaven . But I dare not jest with divine truths , or apply these places according as fancy directs . As I thinke this opinion doth not any where contradict Scripture ; so I thinke likewise , that it cannot bee proved from it . Wherefore Campanella's second conjecture may be more probable , that the inhabitants of that world , are not men as we are , but some other kinde of creatures which beare some proportion , and likenesse to our natures . Or it may be , they are of a quite different nature from any thing here below , such as no imagination can describe ; our understandings being capable only of such things as have entered by our senses , or else such mixed natures as may bee composed from them . Now , there may be many other species of creatures beside those that are already knowne in the world ; there is a great chasme betwixt the nature of men and Angels ; It may bee the inhabitants of the Planets are of a middle nature between both these . T is not improbable that God might create some of all kindes , that so he might more compleatly glorifie himselfe in the works of his Power and Wisedome . Cusanus too , thinks they differ from us in many respects ; I will set downe his words as they may be found in the above cited place , Suspicamur in regione solis magis esse solares , claros & illuminatos intellectuales habitatores , spiritualiores etiam quàm in lunâ , ubi magis lunatici , & in terra magis materiales & crassi , ut illi intellectualis naturae solares sint multum in actu & parum in potentia , terreni verò magis in potentia , & parum in actu , lunares in medio fluctuantes . Hoc quidem opinamur ex influentia ignili solis , aquatica simul & aerea lunae , & gravedine materiali terrae , & consimiliter de aliis stellarum regionibus , suspicantes nullam habitationibus carere , quasi tot sint partes particulares mundiales unius universi , quot sunt stellae quarum non est numerus , nisi apud eum qui omnia in numero creavit . Wee may conjecture ( saith hee ) the inhabitants of the Sunne are like to the nature of that Planet , more cleare and bright , more intellectuall than those in the Moone where they are neerer to the nature of that duller Planet , and those of the earth being more grosse and materiall than either , so that these intellectuall natures in the Sunne , are more forme than matter , those in the earth more matter than forme , and those in the Moone betwixt both . This we may guesse from the fierie influence of the Sunne , the watery and aereous influence of the Moone , as also the materiall heavinesse of the earth . In some such manner likewise is it with the regions of the other starres ; for , we conjecture that none of them are without inhabitants , but that there are so many particular worlds and parts of this one universe , as there are starres , which are innumerable , unlesse it be to him who created all things in number . For hee held that the stars were not all in one equall orbe as wee commonly suppose ; but that some were farre higher than others , which made them appeare lesse ; and that many others were so farre above any of these , that they were altogether invisible unto us . An opinion which ( as I conceive ) hath not any great probability for it , nor certainty against it . The Priest of Saturne relating to Plutarch ( as hee faignes it ) the nature of these Selenites , told him they were of divers dispositions , some desiring to live in the lower parts of the Moone , where they might looke downewards upon us , while others were more surely mounted aloft , all of them shining like the rayes of the Sunne , and as being victorious , are crowned with garlands made with the wings of Eustathia or Constancie . It hath beene the opinion amongst some of the Ancients , that their heavens and Elysian fields were in the Moone where the ayre is most quiet and pure . Thus Socrates , thus Plato , with his followers , did esteeme this to bee the place where those purer soules inhabite , who are freed from the Sepulcher , and contagion of the body . And by the Fable of Ceres , continually wandring in search of her daughter Proserpina , is meant nothing else but the longing desire of men , who live upon Ceres earth , to attaine a place in Proserpina , the Moone or heaven . Plutarch also seemes to assent unto this ; but he thinks moreover , that there are two places of happines answerable to those two parts which he fancies to remaine of a man when he is dead , the soule and the understanding ; the soule hee thinks is made of the Moone ; and as our bodies doe so proceede from the dust of this earth , that they shall returne to it hereafter ; so our soules were generated out of that Planet , and shall be resolved into it againe ; whereas the understanding shall ascend unto the Sunne , out of which it was made , where it shall possesse an eternity of well-being , and farre greater happinesse than that which is enjoyed in the Moone . So that when a man dies , if his soule be much polluted , then must it wander up and downe in the middle region of the ayre where hell is , and there suffer unspeakable torments for those sins whereof it is guilty . Whereas the soules of better men , when they have in some space of time beene purged from that impurity which they did derive from the body , then doe they returne into the Moone , where they are possest with such a joy , as those men feele who professe holy mysteries , from which place ( saith he ) some are sent downe to have the superintendance of oracles , being diligent either in the preservation of the good , either from , or in , all perills , and the prevention or punishment of all wicked actions ; but if in these imployments they mis-behave themselves , then are they againe to bee imprisoned in a body , otherwise they remaine in the Moone , till their souls bee resolved into it , and the understanding being cleared from all impediments , ascends to the Sunne which is its proper place . But this requires a diverse space of time , according to the divers affections of the soule . As for those who have beene retired and honest , addicting themselves to a studious and quiet life , these are quickly preferred to a higher happinesse . But as for such who have busied themselves in many broyles , or have beene vehement in the prosecution of any lust , as the ambitious , the amorous , the wrathfull man , these still retaine the glimpses and dreames of such things as they have performed in their bodies , which makes them either altogether unfit to remaine there , where they are , or else keepes them long ere they can put off their souls . Thus you see Plutarchs opinion concerning the inhabitants and neighbours of the Moone , which ( according to the manner of the Academicks ) hee delivers in a third person ; you see hee makes that Planet an inferior kind of heaven , and though hee differ in many circumstances , yet doth hee describe it to bee some such place , as wee suppose Paradise to be . You see likewise his opinion concerning the place of the damned spirits , that it is in the middle region of the aire ; and in neither of these is hee singular , but some more late and Orthodox Writers have agreed with him . As for the place of Hell , many think it may be in the aire , as well as any where else . True indeed , S. Austin affirmes that this place cannot bee discovered ; But others there are who can shew the situation of it out of Scripture ; Some holding it to be in another world without this , because our Saviour calls it 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 outward darknesse . But the most will have it placed towards the center of our earth , because 't is said , Christ descended into the lower parts of the earth ; and some of these are so confident , that this is its situation , that they can describe you its bignesse also , and of what capacity it is . Francis Ribera in in his Comment on the Revelations , speaking of those words , where 't is said , that the blood went out of the wine-presse , even unto the horses-bridles by the space of one thousand and six hundred furlongs , interprets them to be meant of hell , and that that number expresses the diameter of its concavity , which is 200 Italian miles ; But Lessius thinkes that this opinion gives them too much roome in hell , and therefore he guesses that 't is not so wide ; for ( saith hee ) the diameter of one league being cubically multiplyed , will make a spheare capable of 800000 millions of damned bodies , allowing to each six foot in the square ; whereas ( sayes he ) t is certaine , that there shall not bee one hundred thousand millions in all that shall bee damned . You see the bold Iesuit was carefull that every one should have but roome enough in hell , and by the strangenesse of the conjecture , you may guesse that hee had rather bee absurd , than seeme either uncharitable or ignorant . I remember there is a relation in Pliny , how that Dionysiodorus a Mathematician , being dead , did send a letter from this place to some of his friends upon earth , to certifie them what distance there was betwixt the center and superficies : hee might have done well to have prevented this controversie , and enformed them the utmost capacity of that place . However , certaine it is , that that number cannot be knowne ; and probable it is , that the place is not yet determined , but that hell is there where there is any tormented soule , which may bee in the regions of the ayre , as well as in the center : And therefore perhaps it is that the Divell is stiled the prince of the ayre . But of this only occasionally , and by reason of Plutarchs opinion concerning those that are round about the Moone ; as for the Moone it selfe , hee esteemes it to bee a lower kind of heaven , and therefore in another place he calls it a terrestriall starre , and an Olympian or celestiall earth ; answerable , ( as I conceive ) to the paradise of the Schoolemen . And , that paradise was either in , or neere the Moone , is the opinion of some later Writers , who derived it ( in all likelyhood ) from the assertion of Plato , and perhaps , this of Plutarch . Tostatus layes this opinion upon Isiodor . Hispalensis , and the venerable Bede ; and Pererius fathers it upon Strabus and Rabanus his Master . Some would have it to bee situated in such a place as could not bee discovered , which caused the penman of Esdras to make it a harder matter to know the out-goings of Paradise , than to weigh the weight of the fire , or measure the blasts of wind , or call againe a day that is past . But notwithstanding this , there bee some others , who think , that it is on the top of some high mountaine under the line ; and these interpreted the torrid Zone to be the flaming sword whereby Paradise was guarded . 'T is the consent of divers others , that Paradise is situated in some high and eminet place . So Tostatus : Est etiam Paradisus situ altissima , supra omnem terrae altitudinem , Paradise is situated in some high place above the earth : and therefore in his Comment upon the 49 of Genesis , he understands the blessing of Iacob concerning the everlasting hills to bee meant of Paradise , and the blessing it selfe to bee nothing else but a promise of Christs comming , by whose Passion the gates of Paradise should bee opened . Unto him assented Rupertus , Scotus , and most of the other Schoolemen , as I find them cited by Pererius , and out of him in Sir Walter Rawleigh . Their reason was this : because in probability , this place was not overflowed by the Flood , since there were no sinners there , which might draw that curse upon it . Nay Tostatus thinks , that the body of Enoch was kept there ; and some of the Fathers , as Tertullian and Austin , have affirmed , that the blessed soules were reserved in that place till the day of Judgement ; and thereford 't is likely that it was not overflowed by the Flood , It were easie to produce the unanimous consent of the Fathers , to prove that Paradise is yet really existent . Any diligent peruser of them , may easily observe how they doe generally interpret the Paradise whereto Saint Paul was wrapt , and that wherein our Saviour promised the Thiefe should be with him , to bee locally the same from whence our first parents were banished . Now there cannot be any place on earth designed where this should bee : And therefore it is not altogether improbable that it was in this other world . And besides , since all men should have went naked if Adam had not fell , 't is requisite therefore that it should be situated in some such place where it might be priviledged from the extremities of heat and cold . But now this could not be ( they thought ) so conveniently in any lower , as it might in some higher ayre . For these and such like considerations , have so many affirmed , that Paradise was in a high elevated place . Which some have conceived could bee nowhere but in the Moone : For it could not b● in the top of any mountaine ; nor can wee thinke of any other body separated from this earth , which can be a more convenient place for habitation than this Planet ; therefore they concluded that it was there . It could not bee on the top of any mountaine . 1. Because we have expresse Scripture , that the highest of them was overflowed . 2. Because it must be a greater extension , and not some small patch of ground , since t is likely all men should have lived there , if Adam had not fell . But for a satisfaction of the argum̄ets , together with a farther discourse of Paradise , I shall referre you to those who have written purposely upon this subject . Being content for my owne part to have spoken so much of it , as may conduce to shew the opinion of others concerning the inhabitants of the Moone ; I dare not my selfe affirme any thing of these Selenites , because I know not any ground wheron to build any probable opinion . But I thinke that future ages will discover more ; and our posterity , perhaps , may invent some meanes for our better acquaintance with these inhabitants . Proposition 14. That t is possible for some of our posteritie , to find out a conveyance to this other world ; and if there be inhabitants there , to have commerce with them . ALL that hath been said , concerning the people of the new world , is but conjecturall , and full of uncertainties ; nor can we ever looke for any evident or more probable discoveries in this kind , unlesse there bee some hopes of inventing means for our conveyance thither . The possibilitie of which , shall bee the subject of our enquiry in this last Proposition . And , if we doe but consider by what steps and leasure , all arts doe usually rise to their growth , we shall have no cause to doubt why this also may not hereafter be found out amongst other secrets . It hath constantly yet been the method of providence , not presently to shew us all , but to leade us on by degrees , from the knowledge of one thing to another . 'T was a great while , ere the Planets were distinguished from the fixed stars and some time after that , ere the morning and evening starre were found to be the same . And in greater space ( I doubt not ) but this also , and other as excellent mysteries will be discovered . Time , who hath alwayes been the father of new truths , and hath revealed unto us many things , which our Ancestors were ignorant of , will also manifest to our posteritie , that which wee now desire , but cannot know . Veniet tempus ( saith Seneca ) quo ista quae nunc latent , in lucem dies extrahet , & longioris aevi diligentia . Time will come , when the indeavors of after ages , shall bring such things to light as now lie hid in obscuritie . Arts are not yet come to their solstice . But the industrie of future times , assisted with the labors of their forefathers , may reach that height which wee could not attaine to . Veniet tempus quo posteri nostri nos tam aperta nescisse mirentur . As wee now wonder at the blindnesse of our Ancestors , who were not able to discerne such things , as seeme plaine and obvious unto us ; so will our posterity , admire our ignorance in as perspicuous matters . In the first ages of the world the Ilanders thought themselves either to bee the only dwellers upon earth , or else if there were any other , they could not possibly conceive how they might have any commerce with them , being severed by the deepe and broade Sea. But after times found out the invention of ships , in which notwithstanding , none but some bold , daring men durst venture , according to that of the Tragoedian . Audax nimium qui freta primus Rate tam fragili perfida rupit . Too bold was he , who in a ship so fraile , First venturd on the trecherous waves to saile . And yet now , how easie a thing is this even to a timorous and cowardly nature ? And questionlesse , the invention of some other means for our conveiance to the Moone , cannot seeme more incredible to us , than this did at first to them , and therefore we have no just reason to bee discouraged in our hopes of the like successe . Yea , but ( you will say ) there can be no sayling thither , unlesse that were true which the Poëts doe but faine , that she made her bed in the Sea. Wee have not now any Drake , or Columbus , to undertake this voyage , or any Daedalus to invent a conveiance through the ayre . I answer , Though wee have not , yet why may not succeeding times , rayse up some spirits as eminent for new attempts and strange inventions , as any that were before them ? T is the opinion of Keplar , that as soone as the art of flying is found out , some of their nation will make one of the first Colonies , that shall transplant into that other world . I suppose , his appropriating this preheminence to his owne Countreymen , may arise from an overpartiall affection to them . But yet thus far I agree with him , That when ever that Art is invented , or any other , wherby a man may be conveyed some twenty miles high , or thereabouts , then , t is not altogether improbable that some or other may be successefull in this attempt . For the better clearing of which I shall first lay downe , and then answer those doubts that may make it seeme utterly impossible . These are chiefly three . The first , taken from the naturall heavinesse of a mans body , whereby it is made unfit for the motion of ascent , together with the vast distance of that place from us . 2. From the extreme coldnes of the aethereall ayre . 3. The extreme thinnesse of it . Both which must needs make it impassible , though it were but as many single miles thither , as it is thousands . For the first . Though it were supposed that a man could flie , yet wee may well think hee would be very slow in it , since hee hath so heavy a body , and such a one too , as nature did not principally intend , for that kind of motion . T is usually observed , that amongst the varietie of birds , those which doe most converse upon the earth , and are swiftest in their running , as a Pheasant , Partridge , &c. together with all domesticall fowle , are lesse able for flight , than othhrs which are for the most part upon the wing , as a Swallow , swift , &c. And therefore wee may well think , that man being not naturally endowed with any such condition as may inable him for this motion ; and being necessarily tied to a more especiall residence on the earth , must needs be slower than any fowle , and lesse able to hold out . Thus is it also in swimming ; which Art though it bee growne to a good eminence , yet he that is best skilled in it , is not able either for continuance , or swiftnesse , to equall a fish ; Because he is not naturally appointed to it . So that though a man could fly , yet hee would be so slow in it , and so quickly weary , that hee could never think to reach so great a journey as it is to the Moone . But suppose withall that hee could fly as fast , and long , as the swiftest bird : yet it cannot possibly bee conceived , how he should ever be able to passe through so vast a distance , as there is betwixt the Moone and our earth . For this Planet , according to the common grounds , is usually granted to bee at the least , 52 semidiameters of the earth from us . Reckoning for each semidiameter 3456 English miles , of which the whole space will be about 179712. So that though a man could constantly keep on in his journey thither by a straite line , though he could fly a thousand miles in a day ; yet he would not arrive thither under 180 dayes , or halfe a yeare . And how were it possible for any to tarry so long without dyet or sleep ? 1. For Diet. I suppose there could be no trusting to that fancy of Philo the Iew ( mentioned before , ) who thinks that the musick of the spheares should supply the strength of food . Nor can wee well conceive how a man should be able to carry so much luggage with him , as might serve for his Viaticum in so tedious a journey . 2. But if he could : yet he must have some time to rest and sleep in . And I yet they have not any present inclination or pronesse to one another . And so consequently , cannot bee styled heavy . The meaning of this will bee more clearely illustrated by a similitude . As any light body ( suppose the Sunne ) dos send forth his beames in an orbicular forme ; So likewise any magneticall body , for instance a round loadstone dos cast abroad his magneticall vigor in a spheare . Thus. Where suppose the inward circle at A to represent the Loadstone , and the outward one betwixt B C , the orbe that dos terminate its vertue . Now any other body that is like affected comming within this sphere , as B , will presently descend towards the center of it , and in that respect may be styled heavy . But place it without this sphere as C , and then the desire of union ceaseth , and so consequently the motion also . To apply then what hath been said . This great globe of earth and water , hath been proved by many observations , to participate of Magneticall properties . And as the Loadstone dos cast forth its owne vigor round about its body , in a magneticall compasse : So likewise dos our earth . The difference is , that it is another kind of affection which causes the union betwixt the Iron and Loadstone , from that which makes bodies move unto the earth . The former is some kind of neerenesse and similitude in their natures , for which , Philosophie as yet has not found a particular name . The latter dos arise from that peculiar qualitie , whereby the earth is properly distinguished from the other elements , which is its Condensitie . Of which the more any thing dos participate , by so much the stronger will bee the desire of union to it . So gold and others metalls which are most close in their composition , are likewise most swift in their motion of discent . And though this may seeme to bee contradicted by the instance of metalls , which are of the same weight , when they are melted , and when they are hard : As also of water , which dos not differ in respect of gravitie , when it is frozen and when it is fluid : yet we must know that metalls are not rarified by melting , but mollified . And so too for frozen waters , they are not properly condensed , but congealed into a harder substance , the parts being not contracted closer together , but still possessing the same extension . But yet ( I say ) t is very probable , that there is such a spheare about the earth , which dos terminate its power of attracting other things unto it . So that suppose a body to bee placed within the limits of this sphere , and then it must needs tend downewards , towards the center of it . But on the contrary , if it be beyond this compasse , then there can bee no such mutuall attraction ; & so consequently , it must rest immoveable from any such motion . For the farther confirmation of this , I shall propose two pertinent observations . The first taken in the presence of many Physitians , and related by an eminent man in that profession , Hieron . Fracastorius . There being divers needles provided of severall kindes , like those in a Mariners Chart , they found , that there was an attractive power , not only in the magnet ; But that iron also and steele , and silver did each of them draw its owne mettle . Whence hee concludes , Omne trahit quod sibi simile est . And as these peculiar likenesses , have such a mutuall efficacy ; so t is probable , that this more generall qualification of condensitie , may bee the cause , why things so affected desire union to the earth . And though 't is likely that this would appeare betwixt two lesser condensed bodies , ( as suppose two peeces of earth ) if they were both placed at libertie in the aethereall ayre , yet being neere the earth , the stronger species of this great globe dos as it were drownd the lesse . 'T is a common experiment , that such a lump of ore or stone , as being on the ground , cannot be moved by lesse than six men , being in the bottom of a deep mine , may be stirred by two . The reason is , because then t is compassed with attractive beams , there being many above it , as well as below it . Whence we may probably inferre ( saith the learned Verulam ) that the nature of gravitie , dos worke but weakly also far from the earth ; Because the appetite of union in dense bodies , must bee more dull in respect of distance . As we may also conclude from the motion of birds , which rise from the ground but heavily , though with much labor ; Whereas being on high , they can keep themselves up , and soare about by the meere extension of their wings . Now the reason of this difference , is not ( as some falsly conceive ) the depth of ayre under them . For a bird is not heavier when there is but a foote of ayre under him , than when there is a furlong . As appeares by a ship in the water , ( an instance of the same nature ) which dos not sinke deeper , and so consequently is not heavier , when it has but five fatham depth , than when it has fifty . But the true reason is , the weaknesse of the desire of union in dense bodies at a distance . So that from hence , there might be just occasion to taxe Aristotle and his followers , for teaching that heavines is an absolute qualitie of it selfe , and really distinct from condensitie : whereas it is onely a modification of it , or rather , another name given to a condensed body in reference to its motion . For if it were absolute , then it should alwayes be inherent in its subject , and not have its essence depend upon the bodies being here or there . But it is not so . For , 1. Nothing is heavy in its proper place , according to his owne principle , Nihil grave est in suo loco . And then 2. Nothing is heavy , which is so farre distant from that proper orbe to which it dos belong , that it is not within the reach of its vertue . As was before confirmed . But unto this it may be objected . Though a body being so placed , be not heavy in actu secundo ; yet it is in actu primo : because it retaines in it an inward proness to move downewards , being once severed from its proper place . And this were reason enough why the quality of heavinesse should have an absolute being . I answer , this distinction is only appliable to such naturall powers as can suspend their acts ; and will not hold in Elementary qualities , whose very essence dos necessarily require an exercise of the second act , as you may easily discerne by an induction of all the rest . I cannot say , that body has in it the quality of heate , coldnesse , drinesse , moisture , hardnesse , softnesse , &c. which for the present , has not the second act of these qualities . And if you meane by the essence of them , a power unto them : why , there is not any naturall body but has a power to them all . From that which hath beene said concerning the nature of gravity , it will follow ; That if a man were above the sphere of this magneticall vertue , which proceeds from the earth , hee might there stand as firmely as in the open aire , as he can now upon the ground : And not only so , but he may also move with a farre greater swiftnesse , than any living creatures here below , because then hee is without all gravity , being not attracted any way , and so consequently will not be liable to such impediments , as may in the least manner resist that kinde of motion which hee shall apply himselfe unto . If you yet enquire , how wee may conceive it possible , that a condensed body should not be heavy in such a place ? I answer , by the same reason as a body is not heavy in its proper place . Of this I will set down two instances . When a man is in the bottome of a deepe river , though hee have over him a multitude of heavy waters , yet he is not burdened with the weight of them . And though another body , that should be but of an equall gravity , with these waters , when they are taken out , would be heavy enough to presse him to death ; yet notwithstanding whilst they are in the channell , they doe not in the least manner , crush him with their load . The reason is , because they are both in their right places ; and t is proper for the man being the more condensed body , to be lower than the waters . Or rather thus , Because the body of the man , dos more nearely agree with the earth , in this affection , which is the ground of its attraction , and therefore doth that more strongly attract it , than the waters that are over it . Now , as in such a case , a body may lose the operation of its gravity , which is , to move , or to presse downewards : So may it likewise , when it is so far out of its place , that this attractive power cannot reach unto it . T is a pretty notion to this purpose , mentioned by * Albertus de Saxonia , and out of him by * Francis Mendoca ; That the aire is in some part of it navigable . And that upon this Staticke principle ; any brasse or iron vessell ( suppose a kettle ) whose substance is much heavier than that of the water , yet being filled with the lighter aire , it will swimme upon it , and not sinke . So suppose a cup , or wooden vessel , upon the outward borders of this elementary aire , the cavity of it being filled with fire , or rather aethereall aire , it must necessarily upon the same ground remaine swimming there , and of it selfe can no more fall , than an empty ship can sinke . T is commonly granted , that if there were a hole quite through the center of the earth , though any heavy body ( as suppose a milstone ) were let fall into it , yet when it came unto the place of the center , it would there rest immoveable in the aire . Now , as in this case , it s owne condensity , cannot hinder , but that it may rest in the open aire , when there is no other place , to which it should be attracted : So neither could it be any impediment unto it , if it were placed without the sphere of the earths magneticall vigor , where there should be no attraction at all . From hence then ( I say ) you may conceive , that if a man were beyond this sphere , hee might there stand as firmely in the open aire , as now upon the earth . And if he might stand there , why might hee not also goe there ? And if so ; then there is a possibility likewise of having other conveniences for travelling . And here t is considerable , that since our bodies will then bee devoide of gravity , and other impediments of motion ; wee shall not at all spend our selves in any labour , and so consequently not much need the reparation of diet : But may perhaps live altogether without it , as those creatures have done , who by reason of their sleeping for many dayes together , have not spent any spirits , and so not wanted any foode : which is commonly related of Serpents , Crocodiles , Beares , Cuckoes , Swallowes , and such like . To this purpose , * Mendoca reckons up divers strange relations . As that of Epimenides , who is storied to have slept 75 yeeares . And another of a rusticke in Germany , who being accidentally covered with a hay-ricke , slept there for all autumne , and the winter following , without any nourishment . Or , if this will not serve : yet why may not a Papist fast so long , as well as Ignatius or Xaverius ? Or if there be such a strange efficacy in the bread of the Eucharist , as their miraculous relations doe attribute to it : why then , that may serve well enough , for their viaticum . Or , if wee must needs feed upon something else , why may not smells nourish us ? * Plutrach , and * Pliny and divers other ancients , tell us of a nation in India that lived only upon pleasing odors . And t is the common opinion of Physitians , that these doe strangely both strengthen and repaire the spirits . Hence was it that Democritus was able for divers dayes together , to feede himselfe with the meere smel of hot bread . Or if it bee necessary that our stomacks must receive the food : why then t is not impossible that the purity of the aethereall aire , being not mixed with any improper vapors , may be so agreeable to our bodies , as to yeeld us sufficient nourishment ; According to that of the Poet ; — Vescitur aurâ Aethereâ — T was an old Platonicke principle , that there is in some part of the world such a place where men might be plentifully nourished , by the aire they breath : Which cannot more properly be assigned to any one particular , than to the aethereall aire above this . I know t is the common opinion that no Element can prove Aliment , because t is not proportionate to the bodies of living creatures which are compounded . But , 1. This aethereall aire is not an element ; and though it be purer , yet t is perhaps of a greater agreeablenesse to mans nature and constitution . 2. If we consult experience and the credible relations of others , wee shall finde it probable enough that many things receive nourishment from meer elements . First , for the earth ; * Aristotle and * Pliny , those two great naturalists , tell us of some creatures , that are fed only with this . And it was the curse of the serpent , Gen. 3. 14. Vpon thy belly shalt thou goe , and dust shalt thou eate all the dayes of thy life . So likewise for the water . * Albertus Magnus speaks of a man who lived seven weeks together by the meere drinking of water . * Rondoletius ( to whose diligence these later times are much beholding for sundry observations concerning the nature of Aquatils ) affirmes that his wife did keep a fish in a glasse of water , without any other food for three yeares : In which space it was constantly augmented , till at first it could not come out of the place at which it was put in , and at length was too big for the glasse it selfe , though that were of a large capacity . Cardan tells us of some wormes , that are bred & nourished by the snow , from which being once separated , they dye . Thus also is it with the aire , which wee may well conceive dos chiefly concurre to the nourishing of all vegetables . For if their food were all sucked out from the earth , there must needs be then , some sensible decay in the ground by them ; especially since they do every yeare renew their leaves , and fruits : which being so many , and so often , could not be produced without abundance of nourishment . To this purpose is the experimēt of trees cut down which will of themselves put forth sproutes . As also that of Onyons , & the Semper-vive , which will strangely shoot forth , and grow as they hang in the open aire . Thus likewise is it with some sensible creatures ; the Camelion ( saith * Pliny and * Solinus ) is meerely nourished by this : And so are the birds of Paradise , treated of by * many ; which reside constantly in the aire , Nature having not bestowed upon them any legs , and therefore they are never seene upon the ground but being dead . If you aske , how they multiply ? T is answered , they lay their egges on the backes of one another , upon which they sit til their young ones be fledg'd . * Rondoletius from the history of Hermolaus Barbarus , tels us of a Priest ( of whom one of the Popes had the custody ) that lived forty yeares upon meer aire . As also of a maide in France , and another in Germany , that for diverse yeares together did feed on nothing but this : Nay , hee affirmes that hee himselfe had seene one , who lived till ten yeares of age without any other nourishment . You may find most of these , and some other examples to this purpose , gathered together by Mendoca Viridar . lib. 4. Prob. 23 , 24. Now , if this elementary aire which is mixed with such improper vapors , may accidentally nourish some persons ; perhaps then , that pure aethereall aire may of it selfe be more naturall to our tempers . But if none of these conjectures may satisfie ; yet there may happily be some possible meanes for the conveiance of other foode , as shall be shewed afterwards . Againe , seeing we do not then spend our selves in any labour , we shall not , it may bee , neede the refreshment of sleepe . But if we doe , we cannot desire a softer bed than the aire , where wee may repose our selves firmely and safely as in our chambers . But here you may aske , whether there be any meanes for us to know , how far this sphere of the earths vertue dos extend it selfe ? I answer , t is probable that it dos not reach much farther than that orbe of thick vaporous aire , that incompasseth the earth ; because t is likely the Sunne may exhale some earthly vapors , near unto the utmost bounds of the sphere alloted to them . Now there are divers wayes used by Astronomers , to take the altitude of this vaporous aire . As , 1. By observing the height of that aire which causeth the Crepusculum , or twilight ; For the finding of which , the Antients used this meanes : As soone as ever they could discerne the aire in the east to be altered with the least light , they would by the situation of the starres find out how many degrees the Sun was below the Horizon , which was usually about 18. From whence they would easily conclude , how high that aire must be above us , which the Sun could shine upon , when hee was 18 degrees below us . And from this observation , it was concluded to bee about 52 miles high . But in this Conclusion , the Antients were much deceived , because they proceeded upon a wrong ground , whilst they supposed that the shining of the Suns direct rayes upon the aire , was the only reason of the Crepusculum ; Whereas t is certain that there are many other things which may also concurre to the causing of it . As , 1. Some bright clouds below the Horizon , which being illuminated by the Sunne , may be the meanes of conveying some light to our aire , before the direct rayes can touch it . 2. The often refraction of the rayes , which suffer a frequent repercussion from the cavitie of this sphere , may likewise yeeld us some light . 3. And so may the orbe of enlightned aire compassing the Sunne , part of which must rise before his body . 2. The second way whereby we may more surely find the altitude of this grosser aire , is by taking the highth of the highest cloud : which may be done , 1 Either as they use to measure the altitude of things that cannot be approached unto , viz. by two stations , when two persons shall at the same time , in severall places , observe the declination of any cloud from the vertical point . Or , 2. which is the more easie way , when a man shall choose such a station , where he may at some distance , discerne the place on which the cloud dos cast its shadow , and withall dos observe , how much both the cloud and the Sun decline from the vertical point . From which he may easily conclude the true altitude of it , as you may more plainely conceive , by this following Diagram . Where A B is a perpendicular from the cloud , C the station of him that measures , D the place where the shadow of the cloud dos fall . The instrument being directed from the station C , to the cloud at A , the perpendicular will shew the Angle B A C. Then letting the Sun shine through the sights of your instrument , the perpendicular of it will give the angle B A D. Afterwards having measured the distance C D by paces , you may according to the common rules , find the heigth B A. But if without making the observation , you would know of what altitude the highest of these are found by observation ; * Cardan answers , not above two miles ; * Keplar , not above 1600 paces , or thereabouts . 3. Another way to finde the height of this vaporous aire , is , by knowing the difference of altitude , which it causeth , in refracting the beames of any star neere the Horizon . And from this observation also , it is usually concluded to bee about two or three miles high . But now you must not conceive , as if the orbe of magneticall vigor , were bounded in an exact superficies , or as if it did equally hold out just to such a determinate line , and no farther . But as it hath bin said of the first region , which is there terminated where the heat of reflexion dos begin to languish : So likewise is it probable , that this magneticall vigor dos remit of its degrees proportionally to its distance from the earth , which is the cause of it : And therefore though the thicker clouds may be elevated no higher , yet this orbe may be continued in weaker degrees a little beyond them . We will suppose it ( which in all likelyhood is the most ) to bee about twenty miles high . So that you see the former Thesis remaines probable ; that if a man could but fly , or by any other meanes get twenty miles upwards , it were possible for him to reach unto the Moone . But it may bee againe objected : Though all this were true ; though there were such an orbe of aire which did terminate the earths vigor : And though the heavinesse of our bodies could not hinder our passage , through the vast spaces of the aetheriall aire ; yet those two other impediments may seeme to deny the possibility of any such voyage . 1. The extreme coldnesse of that aire . If some of our higher mountaines for this reason bee not habitable ; much more then will those places bee so , which are farther from any cause of heate . 2. The extreme thinnesse of it , which may make it unfit for expiration . For if in some mountaines ( as Aristotle tells us of Olympus , and out him * S. Austine ) the aire bee so thin that men cannot draw their breath , unlesse it were through some moistned spunges ; much more then must that aire be thin , which is more remotely situated from the causes of impurity and mixture . And then beside , the refraction that is made by the vaporous aire incompassing our earth , may sufficiently prove that there is a great difference betwixt the aethereall aire and this , in respect of rarity . To the first of these I answer , that though the second region , be naturally endowed with so much coldnesse as may make it fit for the production of meteors ; yet it will not hence follow , that all that aire above it , which is not appointed for the like purpose , should partake of the same condition : But , it may seeme more probable that this aethereal aire , is freed from having any quality in the extremes . And this may be confirmed , from those common arguments , which are usually brought to prove the warmnesse of the third region . As you may see in * Fromundus , and others who treate of that subject . T is the assertion of Pererius , that the second region , is not cold meerly for this reason , because it is distant from the ordinary causes of heat , but because it was actually made so at the first , for the condensing of the clouds , and the production of other meteors that were there to be generated ; which ( as I conceive ) might bee sufficiently confirmed from that order of the creation observed by Moses , who tells us that the waters above the firmament ( by which , in the greatest probability , we are to understand the clouds in the second region ) were made the second day , Gen. 1. 7 , 8. whereas the Sunne itselfe ( whose reflection is the cause of heate ) was not created till the fourth day , ver . 16. 19. To the other objection I answer , that though the aire in the second region ( where by reason of its coldnesse there are many thicke vapors ) doe cause a great refraction ; yet t is probable that the aire which is next the earth , is sometimes , & in some places , of a farre greater thinnesse , nay as thin as the aethereall aire it selfe ; since sometimes there is such a speciall heat of the Sun , as may rarifie it in an eminent degree ; And in some dry places , there are no grosse impure exhalations to mixe with it . But here it may be objected . If the aire in the second region were more condensed and heavy than this wherein wee breath , then that must necessarily tend downewards and possesse the lower place . To this some answer , that the hanging of the clouds in the open aire , is no lesse than a miracle . They are the words of Pliny . Quid mirabilius aquis in caelo stantibus ? what more wonderfull thing is there than that the waters should stand in the heavens ? Others prove this from the derivation of the word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 stupescere and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 aquae : Because the waters do hang there after such a stupendous inconceivable manner ; Which seems likewise to bee favoured by Scripture , where t is mentioned as a great argument of Gods omnipotency , that hee holds up the clouds from falling . He binds up the waters in his thicke clouds , and the cloud is not rent under them . But that which unto me seemes full satisfaction against this doubt , is this consideration ; that the naturall vigor whereby the earth dos attract dense bodies unto it , is lesse efficacious at a distance : and therefore a body of lesse density , which is neare unto it , as suppose this thin aire wherein we breath , may naturally bee lower in its situation , than another of a greater condensity that is farther of ; as suppose the clouds in the second region . And though the one bee absolutely and in it selfe more fit for this motion of descent ; yet by reason of its distance , the earths magneticall vertue cannot so powerfully worke upon it . As for that relation of Aristotle ; If it were true ; yet it dos not prove this aire to be altogether impassible , since moistned spunges might helpe us against its thinnesse : But t is more likely that hee tooke it upon trust , as hee did some other relations concerning the height of the mountaines , wherein t is evident that he was grossely mistaken . As where he tells us of Caucasus , that it casts its shadow 560 miles . And this relation being of the same nature , wee cannot safely trust unto him for the truth of it . If it be here enquired , what meanes there may bee conjectured , for our ascending beyond the sphere of the earths magneticall vigor . I answer . 1. T is not perhaps impossible that a man may be able to flye , by the application of wings to his owne body ; As Angels are pictured , as Mercury and Daedaelus are fained , and as hath bin attempted by divers , particulary by a Turke in Constantinople , as Busbequius relates . 2. If there bee such a great Ruck in Madagascar , as * Marcus Polus the Venetian mentions , the feathers in whose wings are twelve foot long , which can soope up a horse and his rider , or an elephant , as our kites doe a mouse ; why then t is but teaching one of these to carry a man , and he may ride up thither , as Ganymed dos upon an eagle . 3. Or if neither of these wayes will serve : Yet I doe seriously , and upon good grounds , affirme it possible to make a flying Chariot . In which a man may sit , and give such a motion unto it , as shall convey him through the aire . And this perhaps might bee made large enough to carry divers men at the same time , together with foode for their viaticum , and commodities for traffique . It is not the bignesse of any thing in this kind , that can hinder its motion , if the motive faculty be answerable thereunto . We see a great ship swimmes as well as a small corke , and an Eagle flies in the aire as well as a little gnat . This engine may be contrived from the same principles by which Archytas made a wooden dove , and Regiomontanus a wooden eagle . I conceive it were no difficult matter ( if a man had leisure ) to shew more particularly , the meanes of composing it . The perfecting of such an invention , would be of such excellent use , that it were enough , not only to make a man famous , but the age also wherein hee lives . For besides the strange discoveries that it might occasion in this other world , it would be also of inconceiveable advantage for travelling , above any other conveiance that is now in use . So that notwithstanding all these seeming impossibilities , t is likely enough , that there may be a meanes invented of journying to the Moone ; And how happy shall they be , that are first successefull in this attempt ? — Faelicesque animae quas nubila supra , Et turpes fumos , plenumque vaporibus orbem , Inseruit caelo sancti scintilla Promethei . Having thus finished this discourse , I chanced upon a late fancy to this purpose under the fained name of Domingo Gonsales , written by a late reverend and learned Bishop : In which ( besides sundry particulars wherein this later Chapter did unwittingly agree with it ) there is delivered a very pleasant and well contrived fancy concerning a voyage to this other world . Hee supposeth that there is a naturall and usuall passage for many creatures betwixt our earth and this planet . Thus hee saies ; those great multitudes of locusts , wherewith diverse countries have bin destroyed , do proceed from thence . And if we peruse the authors who treat of them , wee shall finde that many times they fly in numberlesse troopes , or swarmes , and for sundry dayes together before they fall , are seene over those places in great high clouds , such as comming nearer , are of extension enough to obscure the day , & hinder the light of the Sunne . From which , together with diverse other such relations , he concludes , that t is not altogether improbable , they should proceed from the Moone . Thus likewise he supposeth the Swallowes , Cuckoes , Nightingales , with divers other fowle , which are with us only halfe the year , to flye up thither , when they goe from us . Amongst which kinde , there is a wilde Swan in the East Indies , which at certain seasons of the year doe constantly take their flight thither . Now this bird being of great strength , able to continue for a long flight , as also going usually in flocks , like our wilde-geese ; he supposeth that many of them together , might be taught to carry the weight of a man ; especially if an engine were so contrived ( as he thinks it might ) that each of them should beare an equall share in the burden . So that by this means , t is easily conceiveable , how once every yeare a man might finish such a voyage ; going along with these birds at the beginning of winter , and againe returning with them at the Spring . And here , one that had a strong fancy , were better able to set forth the great benefit and pleasure to be had by such a journey . And that whether you consider the strangenesse of the persons , language , arts , policy , religion of those inhabitants , together with the new traffique that might be brought thence . In briefe , doe but consider the pleasure and profit , of those later discoveries in America , and wee must needs conclude this to be inconceiveably beyond it . But such imaginations as these , I shall leave to the fancy of the Reader . — Sìc itur ad astra . Reptet humi quicunque velit — Coelo restat iter , coelo tentabimusire . FINIS . 1. Booke . Errata . Pag. 47. lin 24. read Scheiner . p. 48. l 22. Nicrembergius p. 50. l. 11. not for nor p. 52. l. 16. hir for his p. 73. l. 22. Malapertius p. 77. l 17. obsolete for absolute p. 90. l. 12. Philolaus ibid l. 15. Rheticus p. 112. l 20. ( Dele its center , and read ) motion of that magneticall globe to which it did belong . p. 137. l. 21. Cisatus p. 143. l. 20. light for right p. 184. l. 23. read in that late p. 202. l 9. must be of p. 219. l. 25. In the margin . 1. p. 221. l. 15. In the margin . 2. p. 223. l. 17. Plutarch . The Propositions that are proved in this Discourse . Proposition 1. THat the strangenesse of this opinion is no sufficient reason why it should be rejected , because other certaine truths have beene formerly esteemed ridiculous , and great absurdities entertained by common consent . By way of Preface . Proposition 2. That a plurality of worlds dos not contradict any principle of reason or faith . Proposition 3. That the heavens doe not consist of any such pure matter which can priviledge them from the like change & corruption , as these inferiour bodies are liable unto . Prop. 4. That the Moone is a solid , compacted , opacous body . Prop. 5. That the Moon hath not any light of her owne . Prop. 6. That there is a world in the Moone , hath beene the direct opinion of many ancient , with some moderne Mathematicians , and may probably be deduced from the tenents of others . Prop. 7. That those spots and brighter parts which by our sight may be distinguished in the Moone , doe shew the difference betwixt the Sea and Land in that other World. Prop. 8. That the spots represent the Sea ; and the brighter parts the Land. Prop. 9. That there are high Mountaines , deepe vallies , and spacious plaines in the body of the Moone . Prop. 10. That there is an Atmo-sphaera , or an orbe of grosse vaporous aire , immediately encompassing the body of the Moone . Prop. 11. That as their world is our Moone , so our world is their Moone . Prop. 12. That t is probable there may be such Meteors belonging to that world in the Moon , as there are with us . Prop. 13. That t is probable there may bee inhabitants in this other World ; but of what kinde they are , is uncertaine . Prop. 14. That t is possible for some of our posterity to finde out a conveyance to this other world , and if there be inhabitants there , to have commerce with them . FINIS . A DISCOVRSE concerning A NEW PLANET . Tending to prove , That 't is probable our Earth is one of the Planets . The second Booke , now first published . Dignares est Contemplatione , ut sciamus in quo rerum statu scimus : pigerimam sortiti , an velocissimam sedem : circa nos Deus omnia , an nos agat . Sen. Nat. Quest. Lib. 7. Cap. 2. LONDON , Printed by R. H. for Iohn Maynard , and are to be sold at the George in Fleetstreet , neer S. Dunstans Church . 1640. To the Reader . NOt to trouble you with an Invective against those multitudes of Pamphlets which are every day prest into the World ; or an Apology , why this was published amongst the rest ( the usuall matter for such kind of Epistles : ) Let me in briefe admonish you somthing concerning the chiefe scope and manner of this following discourse . 1 'T is not the purpose of it , to set downe an exact Treatise of this kind of Astronomy ; but rather to remove those common prejudices , which usually deterre men from taking any Argument tending this way , into their considerations . For we may obserue , that in those points which are cryed downe by the more generall opinion , men doe for the most part rest themselves in the superficiall knowledge of things , as they seem at their first appearances , thinking they can say enough to any Paradox , against which they can urge the most obvious and easie Objections ; and therefore seldome or never search into the depth of these points , or enter into any serious impartiall examination of those grounds on which they are bottomed . Which as it must needs be a great hinderance to the proficiencie of all kind of Learning : so more especially is it in this particular . We might discerne a greater comelinesse and order in this great Fabricke of the World , and more easily understand the appearances in Astronomy , if we could with indifferencie attend to what might bee said for that opinion of Copernicus , which is here defended . 2 For the manner . It is not maintained with such heate and religion , as if every one that reads it , were presently bound to yeeld up his assent : But as it is in other Warres where victory cannot bee had , Men must be content with peace : So likewise is it in this , and should bee in all other Philosophicall contentions . If there bee nothing able to convince and satisfie the indifferent Reader , hee may still injoy his owne opinion . All men have not the same way of apprehending things ; but according to the varietie of their temper , custome , and abilities , their Vnderstandings are severally fashioned to different assents : Which had it beene but well considered by some of our hot * adversaries , they would not have shewed more violence in opposing the Persons against whom they write , than strength in confuting the cause . 'T is an excellent rule to bee observed in all disputes , That Men should give soft Words and hard Arguments , that they would not so much strive to vex , as to convince an Enemy . If this were but diligently practised in all cases , and on all sides , wee might in a good measure bee freed from those vexations in the search of Truth , which the wise Solomon , by his owne experience did so much complaine of , Ecclesiastes , 1. 18. In much Wisedome there is much Griefe , and he that increaseth Knowledge , increaseth Sorrow . To conclude : Though there should be nothing in this discourse conducible to your Information and Benefit ; yet it may serve in the Perusall , as it did in the Composure for the recreation of such leisure houres , as may conveniently bee spared from more weighty imploiments . Farewell . THE PROPOSITIONS that are insisted on in this Discourse . PROP. I. THat the seeming Novelty and Singularity of this opinion , can bee no sufficient reason to prove it erroneous . PROP. II. That the places of Scripture which seeme to intimate the diurnall motion of the Sun or Heavens , are fairely capable of another interpretation . PROP. III. That the Holy Ghost in many places of Scripture , do's plainly conforme his expressions to the errour of our conceits , and do's not speake of sundry things as they are in themselves , but as they appeare unto us . PROP. IV. That divers learned men have fallen into great absurdities , whilest they have looked for the grounds of Philosophy from the grounds of Scripture . PROP. V. That the words of Scripture in their proper and strict construction , doe not any where affirm the immobility of the Earth . PROP. VI. That there is not any Argument from the words of Scripture , Principles of Nature , or observations in Astronomy , which can sufficiently evidence the Earth to bee in the centre of the Vniverse . PROP. VII . 'T is probable that the Sun is in the centre of the World. PROP. VIII . That there is not any sufficient reason to prove the Earth incapable of those motions which Copernicus ascribes unto it . PROP. IX . That it is more probable the Earth do's move , than the Heavens . PROP. X. That this Hypothesis is exactly agreeable to common appearances . Imprimatur A. FREVVEN , Vicecan . Imprimatur LONDINI , SAMUEL BAKER . That the Earth may be a Planet . PROP. I. That the seeming Noveltie and Singularitie of this opinion , can be no sufficient reason to prove it erronious . IN the search of Theologicall Truths , it is the safest method , first of all to looke unto Divine Authority ; because that carryes with it as cleer an evidence to our Faith , as any thing else can be to our reason . But on the contrary , in the examination of Philosophicall points , it were a preposterous course to begin at the testimony and opinion of others , and then afterwards to descend unto the reasons that may bee drawne from the Nature and Essence of the things themselves : because these inartificiall Arguments ( as the Logicians cal them ) doe not carry with them any cleere and convincing evidence ; and therefore should come after those that are of more necessary dependance , as serving rather to confirme , than resolve the Iudgement . But yet , so it is , that in those points which are besides the common opinion , men are carried away at the first by the generall cry , and seldome or never come so farre as to examine the reasons that may bee urged for them . And therfore , since it is the purpose of this discourse to remove those prejudices which may hinder our judgement in the like case , 't is requisite that in the first place there bee some satisfaction given to those Arguments that may bee taken from the Authoritie of others . Which Arguments are insisted on by our adversaries with much heate and violence . What ( say they ) shall an upstart Noveltie thrust out such a Truth as hath passed by successive tradition through all Ages of the World ? and hath bin generally entertained , not onely in the opinion of the vulgar , but also of the greatest Philosophers and most learned men ? * Shall wee thinke that amongst the multitude of those who in severall times have been eminent for new inventions and strange discoveries , there was none able to finde out such a Secret as this , besides some fabulous Pithagorians , and of late Copernicus ? Is it possible that the World should last for above five thousand yeares together , and yet the Inhabitants of it be so dull and stupid , as to be unacquainted with it's motion ? Nay , shall wee thinke that those excellent men , whom the Holy Ghost made use of in the penning of Scripture , who were extraordinarily inspired with supernaturall Truths , should notwithstanding be so grossely ignorant of so common a matter as this ? Can wee beleeve , if there were any such thing , that Iosuah , and Iob , and David , and Solomon , &c. should know nothing of it ? Certainly it must needs argue a strong affectation of Singularitie , for a man to take up any groundlesse fancy against such antient and generall Authority . I answer : As wee should not bee so fondly conceited of our selves , and the extraordinary Abilities of these present ages , as to thinke every thing that is antient to be absolute : Or , as if it must needs bee with opinions , as it is with cloths , where the newest is for the most part best . So neither should we be so superstitiously devoted to Antiquitie , as to take up every thing for Canonicall , which drops from the pen of a Father , or was approved by the consent of the Antients . 'T is an excellent saying , * 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . It behoves every one in the search of Truth , alwaies to preserve a Philosophicall liberty : not to be so inslaved to the opinion of any man , as to thinke what ever he sayes to be infallible . We must labour to find out what things are in themselves by our owne experience , and a through examination of their natures , not what another sayes of them . And if in such an impartiall enquiry , we chance to light upon a new way , and that which is besides the common rode , this is neither our fault , nor our unhappinesse . Not our fault , because it did not arise from Singularity or Affectation . Not our unhappinesse , because it is rather a Priviledge to be the first in finding out such Truths , as are not discernable to every common eye . If Noveltie should alwaies be rejected , neither would Arts have arrived to that perfection wherein now wee enjoy them , nor could we euer hope for any future reformation : though all Truth be in it self Eternall ; yet in respect of mens opinions , there is scarse any so antient , but had a beginning , and was once counted a Noveltie ; and if for this reason it had been condemned as an errour , what a generall darknesse and ignorance would then have been in the World , in comparison of that light which now abounds ; according to that of the Poet : † Quod si tam Antiquis Novit as invisa fuisset , Quam nobis , quid nunc esset vetus aut quid haberet , Quod legeret tereretque viritim publicus usus ? If our Forefathers had but hated thus , All that were new , what had been old to us ? Or , how might any thing confirmed be , For publicke use , by it's Antiquitie ? But for more full satisfaction of all those scruples that may arise from the seeming Novelty or Singularity of this opinion , I shall propose these following considerations . Suppose it were a Noveltie : Yet 't is in Philosophy , and that is made up of nothing else ; but receives addition from every dayes experiment . True indeed , for Divinity wee have an infallible rule that do's plainly inform us of all necessary Truths ; and therfore the Primitive Times are of greater Authority , because they were neerer to those holy Men who were the pen-men of Scripture . But now for Philosophy , there is no such reason : what ever the Schoole-men may talke ; yet Aristotles works are not necessarily true , and hee himselfe hath by sufficient Arguments proved himselfe to be liable unto errour . Now in this case , if wee should speake properly , Antiquity do's consist in the old age of the World , not in the youth of it . In such Learning as may be increased by fresh experiments and new discoveries : 't is we are the Fathers , and of more Authority than former Ages ; because wee have the advantage of more time than they had , and Truth ( wee say ) is the Daughter of Time. However , there is nothing in this opinion so Magisterially proposed , but the Reader may use his owne liberty ; and if all the reasons considered together , doe not seeme convincing unto him , he may freely reject it . In those naturall points which carry with them any doubt or obscurity , it is the safest way to suspend our assents : and though we may dispute pro or con ; yet not to settle our opinion on either side . In weighing the Authority of others , 't is not their multitude that should prevaile , or their skill in some things that should make them of credit in every thing , but wee should examine what particular insight and experience they had in those times for which they are cited . Now 't is plaine , that common people judge by their senses ; and therefore , their voices are altogether unfit to decide any Philosophicall doubt , which cannot well be examined or explained without discourse and reason . And as for the antient Fathers , though they were men very eminent for their holy lives and extraordinary skill in Divinitie ; yet they were most of them very ignorant in that part of Learning which concernes this opinion , as appeares by many of their grosse mistakes in this kinde , as that concerning the Antipodes , &c. and therefore it is not their opinion neither , in this businesse , that to an indifferent seeker of Truth will bee of any strong Authority . But against this it is * objected , That the instance of the Antipodes do's not argue any speciall ignorance in these learned Men : Or , that they had lesse skil in such humane Arts than others ; since Aristotle himself , and Pliny , did deny this as well as they . I answer : 1 If they did , yet this do's make more to the present purpose : For if such great Schollers , who were so eminent for their knowledge in naturall things , might yet notwithstanding be grossely mistaken in such matters as are now evident and certaine : Why then wee have no reason to depend upon their assertions or Authorities , as if they were infallible . 2 Though these great Naturalists , for want of some experience were mistaken in that opinion , whilest they thought no place was habitable but the temperate Zones ; yet it cannot be from hence inferred , that they denied the possibilitie of Antipodes : since these are such Inhabitants as live opposite unto us in the other temperate Zone ; and 't were an absurd thing to imagine that those who lived in different Zones , can be Antipodes to one another ; and argues that a man did not understand , or else had forgotten that common distinction in Geography , wherein the relation of the Worlds Inhabitants unto one another , are reckoned up under these three heads ; Antaeci , Periaeci , and Antipodes . But to let this passe : 'T is certaine , that some of the Fathers did deny the being of any such , upon other more absurd grounds . Now if such as Chrisostome , Lactantius , &c. who were noted for great Schollers , and such too as flourished in these latter times , when all humane Learning was more generally profest , should notwithstanding be so much mistaken in so obvious a matter : Why then may wee not think that those Primitive Saints , who were the pen-men of Scripture , and eminent above others in their time for holinesse and knowledge , might yet be utterly ignorant of many Philosophicall Truths , which are commonly knowne in these dayes ? 'T is probable , that the Holy Ghost did informe them onely with the knowledge of those things whereof they were to be the pen-men , and that they were not better skilled in points of Philosophy than others . There were indeed some of them who were supernaturally indowed with humane Learning ; yet this was , because they might thereby bee fitted for some particular ends , which all the rest were not appointed unto : thus Solomon was strangely gifted with all kinde of knowledge , in a great measure , because he was to teach us by his owne experience the extreme vanity of it , that we might not so settle our desires upon it , as if it were able to yeeld us contentment . So too the Apostles were extraordinarily inspired with the knowledge of Languages , because they were to preach unto all Nations . But it will not hence follow , that therfore the other holy pen-men were greater Schollers than others . 'T is likely that Iob had as much humane Learning as most of them , because his Booke is more especially remarkable for lofty expressions , and discourses of Nature ; and yet 't is not likely that he was acquainted with all those mysteries which later Ages have discovered ; because when God would convince him of his owne folly and ignorance , he proposes to him such questions , as being altogether unanswerable ; which notwithstanding , any ordinary Philosopher in these dayes might have resolued . As you may see at large in the thirty eighth Chapter of that Booke . The occasion was this : Iob having * before desired that he might dispute with the Almighty concerning the uprightnesse of his owne wayes , and the unreasonablenesse of those afflictions which he underwent , do's at length obtaine his desire in this kinde ; and God vouchsafes in this thirty eighth chapter , to argue the case with him . Where he do's shew Iob how unfit he was to judge of the wayes of Providence , in disposing of Blessings and Afflictions , when as he was so ignorant in ordinary matters , being not able to discerne the reason of naturall and common events . As * why the Sea should bee so bounded from overflowing the land ? What is the † bredth of the Earth ? what is the * reason of the Snow or Hayle ? what was the † cause of the Raine or Dewe , of Ice and Frost , and the like . By which questions , it seemes Iob was so utterly pusled , that hee is faine afterwards to humble himselfe in this acknowledgement : * I have uttered that I understood not , things too wonderfull for me , which I knew not : wherefore I abhorre my selfe , and repent in dust and ashes . So that 't is likely these holy Men had not these humane Arts by any speciall inspiration , but by instruction and study , and other ordinary meanes ; and therefore Moses his skill in this kinde is called the Learning of the Egyptians . Now because in those times all Sciences were taughr onely in a rude and imperfect manner ; therefore 't is likely that they also had but a darke and confuse apprehension of things , and were liable to the common errours . And for this reason is it , why * Tostatus ( speaking of Iosuahs bidding the Moone stand still as well as the Sun ) sayes , Quod forte er at imperitus circa Astrorum doctrinam , sentiens ut vulgares sentiunt : That perhaps hee was unskilfull in Astronomy , having the same grosse conceit of the Heavens , as the vulgar had . From all which it may be inferred , that the ignorance of such good Men and great Schollers concerning these Philosophical points , can bee no sufficient reason , why after examination we should deny them , or doubt of their Truth . 'T is considerable , that in the rudiments and first beginnings of Astronomy , and so in severall Ages after , this opinion hath sound many Patrons , and those too Men of eminent note and learning . Such was more especially Pythagoras , who was generally and highly esteemed for his divine wit , and rare inventions ; under whose mysterious sayings , there be many excellent Truths to bee discovered . But against his testimony , it is againe † objected ; If Pythagoras were of this opinion , yet his Authority should not be of any credit , because he was the author of many other monstrous absurdities . To this I answer : If a mans errour in some particulars should take away his credit for every thing else , this would abolish the force of all humane Authority ; for humanum est errane . Secondly , 't is probable that many of Pythagora's sayings which seeme so absurd , are not to be understood according to their letter , but in a mysticall sense . 2 But he objects again , that Pythagoras was not of this opinion ; and that for two reasons : First , because no antient author that he had read ascribes it unto him . Secondly , it is contradictory to his other opinions , concerning the Harmony that was made by the motion of the Heavens ; which could not consist with this other of the Earth's motion . To the first I answer : The Objector could not chuse but know that this assertion is by many antient authors ascribed to that sect , whereof Pythagoras was the chief . He might have seene it expresly in * Aristotle himselfe : 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . In which the Philosopher do's compendiously reckon up the three chiefe particulars implyed in the opinion of the Pythagorians . First , the Suns being in the centre of the World. Secondly , the earth 's annuall motion about it , as being one of the planets : thirdly , it 's diurnal revolution , wherby it caused day & night . To his second reason I answer : First , that Pythagoras thought the Earth to be one of the Planets ( as appeares by Aristotles testimony concerning him ) and to move amongst them the rest . So that his opinion concerning the motion of the heavens , is not inconsistent with that of the earth . Secondly , but as for the coelestiall harmony , he might perhaps under this mysticall expression , according to his usuall custome , shadow forth unto us that mutuall proportion & harmonical consent , which he did conceive in the severall bignes , distance , motions of the orbs . So that notwithstanding these objections , it is evident that Pythagoras was of this opinion , and that his Authority may adde somwhat for the confirmation of it . Vnto him assented * Aristarchus Samius , who flourished about 280 yeares before the Birth of our Saviour , and was by reason of this opinion , arraigned for prophanes and sacriledge by the Ariopagites , because he had blasphemed the deity of Vesta , affirming the earth to move . To them agreed Philaus , Heraclides , Pontius , Nicetas , Syracusanus , Ecphantus , Lucippus , and Plato himself , ( as some think . ) So likewise Numa Pompilius , as Plutarch relates it in his life ; who in reference to this opinion , built the temple of Vesta round , like the universe : in the middle of it was placed the perpetuall vest all fire ; by which he did represent the Sunne in the centre of the world . All these men were in their severall times of speciall Note , as well for their extraordinarie learning , as for this opinion . 'T is considerable , that since this Science of Astronomy hath bin raised to any perfection , there have been many of the best skill in it , that have assented unto that assertion which is here defended . Amongst whom was the Cardinall Cusanus , but more especially Copernicus , who was a man very exact and diligent in these studies for above 30 yeres together , from the yeare 1500 to 1530 , and upwards : and since him , most of the best Astronomers have been of this side . So that now , there is scarce any of note and skil , who are not Copernicus his followers , and if we should goe to most voices , this opinion would carry it from any other . It would be too tedious to reckon up the names of those that may be cited for it ; I wil only mention some of the chief : Such were Ioachinus Rheticus , an elegant writer , Christopherus Rothman , Mestilin , a man very eminent for his singular skill in this Science ; who though at the first he were a follower of Ptolomy , yet upon his second and more exact thoughts , he concluded Copernicus to be in the right , & that the usual Hypothesis , * praescriptione potiùs quàm ratione valet , do's prevaile more by prescription then reason . So likewise Erasmus Reinholdus , who was the man that calculated the Pratenicall Tables from Copernicus his observations , and did intend to write a Commentarie upon his other Works , but that he was taken out of this life before hee could finish those resolutions . Vnto these also I might adde the Names of Gilbert , Keplar , Gallilaeus , with sundry others , who have much beautified and confirmed this Hypothesis , with their new inventions . Nay I may safely affirme , that amongst the varietie of those opinions that are in Astronomy , there are more ( of those which have skill in it ) that are of this opinion , not only than any other side , but than all the rest put together . So that now it is a greater Argument of Singularitie to oppose it . 'T is probable , that many other of the Antients would have assented unto this opinion , if they had been acquainted with those experiments which later times have found out for the confirmation of it : And therefore * Rheticus and † Keplar doe so oten wish that Aristotle were now alive againe . Questionlesse he was so rational & ingenious a man ( not halfe so obstinate as many of his followers ) that upon such probabilities as these , he would quickly have renounced his owne Principles , and have come over to this side : for in one place , having proposed some questions about the heavens , which were not easie to bee resolved : He sets downe this rule , That in difficulties , a man may take a liberty to speake that which seems most likely to him : and in such cases , an aptnesse to guesse at some resolution , for the satisfying of our Philosophicall thirst , do's deserve rather to bestiled by the name of Modestie , than Boldnes . And in another place , he referres the Reader to the different opinions of Astronomers , advising him to examine their severall tenents , as well Eudoxus as Calippus ; and to entertaine that ( not which is most antient , but ) which is most exact and agreeable to reason . And as for Ptolomy , 't is his counsell , that wee should endeavour to frame such suppositions of the Heavens , as might be more simple , being void of all superfluities : and he confesses , that his Hypothesis had many implications in it , together with sundry intricate and unlikely turnings ; and therefore in the same place , hee seems to admonish us , that wee should not bee too confident the Heavens were really in the same Forme , wherein Astronomers did supposethem . So that 't is likely , 't was his chief intent to propose unto us such a frame of the coelestiall bodies , from which wee might , in some measure , conceive of their different appearances ; and according to which , wee might be able to calculate their motions . But now , 't is Copernicus his endeavour , to propound unto us , the true naturall Causes of these severall Motions , and Appearances : It was the intent of the one , to settle the Imagination ; and of the other , to satisfie the judgement . So , that wee have no reason to doubt of his assent unto this Opinion , if hee had but clearely understood all the grounds of it . 'T is reported of Clavius , that when lying upon his Death-bed , he heard the first Newes of those Discoveries which were made by Gallilaeus his Glasse , he brake forth into these words : Videre Astronomos , quo pacto constituendi sunt orbes Coelestes , ut haec Phaenomena salvari possint : That it did behoove Astronomers , to consider of some other Hypothesis , beside that of Ptolomy , whereby they might salve all those new appearances . Intimating that this old one , which formerly he had defended , would not now serve the turne : and doubtlesse , if it had been informed how congruous all these might have been unto the opinion of Copernicus , hee would quickly have turned on that side . 'T is considerable , that amongst the followers of Copernicus , there are scarce any , who were not formerly against him ; and such , as at first , had been throughly seasoned with the Principles of Aristotle ; in which , for the most part , they have no lesse skil , than those who are so violent in the defence of them . Whereas on the contrary , there are very few to bee found amongst the followers of Aristotle and Ptolomy , that have read any thing in Copernicus , or doe fully understand the Grounds of his opinion ; and I thinke , not any , who having been once setled with any strong assent on this side , that have afterwards revolted from it . Now if we do but seriously weigh with our selves , that so many ingenious , considering men , should reject that opinion which they were nursed up in , and which is generally approved as the truth ; and that , for the embracing of such a Paradox as is condemned in Schooles , and commonly cryed downe , as being absurd and ridiculous ; I say , if a man doe but well consider all this , he must needs conclude , that there is some strong evidence for it to bee found out by examination ; and that in all probabilitie , this is the righter side . 'T is probable , that most of those Authors who have opposed this opinion , since it hath bin confirmed by new discoveries , were stirred up thereunto by some of these 3 insufficient grounds . 1 An over-fond and partial conceit of their proper inventions . Every man is naturally more affected to his owne brood , than to that of which another is the Author ; though perhaps , it may bee more agreeable to reason . 'T is very difficult for any one , in the search of Truth , to find in himselfe such an indifferencie , as that his judgement is not at all swayd by an overweening affection unto that which is proper unto himselfe . And this perhaps might bee the first reason that moved the noble Tycho with so much heat to oppose Copernicus , that so hee might the better make way for the spreding of that Hypothesis , which was of his owne invention . To this I might likewise refer that opinion of Origanus and Mr. Carpenter , who attribute to the earth only a diurnall revolution . It do's more especially concerne those men that are Leaders of severall sides , to beat downe any that should oppose them . 2 A servile and superstitious feare of derogating from the authoritie of the antients , or opposing that meaning of Scripture phrases ; wherein the supposed infallible Church , hath for a long time understood them . 'T is made part of the new Creed , set forth by Pius the fourth , 1564 , That no man should assent unto any interpretation of Scripture , which is not approved of by the authoritie of the Fathers . And this is the reason why the Iesuites , who are otherwise the greatest affectors of those opinions , which seeme to be new and subtill , doe yet forbeare to say any thing in defence of this ; but rather take all occasions to inveigh against it . * One of them do's expressely condemn it for a heresie . And since him , it hath bin called in by † two Sessions of the Cardinals , as being an opinion both absurd and dangerous . And therefore likewise doe they punish it , by casting the Defenders of it into the Popes truest Purgatorie , the Inquisition : but yet neither these Councels , nor any ( that I know of ) since them , have proceeded to such a peremptorie censure of it , as to conclude it a heresie : fearing perhaps , lest a more exact examinanation , and the discoverie of future times , finding it to bee an undeniable Truth , it might redound to the prejudice of their Church , and it's infallibilitie . And therefore he that is most bitter against it , in the heat and violence of opposition , will not call it a heresie : the worst that he dares say of it , is , That it is opinio temeraria quae altero saltem pede intravit haeresios limen ; A rash opinion , and bordering upon heresie . Though unto this likewise he was incited by the eagernesse of disputation , and a desire of victorie , for it seemes many eminent men of that Church before him , were a great deale more milde and moderate in their censures of it . Paul the third , was not so much offended at Copernicus , when he dedicated his Worke unto him . The Cardinall of Cusa , do's expresly maintaine this opinion . Scombergius , the Cardinall of Capua , did with much importunitie and great approbation , beg of Copernicus the commentaries that he writ in this kind . And it seems the Fathers of the Councell of Trent , were not such confident defenders of Ptolomy's hypothesis against Copernicus , as many now are . For speaking of those intricate subtilties , which the Fancies of men had framed , to maintain the practice of the Church , they compared them to Astronomers , who ( say they ) do faine Excentricks and Epicijcles , and such engines of Orbes , to save the Phenomena ; though they know there are no such things . But now , because this opinion of Copernicus in later times hath been so strictly forbidden , and punished , it will concerne those of that Religion , to take heed of medling in the defence of it , but rather to submit the liberty of their reason , unto the command of their Superiors , and ( which is very absurd ) even in naturall Questions , not to assent unto any thing , but what authoritie shall allow of . 3. A iudging of things by sence , rather than by discourse and reason : a tying of the meaning of Scripture , to the letter of it ; and from thence concluding Philosophicall points , together with an ignorance of all those grounds and probabilities in Astronomie , upon which this opinion is bottomed . And this in all likelihood , is the reason why some men , who in other things perhaps are able Schollers , doe write so vehemently against it : and why the common people in generall doe cry it downe , as being absurd and ridiculous . Vnder this head I might referre the opposition of Mr. Fuller , Al. Ross. &c. But now , no prejudice that may arise from the bare authoritie of such enemies as these , will be liable to sway the judgement of an indifferent considering man ; and I doubt not but that hee , who will throughly weigh with himselfe these particulars that are here propounded , may find some satisfaction for these Arguments , which are taken from the seeming Noveltie and Singularitie of this Opinion . PROP. II. That there is not any place in Scriptures , from which ( being rightly understood ) wee may inferre the diurnall motion of the Sunne or Heavens . IT were happy for us , if we could exempt Scripture from Philosophicall controversies : if we could bee content to let it bee perfect for that end unto which it was intended , for a rule of our Faith and Obedience ; and not stretch it also to be a Iudge of such naturall truths , as are to be found out by our owne industry and experience . Though the Holy Ghost could easily have given us a full resolution of all such particulars ; yet hee hath left this travell to the sonnes of men to bee exercised therewith , Mundum reliquit disputationibus hominum : that being busied for the most part in an inquisition after the creatures , we might find the lesse leisure to wait upon our lusts , or serve our more sinfull inclinations . But however , because our Adversaries generally doe so much insult in those Arguments that may be drawne from hence ; and more especially , because Pineda doth for this reason with so many bitter and empty reproaches , revile our learned countryman Dr. Gilbert . In that renewing of this opinion , he omitted an answer to the scripture expressions : therfore 't is requisite , That in the prosecuting of this discourse , wee should lay down such satisfaction as may cleere all doubts that may be taken thence : Especially since the prejudice that may arise from the misapprehension of those Scripture phrases , may much disable the Reader from looking on any other Argument , with an equall and indifferent minde . The places that seem to oppose this , are of two kinds . First , such as imply a motion in the Heavens : or secondly , such as seeme to expresse a rest and immobilitie in the Earth . Those of the first kind seem to beare in them the cleerest evidence , and therfore are more insisted on by our Adversaries . They may be referred unto these three heads . 1 All those Scriptures where there is any mention made of the rising , or setting of the Sunne or Starres . 2 That story in Iosuah , where the Sunne standing still , is reckoned for a miracle . 3 That other wonder in the dayes of Hezekiah , when the Sunne went back ten degrees in the Diall of Ahaz . All which places doe seeme to conclude , That the diurnall motion is caused by the Heavens . To this I answer in generall ; That the Holy Ghost in these Scripture expressions , is pleased to accommodate himselfe unto the conceit of the vulgar , and the usuall opinion : whereas , if in the more proper phrase it had been said , That the Earth did rise and set ; or , that the earth stood still , &c. the people who had been unacquainted with that secret in Philosophy , would not have understood the meaning of it , and therfore it was convenient , that they should be spoken unto in their own Language . I but you will reply , It should seeme more likely , if there had been any such thing , that the Holy Ghost should use the truest expressions : for then he would at the same time have informed them of the thing , and reformed them in an errour : since his authoritie alone had been sufficient to have rectified the mistake . I answer : 1 Though it were , yet 't is beside the chiefe scope of those places , to instruct us in any Philosophicall points , as hath been proved in the former book ; especially when these things are neither necessary in themselves , nor do necessarily induce to a more ful understanding of that which is the maine businesse of those Scriptures . But now the people might better conceive the meaning of the Holy Ghost , when he do's conforme himselfe unto their capacities and opinions , than when hee talks exactly of things in such a proper phrase , as is beyond their reach : And therefore 't is said in Isaiah , I am the Lord which teacheth thee utilia , profitable things : where the glosse ha's it , non subtilia , not such curiosities of Nature as are not easily apprehended . 2 'T is not only besides that which is the chiefe purpose of those places , but it might happen also to be somwhat opposite unto it . For men being naturally unapt to beleeve any thing that seemes contrary to their senses , might upon this begin to question the authoritie of that Booke which affirmed it , or at least to retch Scripture some wrong way , to force it to some other sence which might be more agreeable to their owne false imagination . † Tertullian tels us of some Hereticks , who when they were plainly confuted out of any Scripture , would presently accuse those texts or Books to be fallible ; and of no authority ; and rather yeeld Scripture to bee erroneous , than forgoe those Tenents for which they thought there was so good reason . So likewise might it have been in these points which seem to beare in them so much contradiction to the sences and common opinion : and therfore 't is excellent advise set down by S. † Austin . Quod nihil credere de re obscur â temere debemus , neforte quod postea veritas patefecerit , quamvis libris sanctis sive testamenti veteris , sive novi , nullo modo esse possit adversum , tamen propter amorem nostri erroris oderimus : That wee should not hastily settle our opinions concerning any obscure matter , lest afterwards , the truth being discovered , ( which however it may seeme , cannot bee repugnant to any thing in Scripture ) wee should hate that , out of love to the error that wee have before entertained . A little reading may informe us how these Texts have bin abused to strange and unmeant Allegories , which have mentioned any naturall truth in such a manner as was not agreeable to mens conceits . And besides , if the Holy Ghost had propounded unto us any secrets in Philosophie , we should have bin apt to be so busied about them , as to neglect other matters of greater importance . And therefore Saint Austin proposing the question , what should be the reason , Why the Scripture do's not cleerely set down any thing concerning the Nature , Figure , Magnitude , and Motion of the Heavenly Orbes ; hee answers it thus : The Holy Ghost being to deliver more necessarie Truths , would not insert these , lest men according to the varietie of their dispositions , should neglect the more weighty matters , and bestow their thoughts about the speculative naturall points , which were lesse needfull . So that it might seeme more convenient , that the Scripture should not meddle with the revealing of these unlikely Secrets , especially when it is to deliver unto us many other mysteries of greater necessitie , which seeme to be directly opposite to our sense and reason . And therefore , I say , the holy Ghost might purposely omit the treating of these Philosophicall Secrets , till time and future discoverie , might with leisure settle them in the opinion of others : As he is pleased in other things of a higher kind , to apply himselfe unto the infirmitie of our apprehensions , by being represented , as if hee were a humane nature , with the parts and passions of a man. So in these things likewise , that he might descend to our capacities , do's he vouchsafe to conforme his expressions unto the errour and mistake of our judgements . But before we come to a further illustration , let us a little examine those particular Scriptures , which are commonly urged to prove the motion of the Sun or Heavens . These ( as was said ) might be distributed under these three heads . 1 Those places which mention the rising or setting of the Sunne , as that in the * Psalme , The Sun like a Bridegroome commeth out of his chamber , and rejoyceth as agyant to runne his race : His going forth is from the end of Heaven , and his circuit unto the end of it , and there is nothing hid from the heate thereof . And that in Ecclesiastes , The Sunne ariseth , and the Sunne goeth downe , &c. In which Scriptures , we may observe divers phrases that are evidently spoken in reference to the appearance of things , and the false opinion of the vulgar . And therefore 't is not altogether unlikely , That this , which they seem to affirme concerning the motion of the Heavens , should also bee understood in the same sence . The Sun like a Bridegroome commeth out of his chamber ; alluding perhaps unto the conceit of ignorant people : as if it took rest all the while it was absent from us , and came out of it's chamber , when it arose . And reioyceth as a Gyant to run his race ; because in the Morning it appeares bigger than at other times ; and therfore in reference to this appearance , may then be compared unto a Giant . His going forth is from the end of Heaven , and his circuit unto the ends of it . Alluding againe unto the opinion of the vulgar : who not apprehending the roundnesse of the Heavens , doe conceive it to have two ends : one where the Sun riseth , the other where it setteth . And there is nothing bid from the heate thereof , speaking still in reference to the common mistake , as if the Sunne were actually hot in it self ; and as if the heate of the weather were not generated by reflection , but did immediately proceed from the body of the Sun. So likewise , for that in Ecclesiastes , where 't is said , the Sun riseth , and the Sun goeth downe , &c. which phrases being properly understood , doe import that he is sometimes in a higher place than at others : whereas , in a circumference , there is no place higher or lower , each part being at the same distance from the centre , which is the bottome . But now understand the phrase in reference to the Suns appearance , and then we grant that he do's seem sometimes to rise , and sometimes to go downe , because in reference to the Horizon , ( which common people apprehend to bee the bottome , and in the utmost bounds of it to joyne with the heavens , ) the Sun do's appeare in the Morning to rise up from it , and in the Evening to goe down unto it . Now I say , because the Holy Ghost , in the manner of these expressions , do's so plainly allude unto vulgar errours , and the false appearance of things : therefore 't is not without probabilitie , that hee should be interpreted in the same sence , when he seemes to imploy a motion in the Sun or Heavens . 2 The second place , was that relation in Iosuah : where 't is mentioned as a miracle . That the Sunne did stand still . And Iosuah said , Sunne stand thou still upon Gibeon , and thou Moone in the valley of Ajalon . So the Sun stood still in the midst of Heaven , and hasted not to goe downe about a whole day . And there was no day like that , before it or after it . In which place likewise , there are divers phrases wherin the Holy Ghost do's not expresse things according to their true nature , and as they are in themselves : but according to their appearances , and as they are conceived in common opinion . As , 1 When he sayes , Sun stand thou still upon Gibeon , or over Gibeon . Now the whole Earth being so little in comparison to the body of the Sun , and but as a point , in respect of that Orbe wherein the Sun is supposed to move , and Gibeon being , as it were , but a point of this Globe of Earth : therefore the words cannot be understood properly , but according to appearance . 'T is probable that Iosuah was then at Azecha , a little East from Gibeon , and the Sunne being somewhat beyond the Meridian , did seeme unto him as he was in that place , to bee over against Gibeon ; and in reference to this appearance , and vulgar conceit , do's hee command it to stand still upon that place . 2 And so secondly for that other expression ; And thou Moone in the valley of Ajalon . This Planet was now a little East from the Sun , it being about three or foure dayes old ( as † Commentators guesse . Ajalon was three miles from Gibeon Eastward , and Iosuah commanded the Moone to stand still there : because unto him it did then seeme to be over against that valley ; whereas , 't is certaine , if he had been there himselfe , it would still have seemed to be as much distant from him . Iust as men commonly speak in shewing another the Stars : we point to a Star over such a chimney , or such a tree , because to us it appeares so ; wheras the Star in it selfe is not sensibly more over them , than it is over us . So that in in this phrase likewise the Holy Ghost doth conforme himselfe unto the appearance of things , and our grosser conceit . 3 And the Sun stood still in the midst of Heaven . Now to speake properly , and as the thing is in it selfe , Heaven ha's no midst but the centre ; and therefore , this also must be interpreted in reference to the opinion of the vulgar , and by the midst of Heaven , wee are to understand such a place as was not very neere to either of the ends , the East or West . 4 And there was no day like that , before it or after it : which words are not to be understood absolutely , for there are alwaies longer daies under the Poles : but in respect to the opinion of the vulgar ; that is , there was never any day so long which these ignorant people knew of . 3 As for this last place concerning the Sunnes returning ten degrees in the diall of Ahaz : I thinke it may probably be affirmed , That it is to be understood only concerning the shadow : which though it doe necessarily happen in all horizontall dialls , for any latitude betwixt the Tropickes : and so consequently in all declining dialls , the elevation of whose Pole is lesse than the Sunnes greatest declination ; as Clavius de Horol . cap. 21. observes : yet the circumstances of this relation in scripture , makes the event to differ from that other which is common and naturall : which against it's nature did seem to go backwards , when as the Sunne it selfe was not in the least manner altered from it's usuall course . Of this opinion were Abarbinell ; Arius Montanus , Burgensis , Vatablas Sanctius , &c. The reasons for it may be these ; 1 The miracle is proposed onely concerning the shadow ; Wilt thou that the shadow shall ascend or returne by ten degrees : there being not in the offer of this wonder , any the least mention made concerning the Sunnes going backwards . 2 'T is likely wee should have had some intimation concerning the extraordinarie length of the day , as it is in that of Iosuah ; but in this relation , the chiefe matter that the story takes notice of , is the alteration of the shadow . 3 Had it been by the supposed returne of the Sunnes body , this had been a greater miracle then those which were performed upon more solemne occasions ; it had been more wonderfull then it's seeming rest in Iosuahs time ; then the supernaturall Eclipse at our Saviours death , when the Moone was in the full . And then it is not likely , that the Holy Ghost in relating of this miracle , should chiefly insist in expressing how the shadow returned , and that onely in the diall of Ahaz . 4 This Figure did not appeare in the Sun it selfe ; because in the 2. Chron. 32. 31. 'T is said , that the Embassadors of the king of Babylon did come unto Hezekiah , to enquire of the wonder that was done in the land ; and therefore it seems the miracle did not consist in any change of the Heavens . 5 If it had been in the Sunne , it would have been as well discerned in other parts of the world , as in the land of Iudaea . And then , 1 What need the King of Babylon send thither to enquire after it ? If you reply , because it was occasioned by Hezekiahs recoverie ; I answer , 't is not likely that the heathens would ever beleeve so great a miracle should bee wrought meerly for a signe of one mans recovery from a disease . But would either be apt to thinke that it was done for some more remarkable purpose , and that by some of their owne gods , unto whom they attributed a far greater power , than unto any other . 'T is more probable , that they might heare some flying rumour of a miracle that was seene in Iudaea : which because it happened only in Hezekiahs house and diall ; and that too upon his recoverie from a dangerous sicknesse , they might be more apt to beleeve that it was a signe of it . 2 Why have we no mention made of it in the writings of the Antients ? It is no way likely , that so great a miracle as this was ( if it were in the Sun ) should have been passed over in silence ; Especially , since it happened in those later times , when there were many heathen writers that flourished in the world , Hesiod , Archilochus , Symonides ; and not long after , Homer , with divers others ; and yet none of them have the least mention of any such prodigie . Wee have many relations of matters that were lesse observable , which were done about that time ; the Historie of Numa Pompilius , Gyges ; the fight betwixt the three Brethren , with divers such stories . And 't is scarse credible , that this should have been omitted amongst the rest . Nay , we have ( as many guesse ) some hints from prophane antiquitie , of the miracle wrought by Iosuah . Vnto which , 't is thought the Antients did allude in the fable of Phaëton ; when the Sun was so irregular in his course , that hee burnt some part of the world . And questionlesse then , this which happened in later times , would not have been so wholly forgotten . 'T is an Argument urged by * Origen , That the Eclipse at our Saviours Passion was not universall , because no prophane author of those times mentions it . Which consequence is the very same with that which is urged in this other case ; but by the way , his antecedent was false , since † Tertullian affirmes , That it was recorded amongst the Romane Annels . Now as for that story in Herodotus , where after he had related the flight of Senacherib , he tels us , how the Sunne did foure times in the space of 10340 yeres invert his course , and rise in the West ; which would seeme so unto other nations , if he had only returned , as many conclude , from this Scripture . As for this story , ( I say ) it cannot well bee urged as pertinent to the present busines , because it seems to have reference unto times that never were . So that all these things being well considered , we shall find it more probable , that this miracle doth consist in the returne of the shadow . If you object , That the Scripture do's expresly say , the Sunne it selfe returned tenne degrees ; I answer , 't is a frequent manner of speech in Scripture , to put the cause for the effect ; as that in Ionas , Where 't is said , That the Sunne did beat upon the head of Ionas ; that is , the beames of the Sunne . So that of the Psalmist , The Sunne shall not smite thee by day , that is , the heate which proceeds from the Sunnes reflection . In the same sence may the phrase bee understood in this place ; and the Sunne may be said to returne backe , because the light , which is the effect of it , did seeme to doe so ; or rather , because the shadow , which is the effect of that , did change it's course . This later Scripture then , will not at all make to the present purpose : as for those of the two former kinds , I have alreadie answered , That they are spoken in reference to the appearance of things , and vulgar opinion . For the further illustration of which , I shall endeavour to confirme these two particulars . 1 That the Holy Ghost in many other places of Scripture , do's accommodate his expressions unto the errour of our conceits : and do's not speake of divers things as they are in themselves , but as they appeare unto us . Therefore 't is not unlikely , that these phrases also may bee liable unto the same interpretation . 2 That divers men have fallen into great absurdities , whilest they have looked for the grounds of Philosophy , from the words of Scripture ; and therefore it may bee dangerous in this point also , to adhere so closely unto the Letter of the Text. PROP. III. That the Holy Ghost , in many places of Scripture , do's plainly conforme his expressions unto the errors of our conceits ; and do's not speake of divers things as they are in themselves , but as they appeare unto us . THere is not any particular by which Philosophy hath been more endamaged , than the ignorant superstition of some men : who in stating the controversies of it , doe so closely adhere unto the meere words of Scripture . Quam plurima occurrunt in libris sacris ad naturam pertinentia , &c. They are the words of † Vallesius . There are sundry things in holy Writ concerning naturall points , which most men think are not so to be understood , as if the Holy Ghost did intend to unfold unto us any thing in that kinde : but referring all to the salvation of our soules , do's speak of other matters according to common opinion . And a little after , Ego , divina haec eloquia , &c. I for my part am persuaded , that these divine Treatises were not written by the holy and inspired pen-men , for the interpretation of Philosophy , because God left such things to be found out by mens labour and industrie . But yet whatsoever is in them concerning nature is most true : as proceeding from the God of nature , from whom nothing could be hid . And questionlesse , all those things which the Scripture do's deliver concerning any naturall point , cannot be but certaine and infallible , being understood in that sence , wherein they were first intended ; but now that it do's speake somtimes according to common opinion , rather than the true nature of the things themselves , was intimated before ; wherfore ( by the way ) * Fromondus his triumph upon the later part of this quotation , is but vaine , and to no purpose . 'T is a good rule set downe by a learned † Commentator , to bee observed in the interpretation of Scripture : Scriptura sacra saepè non tam ad veritatem ipsam , quam ad hominum opinionem , sermonem acommodat ; that it do's many times accommodate it's expressions , not so much to the truth it selfe , as to mens opinions . And in this sence is that speech of Gregorie concerning Images and Pictures , attributed by * Calvin unto the Historie of the Creation ; viz. Librum esse ideotarum , that it is a Booke for the simpler and ignorant people . For it being written to informe them , as well as others , 't is requisite that it should use the most plaine and easie expressions . To this purpose likewise is that of † Mersennus , Mille sunt Scripturae loca , &c. There are very many places of Scripture , which are not to bee interpreted according to the Letter ; and that for this reason , because God would apply himselfe unto our capacity and sence : Presertim in ijs , quae adres naturales , oculisque subject as pertinent ; more especially in those things which concerne nature , and are subject to our eyes . And therefore in the very same place , though hee be eager enough against Copernicus , yet hee concludes that opinion not to be a heresie ; because ( saith he ) those Scriptures which seeme to oppose it , are not so evident , but that they may bee capable of another interpretation : Intimating , that it was not unlikely they should be understood in reference to outward appearance and common opinion ; And that this manner of speech is frequently used in many other places of scripture , may be easily manifest from these following examples . Thus though the Moone may be prooved by infallible observation , to bee lesse than any of the visible Stars , yet because of its appearance , and vulgar opinion , therefore doth the Scripture in comparison to them , call it one of the great Lights . Of which place , saith Calvin , Moses populariter scripsit , nos potius respexit quam sydera . Moses did not so much regard the nature of the thing , as our capacitie ; and therefore uses a popular phrase : so as ordinarie people without the help of Arts and Learning , might easily understand him ; And in another place , Non fuit Spiritus Sancti concilium Astrologiam docere : It was not the purpose of the Holy Ghost to teach us Astronomy : but being to propound a Doctrine , that concernes the most rude and simple people , hee do's ( both by Moses , and the Prophets ) conforme himself unto their phrases and conceits : lest any should thinke to excuse his owne ignorance with the pretence of difficultie : As men commonly do in those things which are delivered after a learned and sublime manner . Thus Zanchi † likewise , Moses majorem rationem habuit nostri humaníque judicij , &c. When Moses calls the Moon a great light : he had a more especiall reference to mens opinions of it , than to the truth of the thing it self , because he was to deale with such , who do usually judge rather by their sense , than by their reason . Nor will that distinction of Fromondus and others avoid this interpretation , when he tells us of magnum Materiale : which referres to the bulke and quantitie of the body ; and magnum Formale , which imports the greatnesse of it's light . For we grant , that it is really unto us a greater light then any of the Stars , or than all of them together : yet there is not any one of them , but is in it's selfe a bigger light than this ; And therefore when wee say this speech is to be understood according to it's appearance , we do not oppose this to reality : But 't is implied , that this reality is not absolute , and in the nature of the thing it selfe , but only relative , and in reference to us . I may say a candle is a bigger light then a Star , or the Moone , because it is really so to me . How ever any one will thinke this to be spoken , onely in relation to it's appearance , and not to be understood as if the thing were so in it selfe . But ( by the way ) it do's concerne Fromondus to maintaine the Scriptures authority , in revealing of natural secrets ; because , from thence it is that he fetches the chiefe Argument for that strange Assertion of his , concerning the heavinesse of the winde ; Where Iob sayes , that God makes the weight for the winde . Thus likewise , because the common people usually thinke the rain to proceed from some waters in the expansum : therefore doth Moses in reference to this erroneous conceit , tell us of waters above the Firmament , and the Windowes of Heaven : Of which saith Calvin , Nimis serviliter literae se astringunt . &c. Such men too servilely tye themselves unto the letter of the text , who hence conclude , that there is a Sea in the Heavens : when as we know that Moses and the Prophets , to accommodate themselv's unto the capacitie of ruder people , do use a vulgar expression ; and therefore it would be a preposterous course , to reduce their phrases unto the exact rules of Philososophy . Let me adde , that from this mistake , 't is likely did arise that groundlesse observation of the antient Iewes ; who would not admit any to read the beginning of Genesis , till he was arrived to thirty yeres of age . The true reason of which , was this : not because that Booke was harder than any other ; but because Moses conforming his expression to vulgar conceits , and they examining of them by more exact rules of Philosophy , were faine to force upon them many strange Allegories , and unnaturall Mysteries . Thus also , because for the most part we conceive the Starres to be innumerable , therefore doth the Holy Ghost often speak of them in reference to this opinion . So Ieremy , As the hoast of Heaven cannot be numbred , neither the sand of the Sea measured , so will I multiply the seed of David : So likewise when God would comfort Abraham with the promise of a numberlesse posterite , hee bids him looke up to Heaven , and tells him , that his Seed should be like those Stars for number : Which , saith * Clavius , Intelligendum est secundum communem sententiam vulgi , existimantis infinitā esse multitudinē stellarum , dum eas nocte serena confusè intuetur , is to be understood according to the common opinion of the vulgar , who think the Stars to be of an infinite multitude , whilest they behold them all ( as they seeme confused ) in a cleere night . And though many of our Divines doe commonly interpret this speech to be a Hyperbole ; yet being well considered , we shall finde that Abrahams posteritie , in some few generations , were farre more than there are visible Starres in the Firmament ; and of such onely do's God speake , because hee bids Abraham looke up to the Heavens . Now all these , even unto six differences of Magnitude , are reckoned to bee but 1022. True indeed , at the first viewing of the Heavens , it may seeme an incredible thing , that they should be of no greater a number ; but the reason of this is , because they appeare scattered and confused : so that the eye cannot place them in any such order , as to reckon them up , or take any distinct surveigh of of them . Now 't is a knowne truth , Quod fortius operatur pluralit as partium , ubi ordo abest ; nam inducit similitudinem infiniti , & impedit comprehensionem : That a pluralitie of Parts without order , ha's a more strong operation , because it ha's a kinde of seeming infinitie , and so hinders comprehension . And then besides , there are more appearances of Starres many times , than there are bodies of them ; For the eye , by reason of it's weakenesse and disabilitie , to discerne any thing at so great a distance ; as also , because of those beames which proceed from such remote bodies in a twinkling and wavering manner , and so mixe and confound themselves at their entrance into that Organ : it must needs receive more representations than there are true bodies . But now , if a man doe but leisurely and distinctly compare the Stars of the heaven with those of this number , that are noted in a Coelestiall Globe , hee shall scarse find any in the Skie which are not marked with the Globe ; nay , he may observe many in the Globe , which hee can scarse at all discerne in the heavens . Now this number of the Starres is commonly distributed into 48 Constellations ; in each of which , though wee should suppose tenne thousand Starres , ( which can scarse be conceived ) yet would not all this number equall that of the children of Israel . Nay , 't is the assertion of Clavins , that Abrahams posteritie in some few generations , were farre more then there could be Stars in the Firmament , though they stucke so close that they touched one another : And he proves it thus : A great circle in the Firmament , do's containe the diameter of a Starre of the first Magnitude 14960 times . In the diameter of the Firmament , there are contained 4760 diameters of such a Star : now if wee multiply this circumference by a diameter , the Quotient will be 71209600 , which is the full number of Starres , that the eighth Sphaere ( according to Ptolomies grounds , ) would containe , if they stood so close , that they touched one another . The children of Israel were reckoned at their going out of Aegypt , 603550 , of such as were one and twenty yeares old , and upwards , and were able to go to war ; besides children , & women , and youths , and old men , and the Levites ; which in probabilitie , did alwaies treble the other number . Now if they were so many at one time , we may well conceive , that in all those severall generations , both before and since , the number was much augmented ; and long before this time , did far exceed this supposed multitude of the Stars . From all which , wee may inferre , that the Scripture expressions in this kind , are to be understood acording to appearance and common opinion . Another place usually cited for the same purpose , to shew that the Holy Ghost do's not speake exactly concerning naturall secrets ; as that in the Kings and Chronicles , which relates unto us the measure of Solomons brazen Sea , whose diameter was ten cubites , and it's circumference thirty ; whereas to speake Geometrically , the more exact proportion betwixt the diameter and the circumference , is not as ten to thirty , but rather as seven to twenty two . But against this 't is * objected by our adversaries , 1 This Sea was not perfectly round , but rather inclining to a semicircular Forme , as * Iosephus affirmes . I reply : If it were so , yet this is so much from helping the matter , that it makes it much worse ; for then the disproportion will be far greater . But secondly , Scripture , which is to be beleeved before Iosephus , do's tell us in expresse tearms , that it was round all about , 1. Kings , 7. 23. 2 The proportion of the diameter to the circumference , is not exactly the same : as seven to two and twenty , but rather lesse . I answer , though it be , yet 't is neerer unto that , then any other number . 3 The scripture do's but according to it 's usuall custome , suppresse the lesse number , and mention only that which is bigger and more full . So in some * places , Abrahams posteritie is said to remaine in the land of Aegypt for foure hundred yeares ; when as notwithstanding † other scriptures tell us , that they tarried there thirty yeares longer . Thus likewise in one * place , the number of Iacobs house , who came into Egypt , is reckoned to be seventy ; whereas , elsewhere , they are said to be seventy five . I answer : All this is so far from destroying the force of the present Argument , that it do's rather confirme it , and more cleerely evidence unto us , that the Scripture do's not only , not speak exactly in these subtle and more secret points of Philosophy , but also , in the ordinarie obvious numbring of things , do's conforme unto common custome , and often use the round number for the whole . 4 'T is yet objected by † another adversarie , That wee have no reason to expect , the Holy Ghost should reveale unto us this secret in Nature ; because neither Archimedes , nor any other , had then found it out . I reply , and why then should we thinke that the Scripture must needs informe us of the Earths Motion ; when as neither Pithagoras , nor Copernicus , nor any else , had then discovered it ? 5 In taking the compasse of this vessell , they measured somewhat below the brim , where it was narrower than at the top , and so the circumference there , might bee exactly but thirty cubites ; whereof it 's diameter was ten . I answer : 't is evident this is a meere shift , there being not the least ground for it in the Text. And then besides , why might not we affirme , That the diameter was measured from that place , as wel as the circumference ? since 't is very probable , that the Holy Ghost did speak ad idem ; and not tell us the bredth of one place , and the compasse of another . So that all our adversaries evasions cannot well avoid the force of the Argument that is taken from this Scripture . Again , common people usually conceive the Earth to be such a plaine , as in it's utmost parts is terminated by the Heavens , so that if a man were in the farthermost coasts of it , hee might touch the skie . And hence also , they think that the reason why some countries are hotter than others , is , because they lie neerer unto the Sun. Nay , Strabo tells us of some Philosophers too , who in this point have grossely erred ; affirming , that there was a place towards the utmost coasts of Lusitania , where a man might heare the noise that the Sunne made , as he quencht his Beames in his descent to the Ocean ; which , though it be an absurd mistake , yet we may note , that the Holy Ghost in the expression of these things , is pleased to conforme himselfe unto such kinde of vulgar and false conceits ; And therefore , often speaks of the * ends of Heaven , and the † ends of the world . In this sence , they that come from any far countrey , are said to come from the end of Heaven , Isaiah , 13. 5. And in another place , From the side of the Heavens , Deut. 4. 32. All which phrases , doe plainly allude unto the errour of vulgar capacities ( saith Sanctius ) which hereby is better instructed , † then it would be by more proper expressions . Thus likewise , because ignorant people cannot well apprehend how so great a weight as the Sea and Land , should hang alone in the open aire , without being founded upon some Basis to uphold it : therefore in this respect also , do's Scripture apply it selfe unto their conceits , where it often mentions the foundations of the Earth . Which phrase , in the letter of it , do's manifestly allude unto mens imaginations in this kinde . Thus also the common people usually conceive the Earth to be upon the Water ; because , when they have travelled any way as farre as they can , they are at length stopped by the sea . Therefore doth Scripture in reference to this , affirme , That God stretched the Earth upon the Waters , founded the Earth upon the Seas , and established it upon the Flouds ; Of which places saith Calvin , Non disputat Philosophicè David , de terrae situ ; sed populariter loquens , ad rudium captum se accommodat : 'T was not Davids intent to speak philosophically concerning the Earths scituation ; but rather , by using a popular phrase , to accommodate his speech unto the capacities of the ruder people . In this sence likewise , are wee to understand all those places of Scripture , wherein the coasts of Heaven are denominated from the relations of Before , Behinde , the right hand , or the left . Which do not imply ( saith * Scaliger ) any absolute difference in such places , but are spoken meerely in reference to mens estimations , and the common opinion of those people , for whom the Scriptures were first penned . Thus because it was the opinion of the Iewish Rabbies , that man was created with his face to the East ; therefore the Hebrew word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , signifies Ante , or the East ; 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ▪ Post , or the West ; 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Dextra , or the South ; 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Sinistra , or the North. You may see all of them put together in that place of Iob , Behold I goe forward , and he is not there , and backward , but I cannot perceive him ; on the left hand , where he doth work , but I cannot behold him . He hideth himselfe on the right hand , that I cannot see him . Which expressions , are by some interpreters referred unto the foure coasts of Heaven , according to the common use of those originall words . From hence it is , that many of the Antients have concluded hell to be in the North , which is signified by the left hand : unto which side our Saviour tels us , that the Goats shall be divided . Which opinion , likewise seems to be favoured by that place in Iob , where 't is said , Hell is naked before God , and destruction hath no covering . And presently 't is added , Hee stretched out the North over the empty place . Vpon these grounds , S. Ierome interprets that speech of the Preacher , Eccles. 11. 3. If the tree fals towards the South , or towards the North , in the place where the tree falleth , there shal it be . Concerning those who shal go either to heaven or hell . And in this sence also do's some expound that of Zachary , 14. 4 Where 't is said , that the mount of Olives shall cleere in the midst ; halfe of it shall remove towards the North , and halfe of it towards the South . By which is intimated , that amongst those Gentiles , who shall take upon them the profession of Christ , there are two sorts ; Some that go to the North , that is to Hell ; and others to the South , that is to Heaven . And therefore it is ( say they ) that God so * often threatens evill out of the North ; and upon this ground it is ( saith † Besoldus ) that there is no Religion that worships that way . We read of the Mahumetans , that they adore towards the South ; the Iewes towards the West ; Christians towards the East , but none to the North. But of this onely by the way . However , certaine it is that the Holy Ghost do's frequently in Scripture set forth the severall coasts of Heaven by those relative tearmes of right hand and left hand , &c. which expressions doe not denote any reall intrinsicall difference betwixt those places , but are rather fitted for the apprehension of those men , from whose fancy it is that they have such denominations . * And though Aristotle concludes these severall positions to be naturall unto the Heavens , yet his authoritie in this particular is not available , because he delivers it upon a wrong ground , supposing the Orbs to be living creatures , and assisted with intelligences . Wee may observe , that the meaning of these coasts by the relations of right hand and left hand , &c. is so far from having any ground in the nature of those severall places , that these relations are not onely variously applyed unto them by divers religions ( as was said before , ) but also by divers Arts and Professions . Thus because Astronomers make their observations towards the South parts of the Horizon , where there bee most Stars that rise and set : therefore do they account the West to be at their right hand , and the East their left . The Cosmographers in taking the latitude of places , and reckoning their severall climates must looke towards the North Pole ; and therefore , in their phrase , by the right hand is meant the East ; and by the left hand , the West : and thus ( saith Plutarch , * are we to understand these expressions in Pythagoras , Plato , Aristotle . The Poets count the South to bee towards the left , and the North the right hand . Thus † Lucan speaking of the Arabians comming unto Thessalie , sayes : Ignotum vobis Arabes venistis in orbem : Vmbras mirati nemorum , nonire sinistras . The Augures taking their observations at the East , count the South to be at their right hand , and the North their left : So that these denominations have not any reall ground in the nature of the things , but are imposed upon them by the Scripture phrase , in reference to the account and opinion of the Iewes . Thus also , because heretofore it was generally received , that the Heart was the principall seat of the Faculties ; therefore doth the Spirit apply himself unto this common Tenent ; and in many places , attributes Wisedome and Vnderstanding to the Heart . Whereas , to speake properly , the reason and discurfive Faculties have their principall residence in the Head ( saith Galen and Hypocrates , together with the generalitie of our later Physitians , ) because they are hindred in their operations by the distempers of that part , and recovered by medicines applyed unto it . So likewise are wee to understand those other places : Isaiah , 59. 5. where some translations reade it , Ova Aspidum ruperunt , they have broken the Vipers eggs ; alluding to that common but fabulous story of the Viper , who breakes his passage through the bowells of the female . So Psal. 58. 4 , 5. where the Prophet speaks of the deafe Adder , that stops her eares against the voice of the charmer . Both which relations ( if we may beleeve many naturalists ) are as false as they are common : and yet because they were entertained with the generall opinion of those days , therfore doth the holy Ghost vouchsafe to allude unto them in Holy Writ . 'T is a plaine mistake of Fromondus , when in answer to these places , he is feigne to say , that they are used proverbially only , and doe not positively conclude any thing . For when David writes these words , that they are like the deafe Adder which stoppeth her eares , &c. This affirmation is manifestly implyed , That the deafe Adder do's stop her eares against the voice of the charmer : which because it is not true in the letter of it , ( as was said before ) therefore 't is very probable , that it should bee interpreted in the same sence wherein here it is cited . In reference to this also , wee are to conceive of those other expressions ; Cold commeth out of the North , Iob , 37. 9. and againe , faire weather comes out of the North , ver . 22. So ver . 17. thy garments are quieted when he warmeth the Earth by the South winde . And Prov. 25. 23. The North wind driveth away raine . Which phrases do not containe in them any absolute generall truth , but can so farre only bee verified , as they are referred to generall climates : and though unto us who live on this side of the Line , the North wind be coldest and driest ; and on the contrary , the South wind moist and warme , by reason that in one of these places there is a stronger heate of the Sun to exhale moist vapors , than in the other : yet it is clean otherwise with the inhabitants beyond the other Tropicke ; for there the North wind is the hotest , and moist , and the South the coldest and dry : So that with them , these Scriptures cannot properly bee affirmed , that cold or that faire weather commeth out of the North ; but rather on the contrary . All which notwithstanding , do's not in the least manner derogate from the truth of these speeches , or the omnisciencie of the speaker : but doe rather shew the Wisdome and Goodnesse of the blessed Spirit , in vouchsafing thus to conforme his Language unto the capacitie of those people unto whom these speeches were first directed . In the same sence are we to understand all those places where the Lights of Heaven are said to be darkened , and the Constellations not to give their light , Isai. 13. 10. Not as if they were absolutely in themselves deprived of their light , and did not shine at all ; but because of their appearance to us ; and therefore , in another place answerable to these , God sayes , he will cover the Heavens , and so make the Starres thereof darke , Ezech. 37. 2. Which argues , that they themselves were not deprived of this light ( as those other speeches seem to imply ) but wee . In reference to this likewise are wee to conceive of those other expressions , that the Moone shall blush , and the Sunne bee ashamed , Isai. 24. 23. That they shall be turned into bloud , Math. 24. 29. Not that these things shall bee so in themselves ( saith S. Ierome , ) but because they shall appeare so unto us . Thus also Marke , 13. 25. The Starres shall from Heaven ; that is , they shall be so wholly covered from our sight , as if they were quite fallen from their wonted places . Or if this bee understood of their reall Fall , as it may seeme probable by that place in the Revelations , 6. 13. And the Stars of Heaven fell unto the Earth , even as a Figge-tree casteth her untimely Figges , when she is shaken by a mighty Winde : then is it to be interpreted not of them that are truly Stars , but them that appeare so : alluding unto the opinion of the unskilfull vulgar ( saith * Sanctius ) that thinke the Meteors to be Starres . And † Mersennus speaking of the same Scripture , sayes : Hoc de veris Stell is minimè volunt Interpretes intelligi . sed de Cometis & alijs ignitis Meteoris : Interpreters do by no means understand this of true Starres , but of the Comets and other fiery Meteors . Though the falling of these be a naturall event , yet may it be accounted a strange prodigie , as well as an Earthquake , and the darkening of the Sunne and Moone , which are mentioned in the verse before . In reference to this , doth the Scripture speake of some common naturall effects , as if their true causes were altogether inscrutable , and not to bee found out , because they were generally so esteemed by the vulgar . Thus of the wind it is * said , That none know whence it commeth nor whither it goeth . In another † place God is said to bring it out of his treasures ; and a elsewhere it is called the b breath of God ; And so likewise of the thunder : Concerning which , c Iob proposes this question , The thunder of his power who can understand ? and therefore too d David do's so often stile it , the voice of God. All which places seeme to imply , that the cause of these things was not to be discovered , which yet later Philosophers pretend to know : so that according to their construction , these phrases are to be understood in relation unto their ignorance unto whom these speeches were immediately directed . For this reason is it : Why , though there be in nature many other causes of Springs and Rivers than the Sea , yet Solomon ( who was a great Philosopher , and perhaps not ignorant of them ) do's mention onely this , because most obvious , and easily apprehended by the vulgar . Vnto all these Scriptures , I might adde that in Amos , 5. 8. which speakes of the Constellation commonly called the seven Starres ; whereas , later discoveries have found that there are but sixe of them discernable to the bare eye , as appeares by Gallilaeus his glasse : the seventh of them being but a deceipt of the eye arising from their too great neernes ; and if a man try in a cleere night to number them distinctly , he shall find that there will sometimes appeare but sixe , and some times more . True indeed , the originall word of this Scripture 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , do's not necessarily imply any such number in it's signification , but yet our English translation renders it the seven Starres ; and if it had been expresly so in the Originall too , it might have spoken true enough , because they are usually esteemed of that number . And when it had been said , He made the seven Stars and Orion , we might have easily understood the words thus : Hee made those Constellations that are commonly knowne unto us under such names . From all these Scriptures 't is cleerly manifest , that it is a frequent custome for the Holy Ghost to speake of naturall things , rather according to their appearance and common opinion , than the truth it selfe . Now it is very plaine , and our enemies themselves do grant it , that if the World had bin framed according to the Systeme of Copernicus , futurum esset ut vulgus , de Solis motu & Terrae statu proinde ut nunc loqueretur . The vulgar phrase would have been the same as now it is , when it speakes of the Sunnes motion , and the Earth's standing still . Wherefore 't is not improbable , that such kind of Scripture expressions are to be understood only in relation to outward appearances , and vulgar opinion . PROP. IIII. That divers learned men have fallen into great absurdities , whilest they have looked for the grounds of Philosophy from the words of Scripture . IT ha's bin an antient and common opinion amongst the Iewes , that the Law of Moses did containe in it , not only those things which concerne our Religion and Obedience , but every secret also that may possibly be known in any Art or Science ; so that there is not a demonstration in Geometrie , or rule in Arithmeticke ; not a mysterie in any trade , but it may be found out in the Pentateuch . Hence it was ( say they ) that Solomon had all his wisedome and policie : Hence it was that hee did fetch his knowledge concerning the nature of Vegetables , from the Cedar of Lebanon , to the Hysop that growes upon the wall . Nay from hence , they thought a man might learne the art of Miracles , to remoove a Mountaine , or recover the dead . So strangely have the learneder sort of that Nation been befooled , since their owne curse hath lighted upon them . Not much unlike this foolish superstition of theirs , is that custome of many Artists amongst us ; who upon the invention of any new secret , will presently find out some obscure text or other to father it upon ; as if the Holy Ghost must needs take notice of every particular , which their partiall fancies did over-vallue . Nor are they altogether guiltlesse of this fault , who looke for any secrets of nature from the words of Scripture ; or will examine all it's expressions by the exact rules of Philosophy . Vnto what strange absurdities this false imagination of the learneder Iewes hath exposed them , may be manifest by a great multitude of Examples . I will mention only some few of them . Hence it is , that they proove the shin-bone of Og the Giant to bee above three leagues long ; Or ( which is a more modest relation ) that Moses being fourteen cubites in stature , having a Speare tenne Ells in length , and leaping up ten cubits , could touch this Giant but on the Ancle . All which , they can confirme unto you by a Cabalisticall interpretation of this story , as it is set downe in Scripture . Hence it is , that they tell us of all those strange Beasts which shall be seen at the comming of the Messias ; as first , the Ox , which Iob calls Behemoth , that every day devoures the grasse on a thousand mountaines , as you may see it in the * Psalme , where David mentions the cattell , or 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 upon a thousand hils . If you aske how this Beast do's to finde pasture enough , they answer , that hee remaines constantly in one place , where there is as much grasse grows up in the night , as was eaten in the day . They tell us also of a Bird , which was of that quantitie , that having upon a time cast an egge out of her neast , there were beaten down by the fall of it , three hundred of the tallest Cedars , and no lesse than threescore villages drowned . As also of a Frog , as big as a Town capable of sixty houses ; which Frog , notwithstanding his greatnesse , was devoured by a Serpent , and that Serpent by a Crow ; which Crow as she was flying up to a Tree eclipsed the Sun , and darkned the World ; by which you may guesse what a pretty twig that Tree was . If you would know the proper name of this Bird , you may finde it in Psal. 50. 11. where it is called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , or in our Translation , the Foule of the mountains . It seems it was somewhat of kinne to that other Bird they tell us of , whose legges were so long , that they reached unto the bottome of that Sea where there had bin an axe head falling for 7 yeres together , before it could come to the bottome . Many other relations there are , which containe such horrible absurdities , that a man cannot well conceive how they should proceed from reasonable creatures . And all this arising from that wrong Principle of theirs ; That Scripture did exactly containe in it all kind of Truths ; and that every meaning was true , which by the Letter of it , or by Cabalisticall interpretations might be found out . Now as it hath been with them , so likewise hath it happened in proportion unto others : who by a superstitious adhering unto the bare words of scripture , have exposed themselves unto many strange errours . Thus * S. Basil holds , That next to the Sun , the Moon is bigger than any of the Stars , because Moses do's call them onely two great Lights . Thus others maintaine , That there are waters properly so called above the starry Firmament , because of those vulgar expressions in Scripture , which in their literall sence doe mention them . Of this opinion were many of the Antients , Philo , Iosephus ; and since them the Fathers , a Iustin Martyr , b Theodoret , c Austin , d Ambrose , * Basil , and almost all the rest . Since them , sundry other learned men , as Beda , Strabus , Damascen , Tho. Aquinas , &c. If you aske for what purpose they were placed here , Iustin Martyr tells us , for these two ends : First , to coole the heate that might otherwise arise from the motion of the solid Orbs ; and hence it is ( say they ) that Saturne is colder than any of the other Planets , because though he moove faster , yet hee is neerer to these waters : secondly , to presse and keep downe the Heavens , lest the frequencie and violence of winds might breake and scatter them asunder ; which opinion , together with both it's reasons , are now accounted absurd and rediculous . † S. Austin concludes the visible Stars to be innumerable , because Scripture phrases seeme to imply as much . That the Heavens are not round , was the opinion of a Iustin Martyr , b Ambrose , c Chrysostome , d Theodoret , * Theophilact , doubted of by † S. Austin and divers others . Nay , S. Chrysostome was so confident of it , that he proposes the question in a triumphant manner : 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Where are those men that can proove the Heavens to have a sphaericall Forme . The reason of which was this , Because 't is said in one Scripture , that God stretched forth the Heavens as a curtain , Psal. 104. 2. and spreadeth them as a tent to dwell in , Isai. 40. 22. And so in that place of the Epistle to the Hebrewes , 8. 2. they are called a Tent or Tabernacle : which because it is not sphaericall , therefore they conclude also , that the Heavens are not of that Forme ; whereas now , the contrary is as evident as demonstration can make a thing . And therefore , * S. Ierome in his time , speaking of the same errour , gives it this plaine censure : Est in Ecclesia stulti loquium , si quis Coelum putet fornicis modo curvatum , Esaiae quem non intelligit sermone deceptus . 'T is foolish speaking in the Church , if any through misapprehension of those words in Isaiah , shall affirm the Heavens not to be round . That the Seas not overflowing the land is a miracle , was the opinion of a Basil , b Chrisostome , c Theodoret , d Ambrose , a Nazianzen , and since them , b Aquinas , c Luther , d Calvin , * Marlorate , with sundry others . Which they prooved from these Scripture expressions , that in Iob 38. 8. 11. Who hath shut up the Sea with doores , when it brake forth , as if it had issued out of the womb ; when I did break up for it my decreed place ; and set bars and doores , and said , hitherto shalt thou come , and no further , and here shall the pride of thy waves be staid . So likewise , Prov. 8. 29. God gave to the Sea his decree , that the Waters should not passe his commandement . And Ierem. 5. 22. I have placed the sand for a bound of the Sea by a perpetuall decree that they cannot passe it : and though the waves thereof crosse themselves , yet can they not prevaile ; though they roare , yet can they not passe over , that they turne not againe to cover the Earth . In all which places ( say they ) 't is implied , that the water of it selfe , were it not withheld from it's own naturall inclination by a more speciall power of God , would overflow the Land. Others inferre the same conclusion with that in Ecclesiastes , where the rivers are said to come from the Sea ; which they could not doe , unlesse that were higher . I answer : They should as well consider the later part of that Scripture , which sayes , that the Rivers returne to that place from whence they came , and then the force of this consequence will vanish . To this purpose , some urge that speech of our Saviour , where hee bids Simon to launch forth into the deep ; the Latine word is , in altum ; from whence , they gather that the Sea is higher than the Land. But this savours so much of Monkish ignorance , that it deserves rather to be laughed at , than to bee answered . But now if we consider the true properties of this Element , according to the rules of Philosophy : we shall finde , that it 's not overflowing the Land is so farre from being a miracle , that it is a necessarie consequence of it's nature ; and 't would rather be a miracle , if it should be otherwise , as it was in the generall deluge . The reason is , because the water of it self must necessarily descend to the lowest place ; which it cannot do , unlesse it be collected in a sphaericall Forme , as you may plainly discerne in this Figure . Where the Sea at D. may seeme to be higher than a mountaine at B , or C. because the rising of it in the midst do's so intercept our sight from either of those places , that wee cannot looke in a streight line , from the one to the other . So that it may seem to be no lesse than a miracle , by which the sea ( being a heavy body ) was withheld from flowing down to those lower places of B , or C. But now , if you consider that the ascending of a body is it's motion from the centre , and descent is it's approaching unto it : you shall find ▪ that for the Sea to moove from D. to B ▪ or C. is a motion of Ascent , which is contrary to it's nature , because the mountaine at B , or C. are farther off from the centre , than the Sea at D. the Lines A , B. and A , C. being longer than the other A , D. So that for the Sun to keep alwaies in it's channell , is but agreeable to it's nature , as being a heavy body . But the meaning of those Scriptures , is , to set forth the power and wisedome of God : who hath appointed these channels for it , and beset it with such strong banks to withstand the fury of it's waves . Or if these men doe so much rely on naturall points , upon the bare words of Scripture , they might easily bee confuted from those other places , where God is said to have founded the Earth upon the Seas , and establisht it upon the Flouds . From the literall interpretation of which , many of the Antients have fallen into another errour : affirming the Water to be in the lower place ; and as a basis , whereon the weight of the Earth was borne up . Of this opinion were a Clemens Alexandrinus , b Athanasius , c Hillarie , d Eusebius , and others . So that it seemes , if a man should resolutely adhere to the bare words of the scripture , he might find contradiction in it : of which , the naturall meaning is altogether incapable . * S. Ierome tells us of some who would proove Starres to have understanding , from that place in Isaiah , 45. 13. My hands have stretched out the Heavens , and all their hoast have I commanded . Now ( say they ) none but intelligent creatures are capable of Precepts ; and therefore , the Starres must needs have rationall Soules . Of this opinion was † Philo the Iew : nay , many of the Rabbies conclude , that they do everie houre sing praises unto God with an audible reall voice . Because of that in Iob 38. 7. which speakes of the Morning Starres singing together . And Psal. 19. 3 , 4. where 't is said of the Heavens , that there is no speech nor language where their voice is not heard , and their words are gone to the ends of the World. And whereas wee translate that place in the tenth of Iosuah , concerning the standing still of the Heavens : the originall Word , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 do's properly signifie Silence , and according to their opinion , Iosuah did onely bid them hold their peace . From such grounds , 't is likely did * Origen fetch his opinion , that the Stars should be saved . I might set downe many other the like instances , were it not for being alreadie weary of raking into the errours of antiquitie , or uncovering the nakednesse of our Forefathers . That excuse of † Acosta may justly serve to mitigate the mistakes of these antient Divines : Facilè condonandum est patribus , si cum cognoscendo colendóque Creatoritoti vacarent , de creaturâ minus aptè aliqua ex parte opinati sunt . Those good men were so wholly busied about the knowledge and worship of the Creator , that they had not leisure enough for an exact search into the Essence of the Creatures . However , these examples that have been alreadie cited , may sufficiently manifest , how frequently others have been deceived , in concluding the points of Philosophy from the expressions of Scripture . And therefore , 't is not certaine , but that in the present case also , it may bee insufficient for such a manner of arguing . PROP. V. That the Scripture in it's proper construction , do's not any where affirme the Immobilitie of the Earth . THe same answer which was insisted on before , concerning the conformitie of Scripture expressions to mens capacitie and common opinion , may well enough satisfie all those other Arguments , which seeme thence to affirme the Earth's setlednesse and Immobilitie ; since this is as well agreeable to outward appearance and vulgar apprehension as the other . But now for more full satisfaction , I shall set downe the particular places that are urged for it ; which being throughly examined , wee may plainly discerne , that none of them in their proper meaning , will serve to infer any such conclusion . One of these sayings is that of the Preacher , Eccles. 1. 4. One generation commeth , and another passeth , but the Earth endureth for ever ; where the originall word is , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and the vulgar , stat ; from whence our * adversaries conclude that it is immooveable . I answer : the meaning of the word as it is here applyed , is permanet ; or as we translate it , endureth . For it is not the purpose of this place to deny all kinde of motion to the whole Earth : but that of generation and corruption , to which other things in it are liable . And though Pineda , and others , keep a great deale of impertinent stirre about this Scripture , yet they grant this to be the naturall meaning of it : which you may more cleerely discerne , if you consider the chiefe scope of this Booke ; wherein the Preachers intent is , to shew the extraordinarie vanitie of all earthly contentments , ver . 2. the utter unprofitablenesse of all a mans labours , ver . 3. and this hee illustrates by the shortnesse and uncertaintie of his life ; in which respect , he is below many of his fellow creatures , as may bee manifested from these foure comparisons . 1 From the Earth , which though it seem to be but as the sediment of the World , as the rubbish of the Creation ; yet is this better than man in respect of his lastingnesse , for one generation passeth away , and another commeth ; but the Earth , that abideth for ever , ver . 4. 2 From the Sunne ; who , though he seeme frequently to goe downe , yet hee constantly seemes to rise againe ; and shines with the same glory , ver . 5. But man dyeth and wasteth away ; yea , man giveth up the ghost , and where is he ? he lyeth down , and riseth not till the Heavens be no more . 3 From the wind , the common emblem of uncertaintie ; yet it is more constant than man , for that knowes it's circuits , and whirleth about continually , v. 6. whereas our life passeth away as doth the wind , but returneth not againe . 4 From the Sea ; though it bee as uncertaine as the Moone , by whom 't is governed , yet is it more durable than man and his happinesse . For though the Rivers runne into it , and from it , yet is it still of the same quantitie that it was at the beginning , v. 7. But man grows worser as he growes older , and still neerer to a decay . So that in this respect , hee is much inferior to many other of his fellow creatures . From whence it is manifest ; that this constancie or standing of the Earth , is not opposed to it 's locall motion , but to the changing or passing away of divers men in their severall generations . And therefore , thence to conclude the earth's Immobilitie , were as weake and ridiculous , as if one should argue thus : One Miller goes , and another comes , but the Mill remaines still ; ergo , the Mill hath no motion . Or thus ; one Pilate goes , and another comes , but the Ship remaines still ; ergo , the Ship doth not stirre . * R. Moses tells us , how that many of the Iewes did from this place conclude , that Solomon thought the Earth to be Eternall , because he saith it abideth 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 forever ; & questionles , if we examine it impartially , we shal find that the phrase seemes more to favour this absurditie , than that which our adversaries would collect from hence ; that it is without motion . But M. Fuller urging this text against Copernicus ; tells us , if any should interprete these phrases , concerning the Earth's standing still , ve . 4. and the Suns motion , ver . 5. in reference onely to appearance and common opinion ; he must necessarily also understand those two other verses , which mention the motion of the wind and rivers in the same sence . As if he should say ; because some things appeare otherwise than they are , therefore every thing is otherwise than it appeares ; or , because Scripture speakes of some naturall things , as they are esteemed according to mans false conceit ; therefore 't is necessarie , that every naturall thing mentioned in Scripture , must be interpreted in the like sence : or , because in one place , wee read of the ends of a Staffe , 1 Kings , 8. 8. and in many other places of the ends of the Earth , and the ends of Heaven : Therefore the earth & heavens have as properly ends as a Staffe . 'T is the very same consequence of that in the objection . Because in this place of Ecclesiastes , wee read of the rest of the Earth , and the motion of the Sun ; therefore , these phrases must needs bee understood in the same proper construction as those afterwards , where motion was attributed to the Wind and Rivers . Which inference you see is so weake , that the Objector need not triumph so much in it's strength as he doth . Another proofe like unto this , is taken from S. Peter , epist. 2. cap. 3. ver . 5. where hee speakes of the Earth standing out of the water , and in the water , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; and therefore , the Earth is immooveable . I answer : 't is evident that the word here is equivolent with fuit : and the scope of the Apostle is , to shew that God made all the Earth : both that which was above the water , and that which was under it . So that from this expression , to collect the rest and immobilitie of the Earth , would be such an argument as this other . Such a man made that part of a Mill-wheele , or a Ship , which stands below the water , and that part which stands above the water : ther●fore those things are immoovable . To such vain and idle consequences do's the heate of opposition drive our adversaries . A third Argument stronger than either of the former , they conceive may may be collected from those * scriptures : where 't is said , The World is established , that it cannot be mooved . To which , I answer : These places speake of the World in generall , and not particularly of our Earth ; and therefore may as well proove the immobility of the Heavens , they being the greatest pert of the World ; in comparison to which , our Earth is but as an insensible point . If you reply , that the word in these places is to be understood by a Synechdoche , as being meant only of this habitable World , the Earth . I answer : First , this is onely said , not prooved : secondly , David but a little before seems to make a difference between the World and the Earth , Psal. 90. 2. where he sayes , Before thou hadst formed the Earth and the World. But thir●● , in another place , there is the same original word applyed expresly to the Heavens ; and which is yet more , the same place do's likewise mention this supposed setlednesse of the Earth , Prov. 3. 19. The Lord by wisdome hath founded the Earth : and by understanding hath he established the Heavens . So that these places can no more proove an immobilitie in the Earth than in the Heavens . If you yet reply , That by the Heavens there is meant the seat of the Blessed , which do's not moove with the rest . I answer : though by such an evasion a man might possibly avoid the force of this place : yet , first , 't is but a groundlesse shift , because then , that verse will not containe a full enumeration of the parts in the World , as may seeme more agreeable to the intention of it : but onely shew , that God created this Earth where we live , and the Heaven of Heavens . So that the Heaven of the Starres and Planets , shall be shifted out from the number of the other creature : secondly , there is another place which cannot bee so avoided , Psal. 89. 37. where the Psalmist uses this expression , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 It shall bee established as the Moone . So Psal. 8. 3. The Moone and the Starres , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 which thou hast established . Thus likewise , Prov. 8. 27. when he established the Heavens : and in the next verse , our English translation reads it , when he established the clouds . And yet our adversaries will affirme the Moone , and Starres , and Clouds , to bee subject unto naturall motions : why then should the very same expressions be counted as sufficient Arguments to take it away from the Earth . If it be replyed , That by establishing the Heavens , is meant only the holding of them up , that they doe not fall downe to us ( as Lorinus explaines that in the eighth Psalme : and quotes Euthymius for the same interpretation , ) fundandi verbum significat decidere non posse , aut dimoteri a loco vbi collecti sunt : I answer , why may not we as well interpret the words thus of the Earth : so that by establishing of it , is meant only the keeping of it up in the vast places of the open aire , without falling to any other place . From hence it is plaine , That these Scriptures are to be understood of such an immobilitie in the Earth , as may likewise agree with the Heavens : the same originall word being so promiscuously applyed to both . I but ( you wil say ) there are some other places which do more peculiarly apply this setlednesse and establishment to the Earth . So Psal. 119. 9. Thy faithfulnes is unto all generations : thou hast established the Earth , and it abideth . Thus likewise , Psal. 104. 5. Who laid the foundations of the Earth , that it should not bee removed for ever . The later of which , being well weighed in it's original ( saith M. Fuller ) do's in three emphaticall words strongly conclude the Earth's immobility . As first , when he sayes , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 fundavit , he hath founded it : wherein it is implyed , that it do's not change his place . To which may bee added all those Texts , which so frequently speake of the foundations of the Earth ; as also that expression of the Psalmist , where hee mentions the Pillars of the Earth , Psal. 75. 3. The second word is 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 translated Basis ; and by the Septuagint , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; that is , he hath founded it upon it's owne firmenesse : and therefore it is altogether without motion . The third expression is 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 from the root , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 which signifies , declinare ; implying , that it could not wagge with the least kind of declination . To these I answer severally : First , for the word , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 fundavit , It cannot be understood properly , as if the naturall Frame of the Earth , like other artificiall buildings , did need any bottome to uphold it ; for he hangeth the Earth upon nothing , Iob. 26. 7. But it is a Metaphor , and signifies Gods placing or scituating this Globe of Land and Water . As David tells us of the Pillars of the Earth : so Iob mentions Pillars of the Heavens , Iob , 26. 11. And yet that will not proove them to be immoveable . True indeed , wee reade often concerning the foundations of the Earth : but so we do likewise of the ends , sides , and corners of the Earth ; and yet these Scriptures will not proove it to bee of a long or square forme . Besides , we reade also of the Foundations of Heaven , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 2. Sam. 22. 8. And yet wee must not hence inferre , that they are without all motion ; As also of the planting of the Heavens , Isai. 51. 6. which may as well proove them to be immoovable , as that which followes in the same verse concerning the foundations of the Earth . Which phrase ( as I have observed right ) in severall places of Scripture , is to be understood according to these three interpretations . 1 It is taken somtimes for the lower parts of the Earth , as appeares by that place , 2. Sam. 22. 16. The channels of the Sea appeared , the foundations of the World were discovered . 2 Somtimes for the beginning and first creation of it , Isa. 40. 2. Hath it not been told you from the beginning , have ye not understood from the foundations of the Earth . And in many other places , Before the Foundations of the World was laid ; that is , before the first creation . Sometimes it signifies the Magistrates and chiefe Governours of the Earth . So many interpret that place in Micah , 6. 2. where 't is said , Heare O yee mountaines the Lords controversie , and yee strong foundations of the Earth . So Psal. 82. 5. The foundations of the Earth are out of course ; and in Sam. 2. 8. they are called pillars . For the Pillars of the Earth are the Lords , and he hath set the World upon them . Hence it is , that the Hebrewes derive their word for Master , or Lord : from a root which signifies a Basis or bottome , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . And the Greeke word for King , do's in it's Primitives import as much as the Foundation of the people , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . But now , none of all the severall interpretation of this phrase , will in the least manner conduce to the confirmation of the present Argument . As for the second word , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Basis ejus : I answer , the proper signification of it , is locus dispositus , sedes , or statio , an appointed seat or station ; and according to this sence , is it most frequently used in Scripture . And therefore , the Heavens are sometimes called , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the seat of Gods habitation . And for this reason likewise , doe Aquila and Symmachus translate it by the word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , a seat or appointed scituation , which may as well be attributed to the Heavens . The third expression is 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 that it should not be moved from the Primitive 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 which do's not signifie barely to move ; but declinare , or vacillare , to decline or slip aside from it's usual course . Thus is it used by David , Ps. 17. 5. where he prayes , Hold up my goings in thy paths , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 That my footsteps slide not ▪ He do's not meane that his feet should not move . So Psal. 121. 3. He will not suffer thy foot to bee mooved . Thus likewise , Psal. 16. 8. Because the Lord is at my right hand , I shall not be moved : which last place is translated in the new Testament by the Greeke word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which signifies fluctuare , or vacillare , to be shaken by such an uncertaine motion as the waves of the Sea. Now as Davids feet may have their usuall motion , and yet in this sence be said not to move , that is , not to decline or slip aside : so neither can the same phrase applyed to the Earth , prove it to be immovable . Nor doe I see any reason , why that of Didacus Astunica may not be truly affirmed , That wee may prove the naturall motion of the Earth , from that place in Iob , 9. 6. Qui commovet terram è loco suo , as well as it's rest and immobilitie from these . From all which , it is very evident , that each of these expressions , concerning the founding or establishing both of Heaven or Earth , were not intended to shew the unmovablenesse of either , but rather , to manifest the power and wisedome of Providence , who had so setled these parts of the World in their proper scituations , that no naturall cause could displace them , or make them decline from their appointed course . As for such who doe utterly dislike all new interpretation of Scripture , even in such matters as do meerely concern opinion , and are not fundamentall : I would only propose unto them a speech of S. Hierome , concerning some that were of the same mind in his time . Cur novas semper expetant voluptates , & vulgae eorum vicina Maria non sufficiant , cur in solo studio Scripturarum , veteri sapore contenti sunt . Thus have I in some measure cleered the chiefe Arguments from Scripture , against this opinion . For which notwithstanding , I have not thence cited any : because I conceive the Holy Writ , being chiefly intended to informe us of such things as concerne our faith and obedience : wee cannot thence take any proper proofe for the confirmation of Naturall Secrets . PROP. VI. That there is not any Argument from the words of Scripture , principles of Nature , or observations in Astronomy , which can sufficiently evidence the Earth to bee in the centre of the Vniverse . OVr adversaries doe much insult in the strength of those Arguments which they conceive ; do unanswerably conclude , the Earth to bee in the centre of the World. Whereas , if they were but impartially considered , they would be found altogether insufficient for any such conclusion , as shall be cleerly manifested in this following Chapter . The Arguments which they urge in the proofe of this , are of three sorts ; Either such as are taken , 1 From expressions of Scripture . 2 From principles of naturall Philosophy . 3 From common appearances in Astronomy . Those of the first kinde are chiefly two : The first is grounded on that common Scripture phrase , which speakes of the Sunne , as being above us . So Solomon often mentioning humane affaires , calls them , the works which are done under the Sunne . From whence it appeares that the Earth is below it ; and therefore , neerer to the centre of the Vniverse , than the Sunne . I answer : Though the Sun in comparison to the absolute frame of the World , be in the midst ; yet this do's not hinder , but that in respect to our Earth , he may be truly said to bee above it , because wee usually measure the height or lownesse of every thing , by it's being further off , or neerer unto this centre of our Earth . From which , since the Sunne is so remote , it may properly bee affirmed , that wee are under it ; though notwithstanding that bee in the centre of the World. A second Argument of the same kinde , is urged by Fromundus . 'T is requisite , that Hell ( which is in the centre of the Earth ) should be most remotely scituated from the seat of the Blessed . But now this Heaven , which is the seat of the Blessed , is concentricall to the starry Sphaere . And therefore it will follow , that our Earth must bee in the midst of this Sphaere ; and so consequently , in the centre of the World. I answer : This Argument is grounded upon these uncertainties ; 1 That Hell must needs bee scituated in the centre of our Earth . 2 That the heaven of the Blessed , must needs bee concentricall to that of the Starres . 3 That places must bee as farre distant in scituation as in use : Which because they are taken for granted , without any proofe , and are in themselves but weake and doubtfull : therefore the conclusion ( which alwaies followes the worser part ) cannot bee strong , and so will not need any other answer . The second sort of Arguments taken from naturall Philosophy , are principally these three : 1 First , from the vilenesse of our Earth , because it consists of a more for did and base matter than any other part of the World ; and therefore , must bee scituated in the centre , which is the worst place , and at the greatest distance from those purer incortuptible bodies , the Heavens . I answer : This Argument do's suppose such propositions for grounds , which are not yet prooved ; and therfore not to be granted . As , 1 That bodies must bee as farre distant in place , as in Nobilitie . 2 That the Earth is a more ignoble substance than any of the other Planets , consisting of a more base and vile matter . 3 That the centre is the worst place . All which , are ( if not evidently false ) yet very uncettaine . 2 From the nature of the centre ; which is the place of rest , and such as in all circular motions , is it's selfe immooveable . And theresore will be the fittest scituation for rhe Earth ; which by reason of it's heavinesse , is naturally unfit for motion . I answer : This Argument likewise is grounded upon these two foolish foundations ; As , 1 That the whole Frame of Nature do's moove round , excepting onely the Earth . 2 That the whole Earth , considered in it's whole , and in it's proper place , is heavy ; or more unfit for a naturall motion , than any of the other Planets . Which are so farre from being such generall grounds , from which contro . versies should be discussed , That they are the very thing in question betwixt us and our adversaries . 3 From the nature of all heavy bodies , which is to fall towards the lowest place . From whence they conclude , that our Earth must be in the centre . I answer : This may proove it to be a centre of gravitie , but not of distance ; or that it is in the midst of the World. Yea ( but say our adversaries ) Aristotle for this urges a demonstration , which must needs be infallible . Thus , the motion of light bodies , do's apparantly tend upward towards the circumference of the World : but now the motion of heavy bodies , is directly contrary to the ascent of the other ; wherefore it will necessarily follow , that these doe all of them tend unto the centre of the World. I answer : Though Aristotle were a Master in the art of Syllogismes , and he from whom we received the rules of disputation ; yet in this particular , 't is very plain that hee was deceived with a fallacie , whilst his Argument do's suppose that which it do's pretend to proove . That light bodies doe ascend unto some circumference which is higher and above the Earth , is plaine and undeniable . But that this circumference is the same with that of the World , or concentricall unto it , cannot be reasonably affirmed , unlesse he suppose the earth to bee in the centre of the Vniverse , which is the thing to be prooved . I would fain know from what grounds our adversaries can proove , that the descent of heavy bodies is to the centre ; or the ascent of light bodies , to the circumference of the World. The utmost experience we can have in this kinde , do's but extend to those things that are upon our Earth , or in the aire above it . And alas , what is this unto the vaste frame of the whole Vniverse ? but punctulum , such an insensible point , which do's not beare so great a proportion to the whole , as a small sand do's unto the Earth . Wherefore it were a sencelesse thing , from our experience of so little a part , to pronounce any thing infallibly concerning the scituation of the whole . The Arguments from Astronomy , are chiefly these foure ; each of which , are boasted of to be unanswerable . 1 The Horizon do's everie where divide all the great circles of a Sphaere into two equall parts : So there is always halfe the Equinoctiall above it , and half below . Thus likewise , there will constantly be six signs of the Zodiacke above the Horizon , and other six below it . And besides , the circles of the Heaven and Earth , are each way proportionable to one another : as fifteen Germane miles on the Earth , are every where agreeable to one degree in the Heavens ; and one houre in the Earth , is correspondent to fifteen degrees in the Equator . From whence it may bee inferred , that the Earth must necessarily bee scituated in the midst of these circles ; and so consequently , in the centre of the World. I answer : This Argument do's rightly proove the Earth to be in the midst of these circles : but we cannot hence conclude , that it is in the centre of the World : from which , though it were never so much distant , yet would it still remaine in the midst of those circles , because it is the eye that imagines them to be described about it . Wherefore it were a weake and preposterous collection , to argue thus , That the Earth is in the centre of the World ; because in the midst of those circles ; or because the parts and degrees of the Earth , are answerable in proportion , to the parts and degrees in Heaven . Whereas , it follows rather on the contrary , That these circles are equally distant and proportionall in their parts ; in respect of the Earth , because it is our eye that describes them about the centre of it . So that though a farre greater part of the world did appeare at one time than at another ; yet in respect of those circles which our eye describes about the Earth , all that wee could see at once , would seem to be but a perfect Haemisphere : As may bee manifested by this following Figure . Where if wee suppose A. to bee our Earth , B. C. D. E. one of the great circles which we fancy about it , F. G. H. I. the orbe of fixed Starres , R. the centre of them . Now though the Arke , G. F. I. bee bigger than the other , G. H. I. yet yet notwithstanding , to the eye on the Earth , A. one will appeare a semicircle , as well as the other ; because the imagination do's transferre all those Starres into the lesser circle , B. C. D. E. which it do's fancy to be described above that centre . Nay , though there were a habitable Earth , at a far greater distance from the centre of the world , even in the place of Iupiter , as suppose at Q. yet then also would there bee the same appearance . For though the Arke , K. F. L. in the starry heaven , were twice as big as the other , K. H. L. yet notwithstanding at the Earth , Q. they would both appeare but as equall Hemispheres , being transferred into that other circle , M. N. O. P. which is part of the Sphaere that the eye describes to it selfe above the Earth . From whence wee may plainely discern , That though the Earth be never so farre distant from the centre of the World ; yet the parts and degrees of that imaginarie Sphaere about it , will always be proportionall to the parts and degrees of the Earth . 2 Another demonstration like unto this former , frequently urged to the same purpose , is this : If the Earth be out of the centre of the World , then must it be scituated in these three positions : either in the Equator , but out of the Axis ; or secondly , in the Axis , but out of the Equator ; or thirdly , besides both of them . But it is not placed according to any of these scituations ; therefore must it needs be in the centre . 1 'T is not in the Equator , and beside the Axis . For then , first , there will bee no Equinox at all in some places , when the days and nights shall be of an equall length : secondly , the afternoones and forenoones will not bee of the same length ; because , then our Meridian Line must divide the Hemisphaere into unequall parts . 2 'T is not in the Axis , but out of the Equator ; for then , first , the Equinox would not happen when the Sunne was in the middle line betwixt the two Solstices , but in some other paralell , which might bee neerer to one of them , according as the earth did approach to one Tropicke more than another . Secondly , there would not bee such a proportion between the increase & decrease of days and nights , as now there is . 3 'T is not besides both of them : For then , all these inconveniences , and sundry others must with the same necessity of consequence be inferred . From whence it will follow , That the Earth must be scituated there , where the Axis and Equator meet , which is in the centre of the World. To this we grant , that the Earth must needs be placed both in the Axis and Equator ; and so consequently , in the centre of that sphaere which we imagine about it : But yet this will not prove , that it is in the midst of the Vniverse . For let our adversaries suppose it to bee as far distant from that , as they conceive the Sun to be ; yet may it still be scituated in the very concourse of these two Lines : because the Axis of the World is nothing else but that imaginary Line which passes through the Poles of our Earth , to the Poles of the World. And so likewise the Equator , is nothing else but a great circle in the midst of the Earth , betwixt both the Poles , which by imagination is continued even to the fixed Starres . Thus also , we may affirme the Earth to be in the plane of the Zodiacke , if by it's annuall motion it did describe that imaginarie circle : and in the plane of the Equator , if by it's diurnall motion about it's own Axis , it did make severall paralels , the midst of which should be the Equator . From whence it appeares , that these two former Arguments proceed from one and the same mistake , whilest our adversaries suppose the circumference and centre of the Sphaere , to be the same with that of the World. Another demonstration of the same kinde , is taken from the Eclipses of the Sunne and Moone ; which would not alwaies happen when these two Luminaries are diametrically opposed , but somtimes times when they are lesse distant than a semicircle , if it were so , that the Earth were not in the centre . I answer : This Argument , if well considered , will be found most directly to inferre this conclusion , That in all Eclipses , the Earth is in such a strait Line ( betwixt the two Luminaries , ) whose extremities doe point unto opposite parts of the Zodiacke . Now though our adversaries should suppose ( as Copernicus do's ) the Earth to be scituated in that which they would have to bee the Sunnes Orbe ; yet would there not bee any Eclipse , but when the Sunne and Moone were diametrically opposite , and our Earth betwixt them : As may cleerely bee manifested by this Figure , where you see the two Luminaries in opposite Signes : and according as any part of our Earth is scituated by it's diurnall revolution , so will every Eclipse be either visible , or not visible unto it . The last and chiefe Argument , is taken from the appearance af the Starres ; which in every Horizon , at each houre of the night , and at all times of the yere , seeme of an equall bignesse . Now this could not bee , if our Earth were sometimes neerer unto them by 2000000 Germane miles , which is granted to bee the diameter of that Orbe , wherein the Earth is supposed to move . I answer : this consequence will not hold , if we affirme the Earth's Orbe not to be big enough for the making of any sensible difference in the appearance of the fixed Stars . Yea , but ( you wil say ) t is beyond conceit , and without all reason , to think the fixed Starres of so vast a distance from us , that our approaching neerer unto them by 2000000 Germane miles , cannot make any difference in the seeming quantitie of their bodies . I reply : There is no certaine way to find out the exact distance of the starry Firmament : but we are fain to conclude of it by conjectures , according as severall reasons and observations seem most likely unto the fancies of divers men . Now that this opinion of Copernicus do's not make it too big , may be discerned from these following considerations . The Worlds great & little , are relative tearmes , and do import a comparison to somthing else : So that where the Firmament ( as it is according to Copernicus ) is said to be too big ; 't is likely , that this word is to be understood in reference to some other thing of the same kinde , the least of which , is the Moones Orbe : but now if it 's being so much bigger than this may bee a sufficient reason , why it should be thought too great , then it seemes that every thing which exceeds another of the same kind , in such a proportion , may be concluded to be of too big a quantitie : and so consequently , we may affirme , that there is no such thing in the World. And hence it will follow , that Whales and Elephants are meere Chimaera's , and poeticall fictions , because they doe so much exceed many other living creatures . If all this eighth sphaere ( saith Gallilaeus ) as great as it is , were a light body , and placed so farre from us that it appeared but as one of the lesser Starres , wee should then esteeme it but little ; and therefore , we have no reason now to thrust it out from being amongst the works of nature , by reason of it 's too great immensitie . 'T is a frequent speech of our adversaries , Tycho , Fromundus , and others , in excuse of that incredible swiftnesse which they imagine in their primum mobile , That 't was requisite the motion of the Heavens should have a kind of infinitie in it , the better to manifest the infinitenesse of the Creator . And why may not wee as well affirme this concerning the bignes of the Heavens ? Difficilius est accidens praeter modulum subjecti intendere , quàm subjectum sine accidente augere ( saith Keplar . ) His meaning is , that 't is lesse absurd to imagine the eighth Sphaere of so vast a bignesse , as long as it is without motion , or at least , ha's but a very slow one : than to attribute unto it such an incredible celeritie , as is altogether disproportionable to it's bignesse . 2 'T is the acknowledgement of Clavius , and might easily be demonstrated , That if the centre were fastened upon the Pole of the World , the Orbe wherein he supposes the Sunne to move , would not be able to reach so farre in the eighth Sphaere ( being considered according to Ptolomies Hypothesis ) as to touch the Pole-starre : which notwithstanding ( saith he ) is so neere the Pole it selfe , that wee can scarse discerne it to move : Nay , that circle which the Pole-starre makes about the Pole , is aboue foure times bigger than the Orbe of the Sunne . So that according to the opinion of our adversaries , though our Earth were at that distance from the centre , as they suppose the Sunne to be , yet would not this eccentricitie make it neerer to any one part of the Firmament , than the Pole-starre is to the Pole , which according to his confession , is scarse sensible . And therefore according to their opinion , it would cause very little difference in the appearance of those Stars , the biggest of which do's not seeme to bee of above five cubites in it's diameter . 3 'T is considerable , That the sphaeres of Saturne , Iupiter , Mars , are according to the generall opinion , of very great extension ; and yet each of them is appointed onely to carry about it's particular Planet , which are but very little in comparison of the fixed Starres . Now if for the scituation of these fixed Starres , there should be allotted a proportionable part of the World , 't is certaine , that their Orbe must be farre bigger than it is commonly supposed , and very neer to this opinion of Copernicus . 4 Wee usually judge the bignesse of the higher Orbs , by their different motions . As because Saturne finishes his course in thirty yeares , and Iupiter in twelve , therfore we attribute unto those Orbes such a different proportion in their bignesse . Now if by this rule wee would finde out the quantitie of the eighth Sphaere , wee shall discerne it to be farre neerer unto that bignesse , which Copernicus supposeth it to have , than that which Ptolomy , Tycho , and others , ordinarily ascribe unto it . For the starry Heaven ( say they ) do's not finish his course under 26000 yeares ; whereas Saturne , which is next unto it , do's compasse his Orbe in thirty yeares . From whence it will probably follow , that there is a very great distance betwixt these in place , because they have such different termes of their revolutions . But against this answer : unto the last Argument , our adversaries thus reply : 1 If the fixed Starres be so far distant from us , that our approaching neerer unto them by 2000000 Germane miles , doe not make any sensible difference in their appearance , then Gallilaeus his perspective could not make them seeme of a bigger Forme , than they doe to the bare eye , which yet is contrary to common experience . 2 From hence it may bee inferred , That the least fixed Star is bigger than all this Orbe wherein wee suppose the Earth to move ; because there is none of them but are of a sensible bignesse in respect of the Firmament , whereas , this it seemes is not . 3 Since God did at first create the Starres for the use of all nations that are under the wholeheavens , Deut. 4. 19. it might have argued some improvidence in him , if he had made them of such vast magnitudes : whereas they might as well bestow their light and influences , and so consequently be as serviceable to that end for which they were appointed , if they had been made with lesse bodies , and placed neerer unto us . And 't is a common maxime , that nature in all her operations , do's avoid superfluities , and use the most compendious way . I answer : 1 To the first , whether the perspective do make the fixed Starres appeare bigger than they do to the bare eye , cannot certainly be concluded , unlesse wee had such an exact glasse , by which wee might trie the experiment . But if in this kinde we will trust the authoritie of others , * Keplar tells us from the experience of skilfull men , that the better the perspective is , by so much the lesse will the fixed Starres appeare through it , being but as meer points from which the beames of light doe disperse themselves like haires . And 't is commonly affirmed by others , that the Dog-starre ; which seemes to bee the biggest Starre amongst those of the first magnitude , do's yet appeare through this glasse but as a little point no bigger than the fiftieth part of Iupiter . Hence it is , that though the common opinion hold the Starres of the first magnitude to be two minutes in their diameter , and Tycho three , yet † Gallilaeus , who hath bin most versed in the experiments of his owne perspective , concludes them to bee but five seconds . 2 To the second : First wee affirme , the fixed Starres to be of a vaste magnitude . But however , this Argument do's not induce any necessitie that we should conceive them so big as the earth 's Orb. For it might easily bee prooved , that though a Starre of the sixth magnitude were but equall in diameter unto the Sunne ( which is farre enough from the greatnesse of the Earth's Orbe ) yet the starry heav'n would be at such a distance from us , that the Earth's annuall motion could not cause any difference in it's appearance . Suppose the diameter of the Sunne to be about half a degree , as our adversaries grant ; whereas a Starre of the sixth magnitude is fifty thirds , which is comprehended in that of the Sun 2160 times . Now if the Sunne were removed so far from us , that it's diameter would seeme but as one of that number whereof it now containes 2160 , then must his distance from us , bee 2160 times greater than now it is : which is all one , as if wee should say , that a Starre of the sixth magnitude is severed from us by so many semidiameters of the Earth's Orb. But now according to common consent , the distance of the Earth from the Sun , do's containe 128 semidiameters of the Earth , and ( as was said before ) this supposed distance of the fixed Starres , do's comprehend 2160 semidiameters of the Earth's Orbe . From whence it is manifest , that the semidiameter of the Earth , in comparison to it's distance from the Sunne , will bee almost doubly bigger than the semidiameter of the Earth's Orbe , in comparison to this distance of the Starres . But now the semidiameter of the Earth , do's make very little difference in the appearance of the Sunne , because we see common observations upon the surface of it , are as exactly true to the sence , as if they were made from the centre of it . Wherefore , that difference which would bee made in these fixed Stars , by the annuall course of the earth , must needs be much more unobservable , or rather altogether insensible . 2 The consequence of this Argument is grounded upon this false supposition , That every body must necessarily be of an equall extension , to that distance from whence there do's not appeare any sensible difference in it's quantitie . So that when I see a Bird flying such a height in the aire , that my being neerer unto it , or farther from it , by tenne or twenty foot , do's not make it seem unto my eyes either bigger or lesse ; then I may conclude that the bird must needs be either ten or twenty foot thicke : or when I see the body of a Tree that may be halfe a mile from me , and perceive that my approaching neerer to it by thirty or forty paces , do's not sensibly make any different appearance , I may then inferre , that the Tree is forty paces thicke ; with many the like absurd consequences , that would follow from that foundation upon which this Argument is bottomed . To the third I answer : 'T is too much presumption , to conclude that to bee superfluous , the usefulnesse of which we doe not understand . There be many secret ends in these great works of Providence , which humane wisedome cannot reach unto , and as Solomon speakes of those things that are under the Sunne , so may we also of those things that are above it , That no man can find out the works of God , for though a man labour to seek it out . Yea further : Though a wise man thinke to know it , yet shall he not be able to finde it . He that hath most insight into the works of nature , is not able to give a satisfying reason , why the Planets or Stars should be placed just at this particular distance from the Earth , and no neerer or farther . And besides , this Argument might as well be urged against the Hypothesis of Ptolomy or Tycho , since the Starres , for ought we know , might have been as serviceable to us , if they had been placed farre neerer , than either of those Authors suppose them . Againe , were there any force in such a consequence , it would as well conclude a great improvidence of nature , in making such a multitude of those lesser Stars , which have lately discovered by the perspective . For to what purpose should so many Lights be created for the use of man , since his eyes were not able to discerne them ? So that our disabilitie to comprehend all those ends which might be aimed at in the works of nature , can bee no sufficient Argument to proove their superfluitie . Though Scripture doe tell us that these things were made for our use , yet it do's not tell us , that this is their only end . 'T is not impossible , but that there may be elsewhere some other inhabitants , by whom these lesser Stars may be more plainly discerned . And ( as was said before ) why may not we affirm that of the bignesse , which our adversaries doe concerning the motion of the Heavens ? That God , to shew his owne immensitie , did put a kinde of infinitie in the creature . There is yet another Argument to this purpose , urged by * Al. Ross. which was not referred to any of the former kinde , because I could scarsely beleeve I did rightly understand it : since he puts it in the front of his other Arguments , as being of strength and subtilty enough to be a leader unto all the rest ; and yet in the most likely sence of it , 't is so extremely simple to be pressed in a controversie that every fresh man would laugh at it . The words of it are these : Quod minimum est in circulo debet esse centrum illius , at terra longè minor est Sole , & Aequinoctialis terrestris est omnium in Coelo circulus minimus , ergo , &c. By the same reason , it would rather follow , that the Moon or Mercury were in the centre , since both these are lesse than the Earth . And then , whereas he sayes that the Aequinoctiall of the Earth is the least circle in the Heavens , 't is neither true nor pertinent , and would make one suspect , that hee who should urge such an Argument , did searse understand any thing in Astronomy . There are many other objections like unto this , not worth the citing : The chiefe of all have bin already answered ; by which you may discerne , that there is not any such great necessitie , as our adversaries pretend , why the Earth should bee scituated in the midst of the Vniverse . PROP. VII . 'T is probable that the Sunne is in the centre of the World. THe chiefe reasons for the confirmation of this truth , are implyed in the inconveniences of this Hypothesis above any other ; whereby wee may resolve the motions and appearances of the Heavens into more easie and naturall causes . Hence will the frame of nature bee freed from that deformitie , which it ha's according to the Systeme of Tycho : who though he make the Sunne to be in the midst of the Planets , yet without any good reason , denies it to be in the midst of the fixed Starres ; as if the Planets , which are such eminent parts of the World , should bee appointed to move about a distinct centre of their owne , which was beside that of the Vniverse . Hence likewise are wee freed from many of those inconveniences in the Hypothesis of Ptolomy , who supposed in the Heavens , Eppicides and Eccentrickes , and other Orbes , which he calls the differents of the Apoge and the Perige . As if nature in framing this great engine of the World , had been put unto such hard shifts , that shee was faine to make use of wheeles and screwes , and other the like artificiall instruments of motion . There bee sundry other particulars , whereby this opinion concerning the Sunnes being in the centre , may bee strongly evidenced : which because they relate unto severall motions also , cannot therefore properly be insisted on in this place . You may easily enough discerne them , by considering the whole frame of the Heavens , as they are according to the Systeme of Copernicus ; wherein , all those probable resolutions that are given for divers appearances amongst the Planets , doe mainly depend upon this supposition , that the Sunne is in the centre . Which Arguments ( were there no other ) might be abundantly enough for the confirmation of it . But for the greater plenty , there are likewise these probabilities considerable . 1 It may seem agreeable to reason , that the light which is diffused in severall Starres through the circumference of the World , should be more eminently contained , and ( as it were ) contracted in the centre of it , which can only be by placing the Sunne there . 2 'T is an Argument of * Clavius , and frequently urged by our adversaries , That the most naturall scituation of the Sunnes body was in the midst , betwixt the other Planets ; and that for this reason , because from thence he might more conveniently distribute amongst them both his light and heate . The force of which , may more properly bee applyed to proove him in the centre . 3 'T is probable that the planetarie Orbes ( which are speciall parts of the Vniverse ) doe moove about the centre of the World , rather than about any other centre which is remote from it . But now 't is evident , that the Planet Saturne , Iupiter , Mars , Venus , Mercury , doe by their motion encompasse the body of the Sunne . 'T is likely therefore , that th●s is scituated in the midst of the World. As for the three upper Planet , 't is found by observation , that they are alwaies neerest to the Earth , when in opposition to the Sunne , and farthest from us , when in conjunction with it : which difference is so eminent , that Mars in his Perige do's appeare sixty times bigger than when hee is in the Apoge , and at the greatest distance . Now , that the revolution of Venus and Mercury also is about the Sun , may from hence be evidenced : first , because they are never at any great distance from him : secondly , because they are seen sometimes above , and sometimes below him : thirdly , because Venus , according to her different scituations , do's change her appearance , as the Moone . 4 There is yet another Argument , which † Aristotle himselfe do's repeat from Pythagoras . The most excellent body should have the best place ; but the Sunne is the most excellent body , and the centre is the best place ; therfore 't is likely the Sunne is in the centre . In the frame of nature ( which is supposed to be of an orbicular forme ) there are but two places of any eminency , the circumference and the centre . The circumference being of so wide a capacity , cannot so fitly be the peculiar seat of a body , that is so little in respect of it : and besides , that which is the most excellent part of the World , should bee equally preserved in it selfe , and shared in it's vertues by all the other parts , which can only be done by it's being placed in the midst of them . This is intimated unto us in that frequent speech of Plato , that the Soule of the World do's reside in the innermost place of it : and that in * Macrobius , who often compares the sun in the World , to the Heart in a living creature . Vnto this Aristotle answers by a distinction : There is medium magnitudinis , so the centre is the middle of a Sphaere : and there is medium naturae , or informationis , which is not alwayes the same with the other ; for in this sence the Heart is the middle of a man ; because from thence ( saith hee ) as from the centre , the vitall spirits are conveied to all the members : and yet we know that it is not the centre of Magnitude , or at an equall distance from all the other parts . And besides , the middle is the worst place , because most circumscribed , since that is more excellent which do's limit any thing , than that which is bounded by it . For this reason is it , that Matter is amongst those things which are terminated , and Forme , that which do's circumscribe . But against this answer of Aristotle , it is againe replyed : 1 Though it be true , that in living creatures the best and chiefest part is not placed alwaies just in the midst , yet this may be , because they are not of an orbicular forme , as the World is . 2 Though that which bounds another thing be more excellent than that which is terminated by it , yet this do's not proove the centre to bee the worst place , because that is one of the tearmes or limits of a round body , as well as the circumference . There are likewise other Arguments to this purpose , much insisted on by eminent Astronomers , taken from that harmonicall proportion which there may be betwixt the several distance and bignesse of the Orbs , if we suppose the Sun to be in the centre . For according to this ( say they ) wee may conceive an excellent Harmonie both in the number and the distance of the Planets : ( and if God made all other things numero & mensurâ , much more then those greater Works , the Heavens ) for then the five Mathematicall bodies , so much spoken of by * Euclid , wil beare in them a proportion answerable to the severall distances of the Planets from one another . Thus a Cube will measure the distance betwixt Saturne and Iupiter ; a Pyramis or Tetraëdron , the distance betwixt Iupiter and Mars ; a Dodecaëdron , the distance betwixt Mars and the Earth ; an Icosaëdron , the distance betwixt the Earth and Venus ; and an Octoëdron , the distance betwixt Venus and Mercury ; that is , if we conceive a circumference described immediately without the Cube , and another within it , the distance betweene these two will shew what proportionall distance there is betwixt the Orbe of Saturne , and that of Iupiter . Thus also , if you conceive a circumference described on the outside of a Pyramis or Tetraëdron , and another within it , this will shew such a proportionall distance , as there is betwixt the Orbe of Mars , from that of Iupiter . And so of the rest . Now if any aske why there are but six Planetary Orbs ? Keplar answers : Quia non oportet plures quàm quinque proportiones esse , totidem nempè quot regularia sunt in Mathesi corpora . Sex autèm termini consummant hunc proportionum numerum : Because there are but five proportions , so many as there are regular bodies in Mathematickes , each of whose sides and angles are equall to one another . But now there are six tearmes required to consummate this number of proportions ; and so consequently , there can bee but six primary Planets . Thus likewise by placing the Sunne in the centre , wee may conceive such a proportion betwixt the Bodies of the Planets , as will be answerable unto their severall Sphaeres : Then Mercury , which ha's the least Orbe , will have the least Body ; Venus bigger than that , but lesse than any of the other ; our Earth bigger than Venus , but lesse than the rest ; Mars bigger than the Earth , but lesse than Iupiter ; Iupiter bigger than Mars , and lesse than Saturne ; Saturne being the highest , should also be the biggest . All which Harmony would bee disturbed by putting in the Sunne amongst them ; and therfore , it may be more convenient for him to sit still in the centre . There are sundry other Arguments in this kinde to be found out , by a consideration of this whole Hypothesis : Hee that do's rightly understand it , may therein easily discerne many strong probabilities , why the Sun should be in the midst of the World , rather than in any other position . PROP. VIII . That there is not any sufficient reason to prove the Earth incapable of those motions which Copernicus ascribes unto it . THe two chiefe motions in the World , which are more especially remarkable above the rest , are the Diurnall , and Annuall . The Diurnall , which makes the difference betwixt night and day , is caused by the revolution of our Earth vpon it's owne Axis , in the space of foure and twenty houres . The Annuall , which makes the difference betwixt Winter and Summer , is likewise caused by the Earth , when being carried through the Eclipticke in it's owne Orbe , it finishes it's course in a yeare . The first is usually stiled , Motus revolutionis : The second Motus circumlationis : There is likewise a third , which Copernicus calls Motus inclinationis : but this being throughly considered , cannot properly be stiled a motion , but rather an immutabilitie , it being that whereby the Axis of the Earth do's alwaies keep paralell to it selfe , from which scituation , it is not his annuall course that do's make it in the least manner to decline . As for the difficulties which concern the second of these , they have been alreadie handled in the sixth Proposition , where the Earth's eccentricitie was maintained . So that the chiefe businesse of this Chapter , is to defend the Earth's diurnall motion , against the objections of our adversaries . Sundry of which objections , to speak ( as the truth is ) do beare in them a great shew of probabilitie , and such too ( as it seemes ) was very efficacious , since Aristotle and Ptolomy , &c. men of excellent parts and deep judgements , did ground upon them , as being of infallible and necessarie consequence . I shall reckon them up severally , and set downe such answers unto each , as may yeeld some satisfaction to every indifferent seeker of truth . 1 First then , 't is objected from our sences ; If the Earth did move , we should perceive it . The Westerne mountaines would then appeare to ascend towards the Starres , rather than the Stars to descend below them . I answer : The sight judges of motion according as any thing do's desert the plane whereon it selfe is seated : which plane every where keeping the same scituation and distance , in respect of the eye , do's therefore seem immovable unto it , and the motion will appeare in those Starres and parts of the Heaven ; through which the verticall Line do's passe . The reason of such deceit may be this : Motion being not a proper object of the sight , nor belonging to any other peculiar sence , must therefore be judged of by the sensus communis , which is liable to mistake in this respect ; because it apprehends the eye it self to rest immovable , whilest it do's not feel any effects of this motion in the body : As it is when a man is carried in a Ship ; so that sence it but an ill judge of naturall secrets . 'T is a good rule of Plato , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 : A Philosopher must not bee carried away by the bare appearance of things to sight , but must examine them by reason . If this were a good consequence , The Earth do's not move , because it do's not appeare so to us , we might then as well argue , that it do's move when we goe upon the water , according to the verse : Provehimur portu , terraeque , verbesque recedunt . Or if such Arguments would hold , it were an easie matter to prove the Sunne and Moone not so big as a Hat , or the fixed stars as a Candle . Yea , but if the motions of the Heavens bee onely apparant , and not reall , then the motion of the clouds will be so too , since the eye may bee as well deceived in the one as the other . I answer : 'T is all one , as if he should inferre , that the sence was mistaken in every thing , because it was so in one thing : and this would be an excellent Argument to prove that opinion of Anaxagoras , that the Snow was blacke . The reason why that motion which is caused by the Earth , do's appeare as if it were in the Heavens , is , because the sensus communis in judging of it , do's conceive the eye to be it selfe immovable ( as was said before ) there being no sence that do's discerne the effects of any motion in the body ; and therefore , it do's conclude every thing to move , which it do's perceive to change it's distance from it : So that the clouds do not seem to move sometimes , when as notwithstanding they are every where carried about with our Earth , by such a swift revolution ; yet this can be no hinderance at all , why wee may not judge aright of their other particular motions , for which there is not the same reason . Though to a man in a Ship , the Trees and Bankes may seeme to move ; yet it would be but a weak Argument , to conclude from hence , that therefore such a one could not tell whether his friend do's really stirre , whom he sees to walke up and downe in the Ship : or that hee might as well bee deceived in judging the Oares to move , when they doe not . 'T is againe replyed by the same Objector , That it is not credible , the eve should bee mistaken in judging of the Starres and Heavens ; because those being light bodies , are the primarie and proper Objects of that sence . I answer : The deceit here is not concerning the light or colour of those bodies , but concerning their motion ; which is neither the primarie nor proper Object of the Eye , but reckoned amongst the Objecta Communia . 2 Another common Argument against this motion , is taken from the danger that would thence arise , unto all high buildings , which by this would quickely bee ruinated , and scattered abroad . I answer : This motion is supposed to be naturall : and those things which are according to nature , have contrary effects to other matters , which are by force and violence . Now it belongs unto things of this later kind , to be inconstant and hurtfull ; whereas those of the first kinde must be regular , and tending to conservation . The motion of the Earth is alwaies equall and like it selfe : not by starts and fits . If a glasse of Beere may stand firmely enough in a Shippe , when it moves swiftly upon a smooth streame , much lesse then will the motion of the Earth , which is more naturall ; and so consequently more equall , cause any danger unto those buildings that are erected upon it . And therefore to suspect any such event , would bee like the feare of Lactantius , who would not acknowledge the being of any Antipodes , lest then he might bee forced to grant that they should fall downe unto the Heavens . We have equall reason to be afraid of high buildings , if the whole World above us were whirled about with such a mad celeritie as our adversaries suppose ; for then there would be but small hopes , that this little point of Earth should escape from the rest . But supposing ( saith * Rosse ) that this motion were naturall to the Earth , yet it is not naturall to Townes and Buildings , for these are artificiall . To which I answer : Ha , ha , he . 3 Another Argument to this purpose is taken from the rest and quietnes of the aire about us ; which could not be , if there were any such swift motion of the Earth . If a man riding upon a fleet horse , doe perceive the aire to beat against his face , as if there were a winde , what a vehement tempest should wee continually feele from the East , if the Earth were turned about with such a swift revolution as is supposed . Vnto this 't is usually answered , That the aire also is carried along with the same motion of the Earth : For if the concavitie of the Moones Orbe , which is of so smooth and glabrous a superficies , may ( according to our adversaries ) drive along with it the greatest part of this Elementarie World , all the regions of Fire , and all the vast upper regions of Aire , and ( as some will have it ) the two lower Regions , together with the Sea likewise ; for from hence ( saith Alex. Rosse , lib. 1. sect . 1. cap. 3. ) is it , that betwixt the Tropicks there is a constant Easterne wind , and a continuall flowing of the Sea Westward ; I say , if the motion of the Heavens which are smooth bodies , may bee able to carry with it so great a part of the elementarie World : or if the rugged parts of the Moons Body be able to carry with it so great a part of the aire , as Fromondus ( Ant. c. 16. ) affirms : much more then may our earth , which is a rugged mountainous Body , be able to turne about so little a part of the world , as that vaporous aire next unto it . Suppose the inward circle to represent the Earth ; and the outward , the thicker aire which encompasses it . Now it is easily conceivable , that the revolution of so great a Body as this Globe of Earth , may turne about by it's meere motion ( if there were nothing els ) so little a part of the adjoyning aire , as is here represented : And yet , 1 The disproportion betwixt the thicknesse of the Earth , and this Orb of Aire , is farre greater than could bee exprest in the Figure , being but as twenty miles ; which is at most the thicknesse of this Aire , unto 3456 miles , which is the semidiameter of our Earth , and so is but as an insensible number in respect of this other . 2 Besides the meere motion of the Earth , which in probabilities ( being such a rugged body ) might bee enough to carry so little a part of the aire along with it ; there is also ( as wee suppose ) a magneticall vigor which proceeds from it , whereby 't is more able to make all things that are neere unto it , to observe the same revolution . But if it be so ( saith * Alex. Ross. ) that not only the man , but the medium also , and the Object bee moved : this must needs be such a great hinderance to the sight , that the eye cannot judge exactly of any thing . For suppose the man alone to be in a motion , hee could not see so well as when hee is still ; but now if not only he , but his spectacles , and booke were all mooved , he would not bee able to discerne any thing distinctly . I answer : the consequence were pertinent , if all these were severall motions : but if the Subject , and Medium , and Object were all carried with one and the same equall motion ( as it is here supposed ) this could be no impediment to the act of seeing , but it would bee all one with the rest ; because by this means , they are not severed from one another ; and therefore the species are not disturbed . 'T is an excellent saying of * Gallilaeus , and may serve for the resolution of many such doubts as these : Motus eatenus tanquàm motus operatur , quatenus relationem habet ad eas res quae ìpso distituuntur , in ijs verò-rebus , quae totae aequaliter de eo participant , nihil operatur , & ita se habet ac si nullus esset . If a man be within some roome of a Ship , he may read altogether as easily when the Ship moves , as when it stands still . 4 Another Argument against this circular motion of the earth ▪ is grounded upon that common Principle amongst the Aristotelians : Vnius corporis simplicis unum tantum est motus : One kind of body ha's but one kind of motion . But now the Earth and Water ha's a motion of descent : the Aire , a motion of ascent ; and therefore none of them can have any circular motion naturall unto them . I answer : First , these right motions of elementarie bodies belong onely to the parts of them , and that too when they are out of their proper places ; so that the whole to which they belong , may notwithstanding this , have another motion of it's owne . But secondly , this saying which Aristotle cals a Principle , will not consist with other evident experiments of nature . Thus , though a Loadstone in respect of it's matter and condensitie , naturally tends downward ; yet this do's not hinder , but that in respect of some other qualities , as it 's desire of union and coition to another loadstone , it may also naturally move upwards . From whence it will follow , that the same elementarie bodie may have divers natural motions . 5 The gravitie and magnitude of this Earthy Globe , do make it altogether unfit for so swift a motion . I answer : First , Heavinesse can onely be applyed unto those bodies which are out of their proper places , or unto such parts as are severed from the whole to which they belong . And therefore the Globe of Earth , considered as whole , and in it's right place , cannot truly bee called heavy . I deny not , but that there is in it , and so likewise in the other Planets , an ineptitude to motion , by reason of the matter and condensitie of their bodies : And so likewise there is , as truly ( though not according to the same degrees ) in the least particle of a materiall condensed substance : so that this cannot reasonably be pretended as a just impediment , why the earth should be incapable of such a motion . Secondly , and though this Globe be of so vast a magnitude , yet as nature bestowes upon other creatures ( for instance an Eagle and a Flye ) spirits , and motive powers , proportionable to their severall bodies : so likewise may she indowe the Earth with a motive facultie answerable to it's greatnesse . Or if this may make the Earth incapable of so swift a motion , as is supposed , much more then will the Heavens bee disabled for that greater swiftnesse which is imagined in them . I might adde , the Globe of the Sun and Iupiter are observed to move about their owne centres ; and therefore the Earth , which is farre lesse than either of them , is not by reason of it 's too great magnitude made unfit for such a revolution . Thirdly , as for the swiftnesse of the Earth's course , it do's not exceed ( all circumstances well considered ) the celeritie of some other motions , with which we are acquainted ; as that of the clouds , when driven by a tempestuous wind ; that of a Bullet shot from a Cannon , which in the space , a minute do's fly 4 miles . Or as another hath observed in the second scruple of an hour it may passe the fifteenth part of a Germane mile : Than which , there is not any point in the Earth's Equinoctiall that moves faster ; and though a Bullet bee much slower in moving a greater distance , yet for so little a space , while the force of the pouder is most fresh and powerfull , it do's equal the swiftnesse of the Earth . And yet , 1 A bullet or cloud is carried in it's whole body , being fain to break it's way through the aire round about it : but now the earth ( in respect of this first motion ) do's remaine still in the same scituation , and move onely about it's owne centre . 2 The motion of a Bullet is violent , and against it's nature , which do's strongly incline it to move downwards . Whereas the Earth being considered as whole , and in it's proper place , is not heavy , nor do's it containe any repugnancie to a circular motion . 6 The chiefe Argument , on which our adversaries do most insist , is this : If there were such a motion of the Earth as is supposed , then those bodies which are severed from it in the Aire , would be forsaken by it . The clouds would seeme to rise and set as the Starres . The Birds would be carried away from their nests . No heavy body could fall perpendicular . An Arrow or Bullet being shot from East to West by the same violence , will not bee carried an equall distance from us , but we should by the revolution of our Earth , overtake that which was shot to the East , before it could fall . If a man leaping up should abide in the Aire but one second scruple of an houre , or the sixtieth part of a minute , the Earth in that space , would withdraw it selfe from him almost a quarter of a mile . All these and many other such strange inferences , which are directly contrary to sence and experience , would follow from this motion of the Earth . There are three severall wayes most frequently used for the resolving of these kind of doubts . 1 From those magneticall qualities , which all elementarie bodies do partake of . 2 From the like motions of other things within the roome of a sailing Ship. 3 From the like participation of motion in the open parts of a Ship. 1 For those magneticall properties , with which all these bodies are endowed . For the better understanding of this , you must know , That besides those common elementarie qualities of heat , coldnesse , drinesse , moisture , &c. which arise from the predominancie of severall Elements ; there are likewise other qualities ( not so well known to the Antients ) which wee call magneticall , of which every Particle in the Terrestriall Globe do's necessarily participate : and whether it be joyned to this Globe by continuitie or contiguitie ; or whether it be severed from it , as the Clouds in the second Region , a Bird , or Bullet in the Aire ; yet do's it still retaine it's magneticall qualities , together with all those operations that proceed from them . Now from these properties doe wee suppose the circular motion of the Earth to arise . If you aske , what probabilities there are , to prove that the Earth is indowed with any such affections . I answer : 'T is likely , that the lower parts of this Globe do not consist of such a soft fructifying Earth , as there is in the surface ( because there can be no such use for it , as here , and nature do's nothing in vain ; ) but rather , of some hard rocky substance , since we may well conceive , that these lower parts are pressed close together by the weight of all those heavy bodies above them . Now 't is probable , that this rocky substance is a Load-stone , rather than a Iaspis , Adamant , Marble , or any other ; because experience teacheth us , that the Earth and Loadstone do agree together in so many properties . Suppose a man were to judge the matter of divers bodies ; each of which should bee wrapt up in some covering from his eye , so that he might not only examine them by some other outward signes : If in this examination he should find any particular body which had all the properties that are peculiar to a Load-stone , hee would in reason conclude it to be of that nature , rather than any other . Now there is altogether as much reason why wee should inferre , that the inward parts of the Earth doe consist of a magneticall substance . The agreement of these two you may see largely set forth in the treatise of D. Gilbert . I will instance only in one Example ; which of it self may sufficiently evidence , that the Globe of Earth do's partake of the like affections with the load-stone . In the mariners needle you may observe the magneticall notions of direction , variation , declination ; the two last of which are found to be different , according to the varietie of places . Now this difference cannot proceed from the needle it selfe , because that is the same every where . Nor can we well conceive how it should bee caused by the Heavens ; for then the variation would not be alwaies alike in the same place , but diverse , according to those severall parts of the heaven , which at severall times should happen to bee over it : And therefore , it must necessarily proceed from the Earth , which being it selfe endowed with magneticall affections , do's diversly dispose the motions of the needle , according to the difference of that disponent vertue which is in it's severall Ports . Now to apply this unto the particular instances of the Objection : We say , though some parts of this great Magnet the Earth , may according to their matter be severed from the whole ; yet are they alwayes joyned to it by a communion of the same magneticall qualities ; and doe no lesse observe these kinde of motions , when they are separated from the whole , than if they were united to it . Nor need this seeme incredible , that a heavy Bullet , in such a swift violent course , should bee able to observe this magneticall revolution of the whole Earth ; when as we see that those great bodies of Saturne , Iupiter , &c. hanging in the vaste spaces of the aetheriall Aire , do so constantly and regularly move on , in their appointed courses : Though we could not shew any similitude of this motion in these inferior bodies , with which we are acquainted ; yet wee must know , there may be many things which agree to the whole frame , that are not discernable in the divers parts of it . 'T is naturall unto the Sea to ebbe and flow , but yet there is not this motion in every drop or bucket of Water . So if we consider every part of our bodies severally , the humours , bones , flesh , &c. they are all of them apt to tend downewards , as being of a condensed matter ; but yet consider them according to the whole Frame , and then the bloud or humours may naturally ascend upwards to the Head , as well as descend to any of the lower parts . Thus the whole Earth may move round , though the severall parts of it have not any such particular revolution of their owne . Thus likewise , though each condensed body being considered by it selfe , may seem to have only a motion of descent ; yet in reference to that whole Frame of which it is a part , it may also partake of another motion that may be naturall unto it . But some may here object : Though the Earth were endowed with such magneticall affections , yet what probabilitie is there that it should have such a revolution ? I answer : 'T is observed of those other magneticall bodies of Saturne , Iupiter , and the Sun , that they are carried about their owne centers ; and therefore 't is not improbable , but that it may be so with the Earth also ; which if any deny , he must shew a reason why in this respect they should be unlike . Yea , but though the Earth did move round , what ground is there to affirme that those bodies which are severed from it , as a Bullet , or the clouds , should follow it in the same course ? I answer : Those spots which are discovered about the Sun , and are thought to bee clouds or evaporations from his body , are observed to bee carried about according to his revolution . Thus the Moone is turned round by our Earth : the foure lesser Planets by the body of Iupiter . Nay , thus all the Planets in their severall Orbes , are moved about by the revolution of the Sunne , upon it's owne Axis ( saith Keplar ) and therefore much more may an Arrow or Bullet be carried round by the magneticall motion of our Earth . The second way , whereby some answer unto the instances of this Argument , is , by shewing the like motions of other things within some roome of a sailing Ship. Thus experience teaches ( say they ) that a candle , as also the fumes that come from it , will alwayes keep the same scituation in the swiftest motion of a Ship , as if it did rest immovably , and the flame will not more especially bend one way , or have any troubled fluctuation , but burne as strait and quietly , as if it did stand still . Againe , it ha's been found ( say those that have been versed in these kinde of experiments ) that the same force will cast a body but at an equall distance , whether or no the body do move with , or against the motion of the Ship. As also that any weight being let fall , will descend in as true a perpendicular , as if the Ship did stand still . If a man leaping up , doe tarry in the Aire one second minute of an houre , yet the Ship will not in it's greatest swiftnesse ( as it should according to the calculation of our adversaries ) be carried from him at least fifteen foot . If wee suppose a man to jumpe in such a Ship , he will not be able to passe farther , when he jumps against the motion of it , than when hee jumps with it . All which particulars may argue , that these things are carried along together , by the common motion of the Ship. Now if bodies may be thus jointly moved by such a praeternaturall motion , much more then will they accompanie the Earth in it's diurnall revolution , which we suppose to bee naturall unto them , and as a Law imposed by God in their first Creation . If the flame of a candle , or the smoke that comes from it ( things that are so easily movable ) are notwithstanding carried so equally , and without any disturbance , by the motion of a Ship : then also the Cloudes in the Aire , and all other light Bodies , may well enough be turned about by the revolution of our Earth . If an equall force wil cast an heavy body but at an equall distance , whether or no it move with , or against the motion of the Ship ; then may wee easily conceive , that an Arrow or Bullet being shot with the same violence , will passe but the same space on the Earth , whether or no it be shot towards the East or West . If a heavy Body , while the Ship do's move , will fall downe in a strait Line , then it is not the revolution of our Earth that can hinder a perpendicular descent . If a man leaping up in a Ship , may abide in the Aire on the second scruple of an houre , and yet this Ship in it's greatest swiftnesse not withdraw it selfe fifteene foot ; then will not the Earth in that space go from him almost a quarter of a mile . But against this 't is objected , That the Earth ha's the similitude of an open Ship , and not of any room that is close . And though it bee true , that when the Roofe and the Walls doe all move together , the Aire which is included betwixt them , must bee carried along by the same motion ; yet it is not so with the Earth , because that hath not any such Walls or Roofe , wherein it may containe and carry along with it the medium . And therefore experience will rather argue against this supposed revolution . Thus 't is observed , that a stone being let fall from the Mast of a Ship that moves swiftly , will not descend to the same point , as if the Ship did stand still . From whence it will follow , that if our Earth had such a circular motion , then any heavy body being let fall from some high Tower , or other steep place , would not descend unto that point of Earth which was directly under it at the beginning . To this wee answer ; That the Aire which moves along with our Earth , is as well limited in certaine bounds , as that which is included in a roome . If you aske where these bounds are terminated : I answer neither by the utmost parts of the World , nor yet by the concavitie of the Moons Orb ( as Fromondus would have us affirme ) but by the Sphaere of vaparous Aire that encompasses our Earth ; or which is all one , by the Orbe of magneticall vigor , which proceeds from it . And besides , t is considerable that all Earthly Bodies are not onely contained within these limits , as things are in a close roome , but also as parts in that whole to which they belong . 2 Though the carrying along of the medium may solve the motion of light Bodies in a Ship , as the flame of a candle , smoake , or the like ; yet this cannot concurre to that which hath bin said of heavy Bodies , as a man leaping up , a Bullet descending , &c. since it is not the motion of the meere Aire that is able to make these partake of the same motion with the Ship. Vnto that Argument which he urges from the experiment of a Stone falling in an open Ship , Wee answer : 1 Though the instance of a Ship , may serve as a proofe for this opinion , it being an Argument a minori ad majus , from an accidentall motion to a naturall ; yet it will not serve against it . For though it were not thus in accidentall motions ; yet this would not hinder but that it might be so in those that are supposed to be proper and naturall . 2 As for that experiment it selfe , 't is but a groundlesse imagination , and was never yet confirmed by any particular experience , because 't is certaine the event would be clean otherwise , as shall be prooved in the third way of answering . 3 The third and last way of cleering the doubts in the sixth Argument , is by shewing the like participation of motion , in those things that are in the open parts of a Ship. To which purpose Gallilaeus urges this experiment : If any one should let fall a Stone from an high Mast , he would find lapidem in eundem semper Navis locum decidere , seu consistat illa , seu quantacunque velocitate moveatur : that the Stone would alwayes descend unto the very same place , whether or no the Ship did move or stand still . The reason of which is , because the motion of the Ship is likewise impressed in the Stone : which impression is not equally prevalent in a light body , as a Feather , or Wooll , because the Aire which ha's power over them , is not carried along by the same motion of the Ship. Thus likewise will it be in this other experiment : If a man upon a running Horse should in his swiftest course let fall a Bullet or Stone , these heavy Bodies , besides their owne descent , would also participate that transverse motion of the Horse . For as those things that are throwne from us , do continue the it motion when they are out of the hand in the open Aire : so likewise must it bee when the force is conferred by that motion which the arm ha's from the Horse . While a man is riding , his arme is also carried by the same swiftnes of the Horse ; therefore , if hee should onely open his hand and let fall any thing , it would not descend in a strait Line , but must necessarily be driven forward , by reason of that force impressed in it by the swiftnesse of the Horse , which is also communicated to the arme : it being all one in effect , whether or no the arme be moved by a particular motion of it's owne , as it is in casting of things from us ; or by the common motion of the Body , as it is in dropping of any thing from us , either when wee are on the toppe of some sayling Shippe , as in the Former ; or on some running Horse , as in this Later instance . What hath been said concerning the motion of descent , is likewise applyable , both to that which is upward , and that which is transversall . So that when 't is objected , if the Earth did move , then a Bullet that were shot up perpendicularly would bee forsaken by it , and not descend to the place from whence it arose : Wee answer , that the Cannon which is upon the Earth , together with the Bullet in it , doe partake of the same circular motion , with the Earth , and this perhaps our adversaries will grant , whilest wee suppose the Bullet to remaine still in the Cannon , all the difficultie will bee to shew how it must necessarily observe the same motion , when it is shot out into the open Aire . For the better explication of this , you may note this following Figure . Where wee suppose A. C. to bee a Cannon perpendicularly , erected with a Bullet in it at B. which if it were immovable , wee grant that the Bullet being discharged , must ascend in a just perpendicular . But now conceive this Cannon to move along with the Earth , then in that space of time while the Bullet by the force of the pouder is ascending to the top of the Bore , the Cannon will be transferred to the scituation D. E. so that the Bullet must bee moved according to the Line F. G. which is not directly upright , but somewhat declining . Now the motion of the Bullet in the Aire , must necessarily be conformed unto that direction that is impressed in it by the Cannon from whence it is shot , and so consequently it must bee continued according to the Line F. G. and therefore will alwayes keep perpendicularly over the point from which it did ascend . If you reply , that the motion of the Bullet in the Cannon must needs bee so so swift , that the Earth cannot carry the Cannon from C. to E. in the same space of time , wherein the Bullet do's move from B. to A. I answer : 't is not materiall whether the Earth bee of a greater or lesser swiftnesse than the Bullet , because the declination must alwayes bee proportionable to the motion of the Earth , and if wee suppose this to bee slower than the Bullet , then the declination of the Line F. G. will bee so much the lesse . This truth may yet farther bee illustrated by the practise of those Fowlers , who use to kill Birds as they are flying : Concerning which Art , t is commonly thought that these men direct their aimes to some certaine space in the Aire , just before the Birds , where they conceive the Bullet wil meet with them in their flight ; whereas the truth is , they proceed in this case , the very same way , as if the Birds did stand still , by a direct aiming at their bodies , and following of their flight by the motion of the piece , till at length , having got a perfect aime , they discharge , and do hit altogether as surely , as if the Birds were sitting upon a Tree . From whence wee may observe , that the motion of the piece , as in our aiming , it is made to follow the Birds in their flight ( though it be but slow , ) yet is communicated to the Bullet in the Aire . But here it may seeme very difficult to give any reason according to those grounds concerning the flight of birds ; which being animated , have a liberty to fly here or there , to tarry for a good space of time in the open Aire , and so 't is not easie to conceive what meanes there is , by which they should participate of the Earth's diurnall revolution . To this Gallilaeus answers , that the motion of the Aire , as it do's turne about the Clouds , so doth it also carry with it the Birds , together with such other like things that are in it . For if some violent winde bee able to drive with such swiftnesse a full laden Ship , to throw downe Towers , to turne up Trees , and the like ; much more then may the diurnall motion of the Aire , ( which do's so farre exceed in swiftnesse the most tempestuous winde ) be able to carry with it the bodies of Birds . But if all things bee turned about by this revolution , then it should seeme there is no such thing as a right motion , whether of ascent , or descent in a strait Line . I answer : The moving of heavy or light bodies , may bee considered in a double relation . 1 According to the space wherein they move , and then we grant their motions not to bee simple , but mixed of a direct and circular . 2 According to the body or medium wherein they move , and then they may properly be said to have right motions , because they passe through the medium in a strait Line ; and therefore it is , that unto us they seeme directly to ascend or descend . Aristotle himselfe would not deny , but that Fire may ascend in a strait Line unto it's Sphaere , and yet participate also of that circular motion which hee supposes to bee communicated from the Heavens , unto the upper part of the Aire , and it 's owne Region . So likewise must it bee for the descent of any thing . Suppose a Ship in it's swiftest motion , and a man in it , having some vessell filled with water , should let fall into it a little Ball of Waxe , or some other matter which may be slow in it's sinking , so that in one minute it should scarse descend the space of a cubit , though the Ship ( it may be ) in the same time may passe at least a hundred cubits ; yet would this still seeme unto the eye to descend in a strait Line ; and the other motion which is communicated unto it by the Shippe , would not at all bee discernable in it . And though in this case , the motion were in it selfe composed of a circular and direct ; yet in respect of us it would appeare , and so might be stiled exactly strait . Now if it be thus in those which are generally granted to be praeternaturall motions ; wee need not doubt then the possibilitie of the like effect in that motion which wee conceive to be proper and naturall , both to the Earth , and the things that belong unto it . There is yet another Objection to this purpose urged by * Malapertius , a late Iesuite , who though hee doe with much eagernesse presse this Argument concerning a Bullet or Stone , against the opinion of Copernicus ; yet he grants that it might easily be resolved , if the defenders of it would affirme that the Aire did move round with the earth . But this ( saith he ) they dare not avouch ; for then the Comets would always seem to stand stil , being carried about with the revolution of this aire , and then they could not rise or set , as experience shews they doe . To this it may be answered , that most Comets are above that Sphaere of Aire which is turned round with our Earth , as is manifest by their height . The motion that appeares in them , is caused by the revolution of our Earth , whereby we are turned from them . As for those which are within the Orbe of our Aire , these do seem to stand still . Such a one was that mentioned by † Iosephus , which did constantly hang over Ierusalem ; and that likewise which appeared about the time of Agrippa's death , and for many dayes together did hang over the City of Rome . Wherefore * Seneca do's well distinguish out of Epigenes , betwixt two sorts of Comets , the one being low , and such as seeme immovable , the other higher , and such as did constantly observe their risings and settings , as the Starres . I have done with all the Arguments of any note or difficultie , that are urged against this diurnall motion of the Earth . Many other cavils there are not worth the naming , which discover themselves to be rather the Objections of a captious , than a doubtfull minde . Amongst which , I might justly passe over those that are set down by * Alex. Rosse . But because this Author do's proceed in his whole discourse with so much scorne and triumph , it will not be amisse therefore to examine what infallible evidence there is in those Arguments upon which hee grounds his boastings . We have in one chapter no lesse than these nine . 1 If the Earth did move , then would it bee hotter than the Water , because motion do's produce heate ; and for this reason likewise , the Water would be so hot and rarified , that it could not bee congealed ; since that also do's partake of the same motion with the Earth . 2 The Aire which is next the Earth , would be purer , as being rarified with motion . 3 If the Earth did move the Aire , it would cause some sound , but this is no more audible than Pythagoras his Harmony of the Heavens . 4 'T would have been in vaine for Nature to have endowed the Heavens with all conditions requisite for motion , if they had been to stand still : As first , they have a round Figure . Secondly , they have neither gravitie nor levity . Thirdly , they are incorruptible . Fourthly , they have no contrary . 5 All similarie parts are of the same nature with the whole : But each part of the Earth do's rest in it's place ; therfore also doth the whole . 6 The Sun in the World is as the Heart in a mans Body : But the motion of the Heart ceasing , none of the members do stir ; therefore also if the Sunne should stand still , the other parts of the World would be without motion . 7 The Sun and Heavens do worke upon these inferior Bodies by their light and motion . So the Moone do's operate upon the Sea. 8 The Earth is the Foundation of Buildings ; and therefore must be firme and stable . 9 'T is the constant opinion of Divines , that the Heavens shall rest after the day of Iudgement ; which they prove from Isa. 60. 20. They Sun shall no more goe downe , neither shall thy Moone withdraw it selfe . So likewise Rev. 10. 6. The Angell sweares that there shall be time no longer ; and therefore the Heavens must rest , since by their motion it is that time is measured . And S. Paul sayes , Rom. 8. 20. That all the Creatures are made subject to vanity . Now this can be no other in the Heavens , than the Vanitie of Motion , which the Wise man speaks of , Eccles . 1. 4. The Sunne riseth , and the Sunne goeth downe , &c. To these it may be answered : In the first you may note a manifest contradiction , when hee will have the Earth to bee hotter than the Water , by reason of this motion ; when as notwithstanding he acknowledges the Water to move along with it ; and therefore too in the next Line he infers that the Water , because of that heate and rare faction which it receives from this motion with the earth , must be incapable of so much cold as to be congealed into Ice . But unto that which may be conceived to bee his meaning in this and the next Argument : I answer , if he had fully understood this opinion which hee opposes , he would easily have apprehended that it could not be prejudiced by either of these consequences . For we suppose that not only this Globe of Earth and Water , but also all the vaporous Aire which invirons it , are carried along by the same motion . And therfore , though what hee sayes concerning the heate , which would bee produced by such a motion , were true ; yet it would not bee pertinent , since our Earth and Water , and the Aire next unto them , are not by this meanes severed from one another , and so doe not come within the compasse of this Argument . If any reply , That this will notwithstanding hold true concerning the upper part of the Aire , where there is such a separation of one body from another ; and so consequently , an answerable heate : I answer , 1 'T is not generally granted , That motion in all kind of bodies do's produce heate ; some restraine it onely to follid bodies : affirming , That in those which are fluid , it is rather the cause of coldnesse . This is the reason ( say they ) why running Waters are ever to our sence the coolest : and why amongst those Winds which proceed from the same coasts of Heaven , about the same time of the yeare , the strongest alwaies is the coldest ? If you object , that running Waters are not so soone frozen as others : They answer , this is not because they are thereby heated ; but because unto congellation , it is requisite that a Body should settle and rest , as well as be cold . 2 If wee should grant a moderate heate in those parts of the Aire , we have not any experiment to the contrary , nor would it prejudice the present opinion , or common Principles . As the sound of this motion is not more heard than the Harmony of the Heavens : so neither is there any reason why this motion should cause a sound , more than the supposed motion of the Heavens , which is likewise thought to be continued unto the Aire hard by us . This will prove the Earth to move as well as the Heavens ; For that ha's , first , a round Figure , as is generally granted . Secondly , being considered as whole , and in it's ptoper place , it is not heavy , as was proved before : and as for the two other conditions , neither are they true of the Heavens ; nor if they were , would they at all conduce to their motion . 1 This Argument would prove that the Sea did not ebbe and flow , because there is not the same kind of motion in euery drop of Water : or that the whole Earth is not sphaericall , because every little piece of it is not of the same Forme . This is rather an illustration than a proofe ; of if it do prove any thing , it may serve as well for that purpose unto which it is afterward applyed , where the motion of every Planet is supposed to depend upon the revolution of the Sunne . That the Sunne and Planets do work upon the Earth by their own reall daily motion , is the thing in question ; and therefore must not be taken for a common ground . Wee grant that the Earth is firme and stable from all such motions whereby it is jogged or uncertainly shaken . 1 For the authoritie of those Divines , which hee urges for the interpretation of these Scriptures ; this will be but a weake Argument against that opinion which is already granted to bee a Paradox . 2 The Scriptures themselves , in their right meaning , will not at all conduce to the present purpose . As for that in Isaiah , if wee consult the cohaerence , wee shall finde that the scope of the Prophet is to set forth the Glory of the Church triumphant . Wherein ( hee sayes ) there shall not bee any need of the Sunne or Moone , but Gods presence shall supply them both : For the Lord shall be unto thee an everlasting Light , and thy God thy glory , ver . the nineteenth , and as for this Sunne and Moone , it shall not goe downe , or withdraw it selfe : but hee shall bee an everlasting Light without intermission . So that 't is evident hee speakes of that Light which shall hereafter bee , in stead of the Sunne and Moone . As for that in the Revelations , wee yeeld , that time shall cease ; but to say that this depends upon the cessation of the Heavens , is to beg the question , and to suppose that which is to be proved , viz. that time is measured by the motion of the Heavens , & not of the Earth . * Perrerius ( from whom this last argument was borrowed without acknowledgement ) might have told him in the very same place , that time do's not absolutely , and universally depend upon the motion of the Heavens , sed in motu & successione , cujuslibet durationis , but in any such succession , by which duration may be measured . As for that in the Romans , wee say , that there are other vanities to which the Heavenly Bodies are subject : As first , unto many changes and alterations , witnesse those Comets , which at severall times have been discerned amongst them ; and then likewise to that generall corruption , in which all the creatures shall be involved at the last day . When they shall passe away with a great noise , and the Elements shall melt with fervent heate . Thus you see , there is not any such invincible strength in these arguments , as might cause the Author of them to triumph before hand with any great noise of victory . Another Objection like unto these is taken from the Etymologie of severall words . Thus the Heavens are called Aethera , ab 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 because they are alwaies in motion , and the Earth Vesta , quia vi stat , because of it's immobilitie . To which I answer : 'T were no difficult matter to finde such proofes for this opinion , as well as against it . Thus wee may see that the Hebrew word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 is derived from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 quia currit ; and Terra , non quod terratur , sed quod perenni cursu omnia terat , saith Calcagnius . However , though wee suppose the Etymology to be never so true and genuine ; yet it can at the best but shew what the more common opinion was of those times when such names were first imposed . But suppose all this were so , That the Earth had such a diurnall revolution ; yet how is it conceivable that it should at the same time have two distinct motions . I answer : This may easily bee apprehended , if you consider how both these motions doe tend the same way from West to East . Thus a Bowle being turned out of the hand , ha's two motions in the Aire ; one , whereby it is carried round ; the other , whereby it is cast forward . From what hath been delivered in this Chapter , the indifferent Reader may gather some satisfaction for those Arguments which are usually urged against this diurnall motion of the Earth . PROP. IX . That it is more probable the Earth do's move , than the Sun or Heavens . AMongst those many Arguments that may bee urged for the confirmation of this truth , I shall set down only these five . 1 If we suppose the Earth to be the cause of this motion , then will those vast and glorious Bodies of the Heavens be freed from that inconceivable , unnaturall swiftnes , which must otherwise bee attributed unto them . For if the diurnall revolution be in the Heavens , then it will follow according to the common Hypothesis , that each Starre in the Equator must in every houre move at the least 4529538 Germane miles . So that according to the observation of * Cardan , who tels us , that the pulse of a well tempered man do's beat 4000 times in an houre ; one of these Starres in that space , whilst the pulse beats once , must passe 1132 Germane miles ( saith Alphraganus : ) Or according to Tycho 732 Germane miles . But these numbers seem to be somwhat of the least ; and therefore many others doe much inlarge them , affirming that every Starre in the Equator , in one beating of the pulse , most move 2528 of these miles . 'T is the assertion of † Calvius , that though the distance of the Orbs , and so consequently their swiftnesse , seeme to be altogether incredible ; yet it is rather farre greater in it self , than Astronomers usually suppose it ; & yet ( saith he ) according to the common grounds , every star in the Equator , must move 42398437½ miles in an houre . And though a man should constantly travel 40 miles a day ; yet he would not be able to goe so far as a Star do's in one houre , under 3904 yeares : Or if wee will suppose an Arrow to bee of the same swiftnesse , then must it compasse this great Globe of Earth and Water 1884 times in an hour . And a Bird that could but fly as fast , might go round the World seven times in that space , whilest one could say , Ave Maria , gratia plena , Dominus tecum . Which though it be a pretty round pace ; yet you must conceive that all this is spoken onely of the eighth Sphaere , and so being compared to the swiftnesse of the primum mobile , is but a slow and heavy motion . For ( saith the same author ) the thicknesse of each Orbe is equall to the distance of it's concave superficies from the centre of the Earth . Thus the Orbe of the Moone do's containe as much space in it's thicknesse , as there is betwixt the neerest parts of that and the centre . Thus also the eighth Sphaere is as thicke as that whole space betwixt the centre of the Earth , and it 's owne concave superficies . So likewise must it be in those three other Orbes , which he supposes to bee above the Starry Heaven . Now if we proportion their swiftnesse according to this difference in their bignesse , you may then conceive ( if you can ) what a kinde of celeritie that must be , by which the primum mobile wil be whirled about . Tycho makes the distance of the Stars to bee much lesse , and their motion flower ; and yet hee is faine to confesse , that it is omni cogitatione celerior . Clavius likewise speaking concerning the swiftnesse of the Starry Orbe , do's acknowledge , Quod velocitas ejus captum humani ingenij excedit . What then could he thinke of the primum mobile ? Dr Gilbert being ( it seems ) astonished at the consideration of this strange swiftnesse , sayes of it , that it is motus supra omnes cogitationes , somnia , fabulas & licentias poeticas insuperabilis , ineffabilis , incomprehensibilis . A man may more easily conceive the possibilitie of any Fable or Fiction how Beasts and Trees might talke together , than how any materiall Body should bee moved with such a swiftnesse . Not but that 't is possible for God to turne them about with a farre greater velocitie . Nay 't is possible for Art to contrive a motion , which shall be equally slow in that proportion as this is swift . But however , the question here , is not what can be done , but what is most likely to be don according to the usuall course of Nature . 'T is the part of a Philosopher , in the resolution of naturall events , not to fly unto the absolute Power of God , and tell us what he can doe , but what according to the usuall way of Providence , is most likely to be done , to find out such causes of things , as may seem most easy & probable to our reason . If you ask what repugnancy there is in the Heavens , unto so great a swiftnes : we answer , Their being such vast , materiall condensed substances , with which this inconceivable motion cannot agree . Since Motion and Magnitude are two such Geometricall things , as beare a mutuall proportion to one another ; therefore it may seeme convenient , that slownesse should be more agreeable to a great Body , and swiftnes to a lesser : and so it would bee more consonant to the Principles of Nature , that the Earth , which is of a lesser quantitie , should be appointed to such a motion as is somewhat proportionable to it's bignes , than that the Heavens that are of such a vast magnitude , should bee whirled about with such an incredible swiftnes , which do's as farre exceed the proportion of their bignesse , as their bignesse do's exceed this Earth , that is but as a point or centre to them . 'T is not likely that nature in these constant and great workes , should so much deviate from that usual harmony and proportion which she observes in lesser matters . If this Globe of Earth onely were appointed to move every day round the Orbe of the fixed Starres , though it be but a little Body , and so more capable of a swift motion ; yet that swiftnesse would be so extremely disproportionable unto it , that wee could not with reason conceive it possible , according to the usuall course of nature . But now that the Heavens themselves , of such strange bignesse , with so many Starres , which do so farre exceed the magnitude of our Earth , should bee able to turne about with the same celeritie : Oh 't is altogether beyond the fancy of a Poet or a mad man. For answer unto this Argument , our adversaries tell us , that there is not in the Heavens any repugnancie to so swift a motion ; and that whether wee consider the nature of those Bodies , or secondly , the swiftnesse of this motion . 1 For the nature of those Bodies , either their Qualities . Quantity . 1 There is not in them the Qualities of lightnesse or heavinesse , or any the least contrarietie that may make them reluctant to one another . 2 Their magnitude will helpe them in their swiftnesse : For the greater any body is , the quicker will it be in it's motion , and that not onely when it is moved by an inward Principle , as a milstone will descend faster than a little pibble ; but also when it 's motion do's proceed from some externall Agent , as the Winde will drive a great Cloud , or a heavy Ship , when it is not able to stir a little Stone . 2 As for the swiftnesse of this motion , the possibilitie of it may be illustrated by other particulars in Nature : As , 1 The sound of a Cannon , in a little time is carried for twenty miles distance . 2 Though a Starre bee scituated so remotely from us ; yet the Eye discerns it in a moment , which is not without some motion , either of the Species of the Starre , or the Rayes of the Eye . Thus also the Light do's in an instant passe from one side of the Heaven to another . 3 If the force of Pouder be able to carry a Bullet with so great a swiftnesse , we need not doubt then , but that the Heavens are capable of such a celeritie , as is usually attributed unto them . Vnto these it may be answered : 1 Where they say that the heavenly Bodies are without all gravitie , wee grant it , in the same sence as our Earth also , being considered as whole , and in it's proper place , may bee denied to bee heavy : since this qualitie in the exactest sence ; can onely bee ascribed unto such parts as are severed from the whole to which they belong . But however , since the Heavens or Stars are of a materiall substance , 't is impossible but there should bee in them some ineptitude to motion ; because matter is of it selfe a dull and sluggish thing ; and by so much the more , as it is kept close and condensed together . And though the followers of Ptolomey doe with much confidence deny the Heavens to be capable of any reluctancie to motion ; yet it were easie to prove the contrary out of their owne Principles . 'T is not conceivable , how the upper Sphaere should move the nether , unlesse their Superficies were full of rugged parts ( which they deny : ) or else one of the Orbes must leane upon the other with it's weight , and so make it partake of it's owne motion . And besides , they tell us , that the farther any Sphaere is distant from the primum mobile , the lesse is it hindered by that in it's proper course , and the sooner do's it finish it 's owne revolution . From whence it will easily follow , that these Bodies have resistency from one another . I have often wondred , why amongst the inchanted Buildings of the Poets , they have not fained any Castle to bee made of the same materials with the sollid Orbs , since in such a fabrick there would have been these eminent conveniences . 1 It must needs be very pleasant , by reason of it's perspicuitie , because it is more diaphanous than the Aire it selfe , and so the Walls of it could not hinder the prospect any way . 2 Being so solid and impenitrable , it must needs be excellent against al violence of weathers , as also against the assaults of the enemy , who should not be able to breake it with the most furious batteries of the Ram , or pierce it with any Cannon shot . 3 Being void of all heavinesse , a man may carry it up and downe with him , as a Snaile do's his House : and so whether hee follow the enemy , or fly from him , hee ha's still this advantage , that he may take his castle and defence along with him . But then againe , there are on the other side as many inconveniences . For , 1 It's perspicuitie would make it so open , that a man should not bee able to retire himselfe into any private part of it . And then , 2 Being so extremely sollid , as wel as invisible , a man should be stil in danger of knocking his head against every Wall and Pillar ; unlesse it were also intangible , as some of the Peripatetickes affirme . 3 It 's being without all gravitie , would bring this inconvenience , that every little puffe of wind would blow it up and downe ; since some of the same sect are not ashamed to say , that the Heavens are so utterly devoid of heavinesse , that if but a little Fly should justle against the vast frame of the Coelestiall Sphaeres , hee would move them out of their places . A strong fancy , that could bee at leisure , might might make excellent sport with this Astronomicall fiction . So that this first evasion of our Adversaries , will not shelter them from the force of that Argument , which is taken from the incredible swiftnes of the Heavens . 2 Whereas they tell us in the second place , that a bigger Body , as a Milstone , will naturally descend swifter than a lesse , as a Pibble . I answer : This is not because such a great Body is in it selfe more easily movable ; but because the bigger any thing is which is out of it 's owne place , the stronger will bee it 's naturall desire of returning thither , and so consequently , the quicker it's motion . But now those Bodies that move circularly , are alwayes in their proper scituations , and so the same reason is not applyable unto them . And then , whereas 't is said that Magnitude do's alwayes adde to the swiftnesse of a violent motion ( as Winde will move a great Shippe sooner than a little Stone : ) Wee answer , This is not because a Shippe is more easily movable in it selfe than a little Stone : For I suppose the Objector will not thinke hee can throw the one as farre as the other ; but because these little Bodies are not so liable to that kinde of violence from whence their motion do's proceed . As for those instances which are cited to illustrate the possibilitie of this swiftnesse in the Heavens , wee answer : The passage of a sound is but very slow in comparison to the motion of the Heavens . And then besides , the swiftnesse of the Species of sound or sight , which are accidents , are not fit to infer the like celeritie in a materiall substance : and so likewise for the Light which * Aristotle himselfe , and with him the generalitie of Philosophers , doe for this very reason prove not to bee a Body , because it moves with such swiftnesse , of which ( it seemes ) they thought a Body to bee incapable . Nay , the † Objector himselfe in another place , speaking of Light in reference to a substance , do's say : Lumen est accidens , sic species rei visae , & alia est ratio substantiarum , alia accidentium . To that of a Bullet , wee answer : Hee might as well have illustrated the swiftnes of a bullet , which wil passe 4 or 5 miles in 2 minutes , by the motion of a hand in a Watch , which passes 2 or 3 inches in 12 houres ; there being a greater disproportion betwixt the motion of the heavens , and the swiftnes of a Bullet , than there is 'twixt the swiftnes of a bullet , and the motion of a hand in a watch . Another Argument to this purpose may be taken from the chiefe end of the Diurnall and Annuall motions , which is to distinguish betwixt Night and Day , Winter and Summer ; and so consequently , to serve for the commodities and seasons of the habitable World. Wherfore it may seeme more agreeable to the Wisedome of Providence , for to make the Earth as well the efficient , as the finall cause of this motion : Especially since nature in her other operations do's never use any tedious difficult means to performe that which may as well bee accomplished by shorter and easier wayes . But now , the appearances would be the same , in respect of us , if only this little point of Earth were made the subject of these motions , as if the vast Frame of the World , with all those Stars of such number and bignes were moved about it . 'T is a common Maxime , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Nature do's nothing in vaine , but in all her courses do's take the most compendious way . 'T is not therefore ( I say ) likely , that the whole Fabricke of the Heavens , which do so much exceed our Earth in magnitude and perfection , should bee put to undergoe so great and constant a Worke in the service of our Earth , which might more easily save all that labour by the circumvolution of it's owne Body ; especially , since the Heavens doe not by this motion attaine any farther perfection for themselves , but are made thus serviceable to this little Ball of Earth . So that in this case it may seeme to argue as much improvidence in nature to imploy them in this motion , as it would in a * Mother , who in warming her Childe , would rather turne the fire about that , than that about the sire : Or in a † Cook , who would not rost his Meat by turning it about to the fire ; but rather , by turning the fire about it : * Or in a man , who ascending some high Tower , to save the labour of stirring his head , should rather desire that all the Regions might successively bee turned before his eye , that so hee might easily take a view of them . Wee allow every Watch-maker so much wisdome as not to put any motion in his Instrument , which is superfluous , or may bee supplied an easier way : and shall wee not thinke that Nature ha's as much providence as every ordinary Mechanicke ? Or can wee imagine that She should appoint those numerous and vast Bodies , the Stars , to compasse us with such a swift and restlesse motion , so full of confusion and uncertainties , when as all this might as well be done by the revolution of this little Ball of Earth ? Amongst the severall parts of the World , there are six Planets which are generally granted to move . As for the Sun and the Earth , and the fixed Starres , it is yet in question , which of them are naturally indowed with the same condition . Now common reason will dictate unto us , that motion which is most agreeable to that which in kind and properties is most neer to those Bodies that undoubtedly are moved . But now there is one eminent qualification , wherin the Earth do's agree with the Planets ; wheras the Sun , together with the fixed stars , do in the same respect differ from them : and that is Light , which all the Planets and so too the Earth , are fain to borrow elswhere , whilest the Sun and the Stars have it of their owne . From whence it may bee probably concluded , that the Earth is rather the subject of this motion than the other . To this it may be added , that the Sun and Stars seem to be of a more excellent Nature than the other parts of the World ; and therfore should in reason be indowed with the best qualifications . But now motion is not so noble a condition as rest . That is but a kind of wearisome and servile thing ; wheras , this is usually ascribed to God himself : Of whom 't is said : * Immotus stabilisque manens dans cuncta moveri . † Aristotle tells us , 't is very agreeable to reason that the time appointed for the revolution of each Orbe , should be proportionable to it's bignesse . But now this can onely be by making the Earth a Planet , and the subiect of the annuall and diurnall motions . Wherefore 't is probable , that this do's rather move than the Heavens . According to the common Hypothesis , the primum mobile will move round in a day . Saturne in thirty yeares . Iupiter in twelve . Mars in two . The Sunne , Venus , and Mercury , which have severall Orbes , yet will agree in their revolutions , being each of them about a yeare in finishing their courses : Whereas by making the Earth a Planet , there will be a just proportion betwixt the bignesse of the Orbes , and the time of their motions : For then , next to the Sunne or Centre , there will be the Sphaere of Mercury ; which as it is but narrow in it's diameter , so likewise is it quick in it's motion , running it's course in eighty eight days . Venus , that is next unto it , in 224 dayes . The Earth in 365 daies , or a yeare . Mars , in 687 dayes . Iupiter in 4332 dayes . Saturne , in 10759 dayes . Thus likewise is it with those Medicean Starres that encompasse Iupiter . That which is lowest amongst them , finishes his course in two and twenty houres ; the next in three dayes and a half ; the third , in seven dayes ; and the farthest in seventeen days . Now as it is ( according to Aristotles confession ) more likely that Nature should observe such a due proportion betwixt the Heavenly Orbes : so is it more probable , that the Earth should move , rather than the Heavens . This may likewise be confirmed from the appearance of Comets : Concerning which , there are three things commonly granted , or if they were not , might be easily proved : namely , 1 That there are divers Comets in the Aire , betwixt the Moone and our Earth . 2 That many of these Comets do seeme to rise and set as the Stars . 3 That this appearing motion is not properly their owne , but communicated unto them from somewhat else . But now , this motion of theirs cannot be caused by the Heavens ; and therefore it must necessarily proceed from the revolution of our Earth . That the Moones Orbe cannot carry along with it the greater part of the aire wherein these Comets are placed , might easily be proved from the common grounds . For the concave Superficies of that Sphaere is usually supposed to bee exactly terse and smooth ; so that the meer touch of it cannot turne about the whole Element of Fire , with a motion that is not naturall unto it . Nor could this Elementarie Fire which they imagine to be of a more rarified and subtle Nature , communicate the same motion to the thicker Aire , and that to the waters ( as some affirme : ) For by what meanes could that smooth Orbe take hold of the adjoyning Aire . To this Sarsius answers , that there are great gibbosities , and mountainous inequalities , in the concavitie of the lowest Sphaere , and by these is it inabled to carry along with it the Fire and Aire . But * Fromondus tels him , Fictitiaista & ad fugam reperta sunt . And yet his owne Conjecture is scarse so good , when hee affirmes , that this motion of the aetheriall Aire , as also of that elementary Aire hard by us , is caused by that ruggednesse which there is in the Bodies of the Planets ; of which opinion wee may with as good reason say as hee sayes to Sarsius : Fictitia ista , & ad fugam reperta ; These things are meere fictions invented for shifts , and without any probable ground . But now this appearance of the Comets may easily be resolved , if wee suppose the earth to move . For then , though they did still remaine in their wonted places ; yet this , by it's diurnall revolution successively with drawing it self from them , they wil appear to rise & set . And therefore , according to this common naturall experiment , it is more probable that the Earth should move , than the Heavens . Another Argument urged by some , to prove that this Globe of Earth is easily movable , is taken from the opinion of those who affirme that the accesse of any weight unto a new place : as suppose an army do's make the Earth poise it selfe afresh , and change the centre of gravitie that it had before : but this is not generally granted ; and therefore not to bee insisted on as a common ground . To this purpose likewise is that inference of Lansbergius , who from Archimedes his saying , that hee could move the Earth , if he knew where to stand and fasten his instrument ; concludes , that the Earth is easily movable ; whereas 't was the intent of Archimedes in that speech , to shew the infinit power of Engines : there being no weight so great , but that an instrument might be invented to move it . Before we finish this Chapter , t is requisite that we enquire what kind of facultie that is from which those motions that Copernicus ascribes unto the Earth , do's proceed . Whether or no it be some Animall Power , that do's assist ( as Aristotle ) or informe ( as Keplar thinks ) or else some other naturall motive qualitie which is intrinsicall unto it . Wee may observe , That when the proper genuine cause of any motion is not obvious , men are very prone to attribute unto that which they discerne to be the most frequent Originall of it in other things , Life . Thus the Stoicks affirme , the Soule of the Water to bee the cause of the ebbing and flowing of the Sea. Thus others thinke the Winde to proceed from the Life of the Aire , whereby it is able to move it selfe severall waies , as other living creatures . And upon the same grounds doe the Platonicks , Stoicks , and some of the Peripateticks , affirme the Heavens to bee animated . From hence likewise it is , that so many do maintaine Aristotle his opinion concerning Intelligences : which some of his followers , the Schoole-men , doe confirme out of Scripture . From that place in Mat. 24. 29. where 't is said , The Powers of the Heaven shall bee shaken . In which words , by Powers ( say they ) are meant the Angels , by whose power it is , that the Heavens are moved . And so likewise in that , Iob , 9. 13. Where the vulgar ha's it , Sub quo curvantur , qui portant orbem ; that is , the Intelligences . Which Text , might serve altogether as well to prove the Fable of Atlas and Hercules . Thus Cajetan concludes from that place in the Psalme , 136. 5. Where 't is said , God by wisdome made the heavens : or according to the vulgar , Qui fecit Coelos intellectu , That the Heavens are moved by an intelligent Soule . If wee consider the originall of this opinion , we shall find it to proceed from that mistake of Aristotle , who thought the Heavens to be Eternall ; and therefore to require such a moving cause , as being of an immateriall Substance , might be exempted from all that wearinesse and inconstancie , which other things are liable unto . But now this ground of his is evidently false , since 't is certain , That the Heavens had a beginning , and shall have an end . However , the imploying of Angels in these motions of the World , is both superfluous , and very improbable . 1 Because a naturall Power , intrinsicall to those Bodies , will serve the turne as well . And as for other operations , which are to bee constant and regular , Nature do's commonly make use of some inwarde Principle . 2 The Intelligences being immateriall , cannot immediatly worke upon a Body . Nor do's any one tell us what Instruments they should make use of in this businesse . They have not any hands to take hold of the Heavens , or turne them about . And that opinion of Aquinas , Dur and , Soncinas , with other School-men , seemes to bee without all reason ; who make the faculty , whereby the Angels move the Orbs , to be the very same with their Vnderstandings and Will : So that if an Angell doe but meerely suspend the Act of willing their Motion , they must necessarily stand still ; and on the contrary , his only willing them to move , shall bee enough to carry them about in their severall courses . Since it were then a needlesse thing for Providence to have appointed Angels unto this businesse , which might have been done as well by the only Will of God. And besides , how are the Orbes capable of perceiving this Will in the Intelligences ? Or if they were , yet what motive Facultie have they of themselves , which can inable them to obey it ? Now as it would bee with the Heavens : so likewise is it with the Earth , which may bee turned about in it's diurnall revolution , without the helpe of Intelligences , by some motive Power of it's owne , that may be intrinsicall unto it . If it be yet enquired , what cause there is of it's annuall motion : I answer , 'T is easily conceivable , how the same Principle may serve for both these , since they tend the same way from West to East . However , that opinion of Keplar is not very improbable , That all the Primary Planets are moved round by the Sunne , which once in twenty five , or twenty six dayes , do's observe a revolution about it's owne Axis , and so carry along the Planets that encompasse it ; which Planets are therefore slower or swifter , according to their distances from him . If you aske by what means the Sunne can produce such a motion ? He answers : By sending forth a kind of Magneticke Vertue in strait Lines , from each part of it's Body ; of which there is alwaies a constant succession : so that as soone as one beame of this vigor ha's passed a Planet , there is another presently takes hold of it , like the teeth of a Wheele . But how can any vertue hold out to such a distance ? He answers : First , as light and heate , together with those other secret influences , which work upon Minerals in the Bowels of the Earth : so likewise may the Sunne send forth a magneticke , motive vertue , whose power may bee continued to the farthest Planets . Secondly , if the Moone , according to common Philosophy may move the Sea , why then may not the Sun move this Globe of Earth ? In such Quaere's as these , wee can conclude only from conjectures that speech of the wise man , Eccl. 3. 11. being more especially verified of Astronomicall questions , concerning the Frame of the whole Vniverse , That no man can finde out the Works of God , from the beginning to the end . Though wee may discerne diverse things in the World , which may argue the infinite Wisedome and Power of the Author ; yet there will bee alwaies some particulars left for our dispute and enquiry , and we shall never bee able with all our industry , to attaine a perfect comprehension of the creatures , or to find them wholly out , from the beginning to the end . The Providence of God having thus contrived it , that so man might look for another Life after this , when all his longing and thirst shall be fully satisfied . For since no naturall appetite is in vain , it must necessarily follow , that there is a possibilitie of attaining so much knowledge as shall bee commensurate unto these desires , which because it is not to be had in this World , it will behove us then to expect and provide for another . PROP. X. That this Hypothesis is exactly agreeable to common appearances . IT hath been already proved , that the Earth is capable of such a scituation and motion , as this opinion supposes it to have . It remaines , that in the last place we shew how agreeable this would bee unto those ordinary seasons of Dayes , Moneths , Yeres , and all other appearances in the Heavens . 1 As for the difference betwixt days and nights : 't is evident , That this may be caused as well by the revolution of the Earth , as the motion of the Sunne ; since the Heavenly Bodies must needs seeme after the same manner to rise and set , whether or no they themselves by their owne motion do passe by our Horizon and Verticall point ; or whether our Horizon and Verticall point , by the revolution of our Earth , doe passe by them . According to that of * Aristotle , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . There will not appeare any difference , whether or no the Eye be moved from the Object , or the Object from the Eye . And therfore I cannot chuse but wonder that a man of any reason or sence should make choise of no better an Argument to conclude his booke withall , than that which were read at the later end of Al. Ross. where he infers , that the Earth do's not move , because then the shadow in a Sunne-diall would not be altered . 2 As for the difference of Moneths , we say , That the diverse illumination of the Moone , the different bignes of her Body , her remaining for a longer or shorter time in the earth's shadow , when she is eclipsed , &c. may well enough be solved by supposing her to move above our Earth , in an Eccentricall Epicycle . Thus , In which kinde of Hypothesis there will bee a double difference of motion . The one caused by the different scituation of the Moones Body in it's owne Eccentricke . The other by the different scituation of the Moons Orbe in the Earth's Eccentricke : which is so exactly answerable to the motions and appearances of this Planet , that from hence Lansbergius drawes an Argument for this Systeme of the heavens , which in the strength of his confidence hee calls , Demonstrationem 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , cui nullâ ratione potest contradici . 4 As for the difference betwixt winter & summer ; betwixt the number and length of days , which appertain to each of those seasons : the seeming motion of the sun from one signe to another in the Zodiack : All this may easily be solved , by supposing the Earth to move in an Eccentricall Orbe about the Sun. Thus , Suppose the Earth to bee at C. then the Sunne at A. will seeme to bee in the signe ♋ and at the greatest distance from us , because the Earth is then in the farthest parts of its Eccentricke . When after by it's Annuall Motion it hath passed successively by the Signes ♒ ♓ ♈ ♉ ♊ at length it comes to the other Solstice at B. where the Sunne will appeare in ♑ and seeme biggest , as being in it's Perigie , because our Earth is then in the neerest part of it's Eccentricke . As for all other Appearances of the Sunne which concerne the Annuall Motion , you may see by the following Figure , that they are exactly agreeable to this Hypothesis . The Axis upon which our Earth do's move , is represented by the Line B. C. which Axis do's alwaies decline from that of the Eclipticke , about 23 degrees , thirty minutes . The Points B. C. are imagined to be the Poles , B. the North Pole , and C. the South . Now if we suppose this Earth to turn about its owne Axis , by a diurnall motion , then every Point of it will describe a paralell Circle , which will be either bigger or lesser , according to it's distance from the Poles . The chiefe of them are the Equinoctiall D. E. The two Tropicks , F. G. and H. I. The two Polar Circles M. N. the Arcticke , and K. L. the Antarcticke : of which , the Equinoctiall only is a great Circle , and therefore will alwaies be equally divided by the Line of Illumination M. L. wheras the other paralels are thereby distributed into unequal parts . Amongst which parts , the diurnall Arches of those that are towards B. the North Pole , are bigger than the Nocturnall , when our Earth is in ♑ and the Sunne appeares in ♋ Insomuch , that the whole Arcticke Circle is enlightened , and there is day for halfe a yeare together under that Pole. Now when the Earth proceeds to the other Solstice at ♋ and the Sunne appeares in ♑ then that Hemisphere must be involved in darknesse , which did before partake of Light. And those paralels towards the North & South Poles will still bee divided by the same inequalitie . But those bigger parts which were before enlightened , will now bee darkened , & vice versa . As when the Earth was in N. the Arcticke Circle M. N. was wholly enlightned , and the Antarcticke , K. L. altogether in the dark . So now , when it is in A. the Antarcticke , K. L. will be wholly in the Light , and the other M. N. altogether obscured . Whereas the Sun before was verticall to the inhabitants at the Tropick F. G. So now is he in the same scituation to those that live under the other Tropicke , H. I. And whereas before the Pole did incline twenty three degrees thirty minutes towards the Sunne , so now do's it recline as much from him . The whole difference will amount to 47 degrees , which is the distance of one Tropicke from the other . But now in the two other Figures , when the Earth is in either of the Equinoctialls ♈ ♎ the Circle of Illumination will passe through both the Poles ; and therefore must divide all the paralels into equall parts . From whence it will follow , that the Day and Night must then bee equall in all places of the World. As the Earth is here represented in ♎ it turnes only the enlightened part towards us : as it is in ♈ wee see it 's nocturnall Hemisphere . So that according to this Hypothesis , wee may easily and exactly reconcile every appearance concerning the difference betwixt Dayes , and Nights , Winter and Summer , together with all those other varieties which depend upon them . If you would know how the Planets ( according to the Systeme of the Heavens ) will appeare Direct , Stationarie , Retrograde ; and yet still move regularly about their owne Centers , you may plainely discerne it by this following Diagram . Where suppose the Sun to be at A. the Circle ( B. G. M. ) to be the Orbe of the Earth's motion , and that above it noted with the same Letters , to bee the Sphaere of Iupiter ; and the uppermost of all , to bee a part of the Zodiacke in the Starry Heaven . Now if you conceive the Letters , BCDEF GHIKLM , and bcdef ghiklm , to divide the Earth's Orb , and that of Iupiter , into severall parts , proportionable to the slownesse or swiftnes of their different motions ( Iupiter finishing his course in twelve yeres , and the Earth in one ) then supposing the Earth to be at the point ( B. ) and Iupiter likewise in his Orbe to bee scituated at ( b ) hee will appeare unto us to be in the Zodiacke at the point ( r. ) But afterwards , both of them moving forward to the Letter ( Cc. ) Iupiter will seeme to be in the Zodiacke at ( v ) as having passed directly forward according to the order of the Signes . And so likewise each of them being transferred to the places ( Dd. ) ( Ee. ) Iupiter will still appeare Direct , and to have moved in the Zodiack unto the Points ( yz . ) But now when the Earth comes to be more immediatly interposed betwixt this Planet and the Sunne ; as when both of them are at the Letter ( Ff. ) then will Iupiter be discerned in the Zodiacke at ( x. ) So that all the while the Earth was passing the Arch ( E F ) Iupiter did still remaine betwixt the Points ( z ) and ( x ) and therefore must seeme unto us as if hee were Stationary ; but afterwards , both of them being carried to ( Gg. ) then Iupiter will appeare at ( s ) as if by a hasty motion he had returned from his former course the space ( x s. ) Both of them passing to ( H h ) this Planet will still seeme to bee swiftly Retrograde , and appeare in the Point at ( p ) but when they come to the Points ( I i. ) Iupiter will then seem to be slower in this motion , and to have onely passed the space ( P n. ) Both of them being transferred to ( K k. ) Iupiter will then appeare in the Zodiacke at ( o ) as being againe Direct , going forward according to the order of the Signes , and while the Earth did passe the Arch ( IK ) Iupiter then remain'd between the points ( n o. ) and so consequently , did againe seeme to bee Stationary . Both of them comming to ( L l. ) & thence to ( M. N. ) Iupiter will still appeare Direct , and to have gone forward in the Zodiacke from ( q ) to ( t. ) So that all the space wherein Iupiter is retrograde , is represented by the Arch ( n z. ) In which space , he himselfe moves in his owne Orbe , the Arch ( e i ) and so the Earth in it's Orbe , a proportionall space ( EI. ) As it hath been said of this Planet , so likewise is it applyable to the other . Saturne , Mars , Venus , Mercury ; all which are thus made to appeare direct , Stationarie , and retrograde , by the motion of our Earth , without the helpe of those Epicycles and Eccentricks , and such unnecessary wheele worke , wherewith Ptolomey hath filled the Heavens . Insomuch that here * Fromondus is faine to confesse , Nullo Argumento in speciem probabiliori , motum terrae annuum a Copernicanis astrui , quam illo stationis , directionis , regressionis Planetarum . There is not any more probable Argument to prove the annuall motion of the Earth , than it's agreeablenesse to the station , direction , and regression of the Planets . Lastly , that Copernicus his Systeme of the Heavens , is very answerable to the exactest observations , may bee manifest from this following description of it . Suppose the Sunne to be scituated at A. Now because Mercury is found by experience to be alwaies very neere the Sunne , so that he do's for the most part lye hid under his Raies . As also because this Planet hath a more lively vigorous Light than any of the other ; therefore wee may inferre , that his Orbe is placed next unto the Sunne , as that at B. As for Venus , 't is observed , That She do's alwaies keep at a set distance from the Sunne , never going from him above forty degrees or thereabouts ; that her Body appeares through the perspective to be forty times bigger at one time than at another ; that when She seemes biggest and neerest unto us , wee then discerne her as being perfectly round . Therefore doth this Planet also move in a Circle that incompasses the Sun. Which Circle do's not containe the Earth within it ; because then , Venus would sometimes be in opposition to the Sunne ; whereas , 't is generally granted , that She never yet came so far as to be in a Sextile . Nor is this Circle below the Sun ( as Ptolomey supposeth ) because then this Planet , in † both it's Conjunctions , would appeare horned , which She do's not . Nor is it above the Sunne , because then She would alwaies appeare in the Full , and never Horned . From whence it will follow , that this Orbe must necessarily bee betwixt the Earth and the Sunne ; as that at C. As for Mars : 't is observed , That hee do's appeare sixty times bigger when he is neer us , than at his greatest distance ; that he is sometimes in opposition to the Sunne . From whence we may conclude , that his Orbe do's containe our Earth within it . 'T is observed also , that he do's constantly appeare in the Full , and never Horned ; from whence likewise it is manifest , that the Sunne is comprehended within it's Orbe , as it is in that which is represented by the Circle , E. And because the like appearances are observed in Iupiter and Saturne ( though in lesse degrees ) therefore wee may with good reason conceive them to be in the Heavens , after some such maner as they are here set downe in the Figure , by the Circles , F. G. As for the Moone : because Shee is sometimes in opposition to the Sunne ; therefore must her Orbe comprehend in it the Earth : because She appeares dark in her Conjunction , and sometimes eclipses the Sunne ; therefore that must necessarily be without her Orbe , as it is in that Epicycle at H. In the Centre of which , the Earth must necessarily bee scituated according to all those appearances mentioned before . So that the Orbe of it's annuall motion , will bee represented by the Circle D. All which appearances , cannot so well be reconciled by Ptolomey , Tycho , Origanus , or by any other Hypothesis , as by this of Copernicus . But the application of these to the severall Planets , together with sundry other particulars , concerning the Theoricall part of Astronomy , you may see more fully set downe by those who have purposely handled this subject , Copernicus , Rheticus , Galilaeus ; but more especially Keplar : nnto whom I doe acknowledge my selfe indebted for sundry particulars in this discourse . I have done with that which was the chiefe purpose of the present Treatise ; namely , the removall of those common prejudices that men usually entertaine against this opinion . It remaines , that by way of conclusion , I endeavour to stirre up others unto these kind of Studies , which by most men are so much neglected . 'T is the most rationall way , in the prosecution of severall Objects , to proportion our love and endeavour after every thing , according to the excellencie and desireablenesse of it . But now , amongst all Earthly Contentments , there is nothing either better in it selfe , or more convenient for us , than this kind of Learning ; and that , whether you consider it according to it's generall Nature , as a Science ; or according to it 's more speciall Nature , as such a Science . 1 Consider it as a Science . Certaine it is , that amongst the varietie of Objects , those are more eligible which conduce unto the welfare of that which is our best part , our Soules . 'T is not so much the pleasing of our sences , or the increasing of our Fortunes , that do's deserve our industry , as the information of our Iudgements , the improvement of our Knowledge . Whatever the World may thinke ; yet it is not a vast Estate , a Noble Birth , an eminent place , that can adde any thing to our true reall Worth ; but it must be the degrees of that which makes us Men , that must make us better Men , the endowments of our Soule , the enlargement of our Reason . Were it not for the contemplation of Philosophy , the heathen * Seneca would not so much as thanke the gods for his Being . Nisi ad haec admitterer non fuit opere pretium nasci . Detrahe hoc inestimabile bonum , non est vita tanti , ut sudem , ut aestuem . Take but away this benefit , & he would not thinke Life worth the sweating for . So much happinesse could hee discerne in the Studies of Nature . And therfore as a Science in generall , it may very well deserve our Love and Industry . 2 Consider it as such a particular Science , Astronomy : the Word signifies the Law of the Stars ; and the Hebrewes ( who doe not ordinarily admit of composition ) call it in two words , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Coelorum statuta , or the Ordinances of Heaven ; because they are governed in their courses by a certain rule , as the Psalmist speaks in the hundred forty eighth Psa. ve . 6. God ha's given them a Law which shall not be broken . Now this of all naturall Sciences may best of all challenge our Industry ; and that , whither you consider it , 1 Absolutely , as it is in it selfe : or , 2 As it stands in reference to us . 1 As it is in it selfe . The excellencie of any Science may be judged of ( saith the Philosopher ) first , by the excellency of the Object . Secondly , by the certaintie of it's demonstrations . 1. For the Object . It is no lesse than the whole World ( since our Earth also is one of the Planets ) more especially those vast and glorious Bodies of the Heavens . So that in this respect , it far exceeds all those barren , empty speculations , about Materia prima , and Vniversale , and such like cob webs of learning ; in the study of which , so many doe misplace their younger yeares . And for the same reason likewise is it to be preferr'd before all those other Sciences , whose subjects are not either of so wide an extent , or so excellent a Nature . 2 For the demonstrations of Astronomy , they are as infallible as truth it self ; and for this reason also do's it excel all other knowledge , which do's more depend upon conjectures & uncertaintie . They are onely those who want skill in the Principles of this Science , that mistrust the conclusions of it . Since therefore in these respects , it is one of the most excellent Sciences in Nature , it may best deserve the industry of Man , who is one of the best Works of Nature . Other creatures were made with their Heads and Eies turned downwards : would you know why man was not created so too ? why it was , that he might be an Astronomer ? Os hominum sublime dedit , Celumque tueri Iussit , & erectos ad Syder a tollere vultus . God gave to man an upright face , that he Might view the stars , & learn astronomy . 2 Consider it in reference to us , and so it is , 1 Most Vsefull . 2 Most Pleasant . 1 Most usefull , and that in sundry respects . It proves a God and a Providence , and incites our hearts to a greater admiration and feare of his omnipotencie . We may understand by the Heavens , how much mightier he is that made them ; for by the greatnesse and beauty of the creatures , proportionably the Maker of them is seene , saith the booke of Wisdome , 13. 4. 5. Itwas hence that Aristotle did fetch his chiefe Argument to prove a primus motor . 'T was the consideration of these things that first led Men to the knowledge & worship of God ( saith * Tully . ) Haec nos primum ad Deorum cultum , tum ad modestiam , magnitudinemque animi erudivit . And therefore when God by the Prophet would convince the people of his Deitie , he bids them lift up their eyes on high ; and behold who hath created those things that bringeth out their Host by number , that calleth them all by their Names , &c. Isa. 40. 26. which occasioned that saying of Lactantius : Tanta rerum magnitudo , tanta dispositio tanta in servandis ordinibus , temporibusque constantia ; non potuit aut olim sine provido artifice oriri , aut constare tot saeculis sine incolapotente , aut perpetuum gubernari sine perit● & sciente rectore , quod ratio ipsa declarat . Such a great order and constancy amongst those vast Bodies , could not at first be made but by a wise Providence , nor since preserved without a powerfull Inhabitant , nor so perpetually governed without a skilfull guide . True indeed , an ordinary view and common apprehension of these Coelestiall Bodies , must needs manifest the Excellencie & Omnipotencie of their Maker ; but yet a more accurate and diligent enquiry into their Natures , will raise our Vnderstandings unto a neerer Knowledge , and greater Admiration of the Deitie . As it is in those inferiour things , where the meere outside of a Man , the comelinesse and majesty of his countenance , may bee some Argument from whence to inferre the excellencie of his Creator . But yet the subtle Anatomist , who searches more deeply into this wonderfull structure , may see a cleerer evidence for this in the consideration of the inward Fabricke , the muscles , nerves , membranes , together with all those secret contrivances in the Frame of this little World. Thus also is it in the great Vniverse , where the common apprehension of things is not at all considerable , in comparison to those other discoveries , which may bee found out by a more exact enquiry . As this Knowledge may conduce to the proving of a God , and making Men religious ; so likewise may it serve to confirme unto us the Truth of the Holy Scriptures : since the sacred Story , in the order of it's narrations , do's so exactly agree with the conversions of Heaven , and Logisticall Astronomy . It may also stirre us up to behave our selves answerably unto the noble and divine nature of our Souls . When I consider the Heaven , the Workes of thy fingers , the Moone and the Starres which thou hast ordained , what is Man , that that thou art so mindfull of him ? as to create such vast glorious Bodies for his service . Againe , when I consider with my self the strange immensitie and bignesse of this great Vniverse , in comparison to which , this Earth of ours is but as an undiscernable point : When I consider that I carry a Soule about me , of far greater worth than all this , and desires that are of a wider extent and more unbounded capacity than this whole Frame of Nature ; Then mee thinks it must needs argue a degeneratenesse and poverty of Spirit , to busie my Faculties about so ignoble , narrow a subject as any of these earthly things . What a folly is it in Men to have such high conceits of themselves , for some small possessions which they have in the World above others , to keep so great a bussle about so poore a matter . Hoc est punctum quod inter tot gentes ferro & igni dividitur . 'T is but a little point which with so much adoe is distributed unto so many nations by fire and sword . What great matter is it to be Monarch of a small part of a point ? Might not the Ants as well divide a little Mole-hill into diverse Provinces , and keep as great a stir in disposing of their government ? Punctum est illud in quo navigat is , in quo bellatis , in quo regna dìsponitis . All this place wherin we warre ; and travell , and dispose of Kingdomes , is but a point far lesse than any of those small stars , that at this distance are scarse discernable . Which when the Soule do's seriously meditate upon , it will begin to despise the narrownesse of it's present habitation , and thinke of providing for it selfe a mansion in those wider spaces above , such as may bee more agreeable to the noblenesse and divinity of it's Nature . Why should any one dreame of propagating his name , or spreading his report through the World ? when as though he had more glory than ambition can hope for ; yet as long as all this habitable earth is but an inconsiderable point , what great matter can there be in that fame which is included within such strait contracted limits ? Quicunque solam mente praecipiti petit Summumque credit gloriam , Late patentes aetheris cernat plagas , Arctumque terrarum situm . Brevem replere non valentis ambitum , Pudebit aucti nominis . He that to honour only seeks to mount , And that his chiefest end doth count ; Let him behold the largenes of the skies , And on the strait Earth cast his eyes ; He will despise the glory of his Name , Which cannot fill so small a Frame . Why should any one be taken up in the admiration of these lower outsides , these earthly glories ? Respicite Coeli spatium , firmitudinem , celeritatem , & aliquando desinite vilia mirari . Hee that rightly understands the nature of the Heavens , will scarse esteem any other thing worth his notice , much lesse his wonder . Now when wee lay all this together , that he who hath most in the World , hath almost nothing of it ; That the Earth it selfe , in comparison to the Vniverse , is but an inconsiderable point ; and yet that this whole Vniverse do's not beare so great a proportion to the Soul of man , as the earth do's unto that : I say , when a man in some retired thoughts shall lay all this together , it must needs stir up his spirits to a contempt of these earthly things , and make him place his love & endeavour upon those comforts that may be more answerable to the excellency of his nature . Without this Science , what traffick could wee have with forreine Nations ? What would become of that mutuall Commerce , whereby the World is now made but as one Common-wealth ? Vosque medijs in aquis Stellae , pelagoque timendo , Decretum monstrastis iter , totique dedistis , Legibus inventis hominum , commercia mundo . 'T is you bright Stars , that in the fearfull Sea Doe guid the Pilot through his purpos'd way . 'T is your direction that doth commerce give , With all those men that through the World doe Live. 2 As this Science is thus profitable in these and many other respects : so likewise is it equally pleasant . The eye ( saith the Philosopher ) is the sence of pleasure , and there are no delights so pure and immateriall as those which enter through that Organ . Now to the understanding which is the eye of the soul , there cannot be any fairer prospect , than to view the whole Frame of Nature , the fabrick of this great Vniverse , to discern that order & comlinesse which there is in the magnitude , situation , motion of the severall parts that belong unto it ; to see the true cause of that constant variety and alteration which there is in the different seasons of the yeare . All which must needs enter into a mans thoughts , with a great deale of sweetnes and complacency . And therfore it was that Iulius Caesar in the broiles and tumult of the camp , made choise of this delight : — Media interpraelia semper , Stellarum , Coelique plagis , superisque vacavit . He alwaies leisure found amidst his Wars , To mark the coasts of heav'n , and learn the stars . And for this reason likewise did Seneca amidst the continuall noise & bussle of the Court , betake himselfe to this recreation : O quam iuvabat , quo nihil maius , parens Natura gennit , operis immensi artifex , Coelum intueri Solis , & currus sacros Mundique motus , Solis alternas vices , Orbemque Pheobes , astra quem cingunt vaga Lateque fulgens aetheris magni decus . O what a pleasure was it to survay Natures chief work , the heavens ; where we may View the alternate courses of the Sun , The sacred Chariots , how the World do's run : The Moons bright Orb , when shee 's attended by Those scattered stars , whose light adorns the sky . And certainly those eminent men who have this way bestowed a great part of their imployment , such as were Ptolomey , Iulius Caesar , Alphonsus King of Spain , the noble Tycho , &c. have not only by this means pitched upon that which for the present was a more solid kind of pleasure and contentment ; but also a surer way to propagate their memories unto future ages . Those great costly Pyramides which were built to perpetuate the memory of their founders , shall sooner perish and moulder away into their primitive dust , than the names of such Worthies shall bee forgotten . The monuments of learning are more durable than the Monuments of Wealth or Power . All which encouragements may bee abundantly enough to stir up any considering man , to bestow some part of his time in the study and inquisition of these Truths . Foelices animae , quibus haec cognoscere primum , Inque domos superas scandere cura fuit . FINIS . Faults escaped at the Presse in the second Booke . IN the Epistle line 11. read prae monish . Prop. 4. read words for grounds . page 3. line 18. r. probable for possible . p. 4. l. 15. r. obsolete for absolute . l. 20. r. as to take up every thing for Canonical p. 8. l. 7. r. things for times . p. 16. l. 10. r. move amongst the rest . p. 17. l. 4. Philolaus . p. 18. l. 20. Prutenicall . p. 22. l. 7. marg . 6. Consid. p. 26. l. 8. Scho●bergius . p. 34. l. 14. pravity for variety . p. 38. l. 8. imply for imploy . p. 42. l. 22. signe for figure . p. 43. l. 14. rather for either . p. 58. l. 7. this for a. l. 8. product for quotient . p 59. l. 6. is for as . p. 70. l. 20. severall for generall . p. 72. l. 13. Shall fall from . p. 83. l. 18. tosse for crosse . l. 27. from for with . p. 86. l. 8. Sea for Sun. l. 16. in for on . p. 90. l. 7. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . p. 94. l. 3. with for of . p. 97. l. 4. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 l. 24. dimoveria loco , ubi collocata sunt . p. 100. l. 5. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 l. 13. if for as p. 101. l. 16. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ab 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 p. 104. 3. cum for cur . l. 4. gulae for vulgae . p. 109. l. 6. false for foolish . l. 12. as for in it 's . p. 114. l. 25. about that for above the. p. 115. l. 10. in one of these three . p. 120. l. 22. words for Worlds . p. 123. l. 15. seconds for cubits . p. 130. l. 26. lately bin . p. 133. l. 8. conveniences . p. 134. l. 4. Epicycles . l. 6. Deferents . p 153. l. 10. unus . p. 159. l. 21. might only . p. 160. l. 12. motions for notions . p. 166. l. 11. one second . p. 187. l. 16. say for see . p. 190. l. 12. must for most . p. 205. l. 1. motion is . p. 228. l. 23. r. ( M m ) for ( M N ) p. 237. l. 17. r. O● homini . p. 236. l. 3. r. of all other naturall . Place this against the first Page . Notes, typically marginal, from the original text Notes for div A15364-e420 Mytholog . lib. 3 c. 17. Lib. 7. c. 1. Vid. loseph . Acosta . de nat . novi orbis lib. 1. cap. 1. De civit . Dei. lib. 16. cap. 9. Institut . l. 3. c. 24. De ratione temporum , Cap. 32. De nat . rerum , Lib. 1. Comen ▪ ìn 1. Cap. Gen. Psal. 24. 2. Comment . in 1. Genes . 1 Tim. 2. 4 Mat. 28. 19 Aventinus Annal. Boiorum . lib. 3. Annal. Eccles . A. D. 748. In vita Paul. Aen●il . Metam . Lib. 4. Iuven. Sat. 6. Nat. Hist. Lib. 2. c. 12. Turinens . Episc. LIB . 1. Cap. 2. De Coelo l. 1. c. 8. 9. Ibid. De operibus Dei. part . 2. lib. 2. cap. 2. De Coelo l. 1. c. 9. q. 1. Metaphys . l. 12. c. 8. Diog. Laert. lib. 3. Nic. Hill. de Philosop . Epic. partic 379. Plutarch . de tranq . anim . Iuvenal . Apologia pro Galilaeo . Ethic. l. 1. c. 6. Rev. 16. 4. Part 1. Q. 47. Art. 3. Annal. Eccl. A. D. 748. Ibid. De Phaenom in orbe Lunae . Iob 38 7. Isai. 14. 12. Fromond . Vesta . t. 3. cap. 2. So 2 Reg. 23. 5. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Which is interpreted both for the planets & for the 12 signes . Keplar . introduct . in Mart. In Epist. ad Gilbert . Calvin in 1 Gen. Com. in 1 Gen. 11. Part 1. Q. 68. Art. 3. Epist. 139. ad Cypri . So Pererius in 2 Gen. Gen. 1. 16. Gen. 11. Mala. 3. 10. Sir Walter Rawly c. 7. sect . 6. * Deut. 11. 17. 1 Reg. 3. 35 Luk. 4. 25. l. 2. in Gen. Psal. 136. 6 Hexamer . lib. 2. Item . Basil. Hom. 3. in Genes . Wisd. 2. 4. 17. 5. Ecclus. 43. 3. 4. Com. in c. 1. Gen. Cusanus dc doct . ignor . l. 2. c. 12. Comment . in Gen. Qu. 19. Art. 2. LIB . I. Cap. 3. De Coelo li. 1. cap. 2. * Colleg. Connimb . de coeto . l. 1. c. 2. q. 6. art . 3. In Hexam . lib. 4. Enarrat . in Genes . art . 10. In opere 6. dierum . disput . 5. In lib. de Mundi constit . 2 Pet. 3. 12 By Doctor Hakewill . Ap. l. lib. 2. Plutarch . de plac . philos . l. 2. c. 17. Nat Hist. l 2. c. 9. Nat. quaest . lib. 2. cap. 5 1. Apostcl . De caelo . l. 1. c. 3. De coelo . l. 2 cap. 3. Lib. 4. par . 2 cap 24. 35. Isa. 51. 6. Ant. lect . l. 1. c. 4. Hist. nat . l. 2. c. 11. 13. In lib sup . ● . Gen. ad lit . Lib. 4 p. 11. 2. cap 7. 26 30. De stella l. 15. 72. l. 1. c. 9. De somniis . LIB . 1. Cap. 4. a De coelo . l. 2. com . 49 b Ant. lection . li. 20. c. 4. c De phaenom . Lunae . c. 11. a Plut. de pla . phil . l. 2. c. 13. b Opt. lib. 4. c Com. Purbac . Theo. p. 164. Scaliger Exercit. 80 sect . 13. Plut. de facie Lunae . Thucid. Livij . Plut. de facis Lunae . Herodot . l. 7 c 37. De phaenom . Lunae . c. 11. Prop. 9. In lib. de animalib . LIB . 1. Cap. 5. Tostatus in 1 Gen. Hyeron . de Sancta fide . Hebraeomast . l. 2. c. 4 a Lib. 9. Architecturae . b Narratio Psalmorum . item . ep . 119. De Subtil . lib. 3. Keplar . epit . Astron. cop . l. 6. p. 5. sect . 2. Opt. Astron . c. 7. num . 3. De nova stella . lib. 1. c. 10. Reinhold Comment . in Purb . Theor pag. 164. Somn. Scip. l. 1. c. 20. Lect. antiq . l. 1. c. 15. In lib. de natur . rerum . a De 4. Coaevis . Q. 4 Art. 21. b Exercit. 62. c Epitom . Astron. l. 4. p. 2. d Epit. Astro . Cop. l. 6 part . 5. sect . 2. a Originum l. 3. c. 60. b De Coelo . l. 2. c De ratione tempor . c. 4. Item Plinie lib. 2. ca. 6. Hugo de Sancto Victore . Annot. in Gen. 6. 2 King. 3. 22. 2. Quaest. in hoc cap. LIB . 1. Cap. 6. Plut. de plac . phil . l. 2. c. 13. Ibid. c. 25. Diog. Laert. l. 2. & l. 9. Divin Inst. lib. 3. c. 23. De Coelo . l. 2. cap. 13. Plut. ibid. cap. 30. Plin. Nat. Hist. l. 34. cap. 6. Plat. de conviviis . Macrob. Somn. Scip. lib. 1. c. 11. Exercit. 62. De facie Lunae . Iustit . ad discip . Plat. Coel. Rhodig . l. 1. c. 4. Cusa . de doct . ign . l. 2 cap. 12. Philos. Epicur . part . 434. a In Thesibus . b Dissertatio cum Nunc. c Nuncius Sydereus . Somn. Astr. Dephaenom . lunae . c. 4. Cap. 7. De macula in sole obser . De phaenom . cap. 1. Ibid. c. 6. Cap. 1. Cap. 5. See the second book . 1. Prop. Apologia pro Galilaeo . So Bede in l. de Mund. constit . De subtil . lib. 3. a Occulta . Philos. l. 1. cap. 6. a Plut. de placit . phil . l. 2. c. 25. Iosephus l. 2. con . App. August . de Civit . Dei. l 18. c 41. Nat. Hist. l. 2. c. 9. Opt. lib. 9. Comment . in Purb . pag. 164. Ex qua parte luna est transpicua non solum secundum superficiem , sed etiam secundum substantiam , eatenus clara , ex qua autem parte opaca est , eatenus obscura videtur . De Phaenom . cap. 11. Albert. mag . de Coaevis . Q. 4. Art. 21. Colleg. Con. De Somniis Scalig. exercit . 62. * Eusebius Nicremb . Hist. Nat. l. 8. c. 15. LIB . 1. Cap. 8. Opt. Astro. c. 6 num 9 D●●●●t cum nuncio Gal. Exercit. 38 De Metcoris l. 5. c. 1. Art. 1. LIB . 1. Cap. 6 LIB . 1. Cap. 8 Galilaeus System . coll . 1. De facio lun . Dissertatio . Nunc. Syd . In lib. de coloribus . Apologia pro Galilaeo . Vide Ieron . epist. ad Pammachium . Confession . l. 13. c. 32. Retracted . lib. 2. Retr . cap. 6. 2 Esdr 4. 7. Vide Guli : Nubrigens . de rebus Anglica : lib. 1. LIB . 1. Cap. 9. Nat. hist. l. 36. c. 1. Psal. 104. v. 18. Prov. 8. 25. Psal. 90. 2. Ioseph . Ant. lib. ●● . c. 3. Gen. 49. 26. * Lect. aut . l. 1. c. 15. Plut. de plac . l. 2. c. 25. De Coelo . l. 2. part . 49. De Mundi fab . pars 3. c. 4. Astron. Opt. c. 6. num . 9. Kep append . Selenogra . Nuncius Sydereus . Cap. 11. Syst. mundi coll . 1. Hist. l. 1. c. 7. sect . 11. Poly. histor . c. 21. * Hist. l. 1. c. 7. sect . 11. Meteor . l. 1. c. 11. Comparatio Arist. cum . Platone . Sect. 3. c. 5. Expost . in loc . Math. Arlis loc . 148. Somn. Astr. not . 207. LIB . 1. Cap. 10. Vide Euseb. Nicrem . de Nat. Hist. l. 2. c. 11. So. A. D. 1547. April 24. to the 28. Virgil Georg. lib. 1. Metam . lib. 15 : Scheiner . Ros. Vis. l. 4. pars 2. c. 27. LIB . 1. Cap. 11. De gen animal . l. 4. 12. Golden Number . Plut. de fac . lunae . Somn. Scip. l. 1. c. 19. Ant. lect . l. 1. c. 4. In epist. ad Sebast. Fantonum . Praefat. ad Austriaca syd . Meteor . l. 1. c. 2. Art. 2. De mundi fab . p. 3. c. 3. Ant. Lect. l. 20. c. 5. Progym . 1. Scal. exerc . 62. Epit. Astro. l. 4. part . 2. De doct . ig . l. 2. c. 12. LIB . 1. Cap. 12. Plin. nat . hist. l. 2. c. 26. * Epist. 95. Vide Galilaeum . Syst. mundi . Colloq 3. Clavius in sphaeram . cap. 1. Tycho Progym . l. 1. c. 9. Fromond . Meteor . l. 2. c. 5. art . 2. Item Vesta tract . 5. c. 2. De Comet . l. 5. c. 4. Apol. pro Galil . Meteor . l. 3. c. 2. Art. 6. La●tant . Inst. l. 3. c 23. LIB . 1. Cap. 11. De Civit. Dei l. 21. cap. 8. LIB . 1. Cap. 12. De meteor . l. 3. c. 2. Art. 6. LIB . 1. Cap. 11. Dissert . 2. cum nunc . Galil . item . Somn. Astron. nota ultima Hist. nat . l. 2. c. 11. LIB . 1. Cap. 13. De doct . ignorantia . l. 2. c. 12. Wisd. 9. 16. 2 Esd. 4. 21. De doct . ign . l. 2. c. 12. Ephes. 1. 10. Col. 1. 20. Nat. Com. l. 3. c. 19. De Civit. Dei l. 22. c. 16. Mat. 25. 30. Eph. 4. 9. Rev. 14. 20. De Morib . div . l. 13. c. 24. Cu●silent oracula . Sir W. Raw. l. 1. c. 3. sect . 7. In Genes . 2 Esdr. 4. 7. In Genes . Comment . in 2. Gen. v. 8. L. 1. c. 3. sect . 6. 7. 2 Cor. 12. 4. Luke 23. 43. Gen. 7. 19. Nat. Qu. l. 7. cap. 25. Sen. Med. act . 1. Vide Hora. Od. 3. Iuvenal . sat . 12. Claud. praef ad 1. lib. de rap . Proscr . Disserta . cum Nun. Syder . Prop. 3. Gilbert . de Mganete . l. 2. cap. 7. Lib. de Sympath . & Antip. cap. 7. Vid. Bapt. Masul . exer . Acad. de attract . exer . 4. Nat. Hist. Cent. 1. exper . 33. * Phys. l. 3. Q. 6. art . 2. * Viridar . l. 4 prob . 47. Vide. Arch. l. de insidentibus humido . * Viridar . lib. 4. prob . 24. * De facie in Luna . * Nat. hist. lib. 7. ca. 2. Diog. Laert. lib. 1. ca. 9. Virgil. Arist. de Sens. cap. 5. * Hist. Animal . lib. 8. cap. 5. * Hist. l. 10. cap. 72. The earth The water * De Anim. lib. 7. * De P●sc . l. 1. cap. 12. Subtil . l. 9. The aire Polyhistor . cap. 53. * Hist. li. 8. cap. 33. * Lop hist. Ind. Occid . cap 96. Maiolus Colloq . 3. T is likely that these birds doe chiefly reside in the aethereall aire , wher● they are nourished and upheld . * De Piscibus . lib. 1. cap. 13. Vitell. l. 10. Theo. 7. Keplar . Ep. Coper . l. 1. part . 3. Stevinnius . Geog. l. 3. prop. 3. Pitisc . Trigon . * Subt. l. 17. * Epit. Coper . l. 1. p. 3. * In Gen. ad literam . li. 3. cap 2. * Meteor . lib. 1. ca. 2. art . 1 , Comment . in Gen. 1. 8. Hist. l. 31. cap. 1. Iob 26. 8. Meteor . l. 1. c. 11. Mr. Burton . Melanch . pa. 2. sect . 2 mem . 3. * Lib. 3. c. 40. Notes for div A15364-e17590 * Fromond . Al. Ross. Notes for div A15364-e18230 * Alex. Ross. de Terrae motu , contra Lansb . lib. 1. sect . 1. cap. 10. * Alcinous . † Horat. lib. 2. ep . 1. Consid. 1. Consid. 2. * Alex. R●ss . l. 1. sect . c. 8. Eccl. 1. 18. * Cap. 13. 3. * V. 8. 10 , 11. † Ver. 18. * Ver. 22. † V. 28. 29. * Cap. 42. 3. Acts 7. 22. * Iosh ca. 10. Quaest. 19. Consid. 3. † Alex. Ross. l. 2. s● . 2. c. 10. * De Coelo , lib. 2. ca. 13. * Archime des de araenae numero . 4. Consid. De docta ignor . lib. 2. cap. 12. * Praef. ad Narrat . Rhetici . Ibid. 5 Consid. * in Narratione . † Myst. Cosmogr . cap. 1. Item praef . ad 4. l. Astr. Copern . de Coel. l. 2. c. 12. Met. lib. 12. cap. 8. Alm. lib. 13. cap. 2. 7 Consid. * Serrarius Commen . in Ios. cap. 10. Quaest. 14. So Lipfius Phisiol . l. 2. † Ann. Dom. 1616. item 1633. Fromondus Antarist . cap. 6. Eccles. 3. 10 , 11. Comment . in Eccles. c. 1. v. 4. † Praescript . cap. 17. † In Genes . ad lit . lib. 2. in fine . Ibid. cap. 9. * Ps. 19. 5. 6. Eccles. 1. 5. Ios. 10. 12 , 14 Galilaeus maintaines the literall sense of this place : towards the end of that treatise , which hee calls Nov-Antiqpat . doctrina . Tostat. in locum , Quaest. 16. 17. Arias Montanus in locum . † Tostat. ib. Quaest. 18. Serrarius in Iosh. 10. Quaes . 21. 22. 2. King. 20. 11. Isai. 38. 8. * Tractat 35. in Mat. † Apologet. cap. 21. Lib. 2. Isa. 38. 8. Ionah . 4. 8. Ion. 4. 8. Psal. 121. 6. † Proaem . ad . Phil. sācram * Vest. Trac . 3. cap. 2. † Sanctius in Isa. 13. 5. Item in Zachar . lib. 9. num . 45. * Comment . in Gen. c. 1. † In Gen. c. 1 , v. 10. art . 6 Vide Hiero. in Ier. 28. Aquinas in Iob. 26. 7. Gen. 1. 16. Psal. 136. 7. Comment . in Psa. 136. † De operibus Dei , par . 2. li. 6. cap. 1. De Meteor . lib. 4. cap. 2. art . 5. Iob , 28. 25. Comment . in Psal , 148. 4. Ier. 35. 22. Gen. 15. 5. * In 1. cap. Sphaerae . Sir. Fr. Bac. table of colours , num . 5. In prim . ca. Sphaerae . Num. 1. 46. 1. Kin. 7. 23. 2. Chro. 4. 2. * Ross. lib. 1. sect . 1. c. 8. * Antiq. Iud. lib. 8. cap. 2. Ross. ibid. Ibid. * Gen. 15. 13 Acts , 7. 6. † Exod. 12. 41. Gal. 3. 17. * Gen 46. 27. Acts , 7. 14. † Fromond . Vesta . 4. tract . 3. c. 2. Ibid. * Psa. 19. 6. Mat. 24. 31. † Ps. 22. 27 , &c. † Comment . in Isa. 13. 5. Iob. 38. 4. Psa. 102. 25. Psal. 136. 6. Psal. 24. 2. * Subtil . Exercit. 67. Iob. 23. 8. 9. Mat. 25. 33. Iob , 26. 6 , 7. * Ier. 1. 14. 15. item ca. 4. 6. 6. 1. † Li. de nat . popul . ca. 4. * De Coelo , lib. 2 cap. 2. * De placit . Philos. li. 2. cap. 10. † Lib. 3. D. Hakwel . Apol. lib. 1. c. 1. sect . 2. Prov. 8 , 5. 10 , 8. Eccles. 1. 13 , 16 , 17. & 8. 5. Vesta Trac . 3. cap. 3. Ioel , 2. 31. Item c. 3. 15. Comment . in Ioel. ca. 3. * Comment , in Isai. cap. 13. 5. † Comment . in Gen. c. 3. ve . 10. art . 6. * Iohn , 3. 8. † Ier 10. 13 , Item ca. 51. 16. a Iob. 37. 10. b 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 c Io. 26. 14. d Psal 2. 9. 3 , 4. &c. Eccles. 1. 7. Iob 9. 9. Item 38. 31. Vide Fromond . Mete . l. 3. 6. 1. ar . 1. Fromond . Antar . c. 6. Schickard . Bechin . Haperu . Disp. 5. num . 8. Schickard . ib. Disp. 6. num . 2. Buxtor . Synag . Iuda . cap. 36. * Psa. 50. 10. Vide Parap . Chald. * Enarrat . in Gen. a Respons . ad ques . 93. Orthod . b Que. 11. sup . Gen. c De Civ . Dei , lib. 11. cap. ult . d Hexam . lib. 2. cap. 2. * Homil. 3. in Gen. † De civit . dei , l. 16. c. 23 a Respon . ad quest . 93. b Hexam . lib. 1. cap. 6. c Homil. 14. in epist. ad Hebr. d In ca. 8. Hebr. * In idem c. † In Gen. ad lit . li. 1. c. 9. Item l. 2. c. 6 * Lib 3. Comment . in Galat. ca. 5. a Homil. 4. Hexam . b Commen . in Ioh. c In Psal. 103. d Hexam . lib. 3. c. 2 , 3. a Orat. 34. b Aquinas part . 1. quest . 69 ▪ art . 1. c Commen . in Psal. 24. Item in Ps. 136. 6. Luke 5. 4. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . a Recog . 8. b Orat. con● . Idolos . c In Psal. 136. 6. d Ia Ps. 24. * Comment . in Isai. l. 13. † De plant . Noe. Tostatus in Iosh. cap. 10. quest . 13 , 14. * Tom. 1. in Iohan. † De nat . novi orbis , lib. 1. cap. 2. * Vallesius Sacra Phil. cap. 62. Fuller , Miscell . l. 1. c. 15. Pineda Comment . in locum . Iob , 14. 10. 12. Psal. 78. 39. M. Carpenters Geog. lib. 1. cap. 4. * Perplex . li. 2. cap. 29. * 1. Chron. 16. 30. Psal. 93. 1. Item 96. 10. LIB . 2. Cap. 5. Lorinus Comment . in Psal. 8. Miscel. lib. 1. cap. 15. So Ps. 18. 15. Iohn 17. 24. Ephes. 1. 4. Etimol . mag Acts 2. 25. Comment . in Iob. LIB . 2. Cap. 6. Eccles. 1. 14 , &c. Antar . c. 12. item Vesta . tract 5. c. 2. Arg. 1. Arg. 2. Arg. 3. Arg. 1. Arg. 2. Vid. Carp. Geog. l. 1. c. 5. Arg. 3. Arg. 4. Arist. de coe . lo. li. 2. c. 14. Copern . li. 1. cap. 5 , 6. Comment . in Sphaer . cap. 1. Fromond . Vesta . tract . 5. cap. 1. Ibid. Ibid. * Astron. Copern . lib. 4. par . 1. † System . mundi , C●ll . 3. Vide Galil . ibid. Eccles. 8. 17. * Lib. 1. sect . 2. cap. 1. * In prim . cap. Sphaer . † De Coelo . lib. 2. 6● . 13. * Saturnal . lib. 1. cap. 17 , &c. Keplar . Astr. Copern . lib. 4. par . 2. Maestin . prae . ad Nar●at . Rhetici . Keplar . mysterium Cosmographicum . * Lib. 13. prop. 14 , 15 , &c. LIB . 2. Cap. 6. Al. ●oss . l. 1. sect . 1 cap. 1. Ibid. Coper . l. 1. ●8 Gibert de Magn. lib. 6. cap. 5. * Lib. 1. sect . 1. cap. 3. * Li. 1. sect . 1. cap. 5. * Syst. mundi , Collop . 2. Mae●lin praefat . ad Narrat . Rhet. Fromond . Vesta . tract . 1. cap. 3. Aristot. de Coelo , lib. 2. cap. 13. Fromondus Vesta . tract . 2. cap. 2. Syste . Mundi . Colloq . 2. Gallil . Syst. Colleq . 2. Ob. Sol. * Austriaca Syder . par . 2. prop. 25. † De bello Iudaico , lib. 7. cap. 12. Dion . lib. 54. * Nat. Qu. lib. 7. cap. 6. * Lib. 1. sect . 2 , cap. 6. Arg. 1. Arg. 2. Arg. 3. Arg. 4. Arg. 5. Arg. 6. Arg. 7. Arg. 8. Arg. 9. Ad. 1. & 2. Ad. 3. Ad. 4. Ad. 5. Ad. 6. Ad. 7. Ad. 8. Vid. Revel . 21. 23. item c. 22. ver . 5. * Gen. c. 1. l. 2. quaest . 6. 2. Pet. 3. 10 , 12. Ob. Sol. Vid. Maest. Epit. Astr. lib. 1. in fine . * De Prop. l. 5. prop. 58. † Comment . in prim cap. Sphaerae . De magnete , lib. 6. cap. 3. Ross. lib. 1. sect . 1. ca. 1. Idem lib. 2. sect . 1. ca. 5. Idem lib. 1. sect . 1. cap. 2. * De Animā . lib. 2. cap. 7. † Ross. lib. 2. sect . 1. ca. 4. Arg. 2. Galen . * Lansberg . † Keplar . * Galilaeus . Arg. 3. * Boet. de Consol. Phil. lib. 3. Arg. 4. † De Coelo , li. 2. cap. 10. Arg. 5. * Antarist . cap. 16. Vid. Vasq. lib. 1. disp . 2. cap. 816. Senec. Nat. Qu. lib. 5. cap. 5 , 6. Valles Sacr. Philos. c. ●4 . * De Coelo , lib. 2. cap. 8. * Antarist . cap. 18. Vest. tract . 4. cap. 3. † Matutina Vespertin● . * Praef. ad lib. 1. Nat. Quaest. Iob 38. 33. Ier. 33. 25. * Tuscul. 1. Item Plut. de placit . Phil. l. 1. c. 6. Instit. lib. 2. cap. 5. Psal. 8. 3 , 6. Sen. Nat. Quaest. l. 1. Nonne ô terrena animalia consideratis , quibus praesidere videamini ? Nam si inter mures videres unum aliquem , jus sibi ac potestatem prae caeteris vindicantem , quanto movereris chachinno , &c. Boëtim de Consol. l. 2. Boetis Ibid. Idem lib. 3. Wis. 7. 18 , 19. Lucan . l. 10. 
A34005	----	The sector on a quadrant, or A treatise containing the description and use of four several quadrants two small ones and two great ones, each rendred many wayes, both general and particular. Each of them accomodated for dyalling; for the resolving of all proportions instrumentally; and for the ready finding the hour and azimuth universally in the equal limbe. Of great use to seamen and practitioners in the mathematicks. Written by John Collins accountant philomath. Also An appendix touching reflected dyalling from a glass placed at any reclination. Collins, John, 1625-1683. 1659 Approx. 798 KB of XML-encoded text transcribed from 209 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2007-01 (EEBO-TCP Phase 1). A34005 Wing C5382 ESTC R32501 99899660 99899660 66044 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A34005) Transcribed from: (Early English Books Online ; image set 66044) Images scanned from microfilm: (Early English books, 1641-1700 ; 1524:9 or 2400:6) The sector on a quadrant, or A treatise containing the description and use of four several quadrants two small ones and two great ones, each rendred many wayes, both general and particular. Each of them accomodated for dyalling; for the resolving of all proportions instrumentally; and for the ready finding the hour and azimuth universally in the equal limbe. Of great use to seamen and practitioners in the mathematicks. Written by John Collins accountant philomath. Also An appendix touching reflected dyalling from a glass placed at any reclination. Collins, John, 1625-1683. Lyon, John, professor of mathematics. Appendix touching reflective dialling. Sutton, Henry, mathematical instrument maker. [16], 284; [2], 54, [10], 26 p., [6] leaves of plates (some folded) : ill. (woodcuts) printed by J.M. for George Hurlock at Magnus Corner, Thomas Pierrepont, at the Sun in Pauls Church-yard; William Fisher, at the Postern near Tower-Hill, book-sellers; and Henry Sutton, mathematical instrument-maker, at his house in Thred-needle street, behind the Exchange. With paper prints of each quadrant, either loose or pasted upon boards; to be sold at the respective places aforesaid, London : 1659. The quadrants described were made and engraved by Henry Sutton, who also calculated some of the tables and drew the projections. "The description and vses of a great universal quadrant" has separate title page dated 1658; pagination and register are continuous. "The description and uses of a general quadrant, with the horizontal projection, upon it inverted" has separate title page dated 1658; pagination, and register are separate. "An appendix touching reflective dialling" by John Lyon has separate title page dated 1658; pagination is separate; register is continuous. A reissue, with cancel title page, of the 1658 edition having "printed by J. Macock" in imprint (Wing C5381). In this issue, the 2 contents leaves, bound after p. 275 in the original issue, are bound with the preliminaries, following title page and "To the reader" (A2). The catchword "The" on the verso of the second contents leaf does not match the first word of the following page (a1). "The description and uses of a general quadrant" filmed separately as Wing C5371 on UMI microfilm set "Early English books, 1641-1700", reel 2400. Reproduction of originals in: Harvard University Library; Henry E. Huntington Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. EEBO-TCP is a partnership between the Universities of Michigan and Oxford and the publisher ProQuest to create accurately transcribed and encoded texts based on the image sets published by ProQuest via their Early English Books Online (EEBO) database (http://eebo.chadwyck.com). 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Keying and markup guidelines are available at the Text Creation Partnership web site . eng Mathematical instruments -- Early works to 1800. Astronomy -- Early works to 1800. Navigation -- Early works to 1800. Dialing -- Early works to 1800. 2005-07 TCP Assigned for keying and markup 2006-03 SPi Global Keyed and coded from ProQuest page images 2006-06 Derek Lee Sampled and proofread 2006-06 Derek Lee Text and markup reviewed and edited 2006-09 pfs Batch review (QC) and XML conversion THE SECTOR ON A QUADRANT , OR A Treatise containing the Description and Use of four several QUADRANTS ; Two small ones and two great ones , each rendred many wayes , both general and particular . Each of them Accomodated for Dyalling ; for the Resolving of all Proportions Instrumentally ; And for the ready finding the Hour and Azimuth Universally in the equal Limbe . Of great use to Seamen and Practitioners in the MATHEMATICKS . Written by JOHN COLLINS Accountant Philomath . Also an Appendix touching Reflected Dyalling from a glass placed at any Reclination . London , Printed by J.M. for George Hurlock at Magnus Corner , Thomas Pierrepont , at the Sun in Pauls Church-yard ; William Fisher , at the Postern near Tower-Hill , Book-sellers ; And Henry Sutton , Mathematical Instrument-Maker , at his House in Thred-needle street , behind the Exchange . With Paper Prints of each Quadrant , either loose or pasted upon boards ; to be sold at the respective places aforesaid . 1659. To the Reader . Courteous Reader , THou hast in this Treatise , the Description and Uses of three several Quadrants , presented to thy View and Acceptance ; and here I am to give thee an account of their Occasion and Original . Being in conference with my loving friend M. Thomas Harvie , he told me , that he had often drawn a Quadrant upon Paper pastboard , &c. derived by himself , and never done by any man before , as to his knowledge , from the Stereographick Projection , which for a particular Latitude , would give the Hour in the equal Limb , and would also perform the Azimuth very well ; and but that it was so particular , was very desirous to have one made in Brass for his own use by an Instrument Maker : whereto replying , that with the access of some other Lines to be used with Compasses , it might be rendred general for finding both the Hour and the Azimuth in the equal Limb : He thereupon intimated his desires to M. Sutton , promising within a fortnight after their conference , to draw up full directions for the making thereof . But M. Sutton having very good practise and experience in drawing Projections , speedily found out the drawing of that Projection , either in a Quadrant or a Semicircle , without the assistance of the promised directions , and accordingly , hath drawn the shape of it for all Latitudes , and also found how the Horizontal Projection might be inverted and contrived into a Quadrant without any confusion , by reason of a reverted tail , and let me further add , that he hath taken much pains in calculating Tables for the accurate making of these and other Instruments , in their construction more difficult then any that ever were before ; and the said M. Sutton conceiving that it would be an advancement to their Trade in general , besides satisfactory to the desires of the studious in the Mathematiques , to have the uses of a good Quadrant published , prevailed with me , in regard M. Harvey was not at leisure ( though willing his Quadrant should be made publique ) to write two or three sheets of the use of it , which I intended to have given M. Sutton ( who very well understood the use as well as the making ) to be published in his own name ; whereto he being unwilling , and finding that therein many of the uses of one Quadrant , much less of more could not be comprized , at his earnest request , I wrote what is here digested , succisivè & horis Antelucanis , having little leisure for that purpose , and all this performed before the Instruments were cut , wherefore the description given of them , may not so nearly agree with the Instruments , as if they had been first made , nor possibly some of the examples about finding the hour of the night by the Stars ; which examples were fitted from Tables of present right Ascension , whereas the Quadrant is fitted to serve the better for the future , the difference notwithstanding will be but small . And thus hoping thou wilt cover my failings with the mantle of love , and kindly accept of my endeavours , tending to the publique advancement and increase of knowledge , I still remain a Wellwiller desirous thereof . John Collins . depiction of a quadrant How the Projections on both the Quadrants may be Demonstrated . TO satisfie the inquisitive Reader herein , I shall only in this Edition quote such Latine Authors and Propositions as will evince the truth thereof , the performance whereof in English , is hereafter intended by my loving friend M. Thomas Harvie , in an elaborate Treatise , concerning all the Projections , with their Demonstration and Application , who is accomplished with singular knowledge in that kind , as in general in the Mathematiques . Now the Demonstration of these two Projections is as much included in the Demonstration of the Stereographick Projection , which by Aguilonius in his 6 Book is largely insisted upon , as a peculiar question in Trigonometry , is included in a general Case , and both the Projections on these Quadrants being derived from the grounds of the said general Projection , are necessarily involved in one and the same Demonstration . Stofler in his Astrolabe supposeth the eye in the South Pole Stereographically projecting upon the Plain of the Equator those Circles between the North Pole Horizon and Troprick of Capricorn , neglecting that part under the Horizon . But the Projection on the Quadrant , considered as it may be derived from his Astrolabe , supposeth the eye in the same Position , and makes use of one half of the Projection of the other part of the Circles intercepted between the Horizon and Tropick of Capricorn , namely , of that space between the Tropick below our Horizon , only changing the names of Cancer for Capricorn in their use , and using the depressed Parallels to the Horizon , instead of the Parallels of Altitude ; so that the Azimuths of the Quadrant made by this inversion , are no other then the Azimuths of Stoflers Projection continued below the Tropick of Capricorn where he breaks them off , and the rule he prescribes to draw the parallel of 18d of Depression for the Twylight serves to draw that , and all the other parallels of Altitude in this Quadrant . In like manner the Horizontal Projection supposeth the eye in the Nadir projecting upon the Plain of the Horizon . That part of the Sphere intercepted between the two Tropicks , neglecting that part thereof under the Horizon . But the Projection on the other great Quadrant , considered as derived therefrom , supposeth the eye there projecting that part of the Sphere which is there neglected with the like change of denomination ; and the Parallels of Declination are no other then the continuance of the said Parallels of the Horizontal Projection round to the Midnight Meridian , and the Hour circles the continuance of the said hours , only the Index of Altitudes is fitted to the Depressed Parallels of the Horizon , in stead of the Parallels of Altitude . Now it is evident , either from the Sphere or Analemma , that that part of either of these Projections which falls under the Horizon , will supply the use of that which hapned above , admitting only a change of denomination ; for in the Horizontal Projection , that Parallel of Declination which was called the Winter Tropick , being no other then the same Circle continued about , now in its use and denomination , becomes the Summer Tropick ; and the reason is , because what ever Altitude the Sun hath in any Sign upon any Hour or Azimuth reckoned from the Noon Meridian , he hath the like Depression on the like Hour and Azimuth in the opposite Signe counted from the Midnight meridian . The terms of Noon and Midnight Meridian are afterwards used in relation to some general Proportions : By the Hour in general is meant the Angle between the Meridian of the Sun or Stars , and the Meridian of the place : By the Hour counted from Noon Meridian , is meant the said Angle counted from that part of the Meridian of the place which falls above the Elevated Pole , continued towards the Depressed Pole : and by the Midnight Meridian , the opposite thereto under the Elevated Pole , continued as before . By the Azimuth counted from the Midnight Meridian , is meant an Angle at the Zenith between the Suns Vertical or Azimuthal circle , and the Meridian of the place , measured by the Horizon , counted from the Intersection of the Horizon with the Meridian under the Elevated Pole ; and by the Azimuth counted from the Noon Meridian , is meant the Complement of the said Angle to a Semicircle , counted from the opposite Intersection of the Horizon with the former Meridian continued above the Elevated , and towards the Depressed Pole , according to which acceptions , the general Proportions are fitted for finding it either way in both Hemispheres , without any restriction to North or South . A more immediate account of these Projections . HItherto we have accommodated our Discourse , to shew how these Projections are derived from Stoflers Astrolabe , and from the Horizontal Projection , of which neither Stofler ( as to my knowledge ) for I have only seen his 8 Book ) nor the learned M. Oughtred , give no peculiar Demonstration , as being particular examples of a general case , largely ( as such ) insisted on ; and this we have done for the accommodation of Instrument makers , to whom this Derivation may seem most suitable ; whereas such a deduction is not at all necessary to the Demonstration of the Projections so derived . For in the Projection derived from the Inversion of Stofler , let the eye be supposed to be placed in the North Pole , projecting upon the Plain of the Equinoctial , such Circles in the Sphere , as are described in the Quadrant between the two Tropicks , a quarter of which Projection will be the same with that on the Quadrant , namely , one of those quarters between the South part of the Meridian and hour of six , which will leave out all the outward part of the Almicanters between it and the Tropick of Cancer , and in stead thereof , there is taken in such a like part of the depressed Parallels to the Horizon between the same Hour of six , and Tropick of Capricorn , which is the reverted tail ; for the Parallels of Depression have the same respect to the Tropick of Capricorn , that the Parallels of Altitude have to the Tropick of Cancer , and will work the same in effect . In like manner , the Eye in the other Projection may be supposed in the Zenith , Stereographically Projecting upon the Plain of the Horizon , that part only of the space between the Tropicks , which falls without the Projection of the Horizontal Circle , save only the reverted tail , which is the Projection of so much of the Parallels of South Declination , as is intercepted between the prime Vertical Circle and the Horizon , and is taken in to serve in stead of that part of the Parallels of North Declination , which will fall without the Quadrant . In any of these Positions of the Eye , all Circles passing through the same , will be projected in right lines by 91 Prop. 6 Book of Aguilonius , such are the Azimuths on the Horizontal Quadrant , and the Hours on the other Quadrant , represented by the thred lying over any Ark in the Limb , so also in this latter Quadrant is the Parallel of Altitude equal to the Latitude of the place , a right line . All Circles parallel to the Horizon and Equinoctial , will be projected in concentrick Circles by 94 Prop. 6. Aguilonius , such are the Parallels of Altitude in the Horizontal Quadrant , and the Parallels of Declination in the other Quadrants , represented by the Bead , when it is rectified to the Index of Altitudes in the one , and to the Ecliptick in the other , carried in a circular trace from one side of the Quadrant to the other . All other Circles in the Sphere , whatsoever and howsoever scituated , being projected according to the supposed position of the Plain and Eye , will be represented by Excentrick Circles . by 96 Prop. 6. Aguilonius , and the hours in the Horizontal Projection will ( if they be produced ) meet with the projected Pole points , so also the Azimuths in the other Projection , which by the like parity of Reason may be denominated The Equinoctial Projection , will ( being produced ) meet with the projected points of the Zenith and Nadir ; and how in particular to project and divide any Circle however scituated in the Sphere , is abundantly shewn in the 6th Book of the aforesaid Author , and amplified with many examples , though none of them agreeing with the particular Draughts of these Quadrants , yet if put in practise according to the proposed Scituation of the Eye , will be found to agree with the prescribed Directions for the making of these Quadrants . See also Clavius his Book of the Astrolabe , Guido Ubaldus his Theorick of the general Planispheres , and M. Oughtreds 2d Scheme B in his late Trigonometry in English . An Appendix to the Description of the Small Quadrant . SInce the Printing of the sheet B , we have thought fit to vary a little from the Description there given of the Small Quadrant . The Dyalling Scale of Hours described in page 9 , near the beginning , which I say in Page 191 may be omitted , is accordingly left out , and instead of it , a line of Versed Sines of 90d put on , the uses whereof are handled in the great Equinoctial Quadrant . Also there is two Scales added to the small Quadrant more then was described ; namely , the Scale of Entrance , the same that was placed upon the Horizontal Quadrant , with a Sine of 51d 32′ put through the whole Limb serving to give the Altitude at six , which the thred will intersect , if it be laid over the Declination in the Limb ; but enough of the uses of these Scales is said in the Horizontal Quadrant . Lastly , Those that like it best , instead of having on the Small Quadrant one loose fitted Scale for the Hour , and another for the Azimuth , may have the Hour-Scale only divided into two parts , serving to give the Hour and Azimuth for the Sun , and all the Stars in the Hemisphere , the one part for South Declinations , the other for North Declinations , in imitation of the Diagonal Scale . An Advertisement . ALL manner of Mathematical Instruments , either for Sea or Land , are exactly made in Wood or Brass , by Henry Sutton , in Thredneedle-street , near Christophers Church , or by William Sutton in Upper Shadwel , a little beyond the Church . Pag. Li. Errors to be thus Corrected . 8 33 apply supply 19 25 76 d 54′ 79 d 54′ 20 7 48 d 45 d 23 3 50 d 41′ 50 d 41′ 23 11 58′ 53′ 24 25 a Letter Character . the Character plus + 28 is lesse if lesse 55 14 difference of one of differences of 55 17 of the Leggs from the Leggs of one of the Leggs The affections in page 57 line 16 , 17. wanting Braces , are expressed at large page 140 , 141. also the last affection in that page having a mistake of lesser for greater in the middle brace is reprinted in page 138 60 14 The last term of the 4th Proportion should be the Sine of the angle sought , and not the Cosecant . 92 29 a Leg and its adjacent angle The Hipotenusal and its adjacent angle 30 to find the other angle by 4 to find the side opposite there to by 8 Case Case . See page 138. 103 34 Acquimultiplex Aequimultiplex 35 therefore by therefore by 18 Prop. 7. Euclid . 121 18 Hour 3¼ Altitude 41 d 31′ Altitude for the hour 3¼ is 43 d 31′ 158 1 Line of Line of Sines 159 21 of 90 d at 90 d 164 ●8 any some 174 15 in the Limb in the lesser Sines 181 25 between as also between 27 would find it would in the other Hemisphere find it 184 21 the common as the common 189 1● either it may be found either 192 24 As the second including side As the Sine of the 2d including side 207 1 great Scale great Quadrant 209 7 60 parts 60 equal parts The Angle C in the Scheam page 52 is wrong cut , and should be 113d 22′ , See it in page 156. Page 98 a wrong Scheam printed , the true one is in page 93. Page 102 in the under Triangle the Angle D should be 108d 37′ See page 201. The first ten lines of calculation p. 53 are somwhat misplac'd , & should stand thus .     D●ffs Log ms     B C 126 Legs 169   2,2278867   A C 194   101   2,0042214 Sum with double Radius A B 270 Base 25 1,3979400 24,232208●   Sum 590           half sum 295   Logarith . 2 4698220 3 8677620 former Rectangle       Residue 20,3644461   The half is the tangent of 56 d , 41′ t.       10,1822230   Which Ark doubled is       113 , 22 A C B the Angle sought .   A Table shewing the Contents of the Book . AN account of the original of the Projections , and their Demonstration . In the Preface . The Description and making of the small Quadrant : Page 1. The Vse of the perpetual Almanack . 12 The Vses of the Projection on the small Quadrant . 15 Of the Stars inscribed thereon . 24 Of the Projection drawn in a Semicircle . 33 Of the Stars and quadrant of Ascensions drawn on the back-side of the quadrant . 34 The Vses of the Quadrat and Shaddows . 35 Divers ways to measure the altitude of a Tower or object . 36 Affections of Plain Triangles 45 Proportions for the Cases of right angled plain Triangles 46 Proportions for the Cases of Oblique Plain Triangles 49 Doubtful Cases manifested , and mistakes about them rectified 50 Four several Proportions for finding an angle when three sides are given , not requiring the help of Perpendiculars 52 Affections of Sphoerical Triangles 56 Six several Proportions suited to each of the 16 Cases of right angled Sphoerical Triangles , with all necessary caution 60 Directions for varying of Proportions . 72 Some Cases of oblique Sphoerical Triangles resolved without the help of Perpendiculars 76 , 83 When some of the Oblique Cases will be doubtful , and when not 80 , 81 Six of those Cases demonstrated to be doubtful 86 , 87 Perpendiculars needless in any of those Cases , and not used 88 Some new Proportions applyed to the Tables 88 And mistakes about Calculating the distances of places noted 89 And Proportions esteemed improper to the artificial Tables applyed for that purpose 96 Proportions both Instrumental and others for finding a Sphoerical angle when 3 sides are given 100 , 101 Those Instrumental Proportions how demonstrated and derived from other Proportions in use for the Tables . 103 New Proportions for finding the Hour and Azimuth demonstrated from the Analemma . 108. And applyed to the Calculating of a Table of Hours . 117 A Table Calculated thereby , showing the Suns altitudes on all hours for some Declinations useful for the trial and construction of some Instruments . 121 A Table of the Suns Altitudes for each 5d of Azimuth fitted to the same Declinations . 122 To Calculate a Table of Azimuths to all Altitudes . 124 And a Table of Altitudes to all Azimuths . 128 And the Proportions used laid down from the Analemma . 132 Affections of some doubtful Cases of Sphoerical Triangles determined . 138 The ground of working Proportions on a quadrant . 144 Proportions is equal Parts resolved instrumentally . 146 , 147 All Proportions in Tangents alone resolveable by the tangent line on the quadrant , or by a tangent of 45d. 148 Proportions in Sines and Tangents wrought on the quadrant . 151 Proportions in equal parts and tangents resolved by the quadrant . 152 Proportions in equal Parts and Sines so resolved , being useful in Navigation . 156 , 157 Of a line of Sines , and how from it or the Limb to take off a Sine , Tangent or Secant . 158 Proportions in Sines wrought on the quadrant . 161 How to proportion out lines to any Radius from lines inscribed in the Limbe . 167 To operate Proportions in Sines and Tangents on the quadrant . 168 A general way for finding the Hour . 173 As also of the Azimuth . 174 Particular Scales fitted for finding the same . 177 Another general way for finding the Hour . 181 And for finding the Suns Altitudes on all Hours . 183 Another general way for finding the Azimuth . 183 And of distances of places by the quadrant . 188 How from a quadrant to take off Chords ▪ 190 The Description of the Diagonal Scale . 193 , 194 The said Scale fitted for the ready finding the Hour and Azimuth for all parts of England , Wales , Ireland , and the uses thereof . 195 , 196 The description and uses of the particular Scales in Dyalling . 197 Also the uses of other Scales fitted for finding the Hour and Azimuth near noon . 200 Hitherto the Uses of the small Quadrant . THe Description of the great Equinoctial Quadrant . 2 The Vses of a line of Versed Sines from the Center . 208 And of Versed Sines in the Limb. 214 The Vses of a fitted particular Scale , with the Scale of entrance , for finding the Hour and Azimuth in the equal Limb. 216 As also for finding the same in the Versed Sines of 90d in the Limb. 220 , 221 And of the Diagonal Scale therewith . 222 , 223 New general Proportions for finding the Hour and Azimuth . 225 Divers Proportions demonstrated from the Analemma . 227 Several general Proportions for finding the Hour applyed . 230 And several Proportions applyed for finding the Altitudes on all Hours . 233 General Proportions for finding the Azimuth 237 A new single Proportion in Sines for Calculating a table of hours . 243 The Stars how put on and the hour found by them . 244 , 245 The Construction of the Graduated Circle . 248 The line of Latitudes demonstrated . 249 Vses of the graduated Circle and Diameter in resolving of Proportions , and in finding the Hour and Azimuth universally . 253 Vses of other Lines within the said Circle . 261 To prick down a Horizontal Dyal in a Square or a Triangle by the Dyalling lines on the Quadrants . 262 Proportions for upright Decliners . 265 To prick down upright Decliners in a Square or rather right angled Parralellogram , is likewise in a Triangle from the Substile . 268 To prick them down in a Triangle or Paralellogram from the Meridian . 272 An Advertisement about observing of altitudes . 275 The description and making of the Horizontal quadrant . Page 1 The perpetual Almanack in another form 12 A tide Table with the use of the Epacts in finding the Moons age . 11 The uses of the Horizontal Projection . 18 The uses of the particular curved line and fitted Scales thereto . 20 Some Proportions demonstrated from the Analemma . 26 A particular Scale for finding the Hour and Azimuth fitted thereto , with its uses . 27 The uses of the Scale of entrance , being another particular fitted Scale for finding the Hour and Azimuth in the Limb. 32 A Chord taken off from the equal Limb and the Hour and Azimuth found universally thereby . 34 A new general Proportion for the Azimuth to find it in the equal Limb. 36 Another for the Converse of the fourth Axiom . 38 The Stars how inscribed , and the hour of the night found by them . 39 Some uses of the Dyalling Lines . 44 , 45 The use of the Line of Superficies . 46 , 47 And of the Line of Solids . 48 And of the line of inscribed Bodies and other Sector Lines . 49 , 50 A Table of the Latitudes of the most eminent places in England , Scotland , Wales , and Ireland . 52 , 53 A Table of the right Ascensions and Declinations of 54 of the most eminent fixed Stars . 53 , 54 Lastly , A Table of the Suns Declination and right Ascension for the year 1666 , with a Table of equation to make it serve sooner or longer . An Errour Page 248 , Line 30 and 31 for so is L N to L F read so is L N to N F. Of the Lines on the foreside of the QUADRANT . ON the right edge from the Center is placed a Line of equal parts , of 5 inches in length , divided into 100 equal parts . On the left edge a Line of Tangents , continued to two Radii , or to 63d 26 m the Radius whereof is 2½ inches . These two Lines make a right Angle in the Center , and between them include the Projection , which is no other then a fourth part of Stoflers particular Astrolabe inverted . Next above this Projection , towards the Center , is put on in the Quadrant of a Circle , the Suns declinations . And above that in four other Quadrants of Circles , the days of the Moneth , respecting the four seasons of the year . Underneath the Projection , towards the Limbe is put on , in one half of a Quadrant , one of the sides of the Geometrical Quadrat , and in the other half the Line of shadows . All which is bounded in by the equal Limbe . There stands moreover on the very edges of the Quadrant , two Dyalling Scales , which do not proceed from the Center ; that on the right edge is called the Line of Latitudes ; and that on the left edge the Scale of Hours ( equal in length to the Sines ) which is no other then a double Tangent , or two Lines of Tangents to 45d each set together in the middle , and so might , if there were need , be continued , ad infinitum . The Construction and making of such of these Lines as are not commonly described in other Treatises . To inscribe the Line of Declinations , there will be given the Suns declination to find his right Ascension , which is the Ark of the Limb , that by help of a Ruler , moving on the Center of the Quadrant , and laid over the same , will in-scribe the Declination proposed . The Canon to find the Suns right Ascension from the nearest Equinoctial point , correspondent to the Declination proposed , is As the Radius To the Cotangent of the Suns greatest Declination : So the Tangent of the Declination given : To the Sine of the Suns right Ascension . The four Quadrants for the days of the moneth are likewise to be graduated from the Limb , by help of a Table of the Suns right Ascensions , made for each day in the year . The Geometrical Quadrat is inscribed in half the Quadrant of a Circle , by finding in the Table of natural Tangents , what Arches answer to every equal Division of the Radius , and so to be graduated from the Limb ; so 300 sought in the Tangents gives the Ark of 16d 42 m of the Limb against which 3 of the Quadrat is to be graduated . The Line of shaddows is no other then the continuance of the Quadrat beyond the Radius , and so the making after the same manner ; thus having the length of the shadow assigned , annex the Ciphers of the Radius thereto , and seek in he natural Tangents , what Ark corresponds thereto ; thus the shadow being assigned thrice as long as the Gnomon , I seek 3000 in the natural Tangents , the Ark answering thereto , is 71d 34′ which being counted from the left edge of the Quadrant , towards the right in the Limb , the Line of shadows may from thence be graduated ; the Complement of this Ark is the Suns Altitude , answering to that length of the right shadow , being 18d 26′ . The Canon to make the Line of Latitudes , will be As the Radius to the Chord of 90d so the Tangents of each respective degree of the Line of Latitudes . To the Tangents of ohter Arks : The natural Sines of which Arks are the numbers that from a Diagonal Scale of equal parts shall graduate the Divisions of the Line of Latitudes to any Radius . To draw the Projection . Those Lines that cross each other , are Arches of Circles , whose Centers fall in two streight Lines . Of the Paralels of Altitude . All those Arks whose Aspect denotes them to be drawn from the right edge of the Quadrant towards the left , are called Paralels of Altitude , and their Centers fall in the right edge of the Quadrant , continued both beyond the Center and Limb so far as is needful . To find the Intersections of the Paralels of Altitude , with the Meridian , that is , Points therein limiting the Semi-diameters of the Paralells . Assume any Point in the right edge of the Quadrant , ( which is called the Meridian Line ) near the Limbe to be the Tropick of Cancer ; the distance of this Point from the Center of the Quadrant , must represent the Tangent of 56d 46′ which is half the Suns greatest Declination more then the Radius ; the distance of the Equator from the Center , shall be equal to the Radius of this Tangent . For the finding the Intersections of the other Paralells of Altitude , it will be best to make a Line of Semi-tangents to the same Radius , that is to number each degree of this Tangent with the double Ark , and so every half degree will become a whole one : Out of this Line of Semi-tangents prick off from the Center of the Quadrant 66d 29′ the Complement of the Suns greatest Declination , which will find the Intersection of the Tropick of Capricorn with the Meridian . Now to fit the Projection to any particular Latitude : Out of the said Line of Semi-tangents from the Center of the Quadrant , prick off the Latitude of the place , and it will find a point in the Meridian Line , where the Horizon , or Paralell of 00d of Altitude will intersect the Meridian ; this Point is called the Horizontal Point , and serves for finding the Centers of all the Paralells . To the Latitude of the place add each degree of Altitude successively till you have included the greatest Meridian Altitude ; these compound Arks are such as being prickt from the Center of the Quadrant out of the Line of Semi-tangents will find points in the Meridian Line , limiting the Semi-diameters of the paralells of Altitude . Above the Horizon , and between the Circle that bounds the Projection falls a portion thereof called the Reverted Tail , which otherwise would if it had not been there reverted , have excurred the limits of a Quadrant . To find the Intersections for those Paralells of Altitude , substract successively each degree out of the Latitude of the place , and the remaining Arks prick from the Center out of the Line of Semi-tangents : The use of this Tail being to find the hour and Azimuth before or after 6 in the Summer time only , it need be continued no further above the Horizon then the Ark of the Suns greatest Altitude at 6 , which at London is 18d 12′ . To finde the Centers of the Paralells of Altitude . These are to be discovered by help of a Line of natural Tangents , not numbred with the double Arks , whose Radius must be equal to the distance of the Equator from the Center of the Quadrant , or which is all one to 90d of the Line of Semi-tangents : Out of this Line of Tangents prick off beyond the Center of the Quadrant the Complement of the Latitude , the distance between the Point thereby found , and the Horizontal Point is the Semi-diameter wherewith the Horizon is to be drawn . To find the Centers of the rest of the Paralells . To the Complement of the Latitude add each degree of Altitude successively till you have included the greatest Meridian Altitudes ; The Tangents of these Arks prick beyond the Center , the distance from the Points so discovered to the Horizontal Point , are the Semi-diameters of the Paralells of Altitude ; the extreamities of which Semi-diameters being limited in the Meridian Line ; these extents thence prict , finds their Centers . Some of these Compound Arks will exceed 90 degrees , as generally where any Meridian Altitude is greater then the Latitude . In this case substract those Arkes from 180d and prick the Tangents of the remaining Arks from the Center of the Quadrant on the Meridian Line continued beyond the Limbe , and then as before the distances between those Points and the Horizontal Point , are the Semi-diameters of those Paralells , whose Extremities are limited in the Meridian Line . To find the Centers of the Paralells of the reverted Tail. From the Complement of the Latitude substract each degree of Altitude in order , till you have included the greatest Altitude of 6 the Tangent of the remaining Arks prick from the Center of the Quadrant , and you will find such Points the distances between which and the Horizontal Point are the Semi-diameters of those Paralells . To find the Centers and Semi-diameters of the Azimuths . All those Portions of Arks which issue from the top of the Projection towards the Limb are called Azimuths , the Centers of them all fall upon that Paralell of Altitude which is equal to the Latitude of the place whereto the Projection is fitted , which will always be a streight Tangent Line . Out of the former Line of Tangents , whose Radius is equal to the distance of the Equator from the Center of the Quadrant , prick down the Latitude of the place on the Meridian Line , and thereto perpendicularly erect the Line for finding the Centers of the Azimuths , which must be continued through and beyond the Projection . Out of the said Line of Tangents and beyond the Center prick down the Tangent of half the Complement of the Latitude at London 19d 14 m and it will discover a Point which is called the Zenith Point , because in it all the Azimuths do meet ; The distance between this Point and the Point where the Center Line of the Azimuths intersects the Meridian make the Radius of a Tangent , out of which Tangent prick down each degree successively , both within and beyond the Projection on the Line of Centers , and you have the Centers for all the Azimuths ; where note , that the Centers of all Azimuths which exceed 90d will fall within the Projection , and of all others without , the distances of these respective Points from the Zenith Point , are the Semi-diameters of the Azimuths , with which extents let them be respectively drawn . To draw the Summer and Winter Ecliptick and to divide them . The Summer Ecliptick is drawn from the Point of the Equator in the left edge of the Quadrant to the Tropick of Cancer , and the Winter thence to the Tropick of Capricorn out of a Line of Tangents to the Radius equal to the distance of the Equator , from the Center prick down the Tangent of 23d 31′ the Suns greatest declination from the Center of the Quadrant on the Meridian Line towards the Limbe , and you shall discover the Center of the Summer Ecliptick with the same extent , being the Semi-diameter thereof , set one foot down at the Tropick of Capricorn , and the other will fall beyond the Center of the Quadrant on the right edge , and discovers the Center for drawing the Winter Ecliptick ; to divide them use this Canon . As the Radius to Tangent of the Suns distance from the nearest Equinoctial Point : So the Cosine of the Suns greatest Declination : To the Tangent of the Suns right Ascension , which must be counted in the Limbe , and from it the Suns true place graduated on both the Eclipticks . To draw the two Horizons , and to divide them . One of the Horizons is the Paralel of 00d of Altitude , which being intersected by the Azimuth Circles , is thereby divided into the degrees of the Suns Amplitude ; this is the upper Horizon , and the drawing hereof was shewed already . The other Horizon is but this inverted , and the Divisions transferred from that , the Center of it is found by pricking the Tangent of the Complement of the Latitude on the Meridian Line from the Center of the Quadrant , the distance of the Equator being Radius . But it may be also done from the Limbe by the Proportion following . As Radius , to Tangent of the Latitude ; So the Tangent of the Suns greatest Declination , to the sine of the greatest Ascensional difference ( which converted into Time , gives the time of the Suns rising or setting before or after 6 ) by which Ark of the Limbe the Horizon is limitted ; Then to divide it say As the Radius , to the Tangent of the assigned Amplitude : So is the Sine of the Latitude : To the Tangent of the Ascensional difference agreeing thereto , which counted in the Limb , from it the Amplitudes may be divided on both the Horizons ; and note , if these Amplitudes be not coincident with those the Azimuths have designed , then are the said Azimuths drawn false . To inscribe the Stars on the Projection . Such only , and no other as fall between the two Tropicks , may be there put on . Set one foot of the Compasses in the Center of the Quadrant , and extend the other to that place of either of the Eclipticks , as corresponds to the given declination of the Star , and therewith sweep an occult Ark : I say then that a Thread from the Center of the Quadrant laid over the Limb to the Stars right Ascension where it intersects , the former occult Ark is the place where the proposed Star must be graduated . Of the Almanack . There is also graved in a Rectangular Square , or Oblong , a perpetual Almanack , which may stand either on the foreside or back of the Quadrant , as room shall best permit . On the Backside of the Quadrant there is , 1. On the right edge a Line of Signs issuing from the Center , the Radius whereof is in length 5 inches . 2. On the left edge a Line of Chords issuing from the Center . 3. On the edges of the Quadrant there are also two Scales for the more ready finding the Hour and Azimuths in one Latitude ; the Hour Scale is no other then 62d of a Line of Sines , whose Radius is made equal to half the Secant of the Latitude being fitted for London ) to the common Radius of the Sines ; the prickt Line of Declination annexed to it , and also continued beyond the other end of it , to the Suns greatest Declination is also a portion of a Line of Sines , the Radius whereof is equal to the Sine of the Latitude taken out of the other part of the Scale , or which is all one the Sine of the Suns greatest declination is made equal to the Sine of the greatest Altitude at the hour of 6 taken out of the other part of the Scale , which at London is 18d 12 m 4. The Azimuth Scale is also 62d of a Line of Sines , whose Radius is made equal to half the Tangent of the Latitude to the common Radius of the Sines , the Line of the Declination annexed to it , and continued beyond it : To the Suns greatest Declination is also a portion of a Line of Sines of such a length whereof the Sine of the Latitude is equal to the Radius of the Sines of the other part of this fitted Scale ; or which is all one , the length of the Suns greatest Declination is made equal to the Suns greatest Vertical Altitude , which in this Latitude is 30d 39′ of the other Sine or Line of Altitudes . The Limbe is numbred both with degrees and time , from the right edge towards the left . Between the Limbe and the Center are put on in Circles , the Scales following . 1 , A Line of Versed Sines to 180 degrees . 2. A Line of Secants to 60d the graduations whereof begin against 30d of the Limbe , to apply which Vacancy , and for other good uses , there is put on a Line of 90 Sines , ending where the former graduations begin ; this is called the lesser Sines . 3. A Line of Tangents graduated to 63d 26′ 4. A Line of Versed Sines to 60d through the whole Limbe , called the Versed Sines quadrupled , because the Radius hereof is quadruple to the Radius of the former Versed Sines . 5. A Line of double Tangents , or Scale of hours , being the same Dyalling Scale as was described on the foreside . 6. A Tangent of 45d or three hours through the whole Limbe for Dyalling , which may also be numbred by the Ark doubled to serve for a Projection Tangent , alias a Semi-tangent . 7. In another Quadrant of a Circle may be inscribed a portion of a Versed Sine to eight times the Radius encreased , of that of 180d called the Occupled Versed Sine , and at the end of this from the other edge , another portion of a Versed Sine to 12 times the Radius encreased may be put on . 8. Lastly , above all these is the Scale of Hours or Nocturnal with Stars names graved within it towards the Center ; this is divided into 12 equal hours and their parts , and the Stars are put on from their right Ascensions , only with their declination figured against them . All the Lines put on in Quadrants of Circles must be inscribed from the Limbe by help of Tables , carefully made for that purpose ; an instance shall be given how the Line of Versed Sines to 180d was inscribed , and after the same manner that was put on , must all the rest : Imagine a Line of Versed Sines to 180d to stand upon the left edge of a Quadrant from the Center with the whole length thereof upon the Center sweep the Arch of a Circle , and then suppose Lines drawn through each graduation or degree thereof continued parralel to the right edge till they intersect the Arch formerly swept which shall be divided in such manner as the Line of Versed Sines on this Quadrant is done . But to do this by Calculation , A Table of natural Versed Sines must first be made , which for all Arks under 90d are found by substracting the Sine Complement from the Radius , so the Sine of 20d is 34202 which substracted from the Radius rests 65798 , which is the Versed Sine of 70d : And for all Arks above 90d are got by adding the Sine of the Arks excess above 90d unto the Radius : thus the Versed Sine of 110d is found by adding the Sine of 20d to the Radius , which will make 134202 for the Versed Sine of the Said Ark. This Table , or the like of another kind , being thus prepared , the proportion for inscribing of it will hold . As the length of the Line supposed to be posited on the left edge , Is to the Radius , So is any part of that length To the Sine of an Arch , which sought in the Tables , gives the Arch of the Limbe against which the degree of the Line proposed must be graduated . But in regard the Versed Sine of 180d is equal to the double of the Radius ; the Table for inscribing it will be easily made by halfing the Versed Sine proposed , and seeking that half in the Table of natural Sines , so the half of the Versed Sine of 70d is 32899 which sought in the Table of natural Sines , gives 19d 13′ fore of the Limb against which the Versed Sine aforesaid is to be graduated , and so the half of the Versed Sine of 110d is 67101 which answers to 42d 9′ of the sines or Limb. So likewise the Table for putting on the lesser Sines was made by halfeing the natural Sines , and then seeking what Arks corresponded thereto in the natural Sines aforesaid ; those that think these Lines to many may very well want the Versed Sines so oft repeated ; And they that will admit of a Radius of 6 or 7 inches , may have the Line of Lines Superficies and Solids , put on in the Limb on the foreside , and the Segments Quadrature , Equated Bodies , Mettalls , and inscribed Bodies , or other Lines at pleasure put on upon the backside , as hath been already done upon some Quadrants . Now to the Use . The Vses of the PROJECTION . Of the Almanack . BEfore the Projection can be used , the day of the Moneth , the Suns place or Declination must be known ; but these are commonly given by the knowledge thereof : Now this Almanack will as much help to the obtaining hereof , as any other common Almanack . It consists of a Rectangular Oblong , or long Square divided into 7 Colums in the breadth to represent 7 days of the week , accounting the Lords day first ; and length ways into 9 Columns , the two uppermost represent the months of the year , accounting March the first , the five middlemost the respective days of each Month , and the two undermost some certain leap years , posited in such Columns , as that thereby may be known by Inspection , what day of the Week the first of March happened upon in the said Leap years ; the contrivance hereof owns its original from my Worthy Friend Mr. Michael Darie , for the due placing of the Months over the Columns of days , take the following Rule in his own words . First having March assign'd to lead the round , The rest o' th Months are easily after found ; If that you take the complement in days To 35 of a plac'd Month always , And count it from its place with due Progression It shews you where the next Month takes possession . Thus placing the Month of March first , then if I would place April , or the second Month , March having 31 days , the Complement thereof to 35 is 4 then counting four Columns from the place of March , it falls upon the 5 Column , where the figure 2 is placed for the 2d Moneth , then April being placed ; if I would place May I take 30 , the number of days in April , from 35 there rests 5 , and counting 5 Columns from the place of April where it ends , which is in the 3d Column , the figure 3 is placed for the 3d Moneth or Moneth of May. The next thing to be known is on what day of the Week the first day of March falleth upon , which is continually to be remembred in using the Almanack . This for some Leap years to come , may be known by counting in what Column the said Leap year is graved , thus in Anno 1660 , the first of March falls upon a Thursday , because 60 is graved in the 5 Column , that being the fift day of the Week : But for a general Rule take it in these words . To the number two add the year of our Lord , and a fourth part thereof , neglecting the odd remainder , when there is any ; the Amount divide by 7 the remainder , when the Division is finished , shews the number of Direction , or day of the week , on which the first day of March falleth , accounting the Lords day the first ; but if nothing remain , it falls on a Saturday .   2   Example for the year 1657 The even fourth thereof 414   2073 ( 296 quotient . 7 ) 1 remaining .   By this Rule there will be found to remain one for the year of our Lord 1657 whence it follows that the first day of March fell on the first day of the Week , alias , the Lords day in that year ; so in Anno 1658 , there remains 2 for Munday : in 1659 , rests 3 for Tuesday ; in 1660 rests 5 for Thursday ; so that hence it may be observed , that every 4 years the first of March proceeds 5 days : Upon which supposition the former Rule is built ; say then As 4 to 5 , or as 1 to 1¼ so is the year of the Lord propounded , to the number of days , the first of March hath proceeded in all that Tract , caused by the odd day in each year , and the Access of the days for the Leap years ; this number divided by 7 , the remainder shews the fractionate part of a Week above whole ones , which the said day hath proceeded , which wil not agree with the day of the Week the first of March falls upon , according to common tradition , unless the number two be added thereto , which argues that the first of March , as we now account the days of the week fell upon Munday , or the second day of the week in the year of our Lords Nativity : This is only for Illustration of the former Rule , being to shew that the adding of the even fourth part of the year of our Lord thereto , works the proportion of 4 to 5. The Vse of this Almanack is to know for ever on what day of the Week any day of the Month falls upon . Remembring on what day of the Week the first day of March fell upon in the year propounded ( which doth then begin in the use of this Almanack , and not sooner or later , as upon New-years day , or Quarter day ) all the figures representing the days of the Month do also represent the same day of the week in the respective Months under which they stand ; and the converse , the Moneth being assigned , all the figures that stand as days under it , inform you what days of the said Month the Week day shall be the same , as it was upon the first day of March , and then by a due Progression it will be easie to find upon what day of the Moneth any day of the week falleth , as well as by a common Almanack , without the trouble of always one , and sometimes two Dominical Letters quite shunned in this Almanack , by beginning the year the first of March , and so the odd day for Leap year is introduced between the end of the old , and the beginning of the new-year . Example . In Anno 1657. looking for the figure 10 in the Column for Months , for the Month of December ; under it I find 6 , 13 , 20 , 27 , now the first of March being the Lords day , I conclude also that these respective days in December , were likewise on the Lords day ; and from hence collect , that Christmas day , which is always the 25 of that Month , happened on a Friday . Vses of the Projection . THis Projection is no other then a fourth part of Stoflers particular Astrolabe , fitted for the Latitude of London inverted , that is , the Summer Tropick and Altitudes , &c. turned downwards towards the Limb , whereas in his Astrolabe they were placed upwards , towards the Center ; thus the Quadrant thereof made , is rendred most useful and accurate when there is most occasion for it ; before the projection can be used , the Bead must be rectified , and because the Thread and Bead may stretch , there may be two Beads , the one set to some Circle concentrick to the Limb , to keep the other at a certainty in stretching , and the other to be rectified for use . To rectifie the Bead. LAy the Thread over the day of the Month in its proper Circle , and if the season wherein the Quadrant is to be used , be in the Winter half year , set the Bead by removing it to the Winter Ecliptick ; but in Summer let it be set to the lower or Summer Ecliptick , and then it is fitted for use , One Caution in rectifying the Bead is to be given ; and that is in Summer time if it be required to find the hour and Azimuth of the Sun by the Projection , before the hour of 6 in the morning , or after it in the evening , or which is all one , when the Sun hath less Altitude then he hath at 6 of the clock ; then must the Bead be rectified to the Winter Ecliptick , and the Parralels above the Horizon in the Reverted Tail , are those which will come in vse . To find what Altitude the Sun shall have at 6 of the clock in the Summer half year . This will be easily performed by bringing the Bead that is rectified to the Summer Ecliptick to the left edge of the Quadrant , and-there among the Paralels of Altitude it shews what Altitude the Sun shall have at 6 of the clock : It also among the Azimuths shews what Azimuth the Sun shall have at the hour of 6. Example , So when the Sun hath 17 degrees of North Declination , as about the 27 of April , his Altitude at the hour of 6 will be found to be 13d 14 m and his Azimuth from the Meridian 79d 14 m whence I may conclude if his observed Altitude be less upon the same day , and the Hour and Azimuth sought , the Bead must be set to the Winter Ecliptick , and the Operation performed in the reverted Tail. Here it may be noted also that the exactest way of rectifying the Bead , will be either from a Table of the Suns Declination , laying the Thread over the same in the graduated Circle , or from his true place , laying it over the same in the proper Ecliptick , or from his right Ascension counted in the Limb. Or Lastly from his Meridian Altitude on the right edge of the Quadrant , for these do mutually give each other the Bead , being rectified to the respective Ecliptick as before . for Example . To find the Suns Declination . The Thread laid over the day of the Moneth , intersects it upon that Circle whereon it is graduated , which in the Summer half year is to be accounted on this side the Equinoctial , North , and in the Winter-half year , South ; so laying the Thread over the 27th . day of April , it intersects the Circle of Declination at 17 degrees , and so much was the Suns Declination . To find the Suns true place . The Thread lying as before , shews it on the respective Ecliptick , So the Thread lying over the 17 of April , will cut the Summer Ecliptick , in 17d 7 m of Taurus ; or in 12d 53 m of Leo , which agrees to the 26 day of July , or thereabouts , the Thread intersecting both these days at once ; and the opposite points of the Ecliptick hereto , are 17d● m in Scorpio , about the 20 of October ; and 12d 53 m of Aquarius , about the 22d of January , all shewed at once by the Threads position . To find the Suns right Ascension . Lay the Thread over the day of the Month as before , and it intersects it in the equal Limb ; whence taking it in degrees and minutes of the Equator , whilst the Sun is departing from the Equator towards the Tropicks , it must be counted as the graduations of the Limb , from the left edge towards the right ; but when the Sun is returning from the right edge towards the left ; the right Ascension thus found , must be estimated according to the season of the year . From June 11 to Sept. 13 It must have 90 degrees added to it . Sep. 13 to Dec. 11 It must have 180 degrees added to it . Dec. 11 to Mar. 10 It must have 270 degrees added to it . But in finding the Hour of the night by the Quadrant , we need no more then 12 hours of Ascension , for either Sun or Star , and the Limb is accordingly numbred from the left edge towards the right , from 1 to 6 in a smaller figure , and thence back again to 12 , and the other figures are the Complements of these to 12. so that when the Sun is departing from the Equator towards the Tropicks ; his right Ascension is always less then 6 hours , and the Complement of it more ; but when he is returning from the Tropicks towards the Equator , it is always more then 6 hours , and the Complement of it less ; the odd minutes are to be taken from the Limb , where each degree being divided into 4 parts , each part signifies a Minute of time , and to know whether the Sun doth depart from , or return towards the Equator , is very visible , by the progress and regress of the days of the month , as they are denominated on the Quadrant . Example . So the Thread laid over 17d of Declination , which will be about the 27 April The Suns right Ascension will be 44d 37 m In time 2 h 58′ 26 July The Suns right Ascension will be 135 23 In time 9 2 20 October The Suns right Ascension will be 224 37 In time 2 58 22 January The Suns right Ascension will be 315 23 In time 9 2 But here the latter 12 hours are omitted . Such Propositions as require the use of the Bead , are , To find the Suns Amplitude , or Coast of rising and setting from the true East or West . Bring the Bead , being rectified to either of the Eclipticks , it matters not which , to either of the Horizons , and the Thread will intersect the Amplitude sought , upon both alike : Example ; The Suns Declination being 17 North , or South , the Suns Amplitude , will be found to be 28● 2m. The Amplitude before found for the Summer half year , is to be accounted from East or West Northwards ; and in the Winter half year from thence Southwards . To find the time of the Suns rising or setting . The Thread lying in the same Position , as in the former Proposition , intersects the Ascensional difference in the Limb , which may there be counted either in degrees or Time. Example . So the Bead lying upon the Horizon , being rectified to 17● of Declination , the Thread intersects the Limb at 22d 38 m , which is 1 h 30 m of time , and so it shews the time of Suns rising in Summer , or setting in Winter , to be at half an hour past 4 ; and his rising in Winter , and setting in Summer , to be at half an hour past 7. To find the length of the Day or Night . The time of the Suns rising and setting are one of them ; the Complement of the other to 12 hours ; so that one of them being known , the other will be found by Substraction ; the time of Suns setting is equal to half the length of the day ; and this doubled gives the whole length of the day ; in reference to the Suns abode above the Horizon , the time of setting converted into degrees , is also called the Semi-diurnal Ark ; the time of Sun rising ( so converted is called the Semi-nocturnal Ark ) doubled gives the whole length of the Night ; so upon the 27th day of April , the Sun having 17d of Declination , the length of the day is 15 hours , and the length of the night 9 hours . To find the Suns Altitude on all Hours ; or at any time proposed . In Summer time , if the hour proposed be before 6 in the morning , or after it in the evening ▪ lay the Thread to the hour in the Limb , the Bead being first rectified to the Winter Ecliptick , and amongst the Paralels of Altitude above the upper Horizon , it shews the Altitude sought . Example . So the Sun having 16d of declination Northwards , as about the 24th of April , laying the Thread over the Declination , I set the Bead to the Winter Ecliptick , and if it were required to find what Altitude the Sun shall have at 36 minutes past 6 in the afternoon , lay the Thread over the same in the Limb , and the Bead among the Parralels of Altitude will fall upon 7d , At all other times the Operation is alike ; the Bead being rectified to that Ecliptick that is proper to the season of the year : Lay the Thread over the proposed hour in the Limb , and the Bead amongst the Parralels of Altitude , sheweth the Altitude sought . Example . So if it were required the same day to find what Altitude the Sun should have at 19 m past 2 in the afternoon ; Lay the Thread in the Limb over the time given , and the Bead among the Parralels of Altitude will fall upon 45d for the Altitude sought . To finde the Suns Altitude on all Azimuths . IN the Summer half year , if the Azimuth propounded be more Northward then the Azimuth of the Sun shall have at the hour of 6 ; The Bead must be rectified to the Winter Ecliptick , and brought to the Azimuth proposed above the upper Horizon , and there among the Parralels of Altitude , it sheweth the Altitude sought . So about the 24th of April , when the Suns Declination is 16d his Azimuth at 6 of the clock will be found to be 76d 54 m from the South ; Then if it were required to find the Suns Altitude upon an Azimuth more remote , as upon 107d from the South , laying the Thread over the Declination , I set the Bead to the Winter Ecliptick , and afterwards carrying it to the Azimuth proposed among the Parralels of Altitude above the upper Horizon , it falleth upon 7d for the Suns Altitude sought . In all other Cases bring the Bead rectified to the Ecliptick proper to the season of the year , to the Azimuth proposed ; and among the Parralels of Altitude it sheweth the Altitude sought ; So far the same day , I set the Bead to the Summer Ecliptick , and if it were required to know what Altitude the Sun shall have when his Azimuth is 50d 48′ from the Meridian carry the Bead to the said Azimuth , and among the Parralels of Altitude it will fall upon 45d for the Altitude sought . The Hour of the night Proposed to find the Suns Depression under the Horizon . IMagine the Sun to have as much Declination on the other side the Equinoctial , as he hath on the side proposed ; and this Case will be co-incident with the former of finding the Suns Altitude for any time proposed ; the reason whereof is because the Sun is always so much below the Horizon at any hour of the night , as his opposite Point in the Ecliptick is above the Horizon at the like hour of the Day . Such Propositions as depend upon the knowledge of the Suns Altititude , are to find the Hour of the Day , and the Azimuth ( or true Coast ) of the Sun. THe Suns Altitude is taken by holding the Quadrant steady , and letting the Sun Beams to pass through both the Sights at once , and the Thread hanging at liberty shews it in the equal Limb , if this be thought unsteady , the Quadrant may rest upon some Concave Dish or Pot , into which the Plummet may have room to play ; but for greate Quadrants there are commonly Pedistalls made . The Altitude supposed to find the Hour of the Day , and the Azimuth of the Sun in Winter . REctifie the Bead to the Winter Ecliptick , and carry it along amongst the Parralels of Altitude till it cut or intersect that Parralel of Altitude on which the Sun was observed , and the Thread in the Limb sheweth the hour of the Day , and the Bead amongst the Azimuths sheweth the Azimuth of the Sun. Example . So about the 18 of October , when the Suns Declination is 13d 20′ South if his observed Altitude were 18d the true time of the day would be found to be either 36 minutes after 9 or 24 minutes past 2 and his Azimuth would be 37 degrees from the South . To finde the Hour of the Day , and the Azimuth of the Sun at any time in the Summer half year . IT was before intimated , That if the question were put when the Sun hath less Altitude then he hath at the hour of 6 of the clock , that then the Operation must be performed among those Parralels above the upper Horizon , in the reverted Tail , the Bead being rectified to the Winter Ecliptick ; and that it might be known what Altitude the Sun shall have at 6 of the clock , by bringing the Bead rectified to the Summer Ecliptick , to the left edge of the Quadrant . So admitting the Sun to have 16d of North Declination , which will be about the 24 April , I might finde his Altitude at 6 of the Clock by bringing the Bead rectified to the Summer Ecliptick to the left edge of the Quadrant ; to be 12d 28 m whence I conclude , if his Altitude be less , the Bead must be rectified to the Winter Ecliptick , and be brought to those Parralels above the upper Horizon ; and it may be noted , that the Suns Altitude at 6 is always less then his declination . Example . Admit the 24th of April aforesaid the Suns observed Altitude were 7d laying the Thread over the Suns Declination , or the day of the month ; I rectifie the Bead to the Winter Ecliptick , and bring it to the said Parralel of Altitude above the upper Horizon ; and the Thread intersects the Limb at 9d 3 m shewing the hour of the day to be 24 minutes past 5 in the morning , or 36′ past 6 in the evening , and the Bead amongst the Azimuths shews the Azimuth or Coast of the Sun to be 107d from the South . Another Example . But admitting the Sun to have more Altitude then he hath at the hour of 6 , the Operation notwithstanding differs not from the former , but only in rectifying the Bead , which must be set to the Summer Ecliptick , and then carried to the Parralel of the Suns observed Altitude , and the Thread will intersect the Limb at the true time of the day , and the Bead amongst the Azimuths sheweth the true Coast of the Sun. So upon the 24th of April aforesaid , the Suns observed Altitude being 45d , I bring the Bead rectified to the Summer Ecliptick , to the said Parralel of Altitude , and the Thread intersects the Limb at 55d 15 m shewing the hour to be either 41 m past 9 in the morning , or 19 m past 2 in the ofternoon ; to be known which by the increasing or decreasing of the Altitude , and the Bead amongst the Azimuths shews the Azimuth or true Coast of the Sun to be 50d 40● from the South : Another Example . Admit when the Sun hath 19d 13 m of North Declination which will be about the 6th of May , his observed Altitude were 56d the Bead being set to the Summer Ecliptick , and brought to that Parralel of Altitude amongst the Azimuths shews the Suns true Coast to be 23d from the South , Eastwards in the forenoon , and Westwards in the afternoon , and the Thread in the Limb sheweth the true time of the day to be either 7′ past 11 in the forenoon , or 5● m past 12. The Depression of the Sun supposed to find the true time of the night with us , or the hour of the day to our Antipodes ; As also the true Coast of the Sun upon that Depression . THis Proposition may be of use to know when the Twilight begins or ends , which is always held to be when the Sun hath 18d of Depression under the Horizon , to perform this , Imagine as much Declination on the contrary side the Equinoctial , as the Declination given , and find the time of the Day , as if the Suns Altitude were 18d So when the Suns Declination is 16d North , as about the 24th of April , laying the Thread over it I rectifie the Bead to the Winter Ecliptick , and bringing it to the Parralel of 18d the Thread in the Limb shew the Twilight to begin at 54 m past 1 in the morning , and ends at 6′ past 10 at night , and the Azimuth of the Sun to be 28d 58′ which in this Case is to be accounted from the North. But if the Suns greatest Depression at night be less then 18d as that it may be in any Latitude where the Meridian Altitude at any time in Winter or the opposite Signe is less then 18d there is no dark night which in our Latitude of London will be from the 12th of May to the 11th of July . Of the Stars graduated on the PROJECTION . SUch Stars as are between the two Tropicks only , are there inscribed , and such haue many things common in their Motion with the Sun when he hath the like Declination , as the same Amplitude , Semidiurnal , Arke , Meridian , Altitude , Ascentional difference , &c. These Stars have Letters set to them to direct to the Circle of Ascensions on the back of the Quadrant , where the quantity of their right Ascension , is expressed from one of the Equinoctial points ; those that have more Ascension then 12 hours from the point of Aries , are known by the Character plus + set to them ; many more Stars might be there inserted , but if they have more then 23d 31′ of Declination , the Propositions to be wrought concerning them are to be performed with Compasses , by the general Lines on the Quadrant . To find the true time of the Day or Night when any Star commeth to the Meridian . In the performing of this Proposition we must make use of the Suns whole right Ascension in time , which how that might be known hath been already treated of , as also of the Stars whole right Ascension , which may be had from the Circle of Ascensions on the back of the Quadrant if 12 hours be added to the right Ascension of a Star taken thence that hath a Letter Character † affixed to it . Substract the Suns whole right Ascension from the Stars whole right Ascension , encreased by 24 hours when Substraction cannot be made without it , the remainder is less then 12 shews the time of the afternoon or night when the Star will be upon the Meridian ; but if there remain more then 12 , reject 12 out of it and the residue shews the time of the next morning when that Star will be upon the Meridian . Example . The 23d of December the Suns whole right Ascension is 18 hours 53′ which substracted from 4 ho : 16′ the right Ascension of the Bulls eye encreased by 24 there remains 9 h 23′ for the time of that Stars comming to the Meridian , and being substracted from 6 ho : 30′ the right Ascension of the great Dogg , there rests 11 ho : 37′ for the time of that Stars coming to the Meridian at night . This Proposition is of good use to Sea-men , who have occasion to observe the Latitude by the Meridian Altitude of a Star , that they may know when will be a fit time for observation . In finding the time of the Night by the Stars , we use but 12 ho : of right Ascension , nor no more in finding the time of their rising or setting , so that when it is found whether it be morning or evening is left to judgement , and may be known by comparing it with the former Proposition , if there be need so to do . To find the Declination of any of these Stars . This is engraven or annexed to the Stars names , yet it may be found on the Projection , by rectifying a Bead to the proposed Star , and bringing the Thread and Bead to that Ecliptick it wil intersect ; and in the same Position the Thread will intersect the said Stars declination in the Quadrant of Declinations ; if the Bead meet with the Summer Ecliptick the Declination is North , if with the Winter South . To find the Amplitude and Ascensional difference of any of the Stars on the Projection . BRing the Bead rectified to the Star to either of the Horizons , the Thread being kept in its due Extent , and where it intersects the same it shews that Stars Amplitude which varies not , and is Northward if the Star have North declination , otherwise Southwards , the Thread likewise intersecting the Limb , sheweth the Stars Ascensional difference . Example . So the Bead being rectified to the Bulls eye , and brought to the lower Horizon , shews the Amplitude of that Star to be 25d 54′ Northwards because the Star hath North Declination ; And the Thread lyeth over 20′ 49′ of the Limb which is this Stars Ascensional difference , which in Time is 1 ho 23 m The Thread in the Limb lyeth over 4 ho 37 m from midnight for the Stars hour of rising , and over 7 ho 23 m from the Meridian for the Stars hour of setting always in this Latitude which with the Amplitude varies not , except with a very small allowance in many years . To find a Stars Diurnal Ark , or the Time of its continuance above the Horizon . When the Star hath North Declination add the Ascensional difference of the Star before found in Time to 6 hours , the Sum is half the time . South Declination Subtract . the Ascensional difference of the Star before found in Time from 6 hours , the Residue is half the time . Of that Stars continuance above the Horizon , which doubled , shews the whole time , the Complement wherof to 24 ho is the time of that Stars durance under the Horizon . Example . So the Ascensional difference of the Bulls eye being in time 1 ho : 23 added to 6 hours , and the Sum doubled makes 14 hours 46 m for the Stars Diurnal Ark or abode above the Horizon , the residue whereof from 24 is 9 ho : 14 m for the time of its durance under the Horizon . To find the true time of the Day or night , when the Star riseth or setteth . THe Stars hour of rising or setting found as before , being no other but the Ascensional difference of the Star added to , or substracted from 6 hours ; which the Thread sheweth in the Limb the Bead being rectified to a Star , and brought to that Horizon it will intersect ; is not the true time of the night ; but by help thereof that may be come by ; this we have denominated to be the Stars hour , and is no other but the Stars horary distance from the Meridian it was last upon ; If a Star have North Declination the Stars hour of rising must be reckoned to be before 6 and the time of its setting after 6 South Declination the Stars hour of rising must be reckoned to be after 6 and the time of its setting before 6 Now the time of the Stars rising or setting found by this and the former Propositions must be turned into common time by this Rule . To the Complement of the Suns Ascension add the Stars Ascension , and the Stars hour from the Meridian it was last upon , the Amount if less then 12 shews the the time of Stars rising or setting accordingly ; but if it be more then 12 reject 12 as oft as may be , and the remaind-sheweth it . So upon the 23d of December for the time of the Bulls eye rising .   h m The Complement of the Suns Ascension found by the foreside of the Quadrant is — 5 7 And the said Stars Ascension on the backside is — 4 16 The Stars hour of rising is — 4 37 14 hours . From which 12 rejected rests 2 hours for the time of that Stars rising , which I conclude to be at 2 in the afternoon , because that Star was found to come to the Meridian at 23 m past 9 at night , the like Operation must be used to get the time of that Stars setting , which will be found to be at 4 ho 46 m past in the morning .   h m Complement ☉ Ascension — 5 7 Stars Ascension — 4 16 Stars hour of setting — 7 23 16 h. 46′ To find what Altitude and Azimuth a Star that hath North Declination shall have when it is 6 hours of Time from the Meridian . REctifie the Bead to the Star , and bring the Bead and Thread to the left edge of the Quadrant , and there among the Parralels of Altitude and Azimuths it sheweth what Altitude and Azimuth the Star shall have . Example . So the Bead being set to the Bulls eye , and brought to the left edge of the Quadrant it will be found to have 12′ 17′ Altitude , and 80d 3′ Azimuth from the South , when it is 6 hours of time from the Meridian , which Proposition is afterwards used to know to which Ecliptick in some Cases to rectifie the Bead as hath likewise been intimated before . The Azimuth of a Star proposed , To find what time of the Night the Star shall be upon that Azimuth , and what Altitude it shall then have . SUpposing the Azimuth proposed to be nearer the South Meridian then that Azimuth the Star shal have when it is 6 hours from the Meridian : Bring the Bead rectified to the Star , to the proposed Azimuth , and among the Parralels of Altitude it shews that Stars Altitude , and the Thread in the Limb shews that Stars hour to be turned into common time to attain the true time sought . Example . If the question were What Altitude the Bulls eye shall have when his Azimuth is 62d 48′ from South , this being less Azimuth then he hath at 6 hours from the Meridian , the rectified Bead being brought to the Azimuth sheweth among the Parralels the Altitude to be 39d and the Stars hour shewn by the Thread in the Limb is either 8 ho : 56′ or 3 ho : 4′ from the Meridian ; then if upon the 23 of December you would know at what time the Star shall have this Altitude on this Azimuth , Change the Stars hour into common time by the former Rule . Decemb. 23 Complement of ☉ Ascension 5 h 7′ 5 h 7′   Stars Ascension — 4 16 4 16   Stars hour — 8 56 3 4     18 19 12 27 And you will find it to be at 19′ past 6 in the evening , or at 27 m past midnight . For Stars of South Declination being they have no Altitude above the Horizon at 6 ho : distance from the Meridian , the operation will be the same , void of Caution . But for Stars of North Declination when the proposed Azimuth is more remote from the South Meridian then the Azimuth of that Star 6 ho from the Meridian , another Bead must be rectified to the Winter Ecliptick , and carried to the Azimuth proposed above the upper Horizon , where amongst the Parralels it shews the Altitude sought ; and the Thread in the Limb sheweth the Stars hour to be converted into common time . Example . The Azimuth of the Bulls eye being 107d 53′ from South , which is more then the Azimuth of 6 hours , the other Bead set to the Winter Ecliptick , and carried to that Azimuth in the Tail , shews the Altitude to be 6d and the Stars hour to be 5 ho : 18′ Or 6 ho : 42′ which converted into common time , as upon the 23d of December , will be either 41 m past 2 in the afternoon , or 5 m past 4 in the morning following . h ' h ' December 23 Complement Suns Ascension 5 7 5 7   Stars Ascension — 4 16 4 16   Stars hour — 5 18 6 42 Rejecting 12 the Total is — 2 41 Or 4 5 The Hour of the night proposed to find what Altitude and Azimuth any of the Stars on the Projection that are above the Horizon shall have at that time . FIrst turn common time into the Stars hour , the Rule to do it is , To the Complement of the Stars Ascension add the Suns Ascension , and the time of the night proposed , the Aggregate if less then 12 is the Stars hour ; if more reject 12 as oft as may be , and the remainder is the Stars hour sought . So the 23 of December , at 8 a Clock 59 minutes past at night what shall be the Horarie distance of the great Dogg from the Meridian Complement of great Doggs h ' Ascension — 5 30 Suns Ascension — 6 53 Time of the night — 8 59 The Sum is , 12 rejected — 9 22 Then for Stars of South Declination , rectifie the Bead to the Star proposed , and lay the Thread over the Stars hour in the Limb , and the Bead amongst the Parralels and Azimuths , shews the Altitude and Azimuth of the Star sought . Example . So the Bead being rectified to the great Dogg , and the Thread laid over 9 ho 22′ in the Limb , the Bead will shew the Altitude of that Star at that time of the night to be 14d and its Azimuth 39d from the South . The Operation is the same for Stars of North Declination when the Stars hour found as before is not more remote from the South Meridian then 6 hours on either side . But if it be more then 6 ho distance from the Meridian as before 6 after its rising , or after it before its setting , then as before suggested , one Bead must be rectified to the Star , and brought to the Summer Ecliptick , where the Thread being duly extended , another must be set to the Winter Ecliptick , and afterwards the Thread laid over the Stars hour in the Limb , this latter Bead will shew the Stars Azimuth and Parralel of Altitude in the reverted Tail above the upper Horizon . Example . So upon the 23 of December , I would know what Azimuth and Altitude the Bulls eye shall have at 4 a Clock 5 minutes past the morning following . Time proposed 4 h 5′ Complement of Bulls eye Ascension — 7 44 Suns Asce●sion 23 of December — 6 53 12 rejected rests — 6h 42′ Proceed then and lay the Thread over 42′ past 6 and the Bead among the other Paralels in the Tail sheweth the Stars Altitude to be 6d and its Azimuth from the Meridian 107d 53′ These two Propositions have a good tendency in them to discover such Stars as are upon the Projection if you know them not , but supposing them known the Proposition of chiefest use is By having the Altitude of a Star given to find out the true Time of the night , and the Azimuth of that Star. If the Stars observed Altitude be less then its Altitude at 6 ho : distance from the Meridian ; Bring the Bead , rectified to the Star , to the Summer Ecliptick and set another Bead to the Winter Ecliptick , Then carry it to the Parralell of Altitude above the upper Horizon in the Reverted taile and there it will shew the Azimuth of that Star ; and the thread in the Limbe shews the houre . Example . So if the observed Altitude of the Bulls eye were 6d its Azimuth would be found to be 107d 53′ from the South , and its hour 42′ past 6 from the Meridian the true time would be found to be 5 minutes past 4 in the morning the 24 of December .   ho :   Complement of ☉ Ascension the 23 of December — 5 7 Stars hour — 6 42 Stars Ascension — 4 16   4 5 But for Stars that have South declination or north , when their Altitude is more then their Altitude being 6 hours from the Meridian , this trouble of rectifying two Beads is shunned ; in this Case only bring the Bead that is rectified to the Star to the Parralel of Altitude , and there among the Azimuths it will shew the Stars Azimuth , and the Thread in the Limb intersects the Stars hour sought . Example . December 11th Bulls eye Altitude 39● Azimuth from the South 62d 48 Hours from the Meridian — 8 h 56′ Complement of ☉ Ascension — 6 00 Ascension of Bulls eye — 4 16 The true time of the night was 12′ past 7 of the Clock 7 12 Another Example . The great Doggs observed Altitude being 14d his Azimuth from the South would be 39d. h m And the Stars hour from the Meridian — 9 22 Stars Ascension — 6 30 If this Observation were upon the 31 of December , the Complement of the Suns Ascension would be — 4 30   8 22 And the true time of the night 22 minutes past eight of the Clock . For varieties sake there is also added to the Book a Draught of the Projection for the Latitude of the Barbados ; in the use whereof the Reader may observe that every day when the Sun comes to the Meridian between the Zenith and the Elevated Pole , he will upon divers Azimuths in the forenoon ( as also in the afternoon ) have two several Altitudes , and so be twice before noon , and twice afternoon , at several times of the day , upon one and the same Azimuth , viz. only upon such as lye between the Suns Coast of rising and setting , and his remotest Azimuth from the Meridian , which causeth the going forward and backward of the shaddow ; but of this more hereafter , when I come to treat of Calculating the Suns Altitude on all Azimuths ; It may also be observed that the Sun for the most part in those Latitudes hath no Vertical Altitude or Depression , and so comes not to the East or West . Moreover there is added a Draught of this Projection for the Latitude of Greenland , in the use whereof it may be observed that the Sun , a good part of the Summer half year comes not to the Horizon , and so neither riseth nor sets . And that no convenient Way that this Projection can be made should be omitted , there is also one drawn in a Semi-Circle for our own Latitude , which in the use will be more facile then a Quadrant , there being no trouble before or after six in the Summer time , with rectifying another Bead to perform the Operation in the reverted Taile , neither doth the Drawing hereof occupy near the Breadth , as in a Quadrant , and so besides the ease in the use is more exact in the performance ; there being no other Rule required for rectifying the Bead , but to lay the Thread over the day of the Month , and to set the Bead to that Ecliptick the Thread intersects . A Semi-Circle is an Instrument commonly used in Surveigh , and then it requires a large Center-hole ; however this Projection may be drawn on a Semi-Circle for Surveigh , but when used at home there must a moveable round Bit of brass be contrived to stop up that great Center-hole , in which must be a small Center-hole for a Thread and Plummet to be fastned , as for a Quadrant and some have been so fitted . The Reader will meet with variety of Lines and furniture in this Book to be put in the Limb , or on other parts of the Semicircle , as he best liketh . The Projection for the Barbados & Greenland , are drawn by the same Rules delivered in the Description of the Quadrant , and so also is the Summer part of this Semi-Circle , and the Winter part by the same Rules that were given for drawing the Reverted Taile . Of the Quadrant of Ascensions . The turning of the Stars hour into the Suns hour and the the converse may be also done by Compasses upon the Quadrant of Ascensions on the back side . To turn the Stars Hour into common time , called the Suns hour . THe Arithmetical Rule formerly given is nothing but an abridgment of the Rule delivered by Mr. Gunter , and others , and the work to be done by Compasses , differeth somewhat from it , though it produce the same Conclusion which is : To get the difference between the Ascension of the Sun and the Star by substracting the less from the greater ; this remainder is to be added to the Stars hour , when the Star is before , or hath more Ascension then the Sun , but otherwise to be substracted from it , and the Sum or remainder is the true time sought . To do this with Compasses , take the distance between the Star and the Suns Ascension , and set the Suns foot to the observed hour of the Star from the Meridian it was last upon , letting the other foot fall the same way it stood before , and it sheweth the time sought , if it doth not fall off the Quadrant . If it doth , the work will be to finde how much it doth excur , and this may be done by bringing it to the end beyond which it falleth , letting the other foot fall inward , the distance then between the place where it now falleth , and where it stood before , which was at the Stars hour , is equal to the said excursion , which being taken , and measured on the other end of the Scale , shews the time sought . This trouble may be prevented in all Cases , by having 12 hours more repeated after the first 12 , or 6 hours more may serve turn if the whole 18 hours be also double numbred , and Stars names being set to the Additional hours , possibly the Suns Ascension and Star do not both fall in the same 12 hours , yet notwithstanding the distance is to be taken in the same 12 hours between the quantity of the Suns Ascension and the Stars , and to proceed therewith as before , and the Compasses will never excur ; in the numbring of these hours , after 12 are numbred they are to begin again , and are numbred as before , and not with 13 , 14 , &c. And this trouble may be shunned when there is but 12 hours by assuming any hour to be the Stars hour , with such condition that the other foot may fall upon the Line ; and the said assumed hour representing the Stars hour ; count from it the time duly in order , till you fall upon the other foot of the Compasses , and you will obtain the true time sought . To turn common time , or the Suns hour into the Stars hour . THis is the Converse of the former ; take the distance between the Star and the quantity of the Suns Ascension , and set the Star foot to the Suns hour , letting the other fall the same way it stood before , and it shews the time sought . Of the Quadrat and Shaddows . Both these as was shewed in the Description of the Quadrant , are no other then a Table of natural Tangents to the Arks of the Limb and may supply the use of such a Cannon , though not with so much exactness , all the part of the Quadrate are to be estimated less then the Radius , till you come against 45● of the Limb , where is set the figure of 1 , and afterwards amongst the shadows is to be accounted more then the Radius , and so where the Tangent is in length 2 Radii as against 63d 26 m of the Limb. 3 Radii as against 71 34 of the Limb. 4 Radii as against 75 58 of the Limb. 5 Radii as against 78 42 of the Limb. are set the figures 2 , 3 , 4 , 5 , and because they are of good use to be repeated on the other side of the Radius in the Quadrat , there they are not figured , but have only full points set to them , falling against the like Arks of the Limb from the right edge towards the left , as they did in the shadows from the left edge towards the right . To find a hight at one Observation . LEt A B represent a Tower , whose Altitude you would take , go so far back from it that looking through the sights of the Quadrant , the Thread may hang upon 45 degrees of the Limb , or upon 1 , or the first prick of the Quadrat , and the distance from the foot of the Tower will be equal to the height of the Tower above the eye , which accordingly measure , and thereto add the height of the eye above the ground , and you will have the Altitude of the Tower. So if I should stand at D and find the Thread to hang over 45d of the Limb , I might conclude the distance between my Station and the Tower to be equal to the height of the Tower above my eye , and thence measuring it find to be 96 yards , so much would be the height of the Tower above the eye . If I remove farther in till the Thread hang upon the second point of the Quadrat , then will the Altitude of the Tower above the level of the eye be third point of the Quadrat , then will the Altitude of the Tower above the level of the eye be fourth point of the Quadrat , then will the Altitude of the Tower above the level of the eye be fifth point of the Quadrat , then will the Altitude of the Tower above the level of the eye be twice thrice four times as much as the distance from the Tower is to the Station . five times as much as the distance from the Tower is to the Station . So removing to C ; I find the Thread to hang upon the second point of the Quadrat , and measuring the distance of that Station from the Tower , I find it to be 48 yards , whence I may conclude the Tower is twice as high above my eye , and that would be 96 yards . So if I should remove so much back that the Thread should hang upon 2 of the shaddows &c. as E the distance between 3 of the shaddows &c. at F the distance between 4 of the shaddows &c. 5 of the shaddows &c. the Station and the foot of the Tower would be twice thrice four times five times as much as the height of the Tower above the eye , and consequently if I should measure the distance between D and E where it hung upon 1 and 2 of the Shaddows , or between E and F , where it hung upon 2 and 3 of the shaddows , &c I should find it to be equal to the Altitude ; but other ways of doing it when inaccessible will afterwards follow . A Second way at one Station . WIth any dimension whatsoever of a competent length , measure off from the foot of the Object , whether Tower or Tree , just 10 or 100 , &c. of the said Dimensions , as suppose from B to K , I measure of an hundred yards ; there look through the sights of the Quadrant to the Top of the Object at A , and what parts the Thread hangs upon in the Quadrat or Shadows , shews the Altitude of the Object in the said measured parts , and so at the said Station at K the Thread will hang upon 96 parts , shewing the Altitude A B to be 96 yards above the Level of the eye , and so if any other parts were measured off , they are to be multiplyed by the Tangent of the Altitude , or parts cut by the Thread , rejecting the Ciphers of the Radius , as in the next Proposition . A third way by a Station at Random . TAke any Station at Random as at L , and looking through the sights observe upon what parts of the Quadrat or Shadows the Thread falls upon , and then measure the distance between the Station and the foot of the object , and the Proportion will hold . As the Radius To the Tangent of the Altitude , or to the parts cut in the Quadrat or shadows , So is the distance between the Station and the Object To the height of the Object above the eye . So standing at L , the Thread hung upon 30d 58 m of the Limb , as also upon 600 of the Quadrat , the Tangent of the said Ark and the measured distance L B was 160 yards , now then to work the former Proportion , multiply the distance by the parts of the Quadrat , and from the right hand of the product cut off three places , and you have the Altitude sought . In this Work the Radius or Tangent of 45d is assumed to be 1000. To measure part of an Altitude , as suppose from a window in a Tower to the top of the Tower , may be inferred from what hath been already said ; first get the top of the Tower by some of the former ways , and then the height of the window which substract from the former Altitude and the remainder is the desired distance between the window and the top of the Tower. The former Proportion may also be inverted for finding of a distance by the height , or apprehending the Tower to lye flat on the ground , and so the height to be changed into a distance and the distance into a height , the same Rules will serve only the height of a Tower being measured , and from the top looking to the Object through the sights of the Quadrant , what Angle the Thread hangs upon is to be accounted from the right edge of the Quadrant towards the left ; but in taking out the Tangent of this Ark , after I have observed it , the Thread must be laid over the like Ark of the Quadrant from the left edge towards the right , and from the Quadrat or Shaddows the Tangent taken out by the Intersection of the Thread , and so to measure part of a distance must be done by getting the distances of both places first , and then substract the lesser from the greater . To find the Altitude of any Perpendicular , by the length of its shadow . THis will be like the first Proposition , with the Quadrant take the Altitude of the Sun , if in so doing the Thread hang over the 1st pricks in the Quadrat , the length of the Shaddow is equal to the height of the Object Tree , or Perpendicular 2d pricks in the Quadrat , the length of the Shaddow is double the height of the Object Tree , or Perpendicular 3d pricks in the Quadrat , the length of the Shaddow is triple the height of the Object Tree , or Perpendicular 4th pricks in the Quadrat , the length of the Shaddow is four times the height of the Object Tree , or Perpendicular 5th pricks in the Quadrat , the length of the Shaddow is five times the height of the Object Tree , or Perpendicular whatever it be ; But if it hang 1 in the shaddows 2 in the shaddows 3 in the shaddows 4 in the shaddows 5 in the shaddows the highth of the object is equal to the length of the double the length of the triple the length of the four times the length of the five times the length of the Shaddow which may happen where the Sun hath much Altitude , as in small Latitudes , and so the length of the Shadow being forthwith measured , the height of the Gnomon may be easily attained . If the Thread in observing the Altitude hang on any odd parts of the Quadrant or Shadows , the Proportion will hold as before . As the Radius To the length of the Shadow , So the Tangent of the Suns Altitude , or the parts cut by the Thread To the height of the Gnomon to be wrought as in the third Proposition ; if the length of the Gnomon , and the length of its shadow were given ; without a Quadrant we might obtain the Suns Altitude , for As the length of the Gnomon Is to the Radius So is the Length of its Shadow To the Tangent of the Complement of the Suns Altitude . And the height of the Sun , and the length of the Gnomon assigned ; We may find the length of the Shadow by inverting the Proportion aforesaid . As the Radius To the length of the Gnomon So the Cotangent of the Suns Altitude To the Length of the Shadow . To find an innaccessible Height at two Stations . To work this with the Pen , Out of the Line of Sines take the Sine of 70d with Compasses , and measure it on the equal parts , where admit it reach to 94 parts , Then multiply the said number by the distance 102 , 1 and the Product will be 95 , 974 from which cutting off three figures to the right hand the residue being 95 , 974 , is the Altitude sought feré , but should be 96 caused by omitting some fractionate parts in the distance which we would not trouble the Reader withall . Another more general way by any two Stations taken at randome . ADmit the first Station to be as before at G where the observed Altitude of the Object was 70d and from thence at pleasure I remove to H , where observing again I find the Object to appear at 48d 29 m of Altitude , and the measured distance between G and H to be ●0 yards , a general Proportion to come by the Altitude in this case will hold . As the difference of the Cotangents of the Arks cut at either Station . Is to the Distance between the two Stations , So is the Radius To the Altitude of the Object or Tower. To save the substracting of the two Arks from 90d to get their Complements , I might have accounted them when they were observed from the right edge of the Quadrant towards the left , and have found them to have been 20d and 41d 31 m ; to work this Proportion lay the Thread over these two Arks in the Limb from the left edge towards the right , and take out their Tangents out of the Quadrat and Shadows , then substract the less from the greater , the remainder is the first tearm of the Proportion , being the Divisor in the Rule of three to be wrought by annexing the Ciphers of the Radius to the Distance ; or as Multiplication in Decimalls ; and then dividing by the first tearm the Quotient shews the Altitude sought , 41d 31′ Tangent from the Shadows is — 885 20d Tangent from the Quadrat is — 364 Difference — 521 By which if I divide 50000 — the distance encreased by annexing the Ciphers of the Radius thereto , the Quotient will be 96 fere the Altitude sought . This may be performed otherwise without the Pen , as shall afterwards be shewn ; If the distance from the Stations either to the foot or the top of the Tower be desired , the Proportions to Calculate them will be As the difference of the Cotangents of the Arks cut at either Station Is to the distance between those Stations , So is the Cotangent of the greater Arke to the lesser lesser Arke to the greater distance from the Station to the foot of the Tower : And so is the Cosecant of the greater Ark to the lesser distance lesser Ark to the greater distance from the top of the Tower to the eye , Or having first obtained the Height , we may shun these Secants , for As the Sine of the Ark of the Towers observed Altitude at the first Station . Is to the height of the Tower or Object above the eye , So is the Radius To the distance between the Eye and the Top of the Tower ; and by the same Proportion using the Ark at the second Station , the distance thence between the Eye and the Top of the Tower may be likewise found . If any one desire to shun this Proportion in a difference , as perhaps wanting natural Tables , it may be done at two Operations : The first to get the distance from the eye to the Top of the Tower at first Station , in regard the difference of two Arks is equal to the difference of their Complements , it will hold As the Sine of the Ark of difference between the Angles observed at each Station Is to the distance between the two Stations , So is the Sine of the Angle observed at the furthest Station , To the distance between the eye and the Top of the Object at the first Station , which being had , it then holds , As the Radius To the said Distance , So the Sine of the Angle observed at the first Station , To the Altitude of the Object . The rest of the Lines on the Quadrant are either for working of Proportions , or for Protractions , and Dyalling depending thereon ; wherefore I thought fit to reduce all the common Cases of Plain and Sphoerical Triangles to setled Cannons , and to let them precede their Application to this or other Instruments , which shall be endeavoured ; it being the cheif aim of this Book to render Calculation facil , in shunning that measure of Triangular knowledge hitherto required , and to keep a check upon it . Some Affections of Plain TRIANGLES . THat any two sides are greater then the third . That in every Triangle the greater side subtendeth the greater Angle , and the Converse . That the three Angles of every Triangle are equal to two right Angles , or to 180. That any side being continued , the outward Angle is equal to the two inward Opposite ones . That a Plain right angled Triangle hath but one right Angle , which is equal to both the other Angles , and therefore those two Angles are necessarily the Complements one of another . By the Complement of an Arch is meant the residue of that Arch taken from 90d unless it be expressed the Complement of it to 180d , to save the rehearsal of these long Words , The Tangent of the Complement , The Secant of the Complement ; others are substituted , namely the Cotangent and the Cosecant . An Obutse angular Triangle hath but one Obtuse angle , an Acutangular Triangle hath none . If an Angle of a Triangle be greater then the rest , it is Obtuse , if less Acute . The Side subtending the right Angle is called the Hipotenusal and the other two the Sides or Leggs . 1. To find a side . Given the Hipotenusal , and one of the Acute Angles , and consequently both . As the Radius , To the Sine of the Angle opposite to the side sought : So is the Hipotenusal , To the side sought . 2. To find a Side . Given the Hipotenusal and the other side . As the Hipotenusal To the given side : So is the Radius to the Sine of the Angle opposite to the given side . Then take the Complement of that Angle for the other Angle . As the Radius , to the Hipotenusal : So is the Sine of the Angle opposite , To the side sought , To the side sought 3. To find a Side . Given a Side , and one Acute Angle , and by consequence both As the Radius , To Tangent of the Angle opposite to the side sought : So is the given side , To the side sought . Or , As the Sine of the Angle opposite to the given side Is to the given side : So is the sine of the other Angle To the Side sought . 4. To find the Hipotenusal . Given one of the Sides , and an Acute Angle consequently both , As the Sine of the Angle opposite to the given side , Is to the Radius : So is the given Side , To the Hypothenusal Or , As the Radius , To Secant of the Angle adjacent to the given Side : So is the given side , To the Hipotenusal . 5. To find the Hipotenusal . Given both the Sides . As one of the given Sides . To the other given Side : So is the Radius , To the Tangent of the Angle opposite to the other side , Then take the Complement of the Angle found for the other Angle . Then , As the Sine of the Angle opposite to one of the given Leggs , or Sides , Is to the given Sides : So is the Radius , To the Hipotenusal . 6. To find an Angle . Given the Hipotenusal , and one of the Sides . As the Hipotenusal , Is to the given Side : So is the Radius , To the Sine of the Angle opposite to the given side ; The Complement of the angle found , is the other Angle . 7. To find an Angle . Given both the Sides . As one of the given sides , To the other given Side : So is the Radius , To the Tangent of the angle opposite to this other Side . The Complement of the angle found is the other Angle . Because the Sum of the Squares of the Leggs of a right angled Triangle is equal to the Square of the Hipotenusal by 47 1 Euclid . Therefore the 2d and 5th Case may be otherwise performed . 2. Case , To find a Side or Legg . Given the Hipotenusal , and other Legg . To do it by Logarithmes , Add the Logarithm of the Sum of the Hipotenusa and Legg , to the Logarithm of their difference , the half Sum is the Logarithm of the Side sought . Which in natural Numbers is to extract the Square root of the Product of the Sum and difference of the two Numbers given , namely , the Hipotenusal and Legg , which said root is equal to the side sought . 5. Case , When both the Sides are given to find the Hipotenusal . To do it by Logarithmes , Substract the Logarithm of the lesser side from the doubled Logarithm of the greater , and to the absolute number answering to the remaining Logarithm add the lesser side the half sum of the Logarithmes of the Sum thus composed , and of the lesser side , is the Logarithm of the Hypotenusa sought . Which work was devised , that the Proposition might be performed in Logarithmes ; The same Operation by natural numbers , would be to Divide the Square of the greater of the Sides by the lesser , and to the Quotient to add the lesser Side , then multiply that Sum by the lesser Side , and extract the Square root of the Product for the Hipotenusal sought . Cases of Oblique Plain Triangles . 1. Data To find an Angle , TWo sides with an Angle opposite to one of them to find the Angle Opposed to the other side . As one of the Sides , To the Sine of its opposite Angle : So the other side ; to the Sine of the angle opposed thereto . If the Angle given be Obtuse , the Side opposite to it will be greater then either of the rest , and the other two Angles shall be Acute ; But if the given Angle be Acute , it will be doubtful whether the angle opposed to the greater side be Acute or Obtuse , yet a true Sine of the 4 ●h Proportional . The Sine found will give the angle opposite to the other given side , if it be Acute , and it will always be Acute when the given angle is Obtuse , But if it be fore known to be Obtuse , the Arch of the Sine found substract from a Semicircle , and there will remain the Angle sought . In this Case the quality or affection of the angle sought must be given , and fore-known , for otherwise it is impossible to give any other then a double answer , the Acute angle found , or its Complement to 180d , yet some in this Case have prescribed Rules to know it , supposing the third Side given which is not , if it were then in any Plain Triangle it would hold , That if the Square of any Side be equal to the Sum of the Squares of the other two Sides , the angle it subtends is a right angle , if less Acute , if greater Obtuse ; but if three Sides are given we may with as little trouble by following Proportions come by the quantity of any angle , as by this Rule to know the affection of it . Two Sides with an Angle opposite to one of them , to find the third Side . In this Case as in the former , the affection of the angle opposite to the other given side , must be fore-known , or else the answer may be double or doubtful . In the Triangle annexed there is given the sides A B and A C with the angle A B C to find the angle opposite to the other given side , which may be either the angle at C or D , and the third side , which may be either B C , or B D , the reason hereof is because two of the given tearms the Side A B , and the angle at B remain the same in both Triangles , and the other given side may be either A C or A D equal to it , the one falling as much without as the other doth within the Perpendicular A E. The quality of the angle opposite to the other given side being known ; by the former Case get the quantity , and then having two angles the Complement of their Sum to 180d is equal to the third angle , the Case will be to find the said side , by having choice of the other sides , and their opposite angles as follows . 2. Two Angles with a Side opposite to one of them given to find the Side opposite to the other . As the Sine of the angle opposed to the given Side , Is to the given Side ; So is the Sine of the angle opposite to the side sought ▪ To the side sought . Ricciolus in the Trigonomerical part of his late Almagestum Novum , suggests in the resolution of this Case , that if the side opposite to the Obtuse angle be sought , it cannot be found under three Operations ; as first to get the quantity of the Perpendicular falling from the Obtuse angle on its Opposite side , and then the quantity of the two Segments of the side , on which it falleth , and so add them together to obtain the side sought ; But this is a mistake , and if it were true by the like reason a side opposite to an Acute angle , could not be found without the like trouble ; for in the Triangle above , As the Sine of the angle at B Is to its Opposite side A C or A D , So is the Sine of the angle B C A , or B D A , To its opposite Side B A , where the Reader may perceive that the same side hath opposite to it both an Acute and an Obtuse angle , the one the Complement of the other to 180d , the same Sine being common to both , for the Acute angle A C E is the Complement of the Obtuse angle B C A ; but the angle at C is equal to the angle at D being subtended by equal Sides , and the Proportion of the Sines of Angles to their opposite Sides is already demonstrated in every Book of Trigonometry . 3. Two Sides with the angle comprehended to find either of the other Angles . Substract the angle given from 180d , and there remains the Sum of the two other Angles , then As the Sum of the Sides given , To tangent of the half sum of the unknown Angles : So is the difference of the said Sides , To Tangent of half the difference of the unknown Angles . If this half difference be added to half sum of the angles , it makes the greater , if substracted from it , it leaves the lesser Angle 4. Two Sides with the Angle comprehended , to find the third side . By the former Proposition one of the Angles must be found , and then As the Sine of the angle found , is to its Opposite side : So is the Sine of the angle given , To the Side opposed thereto , If two angles with a Side opposite to one of them be given , to find the side opposite to the third Angle is no different Case from the former , because the third angle is by consequence given , being the Complement of the two given angles to 180d , and the like if two angles with the side between them were given . 5. Three Sides to find an Angle . The Side subtending the Angle sought is called the Base . As the Rectangle or Product of the half Sum of the three sides , and of the difference of the Base therefrom , Is to the Square of the Radius : So is the Rectangle of the difference of the Leggs , or conteining Sides therefrom , to the Square of the Tangent , to half the Angle sought . And by changing the third tearm into the place of the first . As the Rectangle of the Differences of the Leggs from the half Sum of the 3 sides , Is to the Square of the Radius : So is the Rectangle of the said half sum , and of the difference of the Base there from , To the Square of the Tangent of an angle , which doubled is the Complement of the angle sought to 180d , Or the Complement of this angle doubled is the angle sought . To Operate the former Proportion by the Tables . From the half Sum of the three Sides substract each Side severally then from the Sum of the Logarithmes of the Square of the Radius ( which in Logarithms is the Radius doubled ) and of the differences of the Sides containing the angle sought . Substract the Sum of the Logarithms of the half sum of the three sides , and of the difference of the Base therefrom the half of the remainder is the Logarithm of the Tangent of half the angle sought Example . In the Triangle A B C let the three sides be given to find the Obtuse angle at C. Differences from the half sum . B C 126 Leggs — 101 — 2,0043214 A C 194 Leggs — 169 — 2,2278867 A B 270 Base — 25 Logarithms — —   — 1,3979400 Sum with double Radius 24,2322081 Sum 590     half sum 295 — 2,4698220       — 3,8677620     3,8677620 —     — 20,3644461 Tangent of 56d 41′ which doubled is 113d 22′ the angle sought . 10,1822230 half For the 2d Proportion for finding an Angle the Operat on varies ; to the former sum add the double Radius , and from the Aggregate substract the latter sum , the half of the Relique is the Logarithm of the Cotangent of half the Angle sought . Tangent of 33d 19′ the Complement whereof is 56d 41′ which doubled makes 113d 22′ as before The Tables here made use of are Mr. Gellibrands . It may be also found in Sines . As the Rectangle of the Containing Sides or Leggs Is to the Square of the Radius : So the Rectangle of the differences of the said Leggs from half Sum of the three Sides , To the Square of the Sine of half the Angle sought . Or , We may find the Square of the Cosine of half the Angle sought by this Proportion . As the Rectangle of the containing Sides , Is to the Square of the Radius : So the Rectangle of the half sum of the three Sides , and of the difference of the Base there from , To the Square of the Cosine of half the Angle sought , viz. To the Square of the Sine of such an Ark , as being doubled is the Complement of the Angle sought to 180d , or the Complement of the found Ark doubled is the angle sought . All these Proportions hold also in Spherical Triangles if instead of the bare names of Sides you say the Sines of those Sides , and this Case may also be resolved by a Perpendicular let-fall ; but the Reader need not trouble himself with name nor thing in no Case of Plain or Sphoerical Triangles , but when two of the given Sides or Angles are equal . If the Square of the Radius and the Square of the Sine of an Ark be both divided by Radius the Quotients will be the Radius , and the half Versed Sine of twice that Arch , and in the same Proportion that the two tearms propounded , as will afterwards be shewed , upon this Consideration may any of these Compound Proportions be reduced to single Tearms for Instrumental Operations , by placing the two Tearms of the first Rectangle , as two Divisors in two single Rules of three , and the tearms of the other Rectangle as middle tearms . An Example in that Proportion for finding an Angle in the Sineés : As one of the Leggs or including Sides , Is to the difference thereof from the half sum of the three Sides : So is the Difference of the other Legg therefrom , To a fourth Number . Again . As the other Legg , To that fourth Number : So is the Radius , To the half Versed Sine of the Angle sought ; And so is the Diameter or Versed Sine of 180d Or Secant of 60d To the Versed Sine of the Angle sought . And upon this Consideration , that the fourth Tearm in every direct Proportion bears such Proportion to the first Tearm , as the Rectangle or Product of the two middle Tearms doth to the Square of the first Tearm , as may be demonstrated from 1 Prop. 6. Euclid . We may place the Radius or Diameter in the first place of the first Proportion , and still have the half or the whole Versed Sine in the last place as before , therefore As the Radius , To one of the given Leggs : So the other given Legg , To a fourth Number , which will bear such Proportion to the Radius , as the Rectangle of the two given Leggs doth to the Square of the Radius , then it holds , As that fourth number , To the Radius : So the Rectangle of the difference of 〈…〉 the Leggs from the half sum of the three sides ; To the Square of the Sine of half the Angle sought , and omitting the Raidius , it will hold ; As that fourth Number , To the differences of the Leggs from the Leggs from the half sum of the three Sides : So is the difference of the other Legg therefrom , To the half Versed Sine of the Angle sought . And if the Diameter had been in the first place , then would the whole Versed Sine have been in the last . This Case when 3 Sides are given to find an Angle is commonly resolved by a Perpendicular let-fall , it shall be only supposed and the Cannon will hold , As the Base or greater Side , To the sum of the other Sides : So is the difference of the other Sides , To a fourth Number , which taken out of the Base , half the remainder is the lesser Segment , and the said half added to this fourth Number is the greater Segment . Again . As the greater of the other Sides , To Radius : So is the greater Segment , To the Cosine of the Angle adjacent thereto , Or , As the Lesser of the other Sides , To Radius : So is the lesser Segment , To the Cosine of its adjacent Angle : This for either of the Angles adjacent to the Base or greatest side but for the angle opposite to the greatest side , which may be sometimes Obtuse , sometimes Acute ; not to multiply Directions , the Reader is remitted to the former Cannons , or to find both the Angles at the Base first , and by consequence the third angle is also given , being the residue of the sum of the former from a Semicircle . In right angled Spherical Triangles . By the affection of the Angles to know the Affection of the Hipotenusal , and the Converse . If one of the angles at the Hipotenusal be a right angle The Hipotenusal will be A Quadrant . If both be of the same kind , The Hipotenusal will be lesser then a Quadr. If of a different kind , The Hipotenusal will be greater then a Quadr. By the Hipotenusal to find the affection of the Leggs ▪ and the Converse : If the Hipotenusal be A Quadrant one of the Legs wil be a Quadrant If the Hipotenusal be Less then A Quadrant The Leggs , and their Opposit Angles wil be less then Quadrant If the Hipotenusal be Greater , then A Quadrant One Legg will be greater , & the other less then the Quadrant : The Leggs of a right angled Sphoerical Triangle are of the same Affection as their Opposite Angles and the Converse : If a Legg be a Quadrant the Angle opposite thereto will be a Quadr. If a Legg be less then a Quadrant the Angle opposite thereto will be Acute If a Legg be greater then a Quadrant the Angle opposite thereto will be Obtuse . All these Affections are Demonstrated in Snellius ; I shall add some more from Clavius de Astrolabio , and the Lord Nepair . The three Sides of every Sphoerical Triangle are less then a Whole Circle . In an Oblique angular Triangle , If two Acute Angles be equal the Sides opposite to them shall be lesser then Quadrants . Obtuse Angles be equal the Sides opposite to them shall be greater then Quadrants . Reg. 10 ▪ 11 , 4 If an Oblique angular Triangle , if two Acute Angles be unequal the side opposite to the lesser shall be lesser then a Quadrant Obtuse Angles be unequal the side opposite to the greater shall be greater then a Quadrant Reg. 12 , 13.4 . An Acute angular Triangle hath all its Angles Acute , and each side less then a Quadrant . Two sides of any Spherical Triangle are greater then the third . If a Sphoerical Triangle be both right angled and Quadrantal , the sides thereof are equal to their Opposite Angles . If it hath three right Angles , the three sides of it are Quadrants . If it have two right Angles , the two sides subtending them are Quadrants and the contrary , and if it have one right angle , and one side a Quadrant , it hath two right angles , and two Quadrental sides . Any side of a Sphoerical Triangle being continued , if the other sides together are equal to A Semicircle the outward angle wil be equal to the inward opposit angle on the side continued . lesser then A Semicircle the outward angle wil be lesser then the inward opposit angle on the side continued . greater then A Semicircle the outward angle wil be greater then the inward opposit angle on the side continued . If any Sphoerical Triangle have two Sides equal to lesser then greater then a Semicircle , the two angles at the Base or third Side will be equal to lesser then greater then two right Angles . In every right angled Spherical Triangle having no Quadrantal Side , the angle Opposite to that Side that is less then a Quadrant is Acute , and greater then the said Side ; But that angle which is Opposite to the Side , that is greater then a Quadrant , is Obtuse ; and less then the said Side . In every right angled Spherical Triangle all the three angles are less then 4 right angles , that is the two Oblique angles are less then 3 right angles , or 270d. In a right angled equicrural Triangle , if the two equal angles be Acute , either of them will be greater then 45d , but if Obtuse less then 135d. In every right angled Sphoerical Triangle either of the Oblique angles is greater then the Complement of the other , but less then the difference of the same Complement from a Semicircle . Two angles of any Sphoerical Triangle are greater then the difference between the third angle and a Semicircle , and therefore any side being continued , the outward angle is less then the two inward opposite angles . The sum of the three Angles of a Sphoerical Triangle is greater then two right angles , but less then 6. In Spherical Triangles , that angle which of all the rest is nearest in quantity to a Quadrant , and the side subtending it are doubtful , Whether they be of the same , or of a different affection , unless foreknown , or found by Calculation ; But the other two more Oblique angles are each of them of the same kind as their Opposite Sides , which Mr Norwood thus propounds , Two Angles of a Spherical Triangle , shall be of the same affection as their Opposite Sides , and to this purpose , If any Side of a Triangle be nearer to a Quadrant then its opposite Angle , two Angles of that Triangle ( not universally any two ) shall be of the same kind , and the third greater then a Quadrant . But if any Angle of a Triangle be nearer to a Quadrant then its opposite side , two Sides of that Triangle ( not universally any two ) shall be of the same kind , and the third less then a Quadrant . In any Sphoerical Triangle , if one of the angles be substracted from a Semicircle , and the residue so found substracted from a Whole Circle , the Ark found by this latter Substraction , will be greater then the Sum of the other two Angles . In every Sphoerical Triangle the difference between the sum of two angles howsoever taken , and a whole Circle or 4 right angles is greater then the difference between the other Angle and a Semicircle ; The demonstration of most of these Affections are in Clavins his Comment on Theodosius , or in his Book de Astrolabio , where shewing how to project in Plano all the Cases of Sphoerical Triangles , and so to measure the sides and Angles , he delivers these Theorems to prevent such Fictitious Triangles as cannot exist in the Sphere . The 16 Cases of right Angled Sphoerical Triangles , Translated from Clavius de Astrolabio . 1. To find an Angle . Given the Hipotenusal and side opposite to the Angle sought . As the Sine of the Hipotenusal , To Radius : So the Sine of the given side To the Sine of the Angle sought . Or , As Radius , To sine of the Hipotenusal : So the Cosecant of the side , To the Cosecant of the Angle . As Radius , To sine of the side : So Cosecant of the Hipotenusal , To sine of the angle . As Cosecant of the side , To Radius : So Cosecant of the Hipotenusal , To Cosecant of the angle . As Cosecant Hipotenusal , To Radius : So Cosecant of the side , To Cosecant of the angle . As the Sine of the side to Radius : So sine of the Hipotenusal , To Cosecant of the Angle . The Angle found will be Acute if the Side given be less then a Quadrant , Obtuse if greater . 2. To find an Angle . Given the Hipotenusal and side adjacent to the Angle . As Radius , To Cotangent Hipotenusal : So tangent of the side , To Cosine of the angle . As tangent Hipotenusal . To Radius , So tangent of the Side . To Co-sine of the angle . As the Cotangent of the side , To Radius : So Cotangent Hipotenuse , To Cosine of the angle . As Radius , To Cotangent side : So tangent Hipotenusa , To Secant of the angle . As Cotangent Hipotenusal : To Radius : So Cotangent side , To Secant of the angle . As the tangent of the side , To Radius : So tangent Hipot : To Secant of the angle . The Angle found will be Acute , if both the Hipotenusal and the given side be greater , or less then a Quadrant , but Obtuse if one of them be greater , and the other less . 3. To find an Angle . Given the Hipotenusal , and either of the Oblique Angles As the Radius , To Cosine Hip : ∷ So Tangent of the given angle : To the Cotang of sought angle As the Cotangent of the given angle : To Radius ∷ So Cosine of : the Hipot : To the Cotang of the sought angle . As the Cosine of the Hipot : To Radius ∷ So Cotang : of the given angle : To the tang . of the ang : sought As the Radius , To Secant Hip : ∷ So Cotangent of the given angle : To the tang of the angle sought As Secant of the Hipotenusal : To Radius ∷ So the tangent of the angle given : To the Cotan : of the angle sought As the tangent of the given angle : To Radius ∷ So Secant of the Hipotenusal : To tangent of the angle sought . The angle found will be Acute , if the Hipotenusal be less then a Quadrant , and the given angle Acute ; or if the Hipotenusal be greater then a Quadrant , and the given angle Obtuse ; And the said angle will be Obtuse , if the Hipotenusal be less then a Quadrant , and the given angle Obtuse ; Of if the Hipotenusal be greater then a Quadrant , and the given angle Acute . 4. To find an Angle . Given the Side opposite to the Angle sought , and the other Oblique Angle . As the Radius : To sine of the angle given ∷ So is the cosine of the given side : To the Cosine of the angle sought As the Radius : To Cosecant of the given angle ∷ So Secant of the side given : To Secant of the angle sought As the sine of the given angle : To Radius ∷ So the Secant of the given side : To the Secant of the angle As the Cosine of the given side : To Radius ∷ So the Cosecant of the given angle : To the Secant of the angle sought As the Cosecant of the given angle : To Radius : So Cosine of the given side : To the Cosine of the angle sought As the Secant of the given side : To Radius ∷ So sine of the given angle : To the Cosine of the angle sought The angle found will be Acute , if the side given be less then a Quadrant , Obtuse if greater . 5. To find an Angle . Given a side adjacent to the angle sought , and the other Oblique angle , if it be foreknown whether the angle sought be Acute or Obtuse , or whether the Base or other side not given be greater , or lesser then a Quadrant . As the Cosine of the given side : To Radius ∷ So Cosine of the given angle : To the sine of the angle sought As the Radius : To Secant of the given side ∷ So Cosine of the given angle : To Sine of the angle sought As the Radius : To Secant of the given angle ∷ So Cosine of the given side : To Cosecant of sought angle As the Cosine of the given angle : To Radius ∷ So Cosine of the given side : To the Cosecant of the angle sought As the Secant of the given side : To Radius ∷ So is the Secant of the given angle : To the Cosecant of the angle sought As the Secant of the given angle : To Radius ∷ So is the Secant of the given side : To the Sine of the angle sought The angle found will be Acute , if the side not given be less then a Quadrant , Obtuse if greater . In like manner if the Hipotenusal be less then a Quadrant , and the given angle Acute ; Or if the Hipotenusal be greater then a Quadrant , and the given angle Obtuse , the angle found will be Acute . But if the Hipotenusal be less then a Quadrant , and the given angle Obtuse , or if the Hipotenusal be greater then a Quadrant , and the given angle Acute , the angle found will be Obtuse , 6. To find an Angle . Given both the Leggs . As Radius : To sine of the side adjacent to sought angle ∷ So Cotang of the side opposite to the angle sought : To Cotang of the angle sought As the sine of the side adjacent to sought angle : To Radius ∷ So the tangent of the side opposite to the sought angle : To the tang of the angle sought : As the Tangent of the side opposite to sought angle : To Radius ∷ So the sine of the side adjacent to the sought angle : To Cotang of the angle sought : As the Radius : To Cosecant of the side adjacent to sought angle ∷ So the tangent of the side opposite thereto : To the tang of the angle sought : As the Cosecant of the side adjacent to the angle sought To Radius ∷ So is the Cotang of the side opposite to the angle sought : To Cotang of the sought angle : As the Cotangent side opposite to the sought angle : To Radius ∷ So Cosecant of the side adjacent to the angle sought : To the tang of the angle sought The Angle found will be Acute , if the side opposite to the angle sought be less then a Quadrant , but Obtuse if greater . 7 , To find a Side or Legg . Given the Hipotenusal and the other Legg . As the Cosine of the given side : To Radius ∷ So Cosine of the Hipotenusal : To Cosine of the side sought As Radius : To Secant of the side ∷ So Cosine of the Hipotenusal : To Cosine of the side sought As Cosine Hipotenusal : To Radius ∷ So Cosine of the given side : To Secant of the side sought As Radius : To Secant of the Hipotenusal ∷ So Cosine of the given side : To Secant of the side sought As the Secant of the Hipotenusal : To Radius ∷ So Secant of the given side : To Cosine of the side sought As the Secant of the given side : To Radius ∷ So Secant of the Hipotenusal : To the Secant of the side sought The side sought will be less then a Quadrant , if both the Hipotenusal and given sides be less then Quadrants , but greater then a Quadrant if either the Hipotenusal be greater , and the given side less , Or if the Hipotenusal be less , and the given side greater . 8. To find a Side . Given the Hipotenusal , and an Angle opposite to the side fought . As the Radius : To sine of the Hipotenusal ∷ So sine of the given angle : To the sine of the side sought As Radius : To Cosecant of the Hipotenusal ∷ So the Cosecant of the given angle : To Cosecant of the side sought As the sine of the Hipotenusal : To Radius ∷ So Cosecant of the given angle : To Cosecant of the side sought As the Cosecant of the given angle ▪ To Radius ∷ So the sine of the Hipotenusal : To the sine of the side sought As the sine of the given angle : To Radius ∷ So the Cosecant of the Hipotenusal : To the Cosecant of the side sought The side found will be less then a Quadrant , if the Angle opposite thereto be Acute , but greater if Obtuse . 9. To find a Side . Given the Hipotenusal and Angle adjacent to the Side sought As the Radius : To Cosine of the given angle ∷ So tangent of the Hipotenusal : To the tangent of side sought As the Cosine of the given angle : To Radius ∷ So Cotangent of the Hipotenusal : To Cotang of the side sought As the Cotangent of Hipotenusal : To Radius ∷ So the Cosine of the given angle : To tangent of the side sought As the Radius : To Secant of the angle ∷ So Cotangent of the Hipotenusal : To Cotang of the side sought As the Secant of the given angle : To Radius ∷ So tangent of the Hipotenusal : To the tangent of the side sought As the tangent of the Hipotenusal : To Radius ∷ So Secant of the given angle : To Cotang : of the side sought The Side sought will be less then a Quadrant , if the Hipotenusal be less then a Quadrant , and the given angle Acute : Or if the Hipotenusal be greater then a Quadrant , and the given angle Obtuse ; But it will be greater then a Quadrant , if the Hipotenusal be less then a Quadrant , and the given angle Obtuse : Or if the Hipotenusal be greater then a Quadrant , and the given angle Acute . 10. To find a Side . Given a Side , and an Angle adjacent to the sought side . Provided it be foreknown whether the side sought be greater or less then a Quadrant , or whether the other angle not given be Acute or Obtuse ; or finally whether the Hipotenusal be greater or less then a Quadrant . As the Radius : To the Cotangent of the given angle ∷ So tangent of the given side : To the Sine of the side sought As the tangent of the given angle : To Radius ∷ So tangent of the given side : To the sine of the side sought As the Cotang of the given side : To Radius ∷ So the Cotang of the given angle : To the sine of the side sought As Radius : To Cotangent of the given side : So tangent of the given angle : To Cosecant of the side sought As the tangent of the given side : To Radius ∷ So tangent of the given angle : To the Cosecant of the side sought As the Cotangent of the given angle : To Radius ∷ So Cotang of the given side : To the Cosecant of the side sought The Side found will be less then a Quadrant , if the angle opposite thereto and not given be Acute , but greater if it be Obtuse ; In like manner it will be less , if the Hipotenusal be less then a Quadrant , and the side given also less then a Quadrant : Or if the Hipotenusal be less then a Quadrant , and the given side greater , the side found will be greater then a Quadrant ; Lastly , if both the Hipotenusal , and the side given be greater then a Quadrant , the side found will be less then a Quadrant , but greater if the Hipotenusal be greater then a Quadrant , and the given side less . 11. To find a Side . Given a Side , and an Angle opposite to the Side sought As Radius : To sine given side ∷ So tangent given angle : To tangent of the side sought As the sine of the given side : To Radius ∷ So Cotangent of the given angle : To Cotangent of the side sought As the Cotangent of the given angle : To Radius ∷ So sine of the given side : To the tangent of the side sought As the tangent of the given angle : To Radius ∷ So Cosecant of the given side : To Cotangent of the side sought As the Radius : To Cosecant of the given side ∷ So Cotang of the given angle : To Cotangent of the side sought As the Cosecant of the given side : To Radius ∷ So tangent of the given angle : To tangent of the side sought The side found will be less then a Quadrant , if the given Angle opposite thereto be Acute , but greater if Obtuse . 12. To find a Side . Given both the Oblique Angles . As the sine of the angle adjacent to side sought : Is to Radius ∷ So Cosine of the angle opposite to side sought : To Cosine of the side sought As the Radius : To Secant of the angle opposite to side sought ∷ So sine of the angle adjacent to the side sought : To Secant of the side sought As Radius : To Cosecant of the angle adjacent to side sought ∷ So Cosine of the angle opposite to side sought : To Cosine of the side sought As the Cosine of the angle opposite to side sought : To Radius ∷ So side of the angle adjacent to the side sought : To Secant of the side sought As the Secant of the angle opposite to side sought : To Radius ∷ So Cosecant of the angle adjacent to the side sought : To Cosine of the side sought As Cosecant of the angle adjacent to side sought : To Radius ∷ So Secant of the angle opposite to side sought : To Secant of the side sought The side found will be less then a Quadrant , if the given angle Opposite thereto be Acute , but greater if Obtuse . 13. To find the Hipotenusal . Given a side and an Angle adjacent thereto . As the Radius : To Cosine of the given angle ∷ So Cotangent of the given side To Cotang of the Hipotenusal As the Cosine of the given angle : To Radius ∷ So tangent of the given side : To tangent of the Hipotenusal As the tangent of the given side To Radius ∷ So Cosine given angle : To Cotangent of the Hipotenusal As Radius : To Secant of the given angle ∷ So tangent of the given side ; To the tangent of the Hipotenusal As the Secant of the given angle : To Radius ∷ So Cotang of given side : To the Cotang of the Hipotenusal As the Cotangent of given side : To Radius ∷ So Secant of the given angle : To tangent of the Hipotenusal The Hipotenusal found will be less then a Quadrant , if the given side be less then a Quadrant , and the angle given adjacent thereto Acute ; As also if the given side be greater then a Quadrant , and the given angle adjacent thereto be Obtuse . But it will be greater then a Quadrant , if the given side be greater then a Quadrant , and the given Angle adjacent thereto Acute ; As also when the given side is less then a Quadrant , and the given Angle Obtuse . 14. To find the Hipotenusal Given a Side , and an angle Opposite thereto . If it be fore-known whether the Hipotenusal be greater or less then a Quadrant , or whether the other angle not given be Acute or Obtuse ; Or lastly , whether the other side not given , be greater or less then a Quadrant . As the sine of the given angle : To Radius ∷ So sine of the given side : To the sine of the Hipotenusal As the Radius : To Cosecant of angle given ∷ So sine of the given side : To the sine of the Hopotenusal As Radius : To Cosecant given side ∷ So sine of the given angle : To Cosecant of the Hipotenusal As the sine of the given side : To Radius ∷ So sine of the given angle : To Cosecant of the Hipotenusal As Cosecant of given side : To Radius ∷ So Cosecant of the given angle : To sine of the Hipotenusal As Cosecant of the given angle : To Radius ∷ So the Cosecant of the given side : To Cosecant of the Hipotenusal The Hipotenusal found will be less then a Quadrant , if both the Oblique Angles be Acute or Obtuse , or if both the sides be greater or less then Quadrants . It will also be greater then a Quadrant , if one of the Oblique Angles be Acute , and the other Obtuse , or if one of the sides be less and the other greater then a Quadrant : 15. To find the Hipotenusal , Given both the sides , distinguished by the names of first and second . As Radius : To Cosine 1st side ∷ So Cosine 2d side : To Cosine of the Hipotenusal As Radius : To Secant 1st side ∷ So Secant 2d side : To Secant of the Hipotenusal As Secant 1st side : To Radius ∷ So Cosine of the 2d side : To Cosine Hipotenusal As Secant 2d side : To Radius ∷ So Cosine 1st side : To Cosine of the Hipotenusal As Cosine 1st side : To Radius ∷ So Secant 2d side : To Secant of the Hipotenusal As Cosine 2d side : To Radius ∷ So Secant 1 side : To the Secant of the Hipotenusal The Hipotenusal found will be less then a Quadrant , if both the Sides are less or greater ; But otherwise , it will be greater , if one be less and the other greater . 16. To find the Hipotenusal . Given both the Oblique Angles , distinguisht by the names of the first and second . As Radius : To Cotangent 1st angle ∷ So Cotangent 2d angle : To Cosine of the Hipot : As the tangent 1st angle : To Radius ∷ So Cotangent 2d angle : To Cosine of Hipoten : As tangent of 2d angle : To Radius ∷ So Cotangent 1st angle : To Cosine Hipotenusal As the Radius : To tangent 2d angle ∷ So tangent 1st angle : To Secant of the Hipot : As Cotangent 2d angle : To Radius : So tangent 1st angle : To Secant of the Hipotenus ; As the Cotangent 1st angle : To Radius ∷ So Tangent 2d angle : To Secant Hipotenus : The Hipotenusal found will be less then a Quadrant , if both the Oblique angles be Acute or Obtuse , but greater if one of them be Acute , and the other Obtuse . I shall not spend time to shew Examples of all these Cases , but shall onely instance in an Example or two . In the Right angled Sphoerical Triangle P S N , let the side P N represent the Poles height , the side S P the Complement of the Suns declination , the side S N the Suns Amplitude of rising from the North Meridian , the Angle S P N the time of Suns rising from Midnight , and the angle P S N the angle of the Suns Position ; and in it let there be given the side P N 51d 32′ , and the side P S the Complement of the Suns Declination to find the angle S P N the time of the Suns rising ; then in this Case there is given the Hipotenusal , and the side adjacent to the angle sought to find the said angle ; and this is the 2d Case , whence the Proportion taken is , As Radius , To Cotangent of the Hipotenusal : So the Tangent of the given side , To the Cosine of the angle sought ; and so the Proportion to find the time of Suns rising will be As the Radius , To the tangent of the Suns declination : So the tangent of the Latitude , To the Sine of the time of Suns rising before 6 in Summer or after it in Winter , the Complement whereof is the time of its rising from Midnight . Tangent 13d Suns declination — 936336 Tangent 51d 32′ the Latitude — 1,009922 Sine 16d 53′ — , 946328 the Compl : of which Ark is 73 , 6 , which converted into time shews that the Sun riseth in our Latitude when he hath 13d of North Declination at 52● and a half past 4 in the morning ferè . By the same Data we may find the Side S N the Suns Amplitude of rising or setting , and this will agree with the 7 ●h Case ; for here is given the Hipotenusal , and one of the Leggs to find the other Leg the Proportion will be , As the Cosine of the given side : To Radius : So the Cosine of the Hipotenusal , To the Cosine of the side sought ; that is in this Cass , As the Cosine of the Latitude , To Radius : So is the Sine of the Suns Declination , To the Sine of his Amplitude from the East or West . Example , Logme . Sine 13d † Radius is — 1,935208 Sine 38d 28′ — 979383 Sine 21d 12′ — 955825 the Complement wherof , viz 68d 48′ is the side S N sought , and this Proportion is of good use to obtain the Variation of the Compass at Sea by the Suns Coast of rising ; More Examples need not be given , the Reader may try over all the Cases by the Calculated Triangle annexed . Some may say here are more Proportions then needs , especially seeing there are no Logarithmical Tables of Secants ; but Alterna amant Camenae , they have not hitherto been published in English ; the Instruments to be treated of will have Secants ; besides in some Cannons there are Tables of the Arithmetical Complements of the Logarithmical Sines and Cosines , which augmented by Radius , are the Logarithmical Secants of the Complements of those Arks to which they do belong ; and for Instruments , especially Quadrants , a Proportion having Tangents or Secants many times cannot be Operated on the Quadrant without changing the Proportion , by reason those Scales cannot be wholy brought on , being infinite ; Now the chief Grounds for varying Proportions , are built upon a few Theorems . 1. That the Rectangle or Product of a Tangent , and its Complement is equal to the Square of the Radius , or which is all one , that the Radius is a mean Proportional between the Tangent of an Arch , and the Tangent of its Complement , that is , As the Tangent of an Arch , To Radius : So Radius , To tangent of that Arks Complement , And by Inversion . As the Cotangent of an Arch , To Radius : So Radius , To tangent of that Arch , that is , As the 4 h tearm to 3d , So second to first . 2. That the Radius is a mean Proportional between the Sine of an Arch , and the Secant of that Arks Complement . That is , As the Sine of an Arch , To Radius : So is the Radius , To Secant of that Arks Complement , and the Converse . 3. That the Rectangles of all Tangents and their Complements , being respectively equal to the Square of the Radius , are Reciprocally Proportional , That is , As the Tangent of an Arch or Angle : Is to the Tangent of another Arch or Angle : So is the tangent of the Complement of the latter Arch : To the tangent of the Complement of the former , And by varying the Second Tearm into the place of the Third , we may compare the Tangent of one Ark to the Cotangent of another , &c. that is , As the tangent of an Ark or Angle : Is to the Cotangent of another Ark ∷ So is the tangent of this latter Ark To the Cotangent of the former . 4. That the Sines of Arches , and the Secants of their Complements are reciprocally proportional , that is , As the Sine of an Arch : To the Sine of another Arch or Angle : So is the Cosecant of the latter Arch , To the Cosecant of the former , And by changing the 2 and 3 Tearms , a Sine may be compared with a Secant . Now hence to be directed to vary Proportions , observe that if 4 Tearms or Numbers are Proportional , it is not material which of the two middle Terms be in the second or third place ; for instance if it be , As 2 to 4 ∷ So is 3 to 6 : It will also hold , As 2 to 3 ∷ So 4 to 6. Secondly , that when 4 Tearms are in direct Proportion , if a question be put concerning a fifth Tearm not ingredient in the Proportion , it is not material whether the two former , or the two latter Tearms be taken : As if it should be demanded ; When 2 yards of Linnen cost 4sh . What shall 8 yards ? Answer , 16. It might as well be said , If 3 cost 6 , What 8 ? Answer , 16. Hence then in any Proportion , if the two first Tearms be , As the Tangent of an ark , To Radius , to bring the Radius into the first place , it may be said , As the Radius , Is to the Cotangent of that Ark , because there is the same Proportion between these two latter Tearms , as between two former ; Now in all the former Theorems , the two latter Tearms consist either of the parts , or of the Complements of the parts of the two former , whence it will not be difficult to vary any Proportion propounded . 1. From whence it will follow , that a Proportion wholly in Tangents may be changed into their Complements without altering the Order of the Tearms , and the Converse . If it were As Tangent 10d , To tang 20d : So tang 52d , To tan 69d 15′ It would also be , As tang 80d , To tan 70d : So tan 38d , To tan 20d 45′ 2. That if the two latter Tearms of any Proportion being Tangents are only changed into their Complements , it infers a Transportation of the first Tearm into the second place . That is in the first Example , As Tang 20d , To Tangent 10d : So Tangent 38d , To Tangent 20d 45′ . 3. That if the two former Tearms of a Proportion being Tangents are changed into their Complements , it likewise infers a changing of the third Tearm into the place of the fourth . And then if the fourth Tearm be sought , it will hold , As the second Tearm , To the first : So is the third Tearm , as at first propounded to the fourth . In the first Example , as tangent 70d to tangent 80d : So tang ●2 to tang 69d 15′ . 4. That a Proportion wholly in Secants may be changed into a Proportion wholly in Sines , without altering the Order of the places , only by taking their Complements , and the Converse . If it were , As Secant of 80 To Secant 70d ∷ So Secant 60d To Secant 10d It would also hold in Sines , As the Sine 10 to Sine 20d ∷ So the Sine of 30d To Sine 80d 5. That if the two latter Tearms being Secants , should be changed into Sines , and the Converse , if they were Sines to be turned into Secants , it will be done only by taking their Complements , but then must the second and first Tearms change places one with another . If the Proportion were , As Sine 12d to Sine 42d ∷ So is the Secant of 36d to Secant of 75d 26′ . It would also hold , As Sine 42d to Sine 12d ∷ So Sine of 54d to the Sine of 14d 34′ . 6. That if the two former Tearms of a Proportion in Secants , should be changed into Sines and the Converse ; this would infer a changing of the fourth Term of that Proportion into the place of the Third : But the third Tearm not being that which is sought : The Rule to do it , would be to imagine the two first Tearms to change places , and then to take their Complements . If the Proportion were : As Secant of 39d to Secant of 75d 26′ So is the Sine of 12d to the Sine of 42d. It would also hold , As Sine 14d 34′ , to Sine of 52d. So is the Sine of 12d , to the Sine of 42d. 7 Two Tearms whether the former or latter in any Proportion being as a Sine to a Tangent , may be varied . For , As the Tangent of an Arch , To the Sine of another Arch : So is the Cosecant of the latter Arch , To the Cotangent of the former . And by transposing the Order of the Tearm . As a Sine , To a Tangent : So the Cotangent of the latter Arch , To the Cosecant of the former . This will be afterwards used in working Proportions on the Instrument , and there Instances shall be given of it . 8. Lastly , Observe that if 4 Tearms or Numbers are Proportional , their Order may be so transposed , that each of those Tearms may be the last in Proportion ; and so of any 4 Proportional Tearms , if there be given , the other that is unknown may be found , Thus , As first to second ∷ So third to fourth . As second to the first ∷ So the fourth to the third : As the third to the fourth : , So the first to the second . As the fourth , To the third ∷ So the second , To the first . Cases of Oblique Sphoerical Triangles . 1. TWo Sides together less then a Semicircle with the Angle comprehended given to find one of the other Angles . At two Operations they may be both found by a Proportion demonstrated in the late Trigonometry of the Learned Mr. Oughtred . As the Sine of half the sum of the sides , To Cotangent of half the contained angle : So the sine of half the difference of the sides , To the Tangent of half the difference of the other angles . Again , As the Cosine of half the sum of the sides , To Cotangent of half the contained angle : So the Cosine of half the difference of the sides , To the Tangent of half the sum of the other angles . Add the half difference to the half sum , and you have the greater Angle ; but substracted from it , and there remains the lesser angle . If the sum of the two given Sides exceeds a Semicircle , the Opposite Triangle , must be resolved instead of that propounded . Here note that evey Sphoerical Triangle hath opposite to each angular Point , another Triangle , having the side that subtends the said Angle common to both , and the angle opposite thereto equal , the other parts of it are the Complements of the several parts of the former to a Semicircle . So if in the Triangle B C D there were given the sides B C , and C D with their contained Angle B C D to find the Angle C B D because these two sides are greater then a Semicircle , resolve the opposite Triangle C A D , in which there will be given C A , which may be the Complement of the Latitude 38d 28″ , and C D the Complement of the Altitude 83d with the angle A C D , the Suns Azimuth from the North 73d to find the angle C A D the hour from Noon . C A 38d : 28′ Sides , C D 83 : 00 Sides , 121 : 28′ sum 60 : 44 half sum Logarithms Logarith . 44 : 32 difference 22 : 16 difference , Sine 957854 Cosine — 996634 36 : 30 half the Angle 53 : 30 Complement , Tang : 1013079 Idem — 1013079 1970933 2009713 Sine of 60d 44′ half sum 994069 Cosine 968919 Tang : of 30d 24′ ½ — 976864 tan 68d 39′ 1040794 Sum 99 : 3 hour , in Time 36′ before 6 in the morning , or as much after it in the afternoon , difference 38d 15′ Angle of ☉ position . 2 , Two Angles together less then a Semicircle with the side between them , alias , the Interjacent side , To find one of the other sides . This is but the Converse of the former to be performed at two Operations to get them both , and the Proportion thence applyed by changing the sides into Angles . As the Sine of the half sum of the angles , To the Sine of half their difference : So is the Tangent of half the interjacent side , To the Tangent of half the difference of the other sides . Again . As the Cosine of the half sum of the angles , To the Tangent of half the interjacent side : So the Cosine of half their difference , To the Tangent of the half sum of the other sides . If half the difference of the sides be added to half the sum of the sides , it makes the greater side ; but substracted from it , leaves the lesser . If the Sum of the two given Angles exceeds a Semicircle , then , as in the former Case , resolve the Opposite Triangle . So in the Triangle Z P ☉ if there were given the angle ☉ Z P , the Suns Azimuth from the North 63d 54′ , and the hour from Z P ☉ 105● in time 5 in the morning , or 7 in the evening , and the Complement of the Latitude Z P 38d 28′ , to find the Complement of the Altitude Z ☉ 80d 31′ , or the Complement of the Declination ☉ P 66● 29′ , two Operations finds both , and neither with less . Example . Angle Z P ☉ — 105d , 00d P Z ☉ — 63 : 54 difference — 41d 6′ half difference — 20 : 33 Sine — 954533 Cosine 997144 half the side Z P — 19 : 14 Tang — 954268 Idem 954268 Sum of the 〈…〉 — 168 : 54 1908801 1951412 half sum — 84 : 27 Sine — 999796 Cosine 898549 Tangent — 7 : 1′ 909005 ta 73● 30′ 1052863 73 : 30 Sum — 80 31 the greater side Z ☉ Difference — 66 29 the lesser side ☉ P 3. Two sides with an Angle opposite to one of them given , To find the Angle opposite to the other , its Affection being fore-known . As the Sine of the side opposite to the angle given Is to the Sine of its Opposite angle : So is the sine of the side opposite to the angle sought , To the sine of its opposite angle . Here note , that the same Sine is common to an Arch , and to its Complement to 180 , if the Angle sought be foreknown to be Obtuse , substract the Arch found from 180● and there remains the angle sought . Example . So in the former Triangle , if there were given the side ☉ P 66d 29′ the Complement of the Declination with its opposite angle P Z ☉ 63d 54′ , the Suns Azimuth from the North , and the side Z ☉ , the Complement of the ☉ Altitude 80 31′ , the Angle Z P ☉ the hour from Noon would be found to be 105. Sine 63d 54′ — 995329 80 31 — 999402 1994731 Sine 66d 29′ — 9906234 Sine 75d — 998497 The Complement of 75d is the angle sought , being 105d , and so much is the hour from Noon . In some Cases the Affection of the angle sought cannot be determined from what is given ; Such Cases are , When the given Angle is Acute , and the opposite Side less then a Quadrant , and the adjacent or other Side greater then the opposite Side , and its Complement to a Semicircle also greater then the opposite Side . Also when the given Angle is Obtuse , and the opposite Side greater then a Quadrant , and also greater then the other side , and greater then the Complement of the said other Side to a Semicircle . In all other Cases the Affection of the Angle sought may be determined from what is given ; in these it cannot without the help of the third side ( or something else given ) Where Cases are thus doubtful , there can be but a double answer , and both true ; wherefore find the Acute Angle and its Complement to 180d and the like answer give in Case 4 ●h , 5 ●h , 6th , 7th and 8th following . 4 , Two Angles with a Side opposite to one of them being given , To find the Side opposite to the other , its Affection being foreknown . As the Sine of the angle opposite to the given side , Is to the Sine of the given Side : So is the Sine of the angle opposite to the side sought , To the Sine of the side sought . If the side sought be foreknown to be Obtuse , the Complement of the Ark found to 180 will be the side sought . Example . So in the former Triangle , if there were given the angle at Z the Suns Azimuth from the North 63d 54′ , and the Complement of the Suns Declination ☉ P 66d 29′ with the hour from Noon Z P ☉ to find the Side Z ☉ the Complement of the Suns Altitude , it would be found to be 80d 31′ , and the Altitude it self 9d 29′ . Sine 66d 29′ — 996234 Sine 105 that is of 75d is — 998497 1994731 Sine 63d 54′ is — 995329 Sine 80d 31′ — 999402 In some Cases the Affection of the Side sought cannot be determined from what is given ; Such Cases are , When the given Angle is Acute , and the opposite Side less then a Quadrant , and the other Angle greater then the former Angle , and its Complement to a Semicircle also greater then the said former Angle . Also when the given Angle is Obtuse , and the opposite Side greater then a Quadrant , the other Angle being less then this Angle , and its Complement to a Semicircle also less then this Angle : What Snellius hath spoke concerning these doubts , is in some Cases false , in others impertinent , however I conceive not that Learned Author mistakes , but the Supervisors after his death . In all other Cases the determination is certain , as may be hereafafter shewed . 5. Two sides with an Angle opposite to one of them being given , To find the third side , the kind of the angle opposite to the other side being foreknown . First find the Angle opposite to the other side by 3d Case , and then you have two Sides and their opposite Angles . To find the third side by the Inverse of either of the Proportions used in the 2d Case , the former will be , As the Sine of half the difference of the angles given , To tangent of half the difference of the sides given : So is the sine of half the sum of those angles , To the tangent of half the side required . In the latter Case , if the sum of the given Angles exceed a Semicircle , the opposite Triangle must be resolved . Example . If in the former Triangle there were given the side ☉ P , the Complement of the Declination 66d 29′ and angle ☉ Z P , the Azimuth from the North 63d 54′ with the side Z P , the Complement of the Latitude 38d 28′ , to find the side ☉ Z , the Complement of the Suns Altitude on the Proposed Azimuth : The first Operation will be to find the Suns angle of Position Z ☉ P 37d 32′ , which is always Acute when the Sun or Stars do not come to the Meridian between the Zenith and the elevated Pole. The said angle being found by the former Directions , we proceed to the second Operation . Sides 66 29 difference 28d 1′ half 14d 00′ 30′ Tang — 939705 Sides 38 28 difference 28d 1′ half 14d 00′ 30′ Tang — 939705 Angles 63 54 Sum 101d 26 , half 50d 43 Sine — 988875 Angles 37 32 Sum 101d 26 , half 50d 43 Sine — 988875 1928580 26 22 difference , half 13d 11′ Sine — 935806 Tangent of 40d 15′ 30″ — 992774 doubled is 80d 31′ the side sought being the Complement of the Suns Altitude . 6. Two sides with an angle opposite to one of them being given , To find the angle included , or between them , the species of the opposite to the other side being foreknown . First find the angle Opposite to the other side by 3d Case , and then we have two angles and their opposite sides to find the other angle , by the Inverse of either of the Proportions used in the first Case , the former will be , As the sine of halfe the difference of the sides , To the Tangent of halfe the difference of the angles : So is the sine of halfe the sum of the sides . To the Cotangent of half the angle required ; That is , to the Tangent of an Ark , whose Complement is half the angle inquired . If the sum of the given sides be more then a Semicircle , in the resolution of this latter Case resolve the Opposite Triangle . Example . In the former Triangle given ☉ P Comple : Declination 66d 29′ Z P Comple : Latitude — 38 28 Angle ☉ Z P the Azimuth — 63 54 To find the hour Z P ☉ — 105 The first operation wil find the angle of Position as before 37 d 32′ The second Operation . half difference of the given angles 13 d 11 m Tangent — 936966 half sum of the side — 52 , 28′ , 30″ Sine — 989931 1926897 half difference of the sides 14 d 00′ 30″ Sine — 938393 Tangent 37 d 30′ — 988504 Comple : is 52 30 doubled makes 105 d , the Angle sought . 7. Two Angles with a side opposite to one of them being given . To find the third Angle , the kind of the side opposite to the other Angle being foreknown . First find the side opposite to the other Angle by 4th Case , And then we have two angles , and their opposite sides to find the third angle ; by transposing the order of either of the Proportions used in the first Case , the latter will be , As the Cosine of halfe the difference of the sides , To the Tangent of halfe the sum of the angles : So the Cosine of halfe the sum of the sides , To the Cotangent of half the contained angle . Example . In the Triangle Z ☉ P Data angle ☉ — 37 d 32′ Angle P — 105 00 Side ☉ Z — 80 31 To find the angle Z — 63 54 The first Operation will find Z P — 38 28 The second Operation . half sum of the angles — 71 d 16′ Tangent — 1046963 half sum of the sides — 59 d 29′ 30″ Sine Compl : — 970558 2017521 half difference of the sides 21 d 1′ 30″ Cosine — 997007 Tangent 58d 3′ — 1020514 Compl : 31d 57′ doubled is 63● 54′ the angle sought . 8. Two angles with a side Opposite to one of them being given , To find the Interjacent side , the kind of the side opposite to the other angle being fore known . First find the side opposite to the other angle by 4 Case , And then you have two sides , and their opposite angle given to find the 3 side by , tranposing the Order of either of the Proportions used in the 2d Case , the latter will be , As the Cosine of halfe the difference of the two angles , To the tangent of halfe the sum of the two sides : So the Cosine of halfe the sum of the two given angles , To the Tangent of halfe the third side . Example . In the former Triangle given the Hour angle at P 105d 00 Azimuth angle at Z 63 54 Compl Altitude Side Z ☉ 80 31 To find the Compl. of the Latitude the side Z P 38 28 The first Operation will find the side P ☉ 66● 29′ Second Operation . half the sum of the two sides 73d 30′ Tangent 1052839 half the sum of the two angles 84 27 Cosine 898549 1951388 half the difference of the two angles 20d 33′ Cosine 997144 Tangent of 19d 14′ — 954244 Doubled is 38 28 the side sought These 6 last precedent Cases may be called the Doubtful Cases , because that three given terms are not sufficient Data to find one single answer without the quality of a fourth , which is demonstrated by Clavius , in Theodosium , and seeing it passes without due caution in our English Books , I shall insert it from him : LEt A D and A C be two equal sides including the angle D AC , and both of them less or greater then a Quadrant . Draw through the Points C and D , the arch of a great Circle C D , continue it , and draw thereunto another Arch or Side from A , namely A B , neither through the Poles of the Arch C D , nor through the Poles of the Arch A D , so that the angles B and B A D may not be right angles , nor the angle A D B , if then each of these sides A D A C be less then a Quadrant , the two angles C , and A D C will be Acute ; and if these Arks be greater respectively then a Quadrant , the two angles C and A D C , will be Obtuse , whence it comes to pass that the angle A D B is Obtuse , when the angle A D C is Acute , and the contrary : Now forasmuch as the sides A C and A D are equal to each other , the other Data , viz. the side A B , and the angle at Bare common to both , for in each Triangle A B D , and A B C there is given two sides with the angle at B opposite to one of them ; Now this is not sufficient Data to find the angle opposite to the other side , which may be either the acute angle at C , or the Obtuse angle ADB the Complement thereof to a Semicircle : Nor to find the third side , which may be either B D , or the whole side B C , nor the angle included , which may be either B A D , or B A C , therefore in these 3 Cases we have required the quality of the angle opposite to the other given side A B , and though it be not so much observed ; in the other Trigonometry , by Perpendiculars let fall , without the knowledge of the said angle it could not be determined whether the Perpendicular would fall with in or without the Triangle , nor whether the angle found in the first Case be the thing sought , or its Complement to 180● , nor whether the angles or Segments found by 1st and 2d Operation in the other Cases are to be added together , or substracted from each other , to obtain the side or angle sought . So also two angles with a side opposite to one of them , are not sufficient Data to obtain a fourth thing in the said Triangle , without the affection of the side opposite to the other given angle . LEt A B and A C be two unequal sides containing the angle B A C both together equal to a Semicircle , one being greater , the other less then a Quadrant Draw through the Points B and C , the arch of a great Circle B C , continue it , and draw thereto from A another side AD ; but not through the Poles of A C , nor through the Poles of B C , so that the angles D and C A D may not be right angles , nor the angle A C D a right angle ; for if it were a right angle , the angle A B C whereto it is equal , should be also a right angle , and so the two sides A B and A C , by reason of their right angles at B and C should be equal , and be Quadrants contrary to the Supposition ; Now the angles A C D and A B C being equal , which is thus proved : Suppose the two sides A B and B D to be continued to a Semicircle at E , then will the said angle be equal to its opposite angle at B , the side A C by supposition is equal to the side A E , the Complement of the side A B to a Semicircle , but equal sides subtend equal angles , therefore the angle at C is equal to the angle at B or at E , which being admitted retaining the side A D and angle at D , we have another angle opposite thereto , either C or B , which are equal and common to both Triangles , and so if the side opposite to the given angle at D were sought , a double answer should be given , either the side A C , or the other side A B its Complement to 180 , and the interjacent side might be C D or B D , and the third angle the lesser angle C A D , or the greater B A D , which is not commonly animadverted . Two Sides with the Angle comprehended , to find the third Side . That the former Cases might be resolved without the help of Perpendiculars , hath been long since hinted by Mr Gunter , Mr Speidel , and Mr Gellibrand , but so obscurely that I suppose little notice was taken thereof ; but this Case hath not hitherto been resolved by any man , to my knowledge , under two Operations with a Perpendicular let fall , working by Logarithms , unless by Multiplication and Division in the natural Numbers , which being the onely Case left wherein we are to use Perpendiculars , I shall shew how to shun both , with the joynt use of the Natural and Logarithmical Tables , by a novel Proportion of my own , and illustrate the usefulness thereof by some Examples . Two Sides with the Angle comprehended , to find 3d Side . As the Cube of the Radius , To the Rectangle of the Sines of the comprehending sides : So is the Square of the Sine of half the angle contained , To half the difference of the Versed sines of the third side , and of the Ark of difference between the two including sides , Which half difference doubled , and added to the Versed Sine of the difference of the Leggs or containing sides , gives the Versed Sine of the side sought . And if you will make the third Tearm the Square of the Sine of half the Complement of the contained angle to 180d , you will find the half difference of the Versed Sines of the third side , and of the sum of the two including sides to be doubled and substracted from the Versed Sine of the said sum . But to apply the former to Logarithms . Double the Logarithmical Sine of half the angle given , & thereto adde the Logarithms of the sines of the containing Sides , & from the left hand of the Sum , Substract 3 for the Cube of the Radius , so rests the Logarithm of half the difference of those two Versed Sines above . And if instead of the second Tearm be taken into the Proportion , the double of the Rectangle of the Sines of the containing Sides ; that is , if the Logarithm of the Number 2 be added to the Logm of the other middle Tearms , you will have the Logarithm of the whole Difference in the last place ; having found it , take the Number that stands against it , either in the Natural Sines or Tangents , and accordingly add it to the Natural Versed Sine of the Difference of the Leggs , and the summe is the natural Versed Sine of the side sought . This is the Inverse of the 4 h Axiom , used when 3 sides are given to find an angle , and will be of great use to Calculate the Distances of Stars by having their Declinations and right Ascensions , or Longitudes and Latitudes given , by means whereof the Altitudes of two of them , or of the Sun with the difference of time , or Azimuth , being observed at any time off the Meridian , the Latitude may be found , as also for Calculating the distances of places in the Arch of a great Circle , all of them Propositions of good use in Navigation ; as for the latter it hath hitherto been delivered in our English Books doubtfully , erroneously , or not sufficiently for all Cases , the Rules delivered being only true in some Cases , and doubtful in most , not determining whether the side sought be greater or less then a Quadrant . The Reader may observe how necessary it is to have such Tables , as have the natural Sines and Versed Sines , &c. standing against the Logarithmical Sines , for this and other following Proportions discovered by my self for the easie calculating a Table of hours and Azimuths to all Altitudes , as also a Tables of Altitudes to all hours ; but as yet there are none such made as have the Versed Sines , but will in due time be added to Mr. Gellibrands Tables ; in the interim it may be noted , that the Residue of the Natural Sine of an Ark from Radius called its Arithmetical Complement , is the Versed Sine of that Arks Complement ; thus the natural Sine of 40d is 6427876 substracted from Radius , rests 3572124 , the Versed Sine of 50 d. And for Arks above 90 d we need no natural Versed Sines , because the natural Sine of any Arks excess above 90 d added to the Radius is equal to the Versed Sine of the said Ark , thus the Sine of 40 d augmented by the Radius is equal to the Versed Sine of 130 d and is 16427876 Example of this Case . In the Triangle ☉ Z P let there be given the side ☉ Z , the Complement of the Altitude 70 d 53′ and the side Z P the Complement of the Latitude 38 d 28 n with the angle ☉ Z P 145 d the Suns Azimuth from the North , to find the side ☉ P , the Suns distance from the Elevated Pole. Sine 38 d 28 m — 97938317 Sine 70 53 — 99753646 Sine 72 30 Log m dobled 199588390 Natural Sine against 97280353 it doubled is 10691964 Natural V Sine of 32 d 25 m the difference of the sides — 1558280 The Versed Sine of 103 d the — 12250244 side sought , and therefore the Sun hath 13 d of South declination . Another Example of this Case for Calculating the Suns Altitude on all hours . As the Cube of the Radius , To the double of the Rectangle of the Cosines , both of the Latitude , and of the Suns declination . So is the Square of the Sine of half the hour from noon , To the difference of the Sines of the Suns Meridian Altitude , and of the Altitude sought . This Canon will finde two Altitudes at one Operation , and will have very little trouble in it , the double Rectangle , that is the second tearm of the Proportion , being fixed for that Declination . Add the Logarithms of the Number two , and of the Cosines of the Declination and Latitude together the sum may be called the fixed Logarithm . Double the Logarithm of the Sine of half the hour from noon , and add it to the fixed Logarithm the sum rejecting 3 towards the left hand , for the Cube of the Radius is the Logarithm of the difference : Take the natural Sine that stands against it , and substract it from the natural Sine of the Meridian Altitude , both for the Winter and Summer Declination , and there remains the natural Sines of the Altitudes sought . If this difference cannot be substracted from the Sine of the Meridian Altitude , it argues the Sun hath no Altitude above the Horizon in this Case substract that from this , and there will remain the Natural Sine of the Suns Altitude for the like hour from midnight in Summer . Example . Let it be required to Calculate the Suns Altitude when he hath 23d 31 m both of North and South Declination for our Latitude of London at 2 and 5 a Clock in the afternoon , or which is all one for the hours of 10 and 7 in the morning . Sine 38d 28 m Compl Latitude — 97938317 Sine of 66 29 m Compl Declination — 99623428 Logarithm of Number 2 is — 03010300 Fixed Number — 200572045 Logm of Sine of 15d , doubled — 188259924 Nearest natural Sine against it , 761900 — 88831969 61d 59 m Summer Meridian Altitude Natural Sine — 8828110 Substract — 761900 the difference before found Rests — 8066210 the natural Sine of 53d 46′ the Summer Altitude for the hours of 10 and 2 14d 57 m Winter Meridian Altitude Nat Sine — 2579760 Substract the former difference — 761900 Rests the Natural Sine of 10d 27 m the — 1817860 Winter Altitude for the hours of two and ten . The same day for the Altitude of 5 and 7. Fixed number — 200572045 Sine of 37d 30 m Logm doubled — 195688942 Natural Sine against it 4226183 — 96260987 Winter Meridian Altitude , as before Sine 2579760 Rests — 1646423 the natural Sine of 9d 29 m Summer Altitude for 5 in the morning , or 7 in the evening . Natural Sine . Summer Meridian Altitude , as before — 8828110 The former difference — 4226183 Rests the Natural Sine of 27d 24 m — 4601927 The Summer Altitude for 7 in the morning , or 5 in the afternoon . The former Case may also be performed at two Operations by help of a Perpendicular supposed , without the help of Natural Tables . 1. If both Sides are equal , As the Radius , To the sine of the Common side : So the Sine of half the Angle , To the Sine of half the side sought . 2. If one of the sides be a Quadrant , this by continving the other side to a Quadran ( as shall afterwards be shewed ) wil become a Case of right angled Sphoericala Triangles , in which besides the right angle , instead of the quadrantal side , there will be given a Legg , and its adjacent angle to find the other angle by 4 Case of right angled Sphoerical Triangles ; and so if the angle included were 90d it would be a Case of right angled Sphoerical Triangles , in which besides the right angle , there would be given both the Leggs or Sides to find the Hipotenusal . 3. In all other Cases one or both of the including Sides being less then Quadrants , it will hold , As the Radius , To the Cosine of the angle included : So the tangent of the lesser side , To the tangent of a fourth Ark , If the angle included , be less then 90d substract the 4 ●h Ark from the other side ; but if it be more from the other sides Complement to 180d , The remainder is called the Residual Ark. Then , As the Cosine of the 4th Ark , To the Cosine of the Ark remaining : So the Cosine of the lesser side , To the Cosine of the side sought . The side sought may be greater then a Quadrant , and so be doubtfull , but we may determine , That when the Leggs are of the same kind , and the angle comprehended Acute , the side sought is less then a Quadrant . And when the Leggs or containing Sides are of a different kind , and the angle comprehended Obtuse , the side sought is greater then a Quadrant . Or it may be determined from the affection of the Residual Ark in all Cases . When the contained angle is acute , and the residual Ark more then 90d , or when the said angle is Obtuse , and the residual Ark less then a Quadrant , the side sought is greater then a Quadrant , in all other Cases less . Example . In the Triangle ☉ Z P , let there be given Z P , and ☉ Z with the angle at Z , to find the side ☉ P , the Suns distance from the Elevated-Pole . angle included 145d Logm Or , 35 Compl 55d Sine — 99133645 Tangent of 38 28′ lesser side — 99000865 Tangent 33d , 3′ — 98134510 Compl ☉ P to 180d is 109 7 The Ark remaining or differ : 76d 4 m Cosine — 93816434 Lesser side — 51 32 Cosine — 98937452 192753886 Ark found — 33d 3 m Cosine — 99233450 Sine 13 — 93520436 The Complement hereof 77 d should be the side fought , but because the angle was Obtuse , and the residual Ark less then a Quadrant , the side sought is greater , and therefore 103 d the Complement hereof is the side sought . This Case & the Converse of it being the next Case , I have thus setled to apply the to Logarithmical Tables only , in Case the natural ones were wanting , being all the other Cases are thereto fitted ; and as the trouble about the Cadence of a Perpendicular is here shunned , without so much as the name of it ; so may it be done in all the rest of the Oblique Cases , which I had so fitted up for my own use ; but forbear to trouble the Reader with them , apprehending these to be better , and that he would not willingly Calculate for a portion of an angle , or a Segment of a Side , in order to the finding out the thing sought , when with as little trouble he may come by it , and yet Calculate always either for a side or an angle , one of the six principal parts of the Triangle . Otherwise for Instruments . As the Diameter , To the difference of the Versed Sines of the sum , and of the difference of any two sides , including an Angle . Or , As the Cosecant of one of the including Sides , Is to the Sine of the other side : So is the Versed Sine of the angle included . To the difference of the Versed Sines of the Ark of difference between the two including Sides , and of the third side sought , Which difference added to the Versed Sine of the difference of the Leggs , makes the Versed Sine of the side sought . And so is the Versed Sine of the contained angles Complement to 180d To the difference of the Versed Sines of the sum of the Leggs , and of the side sought , which substracted from the Versed Sine of the said sum , there remains the Versed sine of the side sought , Here note , that the same Versed Sine is common to an Ark greater then 180 d , and to its Complement to 360 d , So the Versed Sine of 200 d is also the Versed Sine of 160 d. The Proportions delivered for Instruments having such Tables as before hinted , will not be so unsuitable to the Logarithms as commonly reputed . Example for Calculating the distance of two places in the Arch of a great Circle , otherwise then according to the general Cannon before delivered . As the Secant of one of the Latitudes , To the Cosine of the other , So the Versed Sine of the difference of Longitude , To the difference of the Versed Sines of these two Arks , The one the Ark of distance sought , the other the Ark of difference between both Latitudes , when in the same Hemisphere , or the sum of both Latitudes when in different Hemispheres , which difference added to the Versed Sine of this latter Ark , the sum is the versed Sine of the distance , By turning the Substraction to be made of the first Tearm into an Addition , the two first Tearms of the Proportion will be , As the Square of the Radius , To the Rectangle of the Cosines of both the Latitudes : Then for the third Tearm being the difference of Longitude , take the natural Versed Sine thereof , and seek that Number in the natural Tangents , and that Logarith Tangent that stands against it take into the Proportion instead of the Logarithm of the Versed Sine proposed . Admit it were required to find the Distance between London and Bantam , in the Arch of a great Circle . Logme Bantam Longitude 140 d Latitude 5 d 40′ South Cosine 9,9978725 London Longitude 25 , 50 Latitude 51 , 32 North Cosine 9,7938317 — difference of Long 114 d 10′ Nat V Sine 14093923 equal to the natural Tangent of 54 d 38′ ½ nearest Logm 10,1489900 Natural Sine 8723538 against it — 2 9940694 Nat Versed Sine of 57 d 12′ the sum of both Latitudes 4582918 — Sum — 13306456 the natural Versed Sine of 109 d 18′ 30″ the Ark of distance sought . And if to the said difference , namely — 8723538 Be added the natural Versed Sine of the difference of both Latitudes , namely the V Sine of 45 d 52′ — 3036695 — The sum being the natural V Sine of 100 d 8′ 30″ is — 11760233 the distance of two places , having the same Latitudes , and difference of Longitude , but are both in the same Hemisphere . Here note , that no two places can have above 180 d difference of Longitude , therefore in differencing the two Longitudes if the remainder be more take its Complement to 360 d. The Complements of these two distances , namely 70 d 41′ 30″ and 79 d 51′ 30″ are the distances of two places of the same Latitudes considered as in different Hemispheres , their difference of Longitude being 65 d 50′ the Complement of the former , and two places in a such Position compared with their former Positions may be apprehended to be Diametrically opposite upon the Globe , as thus , Bantam having 5d 40′ South Latitude , let another place have as much North Latitude , the difference of Longitude between them 180 d and consequently so much their distance ; now whatever be the distance between Bantam and the third place , the Complement of it to 180 d shall be the distance between the two other places . 10. Two angles with the Interjacent side given . To find the 3d angle , the proportion derived from the former Case by changing the angles into sides , and holds without any such change supposed is , As the Cube of the Radius , To the double of the Rectangle of the Sines of the two given angles : So is the Square of the Sine of half the given side , To the difference of the Versed Sines of these two Arks , the one is the angle sought , the other the Ark of difference between one of the including angles , and the Complement of the other to a Semicircle , which difference added to the Versed Sine of this Ark gives the Versed Sine of the angle sought . How to work this by Tables need not be shewed after the Logm of the difference is got , if it be less then the Radius , it may be sought either in the Sines or Tangents , and the natural Sine or Tangent that stands against it and comes nearest taken ; but when it exceeds the Radius always seek it in the Tangents , and take the natural Tangent that stands against it , which difference so found , is to be added to the Versed Sine of the difference of the Leggs to obtain the Versed Sine of the angle sought . Otherwise for Tables the common way by a supposed Perpendicular 1. If both the angles are equal , As the Radius . To the Sine of the angle given : So the Cosine of half the given Side , To the Cosine of half the angle sought . In all other Cases not belonging to right angled Triangles if one or both of the given angles be Acute , it holds , As the Radius , To Cosine of the interjacent side : So the Tangent of the lesser angle , To the Tangent of a 4● h Ark. If the interjacent side be more then 90d substract the 4● h Ark from the other angle ; but if less then 90d , substract the 4● h Ark from the other angles Complement to 180d , noting the residual Ark. Then , As the Cosine of the 4th Ark , To the Cosine of the Ark remainmaining : So the Cosine of the lesser angle , To the Cosine of the angle sought . When the interjacent side is less then a Quadrant , and the residual Ark more , or when the interjacent side is greater then a Quadrant , and the residual Ark less , the angle sought is Obtuse , in all other Cases Acute . In the Triangle ☉ Z P let there be given The angle of Position at ☉ — 21d 28′ The hour from noon angle at P — 33 47 And the side ☉ P the Suns distante from the elevated Pole — 103 00 To find his Azimuth the angle ☉ Z P Sine 13 d the Complement of the interjacent side — 93520880 Tangent 21 d 28′ the lesser angle — 95946561 Tangent of 5 d 3′ — 89467441 The other angle — 33 47 The difference being the residual ark 28 44 Cosine — 99429335 Lesser angle — 21 28 Cosine — 99687773 199117108 Ark first found — 5d 3′ Cosine — 99983109 Sine 55 d — 99133999 The Complement whereof 35 d in this Case is not the angle sought , but the residue hereof from a Semicircle 145 d is the angle sought being Obtuse , because the interjacent side is greater then a Quadrant , and the residual Ark less ; the residual Ark in Operation if greater then a Quadrant , take its Complement to 180 d , because there are no Sines to Arks above a Quadrant , and then the Complement of this Ark to 90d is the Complement of the residual Ark the Sine whereof must be taken for the Cosine of the residual Arke . Otherwise for Instruments . As the Diameter , To the difference of the Versed Sines of the sum and difference of the two including angles , Or , As the Cosecant of one of those angles , Is to the Sine of the other , So the Versed Sine of the interjacent side , To the difference of the Versed Sine of an Ark left by substracting one of the including angles from the Complement of the other to a Semicircle , and of the angle sought , which difference added to the Versed Sine of the said Ark , gives the Versed Sine of the angle sought , And so is the Versed Sine of the interjacent sides Complement to 180 d , To the difference of the Versed Sines of an Ark made by adding one of the including angles to the Complement of the other to a Semicircle , and of the angle sought , which substracted from the Versed Sine of the said Ark , leaves the versed sine of the angle sought . 11. Three Sides to find an Angle . The two sides including the angle sought are called Leggs , and the third side the Base . As the Rectangle or Product of the Sines of the half sum of the three sides and of the difference of the Base therefrom . Is to the Square of the Radius : So is the Rectangle of the sines of the differences of the Leggs from the said half sum , To the Square of the Tangent of half the angle sought . And by changing the third Tearm into the place of the first , As the Rectangle of the Sines of the differences of the Leggs from the half sum of the 3 sides , Is to the Square of the Radius : So the Rectangle of the Sines of the half sum of the three sides , and of the difference of the Base therefrom , To the Square of the Tangent of an Ark , whose Complement doubled is the angle sought , or this Ark doubled is the Complement of the angle sought to 180 d , or it might be expressed , To the Square of the Cotangent of half the angle sought . Otherways in Sines . As the Rectangle of the Sines of the containing Sides or Leggs , Is to the Square of the Radius ; So the Rectangle of the Sines of the differences of the Leggs from the half sum of the three sides , To the Square of the Sine of half the angle sought . Or the Cosine may be found . As the Rectangle of the Sines of the containing sides , Is to the Square of the Radius : So the Rectangle of the Sines of the half sum of the 3 sides , and of the difference of the Base therefrom , To the Square of the Cosine of half the angle sought . These two latter Proportions are demonstrated in the Treatises of the Lord Napier , Mr Oughtred , Mr Norwood , and are those from whence I shall educe the Demonstrations of the rest . To work the third Proportion that finds the Square of the Sine of half the angle . To the Arithmetical Complements of the Logarithms of the sines of the containing Sides or Leggs add the Logarithmical Sines of the differences of the said Leggs from the half sum of the three Sides , the half sum of these four Numbers will be the Logarithm of the sine of half the angle sought . In the Triangle ☉ Z P , Data , the three Sides to find the angle a P the hour from noon . 80 d 31′ Base 66 29 Leggs — Ar comp , 0376572 38 28 Leggs — Ar comp , 2061683 Sum-185 , 28 difference of the Leggs half-92 44 from half sum — 26d 15′ Sine 9,6457058 54 , 16 Sine 9,9094190 Sum — 19,7989503 Sine of 52 d 30′ half — 9,8994751 doubled 105 , the angle at P sought . The Arithmetical Complement of a Logarithm , is the residue of that Logarithm from the next bigger Number , consisting of an Unite and Ciphers . Otherwise for Instruments . As the difference of the Versed Sines of the sum , and of the difference of any two sides including an angle , Is to the Diameter , Or , As the sine of one of the said sides , To the Secant of the Complement of the other . So is the difference of the Versed Sines of the third side , and of the Ark of difference between the two including sides , To the Versed Sine of the angle sought . And so is the difference of the Versed Sines of the third , and of the sum of the two including sides , To the versed Sine of the sought angles Complement to 180d. 12. Three Angles to find a Side . The work here for the Canon or Tables , will be by changing the Angles into Sides , the general Rule for changing all the parts of a Triangle , is to draw a new Triangle , and let the angles be wrot against their Opposite sides , and these against those , only taking the Complements of the greatest Angle , and greatest side opposed thereto to 180 d , this for most convenience that the sides or angles of the new framed Triangle may not be too large , and so cause recourse to the Opposite Triangle , otherwise the Complements of any side and its opposite angle to 180 d ▪ might as well have been taken . But for this Case , seeing there are only angles to be changed into sides , take the Complement of the greatest angle to 180 d and proceed as if there were three sides given to find an angle . But the Proportion in Versed Sines , &c. without any such change will be , As the difference of the Versed Sines of the sum , and of the difference of any two angles adjacent to the side sought . Is to the Diameter , Or , As the Sine of one of the said angles , Is to the Cosecant of the other : So is the difference of the Versed Sines of the third or Opposite angle , and of an Ark left by substracting one of the including angles from the Complement of the other to a Semicircle , To the Versed Sine of the side sought . And so is the difference of the Versed Sines of the third angle , and of an Ark made by adding one of the including Angles to the Complement of the other to a Semicircle . To the Versed Sine of the sought sides Complement to 180d . Thus having finished the Cases , it is to be intimated that the Proportions here used in Versed Sines are variously demonstrated in diverse Writers , but in most the latter part for finding the Complement of an angle to 180d , is quite omitted , those that have demonstrated the former part , do it in these tearms following . As the Rectangle of the sines of the containing sides , Is to the Square of the Radius : So is the difference of the Versed Sines of the Base , or third Side , and of the Ark of difference between the two including sides , To the Versed Sine of the angle sought , which the Reader may see in Lansberg , Regiomantanus , Snellius , Pitiscus , and the learned Clavius , who makes 15 Cases , and twice as many Scheams , to demonstrate this part of it . I shall only shew how it may be inferred from the common Proportions in use fitted to the Tables demonstrated by the Lord Napier , Mr Oughtred , Mr. Norwood . We have two Proportions delivered in Rectangles and Squares the one for finding an angle , the other to find its Complement to 180d. The two first tearms are the Proportion between the Rectangle of the Sines of the containing sides , and the Square of the Radius ; these two tearms being divided by the Sine of one of those sides , the Quotient will be the Sine of the other , if the same Divisor divide the Square of the Radius , the Quotient will be the Secant of the Complement of the Ark belonging to the Divisor , because , As the Sine of an Ark , To Radius , So is the Radius , To the Secant of that Arks Complement ; But if any common Divisor divide any two Tearms of a Proportion , the Dividends will be Acquimultiplex to the Quotients ; and therefore by the Quotients will bear such Proportion each to other as the Dividends , and therefore it holds , As the Rectangle of the Sines of the containing sides , Is to the Square of the Radius : So is the Sine of one of those sides , To the Secant of the Complement of the other . Again , for the third Tearm , to find an angle it is proposed . So is the Restangle of the Sines of the differences of the Leggs from the half sum of the three sides . Or which is all one , So is the Rectangle of the Sines of the half sum , and half difference of the Base or third side , and of the Ark of difference between the two including sides , To the Square of the Sine of half the angle sought , And so to find the Complement of an angle to 180 d. So is the Rectangle of the Sines of the half sum of the three sides , and of the difference of the third side or Base therefrom , Or which is equivalent thereto , So is the Rectangle of the Sines of the half sum , and half difference of the Base or third side , and of the sum of the two including sides , To the Square of the Sine of an Ark , which doubled is the Complement of the angle sought to 180 d , or the Complement of that Arch to a Quadrant doubled , is the angle sought . The former of these two expressions of the third Tearm of the Proportion , as being the more facil for memory is now retained ; but the latter , ( formerly used , and now rejected ) agrees best with the Proportion , as applyed to Versed Sines , for the inferring whereof note , that such Proportion , As the difference of two Versed Sines beareth to another Versed Sine , the same Proportion doth the half difference of those Versed Sines , bear to half the Versed Sine of that other Arch : But that is the same that the Rectangle of the Sines of the half sum and half difference of any two Arks doth bear to the Square of the Sine of half that other Arch , which will be thus inferred , because if the said Rectangle and Square be both divided by Radius , the two Quotients will be the half difference of the versed Sines of the two Arks proposed , and half the versed Sine of the 4 ●h Arch. That the Sines of the half sum and half difference of any two Arks are mean Proportionals between the Radius and the half difference of the Versed Sines of those Arks is demonstrated in Mr Gellibrands Trigonometry in Octavo , that is , As the Radius , To the Sine of half the sum of any two arks : So is the sine of half the difference of those two arks , To half the difference of the versed sines of those two arks , and therefore the said Rectangle divided by Radius , the Quotient is half the difference of the versed sines of the two Arks. And that the Sine of any Arch is a mean Proportional between the Radius and half the versed Sine of twice that Arch , That is , As the Radius , Is to the sine of an Arch : So the sine of that Arch , To half the versed sine of twice that Arch , and therefore the Square of the sine of any Arch divided by Radius , the Quotient is the half versed sine of twice that Arch ; whence the Rule to make a Cannon of whole Logarithmical versed sines is to take half the arch proposed , and to the Logarithm thereof doubled , or twice wrot down , to add the Logarithm of the number two , and from the sum to substract the Radius . We have before inferred , that As the Rectangle of the sines of the containing sides , Is to the Square of the Radius : So is the sine of one of those sides , To the Secant of the Complement of the other , and that by dividing those two Plains by one of those sides ; but if we divide the said two Plains , viz. the Rectangle of the sines of the containing sides , and the Square of the Radius , by the Radius as a common Divisor , the latter Quotient will be the Radius , and the former the half difference of the versed sines of those Arks whereof the two containing sides are the half sum and the half difference ; but those Arks are found by adding the half difference to the half sum to get the greater , and substracting it therefrom to get the lesser ; Which is no other then to get the sum and difference of the two containing sides , it therefore holds , As the Rectangle of the sines of the containing sides , Is to the Square of the Radius , Or , As the sine of one of those sides , To the Secant of the Complement of the other : So is the half difference of the versed sines of the sum and difference of those two sides to the Radius , And by consequence so is the whole difference to the Diameter , and this being admitted the whole Proportion in all its parts may be inferred from Mr Daries Book of the Uses of a Quadrant , where he demonstrates , That , As the difference of the versed Sines of the sum and difference of any two sides including an angle , Is to the Diameter : So is the difference of the versed sines of the third side , and of the Ark of difference between the two including sides , To the versed sine of the angle sought , in that Scheme it lyes , As M S , To G H : So is M P , To H C. And I further add , As M S , To G H : as before , So is P S , To G C. that is , retaining the two first Tearms of the Proportion , the same it holds for the third and fourth Tearm . So is the difference of the versed sines of the third side , and of the sum of the two including sides , To the versed sine of the sought angles Complement to 180d. Now from these Proportions thus Demonstrated , are inferred those others that give the answer in the Squares of Tangents , in order whereto observe , That if 4 Numbers are Proportional , their Squares are also Proportional ( quamvis non in eadem rations ) so that any three of those Squares being given , the Square of the 4th will be found by direct Proportion , and the Proportion for making a Table of Natural Tangents from the Tables of natural sines is , As the Cosine of an Ark , To the sine of the said Ark : So is the Radius , To the Tangent of the said Ark. It will therefore hold by 22 Prop. of 6 h Book of Euclid , As the Square of the Cosine of an Ark , Is to the Square of its sine : So is the Square of the Radius , To the Square of its Tangent , Now from the two Demonstrated Proportions for the Tables , the two first Tearms are common to both , and therefore there is the like Proportion between the two latter Tearms of the first Proportion , and the two latter in the second , as between the two latter , and the two former in each Proportion : Now because the latter Proportion finds the Square of the Cosine , and the former the Square of the Sine of the same Ark , it is inferred that the third tearm in the latter Proportion , bears such Proportion to the third Tearm in the former Proportion , as the Square of the Cosine of an Ark , doth to the Square of its Sine , which is the same that the Square of the Radius bears to the Square of the Tangent of the said Ark , it therefore holds when three sides of a Spherical Triangle , are given to find an angle . As the Rectangle of the Sines of the half sum of the three sides , and of the difference of the Base therefrom , Is to the Rectangle of the Sines of the differences of the Leggs therefrom : So is the Square of the Radius , To the Square of the Tangent of half the angle sought , and by changing the 2d Tearm into the place of the first . As the Rectangle of the sines of the differences of the Leggs from the half sum of the 3 sides , Is to the Rectangle of the sines of the half sum of the three sides , and of the difference of the Base therefrom : So is the Square of the Radius , To the Square of the Cotangent of half the angle sought . These Proportions are published in order to their Application to the Serpentine Line , which will be accomodated for the sudden operating of any of them ; the Axioms to be remembred are not many , the Reader will meet with their Demonstration and Application in Mr Newtons Trigonometry now in the Press , and said to be near finished : The four Proportions in plain Triangles , when three sides are given to find an angle without the Cadence of Perpendiculars are demonstrated in the 27 Section of the late Miscellanies of Francis van Schooten . The Construction of diverse Instruments will require a Table of the Suns Altitudes to the Hour and Azimuth assigned ; And for the Acurate bounding in of the Lines , it may be a Table of Hours and Azimuths to any Altitude assigned ; for the easie Calculating whereof , I am desired for the ease and benefit of the Trade , to render this part of Calculation as facil as I can , and therefore shall handle it the more largely . To Calculate a Table of Hours to all Altitudes in all Latitudes . The 1. Proportion shall be to find the Suns Altitude in Summer , or Depression in Winter at the hour of 6. As the Radius , To the sine of the Latitude : So the sine of the Declination , To the sine of the Altitude or Depression sought This remains fixed for all that day the Suns Declination supposed not to vary , and then it holds , As the Cosine of the Declination , To the Secant of the Latitude : So in Summer is the difference in Winter the sum of the sines of the Suns Altitude proposed , and of his Altitude or Depression at 6 To the sine of the hour from 6 towards noon in Winter , and in Summer also , when the given Altitude is greater then the Altitude of 6 , but when it is less towards midnight . This Proportion also holds for Calculating the Horary distance of any Star from the Meridian . In like manner to Calculate the Azimuth . As the sine of the Latitude , To sine of the Declination : So is the Radius , To the side of the Suns Altitude or Depression in the prime Vertical , that is , being East or West . This remains fixed for one day . Then , As the Cosine of the Altitude , To the Tangent of the Latitude : So in Summer is the difference , and in Winter the sum of the sines of the Suns Altitude proposed , and of his Vertical Altitude or Depression , To the sine of the Azimuth towards noon Meridian in Winter and in Summer also , when the given Altitude is greater then the Vertical Altitude or Depression , but when it is less towards Midnight Meridian . This Proportion is general either for Sun or Stars , when the Declination is less then the Latitude of the place ; But when it is more , say as before , As the sine of the Latitude , To the sine of the Declination : So is the Radius , To a fourth we may call it a Secant . Again . As Cosine Altitude , To the Tangent of the Latitude : So in declinations towards the Depressed Pole is the sum ; but towards the Elevated Pole the difference of this Secant , and of the sine of the Sun or Stars Altitude , To the sine of the Azimuth from the Vertical towards the noon Meridian . Before Application be made , the latter part of these Proportions being of my own peculiar Invention , and of very great use both for Calculation , and Instrumentally , it will be necessary to demonstrate the same . For the Hour from the Analemma . Having in the Scheme annexed drawn the Equator and Horizon , the two prickt Lines passing through the Center , as also the Prime Vertical and Axis , the two streight Lines passing through the same . Let I X and L M represent two Parralells of Declination on each side the Equator , and O X a Parralel of the Suns Altitude in Summer , and P Q of his Depression in Winter , at the hour of 6 , because these Parralells pass through the Intersection of the Parralells of Declination with the Axis . Let R S be a Parralel of Altitude after 6 , and T V a Parralel of Altitude before it ; from the Intersections of these Parralells of Altitude with the Parralels of Declination let fall Perpendiculars on the Parralells of the Suns Altitude or Depression at 6 , and then we shall have divers right Lined right angled Triangles Constituted in which we shall make use of the Proportion of the sines of angles to their opposite sides an Axiom of common demonstration . In the Triangle A F E , As the sine of the angle at F the Radius , To its Opposite side A E , the sine of the Declination : So the sine of the Latitude the angle at E to A F , the sine of the Suns Altitude at 6. Again in the two Opposite Triangles A B C , the smaller before the greater after 6. As the Cosine of the Latitude the sine of the angle at A , To its Opposite side B , C , the difference of the sines of the Suns Altitude at 6 , and of his proposed Altitude : So is the Radius sine of the angle at B , To C A , the sine of the hour from 6 in the Parralel of Declination in the lower Triangle before , in the upper after 6. So in the Winter or lower Triangle A B D C. As Cosine of the Latitude sine of the angle at A , To B C , the sum of the sines of the Suns Depression at 6 B D , and of his given Altitude D C : So is the Radius the sine of the angle at B , To A C , the sine of the hour from 6 towards noon in the Parralel of Declination , The sine of the hour thus found in a Parralel , is to be reduced by another Analogy to the common Radius , and that will be , As the Radius of the Parralel I A , the Cosine of the Declination , Is to the common Radius E AE : So is any other sine in that Parralel . To the sine of the said Arch to the common Radius . Now it rests to be proved that both these Analogies may be reduced into one , and that will be done by bringing the Rectangle of the two middle Tearms of the first Proportion with the first Tearm under them as an improper Fraction to be placed as a single Tearm in the second Proportion , being in value the answer found in the Parralel , and then we have the Rule of three to Operate as it were in whole Numbers and mixt . The Proportion will run , As the Cosine of the Declination , To Radius : So the said Improper Fraction ▪ To the Answer . and so proceeding according to the Rules of Arithmetick . The Divisor will be the Rectangle of the Cosine of the Declination , and of the Cosine of the Latitude , one of the middle Tearms would be the Square of the Radius , and the other the former sum or difference . Now if any two Tearms of a Proportion be divided by a common Divisor , the Dividends being Equimultiplex to the Quotients , the Quotients bear the same mutual Proportion as the Dividends by 18● Propos . 7 Euclid . So in this instance if the Rectangle of the Cosines both of the Latitude and of the Declination be divided by one of those Tearms , the Quotient will be the other , and if the Square of the Radius be divided by the Sine of an Arch , the Quotient will be the Secant of that Arks Complement ; So in the present Example , if the former Rectangle be divided by the Cosine of the Latitude ▪ the Quotient is the Cosine of the Declination , if the Square of the Radius be divided by the same Divisor , the Quotient is the Secant of the Latitude , likewise if both those Plains were divided by the Cosine of the Declination , the Quotients would be the Cosine of the Latitude , and the Secant of the Declination , it therefore holds , As the Cosine of the Declination , To the Secant of the Latitude , Or , As the Cosine of the Latitude , To the Secant of the Declination : So is the former sum or difference of sines , To the sine of the hour from 6 , which was to be proved . Corrollarie . As the Radius , To the sine of an Arch in a lesser Circle or Pararlell : So is the Secant of that Parralell , To the sine of the said Arch , to the common Radius . Hence may be observed a general Canon for the double or compound Rule of three , divide the Tearms into two single Rules , by placing two Tearms of like Denomination in each Rule , and the other remaining Tearm may in most Cases be put among either of these two Tearms of like Denomination , and then by arguing whether like require like , or unlike , the Divisor in each single Rule , may be discovered , and then it will hold in all Cases , As the Rectangle or Product of the two Divisors , Is to the product of any two of the other Tearms : So is the other Tearm left , To the Number sought , For the Azimuth . Having drawn the Horizon and Axis , the two prickt Lines , the Vertical Circle Z N , and the Equinoctial Ae Ae , the Parralels of Declination I K and L M , draw T V a Parralel of lesser Altitude then that in the Vertical , and R S a Parralel of greater Altitude ; Draw also P Q a Parralel of Depression equal to the Vertical Altitude , in the point C aboue the Center the Point A being as much below it b , eing the point where the Parralel of Declination intersects the Vertical Circle , and from the point C in the lesser parralel of Altitude , let fall the perpendicular C B on the parralel of Depression P Q , by this means there will be Constituted divers right lined , right angled Triangles , and through those Points where the parralel of Declination , and parralels of Altitude intersect , are drawn Elipses prickt from the Zenith to represent the Azimuths , and in the three several Triangles thus Constituted , the side A B measureth the quantity of the Azimuth in the parralel of Altitude , and B C in the two upper Triangles is the difference of the sines of the Suns proposed Altitude , and of his Altitude in the prime Vertical : But in the lower Triangle the sum of them , it then holds by the Proportion of the sines of Angles to their opposite sides . In the two upper Triangles , As the Cosine of the Latitude , the sine of the angle at A , To its opposite side B C , the difference of the sines of the Suns Vertical , and of his proposed Altitude : So is the sine of the Latitude , that is the sine of the angle at C , To its opposite side B A , the sine of the Azimuth from the East and West , And the like in the lower Triangle , onely there the third Tearm B C , is the sum of the sines of the Suns Vertical Depression , and of his given Altitude : Such Proportion as as the Cosine of an Ark doth bear to the sine of an Ark , doth the Radius bear to the Tangent of the said Ark , this being the Canon by which the natural Tangents are made from the natural sines , and therefore we may change the former Proportion , and instead thereof say , As the Radius , To the Tangent of the Latitude : So the said sum or difference of Sines , To the Sine of the Azimuth in the Parralel of Altitude : The answer falling in a Parralel or lesser Circle is to be reduced to the common Radius by another Analogy , and that is As the Cosine of the Altitude ( the Radius of the parralel ) To the Radius : So any sine in the said parralel , To the like sine in the common Radius . Now it is to be proved that both these Proportions may be brought into one , and that will be as before , by making an improper Fraction whose Numerator shall be the Rectangle of the two middle Tearms of the former Proportion , the first Tearm , viz. the Radius being the Denominator , and placing this as the third Tearm in the second Proportion , and then those that understand how to operate the Rule of three in whole Numbers and mixt , will find their Divisor to be the Rectangle or Product of the Cosine of the Altitude , and of the Radius , and the Dividend the Product of the three other Tearms , namely , of the Tangent of the Latitude , the Radius , and the former sum or difference of sines , whence it holds , As the Rectangle of the Cosine of the Altitude , and of the Radius , Is to the Rectangle of the Tangent of the Latitude , and of the Radius : So is the former sum or difference of sines , To the sine of the Azimuth . The Reader may presently espy that the two former Tearms of this Proportion may be freed from the Radius by dividing them both thereby , and the Quotients will be the Cosine of the Altitude , and the Tangent of the Latitude , It therefore holds , As the Cosine of the Altitude , To the Tangent of the Latitude : So in Summer is the difference , in Winter the sum of the sines of the Suns Vertical and proposed Altitude , To the sine of the Azimuth from the Vertical . This is general either for Sun or Stars , when their Declination is less then the Latitude of the place ; but when it is more , the Case doth but little vary . In the Scheme annexed fitted to the Latitude of the Barbados having drawn H H the Horizon , P P the Axis , Ae Ae the Equator , Z A the Vertical draw two parralells of Declination F R , K A continued till they intersect the Vertical prolonged , draw the parralel of Altitude B ☉ , and parralel thereto from the Point A draw A E , Then doth the latter part of the Proportion lye as evident as before , In the right angled Triangle C G F right angled at G , As the sine of the Latitude the angle at F , To its Opposite side C G the sine of the Declination , So the Radius the angle at G , To the Secant C Z F. Again in Summer . As the Cosine of the Latitude the angle at ☉ , To its opposite side D Z F , the difference between the former Secant and the sine of the Altitude : So is the sine of the Latitude , the angle at F , To its opposite side D ☉ , the sine of the Azimuth from the Vertical in the Parralel of Altitude . In Winter , As Cosine Latitude angle at A , To B E the sum of the former Secant equal to E M , and of the sine of the Altitude M B : So is the sine of the Latitude the angle B , To A E , equal to B D the sine of the Azimuth in a Parallel as before , to be reduced to the common Radius . From this Schem may be observed the reason why the Sun in those Latitudes upon some Azimuths hath two Altitudes , because the Parralel of his Declination F R intersects , and passeth through the Azimuth , namely , the prickt Ellipsis in the two points S , ☉ . I now proceed to the Vse in Calculating a Table of Hours . For those that have occasion to Calculate a Table of Hours to any assigned Altitude and parralel of Declination , it will be the readiest way to write down all the moveable Tearms first , as the natural sines of the several Altitudes in a ruled sheet of Paper , and then upon a peice of Card to write down the natural sine of the Suns Altitude at 6 and removing to every Altitude , get the sum or difference accordingly , which being had , seek the same in the natural sines , and write down the Log m that stands against it , then upon the other end of the piece of Card get the sum of the Arithmetical Complements of the Logarithmical Cosine of the Declination , and of the Logarithmica Cosine of the Latitude , and add this fixed Number to the Logme before wrote down ; by removing the Card to every one of them , and the sum is the Logme of the sine of the Hour from 6 , if the Logmes be well proportioned out to the differences which may be sufficiently done by guess . Example . Comp Latitude 38d 28′ Ar Comp — 0,2061683 Comp Delinat 66 , 29 Ar Comp — 0,0376572 fixed Number — ,2438255 Let the Altitude be 36● 42′ Nat Sine 5976251 Natural sine Altitude at 6 — 3124174 difference — 2852077 Log against 9 4550441 Sine of 30d the hour from 6 towards noon — 9,6988696 Another Example . N S Altitude at 6 — 3124174 Let the Altitude be 13d 46′ N S 2379684 difference — 744490 Logm — 8,8715646 The former fixed Number — 0,2438255 Sine of 7d 30′ the hour from 6 towards midnight because the Altitude is less then the Altitude of 6. 9,1153901 This method of Calculation will dispatch much faster then the common Canon , when three sides are given to find an angle ; the Azimuth may in like manner be Calculated , but will be more troublesome not having so many fixt Tearms in it , and having got the hour , the Azimuth will be easily found ; in this Case we have two sides and an angle opposite to one of them given , to find the angle opposite to the other , and the Proportion , will hold , As the Cosine of the Altitude , To the sine of the hour from the Meridian : So the Cosine of the Declination , To the sine of the Azimuth from the Meridian . And in this Case the three sides being given , we may determine the affection of any of the angles . If the Sun , or Stars have declination towards the depressed Pole , the Azimuth is always Obtuse , and the hour and angle of position-Acute . If the Sun , &c. have declination towards the Elevated Pole , but less then the Latitude of the place the angle of Position is always acute , the hour before 6 obtuse , the hour and Azimuth between the Altitude of 6 , and the Vertical Altitude both acute , afterwards the hour acute , and the Azimuth obtuse . But when the Sun or Stars come to the Meridian between the Zenith and the Elevated Pole , as when their declination is greater then the Latitude of the place , the Azimuth is always acute , the hour before 6 obtuse , afterwards acute . The angle of position from the time of rising to the remotest Azimuth from the Meridian is acute , afterwards obtuse . Another General Proportion for the Hour . As the Radius , To the Tangent of the Latitude : So the Tangent of the Suns declination , To the sine of the hour of rising from six : Again . To the Rectangle of the Cosine of the Latitude , and of the Cosine of the declination , Is to the Square of the Radius : So is the sine of the Altitude , To the difference of the Versed sines of the Semidiurnal Ark , and of the hour sought . Having got the Logarithm of this difference , take the natural number out of the Sines or Tangents that stands against it , accordingly as the Logme is sought , and in Winter add it to the natural sine of the hour of rising from 6 , the sum is the natural sine of the hour from 6 towards noon . In Summer get the difference between this fourth and the sine of rising from 6 , the said difference is the natural sine of the hour from 6 towards noon , when the Number found by the Proportion is greater then the sine of rising , towards midnight when less . The Canon is the same without Variation as well for South declinations as for North , and therefore we may by help thereof find two hours to the same Altitude . Example . Comp Lat 38d 28′ Ar Comp Sine — , 2061683 Comp declin 77d Ar Comp — , 0112761 fixed number — , 2174444 Let the Altitude be 14d 38′ Sine — 9,4024889 Natural sine against it — 41660 , 00 — 9,6199333 Nat sine of rising from 6 — 29058 , 79 Sum — 70718 , 79 N sine of 45d the hour from six in Winter . Difference — 12601 , 21 Sine of 7d 14′ the hour from 6 in Summer towards noon to the former Altitude , and like declination towards Elevated Pole. Another Example for the same Latitude and Declination . Logme Let the Altitude be 20d 25′ Sine — 9,5426321 The former fixed Logme — 2174444 Natural sine against it — 5754811 Sum — 9,7600765 Natural sine of rising — 2905879 Sum — 9,7600765 Sum — 8660690 sine 60d the ho from 6 in Wint Difference — 2848932 sine 16d 33′ the hour from 6 in Summer towards noon ; And thus may two hours be found at one operation for all Altitudes less then the Winter Meridian Altitude , to be converted into usual Time by allowing 15d to an hour , and 4● to a degree . To Calculate a Table of the Suns Altitudes on all Hours . As the Secant of the Latitude , To the Cosine of the Declination , Or which is all one , As the Square of the Radius : To the Rectangle of the Cosines , both of the Latitude and of the Declination : So is the sine of the hour from 6. To a fourth , namely , in Summer the difference of the sines of the Suns Altitude at 6 , and of the Altitude sought , in Winter the sum of the sines of the Suns Depression at 6 , and of the Altitude sought . Having wrote down the Logarithmical sines of the hour from 6 on the Paper , at one end of a piece of Card may be wrote down the sum of the Logarithmical Cosines of the Latitude and Declination , and add the same to the sine of the hour rejecting the double Radius , and take the natural sine that stands against the sum sought in the Logarithmical sines ; having this natural sine , get the sum and difference of it , and of the natural of the Suns Altitude at 6 , the sum is the natural sine of the Altitude for Summer declinations , and the difference for Winter Declinations when the sine of the Suns Altitude is the lesser : But when it is the greater , the said difference is the natural sine of the Altitude for hours beyond 6 towards midnight . Example . Log m Complement Latitude 38d 28′ Sine — 9,7938317 Compl Declination 66 29 Sine — 9,9623428 fixed Logme — 19,7561745 Let the hour be 30d that is 2 hours before and after six in Summer sine 9,6989700 Sum — 9,4551445 Natural sine against it — 2851308 Nat sine of the Altitude at 6 — 3124174 Sum — 5975482 Sine of 36d 42′ being the two Altitudes for 4 and 8 in the morning or afternoon , in Summer . Difference — 272866 Sine of 1 34 being the two Altitudes for 4 and 8 in the morning or afternoon , in Summer . Another Example . Let the hour be 45d from six Sine — 9,8494850 the former fixed Logme — 19,7561745 N Sine against it — 4032791 Sum — 9,6056595 N Sine of Altitude at 6 — 3124174 Sum — 9,6056595 Sum — 7156965 Sine of 45d 42′ being the two Altitudes for the hours of 9 or 3 in Summer or Winter for Declination 23d 31′ both towards the Elevated and Depressed Pole. Difference — 908617 Sine — 5 13 being the two Altitudes for the hours of 9 or 3 in Summer or Winter for Declination 23d 31′ both towards the Elevated and Depressed Pole. By the former Canon was the following Table of Altitudes calculated , and that with much celerity beyond any other way , it will not be amiss to Calculate the Suns Altitude at 6 by the natural Tables only , however the Logarithms will accurately discover the natural sine of at , if duly Proportioned by the differences . A Table of the Suns Altitudes for each Hour and quarter for the Latitude of London .   North.   South .   Declination . 23d , 31 13 Equator . 13d 23 31   XII . 61d , 59 51 , 28 38 , 28. 25 , 28 14 , 57 XII . . 61 , 49 51 , 21 38 , 22 25 , 20 14 , 52   * 61 , 23 50 , 59 38 , 4 25 , 8 14 , 39   . 60 , 40 50 , 24 37 , 36 24 , 43 14 , 18   I. 59 , 42 49 , 36 36 56 24 , 10 13 , 48 XI .   58 , 29 48 , 35 36 , 5 23 , 26 13 , 9     57 , 4 47 , 24 35 , 4 22 , 34 12 , 23     55 , 29 46 , 1 33 , 55 21 , 33 11 , 29   II. 53 , 45 44 , 3● 32 , 36 20 , 25 10 , 28 X.   51 , 53 42 , 51 31 , 8 19 , 8 9 , 19     49 , 54 41 , 4 29 , 34 17 , 44 8 , 3     47 , 51 39 , 1● 27 , 53 16 , 14 6 41   III. 45 , 42 37 1● 26 , 6 14 , 38 5 13 IX .   43 , 31 35 , 9 24 , 12 12 , 55 3 , 39     41 , 16 33 , 2 22 , 15 11 , 7 1 , 59     38 , 59 30 , 52 20 , 13 9 , 15 0 , 15   IIII. 36 , 42 28 , 37 18. 7 7 , 17     VIII .   34 , 23 26 , 22 15 , 58 5 , 17         32 , 4 24 , 5 13 , 46 3 , 12         29 , 43 21 , 46 11 , 32 1 , 4       V. 27 , 23 19. 27 9 , 16     VII .     25 , 4 17 , 7 6 , 58             22 , 46 14 , 47 4 , 39             20 , 28 12 , 27 2 , 20           VI. 18 , 13 10 , 9 00 , 00 VI.         15 , 58 7 , 51                 13 , 46 5 , 34                 11 , 37 3 , 20               VII . 9 , 30 1 , 7 V.             7 , 25     Declination . Ascensionall difference .         5 , 24             3 , 27     13d   16d , 54′       VIII . 1 , 34 IIII. 23 , 31 33 , 12 R A A Table of the Suns Altitudes for every 5 degrees of Azimuth from the Meridian for the Latitude of London . North. South . Declination . 2● d 31 13d Equator . 13● 23d , 31′ Mer Alt 61 , 59 51 , 28 38d 28′ 25d , 28′ 14d , 57   5 61 , 55 51 , 23 38 , 21 25 , 21 14 , 49   10 61 , 42 51 , 7 38 , 2 24 , 57 14 , 22   15 61 , 21 50 , 40 37 , 30 24 , 20 13 , 39   20 60 , 51 50 , 3 36 , 44 23 , 27 12 , 39   25 60 , 11 49 , 14 35 , 45 22 , 16 11 , 19   30 59 21 48 , 13 34 , 32 20 , 51 9 , 43   35 58 , 20 46 , 59 33 , 3 19 , 7 7 , 46   40 57 , 7 45 , 31 31 , 19 17 , 7 5 , 31   45 55 , 43 43 , 50 29 , 19 14 , 50 2 , 57   50 54 , 3 41 , 53 27 , 3 12 , 13 0 , 03   55 52 , 7 39 , 39 24 , 30 9 , 21       60 49 , 56 37 , 9 21 , 40 6 , 11       65 47 , 27 34 , 22 18 , 34 2 , 46       70 44 , 39 31 , 18 15 , 12           75 41 , 34 27 , 58 11 , 37           80 38 , 10 24 , 23 7 , 51           85 34 , 32 20 , 38 3 , 59           90 30 39 16 , 42               95 26 , 34 12 , 40               100 22 , 28 8 , 41               105 18 , 20 4 , 44 Declinat Amplitude .       110 14 , 15 0 , 54 13d ,   21d , 12′       115 10 , 19     23 , 31′ 39d , 54′       120 6 , 36                   125 3 , 7                 Many Tables may want the naturall Tables standing against the Logarithmicall ; therefore the method of Calculation by the Logarithmicall Tables onely , is not to be omitted , albeit we wave the common Proportions , when three Sides are given to find an Angle . A general Proportion derived from the book of the honorable Baron of Marchist●n , which may bee wrought on a Serpentine Line without the use of Versed Sines , or finding the half distance between the 7th Tearme and the Radius , not encumbred with Rectangles , Squares , or Differences of Sines , or Versed Sines . Three Sides to find an Angle ; two of them or all three being lesse then Quadrants . By a supposed perpendicular , which need not to be named . As the Tangent of half the greater of the containing sides , To the Tangent of the half sum of the other sides : So is the Tangent of half their difference , To the tangent of a fourth Arke . If this Arke be greater then the half of the first assumed side ; namely , then the Arke of the first Tearme , in the Proportion , the ( Supposed perpendicular falls without ) Angles opposite to the two other Sides are of a different Affection , the greatest side subtending the Obtuse angle , and the lesser the Accute . If the Angle Opposite to the greater of the other Sides be sought ▪ Take the difference ; if to the lesser , the Sum of the 4th Arke , and of half the containing Side , which half is the first Tearme in the Proportion , Then , As the Radius , To the Cotangent of the other Containing Side : So the Tangent of the said Sum or difference , To the Cosine of the Angle sought . The first Tearme above needs no Restraint , but when one of the Containing Sides is greater then a quadrant : If the 4th Arke be less then the half of the first assumed Side , the Perpendicular falls within , in this Case , the two Angles , opposite to the two other sides may be found , being both Acute . Get the Sum and difference of half the first assumed Side , and of the 4● Arke , the Sum is the greater Segment , and the Difference or residue , the lesser Segment ; the Perpendicular alwayes falling on the side assumed , first into the Proportion ; Then , As the Radius , To the Cotangent of the lesser of the other Containing Sides ; So is the Tangent of the lesser Segment . To the Cosine of the Angle sought . As the Radius , To the Cotangent of the greater of the other Containing Sides ; So is the Tangent of the greater Segment . To the Cosine of the Angle sought . From these general Directions is derived this Canon for Calculating the Azimuth ; As the Tangent of half the Complement of the Altitude ; To the Tangent of the half sum of the Sun or Stars distance from this elevated pole , and of the Complement of the Latitude : So is the Tangent of half their difference , To the Tangent of a 4 h Arke . If this Ark be less then half the Complement of the Altitude , the Azimuth is Acute ; if more obtuse , in both Cases , get the difference of these two Arkes , if there be no difference , the Azimuth is 90d from the Meridian ; Then , As the Radius , To the Tangent of the Latitude ; So the Tangent of the said Arke of difference , To the Sine of the Azimuth from the prime Verticall . This when the Sun or Stars do not come to the Meridian between the Zenith and the elevated pole : but when they do , Let the sum of the 4th Ark , and of half the Complement of the Altitude , be the third Tearme in the latter Proportion . This is a ready Way to Calculate a Table of Azimuths ; two Tearms in each Proportion being fixed for one Declination ; and the Azimuth being known , the Hour may be found by a single Operation , As the Cosine of the Declination , Is to the Sine of the Azimuth , from the Meridian : So is the Cosine of the Altitude , To the Sine of the Hour , from the Meridian . Example , for 13d of North Declination . 77d Complement of Declination the Polar distance . 38. 28 Complement of Latitude at London . 115 , 28 Sum : half sum 57d , 44′ Tangent . 10,1997231 . 38 , 32 difference : half diff 19 , 16 Tangent 9 ▪ 5434594 fixed for that declination — 19,7432225 Altitude 4d , 44′ Comp. 85d 16′ half 42d 38′ Tang. 9,9640811 Tangent of — 31. 1 — 9,7791414 difference — 11 37 Tangent 9,3129675 Tangent of 51d 32′ the Latitude — 10,0999135 Sine of 15d , the Azimuth 9,4128810 from East or West Northwards , because the Ark found by 1st Operation was less then half the Complement of the Altitude . Another Example for the Altitude 34d 22′   Log ● The fixed Number — 19,7432225 Compl. Altitude 55● 38′ half 27 , 49● Tangent 9,7223147 Tangent of — 46 , 23 — 10,0209078 Difference — 18 , 34 Tangent 9,5261966 Tangent of the Latitude — 10,0969135 The Sine of 25d the Azimuth from — 9,6261101 East to West Southwards because the first Ark was more then half the Coaltitude . The hours to these two Azimuths will be found by the latter Proportion to be — 98d , 54′ 50 , 9 from Noon . To Calculate the Suns Altitude on all Hours and Azimuths . The first operation shall be to find such an Ark as may remain fixed in one Latitude to serve to all Declinations in both Cases : So that but one Operation more need be required . The Proportion to find it is As the Radius to the Cotangent of the Latitude , So is the Sine of any Hour from 6 , or Azimuth from the Vertical To the Tangent of a fourth Ark. This 4th Arke ( if the Azimuth be accounted from the Vertical , that is , from the points of East or West towards noon Meridian ) Is the Altitude that the Sun shall have , being in the Equinoctial , upon that Azumuth , and so one of the Quesita . If the hour from 6 be accounted upward on the Equinoctial , this 4 ●h Ark is the ark or portion of the hour Circle , between the Equinoctial and Horizon . This Ark for Hours and Azimuths beyond 6 , or the Vertical , towards the midnight Meridian , is the Depression under the Horizon , according to the Denominations already given it . For the Altitudes on all Hours . When the Sun is in the Equinoctial , As the Radius , is to the Cosine of the Latitude : So is the Sine of the Hour from 6 To the Sine of his Altitude . In all other Cases , If the Hour from noon be more then 6 Substract the Equinoctial Arks that Correspond to such parts of time as you would Calculate Altitudes for ; out of the Suns distance from the Depressed Pole , and then it will hold , If the Hour from noon be less then 6 Substract the Equinoctial Arks that Correspond to such parts of time as you would Calculate Altitudes for ; out of the Suns distance from the Elevated Pole , and then it will hold , As the Cosine of the Ark found by the first common Proportion , Is to the Cosine of the Ark remaining ; So is the Sine of the Latitude , To the Sine of the Altitude sought ▪ For the more speedy Calculating a Table of the Suns Altitudes for this Latitude to any Declination , there is added a Table of these Equinoctial Arks for every hour and quarter , as also for every 5d of Azimuth ; The use whereof shall be illustrated by an Example or two , observing by the way , that the same Ark belongs to two hours alike remote on each side from six , as also like Arks to two Azimuths equally remote on each side the Vertical . Hours on each side six , Azimuths on each side the Vertical .   d ′ VI 0 , 00 fixed Arks       5 , 55   5d 3 , 59   8 , 49   10 7 , 51 VII 11 , 37 V 15 11 , 37   14 , 19         16 , 55   0 15 , 12   19 , 22   25 18 , 34 VIII 21 , 40 IIII 30 21 , 40   23 , 49         25 , 48   35 24 , 30   27 , 39   40 27 , 3 IX 29 , 19 III 45 29 , 19   30 , 52         32 , 13   50 31 , 19   33 , 27   55 33 , 3 X 34 , 32 II 60 34 , 32   35 , 28         36 , 17   65 35 , 45   36 , 57   70 36 , 44 XI 37 , 30 I 75 37 , 30   37 , 55½         38 , 13½   80 38 , 2   38 , 24½   85 38 , 21 XII 38 , 28   90 38 , 28 Equinoctial Altitudes or Depressions . Example . Admit it were required to Calculate the Suns Altitude for 2 or 10 of the Clock , when his declination is 23d 31′ North. Suns distance from the Elevated Pole — 66 : 29 fixed Ark for 2 or 10 is — 34 : 32 Residue — 31 : 57 Complement of the Residue 58d 3′ Sine — 9,9286571 Sine of — 51 32 the Latitude — 9,8937452 19,8224023 Sine of — 55 28 Com first ark 9,9158200 Sine of — 53 45 the — 9,9065823 Altitude sought — 9,9065823 So if it were required to Calculate the Suns Altitude for the hour ▪ of 5 in the morning when his declination is 20d North ☉ distance from depressed Pole — 110d fixed Ark — 11 : 37 The Residue is 81d , 33′ Or — 98 23 Sine of 8d , 23′ the Compl of the Residue — 9,1637434 Sine of the Latitude — 9,8937452 19,0574886 Sine of 78d 23′ the Compl fixed ark — 9,9910119 Sine of 6d 42′ the Altitude sought — 9,0664767 For the Altitudes on all Azimuths . As the Sine of the Latitude , Is to the Cosine of the Equinoctial Altitude : So is the Sine of the Declination , To the Sine of a fourth Ark. Get the sum and difference of the Equinoctial Altitude , and of this fourth Ark the sum is the Summer Altitude for Azimuths from the Vertical towards noon Meridian . The difference when this 4th Ark is lesser greater then the Equinoctial Altitude is the Winter Summer Altitude for Azimuths from the Vertical towards Noon Midnight Meridian Example . Let it be required to Calculate Altitudes for the Suns Azimuth 30d from the Meridian , that is 60d from the Vertical for Declination 23d 31′ both North and South . This will be speedily done , add the Logme of the Sine of the Declination to the Arithmetical Complement of the Logme of the Sine of the Latitude , this number varies not for that declination , and to the Amount add the Logme of the Cosine of the Equinoctial Altitude , the sum rejecting the Radius is the Logarithmical Sine of the 4th Ark. Sine Latitude Ar Comp — 0,1062548 Sine declination — 9,6009901 Sine of 55d 28′ the Complement of Equinoctial Altitude — 9,7072449 9,9158200 Sine — 24d 49′ — 9,6230649 Equinoct Altitude — 34 32 Sum — 59 21 Summer Difference — 9 43 Winter Altitude for that Azimuth . Another Example : The former Number — 9,7072449 Sine 78d 23′ Comp of Equinoct 9,9910119 Altitude for 15d of Azimuth — Sine of 29d 57′ — 9,6982568 Eq Altitude 11 37 Difference — 18 20 Sum — 41 34 The Summer Altitudes for 15d Azimuth each way from the Vertical to that declination . The Suns Declination 20d North to find his Altitudes for 15d Azimuth on each side the Vertical . Sine of 51d 32′ the Latitude Ar Com — 0,1062548 Sine of 20d the declination — 9,5340517 Sine of 78d 23′ Comp Eq Altitude — 9,9910119 Sine of 25d 20′ — 9,6313184 Sine of — 25d 20′ Eq Altitude — 11 37 Difference — 13 43 Sum — 36 57 The Summer Altitudes for 15d Azimuth on each side the Vertical to that Declination . By the Arithmetical Complement of a Number is meant a residue which makes that first Number equal to the other : And so if from a number or numbers given another Number is to be substracted , and instead thereof a third number added , the totall shall be so much encreased more then it should by the sum made of the number to be substracted , and of that was added : That is to say , in this last Example instead of substracting the Sine of the Latitude from another sum we added the residue thereof , being taken from Radius thereto , and so increased the Total too much each time by the Radius , which is easily rejected . If the Sun or Stars come to the Meridian between the Zenith and the Elevated Pole , as when their Declination is more then the Latitude of the place , the former Rule of Calculation varies not only the sum of the Equinoctial Altitude , alias , the fixed Ark , and of the Ark found by the second Proportion will be more then 90● In this Case the Complement of it to 180 d is the Altitude sought . A double Advertisement . The Declination towards the Elevated Pole supposed more then the Latitude of the place . If the Complement of the Declination be more then the Latitude of the place also , as in this case it always is for the Sun ; the Sun or such Stars shall have two Altitudes on every Azimuth between the Coast of rising or setting , and the remotest Azimuth from the Meridian ; To find what Azimuths those shall be , As the Cosine of the Latitude , To Radius ; So is the Sine of the Declination , To the Sine of the Amplitude , And So is the Cosine of the Declination , To the Sine of the remotest Azimuth from the Meridian . Between the Azimuth of rising , and the remotest Azimuth , the angle of Position is Acute , afterwards Obtuse . The Sun upon the remotest Azimuth , the angle of Position being a right angle , will have but one Altitude to find it . As the Sine of the Declination . To Radius ; So is the Sine of the Latitude , To the Sine of that Altitude . Example . In North Latitude 13d of Barbados . Declination 20 d North , the Suns Amplitude or Coast of rising 69 d 23′ from the North , or 20 d 33′ from the East Northwards , and his remotest Azimuth from the North Meridian 74 d 4●′ . His two Altitudes upon the Azimuth of 74 d from the Meridian 27 d 27′ the lesser and 52 d 27′ the greater , the fixed Ark found by the first Operation , being — 50 d 3′ And by the second Operation the Ark found is — 77 30 Difference being the lesser Altitude is — 27 27 The sum 127d 33′ the Comp to 180 d being the greater Alt is 52 27 Altitude on the remotest Azimuth — 41 07 Upon Azimuths nearer the Meridian then the Coast of rising or setting , it need not be hinted that there will be but one Altitude . The Proportion from the 5th Case of Oblique Sphoerical Triangles to find the Suns Altitude on all Azimuths would be As the Cosine of the Declination , To the Sine of the Azimuth from the Meridian : So is the Cosine of the Latitude , To the Sine of the angle of Position . In such Cases when it will be acute or obtuse is already defined , and where two Altitudes are required it will be both , and being accordingly so made , the Proportion to find the Altitudes would be , As the sine of half the difference of the Azimuth and angle of Position , To the Tangent of half the difference of the Polar distance and Colatitude So the Sine of half the sum of the Azimuth and angle of Position , To the Tangent of half the Complement of the Altitude . The Azimuth being an angle always accounted from the Midnight Meridian ; but the former Proportion derived from the other Trigonometry in this Case is more speedy . Such Stars as have more Declination then the Complement of the Latitude never rise nor set , if their declination be also more then the Latitude of the place , they will have two Altitudes upon every Azimuth , except the remotest from the Meridian , and the Calculation the same as before . Example for the Latitude of London . The middlemost in the great Bears Rump , declination 56d 45′ , The remotest Azimuth will be 61 d 49′ from the Meridian , and the Altitude thereto 69 d 26′ . If that Star have 30 d of Azimuth from the Meridian , The first ark will be 34 d 22′ difference being the lesser Alt 27● 7′ The second ark — 61 39 difference being the lesser Alt 27● 7′ Sum — 96 11 Comp the greater Altitude — 83 49 This will be very evident on a Globe for having rectified it to the Latitude extend a Thread from the Zenith over the Azimuth in the Horizon , then turn the Globe round , and such Stars as have a more utmost remote Azimuth from the Meridian , and do not rise or set will pass twice under the Thread , the Azimuth Latitude and Declination being assigned if it were required to know the time when the Star shall be twice on the same Azimuth it may be found without finding the Altitudes first by 6 ●h Case of Oblique Spherical Triangles , As before get the angle of Position . As the Sine of half the difference of the Complement of the Latitude , and of the Complement of the declination . To the Sine of half their sum : So the Tangent of half the difference of the Azimuth from the Meridian , and of the angle of Position , To the Cotangent of half the hour from the Meridian , to be converted into common time if it relate to Stars : In each Proportion there is two fixed Tearms . The Illustration how these two fixed Arks are obtained , is evident from the Analemma in the Scheme annexed . AE E represents the Equator . H K the Horison , P T the Axis , Z N the Prime , Vertical S D a Parralel of North declination , ☉ another of South , declination , P S ☉ and P A N the Arks of two hours Circles between six and noon , and P D T another before 6. In the Triangle E L B right angled , there is given the angle at E , the Complement of the Latitude , the side E L the hour from 6 , with the right angle at L to find the side L B the ark of the hour Circle contained between the Equinoctial and the Horzion by 11th Case of right angled Sphoerical Triangles , the Proportion will be , As AE E Radius , To AE H Cotangent Latitude : So E L Sine of the hour from 6 , To L B The Tangent of the said Ark. From Z draw the Arches Z S and Z ☉ ( being Ellipses ) through the Points where the Hour Circle , and Parralels of Declination intersect , and they represent the Complements of the Altitudes sought , and let fall a Perpendicular from Z to R , then will P R be equal to L B , because the Proportion above is the same that would Calculate R P ; Which substracted from P S or P ☉ the Suns distance in Summer or Winter from the Elevated Pole rests R S or R ☉ : Now in an Oblique Spherical Triangle reduced to two right angled Triangles by the Demission of a Perpendicular , the Cosines of the Bases are in direct Proportion to the Cosines of the Hipotenusals a consequence derived from the general Axiom of the Lord Napier , and therefore it holds , As the Cosine of the Ark R P , or B L , that we call the common fixed ark , Is to the Sine of the Latitude , the Complement of Z P : So the Cosine of the Ark remaining , that is the Complement of R S or S O , To the Sine of the Altitude , the Complement of Z S or Z ☉ : This for all hours under 90● from the Meridian , but for those before or after 6 in the Summer it may be observed in the opposite Triangles E A N and E A I , counting the hour E A each way from 6 that the Ark of the hour Circle A N equal to A I , as much as it is above the Horizon in Winter , so much is it below the same in Summer , and the Suns distance from the Elevated Pole then equal to his distance from the Depressed Pole now : and the Zenith distance then equal to the Nader distance now , as is evident in the Triangle T N D. So that in this Case the Sun is only supposed to have Winter instead of Summer Declination , and the Rule for Calculating his Altitude the same as for Winter Altitudes . In like manner for the Azimuth . In the Schem following H Q represents the Horizon , AE F the Equator , S G a Parralel of Summer declination , and another passing through M of Winter declination , Z S L and Z N A two Azimuths between the Vertical and Noon Meridian , Z K I N another between it and the Midnight Meridian , from the Points S M I let fall the Perpendiculars S D , M O , I G representing the ☉ Declination in the Ellipses of several hour Circles ; So will L S , M L , A K , represent the Altitudes of these 3 Azimuths respectively , according to the proper Declination , for the finding whereof there is given in the Triangle E L B the side E L the Azimuth from the Vertical the angle B E L , the Complement of the Latitude and the right angle , and the Proportion by 11th Case of right angled Sphoerical Triangle is As AE H the Radius , To H AE the Cotangent of the Latitude : So E L the Sine of the Azimuth from the Vertical , To L B the Tangent of the Equinoctial Altitude to that Azimuth . Thut we see the first Proportions common to both , this Case issuing from the 2d Axiom of Pitiscus , that in many right angled Sphoerical Triangles having the same Acute angle at the Base , the Sines of the Bases and Tangents of the Perpendiculars are proportional . For the second Operation to find B S. Though the Analogy is derivable from the general Proposition of the Lord Napier , yet here I shall take it from Ptitiscus the 1 Axiom . That in many right angled Sphoerical Triangles , having the same acute angle at the Base the Sines of the Perpendiculars and Hipothenusals are in direct Proportion . Therefore in the Triangle AE Z B , and D S B it will hold , As AE Z the Sine of the Latitude , To Z B the Cosine of the Equinoctial Altitude , So is D S , the Sine of the Declination , To the Sine of B S , which is equal to B M : See 29th Prop. of 3d book Regiomontanus , I prove it thus , The opposite angles at B are equal , and the angles at D and O are equal , and the side D S , equal to M O , it will then be evinced by Proportion , As the Sine of the angle at B , To its opposite side M O or D S : So is the Radius , that is the angle at O or D , To its opposite side S B , or M B. This equality being admitted , if unto L B we add B S , the sum is L S the Altitude for Summer Declination , if from B L we take B M equal to B S , the remainder M L is the Altitude for the like Declination towards the Depressed Pole , being the Winter Altitude of that Azimuth . But for Azimuths above 90 d from the Meridian it may be observed in the two Opposite Triangles E A N , and E A I , counting the Azimuth E A each way from the Vertical its Equinoctial Altitude A N in the Winter is equal to its Equinoctial Depression A I in the Summer , and is to be found by the 1 Proportion . The second Proportion varies not . As the Sine of the Latitude N F equal to AE Z , Is to N I equal to Z B the Cosine of the Equinoctial Altitude or Depression : So is the Sine of the Declination , I G equal to D S : To Sine I K , from which taking A I , the Equinoctial Depression rests A K , the Altitude sought . To Calculate a Table of the Suns Altitude for all Azimuths and hours under the Equinoctial . This will be two Cases of a Quadrantal Sphoerical Triangle . 1. For the Altitudes on all Azimuths . There would be given the side A B a Quadrant , the angle at B the Azimuth from the Meridian , and the side A D the Complement of the Suns Declination . If the side B D be continued to a Quadrant , the angle at C will be a right angled , besides which in the Triangle A D C , there would be given A D as before the Complement of the Suns Declination , and A C the measure of the angle at B to find D C the Suns Altitude being the Complement of B D , and so having the Hipotenusal , and one of the Leggs of a right angled Sphoerical Triangle , by the 7th Case we may find the other Legg , the Proportion sutable to this question would be As the Sine of the Azimuth from East or West , Is to the Radius : So is the Sine of the Declination , To the Cosine of the Altitude sought . 2. For the Altitudes on all Hours . There would be given the side A B a Quadrant , A D the Complement of the Suns declination with the contained angle B A D the hour from noon , to find the side B D the Complement of the Suns Altitude . Here again if B D be continued to a Quadrant , the angle at C is a right angle , the side A D remains common , the angle D A C is the Complement of the Angle B A D , See Page 57 where it is delivered , That if a Sphoerical Triangle have one right angle , and one side a Quadrant , it hath two right angles , and two Quadrantal sides , and therefore the angle B A C is a right angle ; this is coincident with the 8th Case of right angled Spherical Triangles , the Proportion thereof is , As the Radius , Is to the Cosine of the Declination , So is the Sine of the hour from six , To the Sine of the Altitude , sought . Affections of Sphoerical Triangles . BEcause the last Affection in page 57 is not Braced in the beginning , and a mistake of lesser for greater , in the last Brace but one , I thought fit to recite it at large . Any side of a Sphoerical Triangle being continued , if the other sides together are equal to a Semicircle , the outward angle on the side continued shall be equal to the inward angle on the said side opposite thereto . If the sides are less then a Semicircle , the outward angle will be greater then the inward opposite angle ; But if the said sides are together greater then a Semicircle , the outward angle will be less then the inward opposite angle . In the Triangle annexed , if the sides A B and A C together are equal to a Semicircle , then is the angle A C D equal to the angle A B C. If less then a Semicircle then is the said angle greater then the angle at B. But if they be greater , then is the said angle A C D less then the angle at B. By reason of the first Affection in page 58 ( which wants a Brace in the first Line ) after the words two sides ) We require in the first , second , and other Cases of Oblique angled Sphoerical Triangles , the sum of the two sides or angles given , to be less then a Semicircle . Before I finish the Trigonometrical part , I think it not amiss to give a Determination of the certain Cases about Opposite sides and Angles in Sphoerical Triangles , having before shewn which are the doubtful , and the rather because that this was never yet spoke to . Two sides with an Angle opposite to one of them , to determine the Affection of the Angle opposite to the other . 1. If the given angle be Acute , and the opposite side less then a Quadrant , and the adjacent side less then the former side . The angle it subtends is acute because subtended by a lesser side , for in all Sphoerical Triangles the lesser side subtends the lesser angle and the Converse . 2. If the given angle be acute , and the opposite side less then a Quadrant , and the other side greater then the former side : This is a doubtfull Case , if it be less then a Quadrant it may subtend either an Acute or an Obtuse angle , and so it may also do if it be greater then a Quadrant , yet we may determine , That when the given angle is acute , and the opposite side less then a Quadrant , but greater then the Complement of the adjacent side to a Semicircle ( which it cannot be unless the adjacent side be greater then a Quadrant ) the angle opposite thereto will be obtuse . 3. The given angle Acute , and the opposite side greater then a Quadrant , and the other side greater . If two sides be greater then Quadrants , if one of them subtends an Acute angle , the other must subtend an Obtuse angle , by the 1st . Affection in pag 58. 4. The given angle Acute , and the opposite side greater then a Quadrant ; The other side cannot be lesser then the former , by what was now spoken . 5. If the given angle be Obtuse , and the opposite side less then Quadrant , the other side less subtends an Acute angle . 6. If the given angle be Obtuse , and the opposite side less then a Quadrant ; The other side greater then the former side must of necessity be also greater then a Quadrant , otherwise two sides less then Quadrants should subtend two Obtuse angles , contrary to the first Affection in p 58. 7. If the given angle be Obtuse , and the Opposite side greater then a Quadrant ; If the other side be greater then the former it will subtend a more Obtuse angle . 8. If the given angle be Obtuse , and the Opposite side greater then a Quadrant , If the other side be less then the former , whether it be lesser or greater then a Quadrant it may either subtend an Acute or Obtuse angle . But we may determine That when the given angle is Obtuse , and the Opposite side greater then a Quadrant ; If the Complement of the adjacent side to a Semicircle be greater then the said opposite side , the angle subtended by the said adjacent side is Acute . Two Angles with a side Opposite to one of them , to determine the Affection of the side opposite to the other . 1. If the given angle be Acute , and the opposite side less then a Quadrant ; If the other angle be less , the side opposite thereto shall be less then a Quadrant because it subtends a lesser angle . 2. If the given angle be Acute , and the Opposite side less then a Quadrant , If the other angle be greater the Case is ambiguous , yet we may determine , If the given angle be Acute , and the opposite side lesser then a Quadrant , if the Complement of the other angle to a Semicircle be less then the Acute angle ( which it cannot be but when the latter angle is Obtuse ) the side subtending it shall be greater then a Quadrant . 3. If the given angle be Acute , and the opposite side grnater then a Quadrant , if the other angle be lesser . Then by 12 of 4 book of Regiomontanus , if two Acute angles be unequal , the side opposite to the lesser of them shall be less then a Quadrant . 4. If the given angle be Acute , and the opposite side greater then a Quadrant , If the other angle be greater , It must of necessity be Obtuse , because otherways two Acute unequal angles , the side opposite to the lesser of them should not be lesser then a Quadrant , contraty the former place of Regiomontanus . 5. If the given angle be Obtuse , and the opposite side lesser then a Quadrant , If the other angle be lesser , It must of necessity be Acute , and the side subtending it less then a Quadrant , otherways two sides less then Quadrants should subtend two Obtuse angles , contrary to 1st Affection in page 58. 6. If the given angle be Obtuse , and the opposite side less then a Quadrant , If the other angle be greater , By 13 Prop of 4 h of Regiomontanus , if a Triangle have two Obtuse unequal angles , the side opposite to the greater of them shall be greater then a Quadrant . 7. If the given angle be Obtuse , and the opposite side greater then a Quadrant , If the other angle be greater or more obtuse then the former ; it is subtended by a greater side . 8. If the given angle be Obtuse , and the opposite side greater then a Quadrant , If the other angle be less then the former , the Case is ambiguous ; yet we may determine , That when the given angle is Obtuse , and the opposite side greater then a Quadrant , if the other angle be less then the Complement of the said Obtuse angle to a Semicircle , the side subtending it shall be less then a Quadrant . The former Cases that are still , and alwais will be doubtful , may be determined when three sides are given . A Sphoerical Triangle having two sides less then Quadrants and one greater , will always have one Obtuse angle opposite to that greater side , and both the other angles Acute . A Sphoerical Triangle having three sides less then Quadrants , can have but one obtuse angle ( and many times none ) and that obtuse angle shall be subtended by the greatest side ; But whether the greatest side subtend an Acute or Obtuse angle cannot be known , unless given or found by Calculation , and that may be found several ways . First by help of the Leggs or Sides including the angle sought by 15● Case of right angled Sphoerical Triangles . As the Radius , To the Cosine of one of those Leggs ; So is the Cosine of the other Legg , To the Sine of a fourth Arch. If the third side be greater then the Complement of the fourth Arch to 90d , the angle included is Obtuse , if equal to it a right angle , if less an Acute angle . Secondly , By help of one of the Leggs and the Base or Side subtending the angle sought by 7th Case of right angled Sphoerical Triangles . As the Cosine of the adjacent side , being one of the lesser sides , Is to the Radius : So the Cosine of the opposite side , To the sine of a fourth Arch. If the third side be greater then the Complement of the 4th Arch to 90d , the angle subtended is Acute , if equal to it a right angle , if less an Obtuse angle . All other Cases need no determination , if a Triangle have two sides given bigger then Quadrants , make recourse to the opposite Triangle and it will agree to these Cases . If three angles were given to determine the Affection of the sides if they were all Acute the three sides subtending them will be all less then Quadrants . But observe that though a Triangle that hath but one side greater then a Quadrant , can and shall always have but one Obtuse angle , yet a Triangle that hath but one Obtuse angle may frequently have two sides greater then Quadrants . In this and all other Cases let the angles be changed into sides , and the former Rules will serue , I should have added a brief Application of all the Axioms that are necessary to be remembred , and have reduced the Oblique Cases to setled Proportions ( with the Cadence of Perpendiculars only to shew how they arise ) whereby they will be rendred very facil ; as also the Demonstration of the Affections , which may be hereafter added to some other Treatise to be bound with this Book . Of working Proportions by the Lines on the Quadrant . BEfore I come to shew how all Proportions may in some measure be performed upon the Lines of this Quadrant , it is to be intimated in general , That the working of a Proportion upon a single natural Line , was the useful invention of the late learned Mathematician , Mr Samuel Foster , and published after his decease as his ; In the use of his Scale , a Book called Posthuma Fosteri , as also by Mr Stirrup in a Treatise of Dyalling ; in which Books , though it be there prescribed , and from thence may be learned , yet I acknowledge I received some light concerning it , from some Manuscripts lent me by Mr Foster , in his life time to Transcribe for his and my own use touching Instrumental Applications ; Yet withal be it here intimated , that there are no ways used upon this Quadrant for the obtaining the Hour and Azimuth with Compasses , and the Converse of the 4th Axiom , but what are wholly my own , and altogether novel , though not worth the owning , for Instrumental Conclusions not being so exact as the Tables are of small esteem with the learned as in Mr Wingates Preface to the Posthuma ; besides the taking off of any Line from the Limb to any Radius ; the Explanation of the reason of Proportions so wrought , the supply of many Defects , and the inscribing of Lines in the Limb , I have not seen any thing of Mr Fosters , or of any other mans , tending thereto . Of the Line of equal Parts . THis Line issueth from the Center of the Quadrant on the right edge of the foreside , and will serve for Mensurations , Protractions and Proportional work . The ground of working Proportions by single natural Lines , is built upon the following grounds . That Equiangled Plain Triangles have the sides about their equal angles Proportional , and this work hath its whole dependance on the likeness of two equiangled Plain Right angled Triangles ; as in the figure annexed , let A B represent a Line of equal parts , Sines or natural Tangents issuing from the Center of the Quadrant supposed at A , and let A C represent the Thread , and the Lines B C , E D making right angles with the Line A C , or with the Thread , the nearest distances to it from the Points B and E. I say then that this Scheme doth represent a Proportion of the greater to the less , and the Converse of the less to the greater . First of the greater to the less , and then it lies , As A B to B C : So A E to A D , whence observe that the length of the second Tearm B C must be taken out of the common Scale A B , and one foot of that extent entred at B the first Tearm , the Thread must be laid to the other foot at C , according to the nearest distance then the nearest distance , from the Point E to the Thread that is from the third Tearm called Lateral entrance , being measured in the Scale A B , gives the quantity of the 4 ●h Proportional . Secondly of the less to the greater . And then it lies , As B C to A B : So E D to A E , Or , As E D to A E : So B C to A B , by which it appears that the first Tearm B C must be taken out of the common Scale , and entred one foot at the second Tearm at B , and the Thread laid to the other at C according to nearest distance then the third Tearm E D must be taken out of the common Scale and entred between the Thread and the Scale , so that one foot may rest upon the Line , as at E , and the other turned about may but just touch the Thread , as at D , so is the distance from the Center to E the quantity of the 4th Proportional ; and this is called Parralel entrance , because the extent E D is entred Parralel to the extent B C : To avoid Circumlocution , it is here suggested , that in the following Treatise , we use these expressions to lay the Thread to the other foot , whereby is meant to lay it so according to nearest distance , that the said foot turned about may but just touch the Thread , and so to enter an extent between the Thread and the Scale is to enter it so that one foot resting upon the Scale , the other turned about may but just touch the Thread . Another chief ground in order to working Proportions by help of Lines in the Limb is , That in any Proportion wherin the Radius is not ingredient the Radius may be introduced by working of two Proportions in each of which the Radius shall be included , and that is done by finding two such midle tearms ( one whereof shall always be the Radius ) as shall make a Rectangle or Product equal to the Rectangle or Product of the two middle Tearms proposed , to find which the Proportion will be . As the Radius , To one of the middle Tearms : So the other middle Tearm , To a fourth , I say then , that the Radius and this fourth Tearm making a Product or Rectangle equal to the Product of the two middle Tearms , these may be assumed into the Proportion instead of those , and the answer or fourth Tearm will be the same without Variation , and therefore holds , As the first Tearm of the Proportion , To the Radius : So the fourth found as above , To the Tearm sought . Or , As the first Tearm of the Proportion , Is to the fourth found as above : So is the Radius , To the Tearm sought ; and here observe , that by changing the places of the second and third Tearm , many times a Parralel entrance may be changed into a Lateral , which is more expedite and certain then the other , having thus laid the foundation of working any Proportion , I now come to Examples . 1. To work Proportions in equal parts alone . If the first Tearm be greater then the second , take the second Tearm out of the Scale , and enter one foot of that extent at the first Tearm , laying the Thread to the other foot , then the nearest distance from the third Tearm to the Thread gives the 4th Proportional sought , to be measured in the Scale from the Center . If the first Tearm be less then the second , still as before keep the greatest Tearm on the Scale , and enter the first Tearm upon it , laying the Thread to the other foot , then enter the third Tearm taken out of the Scale between the Thread and the Scale and it finds the 4th Proportional . Example . Admit the Sun shining , I should measure the length of the Shaddow of a Perpendicular Staff and find it to be 5 yards , the length of the Staff being 4 yards , and at the same time the length of the Shaddow of a Chimny , the Altitude whereof is demanded , and find it to be 22½ yards , the Proportion then to acquire the Altititude would be , As the length of the shaddow of the Staff , To the length of the Staff : So the length of the shadow of the Chimney , To the height thereof , that is As 5 to 4 : So 22 ‑ 5 to 18 yards the Altitude or height of the Chimney sought , Enter 4 or the great divisions upon 5 , laying the Thread to the other foot , then the nearest distance from 22 ‑ 5 to the Thread measured will be 18 , and in this latter part each greater division must be understood to be divided into ten parts . And so if the Sun do not shine , the Altitude might be obtained by removing till the Top of a Staff of known height above the eye upon a level ground be brought into the same Visual Line with the Top of the Chimney , and then it holds , As the distance between the Eye and the Staff , To the height of the Staff above the eye : So the distance between the Eye and the Chimney . To the height of the Chimney above the Eye . Some do this by a Looking Glass , others by a Bowl of Water , by going back till they can see the top of the object therein , and then the former Proportion serves , mutatis mutandis . But Proportions in equal parts will be easily wrought by the Pen , the chief use therefore of this Line will be for Protraction , Mensuration , and to divide a Line of lesser length then the Radius of the Quadrant Proportionally into the like parts the Scale is divided , which may be readily done , and so any Proportional part taken off , to do it Enter the length of the Line proposed at the end of the Scale at 10 , and to the other foot lay the Thread the nearest distances from the several parts of the graduated Scale to the Thread shall be the like Proportional parts to the length of the Line proposed , the Proportion thus wrought is , As the length of the graduated Scale , To any lesser length : So the parts of the Scale , To the Proportional like parts to that other length . Of the Line of Tangents on the left edge of the Quadrant . THe chief Uses of this Scale will be to operate Proportions either in Tangents alone or jointly , either with Sines or equal parts , to prick down Dyals , and to proportion out a Tangent to any lesser Radius ▪ To work Proportions in Tangents alone . 1. Of the greater to the less . Enter the second Tearm taken out of the Scale upon the first , laying the Thread to the other foot , then the nearest distance from the third Tearm to the Thread being taken out and measured from the Center shews the 4th Proportional . But if the Proportion be of the less to the greater , Enter the first Tearm taken out of the Scale upon the second , and lay the Thread to the other foot , then enter the third Tearm taken out of the Scale between the Thread and the Scale , and the foot of Compasses will shew the 4 Proportional . Example . Of the greater to the less , As the Tangent of 50d , To the Tangent of 20d : So the Tangent of 30 , To the Tangent of 10d. To work this take the Tangent of 20● in the Compasses , and entring one foot of that extent at 50d , lay the Thread to the other , according to the nearest distance , then will the nearest distance from the Tangent of 30d to the Thread being measured on the Line of Tangents from the Center be the Tangent of 10d the fourth Proportional . By inverting the Order of the Tearms , it will be , Of the less to the greater . As the Tangent of 20d , To the Tangent of 50d : So the Tangent of 10d , To the Tangent of 30d , to be wrought by a Parralel entrance . This Scale of Tangents is continued but to two Radii , or 63d 26′ whereas in many Cases the Tearms given or sought may out-reach the length of the Scale , in such Cases the Propprtion must be changed according to such Directions as are given for varying of Proportions at the end of the 16 Cases of right angled Sphoerical Triangles . In two Cases all the Rules delivered for varying of Proportions will not so vary a Proportion as that it may be wrought on this Line of Tangents . First when the first Tearm is greater then 63d 26′ the length of the Scale , and the rwo middle Tearms each less then 26d 34′ the Complement of the Scale wanting ; In this Case if any two Tearms of the Proportion be varied according to the Rules for varying of Proportions , there will be either in the given Tearms or Answer such a Tangent as shall exceed the length of the Scale , but it may be remedied by a double Proportion by the reason before delivered for introducing the Radius into a Proportion wherein it is not ingredient . As the Radius , To the Tangent of one of the middle Tearms : So the Tangent of the other middle Tearm , To a fourth Tangent : Again . As the Radius , To that fourth Tangent : So is the Cotangent of the first Tearm , To the Tangent of the fourth Ark sought . The Radius may be otherways introduced into a Proportion then here is done , but not conducing to this present purpose , and therefore not mentioned till there be use of it , which will be upon the backside of a great Quadrant of a different contrivance from this , upon which this trouble with the Tangents will be shunned . An Example for this Case . As the Tangent of 65d , To Tangent of 24d : So the Tangent of 20d , To what Tangent ? the Proportion will find 4d , 10′ . Divided into two Proportions will be , As Radius , To Tangent 24d : So Tangent of 20d , To a fourth , the quantity whereof need not be measured . Again . As Radius , To that fourth : So the Tangent of 25d , the Complement of the first Tearm , To the Tangent of 4d 26′ , the fourth Tangent sought . Operation . First enter the Tangent of 24d on the Radius or Tangent of 45d laying the Thread to the other foot , then take the nearest distance to it from 20d , and enter that extent at 45d , laying the Thread to the other foot , then will the nearest distance from 25d , to the Thread if measured from the Center be the Tangent of 5d 26′ sought . The second Case is when the first Tearm of the Proportion is less then the Complement of the Scale wanting , and the two middle Tearms greater then the length of the Scale . This ariseth from the former , for if the Tearms given were the Complements of those in the former Example , they would be agreeable to this Case , and so no further direction is needful about them , for the Tangent sought would be the Complement of that there found , namely 84d 34′ . Hence it may be observed , that a Table of natural Tangents only to 45d , or a Line of natural Tangents only to 45d may serve to operate any Proportion in Tangents whatsoever . To Proportion on out a Tangent to any Radius . Enter the length of the Radius proposed upon the Tangent of 45d and to the other foot of the Compasses lay the Thread according to the nearest distance , then if the respective nearest distances from each degree of the Tangents to the Thread be taken out they shal be Tangents to the assigned Radius : Because the Tangents run but to 63d 26′ whereas there may be occasion in some declining Dyalls to use them to 75d though seldom further ; to supply this defect , they may be supposed to break off at 60 and be supplied in a Line by themselves not issuing from the Center , or only pricks or full-points made at each quarter of an hour , for the 5th hour , that is , from 60d to 75d , and so these distances prickt again from the Center as here is done , either one way or other , the Proportion will hold , As the common Radius of the Tangents , Is to any other Assigned Radius : So is the difference of any two Tangents to the common Radius . To their Proportional difference in that Assigned Radius , And so having Proportioned out the first four hours , the 5th hour may be likewise Proportioned out and pricked forward in one continued streight Line from the end of the 4th hour . To work Proportions in Sines and Tangents by help of the Limb and Line of Tangents issuing from the Center . THough this work may be better done on the backside where the Tangents lye in the Limb , and the Sines issue from the Center , and where also there is a Secant meet for the varying of some Proportions that may excur , yet they may be also performed here supposing the Radius introduced into any Proportion wherein it is not ingredient , the two middle Tearms not being of the same kind as both Tangents or both Sines . To find the 4th Proportional if it be a Sine . Lay the Thread to the Sine in the Limb being one of the middle Tearms , and from the Tangent being the other middle Tearm take the nearest distance to it , then entring this extent upon the first Tearm being a Tangent lay the Thread to the other foot , and in the equal Limb it shews the Sine sought . So if the Example were , As the Tangent of 50d , To the Sine of 40d : So is the Tangent of 36d , To a Sine , the 4th Proportion would be found to be the Sine of 23d , 4′ . If a Tangent be sought . Lay the Thread to the Sine in the Limb being one of the middle Tearms , and from the Tangent being the other middle Tearm , take the nearest distance to it , then lay the Thread to the first Tearm in the Limb , and the former extent entred between the Scale and the Thread finds the Tangent , being the 4th Proportional sought . If the Example were , As the Sine of 40d , To the Tangent of 50d : So is the Sine of 23d 4′ To a fourth a Tangent , it would be found to be the Tangent of 36. These Directions presuppose the varying of the Proportion , as to the two Tangents , when either of them will excur the length of the Scale , of which more when I come to treat of the joint use of the Sines and Tangents on the backside . If both the middle Tearms be Sines , the 1st Operation will be wholly on the Line of Sines on the backside , by introducing the Radius , and the second upon the Line of Tangents on the foreside , likewise , if both the middle Tearms were Tangents , the first Operation would be on the Line of Tangents on the foreside , and the second on the Line of Sines on the backside ; but this is likewise pretermitted for the present , for such Cases will seldom be reducible to practise . To work Proportions in equal Parts and Tangents . Because the Lines to perform this work do both issue from the Center , the Radius need not be introduced in this Case ; but here it must be known whether the first or second Tearm of the Proportion taken out of its proper Scale be the longer of the two , and accordingly the work to be performed on the Scale of the longer Tearm , which shall be illustrated only by a few Examples , the ground of what can be said being already laid down . Example . To find the Suns Altitude , the length of the Gnomon or Perpendicular being assigned , and the length of its Shadow measured . As the length of the Shadow . Is to the Radius : So is the length of the Gnomon , To the Tangent of the Suns Altitude . Example . If the length of the Shaddow were 8 foot , and the length of the Gnomon but 5 foot , because 8 of the greater divisions of the equal parts are longer then the Tangent of 45d take the said Tangent or Radius , and enter it at 8 , laying the Thread to the other foot , then the nearest distance from 5 of the equal parts to the Thread measured on the Tangents sheweth 32d for the Suns Altitude sought . So the distance from a Tower and its Altitude being observed the Proportion , to get the height of the Tower is , As the Radius , To the measured distance : So the Tangent of the Altitude . To the height of the Tower. So in the Example in Page 38 , the measured distance K B was 100 yards , and the Altitude 43d 50′ to find the height of the Tower take the Tangent of 45 d , and enter it on 10 at the end of the equal Scale , laying the Thread to the other foot , then take the Tangent of 43 d 50′ , and enter it between the Scale and the Thread , and the Compasses will rest at 96 the height of the Tower in yards , sometimes each grand division of the equal Scale must represent but one sometimes 10 , and sometimes 100 , as in Case L B , and the Altitude thereto were given to find the height assigned . Another Example . As the Tangent of 60d , Is to 50 : So is the Tangent of 40d , To 24 ‑ 2 as before . Take 50 equal parts , and enter it upon the Tangent of 60 d laying the Thread to the other foot , then the nearest distance from the Tangent of 40 d to the Thread measured on the equal parts from the Center will be 24 ‑ 2 as before . Otherwise . Enter the Tangent of 40 d upon the Tangent of 60 d laying the Thread to the other foot , then enter 50 equal parts down the Line of Tangents from the Center , and the nearest distance from the termination to the Thread measured in the equal parts will be 24 ‑ 2 as before . If both the Tangents in any Proportion be too long , they may be changed into their Complements if one of them may and the other may not be so changed without excursion , then the Proportion may be wrought by the Pen , taking the Tangents out of the Quadrat and Shaddows , or it may be made two Proportions by introducing the Radius as before shewed ; it will not be needful to speak more to this , only one Example for obtaining the Altitude of a Tower at two Stations . As the difference of the Cotangents of the Arks cut at either Stations : Is to Radius : So the distance between those Stations : To the Altitude of the Tower. In the Diagram for this Case the Complements of the angles observed at the two Stations , viz. at G were 20 d , at H 41 d 31′ . Take the distance on the Line of Tangents between these two Arks , and because equal parts are sought , and the said Extent less then 50 , the measured distance changing the second Tearm of the Proportion into the place of the third , Enter the said Extent upon 50 in the equal parts , laying the Thread to the other foot , then if the Tangent of 45 d be entred between the Scale and the Thread , the Compasses will rest upon 96 for the Altitude sought . To work Proportions in equal Parts and Sines by help of the Limb. TO suppose both the middle Tearms to be either equal Parts or Sines , will not be practical , yet may be performed as before hinted , without introducing the Radius , if it be not ingredient , because both these Lines issue from the Center , and may also be performed by the Pen by measuring the Sines one the Line of equal parts , as was instanced in page 41. But supposing the middle Tearms of a different kind . 1. If a Sine be sought , Operate by introducing the Radius . Lay the Thread to the Sine in the Limb being one of the middle Tearms , and from the other middle Tearm being equal parts , take the nearest distance to it , one foot of this extent enter at the first Tearm , and the Thread laid to the other foot cuts the Limb at the Ark sought . If the Ark sought be above 70 d this work may better be performed with the Line of equal parts and Sines jointly , as issuing from the Center . 2. If a Number be sought ▪ Lay the Thread to the Sine in the Limb being one of the middle Tearms , and from the other middle Tearm being equal parts take the nearest distance to it , Then lay the Thread to the first Tearm in the Limb being a sine , and enter the former extent between the Scale and the Thread , and the foot of the Compasses will on the Line of equal parts shew the fourth Proportional . The Proportion for finding the Altitude of a Tower at one Station by the measured distance , may also be wrought in in equal parts and Sines . For , As the Cosine of the Ark at first Station , To the measured distance thereof from the Tower : So is the Sine of the said Ark , To the Altitude of the Tower. In that former Scheme , the measured distance B H is 85 , and the angle observed at H 48 d 29′ Wherefore I lay the Thread to the Sine of the said Ark in the Limb , counted from the right edge , and from the measured distance in the equal parts take the nearest extent to the Thread , then laying the Thread to the Cosine of the said Ark in the Limb , and entring the former extent between the Thread and the Scale , I shall find the foot of the Compasses to fall upon 96 the Altitude sought . So also in the Triangle A C B , if there were given the side A C 194 , the measured distance between two Stations on the Wall of a Town besieged , and the observed angles at A 25 d 22′ , at C 113 d 22′ , if B were a Battery we might by this work find the distance of it from either A or C , for having two angles given all the three are given , it therefore holds , As the Sine of the angle ot B 41d 16′ , To its opposite side A C 194 , So the Sine of the angle at C 66d , 38′ the Complement , To its Opposite side B A 270 , the distance of the Battery from A Such Proportions as have the Radius in them will be more easily wrought , we shall give some few Examples in Use in Navigation . 1. To find how many Miles or Leagues in each Parralel of Latitude answer to one degree of Longitude . As the Radius , To the Cosine of the Latitude . So the number of Miles in a degree in the Equinoctial , To the Number of Miles in the Parralel . So in 51 d 32′ of Latitude if 60 Miles answer to a degree in the Equinoctial 37 ‑ 3 Miles shall answer to one degree in this Parralel . This is wrought by laying the Thread to 51 d 32′ in the Limb from the left edge towards the right , then take the nearest distance to it from 60 in the equal parts which measured from the Center will be found to reach to 37 ‑ 3 as before . The reason of this facil Operation is because the nearest distance from the end of the Line of equal parts to the Thread is equal to the Cosine of the Latitude , the Scale it self being equal to the Radius , and therefore needs not be taken out of a Scale of Sines and entred upon the first Tearm the Radius as in other Proportions in Sines of of the greater to the less , when wrought upon a single Line only issuing from the Center , where the second Tearm must be taken out of a Scale , and entred upon the first Tearm . 2. The Course and Distance given to find the difference of Latitude in Leagues or Miles . As the Radius , To the Cosine of the Rumb from the Meridian : So the Distance sailed , To the difference of Latitude in like parts . Example . A Ship sailed S W by W , that is on a Rumb 56 d 15′ from the Meridian 60 Miles , the difference of Latitude in Miles will be found to be 33 ‑ 3 the Operation being all one with the former , Lay the Thread to the Rumb in the Limb , and from 60 take the nearest distance to it , which measured in the Scale of equal parts will be found as before , 3. The Course and Distance given to find the Departure from the Meridian , alias the Variation . As the Radius , To the Sine of the Rumb from the Meridian : So the distance Sailed , To the Departure from the Meridian . In the former Example to find the Departure from the Meridian , Lay the Thread to the Rumb counted from the right edge towards the left , that is to 56d 15′ so counted , and from 60 in the equal parts being the Miles Sailed , take the nearest distance to it ; this extent measured in the said Scale will be found to be 49 ‑ 9 Miles , and so if the converse of this were to be wrought , it is evident that the Miles of Departure must be taken out of the Scale of equal parts and entred Parralelly between the Scale and the Thread lying over the Rumb . Many more Examples and Propositions might be illustrated , but these are sufficient , those that would use a Quadrant for this purpose may have the Rumbs traced out or prickt upon the Limb : Now we repair to the backside of the Quadrant . Of the Line of on the right Edge of the Backside . THe Uses of this Line are manifold in Dyalling in drawing Projections in working Proportions , &c. 1. To take of a Proportional Sine to any lesser Radius then the side of the Quadrant , or which is all one , to divide any Line shorter in length then the whole Line of Sines in such manner as the same is divided . Enter the length of the Line proposed at 90 d the end of the Scale of Sines , and to the other foot lay the Thread according to nearest Distance , or measure the length of the Line proposed on the Line of Sines from the Center , and observe to what Sine it is equal , then lay the Thread over the like Arch in the Limb , and the nearest distances to it from each degree of the Line of Sines shall be the Proportional parts sought . And if the Thread be laid over 30 d of the Limbe the nearest distances to it will be Sines to half the Common Radius . 2. From a Line of Sines to take off a Tangent , the Proportion to do it is , As the Cosine of an Arch , To the Radius of the Line proposed : So the Sine of the said Arch , To the Tangent of the said Arch. Enter the Radius of the Tangent proposed at the Cosine of the given Arch , and to the other foot lay the Thread then from the Sine of that Arch take the nearest distance to the Thread , this extent is the length of the Tangent sought ; thus to get the Tangent of 20 d enter the Radius proposed at the Sine of 70 d , then take the nearest distance to the Thread from the Sine of 20 d , this extent is the Tangent of the said Arch in reference to the limited Radius . Otherways by the Limb. Lay the Thread to the Sine of that Arch counted from the right edge whereto you would take out a Tangent , and enter the Radius proposed down the Line of Sines from the Center and take the nearest distance to the Thread then lay the Thread to the like Arch from the left edge , and enter the extent between the Scale and the Thread , the distance of the Foot of the Compasses from the Center shall be the length of the Tangent required . 3. From the Sines to take off a Secant . The Proportion to do it is , At the Cosine of the Arch proposed , To Radius of the Line proposed So the Sine of 90d , the common Radius , To the length of the Secant of that Arch , to the limitted Radius . By the Limb , Lay the Thread to that Arch in the Limb counted from left edge whereto you would take out a Secant , then enter the Limitted Radius between the Scale and the Thread and the distance of the foot of the Compasses from the Center shall be the length of the Secant sought , and the Converse if a Secant and its Radius be given to find the Ark thereto enter the Secant of 90 d then enter the Radius of it between the Thread and the Sines , and the Compasses shews the Ark thereto , if counted from 90 d towards the Center . Otherways . Enter the Radius of the Line you would devide into Secants at the Cosine of that Arch whereto you would take out a Secant , and to the other foot lay the Thread then the nearest distance to the Thread from the Sine of 90 d is the length of the Secant sought : Thus to get the Secant of 20 d enter the Radius limited in the Sine of 70 d then the nearest distance from 90 d to the Thread , is the length of the Secant sought . And here it may be noted , that if you would have the whole length of the Line of Sines to represent the Secant sought , then the Cosine of that Arch which it represents shall be the Radius to it ; so the whole Line of Sines representing a Secant of 70 d , the length of the Sine of 20 d shall be the Radius thereto . It may also be observed , that no Tangent or Secant can be taken of at once larger then the Radius of the Quadrant , nor no Radius entred longer then that is , and that if the Radius entred be in Length ½ ⅓ ¼ of the Sines Tangents to 63 h 26′ 71 34 75 58 Secants to 60d●′ 70 32 75 32 may be taken off by help of the Line of Sines . And here it may be observed , That if the Tangent and Secant of any Arch be added in one streight Line or otherwise in Numbers , the Amount shall be equal to the Tangent of such Ark as shall bisect the remaining part of the Quadrant , as is demonstrated in Pitiscus & Sn●llius . Whence it follows , That if we have a Tangent and Secant no further then to 60 d each , yet a Tangent by the joint use of both Lines may from them be prickt down to 75 d : Wherefore at anty time to lengthen the Tangents double the Arch proposed , and out of the Amount reject 90 d ; The Tangent and Secant of the remainder connected in one streight Sine shall be the Tangent of the Arch sought . Thus to get the Tangent of 70 d the double is 140 d whence 90 d rejected rests 50 d ; the Tangent and Secant of 50 d joined in one streight Line shall be the Tangent of such an Arch as bisects the remaining part of the Quadrant , namely of 70 d. It may also be observed , That the Tangent of an Ark , and the Tangent of half its Complement is equal to the Secant of that Arch as is obvious in drawing of any Projection . A Chord may also be taken off from the Line of Sines , but more facilly by the Line of Chords on the left edge of the Quadrant , and is therefore pretermitted . To work Proportions in Sines alone . Frst , Without the help of the Limb or lesser Sines without introducing the Radius , but upon this Line alone independently . There will be two Cases , 1. If the first Tearm be greater then the second , the entrance is lateral ; Enter the second Tearm upon the first , laying the Thread to the other foot . Then from the third Tearm in the Scale take the nearest distance to the Thread , and measure that Extent from the Center , and it shews the Tearm sought , and so if it were , As Sine 30d , To Sine 10d : So Sine 80d , the fourth Proportional would be found to be 20d. In giving Examples to illustrate the matter , I shall make use of that noted Canon for making the Tables , As the Semiradius , or Sine of 30d , To the Sine of any Arch : So the Cosine of that Arch , To the Sine of that Arch doubled . But when the first Tearm is less then the second , Enter the length of the first Tearm upon the second , laying the Thread to the other foot of that Extent , then enter the third Tearm Parralelly between the Scale and the Thread , and it shews the fourth Proportional sought . So if it were , As the Sine of 10d , To the Sine of 30d : So the Sine of 20d , To a fourth , the 4th Proportional would be found to be 80 d. Another general way will be to do it by help of the Limb , by introducing the Radius in such Proportions wherein it is not Lay the Thread to one of the middle Tearms in the Limbe , and from the other middle Tearm on the Line of Sines take the nearest distance to it , then enter one foot of that extent at the first Tearm on the Line of Sines , and lay the Thread to the other foot , and in the Limbe it shews the 4th Proportional sought . Example . If the three Proportionals were , As Sine 55 d , To Sine 70 d : So Sine 30 d , To a fourth , the fourth Proportional would be found to be 35 d. But if the first Tearm of the Proportion be either a small Ark or the answer above 70 d , the latter part of this general direction for more certainty may be turned into a Parralel entrance , that is to say instead of entring the Extent taken from one of the middle Tearms in the Sines to the Thread laid over the other middle Tearm in the Limb , and entring it at the first Tearm in the Sines finding the Answer in the Limb lay , the Thread to the first Tearm in the Limb , and find the Answer in the Line of Sines by , entring the former extent parralelly between the Scale and the Thread . What hath been spoken concerning the Limb may also be performed by the Line of lesser Sines in the Limb by the same Directions . So if it were , As the Sine of 5d , To Sine 30d : So the Sine of 10d To a fourth , the 4th Proportional would be found to be the Sine of 85d , and the Operation best performed by the joint use of the Line of Sines , and the lesser Sines by making the latter entrance a Parralel entrance . When the Radius is in the third place of a Proportion in Sines of a greater to a less ▪ the Operation is but half so much as when it is not ingredient . Example . As the Cosine of the Latitude , To the Sine of the Declination , So the Radius , To the Sine of the Suns Amplitude . If the Suns declination were 13d , to find his Amplitude in our Latitude for London , take the Sine of 13d and enter one foot of it on the Sine of 38d 28′ and to the other foot lay the Thread , and in the Limb it shews the Amplitude sought to be 21d 12′ . By changing the places of the two middle Tearms , this Example will be turned into a Parralel entrance . Lay the Thread to the Complement of the Latitude in the Limb , and enter the Sine of the Declination between it and the Scale , and you will find the same Ark in the Sines for the Amplitude sought , as was before found in the Limb. Such Proportions of the greater to the less wherein the Radius is not ingredient , that have two fixed or constant Tearms , may be most readily performed by the single Line of Sines without the help of the Limb. An Example for finding the Suns Amplitude . As the Cosine of the Latitude , To the Sine of the Suns greatest declination : So the Sine of the Suns distance from the next Equinoctial Point , To the Sine of the Suns Amplitude . Because the two first Tearms of this Proportion are fixed , the Amplitude answerable to every degree of the Suns place may be found without removing the Thread ; To do it enter the Sine of the Suns greatest Declination 23d 31′ , at the Sine of the Latitudes Complement , and to the other foot lay the Thread , where keep it without alteration , then for every degree of the Suns place counted in the Sines take the nearest distance to the Thread , and measure those extents down the Line of Sines from the Center , and you will find the correspondent Amplitudes . Example . So when the Sun enters ♉ ♍ ♏ ♓ , his Equinoctial distance being 30 d , the Amplitude will be 18 d 41′ , and when he enters ♊ ♌ ♐ ♒ Equinox distance 60 d , the Amplitude will be 33 d 42′ ; and when he enters ♋ ♑ the greatest Amplitude will be 39d 50′ , his distance from the nearest Equinoctial Point being 90 d. But for such Proportions in which there is not two fixed Tearms , the best way to Operate them will be by the joint help of the Limbe and Line of Sines . An Example for finding the Time of the day the Suns Azimuth Declination and Altitude being given . By the Suns Azimuth is meant the angle thereof from the midnight part of the Meridian , the Proportion is As the Cosine of the Declination , To the Sine of the Azimuth : So the Cosine of the Suns Altitude . To the Sine of the hour from the Meridian . Example . So when the Sun hath 18 d 37′ North Declination , if his Azimuth be 69 d from the Meridian , and the Altitude 39 d , the hour will be found to be 49 d 58′ from Noon . So if there were given the Hour , the Declination and Altitude by transposing the Order of the former Proportion , it will hold to find the Azimuth , As the Cosine of the Suns Altitude , To the Sine of the hour from the Meridian : So the Cosine of the Suns Declination , To the Sine of the Azimuth from the Meridian . Commonly in both these Cases the Latitude is also known , and the Affection is to be determined according to Rules formerly given . A Proportion wholly in Secants we have shewed before may be changed wholly into Sines ; but the like mutual conversion of the Sines into Tangents is not yet known , however it may be done in 〈◊〉 of the 16 Cases wherein the Radius is ingredient , for instance , let the Proportion be to find the time of Sun rising . As Radius , To Tangent of Latitude : So the Tangent of the Declination , To the Sine of the hour from 6. Instead of the two first Tearms it may be , As the Cosine of the Latitude , To the Sine of the Latitude , then instead of the Tangent of the Declination say , So is the Sine hereof to a fourth . Again , As the Cosine of the Declination , To that fourth : So Radius , To the Sine of the hour from six : This being derived from the Analemm● by resolving a Triangle , one side whereof is the Arch of a lesser Circle . If a Quadrant want Tangents or Secants in the Limb , but may admit of a Sine from the Center , the Tangent and Secant of the Latitude , &c , may be taken out by what hath been asserted , to half the common Radius , and marked on the Limb , and the Quadrant thereby fitted to perform most of the Propositions of the Sphoere in one Latitude , and how to supply the Defect of a Line of Versed Sines in the Limb shall afterwards be shewne . What hath been spoken concerning a Line of Sines graduated on a Quadrant from the Center , may by help of the equal Limb be performed without it . 1. A Proportional Sine may be taken off to any diminutive Radius . By the Definition of Sines the right Sine of an Arch is a Line falling from the end of that Arch Perpendicularly to the Radius drawn to the other end of the said Arch ; So the Line H K falling Perpendicularly on the Radius F G shall be the Sine of the Arch H G , and by the same Definition the Line G I falling perpendicularly on the Radius F H shall also be the Sine of the said Arch , and whether the Radius be bigger or lesser , this Definition is common , but the Line G I on a Quadrant represents the nearest distance from the Radius to the Thread , therefore a Sine may be taken off from the Limb to any Diminutive Radius , to perform which , Enter the length or Radius proposed down the streight Line that comes from the Center of the Quadrant , and limits the Limb ; observe where the Compasses rests , this I call the fixed Point , because the Compasses must be set down at it , at every taking off , then to take off the Sine of any Arch to that Radius , lay the Thread over the Arch counted in the Limb from the said edge of the Quadrant , and take the nearest distance to it for the length of the Sine sought : But to take out Sines to the Radius of the graduated Limb set down one foot at the Ark in the Limb , and take the nearest distance to the two edge Lines of the Limb , the one shall be the Sine , the other Co-sine of the said Ark. 2. A Proportion in Sines alone may be wrought by help of the Limbe . Take out one of the middle Tearms by the former Prop. and entring it down the right edge from the Center , take the nearest distance to the Thread laid over the other middle Tearm in the Limbe , counted from right edge , then lay the Thread to the first Tearm in the Limb , and enter that extent between the right edge Line and the Thread , the distance of the foot of the Compasses from the Center , is the length of the Sine sought , to be measured in the Limb by entring one foot of that Extent in it : So that the other turned about may but just touch one of the edge or side Lines of the Limb issuing from the Center , or enter that Extent at the concurrence of the Limbe with the said Line , and lay the Thread to the other foot according to the nearest distance , and in the Limbe it shews the Ark sought : Whence may be observed how to prick of an angle by Sines instead of Chords . From this and some other following Propositions I assert the Hour and Azimuth may be found generally by the sole help of the Limb of a Quadrant without Protraction . How from the Lines inscribed in the Limbe to take off a Sine , Tangent , Secant and Versed Sine to any Radius , if less then half the common Radius of the Quadrant . IT hath been asserted , that a Sine may be taken off from the Limb , and by consequence any other Line there put on ; for by being carried thither they are converted into Sines , and put on in the same manner , for by the Definition of Sines , if Lines were carryed Parralel to the right edge of the Quadrant from the equal degrees of the Limb to the left edge they would there constitute a Line of Sines and the Converse . To find the fixed Point enter the Radius proposed twice down the Line of Sines from the Center , or which is all one , Lay the Thread over 30 d of the Limb counted from the right edge towards the left , and enter the limitted Radius between the Thread and the Scale ; so that one foot turned about may just touch the Thread , and the other resting on the Line of Sines , shews the fixed Point , at which if the Compasses be always set down , and the Thread laid over any Ark in the Tangent , Secant or lesser Sines , the nearest distances from the said Point to the Thread shall be the Sine , Tangent , Secant , of the said Ark to the limitted Radius . But for such Lines as are put on to the common Radius , as the Tangent of 45 d , &c. the Radius is to be entred but once down from the Center to find the fixed Point . Of the Line of Secants . This Line singly considered is of small use , but junctim with other Lines of great use for the general finding the Hour and Azimuth : Mr Foster makes use of it in his Posthuma to graduate the Meridian Line of a Mercators Chart , which is done by the perpetual addition of Secants , and the like may be done from this Line lying in the Limb but a better way wil be to do it from a well graduated Meridian Line by doubling or folding the edge of the Chard thereto , and so graduate it by the Pen. Of the Line of Tangents . The joint use of this Line with the Line of Sines is to work Proportions in Sines and Tangents , in any Proportion wrought by help of Lines in the Limb wherein the Radius is not ingredient , the Radius must be introduced according to the general Direction . If the two middle Tearms be Sines there must be one Proportion wrought wholly on the Line of Sines on the Backside , and another on the Line of Tangents on the foreside ; but such Cases are not usual : But if the two middle Tearms be Tangents , the first Operation must be on the line of Tangents on the foreside , and the latter on the line of Sines on this backside , unless the Radius be ingredient . A general Direction to work Proportions when the middle Tearms are of a different Species . If a Sine be sought , Lay the Thread to the Tangent in the Limb being one of the middle Terms , and from the Sine being another of the middle Terms take the nearest distance to it , then lay the Thread to the other Tangent in the Limb , being the first Tearm , and enter the former extent between the Scale and the Thread , and the foot of the Compasses on the Line of Sines will shew the fourth Proportional . Example . If the Proportion were , As the Tangent of 30 d , To the Sine of 25d So is the Tangent of 20 d , To the Sine of 15 d 27′ . Lay the Thread over the Tangent of 20 d in the Limb , and from the Sine of 25 d take the nearest distance to it , then lay the Thread to the Tangent of 30 d , and the former extent so entred that one foot resting on the Sines , the other foot turned about may but just touch the Thread , and the resting foot will shew 15 d 27′ for the Sine sought . 2. If a Tangent be sought . Lay the Thread to the Tangent being one of the middle Tearms , and from the other middle Tearm being a Sine take the nearest distance thereto , then Enter one foot of that extent at the first Tearm being a Sine , and the Thread laid to the other foot shews the fourth Proportional in the Line of Tangents in the Limb. Example . So if the Proportion were , As the Sine of 25 d , To the Tangent of 30 d : So is the Sine of 32 d , To a Tangent , the fourth Proportional would be found to be the Tangent of 35 d 54′ . If the answer fall near the end of the Scale of Tangents , the latter entrance may be made by laying the Thread to the first Tearm in the Limb , and by a Parralel entrance an Ark found on the Line of Sines , then if the Thread be laid over the like Ark in the Limb it will intersect the Tangent sought . These Directions presuppose the varying of the Proportion when the Tangens excur the length of the Scale , according to the Directions in the Trigonometrical part ; but as before suggested , those Directions are insufficient when one of the Tearms or Tangents are less then the Complement of the Scale wanting , and the other greater then the length of the Scale , for two such Arks cannot be changed into their Complements without still incurring the same inconvenience ; in this Case only change the greater Tearm , which may be done by help of the Line of Secants , for , As the Tangent of an Arch , To the Sine of another Arch ; So is the Cosecant of the latter Arch , To the Cotangent of the former . And by Transposing the Order of the Tearms . As a Sine , To a Tangent : So the Cotangent of the latter Arch , To the Cosecant of the former . Example . If the Proportion were , As the Sine of 8d , To the Tangent of 25d So is the Sine of 60d , To the Tangent of 71d : Here we might foreknow by the nature of the Tearms that the Tangent sought would be large or finde by tryal that it cannot be wrought upon the Quadrant : We may therefore vary it thus , As the Tangent of 25d To the Sine of 8d : So the Secant of 30d , To the Tangent of 19d , the Complement of 71d , the Arch sought . Lay the Thread over 8d in the lesser Sines , and set down one foot of the Compasses at the Sine of the same Arch the Thread lyes over in the Limb ; and take the nearest distance to the Thread laid over the Secant of 30 , then lay the Thread to the Tangent of 25d , and enter the former extent between the Thread and the Line of Sines , and the distance of the foot of the Compasses from the Center measured on the Tangents on the foreside sheweth 19d. But a more general Caution in this Case without the help of the Secants , would be by altring the larger Tangent into its Complement by introducing the Radius , and operating the Proportion on the greater Tangent of 45d. If the Proportion were , As the Tangent of 70d , To the Sine of 60d : So the Tangent of 25d , To the Sine of 8d 27′ . By introducing the Radius at two Operations it would be easily wrought , As Radius , To Tangent 25d , So Sine 60d , To a fourth , Again , As the Radius , To the Tangent of 20 d : So that fourth , To the Sine sought . So the former Example wherein a Tangent is sought may be likewise varied . As Radius , To Tangent 25d : So Sine 60d , To a fourth , Again , As that fourth , To the Radius : So is the Sine of 8d , To the Cotangent of the Arch sought , namely to the Tangent of 19d as before . Two Proportions with the Radius in each are as suddenly done as one without the Radius . Operation . Lay the Thread over the Tangent of 25d in the greater Tangents , and from the Sine of 60d take the nearest distance to it , enter that extent at 90 , or the end of the Line of Sines , laying the Thread to the other foot according to the nearest distance , then enter the Sine of 8 parralelly between the Scale and the Thread and the distance of the foot of the Compasses from the Center is the Tangent of the Complement of the Ark sought to be measured in the greater Tangents by setting down one foot at 90d , and the Thread laid to the other , according the nearest-will lye over the Tangent of 19 d. An Example with the Radius ingredient and a Sine sought , Data , Latitude , and Declination , to find the time when the Sun shall be East or West . As the Radius , To the Cotangent of the Latitude : So the Tangent of the Declination , To the Sine of the hour from 6. To be wrought by the help of the lesser Tangents . When the Radius comes first and two Tangents in the middle , change the largest Ark into its Complement to bring it into the first place , and the Radius into the second ; then take out the Tangent of the other middle Ark , either from the foreside from the Scale , or out of the Limb by setting one foot at the Sine of 90 d , and taking the nearest distance to the Thread laid over the Tangent given , then laying the Thread to the Tangent of the first Ark , enter the former extent between the Scale and the Thread , and the foot of the Compasses will shew the Sine sought . Otherways the two middle Tearms being Tangents , as also when the first Tearm and one of the middle Tearms is a Tangent , change the Radius and one of those Tangents into Sines . For , As the Radius , To the Tangent of any Ark : So is the Cosine of the said Ark , To the Sine thereof . And , As the Tangent of any Ark , To Radius : So is the Sine of that Ark , To the Cosine thereof . And so the former Proportion changed will be , As the Sine of the Latitude , To the Cosine of the Latitude : So the Tangent of the Declination , To the Sine of the hour from six , When the Sun shall be East or West . Example . If the Declination were 23d 30′ North , in our Latititude of London 51d 32′ to find the Sine sought , Lay the Thread to the Tangent of the Declination in the Limb , and from the Complement of the Latitude in the Sines take the nearest distance to it , then lay the Thread to the Sine of the Latitude in the lesser Sines and enter the former extent between the Thread and the Scale and the foot of the Compasses sheweth the answer in degrees , if the Thread be laid to the Ark found in the Limb it there sheweth it in Time ; So in this Example the time sought is 20d 14′ , or in Time 1 h 17 h before 6 in the morning or after it in in the Evening . If the Latitude and Declination were given , To find the Suns Azimuth at the Hour of 6. As the Radius , To Cosine of the Latitude : So the Tangent of the Suns Declination , To the Tangent of his Azimuth from the Vertical . In this Case a Tangent being the 4th Tearm sought , the Operation is very facil . Lay the Thread to the Tangent of the Declination in the lesser Tangents , and from the Cosine of the Latitude take the nearest distance to it , and either measure that extent on the Tangents on the foreside , or set one foot of that extent upon the Sine of 90d , and to the other lay the Thread and it will intersect the Tangent sought in the Limb : So in our Latitude when the Sun hath 23d 30′ of declination , his Azimuth at the hour of 6 will be 15 d 9′ from the East or West . Another Example , So if the Suns distance from the nearest Equinoctial Point were 60 d , his right Ascension would be found to be 57 d 48′ . The Proportion to perform this Proposition is , As the Radius , To the Cosine of the Suns greatest Declination : So the Tangent of the Suns distance from the next Equinoctial Point , To the Tangent of the Suns right Ascension , or when the Tangents are large , As the Cosine of the Suns greatest declination , To Radius : So the Cotangent of the Suns distance from the Equinoctial Point . To the Cotangent of his right Ascension . By what hath been said it appears that the working Proportions by the natural Lines is more troublesome then by the Logarithmical , however this trouble wil be shunned in the use of the great Quadrant by help of the Circle on the backside . I now come to shew how the Hour of the Day , and the Azimuth of the Sun may be found universally by the Lines on the Quadrant , which is the principal thing intended . The first Operation for the Hour will be to find what Altitude or Depression the Sun shall have at the hour of 6. The Proportion to find it is , As the Radius , To the Sine of the Latitude : So the sine of the Suns Declination , To the sine of the Altitude sought . Example . So in Latitude 51 d 32′ , the Suns declination being 23 d 31′ , To find his Altitude or Depression at 6 , Lay the Thread to the Sine of the Latitude in the Limb , and from the sine of the Suns Declination take the nearest distance to it , which extent measured from the Center will be found to be 18 d 12′ . This remains fixed for one Day , and therefore must be recorded , or have a mark set to it . Afterwards the Proportion is , As the Cosine of the Declination , To the Secant of the Latitude , Or , As the Cosine of the Latitude , To the Secant of the Declination : So in Summer is the difference , but in Winter the Sum of the sines of the Suns proposed or observed Altitude , and of his Altitude or Depression at 6 , To the Sine of the hour from 6 towards Noon in Winter , as also in Summer when the Altitude is more then the Altitude of 6 , otherways towards Midnight . To Operate this . In Winter to the sine of the Suns Depression at 6 , add the sine of the Altitude proposed , by setting down the extent hereof outward at the end of the former extent ; in Summer take the distance between the sine of the Suns Altitude , and the sine of his Altitude at 6 , and enter either of these extents twice down the Line of sines from the Center , then lay the Thread to the Secant being one of the middle Tearms , and take the nearest distance to it . Lastly , enter one foot of this extent at the first Tearm , being a Sine , and to the other foot lay the Thread , and in the equal Limb it shews the hour from 6 , which is accordingly numbred with hours . But when the Hour is neer Noon , the answer may be found in the Line of Sines with more certainty by laying the Thread to the first Tearm in the Limb , and entring the latter extent Parralelly between the Scale and the Thread . Otherways . Enter the aforesaid sum or difference of sines once down the Line of Sines from the Center , and laying the Thread to the Secant , being one of the middle Tearms , take the nearest distance to it , then lay the Thread to the first Ark in the lesser sines , and enter the former extent between the Thread and the Scale , and the foot on the Compasses on the Line sheweth the Sine of the Hour . Example . If the Altitude were 45d 42′ , take the distance between it and the sine of 18 d 12′ before found enter this extent twice down the Line of sines from the Center , and laying the Thread over the Secant of 51 d 32′ take the nearest to it , then entring one foot of this extent at 66 d 29′ in the Line of Sines the Thread being laid to the other according to nearest distance will lye over 45 d in the Limb shewing the hour to be either 9 in the morning , or 3 in the afternoon , and so it will be found also in the latter Operation by entring the first extent once down the sines , and taking the distance to the Thread lying over the Secant of the Latitude , and then laying the Thread to 66 d 29′ in the 〈◊〉 , and entring that extent between the Scale and the Thread . To find the Suns Azimuth The first Operation will be to get the Suns Altitude in the Vertical Circle , that is , being East ar West . As the sixe of the Latitude , To Radius : So is the Sine of the Declination , To the sine of the Altitud . So in our Latitude of London , when the Sun hath 23d 31′ of declination , his Vertical Altitude in Summer will be found to be 30d 39′ and so much is the Depression when he hath as much South declination . This found either by a Parralel entrance on the Line of Sines by laying the Thread to the sine of the Latitude in the Limb , and entring the sine of the Declination between the Scale and the Thread , or by a Lateral entrance in the Limbe changing the Radius into the third place , and then enter the sine of the Declination on the Sine of the Latitude , laying the Thread to the other foot , and in the Limb it shewes the Altitude sought ; having found this Ark let it be recorded or have a mark set to it , because it remains fixed for one Day , afterwards the Proportion to be wrought is , As the Cosine of the Altitude , To the Tangent of the Latitude : So in Summer is the difference in Winter the sum of the Sines of the Suns Altitude , and of his Vertical Altitude or Depression : To the Sine of the Azimuth from the East or West towards noon Meridian in Winter as also in Summer , when the given Altitude is more then the Vertical Altitude , but if less towards the Midnight Meridian . This Proportion may be wrought divers ways on the Quadrant after the same manner as the former , I shall therefore illustrate it by some Examples . Declination 13d , Latititude 51d 32′ , Vertical Altitude 16d 42′ , Proposed Altitude in Summer — 41d , 53′ . Proposed Altitude in Winter — 12 13 Enter the aforesaid sum or difference of Sines twice down from the Center of the Quadrant , and take the nearest distance to the Thread being laid over the Tangent of the Latitude , this extent set down at the Cosine of the Altitude , and lay the Thread to the other foot and in the Limbe it shews the Azimuth sought . So in this Example the Azimuth will be found to be 40d both in Summer and Winter from East or West towards Noon Meridian . Otherways . Enter the aforesaid sum or difference of sines but down from the Center , and take the nearest distance to the Thread laid over the Tangent of the Latitude , then lay the Thread to the Complement of the Altitude in the lesser sines , and enter the former extent between the Scale and the Thread , and the answer will be given in the Line of Sines , supposing the declination unchanged , if the Altitude were 9d 21′ both for the Winter and the Summer Example , the Azimuth at London would be 9d 22′ from the East or West Northwards in Summer , and 35 d Southwards in Winter . Hitherto we suppose the Latitude not to exceed the length of the Tangents , whether it doth or not this Proportion may be otherways wrought by changing the two first Tearms of it ; Instead of the Co-sine of the Altitude to the Tangent of the Latitude , we may say , As the Cotangent of the Latitude , To the Secant of the Altitude : So when the Sun hath 23 d 31′ of North Declination in our Latitude , and his Altitude 57 d 7′ , take the distance between the sine thereof and the sine of 30 d 39′ the Altitude of East , and enter it once down from the Center , and take the nearest distance to the Thread laid over the Secant of the Altitude , viz. 57 d 7′ , then lay the Thread to 38 d 28′ in the Tangents , and enter the former extent between the Scale and the Thread , and the Compasses on the Line of Sines will rest at 50 d for the Azimuth from East or West Southwards , because the Altitude was more then the Vertical Altitude . Otherways without the Secant in all Cases by help of the greater Tangent of 45d . Enter the aforesaid Sum or difference of the Sines once down from the Center and lay the Thread to the Tangent or Cotangent of the Latitude in the greater Tangents , and take the nearest distance to it . Then for Latitudes under 45d enter the former extent at the Complement of the Altitude in the Line of Sines , and find the answer in the Limb by laying the Thread to the other foot , or if it be more convenient make a Parralel entrance of it , and find the answer in the Sines as before hinted . But for Latitudes above 45 d , first find a fourth by entring the sum or difference of sines between the Scale and the Thread , and then it will hold , As the first Tearm , To that fourth : So Radius , To the Sine of the Azimuth , and may be either a Lateral or Parralel entrance , according as it falls out , and as the Radius is put either in the second or third place , in all these Directions the introducement of the Radius is supposed according to to the general Advertisement . The finding of the Amplitude this way presupposeth the Vertical Altitude known , and then the Proportion derived from the Analemma , not from the 16 Cases is , As the Radius , To the Tangent of the Latitude , So the Sine of the Vertical Altitude , To the Sine of the Amplitude : So also to find the time of Sun rising . As the Cosine of the Declination , To Secant of the Latitude : So the sine of the Suns Altitude at 6 , To the Sine of the hour of rising from six . To find the Suns Azimuth at six of the clock otherways then by the 16 Cases . As the Cosine of the Suns Altitude at 6 , To Tangent of the Latitude , So is the difference of the sines of the Suns Altitude at 6 , and of his Vertical Altitude , To the sine of the Azimuth from the Vertical . To find the time when the Sun shall be due East or West . As Cosine of the Declination , To Secant of the Latitude : So the difference of the Sines of the Suns Altitude at 6 , and of his Vertical Altitude , To the Sine of the hour from 6 , When the Sun shall be due East or West . These Proportions derived from the Analemma , are general both for the Sun and Stars in all Latitudes ; but when the Declination either of Sun or Stars exceed the Latitude of the place , this Proportion for finding the Azimuth cannot be at some times conveniently performed on a Quadrant , but must be supplyed from another Proportion , whereof more hereafter . Of the Hour and Azimuth Scales on the Edges of the Quadrant . These Scales are fitted for the more ready finding the Hour and Azimuth in one Latitude , being only to facilitate the former general Way . The Labour saved hereby is twofold , first the Suns declination is graved against the Suns Altitude of 6 in the Hour scale , and the said Declinations continued at the other end of the said hour Scale to give the quantity of the Suns Depression in Winter equal to his Altitude in Summer ; and secondly they are of a fitted length as was shewed in the Description of the Quadrant , and thereby half the trouble by introducing the Radius shunned . The Vse of the Azimuth Scale . The Altitude and Declination of the Sun given to find his Azimuth . Take the distance between the Suns Altitude in the Scale , and his Declination in Summer time in that Scale that stands adjoyning to the side ; in Winter in that Scale that is continued the other way beyond the beginning , and laying the Thread to the Complement of the Suns Altitude in the lesser sines , which is double numbred , enter this extent between the Scale and the Thread parralelly , and the foot of the Compasses sheweth in the Line of Sines the Azimuth accordingly , Declination 23 d 31′ , Altitude 47 d 27′ , the Azimuth thereto would be 25 d from East or West in Summer , and if the Altitude were 9 d 43′ in Winter the Azimuth thereto would be 30 d either way from the Meridian . And so when the Sun hath no Altitude , lay the Thread over 90 d in the lesser Sines and enter the extent from the beginning of the Azimuth Scale to the Declination , and you will finde the Amplitude which to this Declination will be 39 d 50′ . The Vses of the Hour Scale . To find the Hour of the Day . TAke the distance between the Suns Altitude in the hour Scale , and his Declination proper to the season of the year , then laying the Thread to the Complement of the Suns Declination in the lesser sines enter the former extent between the Scale and the Thread and the foot of the Compasses sheweth the sine of the hour . Example . If the Declination were 13 d North , and the Altitude 37d 13′ take the distance between it in the Scale and 13 d in the prickt Line , then laying the Thread to 77 d in the lesser sine enter that extent between the Scale and the Thread , and the resting foot will shew 45 d for the hour from 6 , that is either 9 in the forenoon , or 3 in the afternoon . The Converse of the former Proposition will be to find the Suns Altitude on all Hours . The Thread lying over the Complement of the Suns Declination in the lesser sines from the sine of the hour , take the nearest distance to it , then set down one foot of that extent in the hour Scale at the Declination , and the other will reach to the Altitude . Example . At London , for these Scales are fitted thereto , I would find the Suns Altitude at the hours of 5 and at 7 in the morning in Summer when the Sun hath 23 d 31′ of Declination . Here laying the Thread to 23 d 31′ the Suns declination from the end of the lesser Sines being double numbred , from the sine of 15 d , taking the nearest distance to it , set down one foot of this extent at 23 d 31′ the declination it reaches downwards to 9 d 30′ , and upwards to 27 d 23′ the Suns Altitude at 5 and 7 a clock in the morning in Summer . Another Example . Let it be required to find the Suns Altitudes at the hours of 10 or 2 when his declination is 23d 31′ both North and South . The Thread lying as before over the lesser sines take the nearest distance to it from 60d in the sines , the said extent set down at 23d 31′ in the prickt Line reaches to 53 d 44′ for the Summer Altitude , and being set down at 23d 31′ on the other or lower continued Line reaches to 10d 28′ for the Winter Altitude . The Hour may be also sound in the Versed sines by help of this fitted hour Scale , Take the distance between the Suns Altitude , admit 36d 42′ , and his Meridian Altitude to that Declination 61 d 59′ , and enter one foot of this extent at the sine of 66 d 29′ , and laying the Thread to the other foot according to nearest distance and it will lye over the hours of 8 in the morning , or 4 in the afternoon in the Versed sines in the Limb , and thereby also may the time of Suns rising be found by taking the distance from 0 to the Meridian Altitude and entring it at the Cosine of the Declination as before and the Converse will find the Suns Altitudes on all hours by taking the distance from the Co-sine of the Declination to the Thread laid over the Versed sine of the hour from Noon , and the said Extent will reach from the Mridian Altitude in the fitted Scale to the Altitude sought . To find the time of Sun rising or setting , Lay the Thread over the Complement of the declination as before , in the lesser sines , and enter the extent between the ☉ Altitude , which is nothing that is from the beginning of the Hour Scale to the Declination between the Scale and the Thread and the foot of the Compasses shews it in the Line of sines , which may be converted into Time by help of the Limb. If these Scales be continued further in length as also the Declinations they will after the same manner find the Stars hour for any Star whatsoever to be converted into common Time , as in the uses of the Projection , as also the Azimuth of any Star that hath less declination then the place hath Latitude , but of this more in the next Quadrant . In Dyalling there will be often use of natural sines , whereas these Scales are continued but to 62 d , if therefore it be desired to take out any sine to the same Radius , the rest of the Scale wanting may be easily supplyed , for the difference of the sines of any two Arks equidistant from 60 d is equal to the sine of their distance . Thus the sine of 20 d is equal to the difference of the sines of 40 d and 80 d Arks of like distance from 60 d on each side , and so may be added either to 40 d forward , or the other way from the end of the Scale . In finding the Hour and Azimuth by these Scales , not in the Versed sines , the Directions altogether prescribe a Parralel entrance , but if the Extent from the Altitude to the Declination be entred at the Cosine of the Altitude or of the Declination in the Line of sines according as the Case is , and the Thread laid to the other foot , the Hour and Azimuth may be found in the lesser sines by a Lateral entrance . Or if the said Extent be doubled and entred as before hinted , the answer will be found in the equal Limb. Example to find the Suns Azimuth . Declination 23 d 31′ North. Altitude — 41 : 34 Having taken the distance between these two Tearms in the Azimuth Scale and doubled it , enter one foot in the Line of sines at 48 d 26′ , the Complement of the Altitude , and laying the Thread to the other according to nearest distance it will lye over 15 d of the equal Limb for the Suns Azimuth from the East or West Southwards . The Vse of the Versed Sin 's in the Limbe . It may be noted in the former general Proportion , I have used the word Azimuth from Noon or Midnight Meridian , though not so proper , because they are more universal and common to both Hemispheres , other expressions besides their Verbosity would be full of Caution for the following Proportion in our Northern Hemispere , without the Tropick that finds it from the South between the Tropick of Cancer and the Equinoctial , when the Sun comes to the Meridian between the Zenith and the Elevated Pole would find it from the North , wherefore it is fit to be retained . A general Proportion for finding the Hour . As the Cosine of the Declination , To the Secant of the Latitude : Or , As the Cosine of the Latitude , To the Secant of the Declination : So is the difference of the Sines of the Suns Altitude proposed , and of his Meridian Altitude , To the Versed Sine of the hour from Noon● And So is the sum of the sines of the Suns proposed Altitude , and of his Midnight Depression , To the Versed sine of the hour from Midnight : And So is the sine of the Suns Meridian Altitude , To the Versed sine of the Semidiurnal Ark : And So is the sine of the Suns Midnight Depression , To the Versed sine of the Seminocturnal Ark. The Operation will be like the former , I shall therefore onely illustrate it by one Example , the Meridian Altitude is got in Winter by differencing , in Summer by adding the Declination to the Complement of the Latitude , if the sum exceed 90 d the Complement thereof to 180 d is the Meridian Altitude . An Example for finding the Hour from Noon . Declination — 23d 31′ North the 11th June . Comp. Latitude — 38 28 London .   61 59 Meridian Altitude . Proposed Altitude — 36 42 , take the distance between the sines of these two Arks , and enter it once down the Line of sines from the Center , and take the distance to the Thread laid over the Secant , then enter one foot of that extent at the sine being the first Tearm , and to the other lay the Thread , and in the Versed sines in the Limb it will lye over the Versed Sine of the hour from Noon . In this Example , if the Thread be laid over the Secant of 51d 32′ the extent must be entred at the sine of 66d 29′ 23 31 the extent must be entred at the sine of 38 28 either way the answer will fall upon 60 d of the Versed sine shewing the Hour to be either 8 in the forenoon , or 4 in the afternoon . If the hour fall near noon , then the extent of the Compasses may be Quadrupled and entred as before , and look for the answer in the Versed Sines Quadrupled : Or before the distance be took to the Thread the extent of difference may be entred four times down from the Center . The Converse of this Proposition will be to find the Suns Altitude on all Hours universally . As the Secant of the Latitude , To Cosine Declination , Or , As the Secant of the Declination , To Cosine Latitude : So the Versed sine of the hour from Noon , To the difference of the sines of the Suns Meridian Altitude , and of his Altitude sought , to be substracted from the sine of the Meridian Altitude , and there will remain the sine of the Altitude sought . So in Latitude of London , if the Suns Declination were 13 d 00′ , and the hour from noon 75 d , that is either 7 in the morning , or 5 in the afternoon . Lay the Thread over the Versed sine of the hour from noon , namely , 75 d , and from the sine of 77 d the Complement of the Declination , take the nearest distance to it , then lay the Thread to the Secant of the Latitude , and enter the former extent between the Scale and the Thread , and you will find a sine equal to the difference sought , which sine take between the Compasses and setting down one foot at the sine of 51 d 28′ the Meridian Altitude , the other foot turned towards the Center will fall upon the sine of 19 d 27′ the Altiude sought . A General Proportion for the Azimuth . Get the Remainder or Difference between these two Arks , the Suns Altitude and the Complement of the Latitude by Substracting the less from the greater , and then the Proportion will hold , As the Cosine of the Latitude , Is to the Secant of the Altitude , Or , As the Cosine of the Altitude , To the Secant of the Latitude : So is the sum of the sines of the Suns Declination ▪ and of the aforesaid Remainder , To the Versed Sine of the Azimuth from the Noon Meridian in Summer only when the Suns Altitude is less then the Complement of the Latitude . In all other Cases , So is the difference of the said sines , To the Versed sine of the Azimuth , as before from Noon Meridian . Example . The 11th of June aforesaid , the ☉ having 23 d 31′ of North declination , his Altitude was observed to be 18 d 20′ , which substracted from 38 d 28′ the remainder is 20 d 8′ , take out the sine thereof , and set down one foot at the sine of 23 d 31′ , and set the other forwards towards 90 d , then take the nearest to the Thread laid over the Secant of the Latitude 51 d 32′ , enter one foot of this Extent at the Complement of the Altitude by reckoning the Altitude it self from 90 d towards the Center , and the Thread laid to the other foot cuts the Line of Versed sines at 105 d the Azimuth from the South . The same day when the Altitude was more then the Colatitude , suppose 60 d 11′ the Remainder will be found to be 21 d 43′ , take the distance between the sine thereof and of 23 d 31′ , and because the Extent is but small enter it four times down the Line of sines from the Center , and take the nearest distance to the Thread laid over the Secant of the Latitude , which entred at the Cosine of the Altitude , the Thread laid to the other foot shews 25 d in the Quadrupled Versed Sines for the Azimuth from the South . The Proportion hence derived for the Amplitude . As the Cosine of the Latitude , To Secant of the Declination , &c. as before . So in Summer is the sum in Winter , the difference of the sines of the Suns Declination , and of the Complement of the Latitude , To the Versed Sine of the Amplitude from Noon Meridian . The Proportion for the Azimuth will be better exprest by making the difference to be a difference of Versed sines . How the Versed sines in the Limbe may be spared in Case a Quadrant want them . If a Quadrant can only admit of a Line of sines from the Center , the common Quadrant of Mr Gunters very well may , on the right edge above the Margent for the Numbers of the Azimuths , it may be easily fitted for any or many Latitudes by setting Marks or Pricks to the Tangent and Secant of the Latitudes in the Limbe , which may be taken out by help of the Limb , Line of Sines , or by Protraction , and either of these general Proportions wrought upon it , or those which follow , if it be observed that whensoever the Thread lyes over the Versed sine of any Ark in the Limbe , it also at the same Time lyeth over a Sine equal to half that Versed sine to the common Radius : Now because the sine of 30d doubled is equal to the Radius , let it be observed whether the sine cut by the Thread be greater or less then 30 deg . When it is less let the Line of Sines represent the former half of a Line of Versed Sines , and take the sine of the Ark the Thread lay over , and enter it twice forward from the end of the Scale towards the Center , and you will obtain the Versed sine of the angle sought . When it is more take the distance between the sine of 30 d and the said sine , and letting the Line of sines represent the latter half of a Line of Versed sines , enter the said distance twice from the Center , and you will obtain the Versed sine of the Arch sought , namely , the sine of an Arch , whereto 90 d must be added . Three sides to find an Angle , a general Proportion . As the Sine of one of the Sides including an angle , Is to the Secant of the Complement of the other including side : So is the difference of the Versed Sines of the third side , and of the Ark of difference betwen the two including sides , To the Versed Sine of the Angle sought . And So is the difference of the Versed sines of the third side , and of the sum of the two including sides , To the Versed sine of the sought angles Complement to 180d . To repeat the Converse when two sides and the angle comprehended are given to find the third side were needless . If one of the containing sides be greater then a Quadrant , instead of it in referrence to the two first Tearms of the Proportion , take the Complement thereof to 180d for the reputed side , but in differencing or summing the two containing sides alter it not : And further note , that the same Versed sine is common to an Ark less then a Semicircle , and to its Complement to 360 d. The Operation of this Proportion will be wholly like the former , so that there needs no direction but only how to take out a difference of two Versed sines to the common Radius , seeing this Quadrant of so small a Radius is not capable of such a Line from the Center . And here note that the difference of two Versed sines less then a Quadrant , is equal to the difference of the natural sines of the Complements of those Arks. And the difference of two Versed sines greater then a Quadrant is equal to the difference of the natural sines of the excess of those Arks above 90 d. And by consequence the difference of the Versed sines of two Arks the one less , the other greater then a Quadrant is equal to the sum of the natural sines of the lesser Arks Complement to 90d , and the greater Arks excess above it . And so a difference of Versed sines may be taken out of the Line of natural sines considered as such . Or the Line of sines may be considered sometimes to represent the former half of a Line of Versed Sines as it is numbred with the small figures by its Complements from the end of it to 90d at the Center , and sometimes the latter half of it , and then the graduations of it as Sines must be considered as numbred from 90 d to 180 d at the end of it , and so a difference to be taken out of it by taking the distance between the two Tearms , which if the two Arks fall the one to be greater the other less then 90 d will be a sum of two sines , as before hinted , and in this Case the sine of the greater Arks excess above 90 d to be set down outwards if it may be , at the Versed sine of the lesser Ark , or which is all one , at the sine of that Arks Complement , and the distance from the Exterior foot of the Compasses to the Center will be equal to the difference of the Versed sines of the Arks proposed . To measure a difference of Versed sines to the common Radius . In this Case also the Line of sines must sometimes represent the former , sometimes the latter half of a Line of Versed sines , and then one foot of the difference applyed to one Ark , the other will fall in many Cases upon the Ark sought , each Proportion variously exprest , so that possibly either one or the other will serve in all Cases . But if one of the feet of the Compasses falls beyond the Center of the Quadrant : To find how much it falls beyond it , bring the said foot to the Center , and let the other fall backward on the Line , then will the distance between the said other foot , where it now falleth , and the place where it stood before be equal to the excess of the former foot beyond the Center , which accordingly thence measured helps you to the Arch sought , and its Complement both at once with due regard to the representation of the Line ; this should be well observed , for it will be of use on other Instruments . A difference of Versed sines thus taken out to the Common Radius must be entred but once down from the Center . To take out a Difference of Versed sines to half the common Radius . Count both the Arks proposed on the Versed sines in the Limbe , and find what Arks of the equal Limbe answer thereto , then out of the Line of sines take the distance between the said Arks , and you have the extent required , which being but half so large as it should be is to be entred twice down from the Center . To measure a difference of Versed sines to half the common Radius . The Versed sines are largest at that end numbred with 180d , count the given Ark from thence , and laying the Thread over the equal Limb find what Ark answers thereto , then setting down the Compasses at the like Ark in the Line of sines from the end of it towards the Center mind upon what Ark it falls , the Thread laid to the like Ark in the Limb sheweth on the Versed sines the Ark sought . To save the labour of drawing a Triangle , I shall deliver the Proportion for the Azimuth derived from the general Proportion , As the Cosine of the Latitude , To the Secant of the Altitude , Or , As the Cosine of the Altitude , To the Secant of the Latitude : So is the difference of the Versed sines of the Sun or Stars distance from the Elevated Pole , and of the Ark of difference between the Latitude and Altititude . To the Versed sine of the Azimuth sought ; as it falls in the Sphoere that is from the Midnight Meridian . And So is the difference of the Versed sines of the Polar distance , and of the Ark of difference between a Semicircle and the sum of the Latitude and Altitude , To the Versed Sine of the Azimuth from Noon Meridian . A Canon derived from the Inverse of the general Proportion to finde the Distance of places in the Ark of a great Circle . As the Secant of one of the Latitudes , To the Cosine of the other . So the Versed sine of the difference of Longitude , To the difference of the Versed sines of the Ark of distance sought , and of the Ark of difference between both Latitudes , when in the same Hemisphere , or the Ark of the sum of both Latitudes when in both Hemispheres , which difference added to the Versed sine of the said Ark gives the Versed sine of the Ark of distance sought . And So is the Versed sine of the Complement of the difference of Longtitude to 180 d. To the difference of the Versed sines of the Ark of distance sought , and of an Ark being the sum of the Complements of both Latitudes when in one Hemisphere ; Or the sum of the lesser Latitude encreased by 90d , and of the Complement of the greater Latitude when in different Hemispheres , which difference substracted from the Versed sine of the said Ark , there will remain the Versed sine of the Ark of distance sought . This Proportion is to be wrought after the same manner as we found the Suns Altitudes on all hours universally , and the difference to be measured in the Line of sines as representing the former half of a Line of Versed sines , according to the Directions given for measuring of a difference of Versed sines to the common Radius or Radius of the Quadrant . By altring the two first Tearms of the Proportion above , we may work this Proposition by positive entrance . As the Radius , To the Cosine of one of the Latitudes : So the Cosine of the other Latitude , To a fourth . Again . As the Radius , To the Versed sine , as above expressed in both parts , So is that fourth , To the difference as above expressed . An Example for finding the distance between London and Bantum in the Arch of a great Circle the same that was proposed in Page 96. Bantam Longitude 140d Latitude 5d 40′ South . London Longitude 25 , 50′ Latitude 51 32 North. difference of Longitude 114 : 10 Sum 57 12 Lay the Thread to 5d 40′ in the Limb counted from left edge and from 38d 28′ in the sines the Complement of our Latitude take the nearest distance to it , then lay the Thread to 114d 10′ in the Versed sines and entring the former extent down the Line of sines from the Center take the nearest distance to it , then laying the Thread over 57d 12′ in the Versed sine , it cuts the Limbe at 13d 15′ from the right edge , at the like Ark set down one foot of the former extent in the Line of sines , and the other will reach to the Sine of 41d 42′ , then laying the Thread over the like Ark in the Limb , it will intersect the Versed sines at 109d 18′ the Ark of distance sought to be converted into Leagues or Miles according to the number of Leagues or Miles that answer to a degree in each several Country . Thus when we have two sides with the angle comprehended to find the third side , either to half or the whole common Radius without a Line of natural Versed sines from the Center , or by the Proportions in page 93 , or a third way , which I pretermit to the great Quadrant ; and thus the Reader may perceive this small Quadrant to be many ways both Universall and particular , which are of sudden performance though tedious in expression . Three sides to find an angle . Each of the Proportions in Rectangles and Squares before delivered for the Tables , may as before suggested be reduced to single Tearms , an instance shall be given in that which finds the Square of the sine of half the Angle sought . Add the three sides of the Triangle together , and from the half sum substract each of the sides including the angle sought , then it will hold , As the sine of one of the Comprehending sides , ( rather the greater that the entrance may be Lateral . ) Is to the sine of the difference of the same side from the half sum : So is the sine of the difference of the other comprehending side , To a fourth sine , Again . As the Sine of the other comprehending side , Is to that fourth sine : So is the Radius , To half the Versed sine of the angle sought , And So is the Diameter , To the whole Versed sine . To work this on the Quadrant . Upon the first Tearm in the Line of sines being the greatest containing side , enter the extent of the second , and to the other foot lay the Thread , then from the third Tearm in the sines take the nearest distance to it , Which extent enter at the sine of the first Tearm in the second Proportion , and to the other foot lay the Thread , and it will cut the Versed sine at the angle sought . Having shewed how all Proportions may be performed upon the Quadrant : I now proceed to the rest of the Lines . Of the Line of Chords on the left edge of the Backside . I shall not at present speak any thing as to the use thereof , that is intended to be done in a Treatise of the general Scale ; the principal use of a Line of Chords is to prick off readily the quantity of any Arch of a Circle , to do which take the Chord of 60d , and draw a Circle with that Extent then any Arch being to be prict off it is to be taken out of the Line of Chords , and to be transferred into the Circle swept , this supposeth the Radius not to vary . But to do it to any Radius that is lesser take the Semidiameter of the Circle , and enter it at the Chord of 60d laying the Thread to the other foot , and the nearest distances to the Thread will be Chords to the Semidiameter assigned , and the Converse will measure the Chord of any Arch by a Parralel entrance . A Chord may be taken off though no Line of Chords be graduated . The Bead wheresoever it be set carryed from one edge of the Quadrant to the other , the Thread being extended doth describe the Quadrant of a Circle , if therefore extending the Thread down one edge of the Quadrant you set the Bead to the distance of the Radius ( or Semidiameter of the Circle swept ) from the Center , and at it set down one foot of the Compasses , and lay the Thread kept at a certainty in stretching over the Limb to any Arch , & then open the Compasses to the Distance of the Bead , you shall take out the Chord of the said Arch. A Chord may very conveniently be taken off from any Circle swept Concentrick to the Limbe , and divers such there are upon both sides of this Quadrant ; Sweep a Circle of the like Radius on Paper as that on the Quadrant , and then setting one foot to the Intersection of the Concentrick Circle with the right edge , the Thread being laid over any Arch whatsoever in the Limbe , take the distance to the Intersection of the Thread with the Concentrick Circle , and transform the said Extent into the Circle drawn upon Paper . Of the Versed Sines Augmented . These are to be used with fitted Scales thereto , to stand upon a loose Ruler for the ready and more Exact finding the Hour and Azimuth near Noon , or at other times , and shall be treated of in the use of the Diagonal Scale . Of the Line of Latitudes and Scale of Hours on the spare edges of the foreside . The use of these Scales are for the ready pricking down of any Diall that hath a Center in an Equicrural Triangle from the Substile , as shall be shewed in the Use of the great Quadrant , though the Schems be fitted to small Scales . The Scale of Hours standing on the Edge on the foreside may very well be supplyed from thence to another Radius , as shall in due Time be shewed , though it do not proceed from the Center , and therefore may be spared out of the Limbe on the Backside . The Description of the Diagonal Scale . THe particular Scales handled in Page 181 would find the hour and Azimuth in the equal Limbe without doubling the Extent , if laying the Thread over the Cosine of the Declination in the lesser sines when the hour is sought ; or over the Cosine of the Altitude when the Azimuth is sought , it be minded what Ark of the Limbe the Thread intersects , and then make the entrance of one foot of the Extent at the like Ark in the sines laying the Thread to the other foot according to nearest distance . But because these Scales are more convenient being twice as long , there is accordingly a Diagonal Scale fitted to serve for our English Region , and may be accommodated to any 5 or 6 degrees of Latitude , and placed conveniently on any Instrument for Surveigh to give the hour and Azimuth in the Limbe of the Instrument or on the frame of the plain Table . And here I am to intimate that either the hour or Azimuth Scale before described on the small Quadrant , will serve to finde both the Hour and Azimuth , as conveniently as either ; the foundation whereof is , that the same Proportion demonstrated from the Analemma that finds the hour from six being applyed to other sides of the Triangle will also find the Azimuth from the East or West , an instance whereof I give in the Use of a great Quadrant for finding the Azimuth when the Declination of the Sun or Stars exceeds the Latitude of the place . By the like parity of reason the Proportion that found the Azimuth is a general Proportion to find an angle , when the threee sides are given the Canon will be , As the Cosine of one of the including sides , Is to the Radius : So is the Cosine of the side Opposite to the angle sought , To a fourth a Sine or Secant . Again . As the second including side , Is to the Cotangent of the first including side : So when any one of the sides is greater then a Quadrant is the sum , but when all less the difference between the 4th abovesaid , and the Cosine of the second Includer , To the Cosine of the angle sought . Wee do suppose but one of the three sides given to be greater then a Quadrant , if there be any such it subtends an Obtuse angle , and both the other sides being less then Quadrants subtend Acute Angles . When the 4th Sine is less then the Cosine of the second Includer , the Angle sought is Obtuse , other ways Acute . Hence the peculiar Proportion educed for the hour will be , As the Sine of the Latitude , Is to the Radius : So is the Sine of the Altitude , To a 4th a Sine or Secant . Again . As the Cosine of the Declination , Is to the Tangent of the Latitude , So in Summer is the difference , but in Winter the sum of the sines of the Declination of the Sun or Stars , and of the 4th Sine , To the Sine of the hour from six . When the 4th Ark is less then the Declination the hour is Obtuse , when greater Acute , and in Winter always Acute : But of this Proportion I make no use it being liable in some Cases to Excursion , and will not hold backward to find the Suns Altitudes the hour being assigned . This Diagonal Scale is made after the same manner as the Hour Scale described in the small Quadrant , being but several Lines of sines the greater whereof are made equal to the Secant of the Latitude , whereto they are fitted , the Radius of which Secant is 5 Inches long . The lesser Sines continued the other way , their respective Radii are made equal to the sine of the Latitude of that greater sine whereto they are continued . The parralel Lines fitted to the respective Latitudes are not to be equidistant one from another ; but having determined the distance between the two Extream Latitudes , to which they are fitted for the the larger sine it will hold , As the difference of the Secants of the two extream Latitudes , It to the distance between the Lines fitted thereto : So is the difference of the Secants of the lesser extream Latitude , and any other intermediate Latitude , To the distance thereof from the lesser extream . And so for the lesser sine continued the other way , having placed the two Extreams under the two former Extreams , to place the imtermediate Lines , the Canon would be , As the difference of the sines of the two extream Latitudes , Is to the distance between the Lines fitted thereto : So is the difference of the sines of the lesser extream Latitude , and of any other intermediate Latitude , To the distance thereof from the lesser Extream . Having fitted the distances of the greater sine , streight Lines drawn through the two extream sines shall divide the intermediate Parralels also into Lines of sines , proper to the Latitudes to which they are fitted : Now for the lesser sines they are continued the other way at the ends of the former Parralells , the Line proper to each Latitude should be divided into a Line of sines , whose Radius should be equal to the sine of the Latitude of the other sine whereto it is fitted ; and so Lines traced through each degree to the Extreams ; but by reason of the small distance of these Lines , the difference is so exceeding small , that it may not be scrupled to draw Lines Diagonal wise from each degree of the two outward extream Sines , for being drawn true , they will not be perceived to be any other then streight Lines . Whereas these Lines by reason of the latter Proportion should not fall absolutely to be drawn , at the ends of the former Lines whereto they are fitted , and then they would not be so fit for the purpose , yet the difference being as we said , so insensible that it cannot be scaled , they are notwithstanding there placed and crossed with Diagonals drawn through each degree of the Extreams . The Vses of the Diagonal Scale . 1. To find the time of Sun rising or setting . In the Parralel proper to the Latitude take out the Suns Declination out of the lesser continued sines , and enter one foot of this extent at the Complement of the Declination in the Line of sines , and in the equal Limb the Thread being laid to the other foot will shew the time sought . In the Latitude of York , namely 54d , if the Sun have 20d of Declination Northward he rises at 4 and sets at 8 Southward he rises at 8 and sets at 4 2. To find the Hour of the Day or Night for South Declination . In the Parralel proper to the Latitude account the Declination in the lesser continued sine , and the Altitude in the greater sine , and take their distance , which extent apply as before to the Cosine of the Declination in the Line of sines on the Quadrant , and laying the Thread to the other foot according to nearest distance it shews the time sought in the equal Limbe . Thus in the Latitude of York when the Sun hath 20d of South declination , his Altitude being 5d , the hour from noon will be found 45 minutes past 8 in the morning , or 15 minutes past 3 in the afternoon feré . For North Declination . The Declination must be taken out of the lesser sine in the proper Parralel , and turned upward on the greater sine and there it shews the Altitude at six for the Sun or any Stars in the Northern Hemispere , the distance between which Point and the given Altitude must be entred as before at the Cosine of the declination , laying the thread to the other foot and it shews the hour in the Limb from six towards noon or midnight , according as the Sun or Stars Altitude was greater or lesser then its Altitude at six . So in the Latitude of York , when the Sun hath 20d of North declination if his Altitude be 40d , the hour will be 46 minutes past 8 in the morning , or 14 minutes past 3 in the afternoon . 4. The Converse of the former Proposition will be to find the Altitude of the Sun at any hour of the day , or of any Star at any hour of the night . I need not insist on this , having shewn the manner of it on the small quadrant , only for these Scales use the Limb instead of the lesser sines , for Stars the time of the night must first be turned into the Stars hour , and then the Work the same as for the Sun. 5. To find the Amplitude of ehe Sun or Stars . Take out the Declination out of the greater sine in the Parralel proper to the Latitude , and measure it on the Line of sines on the lesser Quadrant , and it shews the Amplitude sought . So in the Latitude of York 54d when the Sun hath 20d of Declination , his Amplitude will be 35d 35′ . 6. To find the Azimuth for the Sun or any Stars in the Hemisphere . For South Declination . Account the Altitude in the lesser sine continued in the proper Parralel , and the Declination in the greater sine , and take their distance enter one foot of this extent at the Cosine of the Altitude on the Quadrant , and lay the Thread to the other according to nearest distance , and in the Limbe it shews the Azimuth from East or West Southwards . So in the Latitude of York , when the Sun hath 20d of South Declination , his Altitude being 5d , the Azimuth will be found to be 44d 47′ to the Southwards of the East or West . For North Declination . Account the Altitude in the lesser sine continued , and apply it upward on the greater sine and it finds a Point thereon , from whence take the distance to the declination in the said greater sine in the Parralel proper to the Latitude of the place , and enter one foot of this Extent at the Cosine of the Altitude on the Line of sines , and the Thread being laid to the other foot according to nearest distance , shews the Azimuth in the Limbe from East or West . So in the Latitude of York , when the Sun hath 20d of North Declination , and 40d of Altitude , his Azimuth will be 23d 16′ to the Southwards of the East or West . When the Hour or Azimuth falls near Noon , for more certainty you may lay the Thread to the Complement of the Declination for the Hour , or the Complement of the Altitude for the Azimuth , in the Limbe , and enter the respective extents Parralelly between the Thread and the Sines , and find the answer in the sines . We might have fitted one Scale on the quadrant to give both the houre and Azimuth in the Equall Limb by a Lateral entrance , and have enlarged upon many more Propositions , which shall be handled in the great Quadrants . Mr Sutton was willing to add a Backside to this Scale , and therefore hath put on particular Scales of his own for giving the requisites of an upright Decliner in this Latitude , which he hath often made upon Rulers for Carpenters and other Artificers and Diallists , and whereof he was willing to afford them a Print ; whereto I have added other Scales for giving the Hour and Azimuth near Noon . On the Backside are drawn these Lines , A large Dyalling Scale of 6 hours or double Tangents , with a Line of Latitudes fitted thereto . A large Chord . A Line for the Substiles distance from the Meridian . A Line for the Stiles height . A Line for the angle of 12 and 6. A Line for the inclination of Meridians . All these Scales relate to Dyalling . An Azimuth Scale being two Lines of natural sines of the same Radius set together at O , and thence numbred with Declinations , this Scale must be made of the same sine that the hour Scale following is made of continued from O one way to 38d 28′ , and the other way to 23d 31′ or further at pleasure ; but numbred from the beginning which is at the end of that 38d 28′ the Complement of the Latitude with 10d 20′ , &c. up to 60d. The Hour Scale is no other then a Line of sines with the declinations set against the Meridian Altitudes in the Latitude of London , the Radius of which sine is equal in length to the Dyalling Scale of hours . Of the Vses of these Scales . The Line of Hours and Latitudes is general for pricking down all Dialls with Centers as will afterwards be shewed in the Use of the great Quadrant , and by help of the Scale of Hours may the Diameter of a such a Circle be graduated as is placed in on the back of the great Quadrant , and the Line of Latitudes will serve as a Chord to divide the upper Quadrant , and the Hour Scale or Line of Sines will serve as a Chord to divide a Semicircle , whose Diameter is equal to the Scale of Hours into 90 equal parts and their Subdivisions , and hereby may Proportions in sines and Tangents , or Tangents alone be wrought by Protraction , and so the necessary Arks in Dyalling found generally as is done by Mr Foster in the three last Schems of his Posthuma , this will easily be understood if the use of the Circle on this Quadrant be well apprehended . The particular Scales give the requisite Arks of upright Decliners in this Latitude by inspection , for count the plaines Declination in the Line of Chords , and a Square laid over it intersects all those Arks or to be found by applying the Declination taken out of the Chords with Compasses to every other Line . Example . So if an upright Plain decline 35d from the Meridian . The Substiles distance from the Meridian will be — 24d 30′ The Stiles height — 30 38 The Inclinations of Meridians — 41 49′ The angle of 12 and 6 — 54 10 These particular Scales also resolve some of the Cases of right angled Sphoerical Triangles , relating to the Motion of the Sun or Stars thus , Of the Line of the Stiles height . Account the Declination in the Line for the Stiles height , and against it in the Chord stands the Amplitude of the Sun or Stars from the Meridian . Example for Amplitude . So when the Sun hath 18d of Declination , his Amplitude will be 67d 13′ from the Meridian , and 29d 47′ from the Vertical . The reason hereof is because the two first fixed Tearms of the Proportion that Calculate the Stiles height are the Radius and the Co-sine of the Latitude , and the two first Tearms that Calculate the Amplitude are the Cosine of the Latitude and the Radius , and therefore must as well serve in this Case as in that . On this Stile Line may be found the Suns Altitudes on all hours , when he is in the Equinoctial by applying the hour from six taken from the Chords to the other end of the Stile Line . Of the Substiler Line . Hereby we may find the time of Sun rising and setting , take the Declination out of the Substilar Line and measure it on the Line of Chords . Example . So when the Sun hath 18 of North Declination , the Ascensional difference is 24d 9′ in time 1 hour 36½ minutes , and so much the Sun rises and sets from six . Hereby may be also found the Equinoctial Altitudes to every Azimuth . Of the Line for the Angle of 12 and 6. Hereby we may find the time when the Sun will be due East or West . Account the Complement of the Declination in this Scale , and against it in the Chords stands the hour from six . Example . So when the Sun hath 18d of North Declination , he will be East or West at 7 in the morning , or 5 in the afternon . By these Scales the requisites of an East or West Reclining or Inclining Diall in this Latitude may be found . 1. The Substiles distance from the Meridian . Account the Complement of the Reclination Inclination in the Chords , and against it in the Line for 12 and 6 stands the Complement of the angle sought . 2. For the Stiles height . Apply the Reclination in the lesser sines on the Diagonal Scale in the Parralel proper to the Latitude to the greater sine and it shewes the Ark sought . 3. For the Inclination of Meridians . This may be also found on the Diagonal Scale when the Substiles distance is not more then the Latitude , By Accounting the Substiles distance on the greater sine , and applying it to the lesser . 4. For the Angle of 12 and six . Account the Complement of the Reclination in the Chords , and against it in the Substilar Line is the Complement of the angle sought . So if an East or West Plain Recline or Incline 35d. The Substiles distance from the Meridian will be — 45d 52′ The Stiles height — 26 41 The Inclination of Meridians — 66 27 And the angle of 12 and 6 — 56 55 Of the Hour and Azimuth Scales . This Scale is fitted to find the Hour from Noon in the Versed sine : augmented , and the Proportion to be wrought by it the same as delivered in the use of the small Quadrant . As the Cosine of the Declination , Is to the Secant of the Latitude : So is the difference of the sines of the Suns proposed and Meridian Altitude , To the Versed sine of the hour from Noon . And of this one Proportion we make two by introducing the Radius . As the Radius , is to the Secant of the Latitude : So is the former distance , To a fourth . By fitting the Radius of the sines equal in length to the Secant of the Latiude ; this first Proportion is removed for the said difference of sines taken out of this fitted Scale is the 4th Proportional , the Proportion that remains to be wrought upon the Quadrant is , As the Cosine of the Declination , Is to the difference of the sines taken out of this fitted Scale : So is the Radius , To the Versed sine of the hour from Noon . By this means if in the same Proportion as we increase the length of the fitted Scale , we also increase the versed sines lying in the Limb , we may find the hour and Azimuth near noon with certainty if the Altitude be well given : These Scales in their Use presuppose the Hour and Azimuth of the Sun to be nearer the noon Meridian then 60d. Operation to find the Hour . Take the distance between the Altitude and the Declination proper to the season of the year out of the Hour Scale , and enter one foot of this Extent at the Cosine of the Declination in the Line of sines , and laying the Thread to the other foot according to nearest distance , it shews the hour from noon in the Versed sines Quadrupled . Example . When the Sun hath 23d 31′ of North Declination , and 60d of Altitude , the hour from noon will be 13d 58′ to be Converted into time . When the hour is found to be less then 40d from Noon , the former extent may be doubled and entred as before , and it shews the hour in the Versed sines Octupled . And when the hour is less then 30d from Noon , the former extent may be tripled and entred as before , and after this manner it is possible to make the whole Limb give the hour next Noon , the Versed Sine Duodecupled , lies on the other side of the Quadrant ; and in this case , an Ark must first be found in the Limb , and the Thread laid over the said Ark , counted from the other edge , will intersect the said Versed Sine at the Ark sought . To find the Suns Azimuth : TAke the distance in the Azimuth Scale , between the Altitude and the Declination , proper to the season of the year , and entring it at the Cosine of the Altitude , laying the Thread to the other foot , according to nearest distance , it will shew the Azimuth in the Versed Sines quadrupled ; or , when the Azimuth is near Noon , according to the former restrictions for the hour , the extent may be doubled , or tripled , and the answer found in the Versed Sines Octupled , or Duodecupled , as was done for the hour . Example . So when the Sun hath 23d 31′ of North Declination , his Altitude being 60d. The Azimuth will be found to be 26d 21′ from the South . By the like-reason , when we found the Hour and Azimuth in the equal Limb by the Diagonal Scale , if those extents had been doubled , the Hour and Azimuth near six , or the Vertical , might have been found in a line of Sines of 30d , put thorow the whole Limb , but that we thought needless . FINIS . THE DESCRPITION AND VSES Of a Great Universal Quadrant : With a Quarter of Stofters particular Projection upon it , Inverted . Contrived and Written by John Collins Accomptant , and Student in the MATHEMATIqUES . LONDON , Printed in the Year , 1658. The DESCRIPTION Of the Great Quadrant . IT hath been hinted before , that though the former contrivance may serve for a small Quadrant , yet there might be a better for a great one . The Description of the Fore-side . On the right edge from the Center is placed a line of Sines . On the left edge from the Center , a line of Versed Sines to 180d. The Limb , the same as in the small Quadrant . Between the Limb and the Center are placed in Circles , a Line of Versed Sines to 180d , another through the whole Limb to 90d. The Line of lesser Sines and Secants . The line of Tangents . The Quadrat and Shaddows . Above them , the Projection , with the Declinations , Days of the moneth , and Almanack . On the left edge is placed the fitted Hour , and Azimuth Scale . Within the Projection abutting against the Sines , is placed a little Scale , called The Scale of Entrance , being graduated to 62d , and is no other but a small line of Sines numbred by the Complements . At the end of the Secant is put on the Versed Sines doubled , that is , to twice the Radius of the Quadrant , and at the end of the Tangents tripled , to some few degrees , to give the Hour and Azimuth near Noon more exactly . The Description of the Back-side . On the right edge from the Center , is placed a Line of equal part being 10 inches precise , decimally subdivided . On the out-side next the edge , is placed a large Chord to 60● , equal in length to the Radius of the Line of Sines . On the left edge is placed a Line of Tangents issuing from the Center , continued to 63d 26′ , and again continued apart from 60d , to 75d The equal Limb. Within it a Quadrant of Ascensions , divided into 24 equal hours and its parts , with Stars affixed , and Letters graved , to refer to their Names . Between it and the Center is placed a Circle , whereof there is but three Quadrants graduated . The Diameter of this Circle is no other then the Dyalling Scale of 6 hours , or double Tangents divided into 90d. Two Quadrants , or the half of this Circle beneath the Diameter , is divided into 90 equal parts or degrees . The upper divided Quadrant , is called the Quadrant of Latitudes . From the extremity of the said Quadrant , and Perpendicular to the Diameter , is graduated a Line of Proportional Sines ; M Foster call it the Line Sol. Diagonal-wise , from one extremity of the Quadrant of Latitude to the other , is graduated a line of Sines ; that end numbred with ●0 d , that is next the Diameter , being of the same Radius with the Tangents . Opposite and parallel thereto from 45d of the Semicircle , to the other extremity of the Diameter , is placed a Line of Sines equal to the former . Diagonal-wise , from the beginning of the Line Sol , to the end of the Diameter , is graduated a Line of 60 Chords . From the beginning of the Diameter , but below it , towards 45d of the Semicircle , is graduated the Projection Tangent , alias , a Semi-tangent , to 90d , being of the same Radius with the Tangents . The other Quadrant of this Circle being only a void Line , there passeth through it from the Center , a Tangent of 45d , for Dyalling , divided into 3 hours , with its quarters and minutes . Below the Diameter is void space left , to graduate any Table at pleasure , and a Line of Chords may be there placed . Most of these Lines , and the Projection , have been already treated upon in the use of the small Quadrant , those that are added , shall here be spoke to . Of the Line of Versed Sines , on the left Edge , issuing from the Center . THis Line , and the uses of it , were invented by the learned Mathematician , M. Samuel Foster , of Gresham Colledge , deceased , from whom I received the uses of it , applyed to a Sector ; I shall , and have added the Proportions to be wrought upon it , and in that , and other respects , diversifie from what I received ; wherein I shall not be tedious , because there are other ways to follow , since found out by my self . The chief uses of it are , to resolve the two cases of the fourth Axiom of Spherical Trigonometry ; as , when three sides are given to find an Angle , or two sides with the Angle comprehended , to find the third side , which are the cases that find the Hour and Azimuth generally , and the Suns Altitudes on all hours . For the Hour , the learned Author thought meet to add a Zodiaque of the Suns-place annexed to it , both in the use of his Sector , as also in the use of his Scale , published since his death , entituled Posthuma Fosteri , that the Suns place being given , which for Instrumental use might be obtained , by knowing on what day of each moneth the Sun enters into any Signe , and allowing a degree for every days motion , come by it prope verum , and being sought in the annexed Zodiaque ( which is no other then two lines of 90d. Sines , each made equal to the Sine of 23d 31′ the Suns greatest Declination ) just against it stands the Suns Declination , if accounted in the Versed Sine , from 90d each way ; but this for want of room , and because the Declination is more easily given by help of the day of the moneth , I thought fit to omit , the rather , because it may also be taken from the Table of Declinations . But from hence I first observed , that if the two first terms of a Proportion were fixed , if two natural Lines proper to those terms , were fitted of an equal length , and posited together , if any third term be given , to find a fourth in the same proportion , it would be given by inspection , as standing against the third ; but if the Lines stand asunder , or a difference be the third term , application must be made from one Line to the other with Compasses , as in the same Scale there is also fitted a Line of 60 parts , equal in length to the Radius of a small Sine , serving to give the Miles in every several Latitude , answerable to one degree of Longitude . Three sides given to find an Angle , the Proportion , As the difference of the Versed Sines of the Sum , and difference of any two Sides including an Angle , Is to the Diameter , So is the difference of the Versed Sines of the third side , And of the Ark of difference between the two including Sides , To the Versed Sine of the Angle sought ; And so is the difference of the Versed Sines of the third side And of the sum of the two including sides , To the Versed Sine of the sought Angles , Complement to a Semicircle . Corollary . And seeing there is such proportion between the latter terms of the fore-going Proportion , as between the former , omitting the two first terms , it also holds , As the difference of the Versed Sines of the third side , and of the Ark of difference between the two including sides Is to the Versed Sine of the Angle sought , So is the difference of the Versed Sines of the third side , And of the sum of the two including sides , To the Versed Sine of the sought Angles , Complement to 180d. And this is the Proportion M. Foster makes use of in his Scale , page 25 and 27. to find the Hour and Azimuth by Protraction , as also in page 68. in Dyalling , when three sides are given to find an Angle , by constituting two right angled equi-angled plain Triangles , the legs whereof consist of the 4 terms of this Proportion . But in that Protraction work , the first and third terms of the Proportion are given together , with the sum of the second and fourth terms , to find out the said terms respectively . The Proportion for the Hour . As the difference of the Versed Sines of the Sum , and difference of the Complement of the Latitude , and of the Sun or Stars distance from the Elevated Pole , Is to the Diameter or Versed Sine of 180d , So is the difference of the Versed Sines of the Complement of the Altitude , and of the Ark of difference between the Complement of the Latitude , and of the Polar distance , To the Versed Sine of the Hour from Noon . And if the latter clause of the third term be the Sum of the Co-latitude and Polar distance , the Proportion will find the Versed Sine of the hour from midnight , And if the sum of any two Arks exceed a Semicircle , take its Complement to 360d , for the same Versed Sine is common to both . When the Declination is towards the Elevated Pole , the Polar distance is the Complement of it to 90d ; and when towards the Depressed Pole , the Polar distance is equal to the Sum of 90d , and of the Declination added together . Example . Let the Suns Declination be 15d 46′ North , Complement , — 74d 14′ The Complement of the Latitude , — 38 28 Sum — 112 : 42 Difference — 35 : 46 And let the Altitude be 20d , Complement — 70 : 00 Operation . Take the distance between the Versed Sines of 35d 46′ , and of 112d 42′ , and entring one foot of that extent at the end of the Versed Scale at 180d , lay the thred to the other foot , according to nearest distance , then take the distance between the Versed Sines of 35d 46′ , and 70d , and entring that extent parallelly , between the Thred and the Scale , and the other foot will rest upon the Versed Sine of 77d 32′ , the quantity of the Hour from the Meridian being either 50′ past 6 in the morning , or 10′ past 5 in the afternoon . The Reader may observe in this work , that the thred lies over a Star , by entring the first extent ; as also , that there is the same Star graduated at 35d 46′ of the Versed Sine , and this no other then the Bulls eye , having 15d 46′ of North Declination , for which Star in this Latitude , there needs be no summing or differencing of Arks , in regard the Stars declination varies not : So to find that Stars hour at any time , having any other Altitude , only lay the thred over that Star in the Quadrant , and take the distance between the Star in the Scale , and the Complement of its Altitude , and enter that extent parallelly between the Thred and the Scale , and it finds the Stars hour from the Meridian : Thus when that Star hath 39d of Altitude , its hour from the Meridian will be found to be 45d 54′ , in time , 3 hours 3½′ , which to get the true time of the night , must be turned into the Suns hour by help of the Nocturnal on the Back-side : But admitting the Suns Declination and Altitude to have been the same with the Stars , the true time of the day thus found , would have been 56½′ past 9 in the morning , or 3½′ past 3 in the afternoon ; and thus the Reader may have what Stars he pleases put on of any Declination , and for any Latitude ; and they may be put on at such a distance from the Center , that the distance from it to the Star , may be a Chord to be measured in the Limb , to give the Stars Ascensional difference , or the like conclusion : And thus the thred being once laid , and the former point found for one example to the Suns Declination , neither of them varies that day ; which is a ready general way for finding the time of the day for the Sun. To find the Semidiurnal , and Seminocturnal Arks. SUppose the Sun to have no Altitude , and the Complement of it to be 90d , and then work by the former precept , and you will find the Semidiurnal Ark from the beginning of the Line , and the Seminocturnal Ark from the end of the Line , which doubled , and turned into time , shews the length of the Day and Night , and the difference between 90d , and either of those Arks is the Ascensional difference , or time of rising and setting from 6. To find the Azimuth generally . The Proportions for this purpose have been delivered before , from which it may be observed , that there are no two terms fixed , and therefore to every Altitude , the containing sides of the Triangle , namely , the Complements both of the Altitude and Latitude must be summed and differenced , when the Proposition is to be performed on this Line solely , and the Operation will be after the same manner , as for the hour , namely , with a Parallel entrance : and this is all I shall say of the Authors general way ; and of any other that he used , I never heard of ; those ways that follow , being of my own supply . By help of this Line to work a Proportion in Sines alone , wherein the Radius leads . As the Radius Is to the Sine of any Ark , So is the Sine of any other Ark To the Sine of a fourth Ark. This fourth Sine , as I have said before , is demonstrated by M. Gellibrand , to be equal to half the difference of the Versed Sines of the Sum , and difference of the two middle terms of the Proportion . Operation . Let the Proportion be , As the Radius Is to the Sine of — 40d So is the Sine of — 27 To a fourth Sine Sum — 67 Difference — 13 Take the distance between the Versed Sines of the said sum and difference , and measure it on the Line of Sines from the Center , and it will reach to 17d , the fourth Sine sought . By help of this Line may the Divisions of the line Sol , or Proportional Sines , be graduated to any Radius less then half the Radius of the Quadrant , the Canon is , As the Versed Sine of any Ark added to a Quadrant , Is to the Radius , or length of the Line Sol , So is the Versed Sine of that Arks Complement to 90d To that length which pricked backward from the end of the Radius of the said Line , shall graduate the Arch proposed . Example . Suppose you would graduate 20 of the Line Sol , enter the Radius of the said Line upon the Versed Sine of 110d , laying the thred to the other foot ; and from the Versed Sine of 70d , take the nearest distance to the thred , which prick from the end of the Line Sol , towards the beginning , and it shall graduate the said 20d. This Line Sol is made use of by M. Foster in his Scale for Dyalling . The Line of Versed Sines was placed on the left edge of the foreside of the Quadrant , for the ready taking out the difference of the Versed Sines of any two Arks , and to measure a difference of two Versed Sines upon it , which are the chief uses I shall make of it ; whereas to Operate singly upon it , it would be more convenient for the hand to have it lie on the right edge of the Quadrant . An example for finding the Azimuth generally , by help of Versed Sines in the Limb , and of other Lines on the Quadrant . I shall rehearse the Proportion , As the Cosine of the Latitude is to the Secant of the Altitude , Or , As the Cosine of the Altitude is to the Secant of the Latitude , So is the difference of the Versed Sines of the Suns distance from the Elevated Pole , and of the Ark of difference between the Latititude and Altitude , To the Versed Sine of the Azimuth from the midnight meridian . And making the latter clause of the third term the Complement of the Sum of the Latitude and Altitude to a Semicircle , the Proportion will find the versed Sine of the Azimuth from the noon Meridian . Example . Altitude , — 51d 32′ Latitude — 34 : 32 Complement 55d 2● Difference 17 : 00 ☉ distance from elevated Pole , 66 : 29 Operation in the first Terms of the Proportion . On the Line of Versed Sines , take the distance between 17d , and 66d 29′ , and entring it twice down the line of Sines , from the Center , take the nearest distance to the thread laid over the Secant of 51d 32′ , the given Altitude , and entring one foot of this Extent at the Sine of 55d 28′ the Complement of the Latitude , lay the thred to the other foot , according to nearest distance , and in the line of Versed Sines in the Limb , it will lie over 95d , for the Suns Azimuth from the midnight meridian . And the Suns declination supposed the same , he shall have the like Azimuth from the North , in our Latitude of London , when his Altitude is 34d 32′ , for the sides of the Triangle are the same . Another Example . To find it in the versed Sine of 90d Latitude — 47d 27′ Altitude — 51 : 32 Sum — 98 : 59 Complement — 81 : 1 Polar distance — 66 : 29 Take the distance in the Line of Sines , as representing the former half of a Line of Versed Sines , between these two Arks counted towards the Center , viz. 66d 29′ , and 81d 01′ , and enter this extent twice down the Line of Sines from the Center , and take the nearest distance to the thred lying over the Secant of the Latitude 47d 27′ , then enter one foot of this extent at 51d 32′ counted from the end of the Sines towards the Center , laying the thred to the other foot , according to nearest distance , and in the Versed Sine of 90d , it shews the Azimuth to be 65d from the South in this our Northern Hemispere . Of the fitted Particular Scale , and the Line of Entrance thereto belonging . THis Scale serves to find both the Hour and Azimuth in the Latitude of London , to which it is fitted , in the equal Limb , by a Lateral or positive Entrance , it consists of two Lines of Sines . The greater is 62d of a Sine , as large as can stand upon the Quadrant , the Radius of the lesser Sine is made equal to 51d 32′ of this greater , being fitted to the Latitude : The Scale of Entrance standing within the Projection , and abutting on the Line of Sines , is no other but a portion of a Line of Sines , whose Radius is made equal to 38d 28′ of the greater Sine of the fitted Scale ; and this Scale of Entrance is numbred by its Complements up to 62d , as much as is the Suns-greatest meridian Altitude in this Latitude . The ground of this Scale is derived from the Diagonal Scale , the length whereof bears such Proportion to the Line of Sines whereto it is fitted , as the Secant of the particular Latitude doth to the Radius , which is the same that the Radius bears to the Cosine of the Latitude , and consequently , making the Line of Sines to represent the fitted Scale , the Radius of that Sine whereto it is fitted , must be equal to the Cosine of the Latitude : and so we needed no particular Scale , but this would remove the particular Scale , or Scale of Entrance , nearer the Center , and would not have been so ready as this fitted Scale ; however , hence I might educe a general method for finding the hour and Azimuth in the Limb , without Tangents or Secants . The first Work would be to proportion out a Sine to a lesser Radius , which would find the point of Entrance , the next would be to finde the Altitude , or Depression , at 6. the third would be to enter the sum , or difference of the Sines of the Altitude , or depression at 6 at the point of Entrance , and to lay the thred to the other foot ; but I shall demonstrate it from other grounds . 1. To find the time of Sun Rising , or Setting . Take the Declination from the lesser Sine , and enter it at the Declination in the Scale of Entrance , laying the thred to the other foot , according to nearest distance , and it shews the time of Rising or setting in the equal Limb. So when the Sun hath 13d of South Declination , he riseth at 8′ past 7 in the morning f●re , and sets at 52′ past 4 in the afternoon . 2. To find the true time of the day . In Summer , or Northwardly Declination , take the distance between the Altitude in the greater Sine , and the Declination in the lesser Sine . In Winter , take the Declination in the lesser Sine , and with your Compasses add it to the Altitude in the greater Sine . These extents enter at the Declination in the Scale of Entrance , and lay the thred to the other foot , according to nearest distance , and in the equal Limb , it will lye over the true time of the day . In Summer , when the Declination in the fitted Scale is above the Altitude , the hour is found from 6 towards midnight , when below it , towards Noon . Example . When the Sun hath 13d of North Declination , his Altitude being 39d 10′ will be a quarter past 9 in the morning , or 3 quarters past 2 in the afternoon ; and when he hath the same South Declination , his Altitude being 16d 14′ the time of the day will be found the same . The Converse will find the Suns Altitudes on all hours by this fitted Scale , which I shall handle the general way . 3. To find the Amplitude . Take the Declination from the greater Sine , and enter it at the beginning of the Scale of Entrance , laying the thred to the other foot , according to nearest distance , and it shews it in the Limb. When the Sun hath 13d of Declination , his Amplitude will be 21d 12′ . 4. To find the Azimuth of the Sun. In Summer ▪ take the distance between the Altitude in the lesser Sine , and the Declination in the greater . In Winter , or South Declinations , take the Declination from the greater Sine , and add it to the Altitude in the lesser Sine with your Compasses . These Extents , enter at the Altitude in the Scale of Entrance , and lay the thred to the other foot , according to nearest distance ; and in the equal Limb , it shews the Azimuth from the East or West . In Summer , when the Altitude falls below the Declination , the Azimuth is found from the East or West , Northwards ; when above it , Southwards . So when the Sun hath 13d of North Declination , his Altitude being 43d 50′ the Azimuth will be found to be 45d from East or West , Southwards ; and when he hath the same South Declination , his Altitude being 14d 50′ he shall have the same Azimuth . These Scales are fitted to give the Altitude at six , and the Vertical Altitude by Inspection . Against the Declination in the greater lesser Sine stands the Vertical Altitude or Depression , Altitude or Depression at six . When the Hour or Azimuth falls near Noon , mind against what Arch of the Line of Sines the point of Entrance falls , the thred may be laid to the like Arch in the Limb , and the respective extents entred parallelly between the Scale and the thred , and the answer found in the Line of Sines . But we have a better remedy by help of the Versed Sine of 90d put thorow the whole Limb. The joynt use of the Fitted Scale , with the Versed Sine of 90d in the Limb. IN the following Propositions , I shall make no use of the lesser Sine of the Fitted Scale . Get the Summer and Winter Meridian Altitude , by summing and differencing the Declination , and the Complement of the Latitude , which may be done with Compasses in the equal Limb , by applying the Chord of the Declination both ways from the Co-latitude . To find the Hour of the Day in Winter . Take the distance between the Meridian Altitude , and the given Altitude , out of the greater Sine of the fitted Scale , and as before , enter it at the Declination in the Scale of Entrance , laying the thred to the other foot , according to nearest distance , and in the Versed Sine of 90d it shews the hour from Noon . So if the Sun have 13d of South Declination , the Meridian Altitude is 25d 28′ , if the given Altitude be 17d 44′ the time of the day will be half an hour past 9 in the morning , or as much after 2 in the afternoon . To find the Hour of the Day in Summer . Take the distance between the Summer Meridian Altitude , and the proposed Altitude , and if this extent be less then the distance of the Declination in the Scale of Entrance from the Center , enter it at the Declination in the said Scale , and laying the thred to the other foot , it will in the Versed Sine of 90d shew the Hour from Noon . If the Sun have 23d 31′ of North Declination , his Meridian Altitude will be 61 59′ , if his given Altitude be 47d 51′ , the time of the day will be a quarter past 9 in the morning , or three quarters of an hour past 2 in the afternoon . If the Extent be larger then the distance of the point of Entrance ▪ to wit , the distance of the Declination in the Scale of Entrance from the Center , the hour must be found from midnight . In this case , with your Compasses add the Sine of the Winter Meridian Altitude , taken from the greater Sine of the fitted Scale , to the Sine of the Altitude in the said Scale , and enter the said whole extent at the point of Entrance , as before ; and in the Versed Sine of 90d , the thred will shew the hour from midnight . When the Sun hath 23 31′ of North Declination , if his Altitude be 5d 24′ , the time of the day will be half an hour past 4 in the morning , or half an hour past 7 in the evening , the Winter Meridian Altitude to this Declination being 14d 57′ . When the hour in these examples falls near Noon , the extent of the Compasses may be doubled , or tripled , and an Ark first found in the Limb , then if the thred be laid over the like Ark from the other edge , it will accordingly in the Versed Sines doubled or tripled , shew the time sought ; and the like may be done for the Azimuth . To find the Azimuth of the Sun in Winter : Get the Ark of difference between the Suns Altitude , and the Complement of the Latitude , and in the greater Sine of the fitted Scale , take the distance between the said Ark , and the Suns Declination , and enter one foot of this Extent at the Altitude in the Scale of Entrance , laying the thred to the other foot , and in the Versed Sine of 90d , it shews the Azimuth from Noon Meridian . Example . Colatitude , — 38d 28′ Altitude , — 12 : 13 Ark of Difference — 26 : 15 Declination — 13 : 00 The Azimuth to this example , will be 50d from the South . In Summer , get the Ark of difference between the Altitude , and the Complement of the Latitude , then when the Suns Altitude is the lesser of the two , take the sum , but when the greater , the difference of the Sines of the Suns Declination , and of the said Ark , and enter it at the Altitude on the Scale of Entrance , and you will find the Azimuth from the noon Meridian , as before ; but when either of those extents are larger then the distance between the point of Entrance and the Center , the Azimuth must be found from the midnight Meridian . In this case , take the difference , that is , the distance of the Sines of the Suns Declination , and of the Ark ▪ being the sum of the Altitude and Colatitude , out of the greater Sine of the fitted Scale , and enter it at the Altitude in the Scale of Entrance , laying the thred to the other foot , and in the Versed Sine it shews the Azimuth from the North. Example for finding the Azimuth from the North. Colatitude — 38d 28′ Altitude — 14 : 15 Sum — 52 : 43 Declination , — 23 : 31 The Azimuth to this example , will be found to be 70d from the North. Of the joynt use of the Diagonal Scale , with the Line of Sines on this Quadrant . If the respective extents that found the Hour and Azimuth in the Limb on the small Quadrant , be doubled , and applyed here to the Line of Sines issuing from the Center , which in this case becomes the Scale of Entrance , the Hour and Azimuth will be also found in the equal Limb of this Quadrant , for all those respective Latitudes to which the Diagonal Scale is accommodated . Of the Hour and Azimuth Scales on the Back-side thereof . THose Scales were fitted to the Versed Sines quadrupled on that small Quadrant , and consequently , are fitted to the Versed Sine of 90d , and the Line of Sines on this Quadrant , which is just double the Radius of that Quadrant . Those Scales are peculiarly fitted for the Latitude of London , and thereby we may alwaies find the Hour and Azimuth in the Versed Sine of 90 , without the trouble of summing or differencing of Arks. 1. By the Hour Scale , to find the Hour of the Day . Take the distance between the Declination , proper to the season of the year , and the Altitude , and entering one foot of that extent at the Complement of the Declination in the Sines , lay the thred to the other foot , according to nearest distance , and it shews the hour from Noon . Example . When the Sun hath 13d of North Declination , his Altitude being 47● 24′ , the Hour will be 30′ past 10 in the morning , or as much past 1 in the afternoon . In Summer , when this extent is greater then the Cosine of the Declination , and that it will be , when the Sun hath less Altitude then he hath at 6. The Declination is graduated against the Meridian Altitudes . In this case , add the Sine of the Altitude given , to the Sine of the Meridian Altitude in Winter , to that Declination , with your Compasses , and enter that whole extent at the Declination counted in the Line of Sines from 90d laying the thred to the other foot , according to nearest distance , and in the Versed Sine of 90d , it will shew the hour from midnight . Declination , — 23d 31′ North , The hour will be found either 4 in the morning , or 8 at night . Altitude — 1 : 34 The hour will be found either 4 in the morning , or 8 at night . 2. By the Azimuth Scale , to find the Azimuth of the Sun. Take the distance between the Declination proper to the season of the year , and the Altitude , and entering one foot of this extent at the Complement of the Altitude in the Lines of Sines issuing from the Center , to the other lay the thred according to nearest distance , and it shews the Azimuth from the noon Meridian in the Versed Sine of 90d. Declination — 23d 31′ North , The Azimuth hereto will be found 65d from the South . Altitude — 47 : 27 The Azimuth hereto will be found 65d from the South . In Summer , when this extent is greater then the Cosine of the Altitude , and that it will be , when the Sun hath less Altitude then he hath in the Vertical , the Azimuth must be found from the midnight Meridian . In this case , because the Azimuth Scale is not continued far enough , the sum of the Altitude and Colatitude must be gotten , and the distance taken between the said Ark and the Declination , counted in the hour-Scale as a Sine , and that extent entred at the Altitude counted from 90d in the Line of Sines , and the thred laid to the other foot , will shew the Azimuth from the North in the Versed Sine of 90d in the Limb. Colatitude , — 38● 28′ The Azimuth to this example will be 65d from the North. Altitude — 10 : 19 The Azimuth to this example will be 65d from the North. Sum — 48 : 47 The Azimuth to this example will be 65d from the North. Declination — 23 : 31 The Azimuth to this example will be 65d from the North. North. General Proportions . It now remains to be shewed , how the Hour , and Azimuth , &c. may be found generally , either in the equal Limb , or in the Versed Sine of 90d , and that without the help of Tangents or Secants , and possibly with more convenience then with them . In page 55. I have asserted , that the fourth term in any direct Proportion , bears such Proportion to the first term , as the Rectangle of the two middle terms doth to the square of the first term . And in page 105. That the Sine of any Arch bears such proportion to the Secant of the Complement of another Ark , as the Rectangle of the Sines of both those Arks , doth to the Square of the Radius . Whence it follows , That , As the Radius , Is to the Sine of one of the sides including an Angle , So is the Sine of the other containing side , To a fourth Sine . I say then , that this fourth Sine bears such Proportion to the Radius , as the Sine of one of those including sides , doth to the secant of the Complement of the other . And therefore , when three sides are given to find an Angle , it will hold , As the Radius , Is to the Sine of one of those including sides , So is the Sine of the other including side , To a fourth sine . Again , As that fourth Sine , Is to the difference of the Versed Sines of the third side , and of the Ark of difference between the two including sides , So is the Radius , To the Versed Sine of the Angle sought . And as that fourth Sine , Is to the difference of the Versed Sines of the third side , and of the sum of the two including sides , So is the Radius , To the Versed Sine of the sought Angles , Complement to 180d , or a Semicircle . Thus we are freed from a Secant in the two first terms of 3 several Proportions that find 〈…〉 Hour and Azimuth : All which I shall further confirm from the Analemma , and then proceed to Application , in the Scheme annexed . Proportions in the Analemma . UPon the Center C , draw a Circle , and let N C be the Axis of the Horizon , and E P the Axis of the World , AE C the Equator , ☉ F and Z Y two Parallels of Declination on each side the Equator , alike equidistant , S G the parallel of Altitude at 6 , and D E F the parallel of Depression at 6 ; draw a parallel of Altitude less then the Altitude at 6 V R , and another greater M N continued ; also a parallel of Depression less then the Depression at 6 W P , and another greater X Y , and there will be constituted diverse right lined , right angled Triangles , relating to the motion of the Sun or Stars , in which it will hold . As Radius is to the Cosine of the Declination , So is the Cosine of the Latitude To a fourth . Namely the difference of the Sines of the Meridian Altitude , and Altitude at 6 in Summer , equal to the Sum of the Sines of the Meridian Altitude and Depression at 6 in Winter , which is equal to the sum of the Sines of the midnight Depression and Altitude at 6 in Summer . A : B ☉ ∷ B : A ☉ . Again the same , As D : S E ∷ E : D S Again the same — G : B F ∷ B : F G. As that fourth is to the Radius , So is the Sine of the Meridian Altitude , To the Versed Sine of the Semidiurnal Ark A ☉ : ☉ B ∷ ☉ I : ☉ K. The two first terms are common to all the rest of the following Proportions . And so is the Sine of the midnight Depression , To the Versed Sine of the Seminocturnal Ark. G F : B F ∷ F L to K F. And so is the Sine of the Altitude , To the difference of the Versed Sines of the Semidiurnal Ark and Hour sought from Noon , ☉ A : B ☉ ∷ I M : K N. And so is the Sine of the Depression , To the difference of the Versed Sines of the Seminocturnal Ark , and of the hour from Midnight , F G : F B ∷ P L : K O And so is the difference of the Sines of the Suns Meridian , and given Altitude , To the Versed Sine of the hour from Noon , ☉ A : ☉ B ∷ ☉ M : ☉ N. If the Sun have Depression , So is the sum of the Sines of the Suns Meridian Altitude , and proposed Depression , To the Versed Sine of the hour from Noon , A ☉ : ☉ B ∷ ☉ Q : ☉ O. And so is the difference of the Sines of the Midnight and propose Depression , To the Versed Sine of the hour from Midnight , F G : F B ∷ P F : O F. But supposing the Sun to have Altitude , retaining still the two first terms , it holds . And so is the sum of the Sines of the Midnight Depression and given Altitude , To the Versed Sine of the hour from Midnight . F G : F B ∷ F R : F S. And so is the Sine of the Altitude , or Depression at six , To the Sine of the Ascensional difference , A ☉ : ☉ B ∷ A I : B-K. In Summer , if the Sun have Altitude , So is the difference of the Sines of the Altitude at six , and of the given Altitude , To the Sine of the hour from six , towards Noon , if the given Altitude be greater then the Altitude at six , otherwise towards Midnight . A ☉ : ☉ B ∷ A M : B N. Also A ☉ : ☉ B ∷ A T : B S. If he have Depression , So is the sum of the Sines of the Altitude at six , and the given Depression , To the Sine of the Hour from six , towards Midnight . A ☉ : ☉ B ∷ A Q : B O. In Winter , if the Sun have Altitude : So is the the sum of the Sines of his Depression at 6 , and of his given Altitude , To the Sine of the hour from 6 toward Noon , S D : S E ∷ D V : Z E. If he have Depression . So is the difference of the Sines of his Depression at 6 , and of has given Depression . To the Sine of the hour from 6 towards Noon , when the Depression is less then the Depression at 6 , otherways towards Midnight . S D : S E ∷ W D : Q E. S D : S E ∷ D X : E Y. When two terms of a Proportion happen in the common Radius , and two in a Parallel , there needs no Reduction . In Latitudes nearer the Poles then the Polar Circles , the Semidiurnal Arks , when the Declination is towards the Elevated Pole , will be more then the Diameters of their Parallels ; in that case , the difference , is the difference of the Versed Sine of the Hour , and of the fourth Proportional , found by the Proportion that finds the Semidiurnal Ark. General Proportions for the Hour . The Proportion selected for the Hour is , As the Radius , Is to the Cosine of the Latitude , So is the Cosine of the Declination , To a fourth : Namely , the difference of the Sines of the Meridian Altitude , and of the Altitude at 6. Again , 1. As that fourth , Is to the Radius , So in Summer , is the difference ; but in VVinter , the sum of the Sines of the Suns Altitude or Depression at 6 , To the Sine of the Hour from 6 towards Noon or Midnight , according as the Altitude or Depression is greater or less then the Altitude or Depression at 6. 2. And so is the difference of the Sines of the Meridian , and proposed Altitude , To the Versed Sine of the Hour from Noon : And so is the sum of the Sines of the Midnight Depression , and given Altitude , To the Versed Sine of the Hour from Midnight . 3. And so is the Sine of the Altitude , To the difference of the Versed Sines of the Semidiurnal Ark , and of the Hour sought . By the first Proportion , the hour may be found generally , either in the equal Limb , or Line of Sines . By the second Proportion , it may be found generally , either in the Versed Sines of 90d , or 180d. By the third Proportion , it may be found in the Line of Versed Sines issuing from the Center in many cases . I shall add a brief Application of all three ways . The first Work will be to find the point of Entrance . Example , For the Latitude of Nottingham , 53d. Lay the thred to the Declination , admit 20 in the Limb , counted from the left edge , and from the Latitude in the Line of Sines , counted towards the Center from 90d ; take the nearest distance to the thred , the said extent measured from the Center , will fall upon 34 25′ , and there will be the point of Entrance ; let it be recorded , or have a mark set to it . If the Suns Declination be North , the Meridian Altitude in that Latitude , will be 57d , the said extent will reach from the Sine thereof , to the Sine of the Suns Altitude , or Depression at 6 , to that Declination , namely , to 15d 51′ : which may also be found without the Meridian Altitude , by taking the distance from 20d in the Sines , to the thred laid over the Arch 53d , counted from the right Edge , and by measuring that extent from the Center , the point thus found , I call the Sine point . Thirdly , If the respective distances between the Sine point , and the Sine of the given Altitude , be taken and entred upon the point of Entrance , laying the thred to the other foot , according to nearest distance , the hour may be found all day for that Declination , when it is North in the equal Limb. Example , For the Latitude of Nottingham , to the former Declination , being North. When the Sun hath 11d 31′ 20 17 of Altitude , the Hour in each Case will be found half an hour from 6 , to the lesser Altitude beyond it , towards Midnight ; to the greater , towards Noon . And when the Altitude is 38d 19′ , the time of the day will be either half an hour past 8 in the morning , or half an hour past 3 in the Afternoon . An Example for the Latitude of Nottingham , when the Declination is as much South . Let the Altitude be 10d 6′ , In this case add the Sine thereof to the Sine of 15d 51′ , the whole extent will be equal to the Sine of 26d 39′ ; Enter this Extent upon the point of Entrance at 34d 25′ laying the thred to the other foot , according to nearest distance , and the time of the day found in the Limb , will be either half an hour past 9 in the morning , or half an hour past 2 in the afternoon . An Example for working the second Proportion . The Summer Meridian Altitude is 57d , if the given Altitude be 46d 11′ , take the distance between the Sines of these two Arks , and entring this extent upon the point of Entrance , lay the thred to the other foot , according to nearest distance , it will in the Versed Sine of 90d , shew the Hour from Noon to be 37d 30′ , that is , either half an hour past 10 in the morning , or half an hour past 1 in the Afternoon . And when the Hour falls near Noon , we may double or triple the extent of the Compasses , and find an Ark in the Limb , which if counted from the other edge , and the thred laid over it ▪ will give answer in the Versed Sines doubled or tripled accordingly . A third Example . If the Altitude were 3d 15′ , in this case the distance between it and the Meridian Altitude being greater then the distance of the point of Entrance from the Center , the hour must be found from Midnight ; add the Sine thereof to the Sine of 17d , the Winter Meridian Altitude , the whole extent will be equal to the Sine of 20 25′ ; Enter the said extent upon the point of Entrance ▪ as before , and in the Versed Sine of 90d , the hour will be found to be either half an hour past 4 in the Morning , or half an hour past 7 in the Evening . Examples for working the third Proportion . Take the Sine of 30d , and enter it upon the point of Entrance , laying the thred to the other foot , according to nearest distance , and there keep it ; then take the nearest distance to it from the Sine of 57 , the Meridian Altitude ; and the said Extent prick upon the Line of Versed Sines on the left edge , and it will reach to 118● 54′ , set a mark to it . Lastly , the nearest distance from the Sine of each respective Altitude to the thred , being pricked from the said mark , will reach to the Versed Sine of the hour from Noon , for North Declinations . So when the Sun hath 24d 48′ of Altitude , the Hour from 7 : 17 Noon will be found to be — 75d 105 A Winter Example for that Declination . The nearest distance from the Sine of 17d , the Winter Meridian Altitude , to the thred , will reach to the Versed Sine of 61d 6′ , the Complement of the former to a Semicircle , at which set a mark ; then if the Altitude were — 12d 30′ 14 : 26 the nearest distances to the thred prickt from the latter mark , would shew the hours to these Altitudes to be 2 hours 1 ½ hour from Noon This last Proportion in some cases will be inconvenient , being liable to excursion in Latitudes more Northwardly . Two sides with the Angle comprehended , to find the third side . As the Radius , Is to the Sine of one of the Includers , So is the Sine of the other Includer , To a fourth . Again , As the Radius , Is to the Versed Sine of the Angle included , So is that fourth , To the difference of the Versed Sines of the third side , and of the Ark of difference between the two including sides , And so is the Versed Sine of the Included Angles Complement to 180. To the difference of the Versed Sines of the third side , and of the sum of the two including sides . Another Proportion for finding it in Sines , elsewhere delivered . By the former Proportion , having the advantage both of lesser and greater Versed Sines , we may find the side sought , either in the line of Sines , or in the line of Versed Sines on the the left edge ▪ issuing from the Center . The Converse of the Proportion that found the Hour , will find the Suns Altitudes on all Hours . As the Radius , Is to the Cosine of the Latitude , So is the Cosine of the Declination , To a fourth Sine . Namely , The difference of the Sines of the Suns Meridian Altitude , and of his Altitude at 6 in Summer , but the sum of the Sines of his Depression at 6 , and Winter Meridian Altitude , hereby we may obtain the point of Entrance and Altitude , or Depression at 6 , as before , and let them be recorded , then it holds , As the Radius , Is to the Sine of the Hour from 6 , So is that fourth Sine , To the difference of the Sines of the Suns Altitude at 6 , and of his Altitude sought ; But in Winter , To the sum of the Sines of his Depression at 6 , and of the Altitude sought . Hereby we may find two Altitudes at a time . Lay the thred to the Hour in the Limb , and from the point of Entrance , take the nearest distance to it , the said Extent being set down at the Altitude at 6 , shall reach upward to the greater Altitude , and downward , to the lesser Altitude . Example . Admit the hour to be 5 and 7 in the morning , the Altitudes thereto for 20 North Declination for the Latitude of Nottingham , will be found to be 7d 17′ , and 24● 48′ If the Hour be more remote from 6 then the time of Rising , we may find a Winter Altitude to as much South Declination , and a Summer Altitude , to the said North Declination . Thus if the Hour be 45d from 6 , that is either 9 in the morning , or 3 in the afternoon , the nearest distance from the point of Entrance to the thred , will reach from the Sine of 15d 51′ , the Altitude at 6 upwards , to the Sine of 42d 18′ , the Summer Altitude to that Declination : But downwards , it reaches beyond the Center : In this case measure , that extent from the Center , and take the distance between the inward foot of the Compasses , and the Altitude at 6 ▪ which measured on the Sines , will be found to be 7d 17′ for the Winter Altitude to that Hour . So if the hour were 60d from 6 , that is either 10 , or 2 , the Summer Altitude would be found to be 49d 42′ , and the Winter Altitude 12d 30′ . And this may be found in the Versed Sines on the left edge , accounted as a Sine each way from the middle , if use be made of the lesser Sines , instead of the Limb , in finding the point of Entrance , as also , in laying it to the Sine of each hour from 6 , in which case the Compasses will alwaies find two Altitudes at once ; for when they fall beyond the midst of the said Line , it shews the Winter Altitudes counted from thence towards the end of the said Versed Sines . Having found the fourth Sine , which gives the point of Entrance as before , the Altitudes on all hours may be found by the Versed Sines of 90d in the Limb , the Proportion will be , As the Radius , Is to the Versed Sine of the Hour from Noon , So is the fourth abovesaid , To the difference of the Sines of the Meridian Altitude , and of the Altitude sought . But for hours beyond 6 , the Proportion will be , As the Radius , Is to the Versed Sine of the Hour from Midnight , So is the fourth abovesaid , To the sum of the Sines of the Suns Depression at Midnight ( equal to his Winter Meridian Altitude , ) and of his Altitude sought , Hereby also we may find two Altitudes at once . Operation . Lay the thred to the Versed Sine of the Hour from Noon , and from the point of Entrance at 34d 25′ , take the nearest distance to it , the said Extent shall reach from the Summer Meridian Altitude , accounted in the Sines to the Altitude sought , also from the Winter Meridian Altitude , to the Altitude sought . Example . Latitude of Nottingham is 53d , Complement — 37● Suns Declination , — 20 Sum being the Summer Meridian Altitude — 57d Difference being Winter Meridian Altitude 17 If it were required to find the Altitudes for the hours of 11 and 1 The Extents so taken out will find the Summer Altitudes to be — 55● 00′ And the Winter Altitudes to the same hours and Declination — 15● 51● 10 and 2 The Extents so taken out will find the Summer Altitudes to be — 49 , 42 And the Winter Altitudes to the same hours and Declination — 12 , 30 9 and 3 The Extents so taken out will find the Summer Altitudes to be — 42 , 18 And the Winter Altitudes to the same hours and Declination — 7 , 17 8 and 4 The Extents so taken out will find the Summer Altitudes to be — 33 , 47 And the Winter Altitudes to the same hours and Declination — 00 , 32 But for hours more remote from the Meridian then 6 , as admit for 5 in the morning , or 7 at night , which is 75d from the North Meridian ; lay the thred to the said Ark in the Versed Sine of 90d , and the distance from the point of Entrance to it , shall reach from the Sine of 57d , the Meridian Altitude , to the Sine of 24d 48′ , the Summer Altitude for the Hour 75d from Noon , and if that Extent be pricked from the Winter Meridian Altitude , it will reach beyond the Center , in which case , enter that Extent upon the Line of Sines , and take the distance between the point of limitation and 17d , which will ( being measured ) be found to be the Sine of 7d 17′ , the Altitude belonging to the hour 105 from Noon . In like manner , the Altitudes for the hours 97d 30 from Noon that is 82d 30′ from Midnight , will be 11d 31′ and for the like hours from Noon 20d 17′ 112 , 30 from Noon that is 67 , 30 from Midnight , will be 3 : 15 and for the like hours from Noon 29 : 19 In like manner , it might have been found in the Versed Sines issuing from the Center , if in finding the point of Entrance , and in laying the thred to the Versed Sine of the Hour , we make use of the lesser Sines , and of the Versed Sine of 180d in the Limb. For the Azimuth . Two of the former Proportions may be conveniently applied to other sides , for finding the Azimuth universally . As the Radius , Is to the Cosine of the Latitude , So is the Cosine of the Altitude , To a fourth Sine . Get the sum of the Altitude and Colatitude ; or , which is all one , the sum of the Latitude and Colatitude ; and if it exceeds a Quadrant , take its Complement to a Semicircle : This fourth Sine is equal to the difference of the Sines of this Compound Ark , and of another Ark to be thereby found , called the latter Ark. Then it holds , As the fourth Sine , Is to the Radius , So in Summer is the difference , but in Winter , the sum of the Sines of this latter Ark , and of the given Declination , To the Sine of the Azimuth from the Vertical . When the latter Ark is more then the Declination , the Azimuth will be found from the Vertical towards the Noon Meridian , otherwise towards the Midnight Meridian , and in winter , always towards the Noon Meridian . For such Stars as come to the Meridian between the Zenith and the elevated Pole , the fourth Ark will never exceed the Stars declination , and their Azimuth will be alwaies found from the Vertical towards the Meridian they come to , above the Horizon . Example for the Latitude of Nottingham . Complement of the Latitude is — 37d Altitude is 40● — 40 Sum — 77 Let the Declination be 20d North. To find the point of Entrance , take the nearest distance to the thred laid over 50 in the Limb , counted from right edge from the Sine of 37d , the said Extent measured from the Center , falls upon the Sine of 27d 26′ , and there will be the point of Entrance ; the said Extent prickt from 77● in the Sines , will reach to the Sine of 30 51′ , where the Sine point falls . Lastly , The distance between the Sine point , and the Sine of 20d being entred at the point of Entrance , and the thred laid to the other foot , the Azimuth will be found in the equal Limb to be 21d 48′ from the East or West Southwards , because the Sine point fell beyond the Declination . Another Example for that Latitude , the Declination being 20d South Altitude . 12d 30′ The point of Entrance will fall at the Sine of 36● The Sine point may be found without summing or differencing of Arks , by taking the nearest distance from the Sine of the Latitude , to the thred laid over the Altitude , counted in the Limb from the right edge ; which Extent being added to the Sine of 20d the Declination , the whole Extent will be equal to the Sine of 31d , this being entred on the point of Entrance , and the thred laid to the other foot , the Azimuth will be found to be 61d 14′ from the East or West Southwards . A third Example for the Latitude of London , 51d 32′ . Let it be required to find the Azimuth of the middlemost Star in the great Bears tail , Declination is 56d 45′ , let the Altitude be 44d 58′ . The nearest distance from the Sine of 38d 28′ to the thred laid over the Altitude counted from the right edge , will find the point of Entrance to be at the Sine of — 26d 6′ . The nearest distance from the Sine of 51d 32′ to the thred laid over the Altitude , counted from the right edge , need not be known , but the distance between that Extent , and the Sine of 56d 45′ , the Stars Declination being entred on the point of Entrance , will find the Azimuth of that Star , by laying the thred to the other foot , to be 40d from the East or West Northwards . Thus we find it the general way , and so it will also be found by the fitted particular Scale ; for the Hour , the point of Entrance , and Sine point , vary not till the Declination change ; but for the Azimuth , they vary to every Altitude . To find the Azimuth in the Versed Sines . As the fourth , found by the former Proportion ; namely , where the point of Entrance hapned , Is to the Radius , So is the difference of the Versed Sines of the Polar distance , and of the Ark of Difference between the Altitude and the Latitude , To the Versed Sine of the Azimuth from Midnight Meridian . This finds the Angle it self in the Sphere . And so is the difference of the Versed Sines of the Polar distance , and of the Ark of residue of the sum of the Latitude and Altitude taken from a Semicircle . To the Versed Sine of the Azimuth from Noon Meridian . This finds the Complement of the Angle in the Sphere to a Semicircle . The Proportion to find it from Midnight Meridian , the third term being express'd in Sines , will be thus . Get the sum of the Altitude and Colatitude , and when it exceeds a Quadrant , take its Complement to a Semicircle , the Ark thus found , is called the Compound Ark. Then it holds , As the fourth found before . Is to the Radius , So in Summer Declinations , is the difference , but in Winter Declinations , the sum of the Sines of the Suns or Stars declination , and of the compound Ark , To the Versed Sine of the Azimuth from the Midnight Meridian of the place . Use this Proportion alwaies for the Sun or Stars , when they come to the Meridian between the Zenith and elevated Pole. And to find it from the Noon Meridian , Get the difference between the Altitude and Colatitude , and then it holds , As the fourth Sine found before , Is to the Radius , So is the sum of the Sines of the said Ark of Difference , and of the Suns Declination , To the Versed Sine of the Azimuth from the Noon Meridian , in Summer only , when the Suns Altitude is less then the Colatitude . In all other cases , So is the difference of the said Sines , To the Versed Sine of the Azimuth , as before , from Noon Meridian . If by the former Proportion it be required to find the Azimuth in the Versed Sine of 90d , a difference of Versed Sines taken out of the Line of Versed Sines on the left edge must be doubled , and being taken out of the Line of Sines , as sometimes representing the former , sometimes the latter half of a Versed Sine , needs not be doubled . Example : Latitude of Nottingham — 53d Altitude of the Sun — 4 Ark of difference — 49 ☉ Declination 20 North , the Polar distance is — 70 The Point of entrance will fall at the Sine of 36d 54′ And the difference of the Versed Sines of 49● and 70● , equal to the distance between the Sines of 41● and 20 being entred at the Point of entrance , and the Tbread laid to the other foot will lye over 61d 30′ of the Versed Sine of 90● , and so much is the Suns Azimuth from the North. Another Example for finding it from the South when the Altitude is more then the Colatitude . Altitude — 47d Colatitude — 37 of Nottingham . difference — 10 The Point of entrance will fall at the sine of 24d 14′ found by taking the nearest extent from sine of 37d to the Thread lying over 43d of the Limb the Coaltitude . Then the distance between the sines of 10d , the Ark of difference as above , and the sine of 20 the Suns North Declination being entred at the Point of entrance , and the Thread laid to the other foot , will shew 53d 55′ in the Versed sine of 90d for the Suns Azimuth from the South . A third Example when the Altitude is less then the Colatitude in Summer . Complement Latitude 37d of Nottingham . Altitude — 34 difference — 3 The Point of entrance will fall at the sine of 29d 55′ , and the sum of the sines of 3d , and of 20d the Suns declination supposed North , is equal to the sine of 23d 13′ : Which Extent entred at 29d 55′ , the Point of entrance , and the Thread laid to the other foot according to nearest distance , it will intersect the Versed sine of 90d at the Ark of 77d 57′ , and so much is the Suns Azimuth from the South . And if there were no Versed sines in the Limbe , find an Ark of the equal Limbe , and enter the sine of the said Ark down the Line of sines from the other end , and you may obtain the Versed sine of the Ark sought . More Examples need not be insisted upon , having found the Point of entrance , the distance between the Versed sines of the Base or side subtending the angle sought , and of the Ark of difference between the two including sides , being taken out of the streight Line of Versed Lines on the left edge , and entred at the Point of entrance , laying the Thread to the other foot shews in the Versed Sine of 180d in the Limb the angle sought ; and if the said distance or Extent be doubled , and there entred it shews the angle sought in the Versed Sine of 90d , when the Angle is less then a Quadrant , when more , the distance between the Versed Sines of the Base and the sum of the Legs , will find the Complement of the angle sought to a Semicircle without doubling in the Versed Sine of 180d in the Limb , with doubling in the Versed Sine of 90d. Lastly , Three sides , viz. all less then Quadrants , or one of them greater , generally to find an angle in the equal Limb , the Proportion will be , As the Radius , Is to the Cosine of one of the including sides : So is the Cosine of the other Includer , To a fourth Sine . Again , As the Sine of one of the Includers , To the Cosecant of the other : So when any one of the sides is greater then a Quadrant is the sum , but when all less , the difference of the fourth Sine , and of the Cosine of the third side , To the Cosine of the angle sought . If any of the three sides be greater then a Quadrant , it subtends an Obtuse angle , the other angles being Acute ; But when they are all less then Quadrants , if the 4th Sine be less then the Cosine of the third side , the angle sought is Acute , if equal thereto , it is a right angle , if greater an Obtuse angle . From the Proportion that finds the Hour from six , we may educe a single Proportion applyable to the Logarithms without natural Tables for Calculating the Hour of the day to all Altitudes , By turning the third Tearm , being a difference of Sines or Versed Sines into a Rectangle , and freeing it from affection . The two first Proportions to be wrought are fixed for one Declination ; The first will be to find the Suns Altitude or Depression at six . The second will be to find half the difference of the Sines of the Suns Meridian Altitude , and Altitude sought , &c. as before defined , the Proportion to find it is , As the Secant of 60d , To the Cosine of the Declination : So is the Cosine of the Latitude , To the Sine of a fourth Arch. Lastly , To find the Hour . Get the sum and difference of half the Suns Zenith distance at the hour of six ; and of half his Zenith distance to any other proposed Altitude or Depression . Then , As the Sine of the fourth Arch , Is to the Sine of the sum : So is the Sine of the difference , To the Sine of the hour from six towards Noon or Midnight , according as the Altitude or Depression was greater or lesser then the Altitude or Depression at six . Observing that the Sine of an Arch greater then a Quadrant , is the Sine of that Arks Complement to a Semicircle . Of the Stars placed upon the Quadrant below the Projection . ALL the Stars placed upon the Projection are such as fall between the Tropicks and the Hour may be found by them with the Projection , as in the Use of the small Quadrant : Which may also be found by the fitted particular Scale , not only for Stars within the Tropicks , but for all others without , when their Altitude is less then 62d , and likewise their Azimuth may be thereby found when their Declination is not more then 62d. For other Stars without the Tropicks , they may be put on below the Projection any where in such an angle that the Thread laid over the Star shall shew an Ark in the Limb , at which in the Sines the Point of entrance will always fall ; And again , the same Star is to be graved at its Altitude or Depression at six in the Sines , and then to find the Stars hour in that Latitude whereto they are fitted , will always for Northern Stars be to take the distance in the Line of Sines between the Star and its given Altitude , and to enter that Extent at the Point of entrance , laying the Thread to the other foot according to nearest distance , and it gives the Stars hour in the equal Limb from six , which may also be found in the Sines by a Parrallel entrance , laying the Thread over the Star. Example . Let the Altitude of the last in the end of the great Bears Tail be 63d , take the distance between it and the Star which is graved at 37d 30′ of the Sines , the said Extent entred at the Sine of 23d , the Ark of the Limb the Thread intersects when it lies over the said Star , and by laying the Thread to the other foot you will find that Stars hour to be 46d 11′ from six towards Noon Meridian , if the Altitude increase , and in finding the true time of the night , the Stars hour must be always reckoned from the Meridian it was last upon ; in this Example it will be 5 minutes past 9 feré . Of the Quadrant of Ascensions on the backside , This Quadrant is divided into 24 Hours with their quarters and subdivisions , and serves to give the right Ascension of a Star , as in the small Quadrant to be cast up by the Pen. It also serves to find the true Hour of the night with Compasses . First having found the Stars hour , take the distance on the Quadrant of Ascensions in the same 12 hours between the Star and the Suns Ascension ( given by the foreside of the Quadrant ) the said Extent shall reach from the Stars hour to the true hour of the night , and the foot of the Compasses always fall upon the Quadrant ; Which Extent must be applyed the same way it was taken , the Suns foot to the Stars hour . Example . If upon the 30th of December the last in the end of the Bears Tail were found to be 9 hours 05′ past the Meridian it was last upon , the true time sought would be 16 minutes past 3 in the morning . Another Example for the Bulls Eye . Admit the Altitude of that Star be 39 d , that Stars hour as we found it by the Line of Versed Sines was 3 ho 3′ from the Meridian , if the Altitude increase , then that Stars hour from the Meridian it was last upon was 57 minutes past 8 — 8 h : 57′ If this Observation were upon the 23d of October , the Complement of the Suns Ascension would be — 9 : 30 The Ascension of that Star is — 4 : 16 The true time of the night would be forty — 10 : 43 three minutes past ten . The distance between the Star and the Suns Ascension being applyed the same way , by setting the Sun foot at the Stars hour will shew the true time sought . When the Star is past the Meridian , having the same Altitude , the Stars hour will be 3′ past 3 , and the true time sought , will be 49′ past 4 in the next morning . The Geometrical Construction of Mr Fosters Circle . THe Circle on the Back side of the Quadrant , whereof one quarter is only a void Line , is derived from M. Foster's Treatise of a Quadrant , by him published in An●o 1638. the foundation and use whereof being concealed , I shall therefore endeavour to explain it . Upon the Center H describe a circle , and draw the Diameter A C , passing through the Center , and perpendicularly thereto , upon the point C , erect a Line of Sines C I , whose Radius shall be equal to the Diameter A C , let 90d of the Sine end at I ; I say then , if from the point A , through each degree of that Line of Sines , there be streight lines drawn , intersecting the Quadrant of the circle C G , as a line from the point D doth intersect it at B the Quadrant C G , which the Author calls the upper Quadrant , or Quadrant of Latitudes shall be constituted , and if C I be continued as a Secant , by the same reason the whole Semicircle C G A may be occupied ; hence it will be necessary to educe a ground of calculation for the accurate dividing of the said Quadrant , and that will be easie ; for A C being Radius , the Sine C D doth also represent the Tangent of the Angle at A , therefore seek the natural Sine of the Ark C D in the Table of Natural Tangents , and the Ark corresponding thereto , will give the quantity of the Angle D A C , then because the point A falls in the circumference of the Circle , where an Angle is but half so much as it is at the Center , by 31 Prop. 3. Euc. double the Angle found , and from a Quadrant divided into 90 equal parts , and their subdivisions , by help of a Table so made , may the Quadrant of Latitudes be accurately divided : but the Author made his Table in page 5. without doubling , to be graduated from a Quadrant divided into 45 equal parts . Again , If upon the Center C , with a pair of Compasses , each degree of the line of Sines be transferred into the Semicircle C G A it shall divide it into 90 equal parts ; the reason whereof is plain , because the Sine of an Arch is half the chord of twice that Arch , and therefore the Sines being made to twice the Radius of this circle , shall being transferred into it , become chords of the like Arch , to divide a Semicircle into 90 equal parts . Again , upon the point A , erect a line of Tangents of the same Radius with the former Sine , which we may suppose to be infinitely continued , here we use a portion of it A E. If from the point C , the other extremity of the Diameter lines be drawn , cutting the lower Semicircle ( as a line drawn from E intersects it at F ) through each degree of the said Tangent , the said lower Semicircle shall be divided into 90 equal parts ; the reason is evident a line of Tangents from the Center shall divide a Quadrant into 90 equal parts , and because an Angle in the circumference is but half so much as it is in the Center , being transferred thither , a whole Semicircle shall be filled with no more parts . The chief use of this Circle , is to operate Proportions in Tangents alone , or in Sines and Tangents joyntly , built upon this foundation , that equiangled plain Triangles have their sides Proportional . In streight lines , it will be evident from the point D to E , draw a streight line intersecting the Diameter at L , and then it lies as C L to C D ; so is A L to A E : it is also true in a Circle , provided it be evinced , that the points B L F fall in a streight line . Hereof I have a Geometrical Demonstration , which would require more Schemes , which by reason of its length and difficulty , I thought fit at present not to insert , possibly an easier may be found hereafter : As also , an Algebraick Demonstration , by the Right Honourable , the Lord Brunkard , whereby after many Algebraick inferences it is euinced , that as L K is to K B ∷ so is L N to ● F : whence it will follow , that the points B , L , F , are in a right line . If a Ruler be laid from 45d of the Semicircle , to every degree of the Quadrant of Latitudes , it will constitute upon the Diameter , the graduations of the Line Sol , whereby Proportions in Sines might be operated without the other supply . From the same Scheme also follows the construction of the streight line of Latitudes , from the point G , at 90● of the Quadrant of Latitudes , draw a streight Line to C , and transfer each degree of the Quadrant of Latitudes with Compasses , one foot resting upon C into the said streight line , and it shall be constituted . To Calculate it . The Line of Latitudes C G bears such Proportion to C A as the Chord of 90d doth to the Diameter , which is the same that the Sine of 45d bears to the Radius , or which is all one , that the Radius bears to the Secant of 45 d , which Secant is equal to the Chord of 90 d ; from the Diagram the nature of the Line of Latitudes may be discovered . Any two Lines being drawn to make a right angle , if any Ark of the Line of Latitudes be pricked off in one of those Lines retaining a constant Hipotenusal A C , called the Line of Hours , equal to the Diameter of that Circle from whence the Line of Latitudes is constituted , if the said Hipotenusal from the Point formerly pricked off , be made the Hipotenusal to the Legs of the right angle formerly pricked off , the said Legs or sides including the right angle shall bear such Proportion one to another , as the Radius doth to the sine of the Ark so prickt off ; and this is evident from the Schem , for such Proportion as A C bears to C D , doth A B bear to B C , for the angle at A is Common to both Triangles , and the angle at B in the circumference is a right angle , and consequently the angle A C B will be equal to the angle A D C , and the Legs A C to C D bears such Proportion by construction , as the Radius doth to the Sine of an Ark , and the same Proportion doth A B bear to B C , in all cases retaining one and the same Hypotenusal A C , the Proportion therefore lies evident . As the Radius , the sine of the angle at B , To its opposite side A C , the Secant of 45d : So is the sine of the angle at A , To its opposite side B C sought . Now the quantity of the angle at A was found by seeking the natural Sine of the Ark proposed in the Table of natural Tangents ; and having found what Ark answers thereto , the Sine of the said Ark is to become the third Tearm in the Proportion . But the Cannon prescribed in the Description of the small Quadrant is more expedite then this , which Mr Sutton had from Mr Dary long since , for whom , and by whose directions he made a Quadrant with the Line Sol , and two Parrallel Lines of Sines upon it , as is here added to the backside of this Quadrant . Of the Line of Hours , alias , the Diameter or Proportional Tangent . This Scale is no other then two Lines of natural Tangents to 45 d , each set together at the Center , and from thence beginning and continued to each end of the Diameter , and from one end thereof numbred with 90 d to the other end . This Line may fitly be called a Proportional Tangent , for whersoever any Ark is assumed in it to be a Tangent , the remaining part of the Diameter is the Radius to the said Tangent . So in the former Schem , if C L be the Tangent of any Ark , the Radius thereto shall be A L. In the Schem annexed , let A B be the Radius of a Line of Tangents equal to C D , and also parralel thereto , and from the Point B to C draw the Line B C , and let it be required to divide the same into a Line of Proportional Tangents : I say , Lines drawn from the Point D to every degree of the Tangent , A B shall divide one half of it as required from the similitude of two right angled equiangled plain Triangles , which will have their sides Proportional , it will therefore hold , As C F , To C D : So F B , To B E , and the Converse , As the second Tearm C D , To the fourth B E : So is the first C F , To the third F B , and therefore C F bears such Proportion to F B , as C D doth to B E , which is the same that the Radius bears to the Tangent of the Ark proposed . If it be doubted whether the Diameter wil be a double Tangent or the Line here described such a Line , a Proportion shall be given to find by Experience or Calculation , what Line it will be ; for there is given the Radius C D , and the Tangent B E , the two first Tearms of the Proportion , with the Line C B the sum of the third and fourth Tearms , to find out the said Tearms respectively ; and it will hold by compounding the Proportion , As the sum of the first and second Tearm , Is to the second Tearm : So is the sum of the third and fourth Tearm , To the fourth Tearm , that is , As C D + B E , Is to B E : So is C F + F B = C B , To F B , see 18 Prop. of 5 of Euclid , or page 18 of the English Clavis Mathematicae , of the famous and learned Mr Oughtred . After the same manner is the Line Sol , or Proportional Sines made , that being also such a Line , that any Ark being assumed in it to be a Sine , the distance from that Ark to the other end of the Diameter , shall be the Radius thereto . A Demonstration to prove that the Line of Hours and Latitudes will jointly prick off the hour Di●tances in the same angles as if they were Calculated and prickt off by Chords . Draw the two Lines A B and C B crossing one another at right angles at B , and prick off B C the quantity of any Ark out of the line of Latitudes , and then fit in the Scale of Hours ; so that one end of it meeting with the Point C , the other may meet with the other Leg of the right angle at A , from whence draw A E parralel to B C ; So A B being become Radius , B C is the Sine of the Arch first prickt down from the line of Latitudes ; from the Point B through any Point in the line of Proportional Tangents , at L draw the Line B L E , and upon B with the Radius B A draw the Arch A D , which measureth the Angle A B E to the same Radius : I say , there will then be a Proportion wrought , and the said Arch measureth the quantity of the fourth Proportional , the Proportion will be , As the Radius , To the Sine of the Ark prickt down from the Line of Latitudes : So is any Tangent accounted in the Scale , beginning at A , To the Tangent of the fourth Proportional ; in the Schem it lies evident in the two opposite Triangles L C B and L A E , by construction equiangled and consequently their sides Proportional . Assuming A L to be the Tangent of any Ark , L C becomes the Radius , according to the prescribed construction of that Line , it then lies evident , As L C the Radius , To C B the Sine of any Ark , So is L A , the Tangent of any Ark , To A E , the Tangent of the fourth Proportional . Namely , of the Angle A B E , and therefore it pricks down the Hour-lines of a Dyal most readily and accurately : the Proportion in pricking from the Substile being alwaies , As the Radius , To the Sine of the Stiles height , So the Tangent of the Angle at the Pole , To the Tangent of the Hour-line from the Substile . Uses of the Graduated Circle . To work Proportions in Tangents alone . In any Proportion wherein the Radius is not ingredient , it is supposed to be introduced by a double Operation , and the Poportion will be , As the first term , To the second , So the Radius to a fourth . Again , As the Radius is to that fourth , So is the third Term given , To the fourth Proportional sought . In illustrating the matter , I shall make use of that Theorem● for varying of Proportions , that the Tangents of Arches , and the Tangents of their Complements are in reciprocal Proportions . As Tangent 23d , to Tangent 35d , So Tangent 55d to the Tangent of 67d. In working of this Proportion , the last term may be found to the equal Semicircle , or on the Diameter . 1. In the Semicircle . Extend the thred through 23d on the Diameter , and through 3● in the Semicircle , and where it intersects the Circle on the opposite side , there hold one end of it , then extend the other part of it over 55 in the Diameter , and in the Semicircle , it will intersect 67d for the term sought . 2. On the Diameter . Extend the thred over 23d in the Semicircle , and 35d on the Diameter , and where it intersects the void circular line on the opposite side , there hold it , then laying the other end of it over 55 d in the Semicircle , and it will cut 67 d on the Diameter . If the Radius had been one of the terms in the Proportion , the operation would have been the same , if the Tangent of 45 d had been taken in stead of it . To work Proportions in Sines and Tangents joyntly . 1. If a Sine be sought , the middle terms being of a different species . Extend the thred through the first term on the Diameter , being a Tangent , and through the Sine , being one of the middle terms , counted in the unequal Quadrant , and where it intersects the Opposite side of the Circle hold it , then extend the thred over the Tangent , being the other middle term counted on the Diameter , and it will intersect the graduated Quadrant at the Sine sought . Example . If the Proportion were as the Tangent of 14d to the Sine of 29d So is the Tangent of 20d to a Sine , the fourth Proportional would be found to be the Sine of 45d. 2. If a Tangent be sought , the middle terms being of several kinds , Extend the thred through the Sine in the upper Quadrant , being the first term , and through the Tangent on the Diameter , being one of the other middle terms , holding it at the Intersection of the Circle on the opposite side , then lay the thred to the other middle term in the upper Quadrant , and on the Diameter , it shews the Tangent sought . Example . If the Suns Amplitude and Vertical Altitude were given , the Proportion from the Analemma to find the Latitude would be , As the Sine of the Amplitude to Radius , So is the Sine of the Vertical Altitude , To the Cotangent of the Latitude Let the Amplitude be — 39d 54′ And the Suns Altitude being East or West — 30 39′ Extend the thred through 39 54′ , the Amplitude counted in the upper Quadrant , and through 45d on the Diameter , holding it at the intersection with the Circle on the Opposite side , then lay the thred over 30d 39′ , the Vertical Altitude , and it will intersect the Diameter at 38d 28′ , the Complement of the Latitude sought . But Proportions derived from the 16 cases of right angled Spherical Triangles , having the Radius ingredient , will be wrought without any motion of the thred . An Example for finding the Suns Azimuth at the Hour of 6. As the Radius to the Cosine of the Latitude , So the Tangent of the Declination , To the Tangent of the Azimuth , from the Vertical towards Midnight Meridian . Extend the thred over the Complement of the Latitude in the upper Quadrant , and over the Declination in the Semicircle , and on the Diameter . it shews the Azimuth sought . So when the Sun hath 15d of Declination , his Azimuth shall be 9d 28′ from the Vertical at the hour of 6 in our Latitude of London . Another Example to find the time when the Sun will be due East or West . Extend the thred over the Latitude in the Semicircle , and over the Declination on the Diameter , and in the Quadrant of Latitudes it shews the Ark sought . The Proportion wrought , is , As the Radius to the Cotangent of the Latitude , So is the Tangent of the Declination , To the Sine of the Hour from 6. Example . So when the Sun hath 15● of North Declination , in our Latitude of London , the Hour will be found 12d 18′ from 6 in time 49⅕′ past 6 in the morning , or before it in the afternoon . Another Example to find the Time of Sun rising . As the Cotangent of the Latitude , to Radius , So is the Tangent of the Declination , To the Sine of the Hour from 6 before or after it . Lay the thred to the Complement of the Latitude in the Semicircle , and over the Declination on the Diameter , and in the Quadrant of Latitudes , it shews the time sought in degrees , to be converted into common time , by allowing 15● to an hour , and 4′ to a degree . So in the Latitude of London , 51d 32′ when the Sun hath 15● of Declination , the ascensional difference or time of rising from 6 , will be 19d 42′ , to be converted into common time , as before . By what hath been said , it appears , that the Hour and Azimuth may be found generally by help of this Circle and Diameter . For the performance whereof , we must have recourse to the Proportions delivered in page 123. whereby we may alwaies find the two Angle adjacent to the side on which the Perpendicular falleth , which may be any side at pleasure ; for after the first Proportion wholly in Tangents is wrought , to find either of those Angles , will be agreeable to the second case of right angled Spherical Triangles , wherein there will be given the Hypotenusal , and one of the Legs , to find the adjacent Angle , only it must be suggested , that when the two sides that subtend the Angle sought , are together greater then a Semicircle , recourse must be had to the Opposite Triangle , if both those Angles are required to be found by this Trigonometry , otherwise one of them , and the third Angle may be found by those directions , by letting fall the perpendicular on another side , provided the sum of the sides subtending those Angles be not also greater then a Semicircle ; or , having first found one Angle , the rest may be found by Proportions in Sines only . IN the Triangle ☉ Z P , if it were required to find the angles at Z and ☉ , because the sum of the sides ☉ P and Z P are less then a Semicircle they might be both found by making the half of the Base ☉ Z the first Tearm in the Proportion , and then because the angles ☉ Z are of a different affection , the Perpendicular would fal without on the side ☉ Z continued towards B , as would be evinced by the Proportiod , for the fourth Ark discovered , would be found greater then the half of ☉ Z ; hence we derived the Cannon in page 124 , for finding the Azimuth ; Whereby might also be found the angle of Position at ☉ ; so if it were required to find the angles at ☉ and P , the sides ☉ Z and Z P being less then a Semicircle the Perpendicular would fall within from Z on the side ☉ P , as would also be discovered by the Proportion , for the fourth Ark would be found less then the half of ☉ P. But if it were required to find both the angles at Z and P , in this Case we must resolve the Opposite Triangle Z B P , because the sum of the sides ☉ Z and ☉ P are together greater then a Semicircle , and this being the most difficult Case , we shall make our present Example . The Proportion will be , As the Tangent of half Z P , Is to the Tangent of the half sum of Z B and P B : So is the Tangent of half their difference , To a fourth Tangent . That is , As Tangent 19d 14′ , Is to the Tangent of 86d 30′ , : So is the Tangent of 9d 30′ , To a fourth . Operation . Extend the Thread through 19 d 14′ on the Semicircle , and 9 d 30′ on the Diameter , and hold it at the Intersection on the opposite side the Semicircle , then lay the Thread to 86 d 30′ in the Semicircle , and it shews 82 d 44′ on the Diameter for the fourth Ark sought . Because this Ark is greater then the half of Z P , we may conclude that the Perpendicular B A falls without on the side Z P continued to A. fourth Ark — 82d 44′ half of Z P is — 19 14 sum — 101 58 is Z A difference — 63 30 is P A Then in the right angled Triangle B P A , right angled at , A we have P A and B P the Hypotenusal , to , find the angle B P A , equal to the angle ☉ Z P. The Proportion is As the Radius , Is to the Tangent of 13d , the Complement of B P : So is the Tangent of P A 63d 30′ , To the Cosine of the angle at P. Extend the Thread through 13 d on the Diameter , and through 63 d 30′ in the Semicircle counted from the other end , and in the upper Quadrant , it shews 27 d 35′ for the Complement of the angle sought . And letting this Example be to find the Hour and Azimuth in our Latitude of London , so much is the hour from six in Winter when the Sun hath 13 d of South Declination , and 6 d of Altitude , in time 1 ho 50⅓ minutes past six in the morning , or as much before it in the afternoon . To find the Azimuth . Again , in the Triangle Z A B right angled at A , there is given the Leg or Side Z A 101 d 58′ , and the Hipotenusal Z B 96 d , to find the angle B Z P ; here noting that the Cosine or Cotangent of an Ark greater then a Quadrant is the Sine or Tangent of that Arks excess above 90 d , and the Sine or Tangent of an Ark greater then a Quadrant , the Sine or Tangent of that Arks Complement to 180 d , it will hold , As the Radius , To the Tangent of 6d : So is the Tangent 78d 2′ , To the Sine of 29 d 44′ , found by extending the Thread through 78 d 2′ on the Semicircle , counted from the other end , alias , in the small figures , and in the Quadaant it will intersect 29 d 44′ ; now by the second Case of right angled Sphoerical Triangles , the angle A Z B will be Acute , wherefore the angle ☉ Z B is 119 d 44′ the Suns Azimuth from the North , the Complement being 60 d 16′ is the angle A Z B , and so much is the Azimuth from the South . To work Proportions in Sines alone . THat this Circle might be capacitated to try any Case of Sphoerical Triangles , there are added Lines to it , namely , the Line Sol falling perpendicularly on the Diameter from the end of the Quadrant of Latitudes , whereto belongs the two Parrallel Lines of Sines in the opposite Quadrants , the upermost being extended cross the Quadrant of Latitudes . The Proportion not having the Radius ingredient , and being of the greater to the less . Account the first Tearm in the line Sol , and the second in the upper Sine extending the Thread through them , and where it intersects the opposite Parrallel hold it ; then lay the Thread to the third Tearm in the line Sol , and it will intersect the fourth Proportional on the upper Parrallel . As the Sine of 30d , To the sine of any Arch : So is the Cosine of that Arch , To the sine of the double Arch and the Converse . By trying this Canon , the use of these Lines will be suddenly attained . Example . As the sine of 30d , To the sine of 20d : So is the sine of 70d , To the sine of 40d. But if it be of the less to the greater , the answer must be found on the Line Sol. Account the first Tearm on the upper Sine , and the second in the Line Sol , and hold the Thread at the Intersection of the opposite Parrallel , then lay the Thread to the third Tearm on the uper Parrallel , and on the line Sol it will intersect the fourth Proportional if it be less then the Radius . But Proportions having the Radius ingredient , will be wrought without any Motion of the Thread . As the Cosine of the Latitude , To Radius : So is the sine of the Declination , To the sine of the Amplitude . So in our Latitude of London , when the Declination is 20d 12′ the Amplitude will be found to be 33d 42′ . Extend the Thread through 38 d 28′ on the line Sol. and through the Declination in the upper Sine , and it will intersect the opposite Parrallel Sine at 33 d 42′ , the Amplitude sought . The use of the Semi-Tangent and Chords are passed by at present . The line Sol is of use in Dyalling , as in Mr Fosters Posthuma , page 70 and 71 , where it is required to divide a Circle into 12 equal parts for the hours , and each part into 4 subdivisions for the quarters , and into such parts may the equal Semicircle be divided ; that if it were required to divide a Circle of like Radius into such parts , it might be readily done by this . Of the Line of Hours on the right edge of the foreside of the Quadrant . This is the very same Scale that is in the Diameter on the Backside , only there it was divided into degrees , and here into time , and placed on the outermost edge ; there needs no line of Latitudes be fitted thereto , for those Extents may be taken off as Chords from the Quadrant of Latitudes , by help of these Scales thus placed on the outward edges of the Quadrants may the hour-lines of Dyals be prickt down without Compasses . To Draw a Horizontal Dyal . FIrst draw the line C E , for the Hour-line of 12 , and cross it with the Perpendicular A B , then out of a Scale or Quadrant of Latitudes set of C B and C A , each equal to the Stiles height , or Latitude of the place , then place the Scale of 6 hours on the edge of the Quadrant , whereto the Line of Latitudes was fitted , one extremity of it at A , and move the Quadrant about , till the other end or extremity of it will meet with the Meridian line C E ; then in regard the said Scale of Hours stands on the very brink or outward most edge of the Quadrant , with a Pin , Pen , or the end of a black-lead pen , make marks or points upon the Paper or Dyal against each hour ( and the like for the quarters , and other lesser parts ) of the graduated Scale , and from those marks draw lines into the Center , and they shall be the hour-lines required , without drawing any other lines on the Plain , the Scale of Hours on the Quadrant is here represented by the lines A E , and E B , the hour lines above the Center , are drawn by continuing them out through the Center . And those that have Paper prints of this line , may make them serve for this purpose , without pricking down the hour points by Compasses , by doubling the paper at the very edge or extremity of the Scale of Hours . Otherwise to prick down the said Dial without the Line of Latitudes and Scale of hours in a right angled Parallellogram . Having drawn C E the Meridian line , and crossed it with the perpendicular C A B , and determining C E to be the Radius of any length , take out the Sine of the Latitude to the same Radius , and prick it from C to A and B , and setting one foot at E , with the said Extent sweep the touch of an Arch at D and F , then take the length of the Radius C E , and setting down one foot at B , sweep the touch of an Ark at D , intersecting the former , also setting down the Compasses at A , make the like Arch at F , and through the points of Intersection , draw the streight lines A F , B D , and F E D , and they will make a right angled Parallellogram , the sides whereof will be Tangent lines . To draw the Hour-lines : Make E F , or E D Radius , and proportion out the Tangents of 15d and prick them down from E to 1 and 11 and draw lines 30 and prick them down from E to 2 and 10 and draw lines through the points thus found , and through the points F and D , and there will be 3 hours drawn on each side the Meridian line . Again , make A F or B D Radius , and proportion out the Tangent of 15d , and prick it down from A to 5 , and from B to 7. Also proportion out the Tangent of 30d , and prick it down from A to 4 , and from B to 8 , and draw lines into the Center , and so the Hour-lines are finished , and for those that fall above the 6 of clock line , they are only the opposite hours continued , after the like manner are the halfs and quarters to be prickt down . Lastly , By chords prick off the Stiles height equal to the Latitude of the place , and let it be placed to its due elevation over the Meridian line . Of Vpright Decliners . DIvers Arks for such plains are to be calculated , and may be found on the Circle before described . 1. The Substiles distance from the Meridian . By the Substilar line is meant , a line over which the Stile or cock of the Dyal directly hangeth in its nearest distance from the Plain , by some termed the line of deflexion , and is the Ark of the plain between the Meridian of the Plain , and the Meridian of the place . The distance thereof from the Hour-line of 12 , is to be found by this Proportion . As the Radius , To the Sine of the Plains Declination , So the Cotangent of the Latitude , To the Tangent of the Substile from the Meridian . 2. For the Angle of 12 and 6. An Ark used when the Hour-lines are pricked down from the Meridian line in a Triangle or Parallellogram , ( and not from the Substile , ) without collecting Angles at the Pole. As the Radius , Is to the Sine of the Plains Declination , So is the Tangent of the Latitude , To the Tangent of an Ark , the Complement whereof is the Angle of 12 and 6. 3. Inclination of Meridians . Is an Ark of the Equinoctial , between the Meridian of the plain , and the Meridian of the place , or it is an Angle or space of time elapsed between the passage of the shaddow of the Stile from the Substilar line into the Meridian line , by some termed the Plains difference of Longitude ; and not improperly , for it shews in what Longitude from the Meridian where the Plain is ; the said Plain would become a Horizontal Dyal , and the Stiles height shews the Latitude , this Ark is used in calculating hour distances by the Tables and in pricking down Dyals by the Line of Latitudes , and hours from the Substile . As the Radius , Is to the Sine of the Latitude , So the Cotangent of the Plains Declination , To the Cotangent of the Inclination of Meridians . Or , As the Sine of the Latitude to Radius , So is the Tangent of the Plains Declination , To the Tangent of Inclination of Meridians . 4. The Stiles height above the Substile . As the Radius , Is to the Cosine of the Latitude , So is the Cosine of the Plains Declination , To the Sine of the Stiles height . Or the Substiles distance being known , As the Radius , To the Sine of the Substiles distance from the Meridian , So is the Cotangent of the Declination , To the Tangent of the Stiles height . Or , The Inclination of Meridians being known . As the Radius , To the Cosine of the Inclination of Meridians , So is the Cotangent of the Latitude , To the Tangent of the Stiles height . 5. Lastly , For the distances of the Hour-lines from the Substilar Line . As the Radius , Is to the Sine of the Stiles height above the Plain , So is the Tangent of the Angle at the Pole , To the Tangent of the Hours distance from the Substilar Line . By the Angle at the Pole , is meant the Ark of difference between the Ark called the Inclination of Meridians , and the distance of any hour from the Meridian , for all hours on the same side the Substile falls , and the sum of these two Arks for all hours on the other side the Substile . These Proportions are sufficient for all Plains to find the like Arks , without having any more , if the manner of referring Declining Reclining Inclining Plains to a new Latitude , and a new Declination in which they shall stand as upright Plains , be but well explained , for East or West Reclining Inclining Plains , their new Latitude is the Complement of their old Latitude , and their new Declination , is the Complement of their Reclination Inclination , which I count always from the Zenith , and upon such a supposition , taking their new Latitude and Declination , those that will try , shall find that these Proportions will calculate all the Arks necessary to such Dials . So if an Upright Plain decline 25d in our Latitude of London from the Meridian . The Substiles distance from the Meridian is — 18d 34′ The Angle of 12 and 6 is — 62 : 00 The Inclination of Meridians is — 30 : 47 The Stiles height is — 34 : 19 To Delineate the same Dial from the Substile by the Line of Latitudes , and Scale of hours in an Equicrutal Triangle . To Draw an Vpright Decliner . An Vpright South Plain for the Latitude of London , Declining 25d Eastwards . TO prick down this Dial by the line of Latitudes , and Scale of Hours in an Isoceles Triangle . Draw C 12 the Meridian Line perpendicular to the Horizontal line of the Plain , and with a line of Chords , make the Angle F C 12 , equal to the Substiles distance from the Meridian , and draw the line F C for the Substile ; Draw the line B A perpendicular thereto , and passing through the Center at C , and out of the line of Latitudes on the other Quadrants , or out of the Quadrant of Latitudes on this Quadrant , set off B C and C A each equal to the Stiles height , then fit in the Scale of 6 hours , proper to those Latitudes , so that one Extremity meeting at A , the other may meet with the Substilar line at F. Then get the difference between 30d 47′ , the inclination of Meridians , and 30d the next hours distance lesser then the said Ark , the difference is 47′ in time , 3′ nearest then fitting in the Scale of hours as was prescribed . Count upon the said Scale , Hour . Min.   0 3 from F to 10 1 3 11 2 3 12 3 3 1 4 3 2 5 3 3 And make points at the terminations with a pin or pen , & draw lines from those points into the Center at C , & they shall be the true hour-lines required on this side the Substile . Again , Fitting in the Scale of Hours from B to F , count from that end at B the former Arks of time . Ho Min   00 , 03 from B to 4 1 , 3 5 2 , 3 6 3 , 3 7 4 , 3 8 5 , 3 9 And make Points at the Terminations , through which draw Lines into the Center , and they shall be the hour Lines required on the other side the Substile . The like must be done for the halfs and quarters , getting the difference between the half hour next lesser ( in this Example 22d 30′ ) under the Ark called the inclination of Meridians , the difference is 1d 17′ in time 33′ nearest to be continually augmented an hour at a time , and so prickt off as before was done for the whole hours . By three facil Proportions , may be found the Stiles height , the Inclination of Meridians , and the Substiles distance from the Plains perpendicular , for all Plains Declining , Reclining , or Inclining , which are sufficient to prick off the Dyal after the manner here described , which must be referred to another place . If the Scale of hours reach above the Plain , as at B , so that B C cannot be pricked down , then may an Angle be prickt off with Chords on the upper side the Substile , equal to the Angle F C A , on the under side , and thereby the Scale of hours laid in its true situation , having first found the point F on the under side . To prick down the former Dyal in a Rectangular ☉ blong , or long square Figure from the Substile . Having set off the Substilar F C , assume any distance in it , as at F to be the Radius , and through the fame at right Angles , draw the line E F D , then having made F C any distance Radius , take out the Sine of the Stiles height to the same Radius , and entring it at the end of the Scale of three hours , make it the Radius of a Tangent , and proportion out Tangents to 3′ and set them off from F to 10 1 hour 3 and set them off from F to G 2 3 and set them off from F to H Again , Take out the Tangents of the Complement of the first Ark , increasing it each time by the augmentation of an hour , namely 57′ and prick them from F to I and from the points 1 ho. 57 and prick them from F to K and from the points 2 57 and prick them from F to E and from the points thus found , draw lines into the Center . Then for the other sides of the Square , make C F the Radius of the Dyalling Tangent of 3 hours , and proportion out Tangents to the former Arks , namely , 3′ and prick them from B to P Also to the latter Arks , 57′ and prick them from A to — N 1 ho. 3 and prick them from B to O Also to the latter Arks. 1 h. 57 and prick them from A to — M 2 3 and prick them from B to L Also to the latter Arks. 2 57 and prick them from A to — D and draw lines from these terminations into the Center , and the Hour-lines are finished ; after the same manner must the halfs and quarters be finished . And how this trouble in Proportioning out the Tangents may be shunned without drawing any lines on the Plain , but the hour-lines , may be spoke to hereafter , whereby this way of Dyalling , and those that follow , will be rendred more commodious . Lastly , the Stile may be prickt off with Chords , or take B C , and setting one foot in F , with that Extent sweep the touch of an occult Arch , and from C , draw a line just touching the outward extremity of the said Arch , and it shall prick off the Angle of the Stiles height above the Substile . To prick off the former Dyal in an Oblique Parallellogram , or Scalenon alias unequal sided Triangle from the Meridian . First , In an Oblique Parallellogram . DRaw CE the Meridian line and with 60d of a line of Chords , draw the prickt Arch , and therein from K , contrary to the Coast of Declination , prick off 62d , the angle of 12 and 6 , and draw the line C D for the said hour line continued on the other side the Center , and out of a line of Sines , make C E equall to 65d the Complement of the Declination ; then take out the sine of 38d 28′ the Complement of the Latitude , and enter it in the line D C , so that one foot resting at D , the other turned about , may but just touch the Meridian line , the point D being thus found , make C F equall to C D , and with the sides C F and C E make the Parallellogram D G F H , namely , F H and G D equal to C E : and E G and E H equal to D C. And where these distances ( sweeping occult arches therewith ) intersect will find the points H and G limiting the Angles of the Parallellogram . Then making E H or C D Radius , proportion out the Tangents of 15d and prick them down from E to 1 and 11 and 30 and prick them down from E to 2 and 10 and draw lines into the Center through those points , and the angular points of the Parallellogram at H and G , and there will be 6 hours drawn , besides the Meridian line or hour line of 12. Then making D G Radius , proportion out the Tangent of 15d , and prick it down from D upwards to 5 , and downward to 7 , also proportion out the tangent of 30d and prick it from D to 8 , and from F to 4 , and draw lines into the Center , and so the hour lines are finished ; after the same manner are the halfs and quarters to be proportioned out and pricked down : and if this Work is to be done upon the Plain it selfe , the Parallel F H will excur above the plain , in that case , because the Parallel distance of F H from the Meridian , is equal to the parallel distance of D G the space G. 8. may be set from H to 4 , and so all the hour lines prickt down . To prick down this Dyal in a Scalenon , or unequal sided triangle from the Meridian , from E to D draw the streight line D E , and from the same point draw another to F , and each of them ( the former hour lines being first drawn ) shall thereby be divided into a line of double tangents , or scale of 6 hours , such a one as is in the Diameter of the Circle on this quadrant , or on the right edge of the foreside ; and therefore by helpe of either of them lines , if it were required to prick down the Dyal , it might be done by Proportioning them out , take the extent D E , and prick it from one extremity of the Diameter in the Semicircle on the quadrant , and from the point of Termination draw a line with black Lead to the other extremity , ( which will easily rub out again either with bread or leather parings ) and take the nearest distance from 15 of the Diameter to the said line , and the said extents 30 of the Diameter to the said line , and the said extents 45 of the Diameter to the said line , and the said extents shall reach from , E to 11 and from D to 7 shall reach from , E to 10 and from D to 8 shall reach from , E to 9 and from D to 9 and the like must be done for the line E F , entring that in the Semicirle as before ; or without drawing lines on the quadrant , if a hole be drilled at one end of the Diameter , and a thred fitted into it , lay the thred over the point in the Diameter , and take the nearest distances thereto . Lastly , from a line of Chords , prick off the substilar line , and the stiles height as we before found it . This way of Dyalling in a Parallellogram , was first invented by John Ferrereus a Spaniard , long since , and afterwards largely handled by Clavius , who demonstrates it , and shews how to fit it into all plains whatsoever , albeit they decline , recline , or incline , without referring them to a new Latitude ; the Triangular way is also built upon the same Demonstration , and is already published by Mr Foster in his Posthuma , for it is no other then Dyalling in a Parallellogram , if the Meridian line C E be continued upwards , and C E set off upwards , and lines drawn from the point , so found to D and E , shall constitute a Parallellogram . An Advertisement about observing of Altitudes . IMagine a line drawn from the beginning of the line Sol , to the end of the Diameter , and therein suppose a pair of sights placed with a thred and bullet hanging from the begining of the said line , as from a Center ; I say the line wherein the sights are placed , makes a right angle with the line of sines on the other side of Sol , and so may represent a quadrant , the equal Limbe whereof is either represented by the 90d of the equal Semicirle , or by the 90d of the Diameter and thereby an Altitude may be taken . Now to make an Isoceles equicrural , or equal legged triangle made of three streight Rulers , the longest whereof will be the Base or Hipotenusal line ; thus to serve for a quadrant to take Altitudes withal , will be much cheaper , and more certain in Wood , then the great Arched wooden framed quadrants . Moreover , the said Diameter line supplies all the uses of the Limbe , from it may be taken off Sines , Tangents , or Secants , as was done from the Limbe ; and therein the Hour and Azimuth , found generally by helpe of the line of Sines on the left edge , as is largely shewed in the uses of this quadrant , besides its uses in Dyalling , onely when such an Instrument is made apart , it will be more convenient to have the line of Sines to be set on the right edge , and the Diameter numbred also by its Complements ; this Diameter or double Tangent , or Hipotenusal line being first divided on , all the other lines may from it , by the same Tables that serve to graduate them from the equal Limbe be likewise inscribed : and here let me put a period to the uses of this quadrant . Gloria Deo. The Description of an Universal small Pocket Quadrant . THis quadrant hath only one face . On the right edge from the Center is placed a line of sines divided into degrees and half degrees up to 60 d. afterwards into whole degrees to 80 d. On the left edge issueth a line of 10 equal parts , from the Center being precise 4 inches long , each part being divided into 10 subdivisions and each subdivision into halfs . These two lines make a right angle at the Center , and between them include a Projection of the Sphere for the Latitude of London . Above the Projection are put on in quadrants of Circles a line of Declinations 4 quadrants for the dayes of the moneth , above them the names of 5 Stars with their right Ascensions graved against them , and a general Almanack . Beneath the Projection are put on in quadrants of Circles a particular sine and secant , so called , because it is particular to the Latitude of London . Below that the quadrat , and shadowes . Below that a line of Tangents to 45 d. Last of all the equal Limbe . On the left edge is placed the Dialling scale of hours 4 Inches long , outwardmost on the right edge a line of Latitudes fitted thereto . Within the line of sines close abutting thereto is placed a small scale called the scale of entrance beginning against 52 d. 35 min. of the sines numbred to 60 d. The line of sines that issueth from the Center should for a particular use have been continued longer to wit to a secant of 28 d. because this could not be admitted , the said secant is placed outward at the end of the scale of entrance towards the Limbe , and as much of the sine as was needful placed at its due distance , at the other end of the scale of entrance . Of the uses of the said quadrant . THe Almanack hath been largely spoke to in pag. 12 , and 13 , also again in the uses of the Horizontal quadrant pag. 11 , 12. The quadrat and shadowes from pag. 35 to 44. The line of Latitudes and scale of hours pag. 250. Again , from page to 262 to 274 , also the line of sines , equal parts , and Tangents , in other parts of the Booke . The use of the Projection . THis projection is only fitted for finding the hour in the limb , and not the Azimuth , all the Circular lines on it are parallels of Altitude or Depression except the Ecliptick and Horizon , the Ecliptick , is known by the Characters of the signes , and the Horizon lyeth beneath it , being numbred with 10 , 20 , 30 , 40. The parallels of Altitude are the Winter parallels of Stofler's Astrolable , and are numbred from the Horizon upwards towards the Center , the parallels of Depression which supply the use of Stoflers Summer Altitudes are numbred downwards from the top of the Projection towards the limb . To find the time of Sun rising , and his Amplitude . LAy the thread over the day of the moneth , and set the Bead to the Ecliptick , then carry the thread and Bead to the Horizon , and the thread in the limb , shewes the time of rising , and the Bead on the Horizon the quantity of the Amplitude . Example . So on the second of August the Suns Declination being 15 d ▪ his Amplitude will be 24 d. 35 min. and the time of rising 41′ past 4 in the morning . To find the Hour of the Day . HAving taken the Suns Altitude and rectified the Bead as before shewed , if the Sun have South Declination bring the Bead to that parallel of Altitude on which the Suns height was observed , amongst those parallels that are numbred upward towards the Center , and the thread in the limb sheweth the time of the day . Eample . So when the Sun hath 15 d. of South Declination , as about 28th of January , if his Altitude be 15 deg . the time of the day will be 39 m. past 2 in the afternoon , or 21 m. past 9 in the morning . But in the Summer half year bring the Bead to lye on those parallels that are numbred downwards to the limb , and the thread sheweth therein the time of the day sought . Example . If on the second of August his Declination being 15 d. his Altitude were 40 d. the true time of the day would be 8 m. past 9 in the morning , or 52 m. past 2 in the afternoon . If the Bead will not meet with the Altitude given amongst those parallels that run donwnwards towards the right edge , then it must be brought to those parallels that lye below the Horizon downward towards the left edge , and the thread in the Limb shewes the time of the day before six in the morning or after it in the evening in Summer . Example . When the Sun hath 15 d. of North Declination as on the second of August if his Altitude be 5 d. the time of the Day will be 44 m. before 6 in the morning , or after it in the evening . Of the general lines on this quadrant . THe line of sines on the right edge is general for finding either the hour or the Azimuth in the equal limb , or in the said line of sines , as I have largely shewed in page 231 for finding the hour , also for finding the Suns Altitudes on all hours , as in page 234 , for finding the Azimuth from page 237 to pag. 2.9 . Though this quadrant hath neither secants nor versed sines as the rest have , yet both may be easily supplyed , let it be required to work this Proportion . As the Co-sine of the declination , Is to the secant of the Latitude , So is the difference of the sines of the Suns Meridian and given Altitude , To the versed sine of the hour from noon , before or after six the hour may be found from midnight by the proportions in page 230. Let the Radius of the sines be assumed to represent the secant of the Latitude , the Radius to that secant will be the cosine of the Latitude , then lay the thread to the complement of the Declination in the limb counted from right edge , and take the nearest distance to it . I say that extent shall be the cosine of the Declination to the Radius of the Secant enter this at 90 d. of the line of sines laying the thread to the other foot according to nearest distance , then in the sines take the distance between the Meridian Altitude and the given Altitude , and enter that extent so upon the sines that one foot resting thereon , the other turned about may just touch the thread the distance between the resting foot and the Center is equal to the versed sine of the ark sought and being measured from the end of the line of sines towards the Center shewes the ark sought . Example . When the Suns Declination is 15 d. North if his Altitude were 35 d. 21 m. the time of the day would be found 45 d. from noon , that is 9 in the morning or 3 in the afternoon . Of finding the Azimuth generally . THough this may be found either by the sines alone in the equal limbe as before mentioned , or by versed sines as was instanced for the hour , see also page 239 , 240 , 241 , yet where the Sun hath vertical Altitude or Depression , as in places without the Tropicks towards either of the Poles , it may be found most easily in the equal limb by the joynt help of sines and tangents by the proportions in page 175. First , find the vertical Altitude as is shewed in page 174. Then for Latitudes under 45 d. Enter in Summer Declinations the difference , but in Winter Declinations the sum , of the sines of the vertical Altitude , and of the proposed Altitude once done the line of sines from the Center , and laying the thread over the Tangent of the Latitude take the nearest distance to it , then enter that Extent at the complement of the Altitude in the Sines , and lay the thread to the other foot , and in the limb it shewes the Azimuth from the East or West . Example . For the Latitude of Rome to witt 42 d. If the Sun have 15 d. of North Declination his vertical Altitude is 22 d. 45 m. If his given Altitude ●e 40 d. the Azimuth of the Sun will be 17 d. 33 m. to the Southward of the West . If his declination were as much South and his proposed Altitude 18 d. his Azimuth would be 41 d. 10 m. to the Southwards of the East or West . For Latitudes above 45. If we assume the Rad. of the quadrant to be the tangent of the Latit . the Rad. to that Tang. shall be the co-tangent of the Latit . wherefore lay the thread to the complement of the Latitude in the line of Tangents in the limb , and from the complement of the Altitude in the Sines take the nearest distance to it , I say that extent shall be cosine of the Altitude to the lesser Radius which measure from the Center , and it finds the Point of entrance whereon enter the former Sum or difference of sines as before directed , and you will find the Azimuth in the equal limb . Or if you would find the answer in the sines , enter the first extent at 90 d. laying the thread to the other foot , then enter the Sum or difference of the Sines of the vertical and given Altitude , so between the scale and the thread , that one foot turned about may but just touch the thread , the other resting on the sines , and you will find the sine of the Azimuth sought . Example . For the Latitude of Edinburg 55 d. 56 m. If the Sun have 15 d. of Declination , his vertical Altitude or depression is 18 d. 14 m. the Declination being North , if his proposed Altitude were 35 d. the Azimuth of the Sun would be 28 d. to the South-wards of the East or West . But if the Declination were as much South , and the Altitude 10 d. the Azimuth thereto would be 46 d. 58 m. to the South-wards of the East or West . The first Operation also works a Proportion to witt . As the Radius Is to the cotangent of the Latitude . So is the cosine of the Altitude , To a fourth sine . I say this 4th sine beares such Proportion to the Radius as the cosine of the Altitude doth to the tangent of the Latitude , for the 4th term of every direct Proportion beares such Proportion to the first terms thereof , as the Rectangle of the two middle terms doth to the square of the first term . But as the rectangle of the co-tangent of the Latitude and of the cosine of the Altitude is to the square of the Radius , So is the cosine of the Altitude is to the tangent of the Latitude , or which is all one , So is the co-tangent of the Latitude , To the secant of the Altitude , as may be found by a common division of the rectangle , and square of the Radius by either of the terms of the said rectangle , by help of which notion I first found out the particular scales upon this quadrant . All Proportions in sines and Tangents may be resolved by the sine of 90 d. and the Tangent of 45 d. on this quadrant if what hath been now wrote , and the varying of Proportions be understood , as in page 72 to 74 it is delivered . Because the Projection is not fitted for finding the Azimuth there are added two particular scales to this quadrant , namely , the particular sine in the limb , and the scale of entrance abutting on the sines fitted for the Latitude of London . Lay the thread to the day of the moneth , and it shewes the Suns Declination in the scales proper thereto . Then count the Declination in the Limbe laying the thread thereto , and in the particular sine , it shewes the Suns Altitude or Depression being East or West . To find the Suns Azimuth . FOr North Declinations take the distance between the sines of the vertical Altitude and given Altitude , but for South Declinations adde with your compass the sine of the given Altitude to the sine of the vertical Altitude , enter the extent thus found , at the Altitude in the scale of entrance laying the thread to the other foot according to nearest distance , and in the equal limb it shewes the Azimuth sought from the East or West , or it may be found in the sines by laying the thread to that arch in the limb that the Altitude in the scale of entrance stands against in the sines , and entring the former extent paralelly between the thread and the sines . Example . So when the Sun hath 13 d. of Declination his vertical Altitude or Depression is 16 d. 42 m. If the Declination were North and his Altitude 8 d. 41 m. his Azimuth would be 10 d. to the North-wards of the East or West . But if it were South and his Altitude 12 d. 13 m. the Azimuth would be 40d to the South-wards of the East or West . By the same particular scales the hour may be also found . To find the time of Sun rising or setting . TAke the sine of the Declination , and enter it at the Declination in the Scale of entrance and it shewes the time sought in the equal lim●e from six . Example . When the hath 10 d. of Declination the Ascensional difference is 49 m. which added to , or substracted from six shewes the time of rising and setting . To find the hour of the day for South Declination . IN taking the Altitude , mind what Ark in the particular Sine the thread cut , adde the Sine of that Ark to the Sine of the Declination , and enter that extent at the Declination in the Scale of entrance laying the thread to the other foot according to nearest distance , and in the equal limb it shewes the hour from six . So if the Declination were 13 d. South and the Suns Altitude 14 d. 38 m. the thread in the particular Sine would cut 18 d. 49 m. and true time of the day would be 9 in the morning or 3 in the morning . To find the time of the day for North Declination . HAving observed what Ark the thread in taking the Altitude hung over in the Particular Sine take the distance between the Sine of the said Arke , and the Sine of the Declination and entring that extent at the Declination in the Scale of entrance the thread in the limbe shewes the hour from six . Example . If the Suns Declination were 23 d. 31 m. North , and his Altitude 39 d. the Arch in the particular Sine would be 53 d. 32 m. and the time of the day would be about 3 quarters past 3 in the afternoon , or a quarter past 8 in the morning . When the Altitude is more then the Latitude the thread will hang over a Secant in the particular Scale , this happens not till the Sun have more then 13 d. of North Declination , in this case take the distance between the Secant before the beginning of the Scale of entrance , and the Sine of the Declination at the end of the same and enter it as before . Example . The Suns declination being 23 d. 31 m. North if his Altitude were 55 d. 29 m. the thread in the particular Scale would hang over the Secant of 18 d. 11 m. and the true time of the day would be a quarter past 10 in the morning , or 3 quarters past 1 in the afternoon . The Proportions here used are expressed in Page 193. The Stars hour is to be found by the projection by rectifying the Bead to the Sar and then proceed as in finding the Suns hour , afterwards the ●ue time of the night is to be found as in page 32. ERRATA . In the Treatise of the Horizontal quadrant , pag. 43 line 6 for the 3 January read the 30th . In the Reflex Dialling pag. 5 , adde to the last line these words , As Kircher sheweth in his Ars Anaclastica . FINIS . THE DESCRIPTION AND USES OF A GENERAL QUADRANT , WITH THE HORIZONTAL PROJECTION , UPON IT INVERTED . Written and Published By JOHN COLLINS Accountant , and Student in the Mathematicks . LONDON , Printed Anno M. DC . LVIII . The Description OF THE HORIZONTAL QUADRANT . THis Denomination is attributed to it because it is derived from the Horizontal projection inverted . Of the Fore-side . On the right edge is a Line of natural Sines . On the left edge a Line of Versed-Sines . Both these Lines issue from the Center where they concurre and make a right Angle , and between them and the Circular Lines in the Limb is the Projection included , which consists of divers portions and Arkes of Circles . Of the Parallels of Declination . THese are portions of Circles that crosse the quadrant obliquely from the left edge , towards the right . To describe them . OBserve that the left edge of the quadrant is called the Meriridian Line , and that every Degree or Parallel of the Suns Declination if continued about would crosse the Meridian in two opposite points , the one below the Center towards the Limbe , and the other above , and beyond the Center of the quadrant , the distance between these two points is the Diameter of the said Parallel , and the Semidiameters would be the Center points . It will be necessary in the first place , to limit the outwardmost Parallel of Declination , which may be done in the Meridian Line at any point assumed . The distance of this assumed point from the Center in any Latitude , must represent the Tangent of a compound Arke , made by adding halfe the greatest Meridian Altitude to 45 Deg. which for London must be the Tangent of 76 Degr. And to the Radius of this Tangent must the following work be fitted . In like manner , the Semidiameters of all other Parallels that fall below the Center , are limited by pricking downe the Tangents of Arkes , framed by adding halfe the Meridian Altitude suitable to each Declination continually to 45 Degr. Now to limit the Semidiameters above or beyond the Center onely prick off the respective Tangents of half the Suns mid-night Depression from the Center the other way , retaining the former Radius , by this meanes there will be found two respective points limiting the Diameters of each Parallel , which had , the Centers will be easily found falling in the middle of each Diameter . But to doe this Arithmetically , first , find the Arke compounded of halfe the Suns meridian Altitude , and 45 Degr. as before , and to the Tangent thereof , adde the Tangent of halfe the Suns mid-night depression , observing that the Suns mid-night depression in Winter-Summer , is equal to his Meridian Altitude in Summer-Winter , his declination being alike in quantity , though in different Hemispheres , the halfe summe of these two Tangents are the respective Semidiameters sought , and being prickt in the meridian line either way from the former points limiting the Diameters , will find the Centers . Or without limiting those Points for the Diameters : first , get the Difference between the Tangents of those Arkes that limit them on either side , and the halfe summe above-said , the said difference prickt from the Center of the quadrant in the meridian line finds the respective Centers of those Parallels , the said halfe summes being the respective Semidiameters wherewith they are to be described . Of the Line or Index of Altitudes . THis is no other then a single prickt line standing next the Meridian line , or left edge of the quadrant , to which the Bead must be continually rectified , when either the houre or Azimuth is found by help of the projection . To graduate it . ADde halfe the Altitudes respectively whereto the Index is to be fitted to 45 Degr. and prick downe the Tangents of these compound arkes from the Center . Example . To graduate the Index for 40 Degr. of Altitude , the halfe thereof is 20 , which added to 45 Degr. makes 65 Degr. which taken from a Tangent to the former Radius , and prickt from the Center , gives the point where the Index is to be graduated with 40 Degrees . Hence it is evident that where the divisions of the Index begin marked ( 0 ) the distance of that point from the Center is equal to the common Radius of the Tangents . Because this quadrant ( as all natural projections ) hath a reverted taile , the graduations of the Index are continued above the Hozontal point ( 0 ) towards the Center to 30 Degr. 40′ as much as is the Sunnes greatest Vertical Altitude in this Latitude , and the graduations of the Index are set off from the Center by pricking downe the Tangents of the arkes of difference between half the proposed Altitude , and 45 Deg. thus to graduate 20 deg . of the Index the halfe thereof is 10 Degrees , which taken from 45 Degrees , the residue is 35 Degrees , the Tangent thereof prickt from the Center gives the point where the Index is to be graduated with 20 Degrees . Of the houre Circles . THese are knowne by the numbers set to them by crossing the Parallels of Declination , and by issuing from the upper part of the quadrant towards the Limbe . To describe them . LEt it be noted that they all meet in a point in the Meridian Line below the Center of the quadrant : the distance whereof from the Center is equal to the Tangent of halfe the Complement of the Latitude taken out of the common Radius , which at London will be the Tangent of 19 Deg. 14′ . The former point which may be called the Pole-point , limits their Semidiameters , to find the Centers prick off the Tangent of the Latitude and through the termination raise a line Perpendicular to the Meridian line , the distance from the Pole-point being equal to the Secant of the Latitude , must be made Radius . And the Tangents of 15 Degrees , 30 Degrees &c. prickt off on the former raised line , gives the respective Centers of the houre Circles , the distances whereof from the Pole point are the Semidiameters wherewith those houre Circles are to be drawne . Of the reverted Tail. THis needs no Rule to describe it , being made by the continuing of the parallels of Declination to the right edge of the quadrant and the houre Circles up to the Winter Tropick or parallel of Declination neerest the Center , however the quantity of it may be knowne by setting one foot of a paire of Compasses in the Center of the quadrant , and the other extend to 00 Degrees of Altitude in the Index ; an Arch with that extent swept over the quadrant as much as it cuts off will be the Reverted Taile , and so much would be the Radius . Of a Quadrant made , of this Projection not inverted . BY what hath been said it will be evident to the judicious that this inversion is no other then the continance of the extents of one quarter of the Horizontal projection . Which otherwise could not with convenience be brought upon a quadrant . Hence it may be observed that . Having assigned the Radius , a quadrant made of the Horizontal Projection without inversion , to know how big a Radius it will require when inverted the proportion will hold . AS the Radius , is to the distance of the intersection of the Aequinoctial point with the Horizon from the Center equall to the Radius of the said Projection when not inverted , in any common measure . So is the Tangent of an Arke compounded of 45 Degrees , and of half the Suns greatest Meridian Altitude . To the distance between the Center and the out-ward Tropick next the Limbe in the said known measure when inverted , whence it followes that between the Tropicks this projection cannot be inverted , but the reverted taile will be but small , and may be drawne with convenience without inversion . Of the Curved Line and Scales belonging to it . BEyond the middle of the Projection stands a Curved or bending Line , numbred from the O or cypher both wayes , one way to 60 Degrees , but divided to 62 Degrees , the other way to 20 Degr. but divided to 23 Deg. 30′ . The Invention of this Line ownes Mr. Dary for the Author thereof , the Use of it being to find the houre or Azimuth in that particular latitude whereto it is fitted by the extension of a threed over it , and the lines belonging to it . The lines belonging to it are two , the one a Line of Altitudes , and Declinations standing on the left edge of the quadrant , being no other but a line of Sines continued both wayes , from the beginning one way to 62 Degrees , the other way to 23. Degrees 30′ . The other line thereto belonging is 130 Deg. of a line of Versed Sines , which stands next without the Projection being parallel to the left edge of the quadrant . To dravv the Curve . DRaw two lines of Versed Sines , it matters not whether of the same Radius or no , nor how posited ; provided they be parallel , let each of them be numbred as a Sine both ways , from the middle at ( 0 ) and so each of them will containe two lines of Sines , to the right end of the uppermost set C , to the left end D , and to the right end of the undermost set A , and to the left end B. First , Note that there is a certaine point in the Curve where the Graduations will begin both upwards and downwards , this is called the Aequinoctial point ; to find it , lay a ruler from A to the Complement of the Latitude counted from ( 0 ) in the upper Scale towards D , and draw a line from A to it , then count it the other way towards C , viz. 38 Degrees 28′ . for the Co-latitude of London , and lay a ruler over it , and the point B , and where it intersects the line before drawn , is the Aequinoctial point to be graduated . Then to graduate the Division on each side of it , requires onely the making in effect of a Table of Meridian altitudes to every degree of Declination ( which because the Curve will also serve for the Azimuth in which case the graduations of the Curve , which in finding the houre were accounted Declinations must be accounted Altitudes ) must be continued to 62 Degrees for this Latitude , and further also if it be intended that the Curve shall find a Stars houre that hath more declination . To make this Table . GEt the Summe and difference of the Complement of the latitude and of the Degrees intended to be graduated , and if the summe exceed 90 Degrees , take its complement to 180 degrees instead of it : being thus prepared the Curve will be readily made . To graduate the under part of the Curve . Account the summe in the upper line from O towards D , and from the point A in the under line draw a line to it . Account the difference in the upper lfne when the degree proposed to be graduated is lesse then the complement of the Latitude from O towards C : but when it is more towards D , and from the point B lay a Ruler over it , and where the Ruler intersects , the line formerly drawn is the point where the degree proposed is to be graduated . Example . Let it be required to find the point where 60 deg . of the Curve is to be graduated . Arke proposed 60 deg . Co-latitude 38 : 28   98 : 28 Summe 81 : 32 Difference 21   32 Count 81 deg . 32′ in the upper line from O towards D , and from the point A draw a line to it . Count the difference 21 degrees 32′ from O towards D , because the co-latitude is lesse then the arke proposed , and lay a Ruler over it , and the point B , and where it intersects the former line is the point where 60 deg . of the Curve is to be graduated on the lower side . Another Example . Let it be proposed to graduate the same way , The arke of 30 degr . 30 degr . Co-latitude 38 : 28 Summe 68 : 28 Difference 8 : 28 Count 68 deg . 28′ from O towards D , and from the point A draw a line to it . Again in the said upper line , count 8 deg . 28′ upwards from O towards C , & from the point B lay a ruler over it , & where it intersects the line last drawn is the point where 30 d. of the curve is to be graduated . To graduate the upper part of the curve requires no other directions , the same arkes serve , if the account be but made the other way , and in accounting the summe the ruler laid over B. in the lower line instead of A , and in counting the difference over A , instead of B , neither is there any Scheme given hereof , the Practitioner need onely let the upper line be the line of altitudes on the left edge of the quadrant continued out to 90 deg . at each end , and to that end next the Center set C , and to the other end D. So likewise let that end of the Versed Scale next the right edge of the quadrant be continued to 180 deg . whereto set A , and at the other end B , and then if these directions be observed , and the same distance and position of the lines retained , it will not be difficult to constitute a Curve in all respects agreeing with that on the fore-side of the quadrant . Of the houre and Azimuth Scale on the right edge of the Quadrant . THis Scale stands outwardmost on the right edge of the quadrant , and consists of two lines , the one a line of 90 sines made equal to the cosine of the Latitude , namely , to the sine of 38 deg . 28′ , and continued the other way to 40 deg . like a Versed sine . The annexed line being the other part of this Scale , is a line of natural Tangents beginning where the former sine began , the Tangent of 38 deg . 28′ being made equal to the sine of 90 deg . this Tangent is continued each way with the sine ; towards the Limbe of the quadrant it should have been continued to 62 deg . but that could not be without excursion , wherefore it is broken off at 40 degrees , and the residue of it graduated below , and next under the Versed sine belonging to the Curve that runnes crosse the quadrant being continued but to halfe the former Radius . Of the Almanack . NExt below the former line stands the Almanack in a regular ob-long with moneths names graved on each side of it . Below the Almanack stands the quadrat● , and shadowes in two Arkes of circles terminating against 45 deg . of the Limbe , below them a line of 90 sines in a Circle equal to 51 deg . 32′ of the Limbe broken off below the streight line , and the rest continued above it . Below these are put on in Circles a line of Tangents to 60 degrees . Also a line of Secants to 60 deg . with a line of lesser sines ending against 30 deg . of the Limbe ( counted from the right edge ) where the graduations of the Secant begins . Last of all the equal Limbe . Prickt with the pricks of the quadrat . Abutting upon the line of sines , and within the Projection stands a portion of a small sine numbred with its Complements beginning against 38 deg . 28′ of the line of sines , this Scale is called the Scale of entrance . Upon the Projection are placed divers Stars , how they are inscribed shall be afterwards shewne . The description of the Back-side . Put on in quarters or Quadrants of Circles . 1 THe equal Limbe divided into degrees , as also into houres and halves , and the quarters prickt to serve for a Nocturnal . 2 A line of Equal parts . 3 A line of Superficies or Squares . 4 A line of Solids or Cubes . 5 A Tangent of 45 degrees double divided to serve for a Dyalling Tangent , and a Semitangent for projections . 6 The line Sol , aliàs a line of Proportional Sines . 7 A Tangent of 51 degrees 32′ through the whole Limbe . 8 A line of Declinations for the Sun to 23 deg . 31′ . Foure quadrants with the days of the Moneth . 9 10 11 12 13 The Suns true place , with the Charecters of the 12 Seignes . 14 The line of Segments , with a Chord before they begin . 15 The line of Metals and Equated bodies . 16 The line of Quadrature . 17 The line of Inscribed bodies . 18 A line of 12 houres of Ascension with Stars names , Declinations , and Ascensional differences . Above all these a Table to know the Epact , and what day of the Weeke , the first day of March , hapned upon , by Inspection continued to the yeare 1700. All these between the Limbe and the Center . ON the right edge a line of equal parts from the Center decimally sub-divided , being a line of 10 inches ; also a Dyalling Tangent or Scale of 6 houres , the whole length of the quadrant not issuing from the Center . On the left edge a Tangent of 63 deg . 26′ from the Center . Also a Scale of Latitudes fitted to the former Scale of houres not issuing from the Center , and below it a small Chord . The Vses of the Quadrant . Lords-day 1657 63 68 74 ☉ 85 91 96 anno 25 1 26 3   4 11 6 epact Monday 58 ☽ 69 75 80 86 ☽ 97 anno 6   7 14 9 15   17 epact Tuesday 59 64 70 ♂ 81 87 92 98 anno 17 12 18   20 26 22 28 epact Wenesday ☿ 65 71 76 82 ☿ 93 99 anno   23 29 25 1   3 9 epact Thursday 60 66 ♃ 77 83 88 94 ♃ anno 28 4   6 12 7 14   epact Friday 61 67 72 78 ♀ 89 95 700 anno 9 15 11 17   18 25 20 epact Saturday 62 ♄ 73 79 84 90 ♄ 701 anno 20   22 28 23 29   1 epact Dayes the same as the first of March. March 1 8 15 22 29 November August 2 9 16 23 30 August May 3 10 17 24 31 Jnuary October 4 11 18 25 0 October April 5 12 19 26 00 July Septem . 6 13 20 27 00 December June 7 14 21 28 00 February Perpetual Almanack . Of the Vses of the Projection . BEfore this Projection can be used , the Suns declination is required , & by consequence the day of the moneth for the ready finding thereof there is repeated the same table that stands on the Back-side of this quadrant in each ruled space , the uppermost figure signifies the yeare of the Lord , and the column it is placed in sheweth upon what day of the Weeke the first day of March hapned upon in that yeare , and the undermost figure in the said ruled space sheweth what was the Epact for that yeare and this continued to the yeare 1701 inclusive . Example . Looking for the yeare 1660 I find the figure 60 standing in Thursday Column , whence I may conclude that the first day of March that yeare will be Thursday , and under it stands 28 for the Epact that yeare . Of the Almanack . HAving as before found what day of the Weeke the first day of March hapned upon , repaire to the Moneth you are in , and those figures that stand against it shewes you what dayes of the said moneth the Weeke day shall be , the same as it was the first day of March. Example For the yeare 1660 , having found that the first day of March hapned upon a Thursday , looke into the column against June , and February , you will find that the 7th , 14th , 21th and 28th dayes of those Moneths were Thursdayes , whence it might be concluded if need were that the quarter day or 24th day of June that yeare hapneth on the Lords day . Of the Epact . THe Epact is a number carried on in account from yeare to yeare towards a new change , and is 11 dayes , and some odde time besides , caused by reason of the Moons motion , which changeth 12 times in a yeare Solar , and runnes also this 11 dayes more towards a new change , the use of it serves to find the Moones age , and thereby the time of high Water . To know the Moons age . ADde to the day of the Moneth the Epact , and so many days more , as are moneths from March to the moneth you are in , including both moneths , the summe ( if lesse then 30 ) is the Moones age , if more , subtract 30 ; and the residue in the Moons age ( prope verum . ) Example . The Epact for the year 1658 is 6 , and let it be required to know the Moons age the 28 of July , being the fift moneth from March both inclusive 6 28 5 The summe of these three numbers is 39 Whence rejecting 30 , the remainder is 9 for the Moons age sought . The former Rule serves when the Moneth hath 31 dayes , but if the Moneth hath but 30 Dayes or lesse , take away but 29 and the residue is her ages To find the time of the Moones comming to South . MUltiply the Moones age by 4 , and divide by 5 , the quotient shewes it , every Unit that remaines is in value twelve minutes of time , and because when the Moon is at the full , or 15 dayes , old shee comes to South at the houre of 12 at midnight , for ease in multiplication and Division when her age exceedes 15 dayes reject 15 from it . Example , So when the Moon is 8 dayes old , she comes to South at 24 minutes past six of the clock , which being knowne , her rising or setting may be rudely guessed at to be six houres more or lesse before her being South , and her setting as much after , but in regard of the varying of her declination no general certaine rule for the memory can be given . Here it may be noted that the first 15 dayes of the Moones age she commeth to the Meridian after the Sun , being to the Eastward of him , and the later 15 dayes , she comes to the Meridian before the Sun , being to the Westward of him . To find the time of high Water . TO the time of the Moones comming to South , adde the time of high water on the change day , proper to the place to which the question is suited , the summe shewes the time of high waters For Example , There is added in a Table of the time of high Water at London , which any one may cast up by memory according to these Rules , it is to be noted , that Spring Tides , high winds , and the Moon in her quarters causes some variation from the time here expressed . Moones age Moon South Tide London Dayes . Ho. mi. Ho. Mi 0 15 12 — 3 00 1 16 12 : 48 3 : 48 2 17 1 : 36 4 : 36 3 18 2 : 24 5 : 24 4 19 3 : 12 6 : 12 5 20 4   7 00 6 21 4 : 48 7 : 48 7 22 5 : 36 8 : 36 8 23 6 : 24 9 : 24 9 24 7 : 12 10 : 12 10 25 8 : 00 11 : 00 11 26 8 : 48 11 : 48 12 27 9 : 36 12 : 36 13 28 10 : 24 1 : 24 14 29 11 : 12 2 : 12 This Rule may in some measure satisfie and serve for vulgar use for such as have occasion to go by water , and but that there was spare roome to grave on the Epacts nothing at all should have been said thereof . A Table shewing the houres and Minutes to be added to the time of the Moons comming to South for the places following being the time of high Water on the change day .   H. m. Quinborough , Southampton , Portsmouth , Isle of Wight , Beachie , the Spits , Kentish Knocke , half tide at Dunkirke . 00 :  00 Rochester , Maulden , Aberdeen , Redban , West end of the Nowre , Black taile . 00 :  45 Gravesend , Downes , Rumney , Silly half tide , Blackness , Ramkins , Semhead . 1 :  30 Dundee , St. Andrewes , Lixborne , St. Lucas , Bel Isle ; Holy Isle . 2 :  15 London , Tinmouth , Hartlepoole , Whitby , Amsterdam , Gascoigne , Brittaine , Galizia . 3 :  00 Barwick , Flamborough head , Bridlington bay , Ostend , Flushing , Bourdeaux , Fountnesse . 3 :  45 Scarborough quarter tide , Lawrenas , Mountsbay , Severne , King sale , Corke-haven , Baltamoor , Dungarvan , Calice , Creeke , Bloy seven Isles . 4 :  30 Falmouth , Foy , Humber , Moonles , New-castle , Dartmouth , Torbay , Caldy Garnesey , St. Mallowes , Abrowrath , Lizard . 5 :  15 Plymouth , Weymouth , Hull , Lin , Lundy , Antwerpe , Holmes of Bristol , St. Davids head , Concalo , Saint Malo. 6 :  00 Bristol , foulnes at the Start. 6 :  45 Milford , Bridg-water , Exwater , Lands end , Waterford , Cape cleer , Abermorick Texel . 7 :  20 Portland , Peterperpont , Harflew , Hague , St. Magnus Sound , Dublin , Lambay , Mackuels Castle . 8 :  15 Poole , S. Helen , Man Isle , Catnes , Orkney , Faire Isles , Dunbar , Kildien , Basse Islands , the Casquers , Deepe at halfe tide . 9 :   Needles , Oxford , Laysto , South and North Fore-lands . 9 :  45 Yarmouth , Dover , Harwich , in the frith Bullen , Saint John de luce , Calice road . 10 :  30 Rye , Winchelsea , Gorend , Rivers mouth of Thames , Faire Isle Rhodes . 11 :  15 To find the Epact for ever . IN Order hereto , first , find out the Prime Number divide the yeare of the Lord by 19 the residue after the Division is finished being augmented by an Unit is the Prime sought , and if nothing remaine the Prime is an Unit. To find the Epact . MUltiply the Prime by 11 , the product is the Epact sought if lesse then 30 , but if it be more , the residue of the Product divided by 30 is the Epact sought , there note that the Prime changeth the first of January , and the Epact the first of March. Otherwise . Having once obtained the Epact adde 11 so it the Summe if lesse then 30 is the Epact for the next yeare if more reject 30 , and the residue is the Epact sought . Caution . When the Epact is found to be 29 for any yeare , the next yeare following it will be 11 and not 10 , as the Rule would suggest . A Table of the Epacts belonging to the respective Primes . Pr. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Ep. 11 22 3 14 25 6 17 28 9 20 1 12 23 4 15 26 7 18 29 The Prime number called the Golden Number , is the number of 19 years in which space the Moone makes all variety of her changes , as if she change on a certain day of the month on a certain yeare she shall not change the same day of the moneth again till 19 yeares after : and then it doth not happen upon the same houre of the day , yet the difference doth not cause one dayes variation in 300 yeares , as is observed by Mr. Philips . The Vses of the Quadrant . WIthout rectifying the Bead nothing can be performed by this Projection , except finding the Suns Meridian Altitude being shewn upon the Index , by the intersection of the Parallel of declination therewith . Also the time when the Sun will be due East or West . TRace the Parallel of Declination to the right edge of the Projection , and the houre it there intersects ( in most cases to be duly estimated ) shewes the time sought , thus when the Sun hath 21 deg . of North declination , we shall find that he will be due East or West , about three quarters of an houre past 4 in the afternoon , or a quarter past 7 in the morning . The declination is to be found on the Back-side of the quadrant by laying the thread over the day of the moneth . To rectifie the Bead. LAy the thread upon the graduated Index , and set the Bead to the observed or given Altitude , and when the Altitude is nothing or when the Sun is in the Horizon set the Bead to the Cypher on the graduated Index , which afterwards being carried without stretching to the parallel of Declination the threed in the Limbe shewes the Amplitude or Azimuth , and the Bead amongst the houres shewes the true time of the day . Example . Upon the 24th of April the Suns declination will be found to 16 deg . North. Now to find his Amplitude and the time of his rising , laying the threed over the graduated Index , set the Bead to the beginning of the graduations of the Index , and bring it without stretching to the parallel of declination above being 16 d ▪ and the threed in the limbe will lye over 26 deg . 18′ for the Suns Amplitude or Coast of rising to the Northward of the East , and the Bead amongst the houres sheweth 24 minutes past 4 for the time of Sun rising . Which doubled gives the length of the night 8 houres 49 min. In like manner the time of setting doubled gives the length of the day . The same to find the houre and Azimuth let the given Altitude be 45 degrees . HAving rectified the Bead to the said Altitude on the Index and brought it to the intersect , the parallel of declination the thread lyes over 50 degrees 48′ . For the Suns Azimuth from the South . And the Bead among the houres shewes the time of the day to be 41 minutes past 9 in the morning , or 19 minutes past two in the afternoon . Another Example wherein the operation will be upon the Reverted taile . Let the altitude be 3 deg . 30′ And the declination 16 deg . North as before . TO know when to rectify the Bead to the upper or neather Altitude will be no matter of difficulty , for if the Bead being set to the neather Altitude will not meet with the parallel of declination , then set it to the upper Altitude , and it will meet with Winter parallel of like declination , which in this case supplyes the turn . So in this Example , the Bead being set to the upper Altitude of 3 deg . 30′ and carried to the Winter parallel of declination . The thread in the Limbe will fall upon 68 deg . 28′ for the Suns Azimuth from the North , and the Bead among the houres shewes the time of the day to be either 5 in the morning or 7 at night . Another Example . Admit the Sun have 20 degr . of North Declination ( as about the 9th of May ) and his observed altitude were 56 deg . 20′ having rectified the Bead thereto , and brought it to intersect the parallel of 20 deg . among the houres it shewes the time of the day to be 11 in the morning or 1 in the afternoon , and the Azimuth of the Sun to be 26 deg . from the South The Vses of the Projection . TO find the Suns Altitude on all houres or Azimuths will be but the converse of what is already said , therefore one Example shall serve . When the Sun hath 45 deg . of Azimuth from the South . And his Declination 13 deg . Northwards . Lay the threed over 45 deg . in the Limbe , and where the threed intersects the Parallel of Declination thereto remove the Bead which carried to the Index without stretching , shewes 43 deg . 50′ for the Altitude sought . Likewise to the same Declination if it were required to find the Suns Altitude for the houres of 2 or 10. Lay the threed over the intersection of the houre proposed with the parallel of Declination , and thereto set the bead which carried to the Index shewes the Altitude sought namely 44 deg . 31′ . The same Altitude also belongs to that Azimuth the threed in the former Position lay over in the Limbe . This Projection is of worst performance early in the morning or late in the evening , about which time Mr. Daries Curve is of best performance whereto we now addresse our selves . Of the curved line and Scales thereto fitted . This as we have said before was the ingenious invention of M. Michael Dary derived from the proportionalty of two like equiangled plain Triangles accommodated to the latitude of London , for the ready working of these two Proportions . 1. For the Houre . As the Cosine of the Latitude , is to the secant of the Declination , So is the difference between the sine of the Suns proposed and Meridian Altitude . To the versed sine of the houre from noone , and the converse , and so is the sine of the Suns Meridian Altitude , to the versed sine of the semidiurnal Arke . 2. For the Azimuth . The Curve is fitted to find it from the South and not from the North , and the Proportion wrought upon it will be . As the cosine of the Latitude , is to the Secant of the Altitude . So is the difference of the versed sines of the Suns ( or Stars ) distance from the elevated Pole , and of the summe of the Complements both of the Latitude and Altitude , to the versed sine of the Azimuth from the noon Meridian . Which will not hold backward to find the Altitude on all Azimuths , because the altitude is a term involved , both in the second and third termes of the former proportion . If the third terme of the former Proportion had not been a difference of Sines , or Versed sines , the Curved line would have been a straight-line , and the third term always counted from one point , which though in the use it may seem to be so here , yet in effect the third term for the houre is always counted from the Meridian altitude . Here observe that the threed lying over 12 or the end of the Versed Scale , and over the Suns meridian altitude in the line of altitudes , it will also upon the curve shew the Suns declination , which by construction is so framed that if the distance from that point to the meridian altitude , be made the cosine of Latitude , the distance of the said point from the end of the versed Scale numbred with 12 shall be the secant of the declination to the same Radius , being both in one straight-line by the former constitution of the threed , and instead of the threed you may imagine a line drawn over the quadrant , then by placing the threed as hereafter directed it will with this line & the fitted scales constitute two equiangled plaine triangles , upon which basis the whole work is built . In the three first Proportions following relating to time , the Altitude must alwayes be counted upwards from O in the line of Altitude , and the Declination in the Curve upwards in Summer , downwards in Winter . 1 To find the time of the Suns rising and setting by the Curve . WE have before intimated that the suns Declination is to be found on the back of the quadrant , having found it , lay one part of the thread over 0 deg . in the Line of Altitude , and extending it , lay the other part of it over the Suns Declination counted from O in the Curve , and the thread upon the Versed scale shewes the time of Suns rising and setting , which being as much from six towards noon in Winter as towards mid-night in Summer , the quantity of Declination supposed alike both wayes on each side the Equinoctial , the thread may be layd either way from O in the Curve to the Declination . Example . When the Sun hath 20 deg . of Declination , the thread being laid over 20 deg . in the Curve and O in the Altitude on the left edge shewes that the Sun riseth setteth 1 houre 49′ before after six in the Summer and riseth setteth as much after before six in the Winter . 2 The Altitude and Declination of the Sun being given to find the houre of the day . COunt the Altitude from O in the Scale of Altitudes towards the Center , and thereto lay the thread , then count the Declination from O in the Curve , if North upwards towards the Center , if South downwards towards the Limbe . And lay the thread extended over it , and in the Versed Scale it shewes the time of the day sought . Example . The Altitude being 24 d. 46′ and the Declination 20 d. North counting that upwards in the Scale of Altitudes , and this upward in the curve , and extending the through thread , it will intersect the Versed Scale at 7 and 5 , shewing the houre to be either 7 in the morning , or 5 in the afternoon . Another Example for finding when twliight begins . Let the Suns Declination be 13 deg . North , the Depression supposed 18 degr . under the Horizon . In stead of the case propounded , suppose the Sun to have 13 deg . of South Declination , and Altitude 18 deg . above the Horizon accordingly extending the thread through 18 in the Altitudes counted upward from O in the line of Altitudes and through 13 deg . counted downward in the Curve from O , and upon the Versed Scale , the thread will shew that the Twilight begins at 28 minutes past 2 in the morning , and at 32 min. past 9 at night . 3 The Converse of the last Proposition is to find the Suns altitudes on all houres . EXtend the thread over the houre proposed in the versed Scale and also over the Declination in the Curve counted upward if North , downward if South . And in the Scale of Altitudes it shewes the Altitude sought . Example . If the Sun have 13 deg . of North Declination his Altitude for the houre of 7 in the morning , or 5 in the after-noon will be found to be 19 deg . 27′ . In the following Propositions the altitude must alwayes be counted from O in the Curve downwards , and the Declination in the line of altitudes , if North downward , if South upwards . 4 To find the Suns Amplitude or coast of rising and setting . Example . If the Sun had 20 deg . of Declination the thread being laid to O in the Curve , and to 20 in the line of altitudes or Declinations , either upwards or downwards the thread will lye 33 deg . 21′ from 90 in the Versed Scale , for the quantity of the Suns Coast of rising or setting from the true East or West in Winter Southward , in Summer Norhward . 5 The Suns altitude and Declination being proposed to find his Azimuth . COunt the altitude from O in the Curve downward , and the declination in the Winter upon the line of Declinations from O upwards , in Summer downwards , and the thread extended sheweth the Azimuth sought , on the Versed Scale . Example . So when the Sun hath 18 deg . 37′ of North Declination , as as about 19 July , if his altitude were 39 deg . the Suns Azimuth would be found to be 69 deg . from the South . 6 The Converse of the former Proposition will be to find the Suns Altitude on all Azimuths . THe Instrument will perform this Proposition though the Porportion for finding the Azimuth cannot be inverted . Lay the thread to the azimuth in the Versed Scale , and to the Declination in the Scale on the left edge , and upon the Curve it will intersect the altitude sought . Example . If the Sun had 16 deg . 13′ of South Declination , as about the 27th of October , if his Azimuth were 39 deg . from the South the altitude agreeable thereto would be found to be 14 deg . These Uses being understood ▪ if the houre and altitude or the azimuth and altitude were given to find the Declination , the manner of performance cannot lurke . Of the Houre and Azimuth Scale on the right Edge of the Quadrant . THis Scale being added by my selfe , and derived from Proportions in the Analemma , I shall first lay them down , and then apply them . In the former Scheme draw F C V the Horizon , Z C the Axis of the Horizon , C P the axis of the Spheare G C continued to N the Equator , O L a parallel of North , and E I a parallel of South Declination , W X a parallel of winter altitude , S L a parallel of altitude lesse then the Complement of the latitude , N Z P a parallel of greater altitude , and from the points E and B. let fall the perpendiculars E F and B H , and from the points B G and N let fall the perpendiculars B G , G M , and N O which will be the sines of the Suns declination , by this meanes there will be divers right lined right angled plaine Triangles constituted from whence are educed , the Proportions following to calculate the Suns houre or Azimuth . Note , first , that T V is the Versed sine of the Semidiurnal arke in Summer , and E I in Winter , and Y V the sine of the houre of rising before six in Summer , equal to the distance of I from the Axis continued in Winter , which may be found in the Triangle C Y V , but the Proportion is . As the Cotangent of the latitude , To Radius . So the Tangent of the Suns Declination , To the sine of his ascentional difference , being the time of his rising from six , thus we may attaine the Semidiurnal arke . Then for the houre in the Triangle B H I it holds . As the Cosine of the latitude , to the sine of the altitude . So is the Secant of the Declination . To the difference of the Versed sines of the Semidiurnals arke , and of the houre sought . In the Triangle B H I it leys . As the Cosine of the Latitude the sine of the angle at I. To its opposite side B H the sine of the altitude . So is the Radius or the angle at H. To B I h difference of the Versed sine of the Semidiurnal arke , and of the houre sought , in the parallel of declination and by consequence , so is the secant of the Declination , to the said difference in the Common Radius as we have else where noted , if this difference be subtracted from the Versed sine of the semidiurnal arke there will remaine E B the versed sine of the houre from noon , the like holds , if perpendiculars be let fall from any other parallel of Declination , from the same Scheme it also followes . As the Cosine of the Latitude , Is to the secant of the Declination . So is the sine of the Meridian Altitude . To the versed sine of the semidiurnal arke . Here observe the like Proportion between the two latter terms , as between the two former which may be of use on a Sector . If the Scheme be considered not as fitted to a peculiar question for finding the houre , but as having three sides to find an angle , it will be found upon such a consideration in relation to the change of sides , that the Proportion for the Azimuth following is no other then the same Proportion applyed , to other sides of the Triangle , and so we need have no other trouble to come by a Proportion for the Azimuth , but it also followes from the same Scheme . In the Triangles C D A and C K G , and C Z N the first operation will be to find A D , and G K , and N ● in all which the Proportion will hold . As the Radius to the Tangent of the Latitude . Or as the Cotangent of the Latitude to Radius . So is the Tangent of the Altitude , to the said respective quantities , which when the Altitude is lesse then the Complement of the Latitude , are the sins of the Suns Azimuth from the Vertical belonging to the proposed Altitudes when the Sun is in the Equinoctial , or hath no declination . The next proportion will be . As the Cosine of the Latitude , Is to the Secant of the Altitude . So is the Sine of the declination . To the difference sought being a 4 Proportional . Hereby we may find A B in the Winter Triangle A G B which added to A D , the summe is the sine of the Azimuth from the Vertical consequently W B , is the Versed sine of the Azimuth , from the noon Meridian . Also we find G L in the Summer triangle L M G , when the Altitude is lesse then the Complement of the Latitude , which added to S G the summe S L is the Versed sine of the Azimuth from the South . Likewise we may find N R in the Triangle R O N , and by subtracting it from N Z , there will remaine R Z , and consequently Q R the versed sine of the Azimuth from the Meridian in Summer when the Altitude is greater then the Co-latitude . And for Stars that come to the Meridian between the Zenith , and the Elevated Pole , we may find N c , in the Triangle N c d where it holds , as the sine of the Angle at N , the complement of the Latitude , to its opposite sides c d , the prickt line , the sine of the Declination : so is the Radius to N c , the parallel of altitude the Azimuth sought . The latter Proportion lyes so evident , it need not be spoken to , if what was said before for the houre be regarded , and the former Proportion lyes . As the Cosine of the Latitude , the sine of the Angle at A. To its Opposite side D C , the sine of the altitude . So is the sine of the Latitude , the angle at C. To its opposite side A D in the parallel of altitude . And in stead of the Cosine , and sine of the Latitude . We may take the Radius , and the Tangent of the Latitude . Another Analogy will be required to reduce it to the common Radius . As the Cosine of the Altitude to Radius . So the fourth before found in a parallel . To the like quantity to the Common Radius . These Analogies or Proportions being reduced into one , by multiplying the termes of each Proportion , and then freed from needlesse affection will produce the Proportion at first delivered . The Vses of the said Scale . WE have before noted , that if two termes of a Proportion be fixed , and naturall lines thereto fitted of an equal length , that if any third term be sought in the former line , the fourth term will be found in the other line by inspection , as standing against the third . So here , in this Scale which consists of two lines , the one an annexed Tangent , the other a line of Sines continued both Wayes , the Radius of the Sines being first fittted , the Tangent annexed must be of such a Radius , as that 38 deg . 28′ , of it may be equall in length to the Radius of the Sine to which it is adjoyned , and then looking for the Declination in the Tangent just against it stands the time of rising , from six or ascentional difference , or the Semidiurnal arke , if the same be accounted from the other end as a Versed Sine . So if the Suns Altitude be given , and accounted in the Tangent , just against it stands the Suns Azimuth , when he is in the Equinoctial upon the like altitude , and thus the point N will be found in the Tangent at the altitude , when it is more then the Colatitude . 1 An Example for finding the time of the Sun rising . If the Declination be 13 deg . looke for it in the annexed Tangent , and just against it in the houre Scale stands 16 deg . 53′ the ascentional difference in time 1 houre 7½ min. shewing that the Sun riseth so much before , and setteth so much after 6 in Summer , and in Winter riseth so much after , and setteth before 6 , for this arke may be found on either side of six where the declination begins each way . 2 To find the time of the day . To perform this Proposition wee divide the other Proportion into two , by introducing the Radius in the Middle . As the Radius is to the Secant of the Declination . So is the sine of the altitude to a fourth . Again . As the Cosine of the Latitude to Radius . So the fourth before found . To the difference of the Versed Sines of the Semidiurnal arke , and of the houre sought . The former of these Proportions must be wrought upon the quadrant , the latter is removed by fitting the Radius of the Sines that gives the answer , equal in length to the Cosine of the latitude . Wherefore to find the time of the day , lay the thread to the Secant of the declination in the limbe , and from the sine of the altitude take the nearest distance to it , and because the Secant is made , but to halfe the Common Radius , set downe one foot of this extent at the Declination in the annexed Tangent , and enter the said extent twice forward , and it will shew the time of the Day . Example . Let the Declination be supposed 23 deg . 31′ North , and the Altitude 38 deg . 59′ the nearest distance from the Sine thereof , to the thread laid over the Secant of 3● deg . 31′ will reach being turned twice over from 3● d. 31′ in the annexed Tangent neerest the Center to 33 deg . 45′ in the Sines , aliàs to 56 d. 15′ counted as a Versed Sine shewing the time of the day to be a quarter past 8 in the morning , or three quarters past three in the afternoon . 3 To find the Suns Altitude on all houres . Take the distance between the houre and the Declination in the fitted Scale , and enter it downe , the line of Sines from the Center , then laying the thread over the Cosine of the Declination in the Limbe , the nearest distance to it shall be the sine of the Altitude sought . Example . Thus whee the Sun hath 13 deg . of South Declination , count it in that part of the annexed Tangent nearest the Limbe , if then it were required to find the Suns Altit . for the houres of 10 or 2 by the former Prescriptions the Altitude would be found 10 d. 25′ 4 To find the Suns Amplitude . Take the Sine of the Declination from the line of the Sines , and apply it to the fitted Scale where the annexed Tangent begins , and either way it will reach to the Sine of the Amplitude . Example . So when the Sun hath 15 deg : of Declination his Amplitude will be found to be 24 deg . 35′ . 5 To find the Azimuth or true Coast of the Sun. Here we likewise introduce the Radius in the latter Proportion . 1 In Winter lay the thread to the Secant of the Altitude in the Limbe , and from the sine of the Declination , take the nearest distance to it , the said extent enter twice forward from the Altitude in the annexed Tangent , and it will reach to the Versed Sine of the Azimuth from the South . Example . So when the Sun hath 15 deg . of South Declination , if his Altitude be 15 deg . the nearest distance from the sine thereof to the thread laid over the Secant of 15 degrees , shall reach in the fitted Scale from the annexed Tangent of 15 deg . being twice repeated forward to the Versed sine of 39 deg . 50′ for the Suns Azimuth from the South . 2 In Summer when the Altitude is lesse then 40 deg . enter the former extent from the sine of the Declination to the thread laid over the Secant of the Altitude twice backward from the Altitude in the annexed Tangent , and it will reach to the Versed sine of the Azimuth from the South . Example . So if the Sun have 15 deg . of North Declination , and his Altitude be 30 deg . the prescribed extent doubled shall reach from the annexed Tangent of 30 deg . to the Versed sine of 75 deg . 44′ for the Suns Azimuth from the South . 3 In Summer when the Altitude is more then 40 deg . and lesse then 60 deg . apply the extent from the sine of the Declination to the thread , laid over the Secant of the Altitude once to the Discontinued Tangent placed a Crosse the quadrant from the Altitude backwards minding how farre it reaches , just against the like arke in the annexed Tangent stands the Versed sine of the Azimuth from the South . 4 When the Altitude is more then 60 deg . this fitted Scale is of worst performance , however the defect of the Secant might be supplyed by Varying the Proportion . 6 To find the Suns Altitude on all Azimuths . JUst against the Azimuth proposed stands the Suns altitude in the Equator suitable thereto , which was the first Arke found by Calculation when we treated of this subject , and the second arke is to be found by a Proportion in sines wrought upon the quadrant . This quadrant is also particularly fitted for giving the houre , and Azimuth in the equal limbe . The sine of 90 deg . made equal to the sine if 51 deg . 32′ gives the altitude of the Sun or Stars at six , for if the thread be laid over the Declination counted in the said sine , it shewes the Altitude sought in the limbe , so when the Sun hath 13 deg . of Declination his Altitude or Depression at 6 is 10 deg . 9′ . It also gives the Vertical Altitude if the Declination be counted in the limbe , seeke what arke it cuts in that particular sine , when the Sun hath 13 deg . of Declination , his Vertical Altitude or Depression is 16 deg . 42′ . To find the houre of the Day . HAving found the Altitude of the Sun or Stars at six , take the distance between the sine thereof in the line Sines , and the Altitude given , and entring one foot of that extent at the Declination in the Scale of entrance laying the thread to the other foot according to nearest distance , it will shew the houre from six in the limbe . Example . When the Sun hath 13 deg . of Declination his Altitude , or Depression at six will be 10 deg . 9′ if the Declination be North , and the Altitude of the Sun be 24 deg . 5′ the time of the day will be halfe an houre past 7 in the morning , or as much past 4 in the afternoon . In winter when the Sun hath South Declination as also for such Stars as have South Declination , the sine of their Altitude must be added to the sine of their Depression at six , and that whole extent entred as before . When the Sun hath the same South Declination , if his Altitude be 11 deg . 7′ the time of the day will be half an houre past 8 in the morning , or 30 min. past 3 in the afternoon . To find the Azimuth of the Sun or Stars . LAy the thread over their Altitude in the particular sine fitted to the Latitude , and in the equal Limbe it shewes a fourth Arke . When the Declination is North , take the distance in the line of Sines between that fourth Arke and the Declination , and enter one foot of that extent at the Altitude in the Scale of entrance , laying the thread to the other foot , and in the equal Limbe it shewes the Azimuth from the East or West . Example . When the Altitude is 44 deg . 39′ the Arch found in the equal Limbe will be 33 deg . 20′ then if the Declination be 23 deg 31′ North , the distance in the line of sines between it and the said Arke being entred at 44 deg . 39′ in the Scale of entrance the thread being laid to the other foot will shew the Azimuth to be 20 deg . from the East or West . But if the Declination be South , adde with your Compasses the sine thereof to the sine of the fourth Arke , and enter that whole extent as before , and the thread will shew the Azimuth in the equal limbe . Example . When the Altitude is 12d . 13′ the fourth Arch will be found to be 9 degrees 32 minutes , then admit the Declination to be 13 degrees South , whereto adding the Sine of the fourth Arke , the whole will be equall to the sine of 22 deg . 41 minutes , and this whole extent being entred at 12 deg . 13′ in the Scale of entrance lay the thread to the other foot according to nearest distance , and it will intersect the equal . Limbe at 40 deg . and so much is the Suns Azimuth from the East or West . Because the Scale of entrance could not be continued by reason of the Projection , the residue of it is put on an little Line neare the Amanack the use whereof is to lay the thread to the Altitude in it when the Azimuth is sought , and in the Limbe it shewes at what Arke of the Sines the point of entrance will happen which may likewise be found by pricking downe the Co-altitude on the line of Sines out of the fitted houre Scale on the right edge . How to find the houre and Azimuth generally in the equal limb either with or without Tangents or Secants hath been also shewed , and how that those two points for any Latitude might be there prickt and might be taken off , either from the Limbe , or from a line of Sines , or best of all by Tables , for halfe the natural Tangent of the Latitude of London , is equal to the sine of 〈◊〉 39 deg . And half the Secant thereof equal to the sine of 〈◊〉 53d . 30 Against which Arkes of the Limbe the Tangent and Secant of the Latitude are graduated , but of this enough hath been said in the Description of the small quadrant . Of the Quadrat and Shadowes . THe use thereof is the same as in the small quadrant onely if the thread hang over any degree of the Limb lesse then 45d . to take out the Tangent thereof out of the quadrat count the Arch from the right edge of the quadrant towards the left , and lay the thread over it , the pricks are repeated in the Limbe to save this trouble for those eminent parts . Of the equal Limbe . WE have before shewed that a Sine , Tangent and Secant may be taken off from it , and that having a Sine or Secant with the Radius thereof the correspondent Arke thereto might be found , & that a Chord might be taken off from Concentrick Circles or by helpe of a Bead , but if both be wanting enter the Semidiameter or Radius whereto you would take out a Chord twice downe the right edge from the Center , and laying the thread over halfe the and laying the thread over halfe the Arch proposed , take the nearest distance to it , and thus may a chord be taken out to any number of degrees lesse then a Semicircle . It hath been asserted also that the houre and Azimuth might be found generally without Protraction by the sole helpe of the Limb with Compasses and a thread . Example for finding the houre . THe first work will be to find the point of entrance take out the Cosine of the Latitude by taking the nearest distance to the thread laid over the said Arke from the concurrence of the Limbe with the right edge , and enter it down the right edge line and take the nearest distance to the thread laid over the complement of the Declination counted from the right edge , this extent entred down the right edge finds the point of entrance , let it be noted with a mark . Next to find the sine point take out the sine of the Declin . & enter it dowh the right edge , & from the point of termination , take the nearest distance to the thread laid over the ark of the Latit . counted from the right edge , this extent enter from the Center and it finds the sine point , let it be noted with a marke . Thirdly , take out the sine of the Altitude & in Winter add it in lenght to the sine point , in Summer enter it from the Center & take the distance between it & the sine point which extent entred upon the point of entrance , if the thread be laid to the other foot shewes the the houre from 6 in the equal limb before or after it , as the Sine of the Altitude fell short or beyond the sine point . Example . In the latitude of 39 d. the Sun having 23d . 31′ of North Declination , and Altitude 51 deg . 32′ the houre will be found to be 33 deg . 45′ from six towards noon . Note the point of entrance and sine point Vary not , till the Declination Vary . After the same manner may the Azimuth be found in the limb , by proportions delivered in the other great quadrant . Also both or any angle when three sides are given may be found by the last general Proportion in the small quadrant which finds the halfe Versed sine of the Arke fought , which would be too tedious to insist upon & are more proper to be Protracted with a line of Chords . To find the Azimuth universally . THe Proportion used on the smal quadrant for finding it in the equal limbe ( wherein the first Operation for the Vertical Altitude was fixed for one day , ) by reason of its Excursions will not serve on a quadrant , for the Sun or Stars when they come to the Meridian between the Zenith and the elevated Pole , but the Proportion there used for finding the houre applyed to other sides will serve for the Azimuth Universally , and that is As the Radius , Is to the sine of the Latitude , So is the sine of the Altitude , To a fourth sine . Again . As the Cosine of the Altitude , Is the Secant of the Latitude . Or , As the Cosine of the Latitude , Is the Secant of the Altitude . So In Declinations towards the Elevated Pole is the difference , but towards the Depressed Pole the summe of the fourth sine , and of the sine sine of the Declination . To the sine of the Azimuth from the Vertical . In Declinations towards the Depressed Pole , the Azimuth is alwayes obtuse , towards the elevated Pole if the Declination be more then the fourth Arch it is acute , if lesse obtuse . Example for the Latitude of the Barbados 13 deg . Altitude 27 deg . 27′ . Declination 20 deg . North. Lay the thread to 27 deg . 27′ in the Limbe , and from the sine of 13 deg . tahe nearest distance to it which enter on the line of Sines from the Center , and take the distance between the limited point , and the sine of 20 deg . the Declination , this latter extent enter twice downe the line of the Sines from the Center , and take the nearest distance to the thread laid over the Secant of 27 deg . 27′ this extent enter at the sine of 77 deg . the Complement of the Latitude , and laying the thread to the other foot it will lye over 16 deg . in the equal Limbe , the Suns Azimuth to the Northwards of the East or West . Otherwaies . Another Example for the same Latitude and Declination , the Altitude being 52 deg . 27′ lay the thread to it in the Limbe , and take the nearest distance to it from the sine of 13 deg . as before , and enter it downe the line of sines from the Center , and from the point of the limitation take the distance to the sine of 20 deg . the Suns Declination , this latter extent enter once downe the line of sines from the Center , and take the nearest distance to the Thread laid over the Secant of the Altitude 52 deg . 27′ then lay the thread to 77 deg . the Complement of the Latitude in the lesser sines , and enter the former extent between the Scale and the thread , and the foot of the Compasses sheweth 16 deg . as before , for the Suns Azimuth to the Northward of the Vertical , that the Sun may have the same Azimuth , upon two several Altitudes hath been spoken to before , and how to do this without Secants hath been shewne . Two sides with the Angle comprehended to find the third side . DIvers wayes have been shewed for doing of this before , I shall adde one more requiring no Versed sines nor Tangents . 1 If both the sides be lesser then quadrants , and the Angle at liberty . Or , 2 If one of the sides be greater then a quadrant , and the Angle included acute , it will hold . As the Radius , To the Cosine of one of the including sines . So is the Cosine of the other , To a fourth sine . Again . As the Cosecant of one of the including Sides ● is the Sine of the other , So is the Cosine of the angle included , To a seventh Sine . The difference between the fourth and the seventh Sine , is the Cosine of the Side sought . 1 In the first case if the angle given be obtuse , and the seventh Sine greater then the fourth Sine , the Side sought is greater then a quadrant in other cases lesse . If in the second case the seventh Sine be lesse then the fourth , the side sought is greater then a quadrant in other cases lesse . In this second case when one of the includers is greater then a quadrant , and the angle obtuse resolve the opposite Triangle by the former Rules , or the summe of the fourth and seventh Sine shall be the Cosine of the side sought in this case greater then a quadrant . We have before noted that the Cosine of an Arke greater then a quadrant is the Sine of that Arkes excesse above 90 deg . this no other then the converse of the Proportion for the houre demonstrated from the Analemma , in the Triangle O Z P. Let there be given the Sides O P 113 deg . 31′ the side Z P 38 deg . 28′ and the angle comprehended Z P O 75 to find the Side O Z. Operation . Lay the thread to 51 deg . 32′ in the Limbe , and from 13 deg . 31′ in the Sines take the nearest distance to it which measured from the Center will reach to the sine of 18 deg . 12 minutes the fourth Sine . Again , laying the thread to 23 deg . 31′ in the Limbe , from the Sine of 15 deg . take the nearest distance to it , then lay the thread to the Secant of 51 deg . 32′ and enter the said extent between the Scale and the thread , the distance between the resting foot , and the Sine of 18 deg . 12 minutes before found measured from the Center is equal to the Sine of 9 deg . 32′ being the Cosine of the side sought which in this instance because the seventh Sine is lesse then the fourth sine is greater then a quadrant , and consequently must have 90 deg . added thereto , therefore the side O Z is 99 deg . 28 minutes if the question had been put in this Latitude what depression the Sun should have had under the Horizon at the houres of 5 or 7 in the Winter Tropick it would have been found 9 deg . 28′ and this is such a Triangle as hath but one obtuse Angle yet two sides greater then quadrants , and how to shunne a Secant , and a parallel entrance hath been shewed els-where . Of the Stars on the Projection , and in other places of the fore-side of the quadrant . SUch only are placed on the Projection as fall between the Tropicks being put an according to their true Declinations , and in that respect might have stood any where in the parallel of Declination , but in regard we shall also find the time of the night by them with Compasses , they are also put on in a certain Angle from the right edge of the quadrant , to find the quantity of the Angle for Stars of Northerly declination , get the difference of the Sines of the Stars Altitude six houres from the Meridian , and of its Meridian Altitude , and find to the Sine of what Arch the said difference is equal , against that Arch in the Limbe , let the Star be graduated in its proper declination , but for Stars of Southwardly Declination , get the summe of the Sines of their Depression at six and of their Meridian Altitude , and find what Arke in the Sines corresponds thereto as before . We have put on no Stars of Southwardly Declination that will fall beyond the Winter Tropick , but some of Northerly Declination falling without the Summer Tropick , are put on that are placed without the Projection towards the Limbe . All these Stars must be graduated against the line of Sines at their respective Altitudes or Depressions at the Stars houre of Six from the Meridian , and must have the same letter set to them in both places , as also upon the quadrant of 12 houres of Ascension on the Back-side where they are put on according to their true Ascension with their Declinations and Ascensional differences graved against them with the former Letter , and such of them as have more then 12 houres of right Ascension have the Character plus ✚ affixed , denoting that if there be 12 houres of Ascension added to that Ascension they stand against , the summe is their whole true right Ascension . To find the quantity of a Stars houre from the Meridian by the Projection . SEt the Bead upon the Index of Altitude to the Stars observed Altitude , and bring it to the parallel of Declination the Star is graved in , so will it shew among the houre lines , that Stars houre from the Meridian , and the thread in the Limbe will shew the Stars Azimuth . Example . Admit the Altitude of Arcturus be 52 deg . the houre of that Star from midnight , if the Altitude increase will be 7′ past 10 ferè , and the Azimuth of that Star will be 47 deg . 43′ to the Eastwards of the South . The houre and Azimuth of any Star within the Tropicks , may be also found by the fitted Scale on the right edge of the quadrant , or by the Curve , after the same manner as for the Sun , using the Stars Declination as was done for the Suns , or in the equall limb as we shewed for the Sun , which may well serve for most of the Stars in the Hemisphere . Otherwise with Compasses according to the late suggested placing of them . To find the houre of any Star from the Meridian that hath North Declination . TAke the distance between the Star point in the line of Sines , and it s observed Altitude , and laying the thread over the Star where it is graved on or below the Projection , enter the former extent paralelly between the thread and the Scale , and it shewes the Stars houre from six in the sines towards noone , if the Altitude fell beyond the Star point , otherwise towards midnight . Example . For the Goat Star let its Altitude be 40 deg . and past the Meridian , the houre of that Star will be 44′ from six , for the Compasses fall upon the sine of 11 deg . 4′ the houre is towards noon Meridian , because the Altitude is greater then 34 deg . the point where the Star is graved , the thread lying over the Star intersects , the Limbe at 25 deg . 47′ if the distance between the Star , and its Altitude be entred at the sine of that Arke , and the thread laid to the other foot , the houre will be found in the equal Limbe the same as before . For Stars of Southwardly Declination . BEcause the Star point cannot fall the other way beyond the Center of the quadrant , therefore the distance between the Star point , and the Center must be increasing by adding the sine of the Stars Altitude thereto , which will fall more outwards towards the Limbe , and then that whole extent is to be entred as before . Example . The Virgins Spike hath 9 deg 19′ of South Declination the Depression of that Star at six will be found by help of the particular sine to be 7 deg . 17′ and at that Arke in the sines the Star is graved , if the Altitude of that Star were 20 deg . the sine thereof added to the Star will be equal to the sine of 29 deg . 6′ this whole extent entred at the sine of 37 deg . 52′ the Arke of the Limbe against which the Star is graved , and the thread laid to the other foot , the houre of that Star if the Altitude increase will be 19′ past 9. To find the true time of the right . THis must be done by turning the Stars houre into the Suns houre or common time , either by the Pen as hath been shewed before , which may be also conveniently performed by the back of this quadrant , for the thread lying over the day of the moneth sheweth the Complement of the Suns Ascension in the Limbe . Or with Compasses on the said quadrant of Ascensions . THe thread lying over the day of the moneth , take the distance between it and the Star on the said quadrant , the said extent being applyed , the same way as it was taken the Suns foot to the Stars houre shall reach from the Stars houre to the true houre of the night , and if one of the feet of the Compasses fall off the quadrant , a double remedy is els-where prescribed . Example . If on the 12th of January the houre of the Goat Star was 16′ past 5 from the Meridian , the true time sought would be 49′ past 1 in the morning . Example . If upon the third of January , the houre of the Virgins Spike , were observed to be 19′ past 9 , the true time sought would be 45′ past 2 in the morning . To find the time of a Stars rising and setting . THe Ascentional difference is graved against the Star , the Virgins Spike hath 48′ of Ascentional difference , that is to say , that Stars houre of rising is at 48′ past 6 , and setting at 12′ past 5 , And the true time of that Stars rising upon the third of January , will be at 22′ past 10 at night , and of its setting at 47′ past 8 in the morning , found by the former directions . Of the rest of the lines on the back of this quadrant . THey are either such as relate to the motion of the Sun or Stars , or to Dialling , or such as are derived from Mr Gunters Sector . The Tangent of 51 deg . 32′ put through the whole Limbe is peculiarly fitted to the Latitude of London , and will serve to find the time when the Sun will be East or West , as also for any of the Stars that have lesse Declination then the place hath Latitude . Lay the thread to the Declination counted in the said Tangent , and in the Limbe it shewes the houre from 6 if reckoned from the right edge . Example . When the Sun hath 15 deg . of North Declination the time of his being East or West will be 12 deg . 17′ in time about 49′ before or after six , ferè . The Suns place is given in the Ecliptick line by laying the thread over the day of the moneth in the quadrant of Ascensions , of which see page 16 & 17 of the small quadrant . Of the lines relating to Dialling . SUch are the Line of Latitudes , and Scale of houres , of which before , and the line Sol in the Limbe , of which I shall say nothing at present , it is onely placed there in readinesse to take off any Arke from it , according to the accustomed manner of taking off lines from the Limbe to any assigned Radius . The requisite Arkes of an upright Decliner will be given by the particular lines on the Quadrant for the Latitude without the trouble of Proportionall worke . 1 The substiles distance from the Meridian . ACcount the Plaines declination as a sine in the fitted hour Scale on the right edge of the fore-side , and just against it in the annexed Tangent , stands the substiles distance from the meridian . If an upright Plaine decline 30 deg . the substiles distance will be 21 deg . 41 minutes . 2 The Stiles height . Count the Complement of the Plaines Declination in the said fitted houre scale as a sine and apply it with Compasses to the line of sines issuing from the Center , for the former Plaine the stiles height will be found 32 deg . 37′ . 3 The Inclination of Meridians . Account the stilts height in the annexed tangent of the fitted hour Scale , and just against it in the sine stands the Complement of the Inclination of meridians which for the former plaine will be found to be 36 deg . 25′ 4 The Angle of 12 and 6. Account the Plaines Declination in the Limbe on the Backside from the right edge , and lay the thread over it , and in the particular Tangent it shewes the Angle between the Horizon and six 32 deg . 9′ in this Example the Complement whereof is the Angle of 12 and 6 , namely 57 deg . 51 min. Also the requisite Arkes of a direct East or West , reclining or inclining Dial may be found after the same manner for this Latit . 1 The substiles distance . ACcount the Plaines Reinclination in the Limbe on the Backside from the left edge , and in there lay the thread , and in the particular Tangent it shewes the Arke sought . So if an East or West plain recline or incline 60 deg . the substiles distance will be found to be 32 deg . 12′ . 2 The stiles height . Account the Reinclination in the particular Sine on the foreside and in the Limbe it shewes the stiles height , which for the former Example will be found to be 42 deg . 41′ . 3 The inclination of Meridians . The Proportion is , As the Sine of the Latitude , to Radius . So is the sine of the substiles distance . To the sine of the inclination of Meridians , when the substiles distance is lesse then the Latitude of the place it may be found in the particular sine on the foreside , by the intersection of the thread , and for this Example will be 42 deg . 53′ . 4 The Angle of 12 and 6. Account the Complement of the Reinclination in the peculiar hour Scale as a sine , and just against it in the annexed Tangent stands the Complement of the Angle sought , in this Example the Angle of 12 and 6 is 68 deg . 20′ . In other Latitudes the Operations must be performed by Proportional worke with the Compasses . Of the Lines derived from Mr. Gunters Sector . Such are the Lines of superficies Solids , &c. Of the Line of Superficies or Squares . THe chiefe uses of this Line joyntly with the Line of Lines in the Limbe , is when a square number is given to find the Root thereof , or a Root given to find the square number thereto , these Lines placed on a quadrant will perform this some what better then a Sector , because it is given by the Intersection of the thread without Compasses , the properties of the quadrant casting these lines large where on a Sector they would be narrow . To find the square Root of a number . The Root being given to find the Square Number of that Root . IN extracting the square Root pricks must be set under the first third , fift , and seventh figure , and so forward and as many pricks as fall to be under the square number given , so many figures shall be in the Root , and accordingly the line of lines , and superficies must vary in the number they represent , I am very unwilling to spend any time about these kind of Lines , as being of small performance , and by my self and almost by all men accounted meere toyes . If a number be given in the superficies , the thread in the lines sheweth the Root of it , and the contrary , if a number be given in the lines the thread laid over it intersects the Square thereof . The performance thereof by these lines is so deficient that I shall give no Example of it . When a number is given to find the square thereof , if not to large the Reader may correct the last figure of it by multiplying it in his memory . To three numbers given to find a fourth in a Duplicated Proportion . That is to worke a Proportion between Numbers and Squares . Example . If the Diameter of a Circle whose Area is 154 be 14 , what shall the Diameter of that Circle be whose Area is 616. Example . Lay the thread over 616 in the superficies , and from 14 in the equal parts , take the nearest distance to it , then lay the thread to 154 in the superficies , and enter the former extent between the thread and the Scale , and the foot of the Compasses will rest upon 28 the diameter sought . To find a Proportion between two or more like superficies . ADmit there be two Circles , and I would know what Proportion their Areas bear to each other , in this case the proper use of a Line of superficies would be to have it on a ruler , and to measure the lengths of their like sides , for Circles the lengths of their Diameters upon it , and then I say , the numbers found on the superficies beare such Proportion each to other as the Areas or superficial contents , and for small quantities may be done on the quadrant by entring downe the larger extent of the Compasses on the Line of Lines from the Center , and mind the point of limitation , enter then the other extent on the point of limitation , and lay the thread to the other foot , find what number it cuts in the superficies , and the greater shall beare such Proportion to the lesser as 100 , &c. the length of the whole line doth to the parts cut . The Proportion that two superficies beare each to other is the same that the squares of their like sides , and therefore their sides may be measured either in foot or inch measure , and then the Squares taken out as before shewed . The line of superficies serves for the reducing of Plots to any proportion . ADmit a Plot of a piece of ground being cast up containes 364 Acres , and it were required to draw another Plot which being cast up by the same Scale should containe but a quarter so much , and let one side of the said Plot be 60 inches , against 60 in the lines , the square of it will be found to be 3600 , and the fourth part hereof would be 900 , which account in the superficies and you will find the Square Root of it to be 30 , and so many inches must be the like side of the lesser Plot if being cast up by the same Scale it should containe but ¼ of what it did before . If the line of Superficies were on a streight ruler , then to perform such a Proposition as this , would be to measure therewith the side of the Plot given , minding what number it reaches to in the Superficies , the fourth part of the said Number being reckoned on the Superficies , and thence taken shall be the length of the side in the Proportion required . Of the Line of Solids . IF a number be duly estimated in the said line , and the thread laid over it , it will in the line of lines shew the cube Root of that number , and the converse the Root being assigned , the Cube may be found , but by reason of the sorry performance of these Lines I shall spend no time about it , if this line be placed on a loose Ruler , and the like sides of two like Solids be measured therewith , those Solids shall beare such Proportion in their contents each to other as the measured lengths on the Solids . Three Numbers being given to find the fourth in a Duplicated Proportion . Example . IF a Bullet of 4 inches Diameter weigh 9 pound , what shall a Bullet of 8 inches Diameter weigh ? Answer 72 pounds . In this case let the whole line of Solids represent 100 , alwayes the Solid content whether given or sought , must be accounted in the line of Solids , and the Sides or Diameters in the Equall parts . Lay the thread to 9 in the line of Solids , and from 8 in the inches take the nearest distance to it , enter one foot of that extent at 4 in the inches , and lay the thread to the other foot : and it will lye over 72 in the Solids for the weight of the Bullet sought . An Example of the Converse . If a Bullet whose Diameter is 4 Inches weigh 9 pound , another Bullet whose weight is 40 pound , what shall be the Diameter of it . Lay the thread to 40 in the Solids , and from 4 Inches in the lines take the nearest distance to it . Then lay the thread to 9 in the Solids , and enter the said extent at the equal Scale , so that the other foot turned about may but just touch the thread , and it it will rest at 6½ Inches nearest , which is the Diameter sought . Of the Line of inscribed Bodies . This Line hath these letters set to it . D Signifying the Sides of a Dodecahedron S Signifying the Sides of a _____ I Signifying the Sides of a Icosahedron C Signifying the Sides of a Cube O Signifying the Sides of a Octohedron T Signifying the Sides of a Tetrahedron And the Letter S Signifieth the Semidiameter of a Sphere , the use whereof are to find the Sides of the five Regular Bodies that may be inscribed in a Sphere . Example . A joyner being to cut the 5 Regular Bodies desires to know the lengths of the sides of the said 5 Regular Bodies that may be inscribed in a Sphere where Diameter is 6 inches . Lay the thread over S ▪ and take 3 inches out of the line of equal parts or Inches , and enter that extent so that one foot resting on the said Scale of inches , the other turned about may but just touch the thread , the resting point thus found , I call the point of entrance , from the said point take the nearest distances to the thread laid over the Letters .   Inch. Dec. parts D And measure those Extents on the Line of Inches , and you will find them to reach to 2.13 I 3.15 C 3.45 O 4.23 T 4.86 Which are the Dimensions of the respective sides of those Bodies to which the Letters belong . The uses of the Lines of quadrature , Segments , Mettals and Equated Bodies , I leave to the Disquisition of the Reader , when he shall have occasion to put them in practice , which I think will be seldome or never ; and wherein the assistance of the Pen will be more commendable . These lines were added to this quadrant to fill up spare room , and to shew that what ever can be done on the Sector , may be performed by them on a quadrant . A TABLE Of the Latitude of the most eminent Places in England , Wales , Scotland and Ireland .   d. m. Bedford 52 8 Barwick 55 54 Bristol 51 27 Buckingham 52   Cambridge 52 12 Canterbury 51 17 Carlisle 55   Chichester 50 48 Chester 53 16 Colchester 51 58 Derby 52 58 Dorchester 50 40 Durham 54 50 Exceter 50 43 Gilford 51 12 Gloucester 51 53 Hartford 51 49 Hereford 52 7 Huntington 52 19 Ipswich 52 8 Kendal 54 23 Lancaster 54 10 Leicester 52 40 Lincolne 53 14 London 51 32 Northampton 52 14 Norwich 52 42 Nottingham 53   Oxford 51 46 Reading 51 28 Salisbury 51 4 Shrewsbery 52 47 Stafford 52 52 Stamford 52 38 Truero 50 30 Warwick 52 20 Winchester 51 3 Worcester 52 14 Yorke . 53 58 WALES d. m. Anglezey 53 28 Barmouth 52 50 Brecknock 52 1 Cardigan 52 12 Carmarthen 51 56 Carnarvan 53 16 Denbigh 53 13 Flint 53 17 Llandaffe 51 35 Monmouth 51 51 Montgomeroy 51 56 Pembrooke 51 46 Radnor 52 19 St. David 52 00 The ISLANDS . d. m Garnzey 49 30 Jersey 49 12 Lundy 51 22 Man 54 24 Portland 50 33 Wight Isle . 50 39 SCOTLAND . d. m. Aberdean 57 32 Dunblain 56 21 Dunkel 56 48 Edinburgh 55 56 Glascow 55 52 Kintaile 57 44 Orkney Isle 60 6 St. Andrewes 56 39 Skirassin 58 36 Sterling . 56 12 IRELAND . d. m. Autrim 54 38 Arglas 54 10 Armach 54 14 Caterlagh 52 41 Clare 52 34 Corke 51 53 Droghedah 53 38 Dublin 53 13 Dundalk 53 52 Galloway 53 2 Youghal 51 53 Kenny 52 27 Kildare 53 00 Kings towne 53 8 Knock fergus 54 37 Kynsale 51 41 Lymerick 52 30 Queens towne 52 52 Waterford 52 9 Wexford . 52 18 A Table of the right Ascensions and Declinations of some of the most principal fixed Stars for some yeares to come .   R. Ascension . Declination . Magnitude   H m D. m.   Pole Star 00 31 87 34 N 2 Andromedas Girdle 00 50 33 50 N 2 Whales Belly 01 35 12 S 3 Rams head 1 48 21 49 N 3 Whales mouth 2 44 2 42 N 2 Medusas head 2 46 39 35 N 3 Perseus right side 2 59 48 33 N 2 Buls eye 4 16 15 46 N 1 Goat 4 52 45 37 N 1 Orions left foot 4 58 8 38 S 1 Orions left shoulder 5 6 5 59 N 3 First , in Orions girdle 5 15 00 35 S 3 Second , in Orions girdle 5 19 1 27 S 3 Third , in Orions girdle 5 23 2 9 S 3 Orions right shoulder 5 36 7 18 N 2 The Wagoner 5 39 44 56 N 2 Bright foot of the Twins 6 18 16 39 N 3 Great Dog 6 30 16 13 S 1 Castor or Apollo 7 12 32 30 N 2 The little Dog 7 22 6 6 N 2 Pollux or Hercules 7 24 28 48 N 2 Hidra's heart 9 10 7 10 S 1 Lions heart 9 50 13 39 N 1 Lions Neck 9 50 21 41 N 3 Great Beares rump 10 40 58 43 N 2 Lions back 11 30 22 4 N 2 Lions tail 11 31 16 30 N 1 The Virgins girdle 12 38 5 20 N 3 First in the great Bears taile next the rump 12 38 57 51 N 2 Vindemiatrix 12 44 15 51 N 3 Virgins Spike 13 7 9 19 S 1 Middlemost in the Great Beares tail 13 10 56 45 N 2 Last in the end of the Great Beares tail 13 34 51 05 N 2 Arcturus 14 00 21 03 N 1 South Ballance 14 32 14 33 S 2 Brightest in the Crown 15 24 27 43 N 3 North Ballance 14 58 08 03 S 3 Serpentaries left hand 15 56 02 46 S 3 Scorpions heart 16 08 25 35 S 1 Serpentaries left knee 16 18 09 46 S 3 Serpentaries right knee 16 49 15 12 S 3 Hercules head 16 59 14 51 N 3 Serpentaries head 17 19 12 52 N 3 Dragons head 17 48 51 36 N 3 Brightest in the Harp 18 25 38 30 N 1 Eagle or Vultures heart 19 34 08 00 N 2 Upper horn of Capricorn 19 58 13 32 S 3 Swans tail 20 30 44 05 N 2 Left shoulder of Aquarius 21 13 07 02 S 3 Pegasus mouth 21 27 08 19 N 3 Right shoulder of Aquarius 21 48 01 58 S 3 Fomahant 22 39 31 17 S 1 Pegasus upper Wing , or Marchab 22 48 13 21 N 2 Pegasus Lower Wing . 23 55 33 25 N 2 Mr. Sutton knowing that some of the Tables of Declination and Right Ascension in our English Books are antiquated and removed forward , took the pains to Calculate a new Table of Right Ascensions and Declinations to serve for the future , in regard I was not at leisure to accomplish it ; which followeth . Dayes . January ☉ R A. ☉ Decl. H. M. D. M. 1 19 35 21 46 2 19 39 21 36 3 19 43 21 25 4 19 47 21 14 5 19 51 21 03 6 19 56 20 52 7 20 00 20 40 8 20 04 20 27 9 20 09 20 15 10 20 13 20 01 11 20 17 19 48 12 20 22 19 34 13 20 26 19 20 14 20 30 19 05 15 20 34 18 50 16 20 38 18 35 17 20 42 18 19 18 20 46 18 03 19 20 50 17 47 20 20 54 17. 30 21 20 58 17 13 22 21 03 16 56 23 21 07 16 39 24 21 11 16 21 25 21 15 16 03 26 21 19 15 44 27 21 23 15 26 28 21 27 15 07 29 21 31 14 48 30 21 35 14 28 31 21 38 14 09 Dayes . February ☉ R A. ☉ Decl. H. M. D. M. 1 21 42 13 49 2 21 46 13 29 3 21 50 13 08 4 21 54 12 48 5 21 58 12 28 6 22 02 12 06 7 22 06 11 45 8 22 10 11 24 9 22 14 11 03 10 22 17 10 41 11 22 21 10 19 12 22 25 9 57 13 22 29 9 35 14 22 33 9 13 15 22 36 8 51 16 22 40 8 26 17 22 44 8 06 18 22 48 7 43 19 22 52 7 20 20 22 55 6 57 21 22 59 6 34 22 23 03 6 11 23 23 06 5 48 24 23 10 5 24 25 23 13 5 01 26 23 17 4 37 27 23 21 4 14 28 23 25 3 51 29         30         31         Dayes . March ☉ R. A. ☉ Decl. H. M. D. M. 1 23 28 3 27 2 23 32 3 03 3 23 36 2 39 4 23 39 2 16 5 23 43 1 52 6 23 46 1 29 7 23 50 1 05 8 23 53 0 41 9 23 57 0 18 10 0 01 North 6 11 0 05 0 30 12 0 08 0 53 13 0 12 1 17 14 0 15 1 41 15 0 19 2 04 16 0 23 2 28 17 0 26 2 51 18 0 30 3 15 19 0 33 3 38 20 0 37 4 01 21 0 41 4 24 22 0 44 4 48 23 0 48 5 11 24 0 52 5 34 25 0 55 5 57 26 0 59 6 19 27 1 03 6 42 28 1 06 7 04 29 1 10 7 27 30 1 14 7 49 31 1 17 8 11 Dayes . April . ☉ R. A. ☉ Decl. H. M. D. M. 1 1 21 8 33 2 1 25 8 55 3 1 29 9 17 4 1 33 9 38 5 1 36 9 51 6 1 40 10 21 7 1 44 10 42 8 1 47 11 03 9 1 51 11 24 10 1 54 11 44 11 1 58 12 05 12 2 02 12 24 13 2 06 12 45 14 2 10 13 04 15 2 13 13 24 16 2 17 13 43 17 2 21 14 02 18 2 25 14 21 19 2 29 14 40 20 2 32 14 58 21 2 36 15 16 22 2 40 15 34 23 2 44 15 52 24 2 48 16 09 25 2 51 16 27 26 2 55 16 43 27 2 59 17 00 28 3 03 17 16 29 3 07 17 32 30 3 10 17 48 31         Dayes . May ☉ R. A. ☉ Decl. H. M. D. M. 1 3 14 18 03 2 3 18 18 18 3 3 22 18 33 4 3 26 18 48 5 3 30 19 02 6 3 34 19 16 7 3 38 19 29 8 3 42 19 42 9 3 46 19 55 10 3 50 20 08 11 3 54 20 20 12 3 58 20 32 13 4 02 20 44 14 4 06 20 55 15 4 10 21 05 16 4 14 21 16 17 4 18 21 26 18 4 22 21 36 19 4 26 21 45 20 4 30 21 54 21 4 34 22 02 22 4 38 22 11 23 4 42 22 19 24 4 46 22 26 25 4 50 22 33 26 4 54 22 40 27 4 58 22 46 28 5 02 22 52 29 5 06 22 57 30 5 11 23 02 31 5 15 23 07 Dayes . June . ☉ R. A. ☉ Decl. H. M. D. M. 1 5 19 23 11 2 5 23 23 15 3 5 27 23 19 4 5 31 23 22 5 5 36 23 24 6 5 40 23 26 7 5 44 23 28 8 5 48 23 29 9 5 52 23 30 10 5 56 23 31 11 6 00 23 31½ 12 6 04 23 31 13 6 08 23 30 14 6 12 23 29 15 6 17 23 28 16 6 21 23 26 17 6 25 23 24 18 6 29 23 21 19 6 33 23 18 20 6 38 23 14 21 6 42 23 11 22 6 46 23 06 23 6 50 23 01 24 6 54 22 56 25 6 58 22 51 26 7 02 22 45 27 7 06 22 39 28 7 10 22 32 29 7 14 22 25 30 7 19 22 17 31         Dayes . July ☉ R. A. ☉ Decl. H. M. D. M. 1 7 23 22 09 2 7 27 22 01 3 7 31 21 52 4 7 35 21 43 5 7 39 21 34 6 7 43 21 24 7 7 47 21 14 8 7 51 21 04 9 7 55 20 53 10 7 59 20 42 11 8 03 20 30 12 8 07 20 18 13 8 11 20 06 14 8 15 19 54 15 8 19 19 41 16 8 23 19 28 17 8 27 19 14 18 8 31 19 00 19 8 35 18 46 20 8 39 18 32 21 8 43 18 17 22 8 47 18 02 23 8 51 17 46 24 8 55 17 31 25 8 58 17 15 26 9 02 16 59 27 9 06 16 42 28 9 10 16 25 29 9 14 16 08 30 9 17 15 51 31 9 21 15 33 Dayes . August ☉ R. A. ☉ Decl. H. M. D. M. 1 9 25 15 16 2 9 29 14 58 3 9 33 14 39 4 9 37 14 21 5 9 40 14 02 6 9 44 13 43 7 9 48 13 24 8 9 51 13 04 9 9 55 12 45 10 9 58 12 25 11 10 02 12 05 12 10 06 11 45 13 10 10 11 25 14 10 14 11 04 15 10 17 10 43 16 10 21 10 22 17 10 25 10 01 18 10 28 9 40 19 10 32 9 18 20 10 35 8 57 21 10 39 8 35 22 10 43 8 14 23 10 46 7 52 24 10 50 7 30 25 10 53 7 07 26 10 57 6 45 27 11 01 6 22 28 11 04 6 00 29 11 08 5 37 30 11 11 5 14 31 11 15 4 51 Dayes . September ☉ R. A. ☉ Decl. H. M. D. M. 1 11 19 4 28 2 11 23 4 6 3 11 26 3 42 4 11 30 3 19 5 11 33 2 56 6 11 37 2 33 7 11 41 2 10 8 11 44 1 46 9 11 48 1 23 10 11 51 0 59 11 11 55 0 3● 12 11 59 0 12 13 12 02 South 11 14 12 06 0 35 15 12 09 0 58 16 12 13 1 22 17 12 17 1 46 18 12 20 2 09 19 12 24 2 33 20 12 27 2 56 21 12 31 3 19 22 12 35 3 43 23 12 38 4 06 24 12 42 4 30 25 12 45 4 53 26 12 49 5 16 27 12 53 5 39 28 12 57 6 02 29 13 01 6 26 30 13 04 6 49 31         Dayes . October ☉ R. A. ☉ Decl. H. M. D. M. 1 13 08 7 11 2 13 12 7 34 3 13 15 7 57 4 13 19 8 19 5 13 22 8 42 6 13 26 9 04 7 13 30 9 26 8 13 34 9 48 9 13 38 10 10 10 13 41 10 31 11 13 45 10 53 12 13 49 11 14 13 13 53 11 36 14 13 57 11 57 15 14 00 12 18 16 14 04 12 38 17 14 08 12 59 18 14 12 13 19 19 14 16 13 39 20 14 20 13 59 21 14 24 14 19 22 14 28 14 38 23 14 32 14 57 24 14 36 15 16 25 14 39 15 35 26 14 43 15 5● 27 14 47 16 1● 28 14 51 16 29 29 14 55 16 47 30 14 59 17 04 31 15 03 17 21 Dayes . November ☉ R. A. ☉ Decl. H. M. D. M. 1 15 07 17 38 2 15 11 17 54 3 15 15 18 10 4 15 19 18 26 5 15 23 18 41 6 15 27 18 56 7 15 31 19 11 8 15 36 19 26 9 15 40 19 40 10 15 45 19 53 11 15 49 20 07 12 15 53 20 19 13 15 58 20 32 14 16 02 20 44 15 16 07 20 56 16 16 11 21 08 17 16 15 21 19 18 16 19 21 29 19 16 23 21 39 20 16 28 21 49 21 16 32 21 58 22 16 36 22 08 23 16 40 22 16 24 16 44 22 24 25 16 49 22 32 26 16 53 22 39 27 16 57 22 46 28 17 02 22 52 29 17 06 22 58 30 17 11 23 03 31         Dayes . December . ☉ R. A. ☉ Decl. H. M. D. M. 1 17 15 23 08 2 17 20 23 13 3 17 25 23 17 4 17 29 23 20 5 17 34 23 23 6 17 38 23 26 7 17 42 23 28 8 17 47 23 29 9 17 51 23 30 10 17 56 23 31 11 18 00 23 31½ 12 18 05 23 31 13 18 09 23 30 14 18 14 23 29 15 18 19 23 27 16 18 24 23 25 17 18 28 23 22 18 18 33 23 19 19 18 37 23 15 20 18 41 23 11 21 18 45 23 07 22 18 49 23 02 23 18 54 22 56 24 18 58 22 50 25 19 03 22 43 26 19 07 22 36 27 19 11 22 29 28 19 16 22 21 29 19 20 22 13 30 19 25 22 04 31 19 30 21 55 A Rectifying Table for the Suns Declination .   Years Years Years   1657 1661 1665 1669 1673 1659 1663 1667 1671 1675 1660 1664 1668 1672 1676 Moneths min. min. min. January 3 s 2 a 5 a 4 s 3 a 7 a 5 s 4 a 9 a February 5 s 5 a 10 a 5 s 5 a 11 a 6 s 5 a 11 a March 6 s 5 a 13 s 5 a 5 s 12 a 5 a 5 s 12 a April 5 a 5 s 11 a 5 a 5 s 10 a 4 a 4 s 9 a May 4 a 4 s 8 a 3 a 3 s 6 a 2 a 2 s 4 a June 1 a 1 s 2 a 0 s 0 a 0 s 1 s 1 a 3 s July 2 s 2 a 5 s 3 s 3 a 7 s 4 s 4 a 9 s August . 5 s 5 a 10 s 5 s 5 a 11 s 6 s 5 a 12 s Septēber 6 s 5 a 13 s 6 a 5 s 13 a 6 a 5 s 12 a October 6 a 5 s 12 a 5 a 5 s 11 a 4 a 5 s 9 a Novem. 3 a 4 s 7 a 2 a 3 s 5 a 1 a 2 s 3 a Decemb. 0 a 1 s 1 a 1 s 0 a 1 s 2 s 1 a 3 s The use of the Rectifying Table . NOte that the minutes under the respective years is to be added or substracted to or from the Suns Declination in the former Table , as is noted with the letter a or s : and also note that the first figure in each moneth stands for the first 10 dayes of the moneth , and the second for the second 10 days , & the third for the last 10 dayes , except in March or September , which in March will be the first 9 dayes only , and in September the first 12 dayes . Example . I would know the Suns Declination the 15 day of May 1668. Now because this day of the moneth falls in the second 10 dayes , I look in the Table under the year 1663 , and right against May you shall finde that in the second place of the moneth stands 6 a , which shews me that I must adde 6 minutes to the Suns Declination in the former Table 21 degrees 5 min. that stands against the 15 day of May , and then I find that the Sun will have 21 deg . 11 min. of North Declination , and so for the rest , which will never differ above two minutes from the truth , but seldome so much , and for the most part true . Note that the former Table of the Suns Declination is fitted exactly for the year 1666. by the Rules Mr. Wright gives in his Correction of Errours , and from his Tables , and may indifferently serve for the years 1658 , 1662. 1670 , 1674 , without any sensible errour , and the Table of Right Ascensions will not vary a minute of time in many years . FINIS . Errours in the Horizontal Quadrant . PAge 5 line 6 in an Italian letter should not have been distinct , nor in another letter from the former line . page 5. line 9. for quarter , read half . p. 5. l. 13. r. of a quadrant . p. 11. l. 7. r. 63 d. 26′ . p. 19. l. 7. r. the same day to . p. 23. l. 17. r. and ends at 32′ past 9. p. 27. l. 7. for N R , r. N Z. p. 28. l. 4. r. in the parallel . p. 30. l. 9 , & l. 10. r. 23 d. 31′ . p. 38. l. 4. r. Is to the sine . p. 50. l. 5. r. whereof the Diameter . AN APPENDIX Touching REFLECTIVE DIALLING . By JOHN LYON : Professor of this , or any other part of the Mathematicks , neer Sommerset House in the Strand . LONDON , Printed Anno Domini , 1658. DIRECT DIALLING By a Hole or Nodus . To draw a Dial under any window that the Sun shines upon by help of a thread fastened in any point of the direct Axis found in the Ceiling , and a hole in any pane of glasse , or a knob or Nodus upon any side of the window or window-post . CONSTRUCTIO . FIrst , draw on pastboard or other material , an Horizontal Dial for the Latitude proposed . Then by help of the Suns Azimuth , which may be found by help of a general Quadrant , at any time , or by knowing the true hour of the day with the help of the said Horizontal Dial : and draw that true Meridian from the hole or Nodus proposed , both above on the Cieling , and below on the walls and floor of the Room ; so that if a right line were extended from the said hole or Nodus by any point in any of those lines , it would be in the meridian Circle of the World. To finde a point in the direct Axis of the world , which will ever fall to be in the said Meridian , in which point the end of a thread is to be fastened . FIrst , fix the end of a thread or small silk in the center of the Hole or Nodus , and move the other end thereof up or down in the said meridian formerly drawn on the Cieling or wall , untill by applying the side of a Quadrant to that thread , it is found to be elevated equal to the Latitude of the place ; so is that thread directly scituated parallel to the Axis of the world , and the point where the end of that thread toucheth the meridian either on the Cieling or wall , is that point in the direct Axis sought for , wherein fix one end of a thread , ( which thread will be of present use in projecting of hour-points in any place proposed , then : To find the Hour-points either under the window , or any other convenient place in the Room . Place the center of the said Horizontal Dial in the Center of the Hole or Nodus ; also scituate the said Dial exactly parallel to the Horizon , and the meridian of the said Dial in the meridian of the world , which ( as before ) may easily be done , if at that instant you know the true hour of the day . ) Then take the thread whose end is fixed in a point in the direct Axis , and move it to and fro , until the said thread doth interpose between your eye , and the hour-line on the said Horizontal Dial which you intend to draw , and then keeping your eye at that scituation , make a point or mark in any place where you please , or under the window , so that the said thread or string may interpose between that point or mark so made , and your eye , as aforesaid ; which said point so sound will shew the true time of the day at that hour all the year long , the Sun shining thereon , so will that point , together with the said thread , serve to shew the hour , instead of an hour-line . In like manner , the said thread fixed in the Axis may be again moved to and fro , until the said thread doth interpose between the eye and any other hour-line desired on the said Horizontal Dial and then ( as before ) make another point or mark in any place at pleasure , or under the said window , by projecting a point from the eye , so that the said thread also interpose between that point to be made and the eye , so will that point so found shew the true time of the day for the same hour that did the hour line on the said Horizontal Dial , which was shadowed by the said thread . In like manner may be proceeded ( by help of that thread , and the several hour-lines on the said Horizontal Dial ) to finde the other hour-points which must have the same numbers set to them as have the hour-lines on the said Horizontal Dial. Otherwise to make a Dial from a hole in any pane of glasse in a window , and to graduate the hour-lines below on the Sell , or Beam , or on the ground , that hole is supposed to be the center of the Horizontal Dial , and being true placed , the stile thereof , if supposed continued , will run into the point in the Meridian of the Cieling before found , where a thread is to be fixed ; then let one extend a thread fastned in the center of the Horizontal Dial parallelly to the Horizon , over each respective hour-line , and holding it steady , let another extend the thread fastened in the Meridian , in the Cieling along by the edges of the former Horizontal thread , and so this latter thread will finde divers points on the ground , through which if hour-lines be drawn , and the Sun shine through the hole in the pane of Glasse before made , the spot of the Sun on the ground shall shew the time of the day . For the points that will be thus found on the Beam or Transome , the thread fixed in the Cieling , or instead of it a piece of tape there fixed must be moved so up and down , that the spot of the Sun may shine upon it , and being extended to the Transome or Beam graduated with the hour-lines , as before directed , it there shews the time of the day . Here note , that it will be convenient to have that pane of Glasse darkened through which that spot is to shine . In like manner may a Dial be made from a nail head , a knot in a string tied any where a crosse , or from any point driven into the bar of a window , and the hour-lines graduated upon the Transome or board underneath . To make a Reflected Dial on the Ceiling of the Room is onely the contrary of this , by supposing the Horizontal Diall with its stile to be turned downwards , and run into the true meridian on the ground , where the thread is to be fixed , and to be extended along by the former Horizontal thread ( held over the respective hours as before ) upward , to find divers points in the Cieling , as shall afterwards be shewed . Of Dials to stand in the Weather . These may be also made by help of an Horizontal Dial. DRive two nails or pins into the wall , on which the edge of a Board of competent breadth may rest , then to hold up the other side of the Board , drive two hooks into the wall above , whereto with cord or line the outside of the Board may be sustained , and this Board being Horizontal , place the Horizontal Dial its Meridian-line in the true Meridian of the world . If a Plain look towards the South , the stile of the Horizontal Dial continued by a thread from the center will run into the Plain , which note to be the center of the new Dial , as also that line is the new stile , which must be supported with stayes , when you fix it up . By a thread from the center laid over every hour-line on the Horizontal Dial , cross the Horizontal line of the Plain , which note with the same hours the Horizontal Dial hath . The hour-lines on the Plain are to be drawn from the center before found through those points , and so cut off by the Dial , or continued at pleasure . If the Center of the Dial be assigned before you begin the work , in such Cases you may remove the Horizontal Dial up and down , keeping it still to the true position or hour , till you finde the Axis or stile run into the Center . But if the Plain look into the East or West , then possibly the Axis of the Horizontal Dial will not meet with the Plain : in such Cases you must fix a board so , that it may receive the Axis , ( the board being perpendicular to the Plain ) this stile or Axis is to be fastened to the Plain by two Rests , the hour-lines may be drawn by the eye , or shadowed out by a Light : Bring the thread that represents the Axis or stile into any hour-point ( on the Horizontal Dial ) by your eye or shadow ; at the same time the thread or shadow making marks on the Plain , shews where the hour-lines are to passe . After the same manner any hour-line is to be drawn over any irregular or crooked Plain . Further observe , that any point in the middle , or neer the end of the stile will as well shew the hour of the Day , as the whole stile . Of Refracted Dials . IF you stick up a pin or stick , or assign any point in any concave Boul or Dish , to shew the hour , and make that the center of the Horizontal Dial , assigning the meridian-line on the edges of the Boul , point out the rest of the hour-lines also on the edges of the Boul , and taking away the Horizontal Dial , elevate a string or thread from the end of the said pin fastned thereto over the Meridian-line equal to the Elevation of the Pole or the Latitude of the place ; then with a candle , or if you bring the thread to shade upon any hour-point formerly marked out on the edges of the Boul , at the same time the shade in the Boul is the hour line . And if the Boul be full of water , or any other liquor , you may draw the hour-lines , which will never shew the true hour , unlesse filled with the said Liquor again . Reflected Dialling . To draw a Reflected Dial on any Plain or Plains , be they never so Gibous , and Concave , or Convex , or any irregularity whatsoever , the Glass being fixed at any Reclination at pleasure , ( provided it may cast its Reflex upon the places proposed . ) Together with all other necessary lines or furniture thereon , viz. the Parallels of Declination , the Azimuth lines , the Parallels of Altitude ( or proportions of shadows ) the Planetary Hour-lines , and the Cuspis of those Houses which are above the Horizon , &c. 1. If the Glasse be placed Horizontal upon the Transome of a window , or other convenient place : How upon the Wall or Cieling whereon that Glasse doth reflect to draw the Hour-lines thereon , although it be never so irregular , or in any form whatsoever . CONSTRUCTIO . FIrst , draw on Pastboard or other Material an Horizontal Dial for the Latitude proposed . Then by help of the Azimuth , or at the time when the Sun is in the Meridian ; or by knowing the true hour of Day , whereby may be drawn several lines on the Cieling , Floor , and Walls of the Room : so as in respect of the center of the Glasse they may be in the true Meridian-circle of the World : For if right lines were extended from the center of the said Glasse by any point , though elevated in any of those lines so drawn , it would be directly in the Meridian Circle of the World. Now all Reflective Dialling is performed from that principle in Opticks , which is , That the angle of Incidence is equal to the angle of Reflection . And as any direct Dial may be made by help of a point found in the direct Axis , so may any Reflected Dial be also made by help of any point found in the Reflected Axis . And in regard the reflected Axis for the most part will fall above the Horizon of the Glasse without the window , so that no point there can be fixed , therefore a point must be found in the said Reflected Axis continued below the Horizontal of the said Glasse , until it touch the ground or floor of the Room in some part of the Meridian formerly drawn , which point will be the point in the reversed Axis desired , and may be found , as followeth . One end of the thread , being fixed at or in the center of the said Glasse , move the other end thereof in the meridian formerly drawn below the said Glasse , until the said reversed Axis be depressed below the Horizon , as the direct Axis was elevated above the Horizon , which may be done by applying the side or edge of a Quadrant to the said thread , and moving the end thereof to and fro in the said meridian , until the thread with a plummet cut the same degree as the Pole is above the Horizontal Glasse , and then that point where the end of the thread toucheth the Meridian either on the floor or wall of the room , is the point in the reflected reversed Axis sought for . Now if the Reversed Axis cannot be drawn from the Glasse by reason of the jetting of the window or other impediment , that point in the reverse Axis may be found by a line parallel thereto , by fixing one end of it on the Glasse , and the other end in the meridian , so as that it may be parallel to the floor or wall in which the reversed Axis-point will fall , and finde the Axis point from that other end of the lath : so if the same Distance be set from that point backward in the Meridian on the floor , as is the Lath , the point will be found in the Reversed Axis desired . Thus having found a point in the reflected reversed Axis ; it is not hard , by help whereof and the Horizontal Dial , to draw the reflected hour-lines on any Cieling or Wall , be it never so concave or convex . To do which : First note , that all straight lines in any projection on any Plain , do always represent great Circles in the Sphere , such are all the hour-lines . Place the center of this Horizontal Dial in the center of the Glasse , the hour-lines of the said Dial being horizontal , and the Meridian of the said Dial in the Meridian of the world , which may be done by plumb lines let fall from the meridian on the Cieling : Then fix the end of a thread or silk in the said center of the Dial or Glasse , and draw it directly over any hour-line on the Dial which you intend to draw , and at the further side of the room , and there let one hold or fasten that thread with a small nail . Then in the point formerly found on the reversed Axis on the ●oor , fix another thread there ( as formerly was done in the center of the Diall ) then take that thread , and make it just touch the thread ( on the hour-line of the Horizontal Dial extended ) in any point thereof , it matters not whereabouts , and mark where the end of that thread toucheth the Wall or Cieling , and there make some mark or point . Then again move the same thread higher or lower at pleasure , till it , as formerly touch the said same hour thread , and mark again whereabouts on the wall or Cieling , the end of the said thread also toucheth . In like manner may be found more points at pleasure , but any two will be sufficient for the projecting or drawing any hour-line on any plain , how irregular soever . For if you move a thread , and also your eye to and fro , until you bring the said thread directly between your eye and the points formerly found , you may project thereby as many points as you please at every angle of the Wall or Cieling , whereby the reflected hour-line may be exactly drawn . Again , in like manner remove the said thread fastned in the center of the Horizontal Dial , ( which also is the center of the Glasse ) on any other hour-line desired to be drawn , and as before fasten the other end of the thread , by a small nail , or otherwise at the further side of the room , but so that the said thread may lie just on the hour-line proposed to be drawn on the Horizontal Dial. Then ( as before ) take the thread fastened in the point on the reflected Axis , and bring it to touch the thread of the hour-line in any part thereof , and mark where the end of that thread toucheth the said Wall or Cieling : Then again ( as before ) move the said thread so , as that it only touch the said thread of the hour-line in any other part thereof , and also mark where the end of that thread toucheth the said Wall or Cieling : So is there found two points on the Wall or Cieling , being in the reflected hour-line desired , by help of which two points the whole hour-line may be drawn ; for if ( as before ) a thread be so scituated , that it may interpose between the eye and the said two points found , you may make many points at pleasure , whereunto the said thread may also interpose , which for more conveniency may be made at every angle or bending of the Wall or Cieling , be they never so many : So that if lines be drawn from point to point , that said reflected hour-line will be also exactly drawn . In like manner may the other hour-lines be drawn so , that the Reflex or spot of the Sun from the said Horizontal Glasse scituated in the said window ( as before ) shining amongst the said reflected hour-lines drawn on the wall or Cieling , will exactly shew the hour of the day desired . Now if lines be drawn round about the said Room , equal to the Horizon of the said Glasse , it will shew when the Sun is in or neer the Horizon . To draw the Aequator and Tropicks on any Wall or Cieling to any Horizontal reflecting Glasse . 1 To draw the Reflected Aequator or Equinoctial-line on the Wall or Cieling , which represents a great Circle . TAke the thread fixed in the Center of the Glasse , and move the end thereof to and fro in the meridian line drawn on the Cieling , untill by help of a Quadrant the said thread be elevated equal to the complement of the Latitude , ( which will be alwayes perpendicular to the reversed Axis ) marking in the Meridian where the end of that thread falls , then on that point and the said meridian line on the Cieling erect a perpendicular line , which line may be continued on any plane whatsoever , and is the reflected Equinoctial line desired . Note that all great Circles are right lines , & are alwayes drawn or projected from a right line . 2. To draw the Tropicks . Note , that all Parallels of Declination are lesser Circles , and are Conick Sections . FIrst , make or take out of some Book a Table of the Suns Altitude for each hour of the day , calculated for the place or Latitude proposed , when the Sun is in either of the Tropicks . Then take the thread fixed in the center of the Glasse , and by applying one side of a quadrant to the said thread , and moving one end of it to and fro in the hour-line proposed , elevate the said thread answerable to the Suns height in that hour , when he is in that Tropick you desire to draw , and mark where the end of that thread so elevated toucheth in that hour-line proposed . So may you in like manner finde a several point in each hour-line for the Suns height in that Tropick , whereby a line may be drawn on the Wall or Cieling from point to point formerly made in the said hour-lines , which the Tropick desired . In like manner may any parallel of Declination be drawn : If there be first calculated a Table of the Suns altitude at all hours of the day , when the Sun hath any Declination proposed , whereby may be drawn either the Parallels of the Suns place , or the parallels of the length of the day . To draw the parallels of Declination to any Reflected Glasse most easily , by help of a Trigon first made on past board or other material . FIx the Trigon to the reflected roversed Axis , so that the center of the Trigon may be in the center of the Glasse , then will the Equinoctial on the Trigon be perpendicular to the said Axis : then take the thread fixed in the center of the Glasse , and lay it along either of the Tropicks or other parallels of Declination required , which is drawn on the said Trigon , which thread must be continued so , that the end thereof may touch any hour-line , and on that hour-line mark the point of touch , the thread being still laid on the same parallel of declination on the Trigon : in the same manner finde a point in each hour-line . Lastly , draw a line by those points so found , which will be the Tropick-line or other parallel of declination , as the thread was laid on , on the Trigon . To draw the Azimuth-lines on any Wall or Cieling to any Horizontal reflecting Glasse . Note that all Azimuths are great Circles . FIrst , find a vertical point , either above to the Zenith , or below to the Nadir of the Glasse ( by some called a perpendicular or plumb line ) and mark in what point it cuts the floor of the room , which point I call the reflected vertical point , wherein the end of a thread is to be fixed : For by a point found in the reflected Axis of the Horizon the Azimuths may be drawn , as by a point found in the reflected Axis of the Equinoctial the hour-lines may be drawn . Then on pastboard or other material draw the points of the Compasse or other degrees , and fix the center thereof in the center of the Glasse , and the meridian thereof in the meridian of the world , as was shewn in drawing the hour-lines , being careful to place it horizontal . Then take the thread fixed in the place of the glasse , and draw it over any Azimuth , which is desired to be drawn , and at the further side of the Room fasten that thread with a small nail as it was in drawing the reflected hour-lines : Then take the thread whose end is fastened in the said reflect vertical point , and bring that thread so as just to touch the said horizontal thread , and augment it , until the end thereof touch the wall or Cieling , and there make a mark or point . In like manner , move the said thread , whose end is fastened in the said vertical point , higher or lower at pleasure , till as formerly it touch the said horizontal thread , and mark again whereabouts the end thereof toucheth the said Wall or Cieling : Now by help of these two points found in the reflected Azimuth line , the whole Azimuth line may be drawn ; for if ( as before in drawing the Hour-lines ) a thread be so scituated , that it may interpose between the eye and the said two points , you may make many points at pleasure , to which the said thread so situated may also interpose , which may be made at every angle or bending of the wall or Cieling ( as before ) whereby the reflected Azimuth-line desired may be drawn . In like manner may the other reflected Azimuth lines be drawn . Also there may be lines drawn parallel to the Horizon round about the room , by help of the thread fixed in the center of the Glasse , and a Quadrant for the elevation thereof , which will shew the Suns altitude at any appearance thereof . Thus have I shewed the drawing of a Reflected Dial from an Horizontal Glasse , with all the usual furniture thereon , though the wall or place on which it is to be drawn be never so gibous or irregular , or in what shape soever . Now the Glasse may be exactly situated Horizontal , if you draw a reflected parallel for the present day , and know also the true hour , and so place the Glasse , that the spot or reflex of the Sun may fall thereon on the Cieling , for there is no way by an Instrument to do it , the Glasse is so small . Of Reclining Reflecting Glasses . Reflected Dialling from any Reclining Glasse . I shall now shew how to draw any Reflected Dial , with all the Furniture ( that possible may be ) the Glass being set at any possible Reclination . In the drawing of which there is principally to be considered , 1 The Reflected Horizon . 2 The Reflected Meridian . Note , the Horizon & Meridian are two great circles . 1 To draw the Reflected Horizon according to the situation of any reclining Glasse whatsoever . FIrst , let two pieces of nealed wire be fastened on the window on each side of the said Glasse , the ends thereof being without the room in the air , at whose ends let there be fastned a thread which may be pulled straight at pleasure , by bending of the wire , then bend those wires upward or downward , until the thread fastened at the end of each wire be exactly horizontal with the center of the Glasse , which may be tried by a quadrant : Then I tie a string or thread cross the room , in such sort that I may from most part of the thread see the reflecting glass , and therein the said horizontal thread without the room : Then on the said thread cross the room , I tie a slipping knot to move to and fro at pleasure , which knot I move to and fro on the said thread , until by looking in the said Glasse I finde from my eye the said knot and part of the horizontal thread without , all as it were in a right line , the one interposing the sight of the other . Then being careful to keep the knot in that position , fasten one end of a thread in the place of the center of the reclining reflecting glasse , and bring that thread so , as just to touch the aforesaid knot , augmenting that thread , until the end thereof touch the wall or Cieling , and there make a mark or point , so is there one point found on the Wall or Cieling in the Reflected Horizon of the World. Then I begin again , and remove the position of that thread ( which went overthwart the Room ) either higher or lower at pleasure , still having regard that I may from the most part of the said thread see the Reflecting Glasse , and therein the same horizontal thread without the room . Then , as before , I move the said knot on the said thread to & fro , until ( as before ) by looking in the said Glasse I find from my eye the said knot , and part of the Horizontal thread both in one right line , the one interposing the sight of the other ; and by the said knot I bring that thread , whose end is fastened in the center of the said glasse , and keeping it just to touch the said knot , I continue it , until the end thereof touch the Wall or Cieling , as before , and there I make another mark or point ; so is there two points found in the said reflected Horizon on the wall or Cieling . By which said two points , if a thread ( as before ) be so scituated , that it may interpose between the eye and the said two points , there may be many points made to be in the same interposition of the thread , which ( as before ) may be made at every bending or angle of the Wall or Cieling , whereby the reflected Horizon desired may be drawn , by drawing a line from point to point round about the Room ; Which wil be the true reflected Horizon according to the situation of the glasse . 2 To draw the Reflected Meridian , according to the situation of any Reclining Glasse whatsoever . FIrst , take a lath or thin piece of wood of any convenient length at pleasure , as some one and an half , or two foot long , and at each end thereof make a hole , the one to hang a thread and plummet , and the other is to put a small nail therin to fasten it in some part of the window over the center of the Glasse , so that the thread and plummet may hang without the room : then by help of the Suns Azimuth you may draw the meridian line , ( as before ) as if the Glasse were horizontal , and move the lath with the thread and plummet at the end of it to and fro , until the thread and plummet be in the direct meridian of the world with the center of the Glasse . Then ( as before ) tie a thread crosse the room , in such sort that from or by some part of the said thread both the Reclining glasse and the thread to which the plummet is fastened may be seen at one time . Then ( as before ) on the said thread , which crosses the room , I tie a slipping knot , which I move to and fro on the said string , until by looking in the said Glasse I find from my eye the said knot and some part of the perpendicular thread without , all as it were in one right line , the one shadowing or interposing the sight of the other , being then very careful to keep that knot in the same position , then take the thread ( whose end whereof being fastened in the said center of the Glasse ) and bringing it just to touch the said knot , I augment that thread , until the end thereof touch the said wall or Cieling , and the said thread also touch the knot , as before : then in that place where the end of the said thread toucheth the wall or Cieling , I make a mark , which mark or point will be directly in the reflected meridian of the world , according to the situation of that Glasse . Then again I remove that thread ( overthwart the room ) on which the said knot is , either higher or lower then it formerly was at pleasure , still having regard that from some part of the said thread within , you may see both the Reclining Glasse , and the perpendicular thread without at one time ; and ( as before ) move the said slipping knot on the said thread , until by looking in the said Reclining Glasse , you see the said knot and some part of the perpendicular thread without in one right line , so as the one shadows or hinders the sight of the other , ( as before ) which knot then must not be removed from its situation , then take that thread ( whose end is fastened in the Glasse ) and bring it to touch that knot , the end of the said thread being continued to touch the wall or Cieling : so is that point of touch on the Cieling another point found in the Reflected Meridian of the world . So is there two points found in the said Reflected Meridian , on the wall or Cieling ; by which , if a thread ( as before ) be so situated , that it may interpose between the eye and the said two points , many points thereby in the said reflected Meridian may be made at every bending or angle of the wall or Cieling , whereby the Reflected meridian desired may be drawn , by drawing a line from point to point obliquely in the Room , which will be the true Reflected Meridian of the world , according to the situation of that Glasse . Now this Reflected Horizon and Meridian being first drawn , they will be of great use in drawing the Hour-lines , together with all the furniture that possibly can be drawn on any Diall . To draw the Reflected Hour-lines to any Reclining Glasse on any plane whatsoever , that the Sun will be reflected on : By help of an ordinary Horizontal Dial for that Latitude . FIrst , extend several threads from the center of the Glasse to the extremity of the Reflected Horizon in the Room ( which for more conveniency and use may be the several hour-lines , and may also serve as a bed to situate the Horizontal Diall on the Reflected Horizon ) having regard to situate the center of the Dial on the center of the Glasse , and the Meridian of that Dial on the Reflected Meridian of the World : Then to finde the point in the Reflected reversed Axis on the floor of the Room ; Take a thread , one end thereof being fastened in the center of the Glasse , and move the other end thereof to and fro in the reflected meridian under the Reflected Horizon , until by help of a Quadrant the said thread is found to be depressed under the reflected Horizon , equal to the latitude of the place , and where the end of the said thread intersects or meets the Reflected Meridian either on the floor or wall , that point is the reflected reversed Axis , as was required . In which point fasten one end of a thread , which thread will be of great use in drawing the reflected hour-lines on any wall or Cieling whatsoever . Now if this thread , whose end is fastened in a point on the reflected reversed Axis , be taken and brought to touch any part of any one of the threads of the hour-lines ( produced to and fastened in the reflected Horizon ) the said thread being continued so , as the end thereof may touch the wall or Cieling , and also any part of the said thread touch the hour-line or thread proposed ; that point on the wall or Cieling is in the reflected hour-line desired to be drawn : Also the other point in the same reflected hour-line may be found ; If the said thread , whose end is fastened in the Reflected Axis , be brought to touch some other part of the same hour-thread proposed ; so that when ( as before ) the end of the said thread toucheth the wall or Cieling , some part of that thread may also touch the hour-line desired , which point of touch on the wall or Cieling , is also another point in the said reflected hour-line desired . By which two points so found ( as before ) the reflected hour-line may be drawn by a thread , projecting by those points from the eye , as it was formerly directed in drawing the reflected hour-lines to an Horizontal Glasse . To draw the Reflected Equinoctial line , and also the Tropicks on any wall or Cieling , to any Reclining Reflecting glasse . 1 To draw the reflected Equinoctial line on the Wall or Cieling . TAke that thread , whose end is fastened in the center of the reclining glasse , and move the other end thereof to and fro in the said Reflected meridian formerly drawn , until ( by help of a quadrant ) the said thread is elevated above the reflected Horizon formerly drawn , equal to the Complement of the Latitude , ( which as before will be alwayes perpendicular to the reversed Axis ) and make a point in the said reflected meridian , where the end of the said thread toucheth ; then on that point and the said reflected meridian on the Cieling , raise a perpendicular line , which is the Reflected Equinoctial line desired . 2. To draw the reflected Tropicks , or other Parallels of Declination . FIrst , ( as before ) make or take out of some Book a Table of the Suns Altitude for each hour of the day , calculated for the place or Latitude proposed , when the Sun is in either of the Tropicks , or other parallel of Declination : then take that thread , whose end is fastened in the center of the Glasse , move the other end thereof to and fro in the hour-line proposed , until by applying one side of a quadrant to the said thread you find the said thread elevated above the reflected Horizon answerable to the Suns height in that hour proposed , when he is in that Tropick or degree of Declination proposed . Which altitude required will be found in the foresaid Table for that end calculated , which said thread being of the elevation above the reflected Horizon , as the said Table directeth : then mark where the end of the thread ( so elevated ) toucheth the Wall or Cieling in that hour-line : so is one point found in the reflected parallel of Declination desired to be drawn . In like manner , find in the said Table in the same parallel or degree of declination what altitude the Sun hath at the next hour , and elevate the said thread , whose end is fastened in the center of the Glasse , equal to the Suns altitude in that hour above the said reflected Horizon , by help of the said Quadrant , and where the other end of the said thread falleth in the hour-line proposed , make another mark or point . And so in like manner make the points ( belonging to that parallel of Declination ) in the remaining hour-lines , according to the several Altitudes found in the said Table of Altitudes : Then drawing by hand a line to passe through those several points so found , as before , which line is the reflected parallel of the Suns declination desired . In like manner may be drawn all or any other parallel of Declination , which may have respect to the Suns place , or the length of the day , as shall be desired . Or , To draw the said reflected Tropicks , or other parallels of Declination , without any Tables calculated , only , by help of a Trigon first made on pastboard or other material . Note that all Parallels are lesser Circles . FIrst ( as formerly is shewd in drawing the parallels of Delination to a Reflecting Horizontal Glasse ) fasten the Trigon on the reflected reversed Axis , so that the center of the Trigon may be in the center of the Glasse , then also will the Equinoctial on the Trigon be perpendicular to the said reflected reversed Axis : then take the thread fixed in the center of the said Glasse , ( which is also in the center of the Trigon ) and lay it upon that parallel of Declination , drawn on the said Trigon , whose reflected parallel is required to be drawn on the plane or Cieling : then move the Trigon , the thread lying on the said parallel , until the end of the said thread touch any hour-line on the said wall or Cieling , in which point of touch on that hour-line make a mark , so will that point be in the reflected parallel of Declination desired . In like manner , move the said Trigon , still keeping the thread on the same parallel , until the end of that thread touch another hour-line on the said plane or Cieling , and there also make another mark . And so in like manner find a point in each hour-line through which that reflected parallel must passe ; then drawing a line to passe through those several points on the said plane or Cieling , which line is the reflected parallel of the Suns Declination desired . In like manner may be drawn any other reflected parallel of Declination required . To draw the reflected Azimuth-lines to any reclining Glasse , on any plane whatsoever that the Sun-beams will be reflected on . Here note that Azimuths are great Circles . FIrst , know that the reflected vertical point in the Axis of the Reflected Horizon , will alwayes be found in the reflected meridian . And look how many degrees the reflected Horizon differs from the direct Horizon , so many must the reflected Axis of the Horizon differ from the direct Axis of the Horizon : Hence the reflected vertical point , whereby the reflected Azimuth-lines are drawn , may be thus found . Take that thread whose end is fixed in the center of the Glasse , and move the other end thereof to & fro in the reflected meridian , until by applying one side of a quadrant thereto , you find the said thread depressed just 90 degrees , or perpendicular under the reflected Horizon ; then make a mark or point where the other end of the said thread toucheth the said reflected Meridian on the Wall , Ground , or Floor of the Room , which point so found is the reflected vertical point desired , in which point fasten one end of a thread : Then on pastboard or other material draw the points of the Compasse or other degrees , placing the center thereof in the center of the Glasse , and the meridian thereof in the reflected meridian of the world , which said pastboard must be also situated in the reflected Horizon just as the Horizontal Dial was formerly directed to be situated for drawing the reflected hour-lines : And as the threads from the center fastened in the reflected Horizon were also the hour-lines on the Horizontal Diall , whereby the reflected hour-lines were drawn . So now the threads from the center fastened in the Reflected Horizon may be the Horizontal Azimuth lines , whereby the reflected Azimuth-lines may be drawn : Or if that thread which fastned in the center of the glass be drawn exactly over any Azimuth-line , the end whereof being fastened by a nail or other means in the reflected Horizon on the other side of the Room , there may several points be found in the wall or Cieling , through which the reflected Azimuth line must passe , as followeth : Take that thread , one end of which is fastened in the said vertical point , and bring it just to touch the Azimuth thread formerly fastened , and continue it until the end thereof touch the wall or Cieling , ( and also the thread it self touch the said Azimuth it self , as before ) in which point of touch on the wall or Cieling make a mark , through which point that reflected Azimuth-line must passe . Then move the said string fastened in the said vertical point , so that it may just touch the said thread again , but in another place : then as before continue that thread , untill the end thereof touch the wall or Cieling again , as before , and there make another mark , through which the said reflected Azimuth line must also passe ; In like manner may more points be found for your further guide , in drawing that Azimuth-line . But two points being found will be sufficient . To draw any reflected line by any two points given over any plane whatsoever , without projecting by the eye . FAsten two threads in the place of the center of the said reclining Glasse , drawing the said threads straight , fastening each of the other ends in the two reflected Azimuth-points formerly found on the wall or Cieling . Then situate a thread cross or thwart the room , so as it may crosse those other threads from the center , neer at right angles , and also just touch both of them in that situation . By which said thread crosse the room may any number of points in the said reflected Azimuth-line to be drawn , be found at pleasure : For if the end of another thread be also fastened in the center of the said Glasse , making the other end thereof to touch the wall or Cieling , but so that it may also just touch the said thread , which is fastened crosse the room , which point of touch on the said wall or Cieling is another point in the said reflected Azimuth line required to be drawn . In like manner may more points be found at every angle or bending of the wall or Cieling for the exacter drawing the reflected Azimuth line required , which doth find points , whereby is drawn the same reflected Azimuth line ( or other lines ) as was formerly done by a thread so situated , that it may interpose between the eye and any two points assigned on the wall or Cieling . In like manner , if the thread fastened on the further side of the room were removed on another Azimuth line on the said pastboard , and then fasten it again on the further side of the room ( as before ) you may by help of the said thread fastened in the said vertical point find several points on the wall or Cieling , through which that Azimuth-line will passe ; So may you either by this or the former way draw what Azimuth lines you please , either in points of the Mariners Compasse or degrees , as you please , by drawing it first on pastboard , as before is directed . And note generally , that such relation the point found on the floor or ground in the reflected reversed Axis , hath to the hour-lines drawn on the Horizontal Dial , in drawing the reflected hour-lines ; The same hath the Reflected vertical point found on the floor or ground , to the Azimuths drawn on the pastboard in drawing the reflected Azimuth-lines . To draw the reflected parallels of the Suns altitude , or proportions of shadows to any reclining Glasse on any Plane whatsoever , that the Sun-beams will be reflected on . Here note , that parallels of Altitude are lesser Circles , therefore are not represented by a right line . FIrst , know generally that what respect the parallels of Declination have to the hour-lines , such have the parallels of Altitude to the Azimuths . For if one end of a thread be fastened in the place of the center of the reclining Glasse , and the other end moved to and fro in any reflected Azimuth line , until the said thread be elevated any number of degrees proposed above the reflected Horizon ( the Elevation of which thread being found , by applying a Quadrant thereto , and making a mark or point where the end of the said thread toucheth the said reflected Azimuth drawn on the wall or Cieling , that point so found is the point through which that Almican●er or reflected parallel of the Suns altitude must passe . In like manner , remove the other end of the said thread fastned in the center of the Glasse to another reflected Azimuth-line , and ( as before ) move it higher or lower , untill by applying the edge of a quadrant to that thread , you find the said thread above the reflected Horizon the same number of degrees first proposed , and at the end of the said thread in that Reflected Azimuth-line drawn on the wall or Cieling I make another mark or point , through which the same Reflected Almicanter or parallel of Altitude must also passe : And so in like manner I find a point on each reflected Azimuth-line , through which the same parallel of Altitude must passe . Then drawing by hand a line to passe through these several points so found , as before , that line is the Reflected parallel of the Suns Altitude proposed . In like manner may be drawn all the other parallels of Altitude desired , which will shew the Suns altitude or the Proportion of any shadow to its altitude , at any appearance of the Suns reflex thereon . To draw the Jewish or old unequal hour-lines to any Reclining Glasse on any plane whatsoever that the Sun-beams will be reflected on . Here note that the Jewish hour-lines are great Circles . FIrst , ( by the Rules formerly given ) draw two reflected parallels of Declination of 16 d. 55′ , the one being neer the Summer , and the other neer the Winter-Tropick : for when the Sun hath that Declination , the day is 15 hours long in the Summer , and 9 in the winter : Then ( as is formerly directed ) situate a thread just between the eye , and those three points in the said Reflected Dial , as is expressed in the insuing Table , so may you thereby draw all or any of those Jewish hour-lines desired , which will at any appearance of the spot by the reflex of the Glasse amongst those hour-lines , shew how many of the equal hours is past since Sun-rising , as was desired . Now in this Latitude of 51 deg . 30′ , If the parallels of the Suns declination be drawn , both when the day is 9 and 15 hours long , that is , when it is 16 d. 55′ , any of those Jewish hour-lines will intersect the common hour-lines , either upon the hours , half hours , or quarters . And such a declination may be found , that it shall so do in any Latitude desired . Unequal Hours . 15 H. M Equ . H. 9 H. M. 0 4 30 6 7 30 1 5 45 7 8 15 2 7 00 8 9 00 3 8 15 9 9 45 4 9 30 10 10 30 5 10 45 11 11 15 6 12 00 12 12 00 Unequ . hours 15 H. M. Equ . H. 9 H. M.             7 1 15 1 0 45 8 2 30 2 1 30 9 3 45 3 2 15 10 5 00 4 3 00 11 6 15 5 3 45 12 7 30 6 4 30 To draw the Circles of Position to any reclining Glasse on any plane whatsoever , that the Sun-beams will be reflected on . NOte that all Circles of Position are great Circles of the Sphere , and do alwayes intersect each other in that point of the Reflected meridian which toucheth the Reflected Horizon , which may be called the common intersection ; which said Circles of Position are reckoned upon the Reflected Equinoctial both wayes from the said meridian down to the said Horizon : The Horizon Eastward being the Cuspis of the first House , and the Horizon Westward being the Cuspis of the seventh House ; and the Reflected meridian the cuspis of the tenth House . So that those Meridian-planes , whose Reclination is 60 degrees Westwards , ( being measured from the meridian in the Equinoctial ) lies in the Cuspis of the eighth House , and 30 degr . Westward lies in the Cuspis of the ninth house , and 30 deg . Eastward in the Cuspis of the eleventh House , and 60 deg . Eastward in the Cuspis of the twelfth House : which are all the Houses above the Horizon . Now to draw any Circle of Position , or the Cuspis of any House on any Cieling or wall to any reclining Glasse is done as followeth : First , fasten a thread , in such sort , within the Room , as that it may interpose between the eye and the said common point of intersection on the wall or Cieling , and also between that point where the reflected hour-line of 4 ( being 60 deg . Westward from the said Meridian ) intersects the reflected Equinoctial also on the Cieling , whereby points may be made at every bending or angle of the wall or Cieling , to which the thread so situated may also interpose , by which points the Reflected Cuspis of the eighth House may be drawn . In like manner may the Cuspis of any other House above the Horizon , as the 9 th . or 10 th . which is the Meridian ( or Medium Coell ) or 11 th . or 12 th . be drawn also . For if ( as before ) the said thread be again so fastened within the Room , as that it may also interpose between the eye and the said common point of intersection , and also those points where the reflected hour-line of 2 ( being 30 deg . Westward from the said meridian ) do cut the reflected Equinoctial , whereby may be drawn the reflected Cuspis of the ninth House . Or where the Reflected hour-line of 10 ( being also 30 deg . Eastward from the meridian ) do also cut the said reflected Equinoctial , whereby may be drawn the Cuspis of the 11 th . House . Or where the reflected hour-line of 8 ( being 60 deg . Eastward from the meridian ) do also cut the said reflected Equinoctial , whereby may be drawn the Cuspis of the 12 th . House . The Horizon alwayes being the Cuspis of the first and seventh Houses , and the meridian the Cuspis of the tenth house or Medium Coeli : wherein generally it is to be noted , That in all planes which cut the common Intersection of the meridian and Horizon , ( as doth the Horizontal , and also all meridian planes both Direct and Reclining ) these Circles of Position are all parallel to the meridian , and therefore parallel each to other . For look what respect the hour-lines in all Direct or Reclining Polar Planes , or Direct meridian Planes have to the Axis of the World : Such respect have the Circles of Position , in all Horizontal , or Direct meridian or Reclining meridian Planes , to the Axis of the Prime vertical : For as the hour-lines in the first are all parallel to the Axis of the Equinoctial , in whose Poles they meet : So the Circles of Position in the second are all parallel to the Axis of the Prime Vertical , in whose Poles they also meet . The reason why Glasses reflect a double Spot , is because they are polisht on both sides , which may be remedied with a Pumex-stone . Those that desire to read more of this Subject may see what is written by Kircher , in primitiis Gnomicae Catoptricae , and since him by Magnan and others , VALE . FINIS . 
A52257	----	Cosmographia, or, A view of the terrestrial and cœlestial globes in a brief explanation of the principles of plain and solid geometry applied to surveying and gauging of cask : the doctrine of primum mobile : with an account of the Juilan & Gregorian calendars, and the computation of the places of the sun, moon, and fixed stars ... : to which is added an introduction unto geography / by John Newton ... Newton, John, 1622-1678. 1679 Approx. 1185 KB of XML-encoded text transcribed from 286 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2004-11 (EEBO-TCP Phase 1). A52257 Wing N1055 ESTC R17177 12546927 ocm 12546927 63077 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A52257) Transcribed from: (Early English Books Online ; image set 63077) Images scanned from microfilm: (Early English books, 1641-1700 ; 326:7) Cosmographia, or, A view of the terrestrial and cœlestial globes in a brief explanation of the principles of plain and solid geometry applied to surveying and gauging of cask : the doctrine of primum mobile : with an account of the Juilan & Gregorian calendars, and the computation of the places of the sun, moon, and fixed stars ... : to which is added an introduction unto geography / by John Newton ... Newton, John, 1622-1678. [15], 510, [16] p., [12] leaves of folded plates : ill. Printed for Thomas Passinger ..., London : 1679. "Tables for the measuring of timber" and "Astronomy, the second part, or, An account of the civil year" have special title pages. Advertisement: p. [13]-[16] at end. Reproduction of original in Yale University Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. EEBO-TCP is a partnership between the Universities of Michigan and Oxford and the publisher ProQuest to create accurately transcribed and encoded texts based on the image sets published by ProQuest via their Early English Books Online (EEBO) database (http://eebo.chadwyck.com). The general aim of EEBO-TCP is to encode one copy (usually the first edition) of every monographic English-language title published between 1473 and 1700 available in EEBO. EEBO-TCP aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the Text Encoding Initiative (http://www.tei-c.org). The EEBO-TCP project was divided into two phases. The 25,363 texts created during Phase 1 of the project have been released into the public domain as of 1 January 2015. Anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. Users should be aware of the process of creating the TCP texts, and therefore of any assumptions that can be made about the data. Text selection was based on the New Cambridge Bibliography of English Literature (NCBEL). If an author (or for an anonymous work, the title) appears in NCBEL, then their works are eligible for inclusion. 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Understanding these processes should make clear that, while the overall quality of TCP data is very good, some errors will remain and some readable characters will be marked as illegible. Users should bear in mind that in all likelihood such instances will never have been looked at by a TCP editor. The texts were encoded and linked to page images in accordance with level 4 of the TEI in Libraries guidelines. Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Geometry -- Early works to 1800. Calendar -- Early works to 1800. Geography -- Early works to 1800. Astronomy -- Early works to 1800. 2004-04 TCP Assigned for keying and markup 2004-05 Aptara Keyed and coded from ProQuest page images 2004-08 John Latta Sampled and proofread 2004-08 John Latta Text and markup reviewed and edited 2004-10 pfs Batch review (QC) and XML conversion Imprimatur ; Guil. Iane R. P. D. Hen. Episc. Lond. à Sacris Dom. COSMOGRAPHIA , OR A VIEW OF THE Terrestrial and Coelestial GLOBES , IN A Brief Explanation OF THE PRINCIPLES Of plain and solid GEOMETRY , Applied to Surveying and Gauging of CASK . The Doctrine of the Primum Mobile . With an Account of the Juilan & Gregorian Calendars , and the Computation of the Places of of the Sun , Moon , and Fixed Stars , from such Decimal Tables of their Middle Motion , as supposeth the whole Circle to be divided into an hundred Degrees or Parts . To which is added an Introduction unto GEOGRAPHY . By John Newton , D. D. London , Printed for Thomas Passinger , at the Three Bibles on London-Bridge 1679. TO THE Most Honourable HENRY SOMERSET , Lord Herbert , Baron of Chepstow , Raglan , and Gower , Earl and Marquess of Worcester , Lord President and Lord Lieutenant of Wales and the Marches , Lord Lieutenant of Gloucester , Hereford and Monmouth , and of the City and County of Bristol , Knight of the Most Noble Order of the Garter , and one of His Majestie 's Most Honourable Privy Council . HE that adventures upon any thing contrary to the General received practice , what ever his own courage and resolutions are , had need to be supported , not only by the most Wise and Honourable , but also the most Powerful Persons that are in a Nation or Kingdom ; For let the Proposals be never so advantagious to the Publick , they shall not only be decried and neglected , but it is well , if the Promoter be not both abused and ruined : Yet I , notwithstanding all these discouragements , have not been silent , but in order to Childrens better Education , have long since published my thoughts , and have and do declare , that the multitude of Schools for the learning of the Latine and Greek Tongues , are destructive both to our youth and the Commonwealth ; and if the Opinion of Sir Francis Bacon in his Advice to King Iames concerning Sutton's Hospital , be not sufficient to warrant my Assertion , I could heartily wish that no such Evidence could have been produced , as the late unhappy Wars , in the Bowels of this Kingdom hath afforded us ; for what he saith there by way of Advice , we by woful Experience have found too true ; that by reason of the multitude of Grammar Schools , more Scholars are dayly brought up , than all the Preferments in this Nation can provide for , and so they become uncapable of other Professions , and unprofitable in their own , and at last become , materia rerum novarum ; whether this be an essential or an accidental Effect , I will not here dispute ; the truth of it , I am sure , cannot be denied : but that is not all ; by this means it comes to pass , that four of the seven Liberal Arts , are almost wholly neglected , as well in both Universities , as in all Inferiour Schools ; and setting aside the City of London , there are but few Places in this Nation , where a man can put his Son , to be well instructed in Arithmetick , Geometry , Musick and Astronomy ; and even that Famous City was without a Publick School for Mathematical Learning , till His present Majesty was pleased to lay the Foundation ; nay so averse are men in the general to these Arts ( which are the support of all Trade ) that without a high hand , it will be almost impossible , to make this People wise for their own good : I come therefore to your Honour , humbly to beg your Countenance and Assistance , that the Stream of Learning may be a little diverted , in those Schools that are already erected , and to be instrumental for the erecting more , when they shall be wanting ; that we may not be permitted still to begin at the wrong end ; but that according to the practice of the Ancient Philosophers , Children may be instructed in Arithmetick , Geometry , Musick and Astronomy ; before the Latine and Greek Grammars are thought on , these Arts in themselves , are much more easie to be learned , tend more to a general good , and will in a great measure facilitate the Learning of the Tongues , to as many as shall after this Foundation laid , be continued at School , and provided for in either Universities . Your Honour was instrumental to enlarge the Maintenance for God's Minister in the Place where I live , and perhaps it may please God to make you so , not only in making this Place in particular , but many other Places in this Land happy , by procuring Schools for these Sciences , and not only so , but by your Loyal and Prudent managing the several Trusts committed to you , you may do much for God's Glory , your Countries Good , and the continuance of your own Honour to all Future Generations , which is , and shall be the Prayer of , Your Honour 's Obliged and Devoted Servant , JOHN NEWTON . TO THE READER . MY Design in publishing these Introductions to Geometry and Astronomy , is so well known by all the Epistles , to my other Treatises of Grammar , Arithmetick , Rhetorick , and Logick , that I think it needless to tell thee here , that it is my Opinion , that all the Arts should be taught our Children in the English Tongue , before they begin to learn the Greek or Latin Grammar , by which means many thousands of Children would be fitted for all Trades , enabled to earn their own Livings , and made useful in the Commonwealth ; and that before they attain to twelve years of age ; and by consequence the swarming of Bees would be prevented , who being compelled to leave their Hives , for want of room , do spread themselves abroad , and instead of gathering of Honey , do● sting all that come in their way . We should not have such innumerable company of Gown-men to the loss and prejudice of themselves and the Common-wealth ; and those we had would probably be more learned , and better regarded . His Majesty being pleased to begin this Work , by His Bounty towards a Mathematical School in Christ's Church London ; I am not now without hopes , to see the same effected in many other Places in this Kingdom ; and to this purpose I have to my Introductions to the other Arts , added these also to Geometry and Astronomy ; which I call by the name of Cosmographia ; and this I have divided into four Parts ; in the first I have briefly laid down the first Principles belonging to the three kinds of Magnitude or continued Quantity , Lines , Planes and Solids ; which ought in some measure to be known , before we enter upon Astronomy , and this part I call an Introduction unto Geometry : The second and third Parts treat of Astronomy ; the first of which sheweth the Doctrine of the Primum Mobile , that is , the Declination , Right Ascension , and Oblique Ascensions of the Sun and Stars , and such other Problems , as do depend upon the Doctrine of Spherical Triangles . The second Part of Astronomy , treateth of the motion of the Sun , Moon and Fixed Stars ; in order whereunto , I have first given thee a brief account of the Civil Year , with the cause of the difference between our Julian and Gregorian Calendar , and of both from the true ; for it must be acknowledged that both are erroneous , though ours be the worse of the two ; yet not so bad , but that our Dissenting Brethren have I hope some better Arguments to justifie their Non-conformity ▪ than what I see published in a little Book without any name to it , concerning two Easters in one Year ; by the General Table , saith this learned man , who owneth the Feast of Easter was to be observed Anno 1674. upon the 19 day of April , so the Almanacks for that Year , as well as the General Table set before the Book of Common Prayer ; but by the Rule in the said Book of Common Prayer given , the Feast of Easter should have been upon the twelfth of April , for Easter-Day must always be the first Sunday after the first Full Moon , which happeneth next after the one and twentieth day of March , and if the Full Moon happen upon a Sunday , Easter-Day is the Sunday after ; Now in the Year 1674. the 19 of April being Friday was Full Moon , therefore by this Rule , Easter-Day should be the twelfth , and by the Table and the Common Almanacks April the tenth ; but this learned man must know , that the mistake is in himself , and not in the Rule or Table set down in the Book of Common Prayer ; for if he please to look into the Calendar , he will find that the Golden Number Three , ( which was the Golden Number for that Year ) is placed against the last day of March , and therefore according to the supposed motion of the Moon , that Day was New Moon ; and then the Full Moon will fall upon the fourteenth day of April , and not upon the tenth , and so by consequence the Sunday following the first Full Moon after the 21 day of March was the nineteenth of April and not the twelfth . And thus the Rule and the Table in the Book of Common Prayer for finding the Feast of Easter are reconciled ; and when Authority shall think sit , the Calendar may be corrected and all the moveable Feasts be observed upon the days and times at first appointed ; but till that be , a greater difference than one Week will be found in the Feast of Easter between the Observation thereof according to the Moons true motion , and that upon which the Tables are grounded ; for by the Fathers of the Nicene Council it was appointed , that the Feast of Easter should be observed upon the Sunday following the first Full Moon after the Vernal Equinox , which then indeed was the 21 of March ; but now the tenth , and in the Year 1674. Wednesday the 11 of March was Full Moon , and therefore by this Rule , Easter-Day should have been upon March the fifteenth , whereas according to the Rules we go by , it was not till April the nineteenth . The Tables of the Sun and Moons middle motions are neither made according to the usual Sexagenary Forms , nor according to the usual Degrees of a Circle and Decimal Parts , but according to a Circle divided into 100 Degrees and Parts , and this I thought good to do , to give the World a taste of the excellency of Decimal Numbers , which if a Canon of Sines and Tangents were fitted to it , would be found much better , as to the computing the Places of the Planets ; but as to the Primum Mobile , by reason of the general dividing a Circle into 360 Degrees , I should think such a Canon with the Decimal Parts most convenient , and in some cases the common Sexagenary Canon may be very useful , and indeed should wish and shall endeavour to have all printed together , one Table of Logarithms will serve them all , and two such Canons , one for the Study and another for the Pocket , would be sufficient for all Mathematical Books in that kind ; and then men may use them all or either of them as they shall have occasion , or as every one is perswaded in his own mind . What I have done in this particular , as it was for mine own satisfaction , so I am apt to believe , that it will be pleasing to many others ; and although I shall leave every one to abound in his own sense , yet I cannot think that Custom should be such a Tyrant , as to force us always to use the Sexagenary form , if so , I wonder that men did not always use the natural Canon ; if no alteration may be admitted , what reason can be given for the use of Logarithms ; and if that be found more ready than the natural , in things of this kind , where none but particular Students are concerned , I should think it reasonable , to reduce all things hereafter , into that form , which shall be found most ready and exact ; now the Part Proportional in the Artificial Sines and Tangents in the three first Degrees cannot be well taken by the common difference , and the way of finding them otherwise will not be so easie in the Sexagenary Canon , as in either of the other , and this me thinks , should render that Canon which divides each Degree into 100 Parts more acceptable ; but thus to retain the use of Sines , Degrees , and Decimal Parts , doth not to me seem convenient , and to reckon up , a Planets middle motion , by whole Circles will sometimes cause a Division of Degrees by 60 , which hath some trouble in it also , but if a Circle be divided into 100 Degrees , this inconvenience is avoided , and were there no other reason to be given , this me thinks should make such a Canon to be desirable ; but till I can find an opportunity of publishing such an one , I shall forbear to shew any further uses of it , and for what is wanting here in this subject , I therefore refer thee to Mr. Street's Astronomia Carolina , and the several Books written in English by Mr. Wing . The fourth Part of this Treatise is an Introduction unto Geography , in which I have given general Directions , for the understanding how the habitable part of the World is divided in respect of Longitude and Latitude in respect of Climes and Parallels with such other Particulars as will be found useful unto such as shall be willing to understand History ; in which three things are required ; The time when , and this depends upon Astronomy ; the place where , and this depends upon Geography ; and the Person by whom any memorable Act was done , and this must be had from the Historical narration thereof ; and he that reads History without some knowledge in Astronomy and Geography will find himself at a loss , and be able to give but a lame account of what he reads ; but after the learning of these Arts of Grammar , ( I mean so much thereof , as tends to the understanding of every ones Native Language ) Arithmetick , Geometry and Astronomy ; a Child may proceed profitably to Rhetorick and Logick , the reading of History , and the learning of the Tongues ; and sure there is no studious and ingenious man , but will stand in need of some Recreation , and therefore if Musick in the Worship and Service of God be not Argument enough to allow that a place among the Arts , let that poor end of Delight and Pleasure be her Advocate ; and although that all men have not Voyces , yet I can hardly believe , that he expects any Melodious Harmony in Heaven , that will not allow Instrumental Musick a place on Earth ; and as for those that have Voyces , surely the time of learning Vocal Musick , must be in Youth , and I am perswaded that the Arts and Sciences to some good degree may be learned by Children before they be full twelve years old , and would our Grammer Masters leave off their horrible severity , and apply themselves to such ways of teaching Youth , as the World is not now unacquainted with , I am perswaded that it is no difficult matter , in four years time more to fit Children in some good measure for the University . The great Obstruction in this Work , is the general Ignorance of Teachers , who being unacquainted with this Learning , cannot teach others what they know not themselves . I could propound a remedy for this , Sed Cynthius aurem vellit ; Therefore I will forbear and leave what I have written , to be perused and censured as thou shall think fit . John Newton . Practical Geometry ; OR , THE ART of SURVEYING . CHAP. I. Of the Definition and Division of Geometry . GEometry is a Science explaining the kinds and properties of continued quantity or magnitude . 2. There are three Kinds or Species of Magnitude or continued Quantity , Lines , Superficies and Solids . 3. A Line is a Magnitude consisting only of length without either breadth or thickness . 4. In a Line two things are to be considered , the Terms or Limits , and the several Kinds . 5. The term or limit of a Line is a Point . 6. A Point is an indivisible Sign in Magnitude which cannot be comprehended by sense , but must be conceived by the Mind . 7. The kinds of Lines are two , Right and Oblique . 8. A Right Line is that which lieth between his Points , without any going up or going down on either side . As the Line AB lieth streight and equally between the Points A and B. Fig. 1. 9. An Oblique Line is that which doth not lie equally between its Points , but goeth up and down sometimes on the one side and sometimes on the other . And this is either simple or various . 10. A simple Oblique Line , is that which is exactly Oblique , as the Arch of a Circle ; of Various Oblique Lines there is but little use in Geometry . 11. Thus are Lines to be considered in themselves , they may be also considered as compared to one another , and that either in respect of their distances , or in respect of their meetings . 12. In respect of their distances , they may be either equally distant , or unequally . 13. Lines equally distant are two or more , which by an equal space are distant from one another , and these are called Parallels ; and these though infinitely extended will never concur . 14. Lines unequally distant , are such as do more or less incline to one another , and these being extended will at last concur . 15. Concurring Lines are either perpendicular or not perpendicular . 16. A Perpendicular Line , is a Right Line falling directly upon another Right Line , not declining or inclining to one side more than another ; as the Line AB in Fig. 1. 17. A Perpendicular Line is twofold , to wit , either falling exactly in the middle of another Line , or upon some other Point which is not the middle . 18. A line exactly Perpendicular , may be drawn in the same manner , as any Right Line may be divided into two equal Parts ; the which may thus be done . If from the two Terms or Points of the Right Line given , there shall be described two Arches crossing one another above and below , a Line drawn through the Intersections of those Arches , shall be exactly Perpendicular , and also divide the Right Line given into her equal Parts . Fig. 1. For Example ; Let CD be the Right Line given , and let it be required , to bisect this Line , and to erect a Perpendicular in the middle thereof . 1. Then setting one of your Compasses in the Points C , draw the Arches E and F. 2. Setting one Foot of your Compasses in D , draw the Arches G and H , and from the Intersections of these Arches draw the Right Line KL , so shall the Right Line KL be Perpendicular to the Right-Line CD , and the Right Line CD also divided into two equal Parts , in the Point A. 19. A Line Perpendicular to any other Point than the middle is twofold : for it is either drawn from some Point given in the Line ; or from some Point given without the Line . 20. From a Point given in the Line , at Perpendicular may thus be drawn . In Fig. 2. Let the given Line be CD , and let it be required to draw a Perpendicular Line to the Point C , your Compasses being opened to any reasonable distance , set one Foot in the Point C , and the other in any place on either side the Line CD , suppose at A , then describe the Arch ECF , this done draw the Line EA , and where that Line being extended shall cut the Arch ECF , a Right Line drawn from C to that Intersection shall be Perpendicular to the Point C in the Line CD , as was required . 21. From a Point given without the Line , a Perpendicular may be drawn in this manner . In Fig. 2. Let the given Line be CD , and let it be required to draw another Line Perpendicular thereunto , from the Point F without the Line . From the Point F draw a streight Line to some part of the Line CD at pleasure , as FE , which being bisected , the Point of Bisection will be A , if therefore at the distance of AF , you draw the Arch ECF , the Right Line CF shall be Perpendicular to the Line CD , as was required . 22. Hitherto concerning a Perpendicular Line . A Right Line not Perpendicular , is a Right Line falling indirectly upon another Right Line , inclining thereto on the one side more , and on the other less . 23. Lines unequally distant , and at last concurring , do by their meeting make an Angle . 24. An Angle therefore is nothing else , then the place , where two Lines do meet or touch one another , and the two Lines which constitute the Angle , are in Geometry called the sides of the Angle . 25. Every Angle is either Heterogeneous , or Homogeneous : that is called an Hetorogeneous Angle , which is made by the meeting of one Right Line , and another that is Oblique and Crooked ; and that is called an Homogeneous Angle , which is made by the meeting of two Lines of the same kind , that is , of two Right Lines , or of two curved or Circular Lines . 26. An Homogeneous Angle made of two curved or Circular Lines , is to be considered in Geometry as in Spherical Triangles , but the other which is made of Right Lines , is in all the Parts of Geometry of more frequent use . 27. Right lined Angles are either Right or Oblique . 28. A Right Angle is that whose legs or sides are Perpendicular to one another , making the comprehended space on both sides equal . Thus in Fig. 1. the Line AK is Perpendicular to the Line CD , and the Angles KAC and KAD , are right and equal to one another . 29. An Oblique Angle is that , whose sides are not Perpendicular to one another . 30. An Oblique Angle is either acute or obtuse . 31. An Acute Angle is that which is less than a Right . 32. An Obtuse Angle , is that which is greater than a Right . Thus in Fig. 1. The Angle BAC is an Acute Angle because less than the Right Angle CAK . And the Angle BAD is an Obtuse Angle being greater than the Right Angle DAK . The Geometrical Propositions concerning Lines and Angles are very many , but these following we think sufficient for our present purpose . Proposition I. To divide a Right Line given into any Number of equal Parts . Let it be required to divide the Right Line AB into five equal Parts . From the extream Points of the given Line A and B , let there be drawn two Parallel Lines , then from the Point A at any distance of the Compasses , set off as many equal Parts wanting one , as the given Line is to be divided into , which in our Example is four , and are noted thus , 1. 2. 3. 4. and from the Point B set off the like Parts in the Line BC , and let them be noted likewise thus , 1. 2. 3. 4. then shall the Parallel Lines , 14. 23. 32 , and 41. divide the Right Line AB into 5 equal Parts , as was required . Proposition II. Two Right Lines being given , to find a Mean propertional between them . Let the two Right Lines given be DB and CB , which let be made into one Line as CD , which being besected the Point of bisection is A , from which as from a Centre describe the Arch CED , and from the Point B erect the Perpendicular BE , so shall BE , be the Mean proportional required ; for , BC. BE ∷ BE. BD. Proposition III. Three Right Lines being given , to find a fourth proportional . Let the three given Lines be AB . BC. and AD. Fig. 5. to which a fourth proportional is required : draw AE at any Acute Angle , to the Line AD in the Point A ; and make DE parallel to BC , so shall AE be the fourth proportional required ; for , AB . BC ∷ AD. AE . Proposition IV. Vpon a Right Line given , to make a right-lined . Angle , equal to an Angle given . Let it be required upon the Line CD in Fig. 6. to make an Angle , equal to the Angle DAE in Fig. 5. From the Point A as a Center , at any extent of the Compasses describe the Arch BG , between the sides of the Angle given , and with the same extent describe the Arch HL from the Point D , and then make HL equal to BG , then draw the Line DL , so shall the Angle CDL be equal to the Angle DAE given , as was required . CHAP. II. Of Figures in the general , more particularly of a Circle and the affections thereof . HItherto we have spoken of the first kind of Magnitude , that is , of Lines , as they are considered of themselves , or amongst themselves . 2. The second kind of Magnitude is that which is made of Lines , that is , a Figure consisting of breadth as well as length , and this is otherwise called a Superficies . 3. And in a Superficies there are three things to be considered . 1. The Term or Limit . 2. The middle of the Term. 3. The Thing or Figure made by the Term or Limit . 4. The Term or Limit is that which comprehendeth and boundeth the Figure , it is commonly called the Perimeter or Circumference . 5. The Term of a Figure is either Simple or various . 6. A Simple Term is that which doth consist of a Simple Line , and is properly called a Circumference or Periphery : A Periphery therefore is the Term of a Circle or most Simple Figure . 7. A various Term is that which hath bending or crooked Lines , making Angles , and may therefore be called Angular . 8. The middle of Term is that which is the Center of the Figure ; for every Figure , whether Triangular , Quadrangular , or Multangular , hath a Center as well as the Circular , differing in in this , that the Lines in a Circle drawn from the Center to the Circumference are all equal , but in other Figures they are not equal . 9. The Thing or Figure made by the Term or Limit , is all that Area or space which is included by the Term or Terms . And here it is to be observed , that the Term of a Figure is one thing , and the Figure it self another ; for Example , A Periphery is the Term of a Circle , but the Circle it self is not properly the Periphery , but all that Area or space which is included by the Periphery , for a Periphery is nothing but a Line , but the Circle is that which is included by that Line . 10. As the Term of a Figure is either Simple or Various ; so the Figure it self is either Simple and Round , or Various and Angular . 11. A Simple Figure is that which is contained by a Simple or Round Line , and is either a Circle or an Ellipsis . 12. A Circle therefore is such a Figure which is made by a Line so drawn into it self , as that it is every where equally distant from the middle or Center . 13. An Ellipsis is an oblong Circle . 14. In a Circle we are to consider the affections which are as it were the Parts or Sections thereof , as they are made by the various applications of Right Lines . 15. And Right Lines may be applied unto a Circle , either by drawing them within , or without the Circle . 16. Right Lines inscribed within a Circle , are either such as do cut the Circle into two equal or unequal Parts , as the Diameter and lesser Chords , or such as do cut the Diameter and lesser Chords into two equal or unequal Parts , as the Right and versed Sines . 17. A Diameter is a Right Line drawn through the Center from one side of the Circumference to the other , and divideth the Circle into two equal Parts , As in Fig. 7. The Right Line GD drawn through the Center B is the Diameter of the Circle GEDL dividing the same into the two equal Parts GED , and GLD : and this is also called the greatest Chord or Subtense . 18. A Chord or Subtense is a Right Line inscribed in a Circle , dividing the same into two equal or unequal Parts ; if it divide the Circle into two equal Parts , it is the same with the Diameter , but if it divide the Circle into two unequal Parts it is less than the Diameter , and is the Chord or Subtense of an Arch less than a Semi-circle , and also of an Arch greater than a Semi-circle . As in the former Figure , the Right Line CAK divideth the Circle into two unequal Parts , and is the Chord or Subtense of the Arch CDK , less than a Semi-circle , and of the Arch CGK greater than a Semi-circle : and these are the Lines which divide the Circle into two equal or unequal Parts . And as they divide the Circle into two equal Parts , so do they also divide one another ; The lesser Chords when they are divided by the Diameter into two equal Parts , those Parts are called Right Sines , and the two Parts of the Diameter made by the intersection of the Chords are called versed Sines . 19. Sines are right or versed . 20. Right Sines are made by being besected , by the Diameter , and are twofold , Sinus totus , the whole Sine or Radius , and this is the one half of the Diameter , as the Lines BE or BD , and all Lines drawn from the Center to the Circumference . 21. Sinus simpliter , or the lesser Sines , are the one half of any Chord less than the Diameter , as in the former Figure CA or AK , which are the equal Parts of the Chord CAK , are the Sines of the Arches CD . and DK less than a Quadrant , and also the Sines of CEG and KLG greater than a Quadrant . 22. Versed Sines are the Segments of the Diameter , made by the Chords intersecting it , at Right Angles , as AD is the versed Sine of CD or DG and the other Segment AG is the versed Sine of the Arch CEG or KLG . 23. The Right Lines drawn without the Circle are two , the one touching the Circle , and is called a Tangent , and the other cutting the Circle , and is called a Secant . 24. A Tangent is a Right Line touching the Circle , and drawn perpendicular to the Diameter , and extended to the Secant . 25. A Secant is a Right Line drawn from the Center through the Circumference , and extended to the Tangent . As in the former Figure , the Right Line DF is the Tangent of the Arch CD , and the Right Line BF is the Secant of the same Arch CD . Proposition I. The Arch of a Circle being given to describe the whole Periphery . Let ABC be an Arch given , and let the Circumference of that Circle be required . Let there be three Points taken in the given Arch at pleasure , as A , B , C ; open your Compasses to more than half the distance of A , B , and setting one Foot in A describe the Arch of a Circle , and the Compasses remaining at the same distance , setting one Foot in B , describe another Arch so as it may cut the former in two Points , suppose G , and H , and draw the Line HG towards that Part on which you suppose the Center of the Center of the Circle will fall . In like manner , opening your Compasses to more than half your distance of B , C , describe two other Arches from the Points E and C , cutting each other in E and F , then draw the Line EF till it intersect the former Line HG , so shall the Point of Intersection be the Center of the Circumference or Circle required , as in Fig. may be seen . Proposition II. The Conjugate Diameters of an Ellipsis being given , to draw the Ellipsis . Let the given Diameter in Fig. 24. be LB and ED , the greatest Diameter . LB being bisected in the Point of Bisection , erect the Perpendicular AD. which let be half of the lesser Diameter ED , then open your Compasses to the extent of AB , and setting one Foot in D , with the other make a mark at M and N in the Diameter BL , then cutting a thred to the length of BL , fasten the thred with your Compasses in the Points NM , and with your Pen in the inside of the thred describe the Arch BFKL , so shall you describe the one half of the Ellipsis required , and turning the Thred on the other side of the Compasses , you may with your Pen in the like manner describe the other half of the Ellipsis GBHL . CHAP. III. Of Triangles . HItherto we have spoken of the most Simple Figure , a Circle . Come we now to those Figures that are Various or Angular . 2. And an Angular Figure is that which doth consist of three or more Angles . 3. An angular Figure consisting of three Angles , otherwise called a Triangle , is a Superficies or Figure comprehended by three Right Lines including three Angles . 4. A Triangle may be considered either in respect of its Sides , or of its Angles . 5. A Triangle in respect of its Sides , is either Isopleuron , Isosceles , or Scalenum . 6. An Isopleuron Triangle , is that which hath three equal sides . An Isoscecles hath two equal Sides . And a Scalenum hath all the three Sides unequal . 7. A Triangle in respect of its Angles is Right or Oblique . 8. A Right angled Triangle is that which hath one Right Angle and two Acute . 9. An Oblique angled Triangle , is either Acute or Obtuse . 10. An Oblique acute angled Triangle , is that which hath all the three Angles Acute . 11. An Oblique obtuse angled Triangle , is that which hath one Angle Obtuse , and the other two Acute . Proposition I. Vpon a Right Line given to make an Isopleuron or an Equilateral Triangle . In Fig. 8. let it be required to make an Equilateral Triangle upon the Right Line AB . Open your Compasses to the extent of the Line given , and setting one Foot of your Compasses in A , make an Arch of a Circle above or beneath the Line given , then setting one Foot of your Compasses in B , they being full opened to the same extent , with the other foot draw another Arch of a Circle crossing the former , and from the Intersection of those Arches draw the Lines AC and AB , so shall the Triangle ACB be Equilateral as was desired . Proposition II. Vpon a Right Line given to make an Isosceles Triangle , or a Triangle having two Sides equal . In Fig. 8. let AB be the Right Line given , from the Points A and B as from two Centers , but at a lesser extent of the Compasses than AB ; if you would have AB the greatest Side , at a greater extent ; if you would have it to be the least Side , describe two Arches cutting one another , as at F , and from the Intersection draw the Lines AF , and FB , so shall the Triangle AFB have two equal Sides , as was required . Proposition 3. To make a Scalenum Triangle , or a Triangle , whose three Sides are unequal . In Fig. 9. let the three unequal Sides be EFG make AB equal to one of the given Lines , suppose G , and from A as a Center , at the extent of E describe the Arch of a Circle ; in like manner from B at the extent of F describe another Arch intersecting the former , then shall the Right Lines AC . CB and BA comprehend a Triangle , whose three sides shall be unequal , as was required . CHAP. IV. Of Quadrangular and Multangular Figures . WE have spoken of Triangles or Figures consisting of three Angles , come we now to those that have more Angles than three , as the Quadrangle , Quinquangle , Sexangle , &c. 2. A Quadrangle is a Figure or Superficies , which is bounded with four Right Lines . 3. A Quadrangle is either a Parallelogram or a Trapezium . 4. A Parallelogram is a Quadrangle whose opposite Sides are parallel having equal distances from one another in all Places . 5. A Parallelogram is either Right angled or Oblique . 6. A Right angled Parallelogram , is a Quadrangle whose four Angles are all Right , and is either Square or Oblong . 7. A Square Parallelogram doth consist of four equal Lines . The Parts of a Square are , the Sides of which the Square is made , and the Diagonal or Line drawn from one opposite Angle to another through the middle of the Square . 8. An Oblong is a Right angled Parallelogram , having two longer and two shorter Sides . 9. An Oblique angled Parallelogram , is that whose Angles are all Oblique , and is either a Rhombus or a Rhomboides . 10. A Rhombus is an Oblique angled and equilateral Parallelogram . 11. A Rhomboides is an Oblique angled and inequilateral Parallelogram . 12. A Trapezium is a Quadrangular Figure whose Sides are not all parallel ; it is either Right angled or Oblique . 13. A Right angled Trapezium hath two opposite Sides parallel , but unequal , and the Side between them perpendicular . 14. An Oblique angled Trapezium is a Quadrangle , but not a Parallelogram , having at least two Angles Oblique , and none of the Sides parallel . 15. Thus much concerning Quadrangles or four sided Figures . Figures consisting of more than four Angles are almost infinite , but are reducible unto two sorts , Ordinate and Regular , or Inordinate and Irregular . 16. Ordinate and Regular Polygons are such , as are contained by equal Sides and Angles , as the Pentagon , Hexagon , and such like . 17. Inordinate or irregular Polygons , are such as are contained by unequal Sides and Angles . The construction of these Quadrangular and Multangular Figures is explained in the Propositions following . Proposition . I. Vpon a Right Line given to describe a Right angled Parallelogram , whether Square or Oblong . In Fig. 10. let the given Line be AB , upon the Point A erect the Perpendic●lar AD equal to AB if you intend to make a Square , but longer or shorter , if you intend an oblong , and upon the Points D and B at the distance of AB and AD describe two Arches intersecting one another , and from the Intersection draw the Lines ED and EB , so shall the Right angled Figure AE be a Square , if AB and AD be equal , otherwise an Oblong , as was desired . Proposition II. To describe a Rhombus or Rhomboides . In Fig. 11. To the Right Line AB draw the Line AD at any Acute Angle at pleasure , equal to AB if you intend a Rhombus , longer or shorter if you intend a Rhomboides , then upon your Compasses to the extent of AD and upon B as a Center describe an Arch ; in like manner , at the extent of AB upon D as a Center describe another Arch intersecting the former , then draw the Lines ED and EB , so shall AE be the Rhombus or Rhomboides , as was required . Proposition III. Vpon a Right Line given to make a Regular Pentagon , or five sided Figure . In Fig. 12. Let the given Line be AB , upon A and B as two Centers describe the Circles EBGH and CAGK , then open your Compasses to the extent of BC , and making G the Center , describe the Arch HAFK , then draw the Lines KFE and HFC : so shall AE and BC be two sides of the Pentagon desired , and opening your Compasses to the extent of AB , upon E and C as two Centers describe two Arches intersecting one another , and from the Point of Intersection draw the Lines ED and DC , so shall the Figure AB and DE be the Pentagon required . Proposition IV. To make a Regular Pentagon and Decagon in a given Circle . In Fig. 13. upon the Diameter CAB describe the Circle CDBL , from the Center AErect the Perpendicular AD , and let the Semidiameter AC be bisected , the Point of Bisection is E , set the distance ED from E to G , and draw the Line GD , which is the side of a Pentagon , and AG the side of a Decagon inscribed in the same Circle . Proposition V. In a Circle given to describe a Regular Hexagon . The side of a Hexagon is equal to the Radius of a Circle , the Radius of a Circle therefore being six times applied to the Circumference , will give you six Points , to which Lines being drawn from Point to Point , will constitute a Regular Hexagon , as was desired . Proposition VI. In a Circle given to describe a Regular Heptagon or Figure consisting of seven equal sides . The side of a Heptagon is equal to half the side of a Triangle inscribed in a Circle , having therefore drawn an Hexagon in a Circle , the Chord Line subtending two sides of the Hexagon lying together , is the side of a Triangle inscribed in that Circle , and half that Chord applied seven times to the Circumference , will give seven Points , to which Lines being drawn from that Point , will constitute a Regular Heptagon , as in Fig. 14. is plainly shewed . CHAP. V. Of Solid Bodies . HAving spoken of the two first kinds of Magnitude , Lines and Superficies , come we now to the third , a Body or Solid . 2. A Body or Solid is a Magnitude consisting of length , breadth and thickness . 3. A Solid is either regular or irregular . 4. That is called a regular Solid , whose Bases , Sides and Angles are equal and like . 5. And this either Simple or Compound . 6. A simple regular Solid , is that whith doth consist of one only kind of Superficies . 7. And this is either a Sphere or Globe , or a plain Body . 8. A Globe is a Solid included by one round and convex Superficies , in the middle whereof there is a Point , from whence all Lines drawn to the Circumference are equal . 9. A simple plain Solid , is that which doth consist of plain Superficies . 10. A plain Solid is either a Pyramid , a Prism , or a mixt Solid . 11. A Pyramid is a Solid , Figure or Body , contained by several Plains set upon one right lin'd Base , and meeting in one Point . 12. Of all the several sorts of Pyramids , there is but one that is Regular , to wit a Tetrahedron , or a Pyramid consisting of four regular or equilateral Triangles ; the form whereof ( as it may be cut in Pastboard ) may be conceived by Figure 15. 13. A Prism is a Solid contained by several Plains , of which those two which are opposite , are equal , like and parallel , and all others are Paralellogram . 14. A Prism is either a Pentahedron , a Hexahedron , or a Polyhedron . 15. A Pentahedron Prism , is a Solid comprehended of five Sides , and the Base a Triangle , as Fig. 16. 16. An Hexahedron Prism , is a Solid comprehended of six Sides , and the Base a Quadrangle , as Fig. 17. 17. An Hexahedron Prism , is distinguished into a Parallelipipedon and a Trapezium . 18. An Hexahedron Prism called a Trapezium is a Solid , whose opposites Plains or Sides , are neither opposite nor equal . 19. A Parallelipipedon is either right angled or oblique . 20. A right angled Parallelipipedon is an Hexahedron Prism , comprehended of right angled Plains or Sides ; and it is either a Cube or an Oblong . 21. A Cube is a right angled Parallelipipedon comprehended of six equal Plains or Sides . 22. An Oblong Parallelipipedon , is an Hexahedron Prism , comprehended by unequal Plains or Sides . 23. An Oblique angled Parallelipipedon , is an Hexahedron Prism , comprehended of Oblique Sides . 24. A Polyhedron Prism , is a Solid comprehended by more than six Sides , and hath a multangled Base , as a Quincangle , Sexangle , &c. 25. A regular compound or mixt Solid , is such a Solid as hath its Vertex in the Center , and the several Sides exposed to view , and of this sort there are only three ; the Octohedron , the Icosahedron , of both which the Base is a Triangle ; and the Dodecahedron , whose Base is a Quincangle . 26. An Octohedron is a Solid Figure which is contained by eight equal and equilateral Triangles , as in Fig. 18. 27. An Icosahedron is a Solid , which is contained by twenty equal and equilateral Triangles , as Fig. 19. 28. A Dodecahedron is a Solid , which is contained by twelve equal Pentagons , equilateral and equiangled , as in Fig. 20. 29. A regular compound Solid , is such a Solid as is Comprehended both by plain and circular Superficies , and this is either a Cone or a Cylinder . 30. A Cone is a Pyramidical Body , whose Base is a Circle , or it may be called a round Pyramis , as Fig. 21. 31. A Cylinder is a round Column every where comprehended by equal Circles , as Fig. 22. 32. Irregular Solids are such , which come not within these defined varieties , as Ovals , Frustums of Cones , Pyramids , and such like . And thus much concerning the description of the several sorts of continued Quantity , Lines , Plains and Solids ; we will in the next place consider the wayes and means by which the Dimentions of them may be taken and determined , and first we will shew the measuring of Lines . CHAP. VI. Of the Measuring of Lines both Right and Circular . EVery Magnitude must be measured by some known kind of Measure ; as Lines by Lines , Superficies by Superficies , and Solids by Solids , as if I were to measure the breadth of a River , or height of a Turret , this must be done by a Right Line , which being applied to the breadth or height desired to be measured , shall shew the Perches , Feet or Inches , or by some other known measure the breadth or height desired : but if the quantity of some Field or Meadow , or any other Plain be desired , the number of square Perches must be enquired ; and lastly , in measuring of Solids , we must use the Cube of the measure used , that we discover the number of those Cubes that are contained in the Body or Solid to be measured . First , therefore we will speak of the several kinds of measure , and the making of such Instruments , by which the quantity of any Magnitude may be known . 2. Now for the measuring of Lines and Superficies , the Measures in use with us , are Inches , Feet , Yards , Ells and Perches . 3. An Inch is three Barley Corns in length , and is either divided into halves and quarters , which is amongst Artificers most usual , or into ten equal Parts , which is in measuring the most useful way of Division . 4. A Foot containeth twelve Inches in length , and is commonly so divided ; but as for such things as are to be measured by the Foot , it is far better for use , when divided into ten equal Parts , and each tenth into ten more . 5. A Yard containeth three Foot , and is commonly divided into halves and quarters , the which for the measuring of such things as are usually sold in Shops doth well enough , but in the measuring of any Superficies , it were much better to be divided into 10 or 100 equal Parts . 6. An Ell containeth three Foot nine Inches , aud is usually divided into halves and quarters , and needs not be otherwise divided , because we have no use for this Measure , but in Shop Commodities . 7. A Pole or Perch cotaineth five Yards and an half , and hath been commonly divided into Feet and half Feet . Forty Poles in length do make one Furlong , and eight Furlongs in length do make an English Mile , and for these kinds of of lengths , a Chain containing four Pole , divided by Links of a Foot long , or a Chain of fifty Foot , or what other length you please , is well enough , but in the measuring of Land , in which the number of square Perches is required ; the Chain called Mr. Gunters , being four Pole in length divided into 100 Links , is not without just reason reputed the most useful . 8. The making of these several Measures is not difficult , a Foot may be made , by repeating an Inch upon a Ruler twelve times , a Yard is eight Foot , and so of the rest ; the Subdivision of a Foot or Inch into halves and quarters , may be performed by the seventeenth of the first , and into ten or any other Parts by the first Proposition of the first Chapter , and all Scales of equal Parts , of what scantling you do desire . And this I think is as much as needs to be said concerning the dividing of such Instruments as are useful in the measuring Right Lines . 9. The next thing to be considered is the measuring of Circular Lines , or Perfect Circles . 10. And every Circle is supposed to be divided into 360 Parts called Degrees , every Degree into 60 Minutes , every Minute into 60 Seconds , and so forward this division of the Circle into 360 Parts is generally retained , but the Subdivision of those Parts , some would have be thus and 100 , but as to our present purpose either may be used , most Instruments not exceeding the fourth part of a Degree . 11. Now then a Circle may be divided into 360 Parts in this manner , Having drawn a Diameter through the Center of the Circle dividing the Circle into two equal Parts , cross that Diameter with another at Right Angles through the Center of the Circle also , so shall the Circle be divided into four equal Parts or Quadrants , each Quadrant containing 90 Degrees , as in Fig. 7. GE. ED. DL and LG , are each of them 90 Degrees ; and the Radius of a Circle being equal to the Chord of the sixth Part thereof , that is to the Chord of 60 Degrees , as in Fig. 14. if you set the Radius GB from L towards G , and also from G towards L , the Quadrant GL will be subdivided into three equal Parts , each Part containing 30 Degrees , GM . 30. MH 30 and HL 30 , the like may be done in the other Quadrants also ; so will the whole Circle be divided into twelve Parts , each Part containing 30 Degrees . And because the side of a Pentagon inscribed in a Circle is equal to the Chord of 72 Degrees , or the first Part of 360 , as in Fig. 13. therefore if you set the Chord of the first Part of the Circle given from G to L or L to G , in Fig. 7. you will have the Chord of 72 Degrees , and the difference between GP 72 and GH 60 is HP 12 , which being bisected , will give the Arch of 6 Degrees , and the half of six will give three , and so the Circle will be divided into 120 Parts , each Part containing three Degrees , to which the Chord Line being divided into three Parts , the Arch by those equal Divisions may be also divided , and so the whole Circle will be divided into 360 , as was desired . 12. A Circle being thus divided into 360 Parts , the Lines of Chords , Sines , Tangents and Secants , are so easily made ( if what hath been said of them in the Second Chapter be but considered ) that I think it needless to say any more concerning their Construction , but shall rather proceed unto their Use. 13. And the use of these Lines and other Lines of equal Parts we will now shew in circular and right lined Figures ; and first in the measuring of a Circle and Circular Figures . CHAP. VII . Of the Measuring of a Circle . THe squaring of a Circle , or the finding of a Square exactly equal to a Circle given , is that which many have endeavoured , but none as yet have attained : Yet Archimedes that Famous Mathematician hath sufficiently proved , That the Area of a Circle is equal to a Rectangle made of the Rodius and half the Circumference : Or thus , The Area of a Circle is equal to a Rectangle made of the Diameter and the fourth part of the Circumference . For Example , let the Diameter of a Circle be 14 and the Circumference 44 ; if you multiply half the Circumference 22 by 7 half the Diameter , the Product is 154 ; or if you multiply 11 the fourth part of the Circumference , by 14 the whole Diameter , the Product will still be 154. And hence the Superficies of any Circle may be found though not exactly , yet near enough for any use . 2. But Ludolphus Van Culen finds the Circumference of a Circle whose Diameter is 1.00 to be 3.14159 the half whereof 1.57095 being multiplied by half the Diameter 50 , &c. the Product is 7.85395 which is the Area of that Circle , and from these given Numbers , the Area , Circumference and Diameter of any other Circle may be found by the Proportions in the Propositions following . Proposition I. The Diameter of a Circle being given to find the Circumference . As 1. to 3.14159 : so is the Diameter to the Circumference . Example . In Fig. 13. Let the Diameter IB be 13. 25. I say as 1. to 3. 14159. so IB . 13.25 to 41.626 the Circumference of that Circle . Proposition II. The Diameter of a Circle being given to find the Superficial Content . As 1. to 78539 ; so is the Square of the Diameter given , to the Superficial Content required . Example , Let the Diameter given be as before IB 13.25 the Square thereof is 175.5625 therefore . As 1. to 78539 : so 175.5625 to 137.88 the Superficial Content of that Circle . Proposition III. The Circumference of a Circle being given , to find the Diameter . This is but the Converse of the first Proposition : Therefore as 3.14159 is to 1 : so is the Circumference to the Diameter ; and making the Circumference an Unite , it is . 3. 14159. 1 ∷ 1. 318308 , and so an Unite may be brought into the first place . Example , Let the given Circumference be 41. 626. I say , As 1. to 318308 : so 41.626 to 13. 25. the Diameter required . Proposition IV. The Circumference of a Circle being given to find the Superficial Content . As the Square of the Circumference of a Circle given is to the Superficial Content of that Circle : so is the Square of the Circumference of another Circle given to the Superficial Content required . Example , As the Square of 3.14159 is to 7853938 : so is 1. the Square of another Circle to 079578 the Superficial Content required , and so an Unite for the most easie working may be brought into the first place : Thus the given Circumference being 41. 626. I say , As 1. to 0.79578 : so is the Square of 41.626 to 137.88 the Superficial Content required . Proposition V. The Superficial Content of a Circle being given , to find the Diameter . This is the Converse of the second Proposition , therefore as 78539 is to 1. so is the Superficial Content given , to the Square of the Diameter required . And to bring an Unite in the first place : I say . As 7853978. 1 ∷ 1. 1. 27324 , and therefore if the Superficial Content given be 137.88 , to find the Diameter : I say , As 1. to 1.27324 : so 137.88 to 175.5625 whose Square Root is 13.25 , the Diameter sought . Proposition VI. The Superficial Content of a Circle being given , to find the Circumference . This is the Converse of the Fourth Proposition , and therefore as 079578 is to 1 : so is the Superficial Content given , to the Square of the Circumference required , and to bring an Unite in the first place : I say , As 079578. 1 : : 1. 12.5664 , and therefore if the Superficial Content given be 137.88 , to find that Circumference : I say , As 1. to 12.5664 : so is the 137.88 to 1732.7 whose Square Root is 626 the Circumference . Proposition VII . The Diameter of a Circle being given to find the Side of the Square , which may be inscribed within the same Circle . The Chord or Subtense of the Fourth Part of a Circle , whose Diameter is an Unite , is 7071067 , and therefore , as 1. to 7071067 : so is the Diameter of another Circle , to the Side required . Example , let the Diameter given be 13.25 to find the side of a Square which may be inscribed in that Circle : I say , As 1. to 7071067 : so is 13.25 to 9.3691 the side required . Proposition VIII . The Circumference of a Circle being given , to find the Side of the Square which may be inscribed in the same Circle . As the Circumference of a Circle whose Diameter is an Unite , is to the side inscribed in that Circle ; so is the Circumference of any other Circle , to the side of the Square that may be inscribed therein . Therefore an Unite being made the Circumference of a Circle . As 3.14159 to 7071067 : so 1. to 225078. And therefore the Circumference of a Circle being as before 41.626 , to find the side of the Square that may be inscribed : I say , As 1. to 225078. so is 41.626 to 9.3691 the side inquired . Proposition IX . The Axis of a Sphere or Globe being given , to find the Superficial Content . As the Square of the Diameter of a Circle , which is Unity , is to 3.14159 the Superficial Content , so is the Square of any other Axis given , to the Superficial Content required . Example , Let 13.25 be the Diameter given , to find the Content of such a Globe : I say , As 1. to 3.14159 : so is the Square of 13.25 to 551.54 the Superficial Content required . Proposition X. To find the Area of an Ellipsis . As the Square of the Diameter of a Circle , is to the Superficial Content of that Circle ; so is the Rectangle made of the Conjugate Diameters in an Ellipsis , to the Area of that Ellipsis ; And the Diameter of a Circle being one , the Area is 7853975 , therefore in Fig. 26. the Diameters AC8 and BD5 being given , the Area of the Ellipsis ABCD may thus be found . As 1. to 7853975 : so is the Rectangle AC in BD40 to 3.1415900 , the Area of the Ellipsis required . CHAP. VIII . Of the Measuring of Plain Triangles . HAving shewed the measuring of a Circle , and Ellipsis , we come now to Right lined Figures , as the Triangle , Quadrangle , and Multangled Figures , and first of the measuring of the plain Triangles . 2. And the measuring of Plain Triangles is either in the measuring of the Sides and Angles , or of their Area and Superficial Content . 3. Plain Triangles in respect of their Sides and Angles are to be measured by two sorts of Lines , the one is a Line of equal Parts , and by that the Sides must be measured , the other is a Line of Chords , the Construction whereof hath been shewed in the sixth Chapter , and by that the Angles must be measured , the Angles may indeed be measured by the Lines of Sines , Tangents or Secants , but the Line of Chords being not only sufficient , but most ready , it shall suffice to shew how any Angle may be protracted by a Line of Chords , or the Quantity of any Angle found , which is protracted . 4. And first to protract or lay down an Angle to the Quantity or Number of Degrees proposed , do thus , draw a Line at pleasure as AD in Figure 5 , then open your Compasses to the Number of 60 Degrees in the Line of Chords , and setting one Foot in A , with the other describe the Arch BG , and from the Point A let it be required to make an Angle of 36 Degrees : open your Compasses to that extent in the Line of Chords , and setting one Foot in B , with the other make a mark at G , and draw the Line AG , so shall the Angle BAG contain 36 Degrees , as was required . 5. If the Quantity of an Angle were required , as suppose the Angle BAG , open your Compasses in the Line of Chords to the extent of 60 Degrees , and setting one Foot in A , with the other draw the Arch BG , then take in your Compasses the distance of BG , and apply that extent to the Line of Chords , and it will shew the Number of Degrees contained in that Angle , which in our Example is 36 Degrees . 6. In every Plain Triangle , the three Angles are equal to two right or 180 Degrees , therefore one Angle being given , the sum of the other two is also given , and two Angles being given , the third is given also . 7. Plain Triangles are either Right Angled or Oblique . 8. In a Right Angled Plain Triangle , one of the Acute Angles is the Complement of the other to a Quadrant or 90 Degrees . 9. In Right Angled Plain Triangles , the Side subtending the Right Angle we call the Hypotenuse , and the other two Sides the Legs , thus in Fig. 5 ▪ AE is the Hypotenuse , and AD and ED are the Legs ; these things premised , the several cases in Right Angled and Oblique Angled Plain Triangles may be resolved , by the Propositions following . Proposition I. In a Right Angled Plain Triangle , the Angles of one Leg being given , to find the Hypotenuse and the other Leg. In the Right Angled Plain Triangle ADE in Fig. 5. Let the given Angles be DAE 36 , and DEA 54 , and let the given Leg be AD 476 ; to find the Hypotenuse AE , and the other Leg ED. Draw a Line at pleasure , as AD , and by your Scale of equal Parts set from A to D 476 the Quantity of the Leg given , then erect a Perpendicular upon the Point D , and upon the Point A lay down your given Angle DAE 36 by the fourth hereof , and draw the Line AE till it cut the Perpendicular DE , then measure the Lines AE and DE upon your Scale of Equal Parts , so shall AE 588.3 be the Hypotenuse , and DE 345.8 the other Leg. Proposition II. The Hypotenuse and Oblique Angles given , to find the Legs . Let the given Hypotenuse be 588 , and one of the Angles 36 degrees , the other will then be 54 degrees , Draw a Line at pleasure , as AD , and upon the Point A by the fourth ▪ hereof lay down one of the given Angles suppose the less , and draw the Line AC , and from your Scale of equal Parts , set off your Hypotenuse 588 from A to E , and from the Point E to the Line AD let fall the Perpendicular ED , then shall AD being measured upon the Scale be 476 for one Leg , and ED 345.8 the other . Proposition III. The Hypotenuse and one Leg given to find the Angles and the other Leg. Let the given Hypotenuse be 588. and the given Leg 476. Draw a Line at pleasure as AD , upon which set the given Leg from A to D. 476 , and upon the Point D , erect the Perpendicular DE , then open your Compasses in the Scale of Equal Parts to the Extent of your given Hypotenuse 588 , and setting one Foot of that Extent in A , move the other till it touch the Perpendicular DE , then and there draw AE , so shall ED be 345.8 the Leg inquired , and the Angle DAE , will be found by the Line of Chords to be 36 ▪ whose Complement is the Angle DEA . 54. Proposition IV. The Legs given to find the Hypotenuse , and the Oblique Angles . Let one of the given Legs be 476 , and the other 345.8 , Draw the Line AD to the extent of 476 , and upon the Point D , erect the Perpendicular DE to the extent of 345.8 , and draw the Line AE , so shall AE be the Hypotenuse 588 , and the Angle DAE will by the Line of Chords be found to be 36 Degrees , and the Angle DEA 54 , as before . Hitherto we have spoken of Right angled plain Triangles : the Propositions following concern such as are Oblique . Proposition V. Two Angles in an Oblique angled plain Triangle , being given , with any one of the three Sides , to find the other two Sides . In any Oblique angled plain Triangle , let one of the given Angles be 26.50 and the other 38. and let the given Side be 632 , the Sum of the two given Angles being deducted from a Semi-circle , leaveth for the third Angle 115.50 Degrees , then draw the Line BC 632. and upon the Points B and C protract the given Angles , and draw the Lines BD and CD , which being measured upon your Scale of equal Parts BD will be fou●d to be 312.43 , and BD 431.09 , Proposition VI. Two Sides in an Oblique Angled Triangle being given , with an Angle opposite to one of them , to find the other Angles and the third Side , if it be known whether the Angle Opposite to the other Side given be Acute or Obtuse . In an Oblique Angled Plain Triangle , let the given Angle be 38 Degrees , and let the Side adjacent to that Angle be 632 , and the Side opposite 431. 1. upon the Line BC in Fig. 25. protract the given Angle 38 Degrees upon the Point C , and draw the Line DC , then open your Compasses to the Extent of the other Side given 431. 1. and setting one Foot in B , turn the other about till it touch the Line DC , which will be in two places , in the Points D and E ; if therefore the Angle at B be Acute the third Side of the Triangle will he CE , according therefore to the Species of that Angle you must draw the Line BD or BE to compleat the Triangle , and then you may measure the other Angles , and the third Side as hath been shewed . Proposition VII . Two Sides of an Oblique Angled Plain Triangle being given , with the Angle comprehended by them to find the other Angles and the third Side . Let one of the given Sides be 632 , and the other 431.1 , and let the Angle comprehended by them be Deg. 26.50 , draw a Line at pleasure , as BC , and by help of your Scale of Equal Parts , set off one of your given Sides from B to C 632. then upon the Point B protract the given Angle 26. 50. and draw the Line BD , and from B to D , set off your other given Side 431. 1. and draw the Line DC , so have you constituted the Triangle BDC , in which you may measure the Angles and the third Side , as hath been shewed . Proposition VIII . The three Sides of an Oblique Angled Triangle being given , to find the Angles . Let the length of one of the given Sides be 632 , the length of another 431.1 , and the length of the third 312.4 , and Draw a Line at pleasure , as BC in Fig. 25 , and by help of your Scale of Equal Parts , set off the greatest Side given 632 from B to C. then open your Compasses in the same Scale to the extent of either of the other Sides , and setting one Foot of your Compasses in B , with the other describe an occult Arch , then extend your Compasses in the same Scale to the length of the third Side , and setting one Foot in C with the other describe another Arch cutting the former , and from the Point of Intersection draw the Lines BD and DC . to constitute the Triangle BDC , whose Angles may be measured , as hath heen shewed . And thus may all the Cases of Plain Triangles be resolved by Scale and Compass , he that desires to resolve them Arithmetically , by my Trigometria Britannica , or my little Geometrical , Trigonometry ; only one Case of Right Angled Plain Triangles which I shall have occasion to use , in the finding of the Area of the Segment of a Circle I will here shew how , to resolve by Numbers . Proposition IX . In a Right Angled Plain Angle the Hypotenuse and one Leg being given to find the other Leg. Take the Sums and difference of the Hypotenuse and Leg given , then multiply the Sum by the Difference , and of the Product extract the Square Root , which Square Root shall be the Leg inquired . Example . In Fig. 5. Let the given Hypotenuse be AE 588.3 , and the given Leg AD 476 , and let DE be the Leg inquired . The Sum of AE and AD is 1064.3 , and their Difference is 112.3 , now then if you multiply 1064.3 by 112.3 , the Product will be 119520.89 , whose Square Root is the Leg DE. 345. 8. Proposition X. The Legs of a Right Angled Plain Triangle being gived , to find the Area or Superficial Content thereof . Multiply one Leg by the other , half the Product shall be the Content . Example , In the Right angled plain Triangle ADE , let the given Legs be AD 476 , and DE 345 , and let the Area of that Triangle be required , if you multiply 476 by 345 the Product will be 164220 , and the half thereof 82110 is the Area or Superficial Content required . Proposition XI . The Sides of an Oblique angled plain Triangle being given to find the Area or Superficial Content thereof . Add the three Sides together , and from the half Sum subtract each Side , and note their Difference ; then multiply the half Sum by the said Differences continually , the Square Root of the last Product , shall be the Content required . Example . In Fig. 9. Let the Sides of the Triangle ABC be AB 20. AC 13 , and BC 11 the Sum of these three Sides is 44 , the half Sum is 22 , from whence subtracting AB 20 , the Difference is 2 , from whence also if you substract AC 13 , the Difference is 9 , and lastly , if you subtract BC 11 from the half Sum 22 , the Difference will be 11. And the half Sum 22 being multiplied by the first Difference 2 , the Product is 44 , and 44 being multiplied by the Second Difference 9 , the Product is 396 , and 396 being multiplied by the third Difference 11 , the Product is 4356 , whose Square Root 66 , is the Content required . Or thus , from the Angle C let fall the Perpendicular DC , so is the Oblique angled Triangle ABC , turned into two right , now then if you measure DC upon your Scale of Equal Parts , the length thereof will be found to be 6.6 , by which if you multiply the Base AB 20 , the Product will be 132.0 , whose half 66 , is the Area of the Triangle , as before . Proposition XII . The Sides of any Oblique angled Quadrangle being given , to find the Area or Superficial Content thereof . Let the Sides of the Oblique angled Quadrangle ABED in Fig. 11. be given , draw the Diagonal AE , and also the Perpendiculars DC and BF , then measuring AE upon the same Scale by which the Quadrangular Figure was protracted , suppose you find the length to be 632 , the length of DC 112 , and the length of BF 136 , if you multiply AE 632 by the Half of DC 56 , the Product will be 35392 the Area of ACED . In like manner if you multiply AE 632 , by the half of BF 68 , the Product will be 42976 the Area of ACEB , and the Sum of these two Products is the Area of ABED as was required . Or thus , take the Sum of DC 112 , and BF 136 ; the which is 248 , and multiply AE 632 by half that Sum , that is by 124 , the Product will be 78368 the Area of the Quadrangular Figure ABED , as before . Proposition XIII . The Sides of a plain irregular multangled Figure being given , to find the Content . In Fig. 26. Let the Sides of the multangled Figure . A. B. C. D. E. F. G. H. be given , and let the Area thereof be required , by Diagonals drawn from the opposite Angles reduce the Figure given , into Oblique angled plain Triangles , and those Oblique angled Triangles , into right by letting fall of Perpendiculars , then measure the Diagonals and Perpendiculars by the same Scale , by which the Figure it self was protracted , the Content of those Triangles being computed , as hath been shewed , shall be AF the Content required : thus by the Diagonals AG. BE and EC the multangled Figure propounded is converted into three Oblique angled quadrangular Figures , AFGH . AFEB and BEDC , and each of these are divided into four Right angled Triangles , whose several Contents may be thus computed . Let GA 94 be multiplied by half HL 27 more Half of KF 29 , that is by 23 , the Product will be 21 , be the Area of AHGF. Secondly , OB is 11 , and FN 13 , their half Sum 12 , by which if you multiply AE 132 , the Product will be 1584 the Area of AFEB . Thirdly , let Bp be 18 m D 32 , the half Sum is 25 , by which if you multiply AEC 125 the Product will be 3125 the Area of BEDC , and the Sum of these Products is 6871 the Area of the whole irregular Figure . ABCDEFGH , as was required . Proposition XIV . The Number of Degrees in the Sector of a Circle being given , to find the Area thereof . In Fig. 27. ADEG is the Sector of a Circle , in which the Arch DEG , is Degrees . 23.50 , and by 1. Prop. of Archimed . de Dimensione Circuli , the length of half the Arch is equal to the Area of the Sector of the double Arch , there the length of DE or EG is equal to the Area of the Sector ADEG : and the length or circumference of the whole Circle whose Diameter is 1 according to Van Culen , is 3.14159265358979 , therefore the length of one Centesme of a Degree , is . 0. 01745329259. Now then to find the length of any Number of Degrees and Decimal Parts , you must multiply the aforesaid length of one Centesme by the Degrees and Parts given , and the Product shall be the length of those Degrees and Parts required , and the Area of a Sector containing twice those Degrees and Parts . Example , the half of DEG 23.50 is DE or EG 11.75 , by which if you multiply 0.01745329259 , the Product will be 2050761879325 , the length of the Arch DE , and the Area of the Sector ADEG . Proposition XV. The Number of Degrees in the Segment of a Circle being given , to find the Area of the Segment . In Fig. 27. Let the Area of the Segment DEGK be required , in which let the Arch DEG be Degrees 23.50 , then is the Area of the Sector ADEG 2050761879325 by the last aforegoing , from which if you deduct the Area of the Triangle ADG , the remainer will be the Area of the Segment DEGK . And the Area of the Triangle ADG may thus be found . DK is the Sine of DE 11.75 , which being sought in Gellibrand's Decimal Canon is . 2036417511 , and AK is the Sine of DH 78.25 , or the Cosine of DE. 9790454724 , which being multiplied by the Sine of DE , the Product will be 1993745344 , or if you multiply AG the Radius by half DF the Sine of the double Arch DEG , the Product will be 19937453445 as before , and this Product being deducted from the Area of the Sector ADEG 2050761879325 , the remainer will be 57016434875 the Area of the Segment DEGL , as was desired . Proposition XVI . The Diameter of a Circle being cut into any Number of Equal Parts , to find the Area of any Segment made by the Chord Line drawn at Right Angles through any of those equal Parts of the Diameter . In Fig. 28. The Radius AD is cut into five Equal Parts , and the Segment EDFL is made by the Chord Line ELF at Right Angles to AD in the fourth Equal Part , or at eight tenths thereof : now then to find the Area of this Segment we have given AE Radius , and AL 8 , and therefore by the ninth hereof EL will be found to be 606000 , the Sine of ED 36.87 , by which if you multiply 0.0174532 , the Product is the Area of the Sector AEDF 64350286 , and the Area of the Triangle AEF is 48 , which being deducted from the Area of the Sector , the Remainer 16350286 is the Area of the Sector EDFL , as was required . And in this manner was that Table of Segments made by the Chord Lines cutting the Radius into 100 Equal Parts . Another way . In Fig. 28. Let the Radius AD be cut into 10.100 or 1000 Equal Parts , and let the Area of the Segments made by the Chord Lines drawn at Right Angles through all those Parts be required : first find the Ordinates GK and M. PN . EL , the double of each Ordinate , will be the Chords of the several Arches , and the Sum of these Chords beginning with the least Ordinate , will orderly give you the Area of the several Segments made by those Chord Lines , but the Diameter must be be divided into 100000 Equal Parts , because of the unequal differences at the beginning of the Diameter : but taking the Area of the Circle to be 3. 1415926535 , &c. as before , the Area of the Semicircle will be 1.57079632 , from which if you deduct the Chord GH1999999 , the Chord answering to 999 Parts of the Radius , the remainer is . 1.56879632 the Area of the Segment GDH . And in this manner by a continual deduction of the Chord Lines from the Area of the Segment of the Circle given , was made that Table shewing the Area of the Segments of a Circle to the thousandth part of the Radius . And because a Table shewing the Area of the Segments of a Circle to the thousandth part of the Radius , whose whole Area is Unity , is yet more useful in Common Practice , therefore from this Table , was that Table also made by this Proportion . As the Area of the Circle whose Diameter is . Unity , to wit 3.14149 is to the Area of any part of that Diameter , so is Unity the supposed Area of another Circle , to the like part of that Diameter . Example , the Area answering to 665 parts of the Radius of a Circlewhose Area is 3.14159 is 0.91354794 therefore , CHAP. IX . Of the Measuring of Heights and Distances . HAving shewed in the former Chapter , how all plain Triangles may be measured , not only in respect of their Sides and Angles , but in respect of their Area , and the finding of the Area of all other plain Figures also , that which is next to be considered , is the practical use of those Instructions , in the measuring of Board , Glass , Wainscot , Pavement , and such like , as also the measuring or surveying of Land ; and first we will shew the measuring of Heights and Distances . 2. And in the measuring of Heights and Distances , besides a Chain of 50 or 100 Links , each Link being a Foot , it is necessary to have a Quadrant of four or five Inches Radius , and the larger the Quadrant is , the more exactly may the Angles : be taken , though for ordinary Practice , four or five Inches Radius will be sufficient . Let such a Quadrant therefore be divided in the Limb into 90 Equal Parts or Degrees , and numbred from the left hand to the right , at every tenth Degree , in this manner 10. 20. 30. 40. 50. 60. 70. 80. 90. and within the Limb of the Quadrant draw another Arch , which being divided by help of the Limb into two Equal Parts , in the Point of Interfection set the Figure 1. representing the Radius or Tangent of 45 Degrees , and from thence both ways the Tangents of 63.44 Deg. 71.57 Deg. 75.97 Deg. 78.70 Deg. 80.54 Deg. that is , 2. 3. 4. 5 and 6 being set also , your Quadrant will be fitted for the taking of Heights several ways , as shall be explained in the Propositions following . Proposition I. To find the Height of a Tower , Tree , or other Object at one Station . At any convenient distance from the Foot of the Object to be measured , as suppose at C in Fig. 30. and there looking through the Sights of your Quadrant till you espie the top of the Object at A , observe what Degrees in the Limb are cut by the Thread , those Degrees from the left Side or Edge of the Quadrant to the Right , is the Quantity of the Angle ACB , which suppose 35 Degrees ; then is the Angle BAC 55 Degrees , being the Complement of the former to 90 Degrees . This done with your Chain or otherwise measure the distance from B the Foot of the Object , to your Station at C , which suppose to be 125 Foot. Then as hath been shewed in the 1. Prop. Chap. 8. draw a Line at pleasure as BC , and by your Scale of Equal Parts , set off the distance measured from B to C 125 Foot , and upon the Point C lay down your Angle taken by observation 35 Degrees , then erect a Perpendicular upon the Point B , and let it be extended till it cut the Hypothenusal Line AC , so shall AB measured on your Scale of Equal Parts , be 87.5 Foot for the Height of the Object above the Eye ; to which the Height of the Eye from the Ground being added , their Sum is the Height required . Another way . Let AB represent a Tower whose Altitude you would take , go so far back from it , that looking through the Sights of your Quadrant , to the top of the Tower at A the Thread may cut just 45 Degrees in the Limb , then shall the distance from the Foot of the Tower , to your Station , be the Height of the Tower above the Eye . Or if you remove your Station nearer and nearer to the Object , till your Thread hang over the Figures 2. 3. 4 or 5 in the Quadrant , the Height of the Tower at 2. will be twice as much as the distance from the Tower to the Station , at 3. it will be thrice as much , &c. As if removing my Station from C to D , the Thread should hang over 2 in the Quadrant , and the distance BD 62 Foot , then will 124 Foot be the Height of the Tower , above the Eye . In like manner if you remove your Station backward till your Thread fall upon one of those Figures in the Quadrant ; between 45 and 90 Degrees , the distance between the Foot of the Tower , and your Station will at 2. be twice as much as the Height , at 3. thrice as much , at 4. four times so much , and so of the rest . A Third way by a Station at Random . Take any Station at pleasure suppose at C , and looking through the Sights of your Quadrant , observe what Parts of the Quadrant the Thread falls upon , and then measure the distance between the Station , and the Foot of the Object , that distance being multiplied by the parts cut in the Quadrant , cutting off two Figures from the Product shall be the Height of the Object above the Eye ? Example , Suppose I standing at C , that the Thread hangs upon 36 Degrees , as also upon 72 in the Quadrant which is the Tangent of the said Arch , and let the measured distance be CB 125 Foot , which being multiplied by 72 , the Product is 9000 , from which cutting off his Figures because the Radius is supposed to be 100 , the Height inquired will be 90 Foot , he that desires to perform this work with more exactness , must make use of the Table of Sines and Tangents Natural or Artificial , this we think sufficient for our present purpose . Proposition II. To find an inaccessible Height at two Stations . Take any Station at pleasure as at D , and there looking through the Sights of your Quadrant to the top of the Object , observe what Degrees are cut by the Thread in the Limb , which admit to be 68 Degrees , then remove backward , till the Angle taken by the Quadrant , be but half so much as the former , that is 34 Degrees , then is the distance between your two Stations equal to the Hypothenusal Line at your first Station , viz. AD. if the distance between your two Stations were 326 foot , then draw a Line at pleasure as BD , upon the Point D protract , the Angle ADB 68 Degrees , according to your first Observation , and from your Line of equal parts set off the Hypothenusal 326 Foot from D to A , and from the Point A let fall the Perpendicular AB which being measured in your Scale of Equal Parts , shall be the Altitude of the Object inquired . Or working by the Table of Sines and Tangents , the Proportion is . As the Radius , is to the measured distance or Hypothenusal Line AD ; so is the Sine of the Angle ADE , to the height AB inquired . Another more General way , by any two Stations taken at pleasure . Admit the first Station to be as before at D , and the Angle by observation to be 68 Degrees , and from thence at pleasure I remove to C , where observing aim I find the Angle at C to be 32 Degrees , and the distance between the Stations 150 Foot. Draw a Line at pleasure as BC , and upon Clay down your last observed Angle 32 Degrees , and by help of your Scale of Equal Parrs , set off your measured distance from C to D 150 Foot , then upon D lay down your Angle of 68 Degrees , according to your first Observation , and where the Lines AD and AC meet , let fall the Perpendicular AB , which being measured in your Scale of Equal Parts , shall be the height of the Object as before . Or working by the Tables of Sines and Tangents , the Proportions . 1. As the Sine of DAC to the Distance DC . So the Sine of ACD , to the Side AD. 2. As the Radius , to the Side AD ; so the Sine ADB , to the Perpendicular height AB inquired . The taking of Distances is much after the same manner , but because there is required either some alteration in the sights of your Quadrant or some other kind of Instrument for the taking of Angles , we will particularly shew , how that may be also done several ways , in the next Chapter . CHAP. X. Of the taking of Distances . FOr the taking of Distances some make use of a Semicircle , others of a whole Circle , with Ruler and Sights rather than a Quadrant , and although the matter is not much by which of these Instruments the Angles be taken , yet in all Cases the whole Circle is somewhat more ready , than either a Semicircle or Quadrant , the which with its Furniture is called the Theodolite . 2. A piece of Board or Brass then about twelve or fourteen Inches Diameter , being made Circular like a round Trencher , must be divided into four Quadrants , and each Quadrant divided into 90 Degrees , or the whole Circle into 360 , and each Degree into as many other Equal Parts , as the largeness of the Degrees will well permit : let your Circle be numbred both ways to 360 , that is from the right hand to the left , and from the left to the right . 3. Upon the backside of the Circle there must be a Socket made fast , that it may be set upon a three legged Staff , to bear it up in the Field . 4. You must also have a Ruler with Sights fixed at each end , for making of Observation , either fixed upon the Center of your Circle , or loose , as you shall think best ; your Instrument being thus made , any distance whether accessible or inaccessible may thus be taken . 5. When you are in the Field , and see any Church , Tower , or other Object , whose Distance from you , you desire to know , choose out some other Station in the same Field , from whence you may also see the Object , and measure the distance between your Stations ; then setting your Ruler upon the Diameter of your Circle , set your Instrument so , as that by the Sights on your Ruler , you may look to the other Station , this done turn your Ruler to that Object whose distance you desire to know , and observe how many Degrees of the Circle are cut by the Ruler , as suppose 36 Degrees , as the Angle ACD in Fig. 30. Then removing your Instrument to D , lay the Ruler on the Diameter thereof , and then turn the whole Instrument about till through your Sights you can espy the mark set up at your first Station at C , and there fix your Instrument , and then upon the Centre of your Circle turn your Ruler till through the Sights you can espy the Object whose distance is inquired , suppose at A ; and observe the Degrees in the Circle cut by the Ruler , which let be 112 , which is the Angle ADC , and let the distance between your two Stations be DC 326 Foot ; so have you two Angles and the side between them , in a plain Triangle given , by which to find the other sides , the which by protraction may be done as hath been shewed , in the fifth Proposition of Chapter 8. but by the Table of Sines and Tangents , the Proportion is . As the Sine of DAC , is to DC ; so is the Sine of ACD to the Side AD. Or , as the Sine of DAC , is to the given Side DC . So is the Sine of ADC to the Side AC . 6. There is another Instrument called the plain Table , which is nothing else , but a piece of Board , in the fashion and bigness of an ordinary sheet of paper , with a little frame , to fasten a sheet of paper upon it , which being also set upon a Staff , you may by help of your Ruler , take a distance therewith in this manner . Having measured the distance between your two Stations at D and C , draw upon your paper a Line , on which having set off your distance place your Instrument at your first Station C , and laying your Ruler upon the Line so drawn thereon , turn your Instrument till through the Sights you can espy the Station at D , then laying your Ruler upon the Point C , turn the same about till through the Sights you can espy the Object at A , and there draw a Line by the side of your Ruler , and remove your Instrument to D , and laying your Ruler upon the Line DC , turn the Instrument about , till through the Sight you can espy the Mark at C , and then laying your Ruler upon the Point D , turn the same , till through the Sights you can espy the Object at A , and by the side of your Ruler draw a Line , which must be extended till it meet with the Line AC , so shall the Line AD being measured upon your Scale of Equal Parts , be the distance of the Object from D , and the Line AC shall be the distance thereof from C. 7. And in this manner may the distance of two , three or more Objects be taken , from any two Stations from whence the several Objects may be seen , and that either by the plain Table , or Theodolite . CHAP. XI . How to take the Plot of a Field at one Station , from whence the several Angles may be seen . ALthough there are several Instruments by which the Plat of a Field may be taken , yet do I think it sufficient to shew the use of these two , the plain Table and Theodolite . 2. In the use of either of which the same chain which is used in taking of heights and distances , is not so proper . I rather commend that which is known by the Name of Gunter's Chain , which is four Pole divided into 100 Links ; being as I conceive much better for the casting up the Content of a Piece of Ground , than any other Chain that I have yet heard of , whose easie use shall be explained in its proper place . 3. When you are therefore entered the Field with your Instrument , whether plain Table , or Theodolite , having chosen out your Station , let visible Marks be set up in all the Corners thereof , and then if you use the plain Table , make a mark upon your paper , representing your Station , and laying your Ruler to this Point , direct your Sights to the several Corners of the Field , where you have caused Marks to be set up , and draw Lines by the side of the Ruler upon the paper to the point representing your station , then measure the distance of every of these Marks from your Instrument , and by your Scale set those distances upon the Lines drawn upon the paper , making small marks at the end of every such distance , Lines drawn from Point to Point , shall give you upon your paper , the Plot of the Field , by which Plot so taken the content of the Field may easily be computed . Example . Let Fig. 31. represent a Field whose Plot is required ; your Table being placed with a sheet of paper thereupon , make a Mark about the middle of your Table , as at A. apply your Ruler from this Mark to B and draw the Line AB , then with your Chain measure the distance thereof which suppose to be 11 Chains 36 Links , then take 11 Chains 36 Links from your Scale , and set that distance from A to B , and at B make a mark . Then directing the Sights to C , draw a Line by the side of your Ruler as before , and measure the distance AC , which suppose to be 7 Chains and 44 Links , this distance must be taken from your Scale , and set from A to C upon your paper . And in this manner you must direct your Sights from Mark to Mark , until you have drawn the Lines and set down the distances , between all the Angles in the Field and your station , which being done , you must draw the Lines from one Point to another , till you conclude where you first began , so will those Lines BC. CD . DE. FG. and GB , give you the exact Figure of the Field . 4. To do this by the Theodolite , in stead of drawing Lines upon your paper in the Field , you must have a little Book , in which the Pages must be divided into five Columns , in the first Column whereof you must set several Letters to signifie the several Angles in the Field , from which Lines are to be drawn to your place of standing , in the second and third Columns the degrees and parts taken by your Instrument , and the fourth and fifth , to set down your distances Chains and Links , this being in readiness , and have placed your Instrument direct your Sights to the first mark at B , and observe how many Degrees are comprehended between the Diameter of your Instrument , and the Ruler , and set them in the second and third Columns of your Book against the Letter B , which stands for your first Mark , then measure the distance AB as before , and set that down , in the fourth and fifth Columns , and so proceed from Mark to Mark , until you have taken all the Angles and Distances in the Field , which suppose to be , as they are expressed in the following Table .   Degr. Part Chains Links B 39 75 11 56 C 40 75 7 44 D 96 00 7 48 E 43 25 8 92 F 80 00 6 08 G 59 25 9 73 5. Having thus taken the Angles and Distances in the Field , to protract the same on Paper or Parchment , cannot be difficult ; for if you draw a Line at pleasure as EB representing the Diameter of your Instrument about the middle thereof , as at A , mark a Mark , and opening your Compasses to 60 Degrees in your Line of Chords , upon A as a Center describe a Circle , then lay your Field book before you seeing that your first Observattion cut no Degrees , there are no Degrees to be marked out in the Circle , but the Degrees at C are 40.75 which being taken from your Line of Chords , you must set them from H to I , and draw the Line AI. the Degrees at D are 96 which must in like manner be set from I to K , and so the rest in order . This done observe by your Field-book the length of every Line , as the Line AB at your first Observation was 11 Chains and 36 Links , which being by your Scale set from A will give the Point B in the Paper , the second distance being set upon AI will give the Point C , and so proceeding with the rest , you will have the Points BCDEF and G , by which draw the Lines BC. CD . DE ; EF. FG and GB , and so at last you have the Figure of the Field upon your Paper , as was required . And what is here done at one station , may be done at two or more , by measuring one or two distances from your first station , taking at every station , the Degrees and distances to as many Angles , as are visible at each station . And as for taking the the Plot of a-Field by Intersection of Lines , he that doth but consider how the distances of several Objects may be taken at two stations , will be able to do the other also , and therefore I think it needless , to make any illustration by example . CHAP. XII . How to take the Plot of a Wood , Park or other Champion Plain , by going round the same , and making Observation at every Angle . BY these Directions which have been already given , may the Plot of any Field or Fields be taken , when the Angles may be seen alone or more stations within the Field , which though it is the case of some Grounds , it is not the case of all ; now where observation of the Angles cannot be observed within , they must be observed without , and although this may be done by the plain Table , yet as I judge it may be more conveniently done by the Theodolite , in these cases thereof I chiefly commend that Instrument , I know some use a Mariners Compass , but the working with a Needle is not only troublesom , but many times uncertain , yet if a Needle be joyned with the Theodolite the joynt Observations of the Angles may serve to confirm one another . 2. Suppose the Fig. 32. to be a large Wood whose Plot you desire to take ; Having placed your Instrument at the Angle A , lay your Ruler on the Diameter thereof , turning the whole Instrument till through the Sights you espy the Angle at K , then fasten it there , and turn your Ruler upon the Center , till through the Sights you espy your second Mark at B , the Degrees cut by the Ruler do give the quantity of that Angle BAK , suppose 125 Degrees , and the Line AB 6 Chains , 45 Links , which you must note in your Field-book , as was shewed before . 3. Then remove your Instrument to B , and laying your Ruler upon the Diameter thereof , turn it about , till through the Sights you can espy your third mark at C , and there fasten your Instrument , then turn the Ruler backward till through the Sights you see the Angle at A , the Degrees cut by the Ruler being 106.25 the quantity of the Angle ABC , and the Line BC containing 8 Chains and 30 Links , which note in your Field-book , as before . 4. Remove your Instrument unto C , and laying the Ruler on the Diameter thereof , turn the Instrument about till through the Sights you see the Angle at D , and fixing of it there , turn the Ruler upon the Center till you see your last station at B , and observe the Degrees cut thereby , which suppose to be 134 Degrees , and the Line CD 6 Chains 65 Links , which must be entered into your Field-book also , and because the Angle BCD is an inward Angle , note it with the Mark for your better remembrance . 5. Remove your Instrument unto D , and Iaying the Ruler on the Diameter , turn the Instrument about , till through the Sights , you see the Angle at E , and there fixing your Instrument , turn your Ruler backward till you espy the Mark at C , where the Degrees cut are , suppose 68.0 and the Line DE 8 Chains and 23 Links . 6. Remove your Instrument unto E , and laying the Ruler on the Diameter , turn the Instrument about , till through the Sights you see the Angle at F , and there fix it , then turn the Ruler backward till you see the Angle at D , where the Degrees cut by the Ruler suppose to be 125 and the Line EF 7 Chains and 45 Links . 7. Remove your Instrument unto F , and laying your Ruler upon the Diameter , turn the Instrument about , till through the Sights , you see the Angle at G , where fix the same , and turn the Ruler backward till you see the Angle at E , where the Degrees cut by the Ruler are 70 , and the Line FG 4 Chains 15 Links , which must be set down with this or the like Mark at the Angle . 8. Remove your Instrument unto G , and laying your Ruler upon the Diameter , turn the Instrument about , till through the Sights you see the Angle at H , where fix the same , and turn the Ruler backward till you see the Angle at F , where the Degrees cut by the Ruler are 65.25 , and the Line GH 5 Chains 50 Links . 9. Remove your Instrument in like manner to H and K , and take thereby the Angles and Distances as before , and having thus made observation at every Angle in the Field , set them down in your Field-book , as was before directed , the which in our present Example will be as followeth . A 151.00 6.45 B 106.25 8.30 C 134.00 6.65 D 68.00 8.23 E 125.00 7.45 F 70.25 4.15 G 65.25 5.50 H 130.00 6.50 K 140.00 11.00 The taking of the inward Angles BCD and EFG was more for Conformity sake than any necessity , you might have removed your Instrument from B to D , from E to G , the Length of the Lines BC. CD . EF and G , would have given by protraction the Plot of the Field without taking these Angles by observation ; many other compendious ways of working there are , which I shall leave to the discretion of the Ingenious Practitioner . 10. The Angles and Sides of the Field being thus taken , to lay down the same upon Paper , Parchment , another Instrument called a Protractor is convenient , the which is so well known to Instrument-makers , that I shall not need here to describe it , the chief use is to lay down Angles , and is much more ready for that purpose than a Line of Chords , though in effect it be the same . 11. Having then this Instrument in a readiness draw upon your Paper or Parchment upon which you mean to lay down the Plot of that Field , a Line at pleasure as AB . Then place the Center of your Protractor upon the Point A , and because the Angle of your first observation at A was 115 Degrees 00 Parts , turn your Protractor about till the Line AK lie directly under the 115 Degree ; and then at the beginning of your Protractor make a Mark , ând draw the Line AB , setting off 6 Chains 45 Links from A to B. 12. Then lay the Center of your Protractor upon the Point B , and here turn your Protractor about , till the line AB lie under 106 Degrees 25 Parts , and draw the Line BC , setting off the Distance 8 Chains , 30 Links from B to C. 13. Then lay the Center of your Protractor upon the Point C , and turn the same about till the Line BC lie under 134 Degrees , but remember to make it an inward Angle , as it is marked in your Field-Book , and there make a Mark , and draw the Line CD , setting off 6 Chains , 65 Links from C to D. And thus must you do with the rest of the Sides and Angles , till you come to protract your last Angle at H , which being laid down according to the former Directions the Line HK will cut the Line AK making AK 11 Chains and HK 6 Chains , 50 Links . This work may be also performed by protracting your last observation first ; for having drawn the Line AK , you may lay the Center of your Protractor upon the Point K , and the Diameter upon the Line AK ; and because your Angle at K by observation was 140 Degrees , you must make a Mark by the Side of your Protractor at 140 Degrees ; and draw the Line KH , setting off 6 Chains , 50 Links from K to H. And thus proceeding with the rest of the Lines and Angles , you shall find the Plot of your Field at last to close at A , as before it did at K. CHAP. XIII . The Plot of the Field being taken by any Instrument , how to compute the Content thereof in Acres , Roods , and Perches . THe measuring of many sided plain Figures hath been already shewed in the 13 Proposition of the 8 Chapter , which being but well considered , to compute the Content of a Field cannot be difficult ; It must be remembred indeed that 40 square Pearches do make an Acre . 2. Now then if the Plot be taken by a four Pole Chain divided into 100 Links , as 16 square Poles are the tenth part of an Acre ; so 10.000 square Links of such a Chain are equal to 16 square Pole , or Perches ; and by consequence 100.000 square Links are equal to an Acre , or the square Pearches . 3. Having then converted your Plot into Triangles , you must cast up the Content of each Triangle as hath been shewed , and then add the several Contents into one Sum , and from the aggregate cut off five Figures towards the right hand ; the remainer of the Figures towards the left hand are Acres , and the five Figures so cut off towards the right hand are parts of an Acre , which being multiplied by four , if you cut off five Figures from the Product , the Figures remaining towards the left hand are Roods , and the five Figures cut off are the parts of a Rood , which being multiplied by forty , if you cut off five Figures from the Product , the Figures remaining towards the left hand are Perches , and the Figures cut off are the Parts of a Pearch . Example . Let 258.94726 be the Sum of several Triangles , or the Content of a Field ready cast up , the three Figures towards the left hand 258 are the Acres , and the other Figures towards the right hand 94726 are the Decimal Parts of an Acre , which being multiplied by 4 , the Product is 3.78904 , that is three Roods and 78904 Decimal Parts of a Rood , which being multiplied by 40 , the product is 31.56160 , that is 31 Perches and 56160 Decimal Parts of a Perch ; and therefore in such a Field there are Acres 258 , Roods 3 , Pearches 31 , and 56160 Decimal Parts of a Perch . CHAP. XIV . How to take the Plot of Mountainous and uneven Grounds , and how to find the Content . VVHen you are to take the Plot of any Mountainous or uneven piece of Ground , such as is that in Figure 33 , you must first place your Instrument at A , and direct your Sights to B , measuring the Line AB , observing the Angle GAB , as was shewed before , and so proceed from B to C , and because there is an ascent from C to D , you must measure the true length thereof with your Chain , and set that down in your Book , but your Plot must he drawn according to the length of the Horizontal Line , which must be taken by computing the Base of a right angled Plain Triangle , as hath been shewed before , and so proceed from Angle to Angle until you have gone round the Field , and having drawn the Figure thereof upon your Paper , reduce into Triangles and Trapezias , as ABC . CDE . ACEF and AFG . then from the Angles B. C. D. F and G ; let fall the Perpendiculars , BK . CN . DL . FM . and GH . This done you must measure the Field again from Angle to Angle , setting down the Distance taken in a straight Line over Hill and Dale , and so likewise the several Perpendiculars , which will be much longer than the streight Lines measured on your Scale , and by these Lines thus measured with your Chain cast up the Content ; which will be much more than the Horizontal Content of that Field according to the Plot , but if it should be otherwise plotted than by the Horizontal Lines , the Figure thereof could not be contained within its proper limits , but being laid down among other Grounds , would force some of them out of their places , and therefore such Fields as these must be shadowed off with Hills , if it be but to shew that the Content thereof is computed according to the true length of the Lines from Corner to Corner , and not according to their Distance measured by Scale in the Plot. CHAP. XV. How to reduce Statute Measure into Customary , and the contrary . VVHereas an Acre of Ground by Statute Measure is to contain 160 square Perches , measured by the Pole or Perch of sixteen foot and a half : In many places of this Nation , the Pole or Perch doth by custom contain 18 foot , in some 20. 24. 28 Foot ; it will be therefore required to give the Content of a Field according to such several quantities of the Pole or Perch . 2. To do this you must consider how many square Feet there is in a Pole according to these several Quantities . In 16.5 to the Pole , there are 272.25 sq. feet . In 18 to the Pole there are 324 square feet . In 20 to the Pole there are 400 square feet . In 24 to the Pole there are 576 square feet . In 28 to the Pole there are 784 square feet . Now then if it were desired to reduce 7 Acres , 3 Roods , 27 Perches , according to Statute Measure , into Perches of 18 Foot to the Perch ; first reduce your given quantity , 7 Acres . 3 Rods , 27 Poles into Perches , and they make 1267 Perches . Then say , as 324. to 272. 25. so is 1267 to 1065. 6. that is 1065 Perches , and 6 tenths of a Perch . But to reduce customary Measure into statute measure , say as 272. 25. is to 324 so is 1267 Perches in customary measure , to 1507. 8 that is 1507 Perches and 8 tenths of a Perch in statute measure , the like may be done , with the customary measures of 20.24 and 28 or any other measure that shall be propounded . CHAP. XVI . Of the Measuring of solid Bodies . HAving shewed how the content of all plains may be computed , we are now come to the measuring of solid Bodies , as Prisms , Pyramids and Spheres , the which shall be explained in the Propositions following . Proposition . I. The base of a Prism or Cylinder being given , to find the solid content . The base of a Prism is either Triangular , as the Pentahedron ; Quadrangular , as the Hexahedron , or Multangular , or the Polyhedron Prism , all which must be computed as hath been shewed , which done if you multiply the base given by the altitude , the product shall be the solid content required . Example . In an Hexahedron Prism , whose base is quadrangular , one side of the Base being 65 foot and the other 43 , the Superficies or Base will be 27. 95. Which being multiplyed by the Altitude , suppose 12. 5. the product . 359. 375. is the solid content required . In like manner the Base of a Cylinder being 45. 6. and the altitude 15. 4. the content will be 702. 24. And in this manner may Timber be measured whether round or squared , be the sides of the squared Timber equal or unequal . Example . Let the Diameter of a round piece of Timber be 2. 75 foot . Then , As 1 it to 785397. so is the square of the Diameter 2. 75. to 5.9395 the Superficial content of that Circle . Or if the circumference had been given 8. 64. then , As 1 is to 079578 , so is the square of 8. 64. to 5.9404 the superficial content . Now then if you multiply this Base 5. 94. by the length , suppose 21 foot , the content will be 124. 74. If the side of a piece of Timber perfectly square be 1.15 this side being multiplyed by it self , the product will be 1.3225 the superficial content , or content of the Base , which being multiplyed by 21 the length , the content will be 27. 7745. Or if a piece of Timber were in breadth 1. 15. in depth 1.5 the content of the Base would be 1.725 which being multiplied by 21 the length , the content will be . 36. 225. Proposition . II. The Base and Altitude of a Pyramid or Cone being given , to find the solid content . Multiply the Altitude by a third part of the Base , or the whole Base by a third part of the Altitude , the Product shall be the solid content required . Example . In a Pyramid having a Quadrangular Base as in Fig. 22. The side CF 17. CD 9. 5. the Product is the Base CDEF . 161. 5 , which being multiplyed by 10.5 the third of the Altitude AB 31.5 the Product is 1695.75 the content . Or the third of the Base . viz. 53. & 3 being multiplied by the whole Altitude AB 31.5 the Product will be the content as before . 2. Example . In Fig. 21. Let there be given the Diameter of the Cone AB 3. 5. The Base will be 96. 25. whose Altitude let be CD 16.92 the third part thereof is 5.64 & 96.25 being multiplied by 5.64 , the Product 542.85 is the solid content required . Proposition . III. The Axis of a Sphere being given , to find the solid content . If you multiply the Cube of the Axis given by 523598 the solid content of a Sphere whose Axis is an unite , the Product shall be the solid content required . Example . Let the Axis given be ● , the Cube thereof is 27 , by which if you multiply . 523598 , the Product 14.137166 is the solid content required . Proposition . IV. The Basis and Altitude of the Frustum of a Pyramid or Cone being given , to find the content . If the aggregate of both the Bases of the Frustan and the mean proportional betwe●n them , shall be multiplied by the third part of the Altitude , the Product shall be the solid content of the Frustum . Example . In Fig. 22. Let CDEF represent the greater Base of a Pyramid , whose superficial content let be 1. 92 , and let the lesser Base be HGLKO . 85 the mean proportional between them is . 1. 2775 and the aggregate of these three numbers is . 4. 0475. Let the given Altitude be 15. the third part thereof is . 5 by which if you multiply 4.0475 the Product 20. 2375 is the content of the Frustum Pyramid . And to find the content of the Frustum Cone . I say . As. 1. ro 78539. so 20.23 to 15. 884397 , the content of the Cone required . But if the Bases of the Frustum Pyramid shall be square , you may find the content in this manner . Multiply each Diameter by it self and by one another , and the aggregate of these Products , by the third part of the altitude , the last Product shall be the content of the Frustum Pyramid . Example . Let the Diameter of the greater Base be 144 , the Diameter of the lesser Base 108 , and the altitude 60. The Square of 144 is 20736 The Square of 108 is 11664 The Product of 1444108 is 15552 The Sum of these 3 Products is 47952 Which being multiplyed by 20 the third part of the Altitude , the Product 959040 is the content of the Frustum Pyramid . And this content being multiplied by .785 39 the content of the Frustum Cone will be .753 .228 . Another way . Find the content of the whole Pyramid of the greater and lesser Diameter , the lesser content deducted from the greater , the remain shall be the content of the Frustum . To find the content of the whole Pyramid , you must first find their several Altitudes in this manner . As the difference between the Diameters , Is to the lesser Diameter . So is the Altitude given , to the Altitude cut off . Example . The difference between the former Diameter . 144. and 108 is 36 , the Altitude 60. now then As 36. 108 ∷ 60. 108. the altitude cut off . Now then if you mnltiply the lesser Base 1 1664 by 60 the third part of 180 the Product 699840 is the content of that Pyramid . And adding 60 to 180 the Altitude of the greater Pyramid is 240 , the third part whereof is 80 , by which if you multiply the greater Base before found , 70736 , the Product is the content of the greater Pyramid . 1658880 , from which if you deduct the lesser 699840 the remainer 959040 is the content of the Frustum Pyramid as before . And upon these grounds may the content of Taper Timber , whether round or square , and of Brewers Tuns , whether Circular or Elliptical , be computed , as by the following Propositions shall be explained . Proposition . V. The breadth and depth of a Taper piece of Squared Timber , both ends being given together with the length , to find the content . Let the given Dimensions . At the Bottom be A. 5.75 and B 2.34 At the Top. C. 2.16 and D. 1.83 . And let the given length be 24 Foot. According to the last Proposition , find the Area or Superficial content of the Tree at both ends thus . Multiply the breadth 3.75 0.574031 By the depth 2.34 0.369215 The Product 8.7750 0.943246 2. Multiply the breadth 2.16 0.334453 By the depth 1.82 0.262451 The Product is 3.9528 0.596904 3. Multiply the 1. Content . 87750 0.943246 by the second content . 3.9528 0.596904 And find the square root 5.8986 1.540150     0.770075 The Sum of these 18.6264 being multiplyed by 8 one third of the length , the content will be found to be 149. 0112. Thus by the Table of Logarithms the mean proportional between the two Bases is easily found , and without extracting the square Root , may by natural Arithmetick be found thus . A 4 2 / 2 CX A half C multiplyed by B : And C more half A multiplyed by D being added together and multiplyed by 30 , the length shall give the content . Example . A. 3.75 C 2.16 1 / 2 C. 1.08 1 / 2 A 1.875 Sum 4.83 Sum. 4.035 B - 2.34 D. 1.83 1932 12105 1449 32280 966 4035 11.3022 7.38405   11.30220 The sum of the Products 18.68625 Being multiplyed by 8 the third of the length , the content will be . 149. 49000. The like may be done for any other . Proposition VI. The Diameters of a piece of Timber being given at the Top and and Bottom , together with the length , to find the content . The Proposition may be resolved either by the Squares of the Diameters , or by the Areas of the Circles answering to the Diameters given , for which purpose I have here annexed not only a Table of the Squares of all numbers under a thousand , but a Table sharing the third part of the Areas of Circles in full measure , to any Diameter given under 3 foot . And therefore putting S = The Sum of the Tabular numbers answering to the Diameters at each end . X = The difference between these Diameters . L = the length of the Timber , C = The content . Then 1 ½ S = ½ - XX. + L. = C. If you work by the Table of the squares of Numbers . you must multiply the less side of the Equation , by 0.26179 the third part of 0.78539 the Product being multiplyed by the length , will give the content . But if you work by the Table of the third parts of the Areas of Circles in full measure , the tabular Numbers being multiplyed by the length will give the content . Only instead of the square of the difference of the Diameter , you must take half the Tabular number answering to that Difference , and you shall have the content as before . Example . Let the greatest Diameter by 2.75 , and the less 1. 93. Their difference is 0.83 The square of 2.75 is 7.5625 The square of 1.93 is 3.7249 . The Sum of the Squares 11.2874 The half Sum 5.6437 The Sum of them is 16.9311 Half the square of 0.82 deduct . 0.3362 The Difference is 16.5949 Which being multiplyed by 26179   1493541   1161643   165949   995694   331898 The Product will be . 4.344378871 Or by the Table of Areas . The Area of 2.75 is 1.979857 The Area of 1.93 is 0.975176 The Sum 2.955033 The half Sum 1.477516 The Sum of them 4.432549 Half the Area of 0.82 deduct 0.088016 The former Product 4.344533 Which being multiplyed by 24   17378132   8689066 The content is 104268792 But because that in measuring of round Timber the circumference is usually given and not the Diameter , I have added another Table by which the circumference being given , the Diameter may be found . Example . Let the circumference of a piece of Timber be 8325220 looking this Number in the second column of that Table , I find the next less to be 8.168140 and thence proceeding in a streight Line , I find that in the seventh Column the Number given , and the Diameter answering thereunto to be 2. 65. and thus may any other Diameter be found not exceeding the three foot . The Proportion by which the Table was made , is thus . As 1. to 3.14159 so is the Diameter given , to the circumference required . Or the Circumference being given , to find the Diameter , say : As. 1. to 0.3183 , so is the Circumference given to the Diameter required . And although by these two Tables all round Timber may be easily measured , yet it being more usual to take the Circumference of a Tree , then the Diameter , I have here added a third Table , shewing the third part of the Areas of Circles answering to any circumference under 10 foot , and that in Natural and Artificial numbers , the use of which Table shall be explained in the Proposition following . Proposition . VII . The Circumference of a piece of round Timber at both ends , with the length being given , to find the content . The Circumference of a Circle being given , the Area thereof may be found as hath been shewed , in the 7 Chapter , Proposition 4. and by the first Proposition of this ; and to find the third part of the Area , which is more convenient for our purpose I took a third part of the number given by which to find the whole , that is a third part of 07957747 that is 0.02652582 and having by the multiplying this number by the square of the Circumference computed three or four of the first numbers , the rest were found by the first and second differences . The Artificial numbers were computed by adding the Logarithms of the Squares of the circumference , to 8.42966891 the Logarithm of 0. 02652582. And by these Natural and Artificial numbers the content of round Timber may be found two ways By the Natural numbers in the same manner as the content was computed , the Diameters being given , and by the Natural and Artificial numbers both , by finding a mean proportional between the two Areas at the top and bottom of the Tree , as by Example shall be explained . Let the given Diamensions , or Circumferences be At the Bottom 9.95 Their difference is 6.20 At the Top 3.75 The tabular Numbers .   Natural Artificial . Answering to 9.95 2.626162 0.418931 And to 3.75 0.373019 9.571731 The Sum of the Logarith . 9.990662 The half Sum or Logarith . 989300 9.995331 The Sum of the Number is 3.988481 The Sum of the Natural Numbers is 2 . 9●9181 The half Sum ● . 499190 The Sum of them 4.498771 Half the number answer . to . 6. 20 is 0.509826 The remainer is 3.988945 Which being multiplyed by the length 24 , the content will be 95. 73468. Mr. Darling in his Carpenters Rule made easie , doth propound a shorter way , but not so exact , which is by the Circumference given in the middle of the piece to find the side of the Square , namely by multiplying the Circumference given by 28209 , or 2821. which side of the Square being computed in Inches , and lookt in his Table of Timber measure , doth give the content of the Tree not exceeding 31 foot in length , the which way of measuring may be as easily performed by this Table . Example . The circumference at the top and bottom of the Tree being given 9.95 and 3.75 the Sum is 13.70 The half thereof is the mean circumfer . 6.85 Which sought in the Table , the Numbers are . The Natural number is 1.244657 , which being multiplyed by 3 the Product is 3.733971 , which multiplyed by the length 24 , the content is 89. 615304. The Artificial number is 0.095049 The Logarithm of 24 is 1.380211 The Absolute Number 29.871 1.475260 Which multiplyed by 3 , the Product is 89613 Proposition . VIII . The Diameters of a Brewers Tun at top and bottom being given with the height thereof , to find the content . In Fig. 29. Let the given Diameter . At the top be AC 136 BD 128 At the bottom . KG 152 HF 144 Altit . 51 Inches . The which by the 5 Proposition of this Chap. may thus be computed . AC 139 + ½ KG 76 = 212 × BD 128 the Product is 27136. And KG 1524 ½ AC 68 = 220 × HF 144 the Product is 31680. the Sum of these 2 Products is 58816 which being multiplyed by onethird of 51 , that is by 17 , and that Product multiplyed by 26179 the third of 78539 will give the content . The Logarithm of 58816. is 54.76949 The Logarithm of 17 is 1.230449 The Product 1.999944 The Logarithm of . 26179 9.417968 The content is . 261765 5.417912 Thus the content of a Tun may be found in Inches , which being divided 282 the number of Inches in an Ale Gallon , the quotient will be the content in Gallons . Or thus ; divide the former . 26179 by 282 the quotient will be 00092836. by which the content may be found in Ale Gallons in this manner . The former Product 5.999944 The Logarithm of 0.00092836 6.967719 The content in Gallons 928.24 2.967663 Proposition . IX . The Diameters of a close Cask , at head and bung with the length given , to find the content . In the resolving of this Proposition , we are to consider the several forms of Casks , as will as the kind of the Liquor , with which it is filled , for one and the same Rule will not find the content in all Cask . And a Coopers Cask is commonly taken , either for the middle Frustum of a Spheroid , the middle Frustum of a Parabolical Spindle , the middle Frustum of two Parabolick Conoids , or for the middle Frustum of two Cones abutting upon one common Base . And the content of these several Casks may be found either by equating the Diameters , or by equating the Circles . for the one , a Table of Squares is necessary , and a Table shewing the third part of the Areas of a Circle to all Diameters . The making of the Table of Squares , every one knows , to be nothing else but the Product of a Number multiplyed , by it self , thus the Square of 3 is 9. the Square of 8 is 64 and so of the rest . And the Area of a Circle to any given Diameter may be found , as hath been shewed , in Chap. 7 Proposition 2. But here the Area of a Circle in Inches , will not suffice , it will be more fit for use , if the third part of the Area be found in Ale and Wine Gallons both , the which may indeed be done by dividing the whole Area in Inches by 3 and the quotient by 282 to make the Table for Ale-measure , and by 231 to make the Table for Wine-measure ; but yet these Tables ( as I think ) may be more readily made in this manner . The Square of any Diameter in Inches , being divided by 3.81972 will give the Area of the Circle in Inches : And this Division being multiplyed by 282 will give you 1077.161 for a common Division , by which to find the Area in Ale-Gallons , or being multiplyed by 231 the Product , 882.355 will be a commou Division by which to find the Area in Wine-Gallons . But because it is easier to multiply then divide : If you multiply the several Squares by 26178 the third part of 78539 the Product will give the Area in Inches , or if you divide . 26179 by 282 the quotient will be . 00092886 for a common Multiplicator , by which to find the Area in Ale-Gallons , or being divided by 231 the quotient will be 0011333 a common Multiplicator , by which to find the content in Wine-Gallons . An Example or two will be sufficient for illustration . Let the Diameter given be 32 Inches , the Square thereof 1024 being divided by 3.81970 the quotient is 268.083 , and the same Square 1024 being multiplyed by 261799 , the Product will be 268. 082. Again if you divide 1024 by 1077.161 the quotient will be 9508 , or being multiplied by 00092836 , the Product will be 9508. Lastly if you divide 1024 by 882.755 , the quotient will be 1.1605 , or being multiplied by 00113333 the Product is 1.1605 , And in this manner may the Tables be made for Wine and Beer-measure , but the second differences in these Numbers being equal , three or four Numbers in each Table being thus computed , the rest may be found by Addition only . Thus the Squares of 1. 2. 3. and 4 Inches are . 1. 4. 9 and 16 by which if you multiply 00113333 , the several Products will be third part of the Area , of the Circles answering to those Diameters in Wine-Gallons . Or 00092836 being multiplied by those Squares , the several Products , will be the third part of the Areas of the Circles answering to those Diameters in Ale-Gallons ; the which with their first and second differences are as followeth . The Products or Areas in Wine-Gallons : 1. 00113333     2. 00453332 33999 226666 3. 01019997 566665 226666 4. 01813328 796331   The Products in Ale-Gallons . 1. 00092836     2. 00371344 278508 185672 3. 00835524 464180 185672 4. 01485376 649852   And by the continual addition of the second differences to the first , and the first differences to the products before found , the Table may be continued as far as you please . The construction of the Tables being thus shewed : We will now shew their use in finding the content of any Cask . Let S = the Sum of the Tabular Numbers answering to the Diameters at the Head and Bung. D = their difference X = the difference of the Diameters themselves . L = the length of the Vessel , and C = the content thereof . 1. If a Cask be taken for the middle Frustum of a Spheroid , intercepted between two Planes parallel , cutting the Axis at right Angles : Then 1 ½ S + ½ D × L = C. 2. If a Cask be taken for the middle Frustum of a parabolical Spindle , intercepted between two planes parallel cutting the Axis at right Angles . Then 1 ½ S + ½ D × L = C. 3. If a Cask be taken for the middle Frustum of two Parabolick Conoids , abutting upon one common Base , intercepted between two Planes parallel , cutting the Axis at right Angle : Then 1 ½ S : × L = C. 4. If a Cask be taken for the middle Frustum of two Cones , abutting upon one common bafe , intercepted between two Planes parallel cutting the Axis at Right Angles . Then 1 ½ S — ⅓ XX. × L = C. In all these four Equations , if you work by the Table of Squares of numbers , you must multiply the less side of the Equation by 262 , if you would have the content in Cubical Inches ; by 001133 if you would have the content in Wine-Gallons ; and by 000928 , if you would have the content in Ale-Gallons . But if you work by the Tables of the third parts of the Areas Circle , the Tabular Numbers being multiplyed by the length only will give the content required , only in the fourth Equation instead of half the Square of the Difference of the Diameters , take half the Tabular Number answering to that difference , and you shall have the content required ; as by the following Examples will better appear , then by many words . Examples in Wine-measure by the Table of the Squares of Numbers . The Diameter of a Vessel At the Bung being 32 Inches . At the Head 22 Inches . The difference of the Diameters 10 Inches . And the length of the Vessel 44 Inches . Spheroid . Parabolick Spindle . 1024 1024 484 484 1508 1508 754 754 270 540 2532 23160 2532 23160 7596 69480 7596 69480 7596 69480 28695156 262472280 44 44 114780624 104988912 114780624 104988912 126.2586864 115.4878032 Parabolick Conoid Cone . 1024 1024 484 484 1508 1508 754 754   50 2262 2212 2262 2212 6786 6636 6786 6636 6786 6636 25635246 25068596 44 44 102540984 200274384 102540984 100274384 112.79508241 110.30182224 This which hath been done by the Table of Squares may be more easily performed , by the Table of the third part of the Areas of Circles , ready reduced to Wine-Gallons . Spheroid Parabolick Spindle . 1.16053 1.16053 0.54853 0.54853 1.70906 1.70906 85453 85453 30600 61200 2.86959 2.624790 44 44 1147836 1049916 1147836 10499160 126.26196 115.490760 Parabolick Conoid Cone . 1.16053 1.16053 0.54853 0.54853 1.70906 1.70906 85453 85453   56666 2.56359 2.506924 44 44 1025436 10027696 1025436 10027696 112.79796 110.304656 Examples in Ale-measure by the Table of the Squares of Numbers . Spheroid . Parabolick Spindle . 1024 1024 484 484 1508 1508 754 754 270 540 2532 2316.0 00092836 00092836 22758 20844 5064 4632 20256 18528 7596 6948 15192 138960 235660752 2.150081760 44 44 948623008 860032704 940643008 860032704 103.22673088 94.60359744 Parabolick Conoid Cone . 1024 1024 484 484 1508 1508 754 754   50 2262 2212 20358 19909 4524 4424 18096 17696 6786 6636 13527 13272 2.09995032 2.05423232 44 44 8.39980128 821692928 839980128 821692928 92.39781408 90.38622208 By the Areas of Circles . Spheroid . Parabolick Spindle . 0.95052 0.95052 0.44930 0.44930 1.39982 1.39982 .69991 69991 .25061 050122 2.35034 2.149852 34 44 940136 8599408 940136 8599408 103.41496 94.593488 Parabolick Conoid . Cone . 0.95052 0.95052 0.44930 0.44930 1.39982 1.39982 69991 .69991   46425 209973 2.053305 44 44 839892 8213220 839892 8213220 90.345420 90.345420 And here for the Singularity of the Example , I will set the Dimensions of a Cask lately made in Herefordshire , for that excellent Liquor of Red streak Cyder , the like whereof either for the largeness of the Cask , or incomparable goodness of that kind of Drink , is not to be found in all England , nay and perhaps not in the World. The length of the Cask is 104 Inches . The Diameter at the Bung 92 Inches . And the Diameter at the Head 74 Inches . The Numbers in the Table of Ale-Gallons answering to these Dimensions are . Spheroid Parabolick Spindle . Bung. 92 7.859639 7.859639 Head. 74 5.083699 5.083699 12.941338 12.941338 6.470669 6.470669 1.386770 .277394 20.798777 19.689401 104 104 83195108 78.757604 20798777 19689401 Con. 2163.072808 2047.697704 Parabolick Conoid . Cone . 7.857639 7.857639 5.083699 5.083699 12.941338 12.941338 6.470669 6.470669   0.150394 19.412007 19.261613 104 104 77648028 77046452 19412007 19261613 201. 8. 848728 2003.207752 And thus you have the content of this Cask by four several Ways of Gauging , but that which doth best agree with the true content , found by these that filled the same is the second way or that which takes a Cask to be the middle Frustum of a Parabolick Spindle , according to which the content is 2047 Gallons . That is allowing 64 Gallons to the Hogshead . 32 Hogsheads very near . Proposition . X. If a Cask be not full , to find the quantity of Liquor contained in it , the Axis being posited parallel to the Horizon . To resolve this Proposition , there must be given the whole content of the Cask , the Diameter at the Bung , and the wet Portion thereof , then by help of the Table of Segments , whose Area is unity , and the Diameter divided into 10.000 equal parts , the content may thus be found . As the whole Diameter , is to its wet Portion . So is the Diameter in the Table . 10.000 to its like Portion , which being sought in the Table of Segments , gives you a Segment , by which if you multiply the whole content of the Cask , the Product is the content of the Liquor remaining in the Cask . But in the Table of Segments in this Book , you have the Area , to the equal parts of one half of the Diameter only , when the Cask therefore is more then half full , you must make use of the dry part of the Diameter instead of the wet , so shall you find what quantity of Liquor is wanting to fill up the Cask , which being deducted from the whole content of the Cask ; the remainer is the quantity of Liquor yet remaining , an Example in each will be sufficient , to explane the use of this Table . 1. Example , In a Wine Cask not half full , let the great Diameter be as before 32 Inches , the content 126.25 Gallons , and let the wet part of the Diameter be 12 Inches , First I say . As the whole Diameter 32. is to the wet part 12. so is 10.000 to 3750 , which being sought in the Table , I find , the Area of that Segment to be . 342518 which being multiplyed by the whole content of the Cask 126.25 , the Product is 43.24289750 and therefore there is remaining in the Cask 43 & 1 / 4 ferè . 2. Example . In the same Cask let the wet part of the Diameter be 18 Inches . I say . As 32.18 : : 10000.5625 whos 's Complement to 10000 is 4375 which being sought in the Table , I find the Area answering thereto to be 420630 ; now then I say . As the whole Area of the Circle 1000000 is to the whole content of the Cask 126. 25. So is the Area of the Segment sought . 420630 , to the content 53.1044375 which is in this case the content of the Liquor that is wanting , this therefore being deducted from the content of the whole Cask , 136. 25. the part remaining in the Vessel is . 73. 1455625. Thus may Casks be gauged in whole or in part , in which a Table of Squares is sometimes necessary , as being the Foundation , from whom the other Tables are deduced ; such a Table therefore is here exhibited , for all Numbers under 1000 , by help whereof the Square of any Number under 10.000 may easily be found in this manner . The Rectangle made of the Sum and Difference of any two Numbers , is equal to the Difference of the Squares of these Numbers . Example , Let the given Numbers be 36 and 85 their Sum is 121 , their difference 49 , by which if you multiply 121 , the Product will be 5929. The Square of 36 is 1296 , and the Square of 85 is 7225 , the difference between which Squares is 5929 as before . And hence the Square of any Number under 10.000 may thus be found , the Squares of all Numbers under 1000 being given . Example . Let the Square of 5715 be required . The Square of 571 by the Table is 326041 , therefore the Square of 5710 is 32604100 : the Sum of 5710 and 5715 is 11425 , and the difference 5 , by which if you multiple 11425 , the Product is 52125 which being added unto 32604100 the Sum 32656325 is the Square of 5715. The like may be done for any other . TABLES FOR THE Measuring OF TIMBER , AND THE GAUGING OF CASKS AND Brevvers Tuns . LONDON , Printed for Thomas Passinger at the three Bibles on London-Bridge . 1679. A Table of Squares . 1 1 3 2 4   3 09 5 4 16 7 5 25 9 6 36 11 7 49 13 8 64 15 9 81 17 10 100 19 11 121 21 12 144 23 13 160 25 14 196 27 15 225 29 16 256 31 17 287 33 18 324 35 19 361 37 20 400 39 21 441 41 22 484 43 23 529 45 24 576 47 25 625 49 26 676 51 27 729 53 28 784 55 29 841 57 30 900 59 31 961 61 32 1024 63 33 1089 65 34 1156 67 34 1156 69 35 1225 71 36 1206 73 37 1369 75 38 1444 77 39 1521 79 40 1600 81 41 1681 83 42 1764 85 43 1841 87 44 1936 89 45 2025 91 46 2116 93 47 2209 95 48 2304 97 49 2401 99 50 2500 101 51 2601 103 52 2704 105 53 2809 107 54 2916 109 55 3025 111 56 3136 113 57 3249 115 58 3364 117 59 3481 119 60 3600 121 61 3721 123 62 3844 125 63 3969 127 64 4096 129 65 4225 131 66 4356 133 67 4489 135 67 4489 135 68 4624 137 60 4761 139 70 4900 141 71 5041 143 72 5184 145 73 5329 147 74 5476 149 75 5625 151 76 5776 153 77 5929 155 78 6084 157 79 6241 159 80 6400 161 81 6561 163 82 6724 165 83 6889 167 84 7056 169 05 7225 171 06 7396 173 87 7559 175 88 7744 177 89 7921 179 90 8100 181 91 8281 183 92 8464 185 93 8649 187 94 8836 189 95 9025 191 96 9216 193 97 9409 195 98 9604 197 99 9801 199 100 10000 201 101 10201 203 102 10404 205 103 10609 207 104 10816 209 105 11025 211 106 11236 213 107 11449 215 108 11664 217 109 11881 219 110 12100 221 111 12321 223 112 12544 225 113 12769 227 114 12996 229 115 13225 231 116 13456 233 117 13689 235 118 13924 237 119 14161 239 120 14400 241 121 14641 243 122 14884 245 123 15129 247 124 15376 249 125 15625 251 126 15876 253 127 16129 255 128 16384 257 129 16641 259 130 16900 261 131 17161 263 132 17424 265 133 17689 267 134 17956 269 134 17956 269 135 18225 271 136 18496 273 137 18769 275 138 19044 277 139 19321 279 140 19600 281 141 19881 283 142 20164 285 143 20449 287 144 20736 289 145 21025 291 146 21316 293 147 21609 295 148 21904 297 149 22201 299 150 22500 301 151 22801 303 152 23104 305 153 23409 307 154 23716 309 155 24025 311 156 24336 313 157 24649 315 158 24964 317 159 25281 319 160 25600 321 161 25921 323 162 26244 325 163 26569 327 164 26896 329 165 27225 331 166 27556 333 167 27889 335 167 27889 335 168 28224 337 169 28561 339 170 28900 341 171 29241 343 172 29584 345 173 29929 347 174 30276 349 175 30625 351 176 30976 353 177 31329 355 178 31684 357 179 32041 359 180 32400 361 181 32761 363 182 33124 365 183 33489 367 184 33856 369 185 34225 371 186 34596 373 187 34969 375 188 35344 377 189 35721 379 190 36100 381 191 36481 383 192 36864 385 193 37249 387 194 37636 389 195 38025 391 196 38416 393 197 38809 395 198 39204 397 199 39601 399 200 40000 401 201 40401 403 202 40804 405 203 41209 407 204 41616 409 205 42025 411 206 42436 413 207 42849 415 208 43264 417 209 43681 419 210 44100 421 211 44521 423 212 44944 425 213 45369 427 214 45796 429 215 46255 431 216 46656 433 217 47089 435 218 47524 437 219 47961 439 220 48400 441 221 48841 443 222 49284 445 223 49729 447 224 50176 449 225 50625 451 226 51076 453 227 51529 455 228 51984 457 229 52441 459 230 52900 461 231 53361 463 232 53824 465 233 54289 467 234 54756 469 234 54756 469 235 55225 471 236 55696 473 237 56169 475 238 56644 477 239 57121 479 240 57600 481 241 58081 483 242 58564 485 143 59049 487 244 59536 489 245 60025 491 246 60516 493 247 61009 495 248 61504 497 249 62001 499 250 62500 501 251 63001 503 252 63504 505 253 64009 507 254 64516 509 255 65025 511 256 65536 513 257 66049 515 258 66564 517 259 67071 519 260 67600 621 261 68121 523 262 68644 525 263 69169 527 264 69696 529 265 70225 531 266 70756 533 277 71289 535 267 71289 535 268 71824 537 269 72361 539 270 72900 541 271 73441 543 272 73984 545 273 74529 547 274 75076 549 275 75625 551 276 76176 553 277 76729 555 278 77284 557 279 77841 559 280 78400 561 281 78961 563 282 79524 565 283 80089 567 284 80616 569 285 81225 571 286 81796 573 287 82369 575 288 82944 577 289 83521 579 290 84100 581 291 84681 583 292 85264 585 293 85849 587 294 86436 589 295 87025 591 296 87616 593 297 88200 595 298 88804 597 299 89401 599 300 90000 601 301 090601 603 302 091204 605 303 091809 607 304 092416 609 305 093025 611 306 093636 613 307 094249 615 308 094864 617 309 095481 619 310 096109 621 311 096721 623 312 97344 625 313 97969 627 314 98596 629 315 99325 631 316 99856 633 317 100487 645 318 101124 637 319 101761 639 320 102400 641 321 103041 643 322 103684 645 323 104329 647 324 104976 649 325 105625 651 326 106276 653 327 106929 655 328 107584 657 329 108241 659 330 108900 661 331 109561 663 332 110224 665 333 110889 667 334 111556 669 334 111556 669 335 112225 671 336 112896 673 337 113569 675 338 114244 677 339 114921 679 340 115600 681 341 116281 683 342 116964 685 343 117649 687 344 118336 689 345 119025 691 346 119716 693 347 120409 695 348 121104 697 349 121801 699 350 122500 701 351 123201 703 352 123904 705 353 124609 707 354 125316 709 355 126025 711 356 126736 713 357 127449 715 358 128164 717 359 128881 719 360 129600 721 361 138321 723 362 131044 725 363 131769 727 364 132496 729 365 133225 731 366 133956 733 367 134689 735 367 134689 735 368 135424 737 369 136161 739 370 136900 741 371 137641 743 372 138384 745 373 139129 747 374 139876 749 375 140625 751 376 141376 753 377 142129 755 378 142884 757 379 143641 759 380 144400 761 381 145161 763 382 145924 765 383 146689 767 384 147456 769 385 148225 771 386 148996 773 387 149769 775 388 150544 777 389 151321 779 390 152100 781 391 152881 783 392 153664 785 393 154449 787 394 155236 789 395 156025 791 396 156816 793 397 157609 795 398 158404 797 399 159201 799 400 160000 801 401 160801 803 402 161604 805 403 162409 807 404 163216 809 405 164025 811 406 164836 813 407 165649 815 408 166464 817 409 167281 819 410 168100 821 411 168921 823 412 169744 825 413 170569 827 414 171396 829 415 172225 831 416 173056 833 417 173889 835 418 174724 837 419 175561 839 420 176400 841 421 177241 843 422 178084 845 423 178929 847 424 179776 849 425 180625 851 426 181476 853 427 182329 855 428 183184 857 429 184041 859 430 184900 861 431 185761 863 432 186624 865 433 187489 867 434 188356 869 434 188356 869 435 189225 871 436 190096 873 437 190969 875 438 191844 877 439 192721 879 440 193600 881 441 194481 883 442 195364 885 443 196249 887 444 197136 889 445 198025 891 446 198916 893 447 199809 895 448 200704 897 449 201601 899 450 202500 901 451 203401 903 452 204304 905 453 205209 907 454 206116 909 455 207025 911 456 207936 913 457 208849 915 458 209764 917 459 210681 919 460 211600 921 461 212521 923 462 213444 925 463 214369 927 464 215296 929 465 216225 931 466 217156 933 467 218089 935 467 218089 935 468 219024 937 469 219961 939 470 220900 941 471 221841 943 472 222784 945 473 223729 947 474 224676 949 475 225625 951 476 226576 953 477 227529 955 478 228484 957 479 229441 959 480 230400 961 481 231361 963 482 232324 965 483 233289 967 484 234256 969 485 235225 971 486 236196 973 487 237169 975 488 238144 977 489 239121 979 490 240100 981 491 241081 983 492 242064 985 493 243049 987 494 244036 989 495 245025 991 496 246016 993 497 247009 995 498 248004 997 499 249001 999 500 250000 1001 501 251001 1003 502 252004 1005 503 253009 1007 504 254016 1009 505 255025 1011 506 256036 1013 507 257049 1015 508 258064 1017 509 259081 1019 510 260100 1021 511 261121 1023 512 262144 1025 513 263169 1027 514 264196 1029 515 265225 1031 516 266256 1033 517 267289 1035 518 268324 1037 519 269361 1039 520 270400 1041 521 271441 1043 522 272484 1045 523 273529 1047 524 274576 1049 525 275625 1051 526 276676 1053 527 277729 1055 528 278784 1057 529 279841 1050 530 288900 1061 531 281961 1063 532 283024 1065 533 284089 1067 534 285156 1069 534 285156 1069 535 286225 1071 536 287296 1073 537 288369 1075 538 289444 1077 539 290521 1079 540 291600 1081 541 292681 1083 542 293764 1085 543 294849 1087 544 295936 1089 545 297025 1091 546 298116 1093 547 299209 1095 548 300324 1097 549 301401 1099 550 302500 1101 551 303601 1103 552 304704 1105 553 305809 1107 554 306916 1109 555 308025 1111 556 309136 1113 557 310249 1115 558 311364 1117 559 312481 1119 560 313600 1121 561 314721 1123 562 315844 1125 563 316969 1127 564 318096 1129 565 319225 1131 566 320356 1133 567 321489 1135 567 321489 1135 568 322624 1137 569 323761 1139 570 324900 1141 571 326041 1143 572 327184 1145 573 328329 1147 574 329476 1149 575 330625 1151 576 331776 1153 577 332929 1155 578 334084 1157 579 335241 1159 580 336400 1161 581 337561 1163 582 338724 1165 583 339889 1167 584 341056 1169 585 342225 1171 586 343396 1173 587 344569 1175 588 345744 1177 589 346921 1179 590 348100 1181 591 349281 1183 592 350464 1185 593 351649 1187 594 352836 1189 595 354025 1191 596 355216 1193 597 356409 1195 598 357604 1197 599 358801 1199 600 369000 1201 601 361201 1203 602 362404 1205 603 963609 1207 604 364816 1209 605 366025 1211 606 367236 1213 607 368449 1215 608 369664 1217 609 370881 1219 610 372100 1221 611 373321 1223 612 374544 1225 613 375769 1227 614 376996 1229 615 378225 1231 616 379456 1233 617 380689 1235 618 381924 1237 619 383161 1239 620 384400 1241 621 385641 1243 622 386834 1245 623 388129 1247 624 389376 1249 625 390625 1251 626 391876 1253 627 393129 1255 628 394385 1257 629 395641 1259 630 396900 1261 631 398161 1263 632 399424 1265 633 400689 1267 634 401956 1269 634 401956 1269 635 403225 1271 636 404496 1273 637 405769 1275 638 407044 1277 639 408321 1279 640 409600 1281 641 410881 1283 642 412164 1285 643 413449 1287 644 414736 1289 645 416025 1291 646 417316 1293 647 418609 1295 648 419904 1297 649 421201 1299 650 422500 1301 651 423801 1303 652 425104 1305 653 426409 1307 654 427716 1309 655 429025 1311 656 430336 1313 657 431649 1315 658 432964 1317 659 434281 1319 660 435600 1321 661 436921 1323 662 438244 1325 663 439569 1327 664 440896 1329 665 442225 1331 666 443556 1333 667 444889 1335 667 444889 1335 668 446224 1337 669 447561 1339 670 448900 1341 671 450241 1343 672 451584 1345 673 452929 1347 674 454276 1349 675 455625 1351 676 456976 1353 677 458329 1355 678 459684 1357 679 461041 1359 680 462400 1361 681 463761 1363 682 465124 1365 683 466489 1367 684 467856 1369 685 469225 1371 686 470596 1373 687 471969 1375 688 473344 1377 689 474721 1379 690 476100 1381 691 477481 1383 692 478864 1385 693 480249 1387 694 481636 1389 695 483025 1391 696 484416 1393 697 485809 1395 698 487204 1397 699 488601 1399 700 490000 1401 701 491401 1403 702 492804 1405 703 494209 1407 704 495616 1409 705 497025 1411 706 498436 1413 707 499849 1415 708 501264 1417 709 502681 1419 710 504100 1421 711 505521 1423 712 506944 1425 713 508369 1427 714 509796 1429 715 511225 1431 716 512656 1433 717 514089 1435 718 515524 1437 719 516961 1439 720 518400 1441 721 519841 1443 722 521284 1445 723 522729 1447 724 524176 1449 725 525625 1451 726 527076 1453 727 528529 1455 728 529984 1457 729 531441 1459 730 532900 1461 731 534361 1463 732 535824 1465 733 537289 1467 734 538756 1469 734 538756 1469 735 540225 1471 736 541696 1473 737 543169 1475 738 544644 1477 739 546121 1479 740 547600 1481 741 549081 1483 742 550564 1485 743 552049 1487 744 553536 1489 745 555025 1491 746 556516 1493 747 558009 1495 748 559504 1497 749 561001 1499 750 562500 1501 751 564001 1503 752 565504 1505 753 567009 1507 754 568516 1509 755 570025 1511 756 571536 1513 757 573049 1515 758 574564 1517 759 576081 1519 760 577600 1521 761 579121 1523 762 580644 1525 763 582169 1527 764 583696 1529 765 585225 1531 766 586756 1533 767 588289 1535 767 588289 1535 768 589824 1537 769 591361 1539 770 592900 1541 771 594441 1543 772 595984 1545 773 597529 1547 774 599076 1549 775 600625 1551 776 602176 1553 777 603726 1555 778 605284 1557 779 606841 1559 780 608400 1561 781 609961 1563 782 611524 1565 783 613089 1567 784 614656 1569 785 616225 1571 786 617796 1573 787 619369 1575 788 620944 1577 789 622521 1579 790 624100 1581 791 625681 1583 792 627264 1585 793 628849 1587 794 630436 1589 795 632025 1591 796 633616 1593 797 635209 1595 798 636804 1597 799 638401 1599 800 640000 1601 801 641601 1603 802 643204 1605 893 644809 1607 804 646416 1609 805 648025 1611 806 649636 1613 807 651249 1615 808 652864 1617 809 654481 1619 010 656100 1621 811 657721 1623 812 659344 2625 813 560969 1627 814 562596 1629 815 564225 1631 816 565856 1633 817 567489 1635 818 569124 1637 819 570761 1639 820 672400 1641 821 674041 1643 822 675684 1645 823 677329 1647 824 678976 1649 825 680625 1651 826 682276 1653 827 683929 1655 828 685584 1657 829 687241 1659 830 688900 1661 831 690561 1663 832 692224 1665 833 693889 1667 834 695556 1669 834 695556 1669 835 697225 1671 836 668869 1673 837 700569 1675 838 702244 1677 839 703921 1679 840 705600 1681 841 707281 1683 842 708964 1685 853 710649 1687 844 712336 1689 845 714025 1691 846 715716 1693 847 717409 1695 848 719104 1697 849 729801 1699 850 722500 1701 851 724201 1703 852 725904 1705 853 727609 1707 854 729316 1709 855 731025 1711 856 732736 1713 857 734449 1715 858 736164 1717 859 737881 1719 860 739600 1721 861 741321 1723 862 743044 1725 863 744769 1727 864 746596 1729 865 748225 1731 866 749956 1733 867 751689 1735 867 751689 1735 868 753424 1737 869 755161 1739 870 756900 1741 871 658641 1743 872 760384 1745 873 762129 1747 874 763876 1749 875 765625 1751 876 767376 1753 877 769529 1755 878 770884 1757 879 772641 1759 880 774400 1761 881 776161 1763 882 777924 1765 883 779689 1767 884 781456 1769 885 783225 1771 886 754996 1773 887 786709 1775 888 786544 1777 889 790321 1779 890 792100 1781 891 793881 1783 892 795664 1785 893 797449 1787 894 799236 1789 895 801025 1791 896 802816 1793 897 894609 1795 808 806404 1797 899 808281 1799 900 810000 1801 901 811801 1803 902 813604 1805 903 815409 1807 904 817216 1809 905 819025 1811 906 820836 1813 907 822649 1815 908 824464 1817 909 826281 1819 910 828100 1821 911 829921 1823 912 831744 1825 913 833569 1827 914 835396 1829 915 837225 1831 916 839056 1833 917 840889 1835 918 842724 1837 919 844561 1839 920 846400 1841 921 848241 1843 922 850084 1845 923 851929 1847 924 853776 1849 925 855625 1851 926 857476 1853 927 859329 1855 928 861184 1857 929 863041 1859 930 864900 1861 931 866761 1863 932 868624 1865 933 870489 1867 934 872356 1869 934 872356 1869 935 874225 1871 936 876096 1873 937 877969 1875 938 879844 1877 939 881721 1879 940 883600 1881 941 885481 1883 942 887364 1885 943 889249 1887 944 891136 1889 945 893025 1891 946 894916 1893 947 896809 1895 948 898704 1897 949 900601 1899 950 902500 1901 951 904401 1903 952 906304 1905 953 908209 1907 954 910116 1909 955 912025 1911 956 913936 1913 957 915849 1915 958 917764 1917 959 919681 1919 960 921600 1921 961 923521 1923 962 925444 1925 963 927369 1927 964 929296 1929 965 931225 1931 966 933156 1933 967 935089 1935 967 935089 1935 968 937024 1937 969 938961 1939 970 940900 1941 971 942841 1943 972 944784 1945 973 946729 1947 974 948676 1949 975 950625 1951 976 952576 1953 977 954529 1955 978 956484 1957 979 958441 1959 980 960400 1961 981 962361 1963 982 964324 1965 983 966289 1967 984 968256 1969 985 970225 1971 986 972196 1973 987 974169 1975 988 976144 1977 989 978121 1979 990 980100 1981 991 982081 1983 992 984064 1985 993 986049 1987 994 988036 1989 995 990025 1991 996 992016 1993 997 994009 1995 998 996004 1997 999 998001 1999 1000 1000000 2001   0 1 2 3 4 5 6 7 8 9 1 0.001133 001371 001631 001915 002221 002549 002901 003275 003671 004091 2 0.004533 004997 005485 005995 006527 007083 007661 008261 008885 009531 3 0.010199 010891 011605 012341 013101 013883 014687 015515 016365 017237 4 0.018133 019051 019991 020955 021941 022949 023981 025035 026111 027211 5 0.028333 029477 030645 031835 033047 034283 035541 036825 038125 039451 6 0.040799 042171 043565 044981 046421 047883 049367 050875 052405 053957 7 0.051533 057131 058751 060395 062061 063749 065461 067195 068951 070731 8 0.072533 074357 076205 078075 079967 681883 083821 085781 087765 089771 9 0.091799 093851 095925 098021 100141 102283 104447 106635 108845 111077 10 0.113333 115610 117911 120234 122580 124949 127340 129754 132191 134650 11 0.137132 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1.822963 0.260777 8.30 1.827363 0.261825 8.31 1.831769 0.262870 8.32 1.836181 0.263915 8.33 1.840597 0.264958 8.34 1.845019 0.266001 8.35 1.849480 0.267041 8.36 1.853879 0.268081 8.37 2.858316 0.269119 8.38 1.862760 0.270156 8.39 1.867208 0.271192 8.40 1.871662 0.272227 8.41 1.876121 0.273250 8.42 1.880585 0.274293 8.43 1.885054 0.275324 8.44 1.889529 0.276353 8.45 1.894010 0.277382 8.46 1.898495 0.278409 8.47 1.902886 0.279435 8.48 1.907482 0.280450 8.49 1.911983 0.281484 8.50 1.916490 0.282506 8.51 1.921002 0.283528 8.52 1.925520 0.283748 8.53 1.930042 0.285566 8.54 1.934570 0.286584 8.55 1.939104 0.287601 8.56 1.943642 0.288616 8.57 1.948186 0.289630 8.58 1.952735 0.290643 8.59 1.957290 0.291655 8.60 1.961849 0.292665 8.61 1.966414 0.293675 8.62 1.970985 0.294683 8.63 1.975561 0.295690 8.64 1.980142 0.296696 8.65 1.984728 0.297701 8.66 1.989320 0.298704 8.67 1.993916 0.299707 8.68 1.998529 0.300708 8.69 2.003126 0.301708 8.70 2.007406 0.302707 8.71 2.012357 0.303705 8.72 2.016981 0.304701 8.73 2.021609 0.305697 8.74 2.026243 0.306691 8.75 2.030883 0.307685 8.76 2.035528 0.308677 8.77 2.040177 0.309668 8.78 2.044833 0.310657 8.79 2.049493 0.311646 8.80 2.054159 0.312634 8.81 2.058830 0.313620 8.82 2.063507 0.314606 8.83 2.068189 0.315590 8.84 2.072876 0.316573 8.85 2.077568 5.317555 8.86 2.082266 0.318536 8.87 2.086969 0.319516 8.88 2.091677 0.320494 8.89 2.096391 0.321472 8.90 2.101110 0.322448 8.91 2.105834 0.323424 8.92 2.110564 0.324498 8.93 2.115299 0.325371 8.94 2.120039 0.326343 8.95 2.124784 0.327314 8.96 2.129535 0.328284 8.97 2.134291 0.329253 8.98 2.139053 0.330221 8.99 2.143819 0.331178 9.00 2.148591 0.332153 9.01 2.153368 2.333118 9.02 2.158151 0.334081 9.03 2.162939 0.335044 9.04 2.167732 0.336005 9.05 2.172531 0.337966 9.06 2.177335 0.338925 9.07 2.182144 0.338883 9.08 2.186958 0.339840 9.09 2.191778 0.340796 9.10 2.196603 0.341751 9.11 2.201433 0.342705 9.12 2.206269 0.343658 9.13 2.211110 0.344610 9.14 2.215956 0.345561 9.15 2.220808 0.346511 9.16 2.225665 0.347459 9.17 2.230527 9.348407 9.18 2.235394 0.349354 9.19 2.240267 0.350299 9.20 2.245145 0.351244 9.21 2.250029 0.352881 9.22 2.254917 0.353130 9.23 2.259811 0.354072 9.24 2.264711 0.355012 9.25 2.269615 0.355872 9.26 2.274525 0.356890 9.27 2.279440 0.357828 9.28 2.284361 0.358764 9.29 2.289287 0.359700 9.30 2.294218 0.360634 9.31 2.299154 0.361568 9.32 2.304096 0.362500 9.33 2.309043 0.363432 9.34 2.313996 0.364362 9.35 2.318953 0.365292 9.36 2.323916 0.366220 9.37 2.328885 0.367148 9.38 2.333858 0.368074 9.39 2.338847 0.369000 9.40 2.343821 0.369924 9.41 2.348144 0.370848 9.42 2.353806 0.371770 9.43 2.358806 0.372692 9.44 2.363478 0.373612 9.45 2.368489 0.374532 9.46 2.373838 0.375451 9.48 2.378893 0.376368 9.48 2.383886 0.377285 9.49 2.388918 0.378201 9.50 2.393955 0 . 37911● 9.51 2.398998 0.380029 9.52 2.404045 0.380942 9.53 2.409099 0.381854 9.54 2.414157 0.382765 9.55 2.419221 0.383675 9.56 2.424290 0.384584 9.57 2.429364 0.385492 9.58 2.434444 0.386399 9.59 2.439529 0.387306 9.60 2.444629 0.388211 9.61 2.449715 0.389115 9.62 2.454816 0.390019 9.63 2.459922 0.390921 9.64 2.465034 0.391822 9.65 2.470150 0.392723 9.66 2.475273 0.393623 9.67 2.480400 0.394521 9.68 2.485533 0.395419 9.69 2.490671 0.396316 9.70 2.495814 0.397212 9.71 2.500963 0 . 39810● 9.72 2.506117 0.399001 9.73 2.511243 0.399894 9.74 2.516441 0.400786 9.75 2.521611 0 . 4●1678 9.76 2.526786 0.402568 9.77 2.531966 0.403458 9.78 2.537152 0.404346 9.79 2.542343 0.405234 9.80 2.547540 0.406121 9.81 2.552745 0.407006 9.82 2.557948 0.407891 9.83 2.563164 0.408775 9.84 2.568378 0.409659 9.85 2.573601 0.410541 9.86 2.578829 0.411422 9.87 2.584063 0.412303 9.88 2.589302 0.413182 9.89 2.594546 0.414061 9.90 2.599795 0.414939 9.91 2.605050 0.415816 9.92 2.610310 0.416692 9.93 2.615573 0.417567 9.94 2.620846 0.418441 9.95 2.626122 0.419315 9.96 2.631404 0.420187 9.97 2.636690 0.421059 9.98 2.641982 0.421929 9.99 2.647279 0.422789 10.00 2.652582 0.423668 A Table for the speedy finding of the Length or Circumference answering to any Arch in Degrees and Decimal Parts . A Table for the speedy finding of the Length or Circumference answering to any Arch , in Degrees and Decimal Parts . 1 0.0174 5329 2519 2 0.0349 0658 5038 3 0.0523 5987 7557 4 0.0698 1317 0076 5 0.0872 6646 2595 6 0.1047 1975 5114 7 0.1221 7304 7633 8 0.1396 2634 0152 9 0.1570 7963 2671 10 0.1745 3292 5190 11 0.1919 8621 7709 12 0.2094 3951 0228 13 0.2268 9280 2747 14 0.2443 4609 5266 15 0.2617 9938 7785 16 0.2792 5268 0304 17 0.2967 0597 2823 18 0.3141 5926 5342 19 0.3316 1255 7861 20 0.3490 6585 0380 21 0.3665 1914 2899 22 0.3839 7245 5418 23 0.4014 2572 7937 24 0.4188 7902 0456 25 0.4363 3231 2975 26 0.4537 8560 5495 27 0.4712 3889 8013 28 0.4886 8219 0532 29 0.5061 4548 3051 30 0.5235 4877 5570 31 0.5410 5206 8089 32 0.5585 0536 0608 33 0.5759 5865 3127 34 0.5934 1194 5646 35 0.6108 6523 8165 36 0.6283 1853 0684 37 0.6457 7128 3203 38 0.6632 2511 5722 39 0.6806 7840 8241 40 0.6981 3170 0760 41 0.7155 8499 3279 42 0.7330 3828 5798 43 0.7504 9157 8317 44 0.7679 4487 0836 45 0.7853 9816 3355 46 0.8028 3145 5874 47 0.8203 0474 8393 48 0.8377 5804 0912 49 0.8552 1133 3431 50 0.8726 6462 4950 51 0.8901 1791 8469 52 0.9075 7121 0988 53 0.9250 2450 3507 54 0.9424 7779 6026 55 0.9599 3108 8545 56 0.9773 8438 1064 57 0.9948 3767 3583 58 1.0122 9096 6102 59 1.0297 4425 8621 60 1.0471 9755 1140 61 1.0646 5084 3659 62 1.0821 0413 6178 63 1.0995 5742 8697 64 1.1170 1072 1216 65 1.1344 6401 3735 66 1.1519 1730 6254 67 1.1693 7059 8773 68 1.1868 2389 1292 69 1.2042 7718 3811 70 1.2217 3047 6330 71 1.2391 8376 8849 72 1.2566 3706 1368 73 1.2740 9035 3887 74 1.2915 4364 6406 75 1.3089 9693 8925 76 1.3264 5023 1444 77 1.3439 0352 3963 78 1.3613 5681 6482 79 1.3788 1010 9001 80 1.3962 6340 1520 81 1.4137 1669 4039 82 1.4311 6998 6558 83 1.4486 2327 9057 84 1.4660 7657 1596 85 1.4835 2986 4115 86 1.5009 8315 6634 87 2.5184 3644 9153 88 1.5358 8974 1572 89 1.5533 4303 4191 90 1.5707 9632 6710 91 1.5882 4961 9229 92 1.6057 0291 1748 93 1.6231 5620 4267 94 1.6406 0949 6786 95 1.6580 6278 9305 96 1.6755 1608 1824 97 1.6929 6937 4343 98 1.7104 2266 6862 99 1.7278 7595 9381 100 1.7453 2925 1900 A Common Divisor for the speedy converting of the Table , shewing the Area of the Segments of a Circle whose Diameter is 2.0000 &c. into a Table shewing the Area of the Segment of any Circle whose Area is given . 1 0031 4159 2653 2 0062 8318 5306 3 0094 2477 7959 4 0125 6637 0612 5 0157 0796 3265 6 0188 4955 5918 7 0219 9114 8571 8 0251 3274 1224 9 0282 7433 3877 10 0314 1592 6530 11 0345 5751 9183 12 0376 9911 1836 13 0408 4070 4489 14 0439 8229 7142 15 0471 2388 9795 16 0502 6548 2448 17 0534 0707 5101 18 0565 4866 7754 19 0596 9026 0407 20 0628 3185 3060 21 0659 7344 5713 22 0691 1503 8366 23 0722 5663 1019 24 0753 9822 3672 25 0785 3981 6325 26 0816 8140 8978 27 0848 2300 1631 28 0889 6459 4284 29 0911 0618 6937 30 0942 4777 9590 21 0973 8937 2243 32 1005 3096 4896 33 1036 7255 7549 34 1068 1415 0202 35 1099 5574 2855 36 1130 9733 5508 37 1162 3892 8161 38 1193 8052 0814 39 1225 2211 3467 40 1256 6370 6120 41 1288 0529 8773 42 1319 4689 1426 43 1350 8848 4079 44 1382 3007 6732 45 1413 7166 9385 46 1445 1326 2038 47 1476 5485 4691 48 1507 9644 7344 49 1539 3803 9997 50 1570 7963 2650 51 1602 2122 5303 52 1633 6281 7956 53 1665 0441 0609 54 1696 4600 3262 55 1727 8759 5915 56 1759 2918 6568 57 1790 7078 1221 58 1822 1237 3874 59 1853 5396 6527 60 1884 9555 9180 61 1916 3715 1833 62 1947 7874 4486 63 1979 2033 7139 64 2010 6192 9792 65 2042 0352 2445 66 2073 4511 5098 67 2104 8670 7751 68 2136 2830 0404 69 2167 6989 3057 70 2199 1148 5710 71 2230 5307 8363 72 2261 9467 1016 53 2293 3626 3669 74 2324 7785 6322 75 2356 1944 8975 76 2387 6104 1628 77 2419 0263 4281 78 2450 4422 6934 79 2481 8581 9587 80 2513 2741 2240 81 2544 6900 4893 82 2576 1059 7546 83 2607 5219 0199 84 2638 9378 2852 85 2670 3537 5505 86 2701 7696 8158 87 2733 1856 0811 88 2764 6015 3464 89 2796 0174 6117 90 2827 4333 8770 91 2858 8493 1423 92 2890 2652 4076 93 2921 6811 6729 94 2953 0970 9382 95 2984 5130 2035 96 3015 9289 4688 97 3047 3448 7341 98 3078 7607 9994 99 3110 1767 2647 100 3141 5926 5300 A Table shewing the Ordinates , Arches and Areas of the Segments of a Circle , whose Diameter is 2000 , &c. to every Hundredth Part of the Radius .   Ordinates Deg. & Dec. p. Areas 100 10000000000 90.00000000 1.57079632 99 9999499971 89.42704196 1.55079682 98 9997999799 88.85400799 1.53079890 97 9995498987 88.28987110 1.51080538 96 99919967974 87.70756124 1.49081774 95 9987492177 87.13402020 1.47083808 94 9981983770 86.56018749 1.45086837 93 9975469913 85.98601581 1.43091081 92 9967948635 85.41143529 1.41096718 91 9959417653 84.83639513 1.39103966 90 9949874371 84.26083018 1.37113017 89 9939315871 83.68468641 1.35124084 88 9927738916 83.10789860 1.35137360 87 9915139938 82.53040793 1.31153053 86 9901515035 81.95215479 1.29171372 85 9886859966 81.37307468 1.27192518 84 9871170138 80.79310474 1.25216697 83 9854440623 80.21218180 1.23244118 82 9836666101 79.63024030 1.21274989 81 9817840903 79.04721672 1.19309522 80 9797958971 78.46304188 1.17347924 79 9777013859 77.87762112 1.15390361 78 9754998718 77.29096735 1.13437189 77 9731906288 76.70292903 1.11488481 76 9707728879 76.11243681 1.09544458 75 9682458365 75.52248845 1.07605462 74 9656086163 74.92996014 1.05671627 73 9628603221 74.33573392 1.03743102 72 9600000000 73.73979456 1.01820220 71 9570266454 73.14202474 0.99903143 70 9539392014 72.54239737 0.97992192 69 950●365565 71.94076969 0.96087497 68 9474175425 71.33707564 0.94189323 67 9439809319 70.73122476 0.92297905 67 9439809319 70.73122476 0.92297905 66 9404254356 70.12312662 0.90413479 65 9367496997 69.51268522 0.88536283 64 9329523031 68.89980401 0.86666560 63 9290317540 68.28438326 0.84804557 62 9249864864 67.66631784 0.82950517 61 9208148564 67.04550117 0.81104695 60 9165151389 66.42182324 0.79267345 59 9120855222 65.79516567 0.77438721 58 9075241043 65.16541298 0.75619089 57 9028288874 64.53244020 0.73808713 56 8979977728 63.89612058 0.72007866 55 8930285549 63.25631645 0.70216884 54 8879189152 62.61289754 0.68435845 53 8826664149 61.96570387 0.66665234 52 8772684879 61.31459838 0.64905275 51 8717224755 60.65941181 0.63156249 50 8660254037 60.00000000 0.61418485 49 8601744009 59.33617061 0.59692260 48 8541662601 58.66774875 0.57977892 47 8479976415 57.99454553 0.56275702 46 8416650165 57.31636147 0.54586011 45 8351646544 56.63307065 0.52909299 44 8284926070 55.94420256 0.51245467 43 8216446926 55.24977433 0.49595300 42 8146264741 54.54945742 0.47959008 41 8074032449 53.84299205 0.46336957 40 8000000000 53.13010237 0.44725221 39 7924014134 52.41049708 0.43137885 38 7846018098 51.68386597 0.41560051 37 7765951325 50.94987748 0.39998818 36 7683749084 50.20810657 0.38453683 35 7599342076 49.45831012 0.36925312 34 7512655988 48.70012721 0.35414227 34 7512655988 48.70012721 0.35414227 33 7423610981 47.93293539 0.33920561 32 7332121111 47.15635717 0.32444946 31 7238093671 46.36989113 0.30987884 30 7141428428 45.57299618 0.29549884 29 7042016756 44.76508489 0.28131493 28 6939740629 48.94551977 0.26733268 27 6834471449 43.11360613 0.25355796 26 6726068688 42.26858452 0.23999689 25 6614378277 41.40962595 0.22665594 24 6499230723 40.53580228 0.21354168 23 6380438856 39.64611132 0.20066138 22 6257795138 38.73942400 0.18802248 21 6131068422 37.81448867 0.17563291 20 6000000000 36.86989765 0.16350111 19 5864298764 35.90406873 0.15163601 18 5723635208 34.91520640 0.14004722 17 5577633906 33.90125515 0.12874491 16 5425863986 32.85988059 0.11774053 15 5267826876 31.78833069 0.10704574 14 5102940328 30.68341722 0.09667379 13 4930517214 29.54136121 0.08663902 12 4749736834 28.35773666 0.07695728 11 4559605246 27.12675321 0.06764629 10 4358898943 25.84193282 0.05872590 09 4146082488 24.49464857 0.05021866 08 3919183588 23.07391815 0.04215095 07 3675595189 21.56518547 0.03455313 06 3411744421 19.94844363 0.02746204 05 3122498999 18.19487244 0.02092302 04 2800000000 16 . 260204●1 0.01499411 03 2431049156 14.06986184 0.00975364 02 1989974874 11.47834097 0.00551730 01 1410673597 8.10961446 0.00188278 010 1410673597 8.10961446 0.00188278 009 1338618691 7.69281247 0.00160779 008 1262378707 7.25224680 0.00134761 007 1181143513 6.78328892 0.00110317 006 1093800713 6 . 279●8064 0.00087554 005 0998749217 5.73196797 0.00066616 004 0893532316 5.12640010 0.00047674 003 0774015503 4.43922228 0.00030969 002 0632139225 3.62430750 0.00016860 001 0447101778 2.56255874 0.00005961   1.57079632 999 199999   1.56879632 998 199999   1.56679632   199999 997 1.56479633   199998 996 1.56279634   199997 995 1.56079636   199996 994 1.55879639   199995 993 1.55679644   199994 992 1.55479649   199992 991 1.55299657   199991 990 1.55079666   199988 989 1.54879677   199986 988 1.54679690   199984 987 1.54479706   199981 986 1.54279724   199978 985 1.54079745   199976 984 1.53879769   199972 983 1.53679796 983 1.53679796   199969 982 1.53479827   199965 981 1.53279862   199962 980 1.53079899   199957 979 1.52879941   199953 978 1.52679988   199949 977 1.52480039   199944 976 1.52280095   199939 975 1.52080156   199934 974 1.51880222   199929 973 1.51680293   199924 972 1.51480369   199918 971 1.51280451   199912 970 1.51080539   199906 969 1.50880633   199909 968 1.50680733   199894 967 1.50480839   199887 966 1.50280952 966 1.50280952   199880 965 1.50081072   199873 964 1.49881199   199866 963 1.49681333   199859 962 1.49481474   199851 961 1.49281623   199843 960 1.49081774   199835 959 1.48881938   199827 958 1.48682110   199819 957 1.48482291   199810 956 1.48282480   199801 955 1.48082678   199792 954 1.47882885   199783 953 1.47683102   199774 952 1.47483328   199764 951 1.47283563   199754 950 1.47083808   199744 949 1.46884063 949 1.46884063   199734 948 1.46684328   199724 947 1.46484604   199713 946 1.46284890   199702 945 1.46085187   199691 944 1.45885496   199680 943 1.45685815   199669 942 1.45486146   199657 941 1.45286489   199645 940 1.45086837   199633 939 1.44887204   199621 938 1.44687583   199608 937 1.44487975   199596 936 1.44288379   199585 935 1.44088794   199570 934 1.43889224   199557 933 1.43689667   199543 932 1.43490124 932 1.43490124   199530 931 1.43290594   199516 930 1.43091078   199502 929 1.42891578   199488 928 1.42692090   199473 927 1.42492617   199459 926 1.42293158   199444 925 1.42093714   199429 924 1.41894305   199413 923 1.41694892   199398 922 1.41495494   199382 921 1.41296112   199366 920 1.41096746   199350 919 1.40897396   199334 918 1.40698062   199318 917 1.40498744   199301 916 1.40299443   199284 915 1.40100159 915 1.40100159   199267 914 1.39900892   199250 913 1.39701642   199232 912 1.39502410   199215 911 1.39303195   199197 910 1.39103998   199178 909 1.38904820   199160 908 1.38705660   199142 907 1.38506518   199123 906 1.38307395   199104 905 1.38108291   199085 904 1.37909206   199066 903 1.37710140   199047 902 1.37511093   199027 901 1.37312066   199007 900 1.37113059 900 1.37113017   198987 899 1.36914030   198967 898 1.36715063   198946 897 1.36516117   198925 896 1.36317192   198904 895 1.36118288   198883 894 1.35919405   198861 893 1.35720544   198839 892 1.35521705   198818 891 1.35322887   198797 890 1.35124090   198775 889 1.34925315   198752 888 1.34726563   198729 887 1.34527834   198707 886 1.34329127   198684 885 1.34130443   198661 884 1.33931782   198638 88● 1.33733144 883 1.33733144   198619 882 1.33534525   198590 881 1.33335935   198566 880 1.33137360   198541 879 1.32938819   198517 878 1.32740302   198499 877 1.32541803   198480 876 1.32343323   198449 875 1.32144874   198418 874 1.31946456   198393 873 1.31748063   198367 872 1.31549696   198341 871 1.31351355   198315 870 1.31153053   198289 869 1.30954764   198262 868 1.30756502   198235 867 1.30558267   198209 198209 866 1.30360058   198182 865 1.30161876   198154 864 1.29963722   198127 863 1.29765595   198100 862 1.29567495   198072 861 1.29369423   198044 860 1.29171379   198015 859 1.28973357   197986 858 1.28775371   197958 857 1 . 2857741●   197929 856 1.28379484   197900 855 1.28181584   197871 854 1.27983713   197841 853 1.27785872   197811 852 1.27588061   197781 851 1.27390280   197751 850 1.27192529 850 1.27192518   197721 849 1.26994797   197691 848 1.26797106   197660 847 1.26599446   197629 846 1.26401817   197598 845 1.26204219   197561 844 1.26006658   197534 843 1.25809124   197489 842 1.25611635   197457 841 1.25414178   197427 840 1.25216751   197395 839 1.25019356   197374 838 1.24821982   197341 837 1.24624641   197308 836 1.24427333   197275 835 1.24230058   197241 834 1.24032817   197212 197272 833 1.23835605   197173 832 1.23638432   197139 831 1.23441293   197105 830 1.23244118   197072 829 1.23047046   197036 828 1.22850010   197001 827 1.22653009   196966 826 1.22456043   196930 825 1.22259113   196895 824 1.22062218   196861 823 1.21865357   196825 822 1.21668532   196787 821 1.21471745   196750 820 1.21274989   196714 819 1.21078275   196677 818 1.20881598   196640 817 1.20684958 817 1.20684954   1966●3 816 1.20488355   196565 815 1.20291790   196527 814 1 . 20●95263   196479 813 1.19898774   196451 812 1.19702323   196413 811 1.19505910   196375 810 1.19309525   196347 809 1.19113254   196298 808 1.18916956   196258 807 1.18720698   196219 806 1.18524479   196188 805 1.18328291   196148 804 1.18132143   196100 803 1.17936043   196060 802 1.17739983   196019 801 1.17543964   195978 800 1.17347986 800 1.17347924   195938 799 1.17151986   195897 798 1.16956089   195855 797 1.16760234   195814 796 1.16564420   195773 795 1.16368647   195731 794 1.16172916   195689 793 1.15977227   195646 792 1.15781581   195603 791 1.15585978   195561 790 1.15390417   195518 789 1.15194899   195472 788 1.14999427   195429 787 1.14803998   195388 786 1.14608610   195344 785 1.14413266   195300 784 1.14217966 784 1.14217966   195256 783 1 . 14022●10   195211 782 1.13827499   195166 781 1.13632333   195122 780 1.13437211   195076 779 1.13242135   195031 778 1.13047102   194985 777 1.12852117   194939 776 1.12657178   194893 775 1.12462285   194847 774 1.12267438   194801 773 1.12072637   194755 772 1.11877882   194708 771 1.11683174   194661 770 1.11488487   194614 769 1.11293867   194566 768 1.11099301   194518 194518 767 1.10904783   194471 766 1.10710312   194423 765 1.10515889   194374 764 1.10321515   194325 763 1.10127190   194276 762 1.09932914   194227 761 1.09738687   194173 760 1.09544514   194129 759 1.09350385   194079 758 1.09156306   194029 757 1.08962277   193980 756 1.08768297   193930 755 1.08574367   193878 754 1.08380489   193827 753 1.08186662   193777 752 1.07992885   193726 751 1.07799159 751 1.07799159   193674 750 1.07605485   193622 749 1.07411863   193570 748 1.07218293   193518 747 1.07024775   193466 746 1.06831309   193414 745 1.06637895   193361 744 1.06444534   193308 743 1.06251226   193255 742 1.06057971   193201 741 1.05864770   193147 740 1.05671623   193093 739 1.05478530   193039 738 1.05285491   192985 737 1.05092506   192931 736 1.04899575   192876 735 1.04706699   192821 192821 734 1.04513878   192766 733 1.04321112   192710 732 1.04128402   192655 731 1.03935747   192600 730 1.03743147   192543 729 1.03550604   192486 728 1.03358118   192430 727 1.03165688   192373 726 1.02973115   192316 725 1.02780999   172259 724 1.02588740   192213 723 1.02396527   192155 722 1.02204372   192086 721 1.02012286   192029 720 1.01820221   191970 719 1.01628251   191911 718 1.01436340 718 1.01436340   191853 717 1.01244487   191794 716 1.01052693   191734 715 1.00860959   191674 714 1.00669285   191615 713 1.00477670   191556 712 1.00286114   191505 711 1.00094609   191444 710 0.99903165   191374 709 0.99711791   191313 708 0.99520478   191252 707 0.99329226   191191 706 0.99138035   191129 705 0.98946906   191067 704 0.98755839   191005 703 0.98564834   190943 702 0.98273891   190881 701 0.98183010 190818 700 0.97992192   190755 699 0.97801437   190692 698 0.97610745   190629 697 0.97420116   190566 696 0.97229550   190502 695 0.97039048   190438 694 0.96848610   190376 693 0.96658234   190304 692 0.96467930   190244 691 0.96277686   190179 690 0.96087497   190113 689 0.95897384   190048 688 0.95707336   189983 687 0.95517353   189917 686 0.95327436   189851 685 0.95137585   189784 684 0.94947801   189717   189717 683 0.94758084   189651 682 0.94568433   189584 681 0.94378848   189516 680 0.94189324   189448 679 0.93999876   189381 678 0.93810495   189313 677 0.93621182   189244 676 0.93431938   189176 675 0.93242762   189107 674 0.93053655   189038 673 0.92864617   188969 672 0.92675648   188899 671 0.92486749   188823 670 0.92297905   188769 669 0.92109136   188696 668 0.91920440   188619 667 0.91731821   188549 188549 666 0.91543272   188478 665 0.91354794   188407 664 0.91166387   188336 663 0.90978051   188264 662 0.90789787   188192 661 0.90601595   188120 660 0.90413479   188048 659 0.90225431   187973 658 0.90037458   187900 657 0.89849558   187829 656 0.89661729   187757 655 0.89473972   187685 654 0.89286287   187610 653 0.89098677   187535 652 0.88911142   187461 651 0.88723681   187386 650 0.88536295 650 0.88536284   187311 649 0.88348973   187237 648 0.88161736   187163 647 0.87974573   187087 646 0.87787486   187010 645 0.87600476   186934 644 0.87413542   186858 643 0.87226684   186782 642 0.87039902   186705 641 0.86853197   186628 640 0.86666560   186551 639 0.86480009   186473 638 0.86293536   186395 637 0.86107141   186317 636 0.85920824   186239 635 0.85734585   186161 634 0.85548424   186083 633 0.85362341 633 0.85362341   186004 632 0.85176337   185924 631 0.84990413   185845 630 0.84804557   185764 629 0.84618793   185684 628 0.84433109   185606 627 0.84247503   185525 626 0.84061978   185444 625 0.83876534   185363 624 0.83691171   185281 623 0.83505890   185200 622 0.83320690   185119 621 0.83135571   185038 620 0.82950517   184956 619 0.82765561   184873 618 0.82580688   184790 617 0.82395898   184707   184707 616 0.82211191   184624 615 0.82026567   184540 614 0.81842027   184456 613 0.81657571   184372 612 0.81473199   184288 611 0.81288911   184204 610 0.81104695   184119 609 0.80920576   184035 608 0.80736541   183949 607 0.80552592   183865 606 0.80368727   183780 605 0.80184947   183693 604 0.80001254   183606 603 0.79817548   183519 602 0.79634029   183433 601 0.79450596   183346 600 0.79267250 600 0.79267345   183258 599 0.79084087   183170 598 0.78900917   183082 597 0.78717835   182994 596 0.78534841   182906 595 0.78351935   182818 594 0.78169117   182729 593 0.77986388   182640 592 0.77803748   182551 591 0.77621197   182461 590 0.77438736   182371 589 0.77256365   182281 588 0.77074084   182191 587 0.76891893   182100 586 0.76709793   182009 585 0.76527784   181918 584 0.76345866   131826 583 0.76164040   181734 582 0.75982306   181639 581 0.75800667   181543 580 0.75619124   181458 579 0.75437670   181365 578 0.75256305   181271 577 0.75075934   181178 576 0.74893856   181085 575 0.74712771   180991 574 0.74531780   180897 573 0.74350883   180802 572 0.74170081   180707 571 0.73989374   180611 570 0.73708713   180516 569 0.73628197   180422 568 0.73447775   180326 567 0.73267449   180230 180230 566 0.73087219   180134 565 0.72907085   180037 564 0.72727048   179940 563 0.72547108   279843 562 0.72367265   179745 561 0.72187520   179647 560 0.72007866   179548 559 0.71828318   179450 558 0.71648868   179353 557 0.71469515   179254 556 0.71290261   179155 555 0.71111106   179056 554 0.70932050   178956 553 0.70753094   178856 552 0.70574238   178755 551 0.70395483   178654 550 0.70216829 550 0.70216834   178553 549 0.70038281   178452 548 0.69859829   178352 547 0.69681477   178250 546 0.69503227   178149 545 0.69325078   178048 544 0.69147030   177943 543 0.68969087   177841 542 0.68791246   177738 541 0.68613508   177634 540 0.68435845   177528 539 0.68258317   177423 538 0.68080894   177318 537 0.67903576   177218 536 0.67726358   177114 535 0.67549244   177009 534 0.67372235   176903 533 0.67195332   176799 532 0.67018533   176693 531 0.66841840   176585 530 0.66665234   176479 529 0.66488755   176372 528 0.66312383   176265 527 0.66136118   176158 526 0.65959960   176050 525 0.65783910   175942 524 0.65607968   175834 523 0.65432134   175725 522 0.65256409   175622 521 0.65080787   175512 520 0.64905275   175398 519 0.64729877   175289 518 0.64554588   175179 517 0.64379409   175068   175068 516 0.64204341   174957 515 0.64029384   174846 514 0.63854538   174735 513 0.63679803   174624 512 0.63505179   174512 511 0.63330667   174400 510 0.63156249   174287 509 0.62981962   174174 508 0.62807788   174062 507 0.62633726   173948 506 0.62459778   173835 505 0.62285943   173721 504 0.62112222   173607 503 0.61938615   173492 502 0.61765123   173377 501 0.61591746   173262 500 0.61418484 500 0.61418485   173147 499 0.61245338   173031 498 0.61072307   172914 497 0.60899393   172798 496 0.60726595   172681 495 0.60553914   172564 494 0.60381350   172447 493 0.60208903   172329 492 0.60036574   172211 491 0.59864363   172093 490 0.59692260   171975 489 0.59520285   171856 488 0.59348429   171736 487 0.59176693   171617 486 0.59005076   171498 485 0.58833578   171377 484 0.58662201   171256 483 0.58490948   171136 482 0.58319809   171015 481 0.58148794   170893 480 0.57977892   170771 479 0.57807121   170649 478 0.57636472   170527 477 0.57465945   170406 476 0.57295539   170281 475 0.57125258   170158 474 0.56955100   170034 473 0.56785066   169910 472 0.56615156   169786 471 0.56445370   169661 470 0.56275702   169536 469 0.56106166   169411 468 0.55936755   169285 467 0.55767470   169159 169159 466 0.55598311   169035 465 0.55429278   168901 464 0.55260377   168779 463 0.55091598   168652 462 0.54922946   168524 461 0.54754422   168397 460 0.54586011   168268 459 0.54417743   168139 458 0.54249604   168010 457 0.54081594   167881 456 0.53913713   167751 455 0.53745962   167621 454 0.53578341   167491 453 0.53410850   167360 452 0.53243490   167229 451 0.53076261   167098 450 0.52909163 450 0.52909299   166966 449 0 . 527423●3   166834 448 0.52575499   166702 447 0.52408797   166570 446 0.52242227   166437 445 0.52075790   166302 444 0.51909488   166168 443 0.51743320   166035 442 0.51577285   165900 441 0.51411385   165765 440 0.51245467   165634 439 0.51079833   165494 438 0.50914339   165358 437 0.50748981   165222 436 0.50583759   16508● 435 0.50418673   164949 434 0.50253724   164811 433 0.50088913   164673 432 0.49924240   164535 431 0.49759705   164397 430 0.49595308   164259 429 0.49431049   164120 428 0.49266929   163980 427 0.49102949   163835 426 0.48939114   163700 425 0.48775414   163560 424 0.48611854   163419 423 0.48448435   163277 422 0.48285158   163135 421 0.48122023   162998 420 0.47959025   162843 419 0.47796165   162708 418 0.47633457   162565 417 0.47470892   162422   162422 416 0.47308470   162278 415 0.47146192   162134 414 0.46984058   161989 413 0.46822069   161844 412 0.46660225   161699 411 0.46498526   161570 410 0.46336957   161410 409 0.46175547   161260 408 0.46014287   161113 407 0.45853174   160966 406 0.45692208   160818 405 0.45531390   160670 404 0.45370720   160522 403 0.45210198   160373 402 0.45049825   160223 401 0.44889602   160073 400 0.44729529 400 0.44729522   159923 399 0.44569599   159773 398 0.44409826   159623 397 0.44250203   159472 396 0.44090731   159320 395 0.43931411   159168 394 0.43772243   159016 393 0.43613227   158863 392 0.43454364   158710 391 0.43295654   158557 390 0.43137086   158403 389 0.42978683   158248 388 0.42820435   158093 387 0.42662342   157938 386 0.42504404   157782 385 0 , 42346622   157626 384 0.42188996   157470 383 0.42031526   157313 382 0.41874213   157156 381 0.41717057   156999 380 0.41560058   156841 379 0.41403217   156682 378 0.41246535   156522 377 0.41090013   156363 376 0.40933650   156204 375 0.40777446   156044 374 0.40621402   155883 373 0.40465519   155722 372 0.40309797   155561 371 0.40154236   155399 370 0.39998818   155238 369 0.39843580   155025 368 0.39688555   154911 367 0.39533644   154788 154788 366 0.39378896   154584 365 0.39224312   154419 364 0.39069893   154254 363 0.38915639   154089 362 0.38761550   153923 361 0.38607627   153757 360 0.38453683   153591 359 0.38300092   153424 358 0.38146668   153256 357 0.37993412   153088 356 0.37840324   152920 355 0.37687404   152751 354 0.37534653   152582 353 0.37382071   152443 352 0.37229658   152242 351 0.37077416   152075 350 0.36925315 350 0.36925312   151905 349 0.36773407   151728 348 0.36621679   151556 347 0.36470123   151384 346 0.36318739   151211 345 0.36167528   151038 344 0.36016490   150865 343 0.35865625   150690 342 0.35714935   150515 341 0.35564420   150340 340 0.35414227   150164 339 0.35264063   149988 338 0.35114075   149811 337 0.34964264   149634 336 0.34814630   149457 335 0.34665173   149279 334 0.34515894   149100 333 0.34366794   148921 332 0.34217873   148742 331 0.34069131   148562 330 0.33920561   148381 329 0.33772180   148200 328 0.33623980   148024 327 0.33475956   147842 326 0.33328114   147663 325 0.33180451   147480 324 0.33032971   147288 323 0.32885683   147104 322 0.32738579   146919 321 0.32591660   146735 320 2.32444946   146550 319 0.32298396   146362 318 0.32152034   146175 317 0.32005859   145990   145990 316 0.31859869   145803 315 0.31714066   145614 314 0.31568452   145425 313 0.31423027   145236 312 0.31277791   145047 311 0.31132744   144856 310 0.30987884   144665 309 2.30843219   144474 308 0.30698745   144282 307 0.30554463   144090 306 0.30410373   143897 303 0.30266476   143703 304 0.30122773   143508 303 0.29978265   143315 302 0.29835950   143120 301 0.29692830   142926 300 0.29549904 300 0.29549884   142730 299 0.29407154   142533 298 0.29264621   142335 297 0.29122286   142137 296 0.28980149   141939 295 0.28838210   141741 294 0.28696469   141460 293 0.28555009   141260 292 0.28413749   141191 291 0.28272558   140990 290 0.28131493   140730 289 0.27990763   140527 288 0.27850236   140331 287 0.27709905   140124 286 0.27569781   139920 285 0.27429861   139720 284 0.27290141   139517 283 0.27150624   139311 282 0.27011313   139105 281 0.26872208   138898 280 0.26733268   138690 279 0.26594578   138482 278 0.26456096   138273 277 0.26317823   138063 276 0.26179760   137853 275 0.26041907   137643 274 0.25904264   137432 273 0.25766832   137220 272 0.25629612   137008 271 0.25492604   136795 270 0.25355796   136583 269 0.25219213   136370 268 0.25082843   136153 267 0.24946690   135936 135936 266 0.24810754   135720 265 0.24675034   135504 264 0.24539530   135287 263 0.24404243   135069 262 0.24269174   134850 261 0.24134324   134553 260 0.23999689   134333 259 0.23865356   134189 258 0.23731165   133968 257 0.23597197   133746 256 0.23463451   133523 255 0.23329928   133300 254 0.23196628   133076 253 0.23063552   132801 252 0.22930751   132575 251 0.22798176   132399 250 0.22665777 250 0.22665594   132173 249 0.22533421   131946 248 0.22401475   131718 247 0.22269757   131488 246 0.22138269   131259 245 0.22007010   131029 244 0.21875981   130799 243 0.21745182   130567 242 0.21614615   130334 241 0 21484281   130101 240 0.21354168   129867 239 0.21224301   129632 238 0.21094669   129396 237 0.20965273   129160 236 0.20836113   128924 235 0.20707189   128688 234 0.20578501   128449 233 0.20450052   128208 232 0.20321844   123968 231 0.20193876   127729 230 0.20066138   127488 229 0.19938650   127245 228 0.19811405   127002 227 0.19684403   126758 226 0.19557645   126514 225 0.19431131   126269 224 0.19304862   126023 223 0.19178839   125776 222 0.19053063   125528 221 0.18927535   125279 220 0.18802248   125027 219 0.18677221   124777 218 0.18552444   124529 217 0.18427915   124278   124278 216 0.18303637   124025 215 0.18179612   123771 214 0.18055841   123517 213 0.17932324   123262 212 0.17809062   123006 211 0.17686056   122749 210 0.17563291   122490 209 0.17440801   122232 208 0.17318569   122974 207 0.17196595   121713 206 0.17074882   121451 205 0.16953431   121189 204 0.16832242   120926 203 0.16711316   120663 202 0.16590653   120399 201 0.16470254   120133 200 0.16350121 200 0.16350111   119866 199 0.16230245   119598 198 0.16110647   119329 197 0.15991318   119959 196 0.15872259   118789 195 0.15753470   118518 194 0.15634952   118246 193 0.15516706   117972 192 0.15398733   117698 191 0.15281035   117422 190 0.15163596   117146 189 0.15046450   116869 188 0.14929581   116591 187 0.14812990   116312 186 0.14696678   116032 185 0.14580646   115751 184 0.14464895   115468 183 0.14349427   115084 182 0.14234243   114900 181 0.14119343   114615 180 0.14004728   114328 179 0.13890400   114040 178 0.13776354   113752 177 0.13612602   163462 176 0.13549140   113164 175 0.13435926   112873 174 0.13323103   112587 173 0.13210516   112292 172 0.13098224   111996 171 0.12986228   111700 170 0.12874498   111403 169 0.21763088   111105 168 0.12651983   110805 167 0.12541178   110503 110503 166 0.12430675   110200 165 0.12320475   109896 164 0.12210579   109592 163 0.12100987   109287 162 0.11991700   108980 161 0.11882720   108671 160 0.11774053   108361 159 0.11665692   108047 158 0.11557645   107735 157 0.11449910   107425 156 0.11342485   107110 155 0.11235375   106794 154 0.11128581   106478 153 0.11022103   106159 152 0.10915944   105838 151 0.10810106   105517 150 0.10704589 150 0.10704589   105194 149 0.10599395   104870 148 0.10494525   104545 147 0.10389980   104218 146 0.10285762   105889 145 0.10181873   103560 144 0.10078313   103229 143 0.09975084   102895 142 0.09872199   102561 141 0.09769638   102213 140 0.09667379   101876 139 0.09565503   101550 138 0.09463953   101210 137 0.09362743   100869 136 0.09261874   100526 135 0.09161348   100181 134 0.09061167   99834 133 0.08961333   99461 132 0.08861872   99112 131 0.08762760   98786 130 0.08663902   98433 129 0.08565469   98078 128 0.08467391   97722 127 0.08369669   97364 126 0.08272305   97004 125 0.08175301   96643 124 0.08078658   96280 123 0.07982378   95915 122 0.07886463   95548 121 0.07790915   95179 120 0.07695736   94811 119 0.07600925   94438 118 0.07506487   94061 117 0.07412426   93685   93685 116 0.07318741   93307 115 0.07225434   92901 114 0.07132533   92524 113 0.07040009   92161 112 0.06947848   91774 111 0.06856074   91386 110 0.06764629   90944 109 0.06673685   90551 108 0.06583134   90208 107 0.06492926   89811 106 0.06403115   89412 105 0.06313703   89011 104 0.06224692   88608 103 0.06136084   88202 102 0.06047882   87793 101 0.05960089   87382 100 0.05872707 100 0.05872590   86969 99 0.05785621   86554 98 0.05699067   86137 97 0.05612930   85717 96 0.05527213   85293 95 0.05441920   84867 94 0.05357053   84440 93 0.05272613   84010 92 0.05188603   83666 91 0.05104937   83229 90 0.05121866   82700 89 0.04939166   82259 88 0.04856907   81814 87 0.04775093   81366 86 0.04693727   80916 85 0.04612811   89462 84 0.04532349   80005 83 0.04452344   79545 82 0.04372799   79083 81 0.04293716   78617 80 0.04215095   78147 79 0.04136948   77674 78 0.04058274   77197 77 0.03982077   76707 76 0.03905370   76224 75 0.03829146   75748 74 0.03753398   75250 73 0.03678140   74764 72 0.03603376   34265 71 0.03529111   73752 70 0.3455313   73246 69 0.03382067   72746 68 0.03309321   72232 67 0.03237089   71716 71716 66 0.03165373   71193 65 0.03094180   70664 64 0.03023516   70132 63 0.02953384   69995 62 0.02883789   69054 61 0.02814735   68508 60 0.02746204   67961 59 0.02928243   67405 58 0.02610838   66840 57 0.02543998   66273 56 0.02477725   65701 55 0.02412024   65123 54 0.02346901   64539 53 0.02282362   63950 52 0.02218412   63353 51 0.02155059   62750 50 0.02092309 50 0.02092302   62143 49 0.02030159   61528 48 0.01968631   60906 47 0.01907725   60277 46 0.01847448   59640 45 0.01787808   58996 44 0.01728812   58344 43 0.01670468   57683 42 0.01612784   57016 41 0.01555768   56340 40 0.01499411   55655 39 0.01443756   54960 38 0.01388796   54256 37 0.01334540   53540 36 0.01281000   52815 35 0.01228185   52079 34 0.01176106   51331 33 0.01124776   50572 32 0.01074204   49801 31 0.01024403   49016 30 0.00975364   48217 29 0.00927147   47405 28 0.00879742   46578 27 0.00833164   45734 26 0.00787430   44874 25 0.00742556   43997 24 0.00698559   43102 23 0.00655457   42185 22 0.00613272   41244 21 0.00572028   40273 20 0.00531730   39291 19 0.00492439   38297 18 0.00454142   37248 17 0.00416894   36176   36176 16 0.00380718   35071 15 0.00345647   33929 14 0.00311718   32746 13 0.00278972   31517 12 0.00247455   30236 11 0.00217219   28897 10 0.00188278   27442 9 0.00160836   25959 8 0.00134877   24434 7 0.00110443   22749 6 0.00087694   20925 5 0.00066769   18922 4 0.00047847   16675 3 0.00031172   14061 2 0.00017111   10792 1 0.00006319   6319 0 0.00000000 A TABLE SHEWING THE AREA OF THE SEGMENTS OF A CIRCLE WHOSE Whole Area is Unity , to the ten Thousandth part of the Diameter .   0 1 2 3 4 5 6 7 8 9   0 000000 000004 000007 000011 000014 000018 000025 000032 000039 000046   1 000053 000062 000071 000080 000089 000098 000108 000119 000130 000140   2 000151 000163 000175 000187 000200 000212 000225 000238 000251 000265   3 000278 000292 000307 000322 000336 000351 000366 000382 000397 000413   4 000428 000444 000461 000478 000494 000511 000529 000546 000564 000581   5 000599 000617 000636 000654 000673 000691 000710 000729 000748 000768 19 6 000787 000807 000827 000847 000867 000887 000908 000928 000949 000970 20 7 000991 001012 001034 001056 001077 001099 001121 001144 001166 001188 21 8 001211 001234 001257 001280 001304 001327 001350 001374 001398 001421 23 9 001445 001469 001494 001518 001542 001567 001592 001617 001642 001667 25 10 001692 001717 001743 001769 001794 001820 001846 001873 001899 001925 26 11 001952 001979 002005 002032 002059 002086 002113 002141 002168 002195 27 12 002223 002251 002279 002307 002335 002363 002392 002420 002449 002477 28 13 002506 002535 002564 002593 002623 002652 002681 002711 002741 002770 29 14 002700 002830 002860 002890 002921 002951 002982 003013 003043 003074 30 15 003105 003136 003167 003198 003229 003260 003291 003323 003355 003387 31 16 003419 003451 003483 003515 003548 003580 003612 003645 003678 003710 32 17 003743 003776 003809 003842 0038●6 003909 003942 003976 004009 004043 33 18 004077 004111 004145 004179 004213 004247 004281 004316 004351 004385 34 19 004420 004455 004490 004525 004560 004595 004630 004665 004700 004735 35 20 004770 004806 004843 004879 004915 004952 004988 005024 005061 005097 36 21 005133 005170 005206 005243 005280 005317 005354 005391 005428 005465 37 22 005502 005539 005●77 005615 005652 005690 005728 005766 005804 005842 38 23 005880 005918 005957 005995 006023 006072 006111 006150 006188 006227 39 24 006266 0063●5 006344 006383 006423 006462 006501 006541 006581 006620 39 25 006660 006700 006739 006779 006819 006859 006899 006940 006980 007021 40 26 007061 007102 007142 007183 007223 007264 007305 007346 007387 007429 41 27 007470 007511 007553 007594 007635 007677 007719 007761 007802 007844 42 28 007886 007928 007970 008012 008055 008097 008140 008182 008225 008267 42 29 008310 008353 008396 008439 008482 008525 008568 008611 008654 008698 43 30 008471 008785 008828 008872 008916 008959 009203 009047 009091 009135 44 31 009179 009223 009267 009312 009356 009400 009445 009490 009535 009579 45 32 009624 009669 009714 009759 009804 009849 009894 009939 009985 010030 45 33 010075 010121 010167 010212 010258 010303 010349 010395 010441 010487 46 33 010075 010121 010167 010212 010258 010303 010349 010395 010441 010487 46 34 010533 010580 010626 010672 010719 010765 010812 010858 010905 010952 47 35 010999 011045 011093 011139 011186 011233 011281 011328 011375 011422 47 36 011469 011517 011565 011612 011660 011707 011755 011803 011851 011899 47 37 011947 011995 012043 012092 012140 012188 012237 012285 012334 012382 48 38 012431 012479 012528 012577 012626 012675 012724 012773 012823 012872 49 39 012921 012970 0130●0 013069 013118 013168 013218 013267 013317 013367 50 40 013417 013467 013517 013567 013617 013667 013717 013767 013818 013868 50 41 013919 013969 014020 014071 014121 014172 014223 014274 014325 014375 51 42 014426 014478 014529 014580 014632 014683 014734 014786 014837 014889 51 43 014941 014992 015044 015096 015148 015199 015252 015304 015356 015408 52 44 015460 015512 015565 015617 015669 015721 015774 015827 015879 015932 52 45 015985 016038 016091 016144 016197 016249 016303 016356 0164●9 016462 53 46 016515 016569 016622 016676 016729 016783 016837 016891 016944 016998 54 47 017052 017906 017160 017214 017268 017322 017376 017431 017485 017539 54 48 017593 017648 017703 017757 017812 017866 017921 017976 018031 018086 55 49 018141 018196 018251 018306 018361 018416 018471 018527 018582 018638 55 50 018693 018749 018804 018860 018916 018971 019027 019083 019139 019195 56 51 019251 019307 019363 019419 019475 019531 019588 019644 019701 019757 56 52 019813 019870 019927 019984 020040 020097 020154 020211 020268 020325 57 53 020381 020439 020496 020553 020610 020667 020725 020782 020840 020897 57 54 020954 021012 021070 021128 021185 021243 021301 021359 021416 021474 57 55 021532 021590 021649 021707 021765 021823 021882 021940 021999 022057 58 56 022115 022174 022233 022292 022350 022409 022468 022527 022586 022645 59 57 022703 022763 022822 022881 022949 022999 023058 023118 023177 023237 59 58 023296 023356 023415 023475 023534 023594 023654 023714 023774 023834 60 59 023894 023954 024014 024074 024134 024194 024254 024315 024375 024436 60 60 024496 024557 024617 024678 024738 024799 024860 024921 024981 025042 60 61 025103 025164 025225 025286 025347 025408 025470 025531 025692 025654 61 62 025715 025776 025838 025899 025961 026022 026084 026146 026208 026270 62 63 026331 026393 026455 026517 026579 026641 026703 026766 026828 026890 62 64 026952 027015 027077 027140 027202 027264 027327 027390 027453 027515 63 65 027578 027641 027704 027767 027830 027892 027956 028019 028082 028145 63 66 028208 028271 028335 028398 028461 028524 028588 028652 028715 028779 63 67 028842 028906 028970 029034 029097 029161 029225 029289 02935● 029417 64 68 029481 029545 029610 029674 029738 029802 029867 029931 029996 030060 65 69 030184 030189 030253 030318 030383 030447 030512 030577 030642 030707 65 70 030772 030837 030902 030967 031032 031097 031163 031228 031293 031359 65 71 031424 031489 031555 031620 031686 031751 031817 031883 031949 032014 66 72 032080 032146 032212 032278 032344 032409 032476 032542 032608 032674 66 73 032741 032807 032873 032939 033006 033072 033139 033205 033272 033338 66 74 033405 033472 033538 033605 033672 033738 033875 033879 033939 034006 67 75 034073 034140 034208 034275 034342 034409 034477 034544 034612 034679 67 76 034746 034814 034881 034949 035016 035084 035152 035219 035287 035355 68 77 035423 035491 035559 035627 035695 035763 035831 035899 035968 036036 68 78 036104 036172 036249 036309 036378 036446 036515 036583 036651 036720 69 79 036789 036858 036927 036995 037064 037133 037202 037271 037339 037408 69 80 037477 037546 037615 037684 037752 037822 037891 037961 038030 038099 69 81 038169 038239 038308 038378 038447 038517 038587 038657 038727 038797 70 82 038867 038937 039007 039077 039147 039217 039287 039357 039428 039498 70 83 039568 039638 039709 039779 039849 039919 039990 040061 040131 040202 71 84 040272 040343 040414 040485 040555 040636 040707 040778 040849 040920 71 85 040981 041052 041123 041194 041265 041336 041407 041479 041550 041621 71 86 041692 041764 041835 041907 041978 042050 042122 042193 042265 042336 72 87 042408 042480 042552 042624 042696 042768 042840 042912 042984 043056 72 88 043128 043200 043272 043345 043417 043489 043562 043634 043706 043779 73 89 043852 043924 043697 044069 044142 044214 044287 044360 044433 044505 73 90 044578 044651 044724 044797 044870 044943 045016 045089 045163 045236 73 91 045309 045382 045456 045529 045603 045676 045749 045823 045896 045969 74 92 046043 046117 046190 046264 046338 046411 046485 046559 046633 046707 74 93 046781 046855 046929 047003 047077 047151 047●25 047299 047374 047448 74 94 047522 047596 047671 047745 047819 047894 047969 048043 048118 048192 75 95 048267 048342 048417 048491 048566 048641 048716 048791 048866 048941 75 96 049015 049091 049166 049241 049316 049391 049466 049542 049617 049692 75 97 049767 049843 049918 049994 050069 050144 050226 050296 050371 050447 75 98 050522 050598 050674 050750 050826 050901 050977 051053 051129 051205 76 99 051281 051358 051434 051510 051586 051662 051738 051815 051891 051968 76 100 052044 052120 052197 052273 052350 052426 052503 052579 052656 052733 76 0 1 2 3 4 5 6 7 8 9 D 100 052044 052120 052197 052273 052350 052426 052503 052579 052656 052733 076 101 052810 052886 052963 053040 053117 053193 053271 053348 053425 053502 077 102 053579 053656 053733 053810 053887 053964 054041 054119 054196 054273 077 103 054351 054428 054506 054583 054661 054738 054816 054893 054973 055049 078 104 055127 055204 055282 055360 055438 055516 055594 055672 055750 055828 078 105 055906 055984 056062 056140 056218 056296 056374 056453 006531 056610 078 106 056688 056766 056845 056923 057002 057080 057159 057237 057316 057395 079 107 057474 057552 057631 057710 057789 057868 057946 058025 058104 058183 079 108 058262 058341 058420 058499 058578 058658 058737 058816 058895 058975 079 109 059054 059133 059213 059292 059372 059451 059531 059610 059690 059769 079 110 059849 059929 060009 060088 060168 060248 060328 060408 060488 060560 080 111 060648 060728 060808 060888 060968 061048 061128 061208 061289 061369 080 112 061449 061529 061610 061690 061771 061851 061932 062012 062093 062173 080 113 062254 062334 062415 062496 062576 062657 062738 062819 062900 062981 081 114 063062 063143 063224 063305 063386 063467 063548 063629 063710 063791 081 115 063873 063954 064035 064116 064198 064279 064360 064442 064523 064605 081 116 064686 064768 064849 064931 065013 065095 065176 065258 065340 065421 082 117 065503 065585 065667 065749 065831 065913 065995 066077 066159 066241 082 118 066323 066405 066488 066570 066652 066735 066817 066899 066981 067064 082 119 067146 067229 067311 067393 067476 067559 067642 067724 067807 067889 083 120 067972 068055 068138 068221 068304 068387 068469 068552 068635 068718 083 121 068801 068884 068967 069051 069134 069217 069300 069384 069467 069550 083 122 069633 069717 069800 069884 069967 070051 070134 070218 070301 070385 083 123 070468 070552 070635 070719 070803 070887 070970 071054 071138 071222 084 124 071306 071390 071474 071558 071642 071726 071810 071895 071979 072063 084 125 072148 072232 072316 072400 072484 072569 072653 072733 072822 072906 084 126 072991 073075 073160 073244 073329 073414 073498 073583 073668 073752 084 127 073837 073922 074007 074092 074177 074262 074347 074432 074517 074602 085 128 074687 074772 074857 074942 075027 075112 075197 075283 075368 075453 085 129 075539 075624 075709 075795 075880 075966 076051 076137 076222 076908 085 130 076394 076479 076565 076651 076736 076822 076908 076994 077079 077165 086 131 077251 077337 077423 077509 077595 077681 077767 077853 077939 078025 086 132 078112 078198 078184 078370 078457 078543 078629 078716 078802 078889 086 133 078975 079062 079148 079235 079321 079408 079494 079581 079668 079754 086 133 078975 079062 079148 079235 079321 079408 079494 079581 079668 079754 086 134 079841 079928 080015 080101 080188 080275 080362 080449 080536 080623 087 135 080710 080797 080885 08g972 081059 081147 081234 081321 081408 081495 087 136 081582 081669 081756 081841 081931 032018 082106 082193 082281 082368 087 137 082456 082543 082631 082718 082806 082894 082981 083069 083157 083245 087 138 083333 083420 083508 083596 083684 083772 083860 083948 084036 084124 088 139 084212 084300 084388 084477 084565 084653 084741 084830 084918 085006 088 140 085095 085183 085271 085359 085448 085536 085625 085714 085802 085891 088 141 085979 086068 086157 086246 086334 086423 086512 086601 086689 086778 089 142 086867 086956 087045 087134 087223 087312 087401 087490 087579 087668 089 143 087757 087846 087935 088025 088114 088203 088292 088383 088471 088561 089 144 088650 088740 088829 088920 089009 089099 089188 089278 089366 089456 090 145 089545 089635 089725 089814 089904 089994 090084 090174 090264 090354 090 146 090444 090533 090623 090713 090803 090893 090983 091073 091163 091253 90 147 091344 091434 091524 091614 091704 091795 091885 091975 092066 092156 90 148 092247 092337 092427 092518 092608 092699 092790 092880 092971 093061 90 149 093152 093243 093333 093424 0●3515 093606 093696 093787 093878 093969 91 150 094060 094151 094242 094333 094424 094515 094606 094697 094788 094879 91 151 094971 095062 095153 095244 095335 095427 095518 095609 095701 095792 91 152 095884 095975 096067 096158 096249 096341 096433 096524 096616 096707 92 153 096799 096891 096982 097074 097166 097258 097349 097441 097533 097625 92 154 097717 097809 097901 097993 098085 098177 098269 098361 098453 098545 92 155 098637 098729 098822 098914 099006 099098 099191 099283 099375 099468 92 156 099569 099653 099745 099838 099830 100023 100115 100208 100300 100393 93 157 100486 100578 100671 100763 100856 100949 101042 101135 101227 101320 93 158 101413 101506 101599 101692 101785 101878 101971 102064 102157 101250 93 159 102343 102436 102529 102622 102715 102809 102902 102995 103088 103182 93 160 103275 103368 103462 103555 103649 103742 103836 103929 104023 104116 93 161 104210 104304 104397 104491 104584 104678 104772 104866 104959 105053 94 162 105147 105241 105335 105429 105523 105617 105711 105805 105899 105991 94 193 106087 106181 106275 106369 106463 106557 106651 106745 106840 106934 94 164 107028 107122 107217 107311 107406 107500 107594 107689 107783 107878 94 165 107972 108067 108161 108256 108350 108445 108540 108634 108727 108824 95 166 108919 109013 109108 109203 109298 109393 109488 109583 109678 109773 95 166 108919 109013 109108 109203 109298 109392 109487 109683 109677 109773 95 167 109867 109963 110058 110153 110248 110343 110438 110533 110628 110723 95 168 110818 110913 111009 111104 111295 111390 111485 111485 111581 111676 95 169 111772 111867 111963 112058 112154 112249 112344 112440 112535 112631 96 170 112726 112822 112918 113013 113109 113205 113301 113397 113492 113588 96 171 113684 113780 113876 113972 114068 114164 114260 114356 114452 114548 96 172 114644 114740 114836 114932 115028 115125 115221 115318 115414 115511 96 173 115607 115703 115799 115896 115992 116088 116184 116281 116377 116473 97 174 116570 116666 116763 116860 116956 117053 117150 117246 117343 117439 97 175 117536 117633 117730 117827 117924 118021 118118 118215 118312 118409 97 176 118506 118603 118700 118797 118894 118991 119088 119185 119282 119379 97 177 119476 119574 119671 119768 119866 119963 120060 120158 120255 120352 97 178 120449 120547 120644 120742 120839 120936 121034 121132 121229 121327 98 179 121424 121562 121620 121717 121815 121913 122010 122108 122206 122304 98 180 122402 122500 122597 122696 122794 122892 122990 123088 123186 123284 98 181 123382 123480 123578 123676 123774 123872 123970 124068 124167 124265 98 182 124363 124461 124560 124658 124756 124855 124953 125051 125150 125248 98 183 125347 125445 125544 125642 125741 125840 125938 126037 126136 126234 98 184 126333 126432 126530 126629 126728 126827 126925 127024 127123 127221 99 185 127320 127419 127518 127617 127716 127815 127914 128013 128112 128211 99 186 128310 128409 128508 128607 128706 128805 128905 129004 129103 129202 99 187 129302 129401 129500 129600 129699 129799 129897 139997 130096 130196 99 188 130296 130395 130495 130594 130694 130794 130893 130993 131093 131192 100 189 131292 131392 131491 131591 131691 131791 131890 131990 132090 132190 100 190 132290 132390 132490 132590 132690 132790 132890 132990 133090 133190 100 191 133290 133390 133490 133590 133690 133790 133890 133990 134090 134191 100 192 134292 134392 134492 134593 134693 134794 134894 134994 135095 135195 100 193 135296 135396 135497 135597 135697 135798 135899 135999 136100 136201 101 194 136302 136402 136503 136604 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499773 499871   FINIS . COSMOGRAPHIA , THE Second Part. OR , THE DOCTRINE OF THE PRIMUM MOBILE . AN INTRODUCTION TO Astronomy . The First Part. Of the Primum Mobile . CHAP. I. Of the General Subject of Astronomy . AStronomy , is a Science concerning the Measure and Motion of the Spheres and Stars . 2. Astronomy hath two parts , the first is Absolute , and the other Comparative . 3. The Absolute part of Astronomy is that which treateth of the Measure and Motion of the Orbs and Stars absolutely without respect to any distinction of Time. 4. The Comparative part of Astronomy is that , which treateth 〈◊〉 the Motion of the Stars , in reference to some certain distinction of Time. 5. The Absolute part of Astronomy treateth of the Primum Mobile , or Diurnal Motion of all the Celestial Orbs or Spheres . 6. The Primum Mobile , or Diurnal Motion of the Heavens , is that Motion , by which the several Spheres are moved round the World in a Day 〈…〉 from East towards West , and ●o forward● from West towards East , and so continually returning to the same point from whence they began their Motion . 7. This first and common Motion of the Heavens , will be best understood , by help of an Instrument called a Globe , which is an Artificial representation of the Heavens , or the Earth and Waters under that Form and Figure of Roundness which they are supposed to have . 8. This Representation or Description of the Visible World is by Circles , great and small , some of which are expressed upon , and others are framed without the Globe . 9. The Circles without the Globe are chiefly two ; the Meridian and the Horizon , the one of Brass , and the other of Wood ▪ And these two Circles are variable or mutable ; for although there is but one Horizon and one Meridian in respect of the whole World , or in respect of the whole Heaven and Earth , yet in respect of the particular parts of Heaven , or rather in respect of the diverse Provinces , Countries and Cities on the Earth , there are diverse both Horizons and Meridians . 10. The Meridian then is a great Circle without the Globe , dividing the Globe , and consequently the Day and Night into two equal parts , from the North and South ends whereof a strong Wyre of Brass or Iron is drawn or supposed to be drawn through the Center of the Globe representing the Axis of the Earth , by means whereof the whole Globe turneth round within the said Circle , so that any part may be brought directly under this Brass Meridian at pleasure . 11. This Brass Meridian is divided into 4 equal parts or Quadrants , and each of them are subdivided into 90 Degrees , that is 360 for the whole Circle . The reason why this Circle is not divided in 360 Degrees throughout , but still stoping at 90 , beginneth again with 10. 20. 30 &c. is , for that the use of this Meridian , in reference to its Division in Degrees , requireth no more than that Number . 12. The Horizon is a great Circle without the Globe , which divides the upper part of Heaven from the lower , so that the one half is always above that Circle , and the other under it . 13. The Poles of this Circle are two , the one directly over our Heads , and is called the Zenith ; the other is under feet , and is called the Nadir . 14. The Horizon is either Rational or Sensible . 15. The Rational Horizon is that , which divideth the Heavens and the Earth into two equal parts , which though it cannot be perceived and distinguished by the eye , yet may be conceived i● our minds , in which respect all the Stars may be conceived to rise and set as in our view . 16. The Visible Horizon is that Circle which the eye doth make at its farthest extent of sight , when the body in any particular place doth turn it self round . Of these two Circles there needeth no more to be said at present , only we may observe , that it was ingeniously devised by those , who first thought upon it , to set one Meridian and one Horizon without the Globe , to avoid the confusion , if not the impossibility , of drawing a several Meridian and a several Horizon for every place , which must have been done if this or the like device had not been thought upon . 17. Besides these two great Circles without the Globe , there are 4 other great Circles drawn upon the Globe it self besides the Meridian . 1. The AEquator or Equinoctial Circle . 2. The Zodiack . 3. The AEquinoctial Colure . 4. Solstitial Colure . And these four Circles are imm●table , that is , in whatsoever part of the World you are , these Circles have no variation , as the other two have . 18. The AEquator is a great Circle drawn upon the Globe , in the middle between the two Poles ▪ and plainly dividing the Globe into two equal parts . 19. The AEquator is the measure of the Motion of the Primum Mobile , for 15 Degrees of this Circle do always arise in an hours time ; the which doth clearly shew , that the whole Heavens are turned round by equal intervals in the space of one day or 24 hours . 20. In this Circle the Declinations of the Stars are computed from the mid-Heaven towards the North or South . 21. This Circle gives denomination to the AEquinox , for the Sun doth twice in a Year and no more cross this Circle , to wit , when he enters the first points of Aries , and Libra , and then he maketh the Days and the Nights equal : His entrance into Aries is in March , and is called the Vernal Equinox ; and his entrance into Libra , is in September , and is called the Autumnal Equinox . 22. And from one certain point in this Circle , the Longitude of Places upon the Earth are reckoned ; and the Latitude of Places are reckoned from this Circle towards the North , or the South Poles . 23. The Zodiack is a great Circle drawn upon the Globe , cutting the AEquinoctial Points at Oblique Angles : for although it divides the whole World into two equal parts , in reference to its own Poles ; yet in reference to the Poles of the World , it hath an Oblique Motion . 24. The Poles of this Circle are as far distant from the Poles of the World , as the greatest Obliquity thereof is from the Equinoctial , that is 23 Degrees , and 31 Minutes or thereabouts . 25. This Circle doth differ from all other Circles upon the Globe in this : other Circles ( to speak properly ) have Longitude assigned them , but no Latitude ; but this hath both . Whereas other Circles are in reference to their Longitude or Rotundity only divided into 360 Degrees , this Circle in respect of its Latitude is supposed to be divided into 16 Degrees in Latitude . 26. The Zodiack then in respect of Longitude is commonly divided into 360 Degrees as other Circles are : but more peculiarly in respect of its self it is divided into 12 Parts called Signs , and each Sign into 30 Degrees , and 12 times 30 do make 360. 27. The 12 Signs into which the Zodiack is divided , have these Names and Characters . Aries ♈ . Taurus ♉ . Gemini ♊ . Cancer ♋ . Leo ♌ . Virgo ♍ . Libra ♎ . Scorpio ♏ . Sagittarius ♐ . Capricornus ♑ . Aquarius ♒ . and Pisces ♓ . 28. These two Circles of the Equator and Zodiack are crossed by two other great Circles , which are called Colures : They are drawn through the Poles of the World , and cut one another as well as the Equator at Right Angles . One of them passeth through the Intersections of the Equinoctial points , and is called the Equinoctial Colure . The other passeth through the points of the greatest distance of the Zodiack , from the Equator , and is called the Solstitial Colure . 29. The other great Circles described upon the Globe are the Meridians : Where we must not think much to hear of the Meridians again . That of Brass without the Globe is to serve all turns , and the Globe is framed to apply it self thereto . The Meridians upon the Globe , will easily be perceived to be of a new and another use . 30. The Meridians upon the Globe are either the great or the less : Not that the great are any greater than the less , for they have all one and the same center , and equally pass through the Poles of the Earth ; But those which are called less , are of less use than that , which is called the great . 31. The great is otherwise called the fixt and first Meridian , to which the less are second , and respectively moveable . The great Meridian is as it were the Landmark of the whole Sphere , from whence the Longitude of the Earth , or any part thereof is accounted . And it is the only Circle which passing through the Poles is graduated or divided into Degrees , not the whole Circle but the half , because the Longitude is to be reckoned round about the Earth . 32. The lesser Meridians are those black lines ; which you see to pass through the Poles and succeeding the great at 10 and 10 Degrees , as in most Globes ; or at 15 and 15 Degrees difference , as in some . Every place never so little more East or West than another , hath properly a several Meridian , yet because of the huge distance of the Earth from the Heavens , there is no sensible difference between the Meridians of places that are less than one Degree of Longitude asunder , and therefore the Geographers as well as the Astronomers allow a new Meridian to every Degree of the Equator ; which would be 180 in all : but except the Globes were made of an extream and an unusual Diameter , so many would stand too thick for the Description . Therefore most commonly they put down but 18 , that is , at 10 Degrees distance from one another ; the special use of the lesser Meridians being to make a quicker dispatch , in the account of the Longitudes . Others set down but 12 , at 15 Degrees difference ; aiming at this , That the Meridians might be distant from one another a full part of time , or an hour : for seeing that the Sun is carried 15 Degrees of the Equinoctial every hour , the Meridians set at that distance must make an hours difference in the rising or setting of the Sun in those places which differ 15 Degrees in Longitude . And to this purpose also upon the North end of the Globe , without the Brass Meridian , there is a small Circle of Brass set , and divided into two equal parts , and each of them into twelve , that is , twenty four all ; to shew the hour of the Day and Night , in any place where the Day and Night exceed not 24 hours ; for which purpose it hath a little Brass Pin turning about upon the Pole , and pointing to the several hours , which is therefore the Index Horarius , or Hour Index . 33. Having described the great Circles framed without and drawn upon the Globe , we will now describe the lesser Circles also ; And these lesser Circles are called Parallels , that is , such as are in all places equally distant from the Equator ; and these Circles how little soever , are supposed to be divided into 360 Degrees : but these Degrees are not so large as in the great Circles , but do proportionably decrease according to the Radius by which they are drawn . 34. These lesser Circles are either the Tropicks or the Polar Circles . 35. The Tropicks are two small Circles drawn upon the Globe , one beyond the Equator towards the North Pole , and the other towards the South , Shewing the way which the Sun makes in his Diurnal Motion , when he is at his greatest distance from the Equator either North or South . These Circles are called Tropicks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , that is , from the Suns returning : for the Sun coming to these Circles , he is at his greatest distance from the Equator , and in the same Moment of time sloping as it were his course , he returns nearer and nearer to the Equator again . 36. These Tropical Circles do shew the point of Heaven in which the Sun doth make either the longest Day , or the Shortest Day in the Year , according as he is in the Northern or the Southern Tropick : And are drawn at 23 Degrees and a half distant from the Equator . 37. The Polar Circles are two lesser Circles drawn upon the Globe at the Radius of 23 Degrees and a half distant from the Poles of the World , shewing thereby the Poles of the Zodiack , which is so many Degrees distant from the Equator on both sides thereof . 38. These Polar Circles are 66 Degrees and a half distant from the Equator , and 43 Degrees distant from his nearest Tropick . They are called the Arctick and Antarctick Circles . 39. The Arctick Circle is that which is described about the Arctick Pole , and passeth almost through the middle of the Head of the greater Bear. It is called the Arctick Circle 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 from the two conspicuous Stars towards the North ; called the greater and the lesser Bear. 40. The Antarctick Circle is that which is described about the Antarctick or South Pole. It is so called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 that is , from being opposite to the greater and lesser Bear. Having thus described the Globe or Astronomical Instrument by which the Frame of the World is represented to our view , I will proceed to shew the use for which it is intended . CHAP. II. Of the Distinctions and Affections of Spherical Lines or Arches . THE uses of the Globe as to practice , are either such as concern the Heavens or the Earth , in either of which , if we should descend unto particulars , the uses would be more in number , than a short Treatise will contain : Seeing therefore that all Problems which concern the Globe , may be best and most accurately resolved by the Doctrine of Spherical Triangles , we will contract these uses of the Globe ( which otherwise might prove infinite ) to such Problems as come within the compass of the 28 Cases of Right and Oblique angled Spherical Triangles . 2. And that the nature of Spherical Triangles may be the better understood , and by which of the 28 Cases the particular Problems may be best resolved , I will set down some General Definitions and Affections , which do belong to such Lines or Arches of which the Triangle must be framed , with the Parts and Affections of those Triangles , and how the things given and required in them , may be represented and resolved upon and by the Globe , as also how they may be represented and resolved by the Projection of the Sphere , and by the Canon of Triangles . 3. A Spherical Triangle then is a Figure consisting of three Arches of the greatest Circles upon the Superficies of a Sphere or Globe , every one being less than a semicircle . 4. A great Circle is that which divideth the Sphere or Globe into two equal parts , and thus the Horizon , Equator , Zodiack and Meridians before described are all of them great Circles : And of these Circles or any other , there must be three Arches to make a Triangle , and every one of these Arches severally must be less than a semicircle : To make this plain . In Fig. 1. The streight Line HAR doth represent the Horizon , PR the height of the Pole above the Horizon , PMS a Meridian , and these three Arches by their intersecting one another do visibly constitute four Spherical Triangles . 1. PMR . 2. PMH . 3. SHM. 4. SMR . And every Arch is less than a semicircle , as in the Triangle PMR , the Arch PR is less than the Semicircle PRS , the Arch MR is less than the Semicircle AMR , and the Arch PM is less than the Semicircle PMS , the like may be shewed in the other Triangles . 5. Spherical or circular Lines are Parallel or Angular . 6. Parallel Arches or Circles , are such as are drawn upon the same Center within , without , or equal to another Arch or Circle . Thus in Fig. 1. The Arches ♋ M ♋ and ♑ O ♑ are though lesser Circles , parallel to the Equinoctial AE A Q and do in that Scheme represent the Tropicks of Cancer and Capricorn . The manner of describing them or any other Parallel Circle is thus , set off their distance from the great Circle , to which you are to draw a parallel with your Compasses , by help of your Line of Chords , which in this Example is 23 Degrees and a half from AE to ♋ , then draw the Line A ♋ , and upon the point ♋ erect a Perpendicular , where that Perpendicular shall cut the Axis PAS extended , is the Center of that Parallel . 7. A Spherical Angle , is that which is conteined by two Arches of the greatest Circles upon the Superficies of the Globe intersecting one another : Angles made by the Intersection of two little Circles , or of a little Circle with a great , we take no notice of in the Doctrine of Spherical Triangles . 8. A Spherical Angle is either Right or Oblique . 9. A Spherical Right Angle is that which is conteined , by two Arches of the greatest Circles in the Superficies of the Sphere cutting one another at Right Angles , that is , the one being right or perpendicular to the other : thus the Brass Meridian cutteth the Horizon at right Angles ; and thus the Meridians drawn upon the Globe , as well as the Brass Meridian , do all of them cut the Equator at Right Angles . 10. An Oblique Spherical Angle , is that which is conteined by two Arches of the greatest Circles in the Superficies of the Sphere , not being right or perpendicular to one another . 11. An Oblique Spherical Angle is Obtuse , or Acute . 12. An Obtuse Spherical Angle , is that which is greater than a Right Angle . An Acute is that which is less than a Right Angle . 13. If two of the greatest Circles of the Sphere shall pass through one anothers Poles , those two great Circles shall cut one another at Right Angles : Thus the Brazen Meridian doth intersect the Equinoctial and Horizon . 14. If two of the greatest Circles of the Sphere shall intersect one another , and pass through each others Poles , they shall intersect one another at unequal or Oblique Angles , the Angle upon the one side of the intersection being Obtuse , or more than a Right , and the Angle upon the other side of the intersection being Acute or less than a Right . Thus in Fig. 1. The Arch PM doth intersect the Meridian and Horizon , but not in the Poles of either , therefore the Angle HPM upon one side of the intersection of that Arch with the Meridian , is more than a Right Angle ; And the Angle MPR upon the other side of the Intersection is less . And so likewise the Angle PMH upon the one side of the intersection of the Arch PM with the Horizon HR , is greater than a right Angle ; and the Angle RMP upon the other side of the Intersection is less than a Right . 15. A Spherical Angle is measured by the Arch of a great Circle described from the Angular point between the sides of the Angle , those sides being continued unto Quadrants . Thus the Arch of the Equator TQ in Fig. 1. is the measure of the Angle MPR , or TPQ , the sides PT and PQ being Quadrants . And the measure thereof in the Projection may thus be found : lay a Ruler from P to T , and it will cut the Primitive Circle in V ; and the Arch VQ being taken in your Compasses and applyed to your Line of Chords , will give the Quantity of the Angle propounded . 16. The Complement of a Spherical Arch or Angle , is so much as it wanteth of a Quadrant , if the Arch or Angle given be less than a Quadrant ; or so much as it wanteth of a Semicircle , if it be more than a Quadrant . 17. An Arch of a great Circle cutting the Arch of another great Circle , shall intersect one another at Right Angles , or make two Angles ; which being taken together , shall be equal unto two Right . Thus in Fig. 1. The Axis PAS or Equinoctial Colure doth cut the Equator AE A Q at Right Angles ; but the Meridian PMS doth cut the Horizon HMR at Oblique Angles , making the Angle PMR less than a Right , and the Angle SMR more than a Right , and both together equal to a Semicircle . 18. From these general Definitions proper to Spherical Lines or Arches , the general Affections of these Arches may easily be discerned ; I mean the various Positions of the Globe of the Earth , in respect of all and singular the Inhabitants thereof . 19. And the whole Body of the Sphere or Globe , in respect of the Horizon , is looked upon by the Earths Inhabitants , either in a Parallel , a Right , or an Oblique Sphere . 20. A Parallel Sphere is , when one of the Poles of the World is elevated above the Horizon to the Zenith , the other depressed as low as the Nadir , and the Equinoctial Line joyned with the Horizon . They which there inhabite ( if any such be ) see not the Sun or other Star rising or setting , or higher or lower in their diurnal revolution . And seeing that the Sun traverseth the whole Zodiack in a Year , and that half the Zodiack , is above the Horizon and half under it , it cometh to pass , that the Sun setteth not with them , for the space of six Months , nor giveth them any Light for the space of other six Months , and so maketh but one Day and Night of the whole Year . 21. A Right Sphear is , when both the Poles of the World do lie in the Horizon , and the Equinoctial Circle is at his greatest distance from it , passing through the Zenith of the place . And in this position of the Sphere , all the Coelestiall Bodies , Sun , Moon , and other Planets , and fixed Stars , by the daily turning about of the Heaven , do directly ascend above , and also directly descend below the Horizon , because the Motions which they make in their Daily motion do cut the Horizon Perpendicularly , and as it were at Right Angles . In this Position of the Sphere , all the Stars may be observed to rise and set in an equal space of time , and to continue as long above the Horizon , as they do under it , the Day and Night to those Inhabitants , being always of an equal length . 22. An Oblique Sphere is , when the Axis of the World ( being neither Direct nor Parallel to the Horizon ) is inclined obliquely towards both sides of the Horizon , as in Fig. 1. Whence it cometh to pass ; that so much as one of the Poles is elevated above the Horizon , upon the one side ; so much is the other depressed under the Horizon , upon the other side . And in this Position of Sphere , the Days are sometimes longer than the Nights , sometimes shorter , and sometimes of equal length . When the Sun is in either of the Equinoctial Points , the Days and Nights are equal ; but when he declineth from the Equator towards the elevated Pole , the Days are observed to encrease ; and when he declineth from the Equator towards the opposite Pole , or the Pole depressed , the Days do decrease ▪ as is manifest in Fig. 1. For when the Sun riseth at M , the Line M ♋ above the Horizon is the Semidiurnal Arch of the longest day . When he riseth at C , the Arch C ♑ above the Horizon , is the Semidiurnal Arch of the shortest Day : And when he riseth at A , the Days and Nights are of equal Length , the Semidiurnal Arch AAE , being equal to the Seminocturnal Arch AQ . CHAP. III. Of the kind and parts of Spherical Triangles ; and how to project the same upon the Plane of the Meridian . HAving shewed what a Spherical Triangle is , and of what Circles it is composed , with the general Affections of such Lines : I will now shew how many several sorts of Triangles there are , of what Circular parts they do consist , and such Affections proper to them as will render the so●ition of them more clear and certain . 2. Spherical Triangles are either Right or Oblique . 3. A Right Angled Spherical Triangle , is that which hath one or more Right Angles . 4. A Spherical Triangle which hath three Right Angles , hath always his three sides Quadrants . As in Fig. 1. The Spherical Triangle AZR , the Angles ZRA , RAZ and AZR are right Angles , and the three sides AZ , ZR and AR are Quadrants also . 5. A Triangle that hath two right Angles , hath the sides opposite to those Angles Quadrants , and the third side is the measure of the third Angle . As in Fig. 1. The sides of the Spherical Triangle TPQ , namely TP and PQ are Quadrants , and the Angles opposite to these sides , to wit , PTQ and TQP are Quadrants also , and the third Angle TQ is the measure of the third Angle TPQ . But the Right Angled Triangle which hath one Right and two Acute Angles , is that which cometh most commonly to be resolved . 6. The Legs of a right Angled Spherical Triangle are of the same Affection with their opposite Angles ; as in the Triangle ZAR Fig. 1. The side ZA is a Quadrant , and the Angle at A is right , because Z is the Pole of the Arch AR and ZA is perpendicular thereunto . And in the Triangle RAAE the side RZAE being more then a Quadrant the Angle RAAE is more then a Quadrant also , being more then the Right Angle RAZ . And in the right Angled Spherical Triangle APR the side PR being less then a Quadrant , the Angle PAR is less then a Quadrant also , being less then the right Angle RAZ . 7. An Oblique angled Spherical Triangle is either acute or obtuse . 8. An Acute angled Spherical Triangle hath all his Angles Acute , and each Side less then a Quadrant ; As in the Triangles , ZFP . Fig. 2. The Angles at Z and P are acute , as appeareth by inspection ; and the Angle at F is acute also because the Measure thereof CD = EM is less then a Quadrant . 9. An Oblique Angled Spherical Triangle hath all his Angles either acute or obtuse : viz. Acute and mixt . 10. The Sides of a Spherical Triangle may be turned into Angles , and the Angles into Sides ; The Complement of the greatest Side or greatest Angle to a Semicircle being taken in each conversion . For Example . If it were required to turn the Angles of the Oblique Angled Spherical Triangle ZFP into sides in Fig. 3. EAE is the measure of the Angle at P , and AD in the Triangle ADC equal thereunto , AC is the Complement of FZP to a Semicircle , and KM the the Measure of the Angle at F is equal to DC , and so the Sides of the Spherical Triangle ADC are equal to the Angles of the Spherical Triangle FZP , making the side AC equal to the Complement of the Angle Z to a Semicircle . 11. In Right Angled Spherical Triangles the Sides intending the Right Angle we call the Legs ; The Side subtending it the Hypotenuse . 12. In every Spherical Triangle besides the Area or space contained , there are six parts . viz. Three Sides and three Angles and of these six there must be always three given to find the rest , but in right Angled Spherical Triangles there are but five of the six parts parts which come into question , because one of the Angles being right is allways known , and so any two of the other five being given , the three remaining parts whether Sides or Angles , may be found . But before I come to the solution of these Triangles whether right or oblique , I will first shew how they may be represented upon the Globe , and projected upon the plane of of the Meridian . 13. A right Angled Spherical Triangle may be represented upon the Globe in this manner : Elevate one of the Poles of the Globe above the Horizon , to the quantity of one of the given Legs , so shall the distance between the AEquinox and the Zenith be equal thereunto , and at the Zenith fasten the Quadrant of altitude , so shall there be delineated upon the Globe the right Angled Spherical Triangle AEZB as may be seen in Fig. 1. In which the outward Circle HZR doth represent the Brass Meridian , AEAQ the Equator , and ZC the Quadrant of altitude . 14. An Oblique Angled Spherical Triangle may be represented upon the Globe in this manner . Number one of the given sides from one of the Poles to the Zenith ; and there fasten the Quadrant of Altitude , upon which number another side , the third upon the great Meridian , from the Pole towards the Equinoctial , then turn the Globe till the Side numbred upon the Quadrant of Altitude , and the Side numbred upon the great Meridian shall intersect one another ; so shall there be delineated upon the Globe the Oblique Angled Spherical Triangle ZFP in Fig. 3. In which ZP is numbred upon the Brass Meridian from S the Pole of the World to Z the Zenith , ZF the Azimuth Circle represents the Quadrant of Altitude , and PF the great Meridian upon the Globe intersecting the Quadrant of Altitude at F. 15. A Right or Oblique Angled Spherical Triangle being thus delineated upon the Globe , there needs no further instructions , as to the measure of the sides , all that is wanting , is the laying down the Angles comprehended by those sides , and the finding out the measure of these Angles being so laid down . And that this may be the better understood , I will first shew ; how the several Circles upon the Globe before described , may be projected upon the Plane of the Meridian , and the several useful Triangles that are described by such Projection with such Astronomical Propositions as are conteined and resolvable by these Triangles . 16. The Circles in the first Figure are the Meridian , AEquator , Horizon , AEquinoctial Colure , and the Tropicks . The Brass Meridian without the Globe , is a perfect Circle described by taking 60 Degrees from your Line of Chords , as the Circle HZRN in Fig. 1. Within which all the other are projected . The Horizon , AEquator , AEquinoctial Colure , East and West Azimuths are all streight Lines . Thus the Diameter HAR represents the Horizon , AEAQ the Equator , PAS the Equinoctial Colure and ZAN the East and West Azimuths , in the drawing of these there is no difficulty , PMS is a Meridian , and ZCN an Azimuth Circle , for the drawing of which there are three points given and the Centers of the Meridians do always fall in the Equinoctial extended if need be , the Centers of the Azimuth Circles do fall in the Horizon extended if need be , and for the drawing of these Circles there needs no further direction , supposing the middle point given to be in the AEquator or Horizon , but yet the Centers of these Circles may be readily found , by the Lines of Tangents or Secants , for the Tangent of the Complement of AT set from A to D , or the Secant of the Complement set from A to D will give the Center of the Meridian PTS. The other two Circles in the 1. Fig. are the Tropicks whose Centers are thus found ; each Tropick is Deg. 23 ½ from the Equinoctial , which distance being set upon the Meridian from AE to ♋ and AE to ♑ , if you draw a Line from A to ♋ and another perpendicular thereunto from ♋ it will cut the Axis SAP extended in the Center of that Tropick , by which extent of the compasses the other Tropick may be drawn also . Or thus the Co-tangent of AE ♋ set from ♋ to the Axis extended will give the Center as before , and thus may all other Parallels be described . 17. In the second and third figures , the two extream points given in the Meridians are not eqnidistant from the third , for the drawing of which Circles , if the common way of bringing three points into a Circle be not liked ; you may do thus , from the given point at F and the Center A draw the Diameter TAS , and cross the same at Right Angles with the Diameter BAG , a Ruler laid from G to F will cut the primitive Circle in L , make EL = BL a Ruler laid from G to E will cut the Diameter SAT in V the Center of the Circle BDG . Which Circle doth cut the Diameter HAR in the Pole of ZF , and the Diameter AEAQ in D in the Pole of PFX , and a Ruler laid from Z to C will cut the Primitive Circle in Y , and making Y O equal to Y a Ruler laid from Z to O will cut the Diameter HAR , extended in the Center of the Circle ZF . 18. Having drawn the Circle ZFI , in Fig. 13. The Circle PEX , or any other passing through the point F , may easily be described . Draw AEQ at right Angles to PX , a Ruler laid from G unto ( e ) will cut the Primitive Circle in ( m ) make mn = Bn , a Ruler laid from G to n shall cut the Diameter TFS in p make Fq = Fp so shall FQ be the Radius , and the Center of the Circle PFX as was desired . 19. The preceeding directions are sufficient for the projecting of several Circles of the Globe before described upon the Plane of the Meridian , and the parts of those Circles so described may thus be measured . In Fig. 1. HZ = CZ = AZ 90 Degrees . Whence it followeth , that the Quadrant CZ is divided into Degrees from its Pole M , by the Degrees of the Quadrant HZ , that is a Ruler laid from M to any part of the Quadrant HZ will cut as many Degrees in CZ as it doth in the Quadrant HZ , and thus the Arch CF = HK the Arch CB = HL , and the Arch BF = LK . 20. That which is next to be considered is the projecting or laying down the Angles of a Triangle , and the measuring of them being projected , and the Angles of a Triangle are either such as are conteined between two right Lines as the Angle A in the Triangle PAR ; or such as are conteined by a streight and a Circular Line , as the Angle PMR . Fig. 1. Or such as are conteined by two circular Lines , as the Angles FZP or ZFP in Fig. 3. The projecting or measuring the first sort of these Angles , needs no direction . 21. To project an Angle conteined by a streight and a circular line as the Angle AEBZ in Fig. 1. Do thus , lay a Ruler from N to C , and it will cut the Primitive Circle in K make ZX = HK , a Ruler laid from N to X will cut the Diameter HAR in the point M the Pole of the Circle ZCN , a Ruler laid from M to B the Angular point propounded , will cut the primitive Circle in I , make NY = HL a Ruler laid from N to Y will cut the Circle ZCN in W , a Ruler laid from B to W will cut the Primitive Circle in A , make AQ equal to the Angle propounded , and draw the Diameter BAQ , then is the Angle AEBZ or NBQ = NQ as was required . 22. If the Angle had been projected and the measure required , a Ruler laid from M to B would give L and making NY = HL a Ruler laid from M to Y would give W , from B to W would give A , and AQ would be the measure of the Angle propounded . 23. To project an Angle conteined by two circular lines , one of them being an Arch of the Primitive Circle , as the Angle AEZB , Fig. 1. Do thus , set off the quantity of the Angle given from H to G , a Ruler laid from Z to G will cut the Diameter HAR in the point C , so may you draw the Circle ZCN and the Angle HZC will be equal to the Arch HG = HC as was required . 24. If the Angle had been projected and the measure required , a Ruler laid from Z to C would cut the Primitive Circle in G and HG would be the measure of the Angle propounded . 25. To project an Angle conteined by two oblique Arches of a Circle , as the Angle ZFP in Fig. 3. You must first find the Pole of one of the two Circles conteining the Angle propounded , suppose ZBI , a Ruler laid from C the Pole thereof to F , the Angular point propounded , will cut the Primitive Circle in a make ab equal to the Angle propounded , a Ruler laid from F to b will cut the Diameter AEAQ in D the Pole of the Circle PEX , a Ruler laid from G to e will cut the Primitive Circle in m , make mn = Bm ler laid from G to n will cut the Diameter TAS in p , make Aq = Ap so shall Fp be the Radius and the Center of the Circle PFX and the Angle ZFP = ab , as was propounded . 26. If the Angle had been projected and the measure required ; through the point F draw the Diameter TFS and the Diameter BAG at right Angles thereunto , a Ruler laid from G to F will cut the Primitive Circle in K , and making KE = BK a Line drawn from G to E will cut the Diameter TAS in the Center of the Circle GDB cutting the Diameter HAR in C the Pole of the Circle ZBI , and the Diameter AEAQ in D , the Pole of the Circle PEX and a Ruler laid from F to C and D will cut the Primitive Circle in a and b the measure of the Angle required . Or a Ruler laid from F to K and M will cut the Primitive Circle in Deg. the measure of the Angle propounded as before . Or thus a Ruler laid from C and D to F will cut the Primitive Circle in ae and h set 90 Degrees from e and h to f and l a Ruler laid from C to f will cut ZBI in M and a Ruler laid from D to l will cut PEX in K. This done a Ruler laid from F to K and M will cut the Primitive Circle in g and d the measure of the Angle as before . And in Fig. 2. The quantity of the Angle ZEP may thus be found . A Ruler laid from C the Pole of the Circle ZFI to F the angular point will cut the Primitive Circle in a , set off a Quadrant from a to b , a Ruler laid from C to b will cut the Circle ZFI in the point M. In like manner a Ruler laid from D the Pole of the Circle PEX , will cut the Primitive Circle in D , set off a Quadrant from A to h , a Ruler laid from D to P will cut the Circle PFX in K : Lastly a Ruler laid from F to K , and M will cut the Primitive Circle in NS the measure of the Angle KFM or ZFP , as was propounded . 27. Having shewed how a right or oblique Angled Spherical Triangle may be projected upon the Plane of the Meridian , as well as delineated upon the Globe , we will now consider the several Triangles usually represented upon the Globe , with the several Astronomical and Geographical Problems conteined in them , and resolved by them . 28. The Spherical Triangles usually represented upon the Globe are eight , whereof there are five Right angled Triangles , have their Denomination from their Hypotenusas . The first is called the Ecliptical Triangle , whose Hypotenusa is an Arch of the Ecliptick , the Legs thereof are Arches of the AEquator and Meridian , this is represented upon the Globe , by the Triangle ADF , in Fig. 1. In which the five Circular parts , besides the Right Angle are ; 1. The Hypotenuse or Arch of the Ecliptick AF. 2. The Leg or Arch of the AEquator , AD. 3. The Leg or Arch of the Meridian DF. 4. The Oblique Angle of the Equator with the Ecliptick and the Suns greatest Declination DAF . 5. The Oblique Angle of the Ecliptick and Meridian , or the Angle of the Suns position AFD . The two next I call Meridional , because the Hypotenusas in them both , are Arches of a Meridian . One of these is noted with the Letters MPR in Fig. 1. In which the five Circular parts are ; 1. The Hypotenusa or Arch of a Meridian PM . 2. The Leg or Arch of the Horizon MR , the Suns Azimuth North. 3. The Leg or Arch of the Brass Meridian , representing the height of the Pole PR . 4. The Oblique Angle of the Meridian upon the Globe ; with the Brass Meridian , or Angle of the Hour from Midnight . P. 5. The Oblique Angle of the Suns Meridian with the Horizon , or the Complement of the Suns Angle of Position PMR . The other Right Angled Meridional Triangle is noted with the Letters AEG in Fig. 1. In which the 5 Circular parts are . 1. The Hypotenusa or present Declination of the Sun , AE . 2. The Leg or Suns Amplitude at the hour of six , AG. 3. The other Leg or Suns height at the same time EG . 4. The Angle of the Meridian with the Horizon , or Angle of the Poles elevation , EAG . 5. The Angle of the Meridian with the Azimuth , or the Angle of the Suns position , AEG . The fourth Right Angled Spherical Triangle , I call an Azimuth Triangle , because the Hypotenusa doth cut the Horizon in the East and West Azimuths , as is represented by the Triangle ADV. in Fig. 1. In which the 5 Circular parts are , 1. The Hypotenusa , or Arch of the Sun or Stars Altitude AV. 2. The Leg or Declination of the Sun or Star , DV . 3. The other Leg , or Right Ascension of the Sun or Star , AD. 4. The Oblique Angle or Angle of the Poles elevation , DAV . 5. The other Oblique Angle or Angle of the Sun or Stars Position , DVA . The fifth and last Right Angled Spherical Triangle , that I shall mention , I call an Horizontal Triangle , because the Hypotenusa thereof is an Arch of the Horizon , and is represented by the Triangle AMT in Fig. 1. In which the 5 Circular parts are ; 1. The Hypotenusa and Arch of the Horizon , or Amplitude of the Sun at his rising or setting , AM. 2. The Leg conteining the Sun or Stars Declination TM . 3. The other Leg or Ascensional difference AT , that is , the difference between DT the Right Ascension and DA the Oblique Angle . 4. The Oblique Angle of the Horizon and Equator , or height of the Equator TAM . 5. The other Oblique Angle , or Angle of the Horizon and Meridian AMT . The Oblique Angled Spherical Triangles usually represented upon the Globe are three . The first I call the Complemental Triangle , because the sides thereof are all Complements , and this is represented by the Triangle FZP in Fig. 1. Whose Circular parts are ; 1. The Complement of the Poles elevation ZP . 2. The Complement of the Suns Declination , FP . 3. The Complement of the Suns Altitude or Almicantar FZ . 4. The Suns Azimuth or Distance from the North FZP . 5. The hour of the day or distance of the Sun from Noon ZPF . 6. The Angle of the Suns Position ZFP . The second Oblique Angled Spherical Triangle , I call a Geographical or Nautical Triangle , because it serveth to resolve those Problems , which concern Geographie and Navigation , and this is also represented by the Triangle FZP in Fig. 1. Whose parts are . 1. The Complement of Latitude as before ZP . 2. The distance between the two places at Z and F or side FZ . 3. The Complement of the Latitude of the place at F or side FP . 4. The difference of Longitude between the two places at Z and F or the Angle FBZ. 5. The point of the compass leading from Z to F or Angle FZP . 6. The point of the Compass leading from F to Z , or Angle ZFP . The third Oblique Angled Spherical Triangle is called a Polar Triangle , because one side thereof is the distance between the Poles of the World , and the Poles of the Zodiack . This Triangle is represented upon the Coelestial Globe , by the Triangle FSP in Fig. 4. In which the Circular parts are ; 1. The distance between the Pole of the World , and the Pole of the Ecliptick , or the Arch SP. 2. The Complement of the Stars Declination , FP . 3. The Complement of the Stars North Latitude , from the Ecliptick or the Arch FS . 4. The Angle of the Stars Right Ascension FPS . 5. The Complement of the Stars Longitude FSP . 6. The Angle of the Stars Position SFP . 29. And thus at length I have performed , what was proposed in the 15 of this Chapter , that is , I have shewed how the several Circles of the Globe , may be projected upon the Plane of the Meridian , the several useful Triangles that are described by such projection , with such Astronomical Propositions as are contained and resolveable by those Triangles ; And although the most accurate way of resolution is by the Doctrine of Trigonometry and the Canon of Lines and Tangents , yet it is not impertinent to do the same upon the Globe it self , which as to the sides is easie , but to measure or lay down the Angles is sometimes a little labourious . In the Right Angled Spherical Triangle AEBZ in Fig. 1. The measure of the Angle AEZB is reckoned in the Horizon from H to C but to lay down or measure the Angle AEBZ the readiest way is to describe the Triangle again , making AEZ = AEB and AEB = AEZ , so will the Angle AEBZ stand where the Angle AEZB is , and may be measured in the Horizon as the other was . And so in the Oblique Angled Spherical Triangle FZP in Fig. 1. The Angles at Z and P are easily measured or laid down upon the Globe , but to perform the same with the Angle ZFP , you may represent it at the Pole or Zenith and find the measure in the Equator or Horizon . 30. And now having , as I hope , sufficiently prepared the young Student for the first part of Astronomy , the Doctrine of the Primum Mobile , by shewing how the Heavens and the Earth are represented upon the Globe , or may be projected in Plane , I will now proceed to such Astronomical Propositions as are generally useful , and may be sufficient for an Introduction to this noble Science : to go through the several Triangles before propounded , will be very tedious , I will therefore shew the several Problems in one Right Angled and one Oblique Angled Spherical Triangle and the Canons by which they are to be resolved , and leave the rest for the Practice of my Reader . To this purpose I will next acquaint you with my Lord Nepiers Catholick Proposition for the solution of all Right and Oblique Angled Spherical Triangles . CHAP. IV. Of the solution of Spherical Triangles . IN Spherical Triangles there are 28 Varieties or Cases , 16 in Rectangular , and 12 in Oblique , whereof all the Rectangular and ten of the Oblique may be resolved by the two Axioms following . 1. Axiom . In all Right Angled Spherical Triangles having the same Acute Angle at the Base , the Sines of the Hypotenusas are proportional to the Sines of their Perpendicular . 2. Axiom . In all right Angled Spherical Triangles , the Sines of the Bases and the Tangents of the Perpendicular are proportional . That all the Cases of a Right Angled Spherical Triangle may be resolved by these two Axioms , the several parts of the Spherical Triangle proposed , that so the Angles may be turned into sides , the Hypotenusa , into Bases and Perpendiculars and the contrary . By which means the proportions as to the parts of the Triangle given , are sometimes changed into Co-sines instead of Sines , and into Co-tangents instead of Tangents . Which the Lord Nepier observing ; those parts of the Right Angled Spherical Triangle , which in conversion do change their proportion , he noteth by their Complements . viz. The Hypotenuse and the two Acute Angles : But the sides or Legs are not so noted , as in the Right Angled Spherical Triangle MPR in Fig. 1. And these five he calleth the Circular parts of the Triangle , amongst which the Right Angle is not reckoned . 2. Now if you reckon five Circulat parts in a Triangle , one of them must needs be in the middle , and of the other four , two are adjacent to that middle part , the other two are disjunct , and which soever of the five you call the middle part , for every one of them may by supposition be made so ; those two Circular parts which are on each side of the middle are called extreams adjunct , and the other two remaining parts , are called extream disjunct , as in the Triangle MPR if you make the Leg PR the middle part , then the other Leg MR and the Angle Comp. P. Are the extreams conjunct , the Hyp. Comp. MP and Comp. M , are the extreams disjunct , and so of the rest , as in the following Table . Mid. Part Exctr. conj . Extr. disj●   Leg. MR Comp. M Leg PR       Comp. P Comp. MP   Leg. PR Comp. MP Leg MR       Comp. M Comp. P   Leg. MR Comp. P Comp. M       Comp. MP Leg. PR   Comp. M Leg. PR Comp. MP       Comp. P. Leg. MR   Comp. MP Leg. MR Comp. P       Leg. PR Comp. M 3. These things premised , the Ld. Nepier as a consectory from the two preceeding Axioms hath composed this Catholick and Universal Proposition . The Rectangle made of the Sine of the middle part and Radius is equal to the Rectangle made of the Tangents of the Extremes conjunct or the cosines of the Extremes disjunct . Therefore if the middle part be sought , the Radius must be in the first place ; if either of the extremes , the other extreme must be in the first place . Only note that if the middle part , or either of the extremes propounded be noted with its Comp. in the circular parts of the Triangle , instead of the Sine or Tangent you must use the Cosine or Cotangent of such circular part or parts . That these directions may be the better conceived , we have in the Table following set down the circular parts of a Triangle under their respective Titles , whether they be taken for the middle part , or for the extremes , conjunct or disjunct , and unto these parts , we have prefixed the Sine or Cosine , the Tangent or Co-tangent , as it ought to be by the former Rule . Mid. Par. Extr. Conj . Ext. Disj .   Tang. MR Sine M Sine PR       Tang. P. Sine MP   Tang. PR Sine MP Sine MR       Cotang . M. Sine P   Tang. MR Sine P Cosine M       Cot. MP Cos. PR   Cotang . M. Cos. PR Cos. MP       Cotang . P Cos. MR   Cot. MP Cos. MR Cosine P       Tang. PR Sine M Now then according to this Table and the former Rules . 1. Sine PR x Rad. = t MR x ct P. 2. Sine PR x Rad. = s M x s MP . 3. Sine MR x Rad. = t PR x ct M. 4. Sine MR x Rad. = s MP x s P. 5. Cos. M x Rad. = t MR x ct MP . 6. Cos. M x Rad. = s P x cs PR . 7 Cos. MP x Rad. = ct M x ct P. 8. Cos. MP x Rad. = cos . PR x cs MR. 9. Cos. P x Rad. = ct MP x t PR . 10. Cos. P x Rad. = cos . MR x s M. By these 10 Rectangles may the 16 Cases of a Right angled Spherical Triangle be resolved , and some of them twice over ; for although there are but 16 varieties in all Right angled Spherical Triangles , yet 30 Astronomical Problems may be resolved by one Triangle , as by the following Examples shall more clearly appear . Of Right angled Spherical Triangles . CASE 1. The Legs given , to find the Angles . IN the Right angled Spherical Triangle MPR . The given Legs are MR and RP . The Angles at M and P are required . By the first of the 10 equal Rectangles s PR x Rad. = t MR x ct P. in which P is fought , therefore putting MR in the first place . The proportion is . t MR. x Rad. ∷ s PR . ct P. And by the third equal Rectangle . t PR . Rad. ∷ s MR. ct M. CASE 2. The Legs given , to find the Hypotenuse . In the Right angled Spherical Triangle MPR . The given Legs are MR and PR . The Hypotenuse MP is required . By the eighth of the 10 Rectangles cos . MP x Rad. = cos . PR x cos . MR in which MP the middle part is sought , therefore Radius must be put in the first place , and then the proportion is . Rad : cos . PR ∷ cos . M. R. cos . MP . CASE 3. A Leg with an Angle opposite thereunto being given , to find the other Leg. In the Right angled Spherical Triangle MPR , let there be given . The Leg MR. The Angle P. The Leg PR inquired . By the first of the 10 Rectangles . Rad. tMR ∷ cot . P. Sine PR . or The Leg PR and the Angle M given , to ●ind MR. By the 3 of the 10 Rectangles . Rad. tPR ∷ ct M. Sine MR. CASE 4. A Leg with an Angle conterminate therewith being given , to find the other Leg. In the Right angled Spherical Triangle , MPR , The given Leg is MR , with the Angle M. The Leg PR is required . By the 3 Rectangle . cot . M. Rad ∷ Sine MR. tPR . The given Leg RP , and Angle P. The Leg MR is required . By the 1. Rectangle . ctP. Rad ∷ sine RP . tang . MR. CASE 5. A Leg and an Angle conterminate therewith being given , to find the Hypotenuse . In the Right angled Spherical Triangle MPR , let there be given , The Leg MR and the Angle M PR and the Angle P to find MP . By the 5. Rectangle , t MR. Rad ∷ cos . M. ct MP . By the 9. Rectangle . t PR . Rad. ∷ cos . P. ct MP . CASE 6. The Hypotenuse and a Leg given , to find the contained Angle . In the Right angled Spherical Triangle MPR , let there be given , The Hypotenuse MP , and Leg MR. PR . To find M. By the 5. Rectangle , Rad. ct MP ∷ t MR. cos . M. By the 9. Rectangle , Rad. ct MR ∷ t PR . cos . P. CASE 7. The Hypotenuse and one Angle given , to find the other Angle . In the Right angled Spherical Triangle MPR , let there be given , The Hypotenuse MP & Angle M P. To find the Angle P. M. By the 7. Rectangle , cot . M. Rad ∷ cos . MP . cot . P. By the 7. Rectangle cot . P. Rad ∷ cos . MP . cot . M. CASE 8. The Oblique A●gles given , to find the Hypotenuse . In the Right angled Spherical Triangle MPR , let there be given The Angles at P and M , To find the Hypotenuse PM . By the 7. Rectangle . Rad. ct P ∷ cot . M. cos . MP . CASE 9. The Hypotenuse and an Angle given , to find the Leg conterminate with the given Angle . In the Right angled Spherical Triangle MPR , let there be given , The Hypotenuse PM Angle P. M. To find PR . MR. By the 9. Rectangle , ct PM . Rad ∷ cos . P. t PR . By the 5. Rectangle , ct PM . Rad ∷ cos . M. tMR . CASE 10. The Hypotenuse and an Angle given , to find the Leg opposite to the given Angle . In the Right angled Spherical Triangle MPR , let there be given , The Hypotenuse PM and the Angle M. P. To find PR . MR. By the 2. Rectangle , Rad. s MP ∷ s M. Sine PR . By the 4. Rectangle , Rad. s MP ∷ s P. Sine MR ▪ CASE 11. A Leg and an Angle opposite thereunto being given , to find the Hypotenuse . In the Right angled Spherical Triangle MPR , let there be given , The Leg PR . MR. and the Angle M P to find the Hypotenuse PM . By the 2. Rectangle , s M. Rad ∷ s PR . s MP . By the 4. Rectangle , s P. Rad ∷ s MR. s PM . CASE 12. The Hypotenuse and a Leg given , to find the Angle opposite to the given Leg. In the Right angled Spherical Triangle PMR , the Hypotenuse MP and the Leg MR are given , the Angle at P is required . By the fourth Rectangle Sine MP to , Rad ∷ s MR. s P. The Hypotenuse MP and Leg PR given , the Angle M is required . By the second Rectangle . sMP. Rad ∷ s PR . s M. CASE 13. The Angle and Leg conterminate with it being given , to find the other Angle . In the Right angled Spherical Triangle PMR , let there be given , The Angle M P and the Leg MR PR to find the Angle P. M. By the tenth Rectangle , Rad. cs MR ∷ s M. cs P. By the sixth Rectangle , Rad. s P ∷ cs PR . cs M. CASE 14. An Angle and a Leg opposite thereunto being given , to find the other Angle . In the Right angled Spherical Triangle MPR , let there be given , The Angle P M and the Leg MR PR to find the Angle M. P. By the 10. Rectangle , cs MR. Rad ∷ cs P. csM. By the 6. Rectangle , cs PR . Rad ∷ cs M. sP. CASE 15. The Oblique Angles given , to find a Leg. In the Right angled Spherical Triangle MPR , let there be given , the Angles at M and P , to find the Legs MR and PR . By the 10. Rectangle , sM. Rad ∷ cs P. cs MR. By the 6. Rectangle , s P. Rad ∷ cs M. cs PR . CASE 16. The Hypotenuse and one Leg given , to find the other Leg. In the Right angled Spherical Triangle MPR , let there be given , The Hypotenuse MP and the Leg PR MR to find the Leg MR. PR . By the 8. Rectangle , csPR. Rad ∷ csMP. csMR. csMR. Rad ∷ csMP. csPR. Thus I have given you the Proportions by which the 16 Cases of a Right angled Spherical Triangle may be resolved , In which there are contained 30 Astronomical Problems . Two in every Case except the Second and the Eighth . In both which Cases there are but two Problems . And thus I have done with Right angled Spherical Triangles . 5. If the Angles at the Base be both acute or both obtuse , the Perpendicular shall fall within the Triangle ; but if one of the Angles of the Base be acute and the other obtuse , the Perpendicular shall fall without the Triangle . 6. However the Perpendicular falleth , it must be always opposite to a known Angle , for your better direction , take this General Rule . From the end of a Side given , being adjacent to an Angle given , let fall the Perpendicular . As in the Triangle FPS in Fig. 4. If there were given the Side F S and the Angle at S , the Perpendicular by this Rule must fall from P upon the Side S P extended , if need require . But if there were given the Side P S and the Angle at S , the Perpendicular must fall from F upon the Side F S. 7. To divide an Oblique angled Spherical Triangle into two Right , by letting fall a Perpendicular upon the Globe it self , is not necessary , because all the Cases may be resolved without it , but in projection it is convenient to inform the fancy : and seeing the reason by which it is done in projection doth depend upon the nature of the Globe , I will here shew it both ways , first upon the Globe , and then by projection . An Oblique angled Spherical Triangle may be divided into two Right , by letting fall a Perpendicular upon the Globe it self , in this manner . In the Oblique angled Spherical Triangle FPS in Fig. 4. let it be required to let fall a Perpendicular from P upon the Side FS . Suppose the Point P to stand in the Zenith , where the Arch FS shall cut the Zodiack , which in this Figure is at K , make a mark , and from this Point of Intersection of the Circle upon which the Perpendicular is to fall with the Zodiack , reckon 90 Degrees , which suppose to be at P ; a thin Plate of Brass with a Nut at one end thereof , whereby to fasten it to the Meridian , as you do the Quadrant of Altitude , being graduated as that is , but of a larger extent ( for that a Quadrant in this case will not suffice ) being fastned at P and turned about till it cut the Point L in the Zodiack , will describe upon the Globe the Arch of a great Circle PEL , intersecting the Side F S at Right Angles in the Point E , because the Point L in the Zodiack is the Pole of the Circle SFK , now all great Circles which passing through the Point L , shall intersect the Circle SKG , shall intersect it at Right Angles ; by the 13. of the 2. Chapter . 9. And hence to divide an Oblique angled Spherical Triangle into two Right by projection is easie , as in the Triangle FPS , the Pole of the Circle SFK is L , therefore the Circle BLP shall cut the Arch FS at Right Angles in the Point E. And because the Point M is the Pole of the Circle BFP , therefore the Circle GMS shall cut the Circle BFP at Right Angles in the Point D , the Side F P being extended . Come we now to the several Cases which after this preparation may be resolved , by the Catholick Proposition . CASE 1. Two Sides with an Angle opposite to one of them being given , to find the Angle opposite to the other . In the Oblique angled Spherical Triangle F P S , in Fig. 4. the Sides and Angles given and required will admit of six Varieties ; all which may be resolved by the Catholick Proposition , at two operations , but those two may be reduced to one , as by the following Analogies to every Variety will plainly appear . Given Required   FP   Rad. s PS ∷ s PSF . s PE 1. PS PFS s. PF . Rad ∷ s PE. s PFS PSF   s PF . s PS ∷ s PSF . s PFS FP   Rad. s FP ∷ s F. s PE 2. PS PSF s PS . Rad ∷ s PE. s PSF PFS   s. PS . s FP ∷ s PFS . s PSF PS   Rad. s SF ∷ s F. sDS 3. FS FPS s PS . Rad ∷ s DS. s SPD PFS   s. PS . s SF ∷ s PFS . s PSF PS   Rad. s PS ∷ s SPD . s DS 4. FS PFS s FS . Rad ∷ s DS. s SF FPS   s FS . s PS ∷ s SPF. s SF FS   Rad. s FS ∷ s S. s FC 5. FP FPS s. FP . Rad ∷ s FC . s FPC FSP   s. FP . s FS ∷ s PSF . s FPS FS   Rad. s FP ∷ s FPC . s FC 6. FP FSP s FS . Rad ∷ s FC . s S FPS   s. FS . s FP ∷ FPS . s PSF . CASE 2. Two Sides with an Angle appo●ite to one of them being given , to find the contained Angle . In this Case there are six Varieties , all which may be resolved by the Catholick Proposition , according to the Table following . Given Required   FP   1 : cot PSF . Rad ∷ cs PS . ct EPS 1. PS FPS 2. ct PS . Rad ∷ cs EPS . t EP PSF   3. Rad. t EP ∷ ct FP . cs FPE EPS+EPF = FPS   ct PS . cs EPS ∷ ct FP . ct FPE FP   1. cot PFS . Rad ∷ cs PF . ct EPF 2. PS FPS 2. ct PF . Rad ∷ cs EPF . t EP PFS   3. Rad. t EP ∷ cot PS . cs EPS EPS+EPF = FPS   cot PF . cs EPF ∷ ct PS ct EPS PS   1. cot PFS . Rad ∷ cs FS . ct FSD 3. FS PSF 2. ct FS . cs FSD ∷ Rad. t DS PFS   3. Rad. t DS ∷ ct PS . cs PSD FSD-PSD = PSF   ct FS . cs FSD ∷ ct PS . cs PSD PS   1. cot FPS . Rad ∷ cs PS . ct PSD 4. FS PSF 2. ct PS . cs PSD ∷ Rad. t DS FPS   3. Rad. t DS ∷ ct FS . cs FSD FSD-PSD = PSF   ct PS . cs PSD ∷ ct FS . cs FSD FS   1. cot FSP . Rad ∷ cs FS . ct SFC 5. FP PFS 2. ct FS . cs SFC ∷ Rad. t FC FSP   3. Rad. t FC ∷ ct FP . cs PFC SFC-PFC = PFS   ct FS . cs SFC ∷ ct FP . cs PFC FS   1. cot FPS . Rad ∷ cs PF . ct PFC 6. FF PFS 2. cot FP . cs PFC ∷ Rad. t FC FPS   3. Rad. t FC ∷ ct FS . cs SFC SFC-PFC = PFS   ct FP . cs PFC ∷ ct FS . cs SFC . CASE 3. Two Sides and an Angle opposite to one of them being given , to find the third side . The Varieties in this Case , with their resolution by the Catholick Proposition , are as followeth . Given Required   FP   1. ct PS ∷ cs PSF . t ES 1. PS FS 2. cs ES. cs PS ∷ Rad. cs EP PSF   3. Rad. cs EP ∷ cs FP . cs FE ES+FE = FS   cs ES. cs PS ∷ cs FP . cs FE FP   1. cot FP . Rad ∷ cos PFS . t FE 2. PS FS 2. cos FE . cos FP ∷ Rad. cos EP PFS   3. Rad. cos EP ∷ cos PS . cos SE SE+FE = FS   cos FE . cos FP ∷ cos PS . cos SE PS   1. cot FS . Rad ∷ cos PFS . t FD 3. FS FP 2. cos FD. cos FS ∷ Rad. cs SD PFS   3. Rad. cos SD ∷ cos PS . cs PD FD-PD = FP   cos FD. cos FS ∷ cs PS . cs PD PS   1. cot PS . Rad ∷ cos FPS . t PD 4. FS FP 2. cos PD . cos PS ∷ Rad. cos SD FPS   3. Rad. cos SD ∷ cos FS . cs FD FD-PD = FP   cos PD . cos PS ∷ cos FS . cs FD FS   1. cot FS . Rad ∷ cos FSP . t SC 5. FP PS 2. cos SC. cos FS ∷ Rad. cos FC FSP   3. Rad. cos FC ∷ cos FP . cos PC SP-PC = PS   cos SC. cos FS . cos FP . cos PC FS   1. cot FP . Rod ∷ cos FPS . t PC 6. FP PS 2. cos PC . cos FP ∷ Rad. cos FC FPS   3. Rad. cos FC ∷ cos FS . cos SC SC-PC = PS   cos PC . cos FP ∷ cos FS . cos SC CASE 4. Two Angles with a Side opposite to one of them being given , to find the Side opposite unto the other . The Varieties in this Case , with their Resolution by the Catholick Proposition , are as followeth . Given Required   PFS   Rad. s. PS ∷ s DPS. s SD 1. FPS FS S. FP . Rad ∷ s SD . s FS PS         s. PFS . s PS ∷ s FPS . s FS PFS   Rad. s FS ∷ s PFS . s. SD 2. FPS PS s. FPS . Rad ∷ s SD . s PS FS         s. FPS . s FS ∷ s PFS . s PS FPS   Rad. s FP ∷ s FPS . s FC 3. PSF FS s. PSF . Rad ∷ s FC . s FS FP         s. PSF . s FP ∷ s FPS . s FS FPS   Rad. s FS ∷ s PSF . s FC 4. PSF FP s. FPS . Rad ∷ s FC . s FP FS   s. FPS s FS ∷ s PSF . s FP PSF   Rad. s PS ∷ s PSF . s PE 5. SFP FP s. SFP . Rad ∷ s PE. s FP PS   s. SFP . s PS ∷ s PSF . s FP PSF   Rad. s FP ∷ s PFS . s PE 6. SFP PS s. PSF . Rad ∷ s PE. s PS FP   s. PSF . s FP ∷ s PFS . s PS CASE 5. Two Angles and a side opposite to one of them being given , to find the Side between them . The Varieties and Proportions , are as followeth . Given Required   PFS   1. ct PS . Rad ∷ cs DPS. PD 1. FPS FP 2. ct DPS. s PD ∷ Rad. t DS PS   3. Rad. t DS ∷ ct PFS . s FD FD-PD = FP   ct DPS. s PD ∷ ct PFS . s FD PFS   1. ct DFS. Rad ∷ cs PFS . t FD 2. FPS FP 2. cot PFS . s FD ∷ Rad. t DS FS   3. Rad. t DS ∷ ct FPS . s PD FD-PD = FP     FPS   1. cot FP . Rad ∷ cs FPC . t PC 3. PSF PS 2. cot FPC . s PC ∷ Rad. t FC FP   3. Rad. t FC ∷ ct PSF . s SC SC-PC = PS   cot FPC . s PC ∷ ct PSF . CS FPS   1. cot FS . Rad ∷ cs PSF . t SC 4. PSF PS 2. cot PSF . s SC ∷ Rad. t FC FS   3. Rad. t FC ∷ cot FPS . s PC SC-PC = PS   cot PSF . s SC ∷ cot FPS . s PC PSF   1. cot PS . Rad ∷ cs PSF . t SE 5. SFP FS 2. cot PSF . s SE ∷ Rad. t PE PS   3. Rad. t PE ∷ cot SFP . s FE FE+SE = FS   cot PSF . s SE ∷ cot SFP . s FE PSF   1. cot FP . Rad ∷ cs SFP . t FE 6. SFP FS 2. cot SFP . s FE ∷ Rad. t PE FP   3. Rad. t PE ∷ cos PSF . s SE FE+SE = FS   cot . SFP . s FE ∷ cs PSF . s SE CASE 6. Two Angles and a Side opposite to one of them being given , to find the third Angle . The Varieties and Proportions are as followeth . Given Required   PFS   1. ct DPS. Rad ∷ cs PS . ct PSD 1. FPS PSF 2. s PSD . cs DPS ∷ Rad. cs DS PS   3. cs DS. Rad ∷ cs DFS. s FSD FSD-PSD = PSF   cs DPS. s PSD ∷ cs DFS. s FSD PFS   1. ct PFS . Rad ∷ cs FS . ct FSD 2. FPS PSF 2. s FSD . cs PFS ∷ Rad. cs DS FS   3. cs PDS. Rad ∷ cs DPS. cs PSD FSD-PSD = PSF   cs PFS . s FSD ∷ cs DPS. cs PSD FPS   1. ct FPC . Rad ∷ cs FP . ct PFC 3. PSF PFS 2. s PFC . cs FPG ∷ Rad. cs FC FP   3. cs FC . Rad ∷ cs PSF . s FC SFC-PFC = PFS   cs FPC . s PFC ∷ cs PSF . s SFC FPS   1. cot PSF . Rad ∷ cos FS . ct SFC 4. PSF PFS 2. s SFC . cs PSF ∷ Rad. cs FC FS   3. cs FC . Rad ∷ cs CPF . s PFC SFC-PFC = PFS   cs PSF . s SFC ∷ cs CPF . s PFC PSF   1. cot PSF . Rad ∷ cs PS . ct SPE 5. SFP FPS 2. s SPE . cs PSF ∷ Rad. cs PE PS   3. cs PE. Rad ∷ cs SFP . s FPE FPE+SPE = FPS   cs PSF . s SPE ∷ cs SFP . s FPE PSF   1. cot SFP . Rad ∷ cs FP . ct FPE 6. SFP FPS 2. s FPE . cs SFP ∷ Rad. cs PE FP   3. cos PE Rad ∷ cs PSF . s SPE FPE+SPE = FPS   cs SFP . s FPE ∷ cs PSF . s SPE CASE 7. Two Sides and their contained Angle being given , to find either of the other Angles . The Varieties and Proportions are as followeth . Given Required   FS   1. ct FP . Rad ∷ cs PFS . t FE 1. FP FSP 2. ct PFS . s FE ∷ Rad. t PE PFS   3. t PE. Rad. ∷ s ES. ct PSF FS-FE = ES   s EF. ct PFS ∷ s ES. ct PSF FS   1. cot FS . Rad : : cs PFS . t DF 2. FP FPS 2. cot PFS . s DF : : Rad. t DS PFS   3. t DS. Rad : : s PD . ct SPD FD - FP = PD   s DF. ct PFS : : s PD . ct SPD FP   1. cot FP . Rad : : cos FPC . t PC 3. PS PSF 2. cot FPC . s PC : : Rad. t FC FPS   3. t FC . Rad : : s CS . cot FSP PS+PC = CS s PC . ct FPC : : s CS . ct FSP FP   1. cot PS . Rad : : cos SPD . t PD 4. PS SFP 2. cot SPD . s PD : : Rad. t DS FPS   3. t DS Rad : : s FD. cot SFP FP+PD = FD   s PD . ct SPD : : s FD. cot SFP PS   1. cot PS . Rad : : cs PSF . t SE 5. FS SFP 2. cot PSF . s SE : : Rad. t PE PSF   3. t PE. Rad : : s FE . cot SFP FS-SE = FE   s SE. ct PSF : : s FE . ct SFP PS   1. cot FS . Rad : : cs PSF . t SC 6. FS FPS 2. cot PSF . s SC : : Rad. t FC PSF   3. t FC . Rad : : s PC . cot FPC SC-PS = PC   s SC. cot PSF : : s PC . ct FPC CASE 8. Two Sides and their contained Angle being given , to find the third Side . The Varieties and Proportions are as followeth . Given Required   FS   1. ct FP . Rad : : cs PFS . t FE 1. FP PS 2. cs FE . cs FP : : Rad. cos PE PFS   3. Rad. cs PE : : cs ES. cs PS FS-FE = ES   cs FE . cs FP : : cs ES. cs PS FP   1. ct PS . Rad : : cs SPD . t PD 2. SP FS 2. cs PD . cs PS : : Rad. cos DS FPS   3. Rad. cos DS : : cs FD. cs FS FP+PD = FD   cs PD . cs PS : : cs FD. cs FS PS   1. ct PS . Rad : : cs PSF . t. ES 3. FS FP 2. cs ES. cs PS : : Rad. cos PE PSF   3. Rad. cos PE : : cos FE . cos FP FS-ES = FE   cs ES. cs PS : : cos FE . cs FP CASE 9. Two Angles and their contained Side being given , to find one of the other Sides . Given Required   PFS   1. ct PFS . Rad : : cs FP ct FPE 1. FPS PS 2. ct FP . cs FPE : : Rad. t PE FP   3. t PE. Rad : : cs EPS . ct PS FPS-FPE = EPS   cs FPE . ct FP : : cs EPS . ct PS PFS   1. cot FPC . Rad : : cs FP . t PFC 2. FPS FS 2. cot FP . cs PFC : : Rad. t FC FP   3. t FC . Rad : : cs SFC . ct SF SFP+PFC = SFC   ct FP . cs PFC : : cs SFC . ct SF FPS   1. ct SPD . Rad : : cs PS . ct PSD 3. PSF SF 2. ct PS . cos PSD : : Rad. t DS PS   3. t DS. Rad : : cs FSD . ct SF PSF+PSD = FSD   cs PSD . ct PS : : cs FSD . ct SF FPS   1. ct PSF . Rad : : cs PS . ct SPE 4. PSF FP 2. ct PS . cs SPE : : Rad. t PE PS   3. t PE. Rad : : cs PPE. ct FP FPS-EPS = FPE   cs SPE . ct PS : : cs FPE . ct FP PSF   1. ct PSF . Rad : : cs SF . ct SFC 5. SFP FP 2. ct SF . cs SFC : : Rad. t FC SF   3. t FC . Rad : : cs CFP . ct FP SFC-SFP = CFP   cs SFC . ct SF : : cs CFP . ct FP PSF   1. ct SFP . Rad : : cs FS . ct FSD 6. SFP PS 2. ct FS . cs FSD : : Rad. t SD SF   3. t SD . Rad : : cos PSD . ct PS FSD-FSP = PSD   cs FSD . ct FS : : cs PSD . ct PS CASE 10. Two Angles and the Side between them being given , to find the third Angle . The Varieties and Proportions are as followeth . Given Required   SFP   1. ct SFP . Rad : : cs FP . ct FPE 1. FPS PSF 2. s FPE . cs F : : Rad. cs PE FP   3. Rad. cs PE : : s EPS . cs PST FPS-FPE = EPS   s FPE . cs PFS : : s SPE . cs PSF FPS   1. ct SPD . Rad : : cs PS . ct PSD 2. PSF SFP 2. s PSD . cs SPD : : Rad. cs DS PS   3. Rad. cs DS : : s FSD . cs SFP PSF+PSD = FSD   s PSD . cs SPD : : s FSD . cs SFP PSF   1. ct PSF . Rad : : cs SF . ct SFC 3. SFP FPS 2. s SFC . cs PSF : : Rad. cs FC SF   3. Rad. cs FC : : s PFC . cs FPS SFC-SFP = PFC   s SFC . cs PSF : : s PFC . cs FPS CASE 11. The three Sides being given , to find an Angle . This Case may be resolved by the Catholick Proposition also , according to the direction of the Lord Nepier , as I have shewed at large in the Second Book of my Trigonometria Britannica , Chap. 2. but may as I conceive be more conveniently solved , by this Proposition following . As the Rectangle of the Square of the Sides containing the Angle inquired ; Is to the Square of Radius : So is the Rectangle of the Square of the difference of each containing Side , and the half sum of the three Sides given . To the Square of the Sine of half the Angle inquired . In this Case there are three Varieties , as in the Triangle FZP . Fig. 3. Given Required   ZP   s ZP x s PF . Rad. q. 1. PF ZPF s ½ Z-ZP x s ½ Z-PF . Q FZ   s ½ ZPF ZP   s PF x s PZ . Rad. q. 2. PF PFZ s ½ Z-PF x s ½ Z-FZ . Q FZ   s ½ PFZ ZP   s ZP x s FZ Rad. q. 3. PF FZP s. ½ Z-ZP x ½ Z-ZF . Q FZ   s ½ FZP CASE 12. The three Angles given , to find a Side . This is the Converse of the last , and to be resolved after the same manner , if so be we convert the Angles into Sides , by the tenth of the third Chapter : for so the Sides of the Triangle ACD will be equal to the Angles of the Triangle FZP n Fig. 3. That is AD = AEE the measure of the Angle ZPF . DC = KM the measure of the Angle ZFP . AC = HB the Complement of FZP to a Semicircle . The Angle DAC = QR = ZP . ACD = rM = Hf = Zoe = ZF . ADM = sK = AEl = Ph = PF . And thus the Sides of the Triangle ZPF are equal to the Angles of the Triangle ACD . The Complement of the greatest Side PF to a Semicircle being taken for the greatest Angle ADC . And in this Case therefore , as in the preceding , there are three Varieties which make up sixty Problems in every Oblique angled Spherical Triangle ; which actually to resolve in so many Triangles , as have been mentioned , would be both tedious , and to little purpose ; I will therefore select some few , that are of most general use in the Doctrine of the Sphere , and leave the rest to thine own practice . CHAP. V. Of such Spherical Problems as are of most General Use in the Doctrine of the Primum Mobile or Diurnal Motion of the Sun and Stars . PROBLEM 1. The greatest Declination of the Sun being given , to find the Declination of any Point of the Ecliptick . THe Declination of the Sun or other Star , is his or their distance from the Equator , and as they decline from thence either Northward or Southward ; so is their Declination reckoned North or South . 2. The Sun 's greatest Declination , which in this and many other Problems is supposed to be given , with the Distance of the Tropicks , Elevation of the Equator , and Latitude of the Place , may thus be found . The Sun 's greatest Meridian H ♋ . 61.9916 least Altitude H ♑ . 14.9416 Their difference is the distance of the Tropicks ♋ . ♑ . 47. 050 Half that Difference , is the Sun 's greatest Declination AE ♋ . 23. 525 Which deduct from the Sun 's greatest Altitude , the remainer is the height of the Equator HAE . 38. 467 The Complement is the height of the Pole AEZ or PR . 51. 533 Now then in the Right angled Spherical Triangle ADF in Fig. 1. there being given . 1. The Angle of the Sun 's greatest Declination DAF . 23. 525. 2. The Sun 's supposed distance from ♈ to ♎ AF. 60 deg . The Sun 's present Declination DF may be found , by the 10 Case of Right angled Spherical Triangles . As the Radius Is to the Sine of DAF . 23. 525. 9.60113517 So is the Sine of AF 60. 9.93753063 To the Sine of DF. 20. 22. 9.53866580 PROBLEM 2. The Sun 's groatest Declination , with his Distance from the next AEquinoctial Point being given , to find his Right Ascension . In the Right angled Spherical Triangle ADF in Fig. 1. Having the Angle of the Sun 's greatest Declination DAF . 23. 525. And his supposed distance from ♈ or ♎ , the Hypotenusa AF. 60. The Right Ascension of the Sun , or Arch of the AEquator , AD may be found , by the ninth Case of Right angled Spherical Triangles , As the Cotang . of the Hypot . AF. 60. 9.76143937 Is to the Radius 10.00000000 So is the Cosine of DAF . 23. 525. 9 ▪ 96231533 To the Tang. of AD. 57. 80. 10.20087596 PROBLEM 3. To find the Declination of a Planet or Fixed Star with Latitude . In the Oblique angled Spherical Triangle FPS in Fig. 4. we have given , 1. PS = AE ♋ the greatest Declination of the Ecliptick , 2. The Side FS the Complement of the Stars Latitude from the Ecliptick at K. 3. The Angle PSF the Complement of the Stars Longitude . To find PF the Complement of Declination . By the eighth Case of Oblique angled Spherical Triangles , the Proportions are . As the Cot. of PS . 23. 525. 10.3611802 Is to the Radius . 10.0000000 So is the Cos. of PSF . 20 deg . 9.9729858 To the Tang. of SE. 22. 25. 9.6118056 FS . 86 deg . - ES. 22. 25. = FE . 63. 75. As the Cos. of ES. 22. 25. Comp. Arith. 0.0336046 To the Cosine of PS . 23. 525. 9.9623154 So the Cos. FE . 63. 75. 9.6457058 To the Cos. PF . 64. 01. 9.6416258 Whos 's Complement , is FT . 25. 99. the Declination sought . PROBLEM 4. To find the Right Ascension of a Planet , or other Star with Latitude . The Declination being found by the last Problem , we have in the Oblique angled Spherical Triangle PFS in Fig. 4. All the Sides with the Angle FSP 20 deg . or the Complement of the Stars Longitude . Hence to find FPS by the first Case of Oblique angled Spherical Triangles , I say As the Sine of PF . 64. 01. Comp. Arith. 0.0463059 Is to the Sine of FSP . 20. 9.5340516 So is the Sine of FS . 86. 9.9984407 To the Sine of FPS . 22. 28. 9.5787982 Whos 's Complement 67. 72. is the Right Asc. of a Star II. 10. North Lat. 4. PROBLEM 5. The Poles Elevation , Sun's greatest Declination and Meridian Altitude being given , to find his true place in the Zodiack . If the Meridian Altitude of the Sun be less than the height of the AEquator , deduct the Meridian Altitude from the height of the AEquator , the Remainer is the Sun's Declination towards the South Pole : but if the Meridian Altitude of the Sun be more than the height of the AEquator , deduct the height of the AEquator from the Meridian Altitude , what remaineth , is the Sun's Declination towards the North Pole , in these Northern Parts of the World : the contrary is to be observed in the Southern Parts . Then in the Right angled Spherical Triangle ADF in Fig. 1. we have given the Angle FAD the Sun's greatest Declination . The Leg DF the Sun's present Declination , To find AF the Sun's distance from the next Equinoctial Point . Therefore by the Case of Right angled Spherical Triangles . As the Sine of FAD . 23. 525. Comp. Ar. 0.3988648 Is to the Sine of DF. 23. 5. 9.5945468 So is the Radius . 10.0009000 To the Sine of AF. 80. 04. 9.9934116 PROBLEM 6. The Poles Elevation and Sun's Declination being given , to find his Amplitude . The Amplitude of the Sun 's rising or setting is an Arch of the Horizon intercepted betwixt the AEquator and the place of the Sun 's rising or setting ; and it is either Northward or Southward , the Northward Amplitude is when he riseth or setteth on this Side of the AEquator towards the North Pole ; and the Southern when he riseth or setteth on that Side of the AEquator which is towards the South Pole : That we may then find the Sun's Amplitude or Distance from the East or West Point , at the time of his rising or setting . In the Right angled Spherical Triangle ATM , in Fig. 2. let there be given the Angle TAM . 38. 47. the Complement of the Poles Elevation ; and TM . 23. 15. the Sun 's present Declination : To find AM the Sun's Amplitude . By the eleventh Case of Right angled Spherical Triangles . As the Sine of MAT. 38. 47. Comp. Ar. 0.2061365 Is to the Radim . 10.0000000 So is the Sine of MT . 23. 15. 9.5945468 To the Sine of AM. 39. 19. 9.8006833 PROBLEM 7. To find the Ascensional Difference . The Ascensional Difference is nothing else , but the Difference between the Ascension of any Point of the Ecliptick in a Right Sphere , and the Ascension of the same Point in an Oblique Sphere ; As in Fig. 1. AT is the Ascensional difference between DA the Sun's Ascension in a Right Sphere , and DT the Sun's Ascension in an Oblique Sphere . Now then in the Right angled Spherical Triangle AMT , we have given . The Angle MAT. 38. 47. the Complement of the Poles Elevation . And MT . 23. 15. To find AT the Ascensional difference . As Rad.   To the Cot. of MAT. 38. 47. Com. Ar. 10.0999136 So is Tang. MT . 23. 55. 9.6310051 To the Sine of AT . 32. 56. 9.7309187 PROBLEM 8. Having the Right Ascension and Ascensional Difference , to find the Oblique Ascension and Descension . In Fig. 1. DT represents the Right Ascension , AT the Ascensional Difference . DA the Oblique Ascension which is found by deducting the Ascensional Difference AT . from the Right Ascension DT . according to the Direction following . If the Declination be N. North Subt. Add The Ascentional Difference from the Right , and it giveth the Oblique Ascension . The Ascensional Difference to the Right , and it giveth the Oblique Descension . South Add Subt. The Ascensional Difference to the Right , and it giveth the Oblique Ascension . The Ascensional Difference from the Right , and it giveth the Oblique Descension . Right Ascension of ♊ . 0 deg . 57.80 Ascensional Difference 27.62 Oblique Ascension ♊ . 0 deg . 30.18 Oblique Descension ♊ . 0 deg . 85.42 PROBLEM 9. To find the time of the Sun 's rising and setting , with the length of the Day and Night . The Ascensional Difference of the Sun being added to the Semidiurnal Arch in a Right Sphere , that is , to 90 Degrees in the Northern Signs , or substracted from it in the Southern , their Sum or Difference will be the Semidiurnal Arch , which doubled is the Right Arch , which bisected is the time of the Sun rising , and the Day Arch bisected is the time of his setting . As when the Sun is in 0 deg . ♊ . his Ascensional Difference is 27. 62. which being added to 90 degrees , because the Declination is North , the Sum will be 117.62 the Semidiurnal Arch. The double whereof is 235.22 the Diurnal Arch , which being converted into time makes 15 hours 41 minutes : for the length of the Day , whose Complement to 24 ; is 8 hours 19 minutes the length of the Night ; the half whereof is 4 hours 9 minutes 30 Seconds the time of the Sun 's rising . PROBLEM 10. The Poles Elevation and the Sun's Declination being given , to find his Altitude at any time assigned . In this Problem there are three Varieties . 1. When the Sun is in the AEquator . , that is , in the beginning of ♈ and ♎ in which case supposing the Sun to be at B , 60 degrees or four hours distant from the Meridian , then in the Right angled Spherical Triangle BZ AE , in Fig. 1. we have given , AE Z , 51. 53. the Poles Elevation , and B AE 60 degrees , to find BZ . Therefore by the 2 Case of Right angled Spherical Triangles . As the Radius   To the Cosine of AE Z. 51. 53. 9.7938635 So is the Cosine of B. AE . 60. 9.6989700 To the Cosine of B Z. 71. 88. 9.4928335 Whos 's Complement BC. 18. 12. is the ☉ Altitude required . The second Variety is when the Sun is in the Northern Signs , that is , in ♈ . ♉ . ♊ . ♋ . ♌ . ♍ . in which Case supposing the Sun to be at F in Fig. II Then in the Oblique angled Spherical Triangle FZP , we have given . 1. PZ 38. 47 the Complement of the Poles Elevation . 2. FP . 67. 97 the Complement of Declination . 3. ZPF . 45 the Distance of the ☉ from the Meridian , To find FZ . Therefore by the eighth Case of Oblique angled Spherical Triangles . As the Cotang . of ZP . 38. 47. 10.0997059 Is to the Radius . 10.0000000 So is the Cosine of ZPF . 45. 9.8494850 To the Tang. of SP. 29. 33. 9.7497791 Then from FP . 67.97 Deduct SP. 29.33 There rests FS . 38.64 As the Cosine of SP. 29. 33. Comp. Ar. 0.0595768 To the Cosine of PZ . 38. 47. 9.8937251 So is the Cosine of FS . 38. 64. 9.8926982 To the Cosine of FZ . 45. 45. 9.8460001 Whos 's Complement FC . 44. 55 is the ☉ Altitude required . The third Variety is when the Sun is in the Southern Signs as in ♎ . ♏ . ♐ . ♑ . ♒ . ♓ . And in this Case supposing the ☉ to be ♐ 10 degrees , and his Declination South Db 22. 03. and his Distance from the Meridian 45 as before , then in the Oblique angled Spherical Triangle Z bP in Fig. 1. we have given Z P. 38. 47. The Side bP 112. 03. and the Angle ZPb 45. To find Zb. Therefore by the 8 Case of Oblique angled Spherical Triangles . As the Cotang . of ZP . 38. 47. 10.0997059 Is to the Radius . 10.0000000 So is the Cosine of ZPb . 45. 9.8494850 To the Tang. of SP. 29. 33. 9.7497791 Then from bP. 112.03 Deduct SP. 29.33 There rests bS. 82.70 As the Cosine of P S. 29. 33. Comp. Ar. 0.0595768 To the Cosine of ZP . 38. 47. 9.8937251 So the Cosine of bS. 82. 70 9.1040246 To the Cosine of Zb. 83. 45. 9.0573265 Whos 's Complement 6.55 is the ☉ Altitude required . PROBLEM 11. Having the Altitude of the Sun , his Distance from the Meridian , and Declination , to find his Azimuth . The Azimuth of the Sun is an Arch of the Horizon intercepted between the Meridian and the Vertical Line passing by the Sun , being understood by the Angle HZC in Fig. 1. or Arch HC . And in all the Varieties of the last Problem , may be found , by the first Case of Oblique angled Spherical Triangles . Thus in the Triangle ZBP. As the Sine of BZ . 71. 88. Comp. Ar. 0 . 022090● Is to the Sine of BPZ . 60. 9.9375306 So is the Sine of BP . 90. 10.0000000 To the Sine of BZP. 65. 67. 9.9596209 In the Triangle ZFP . I say . s. ZF . s. ZPF ▪ : : s. FP . s. FZP . In the Triangle ZbP. I say . Sine Zb. Sine ZPb : : Sine bP. Sine bZP. PROBLEM 12. The Poles Elevation , with the Sun's Altitude and Declination given , to find his Azimuth . In the Oblique angled Spherical Triangle FZP in Fig. 1. let there be given . 1. FP . 67. 97 the Complement of the ☉ Declination . 2. ZP . 38. 47 the Complement of the Poles Elevation . 3. FZ . 45. 46 the Complement of the ☉ Altitude . And let the Angle FZP the ☉ Azimuth be required . By the 11 Case of Oblique Angled Spherical Triangles . As the Sine ZP x Sine FZ , Is to the Square of Radius . So is the Sine 1 / 2 Z of the Sides ZP x 1 / 2 Z cr — ZF . To the Square of the Sine of half the Angle FZP . The Sum of the three Sides is 151.89 The half Sum is 75.945 from which deduct PZ 38. 47. The difference is 37.475 And the Difference between 75.945 and FZ is 30. 495. Sine of PZ . 38. 47. Comp. Ar. 0.2061365 Sine of FZ . 45. 45. Comp. Ar. 0.1471308 s. 1 / 2 Z cr — PZ . 37. 475. 9.7842000 s. 1 / 2 Z cr — FZ . 30. 495. 9.7054045 Square of the Sine of 1 / 2 FZP . 19.8428618 Sine of 57. 94. 9.9214309 The double whereof is 115.88 the ☉ Azimuth from the North. And the Complement 64.12 , is the ☉ Azimuth from the South . PROBLEM 13. To find the Point of the Ecliptick Culminating , and its Altitude . Before we can know what Sign and Degree of the Ecliptick is in the Medium Coeli ; we must find the Right Ascension thereof , to do which , we must add the Sun's Right Ascension to the time afternoon , being reduced into Degrees and Minutes of the AEquator , the Sum is the Right Ascension of the Medium Coeli . Example . Let the time given , be March the 20. 1674. at one of the Clock in the Afternoon . At which time the Sun's place is in ♈ . 10 deg . 23 Centesms . To find the Right Ascension thereof , in the Right angled Spherical T●iangle ADF in Fig. 1. we have given ; The Angle of the Sun 's greatest Declination DAF 23. 525 and the Sun's distance from the next Equinoctial Point AF 10. 23. Therefore by the ninth Case of Right angled Spherical Triangles . As the ct . AF. 10. 23. 10.7435974 Is to Radius . 10.0000000 So is cs DAF 22. 525. 19.9623154 To t AD 9. 39. 9.2187180 To which adding the Equinoctial Degrees answering to one hour , viz. 15. the Sum is 24.39 the Right Ascension of the Mid Heaven . Hence to find the Point culminating ; in the Right angled Spherical Triangle ADF in Fig. 1. we have given AD 24. 39 and DAF 23. 525 to find AF. Therefore by the fifth Case of Right Angled Spherical Triangles . As t AD 24. 39. 10.6564908 Is to Radius . 10.0000000 So is cs DAF 23. 525. 9.9623154 To ct . AF 26. 31. 10.3058246 Therefore the Point culminating is ♈ 26. 31. To find the Altitude thereof above the Horizon we have given in the same Triangle DAF 23. 525. and AF 26. 31. to find DF. Therefore by the tenth Case of Right angled Spherical Triangles . As Radius . 10.0000000 Is to s AF — 26 , 31. 9.6466268 So is s DAF 23. 525. 9.6011352 To the s DF 10. 19. 9.2477628 Which is the North Declination of the Point of the Ecliptick culminating , and being added to the height of the AEquator at London 38. 47 the Sum is 48.66 the Altitude of the Mid Heaven as was required . PROBLEM 14. Having the greatest obliquity of the Ecliptick together with the Distance of the Point given from the Equinoctial , to find the Meridian Angle , or Intersection of the Meridian with the Ecliptick . Having drawn the Primitive Circle HZRN in Fig. 5. representing the Meridian , and the two Diameters HAR , and ZAN , set off the height of the Pole from R to P. 51. 53 , and from N to S , and draw the Diameters PAS for the Axis of the World , and AE AQ for the AEquator ; this done , the Right Ascension of the Mid Heaven being given , as in the last Problem 24.39 with the Point culminating . ♈ . 26.31 , and the Declination thereof 10.19 , if you set 10 deg . 19 Centesmes from AE to F and e to X , you may draw the Diameters FAX and cAd at Right Angles thereunto , and because the Imum Coeli is directly opposite to the Point culminating , that is , in ♎ 26.31 , if you set 26.31 from X to b , a Ruler laid from c to b will cut the Diameter FX in G , and then making Xh Z Xb you have the three Points b G h , by which to draw that Circle , which will cut the AEquator AE AQ in ♎ , and so you have the three Points X ♎ F by which to describe the Arch of the Ecliptick ♈ F ♎ X. And in the Right angled Spherical Triangle ♈ AEF we have given . The Angle AE ♈ F. 23.525 the Sun 's greatest Declination , and ♈ F. 26. 31. the Point culminating , to find the Angle ♈ F AE . Therefore by the seventh Case of Right angled Spherical Triangles . As the ct AE ♈ F. 23. 525. 10.3611802 Is to the Radius . 10.0000000 So is the cs ♈ F. 26. 31. 9.9525062 To the cot . ♈ FAE . 68. 60. 9.5913260 Which is the Angle of the Ecliptick with the Meridian . PROBLEM 15. To find the Angle Orient , or Altitude of the Nonagesime Degree of the Ecliptick . In Fig. 5. the Pole of the Ecliptick ♈ F ♎ X is at m , and so you have the three Points Z m N to draw the Vertical Circle Z k N cutting the Ecliptick at Right Angles in the Point a : And then in the Right angled Spherical Triangle F a Z , we have given ; FZ 41. 34 the Complement of FH the Altitude of the Mid Heaven ; And the Angle a FZ 68. 68 the Angle of the Ecliptick with the Meridian . To find Z a. Therefore by the tenth Case of Right angled Spherical Triangles . As the Radius . To the Sine of FZ . 41. 34. 9 . 819889● So is the Sine of Z F a. 68. 68. 9.9691128 To the Sine of Z a. 37. 97. 9.7891027 Whos 's Complement is ak the Measure of the Angle agk 52. 03 the Angle of the Ecliptick with the Horizon , or Altitude of the Nonagesime Degree . PROBLEM 16. To find the place of Nonagosime Degree of the Ecliptick . In Fig. 5. F represents the Point of the Ecliptick in the Mid Heaven , which according to Problem 14 is ♈ . 26.31 which being known , in the Triangle FZa , we have also given , FZ 41. 34 and the Angle ZFa. 68. 68. To find Fa. Therefore by the ninth Case of Right angled Spherical Triangles . As the cot . of FZ . 41. 34. 10.0556361 Is to the Radius . 10.0000000 So is the cos . of ZFa. 6. 8. 6. 8. 9.5605957 To the tang . of Fa. 17. 73. 9.5049596 Which being added to ♈ F 26. 31 the sum is ♈ a. 44. 04 the place of the Nonagesime Degree of the Ecliptick at a. PROBLEM 17. The Mid Heaven being given , to find the Points of the Ecliptick Ascending and Descending . Having found by the last Problem , the place of Nonagesime Degree of the Ecliptick at a to be in ♉ . 14.04 , if you add 90 Degrees or three Signs thereto , the Ascendant at g will be in ♌ 14. 04 , and the Point descending by adding of six Signs will be in ♒ 14. 02. But these with the Cusps of the other Houses of Heaven may be otherwise found in this manner . To the Right Ascension of the Medium Coeli or the tenth House , add 30 , it giveth the Ascension of the eleventh House , to which adding 90 Degrees more , it giveth the Ascension of the twelfth House , &c. According to which direction , the Ascensions of the six Houses towards the Orient , are here set down in the following Table . 10. 24.39 11. 54.39 12. 84.39 1. 114.39 2. 144.39 3. 174.39 Now because the Circles of Position must according to these Directions cut the AEquator at 30 and 30 Degrees above the Horizon , if in Fig. 5. you set 30 Degrees from AE to n , and n to r. A Ruler laid from P to n and r , shall cut the AEquator at B and K , and then you may describe the Circles of Position HBR and HKR , make AT = AK and AV = AB , and so you may describe the Circles HTR and HVR , and where these Circles do cut the Arch of the Ecliptick ♈ F ♎ there are the Cusps of the Coelestial Houses . Thus a Ruler laid from m. the Pole of the Ecliptick to the Intersections ct s. t. g. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . will cut the Primitive Circle in 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . and the Arches 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 = Fs. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 = Ft. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 = Fg. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 = 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 = 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 being added to 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 B will give you the Cusps of the 11. 12. 1. 2 and 3 Houses , the other six are the same Degrees and Parts in the Opposite Signs . Thus a Figure in Heaven may be erected by Projection , the Arithmetical Computation now followeth ; In which the height of the Pole above each Circle of Position is required , the which in the Projection is easily found ; as the Pole of the Circle of Position HBR is at the Point D. and so you have the three Points S , D , P , to describe that Circle by , which will cut the Circle HBR at Right Angles in the Point C. and the Arch PC is the height of the Pole above that Circle of Position , and may be measured by the Directions given in the nineteenth of the third Chapter . In like manner the height of the Pole above the Circle of Position HKR , will be the Arch PE. To compute the same Arithmetically in the Right angled Spherical Triangle HAEB in Fig. 5. we have given AEH . 38. 47 the height of the Equator . AEB 30. the difference of Ascension between the 10 and 11 Houses , to find HBAE the Angle of that Equator with the Circle of Position . Therefore by the first Case of Right angled Spherical Triangles . As the Tang. of H AE , 38. 47. 9.90000652 Is to the Radius . 10.00000000 So is the Sine of AE B. 30 9.69897000 To the Cotang . of AE B H. 57. 81626. 9.79888348 Whos 's Measure in the Scheme is EC , and the Complement thereof is CP . 32. 18374 the height of the Pole required . Therefore the height of the Pole above the Circle of Position HKR . In the Triangle HAEK , we have given , H AE as before , and AE K. 60 to find HKAE . Therefore . As the Tang. of H AE 38. 47. 9.90008652 Is to the Radius . 10.00000000 So is the Sine of AE K 60. 9.93753063 To the Cotang . of HK AE 42. 53308. 10.03744411 Whos 's Measure in the Scheme is GL , and the Complement thereof is PL 47. 46692. the height of the Pole required . The height of the Pole above HDR is the same with HBR , and the height of the Pole above HTR is the same with HKR . Having found the Ascensions of the several Houses together with the Elevation of the Pole above their Circles of Position , in the Oblique angled Spherical Triangle ♈ BS , we have given . 1. The Angle ♈ BS the Complement of HBAE . 2. The Angle B ♈ S. 23. The Sun 's greatest Declination . 3. Their included Side ♈ B. 54. 39 the Ascension of the eleventh House . To find ♈ S the Point of the Ecliptick , which is resolvable by the ninth Case of Right angled Spherical Triangles . But in my Trigonometria Britannica , Problem . 5. for the resolving of Oblique angled Spherical Triangles , I have shewed how this Case as to our present purpose may be resolved , by these Proportions following . 1. s 1 / 2 Z Ang. s 1 / 2 X Ang : : t 1 / 2 ♈ B. t 1 / 2 X Cru . 2. cs 1 / 2 Z Ang. cs 1 / 2 X Ang : : t 1 / 2 ♈ B. t 1 / 2 Z Cru . 1 / 2 Z Cru + 1 / 2 X Cru = ♈ S the Arch of the Ecliptick desired . For the Cusp of the Eleventh House . T B Arch ♈ B. 4439 the half whereof is 27. 195. ♈ B S. 122. 18374. B ♈ S. 23. 525. Z 145.70874 — 1 / 2 Z 72. 85437. X. 198.65874 — 1 / 2 X. 49. 32937. s 1 / 2 Z. 72. 85437. Comp. Arith. 0.01977589 s 1 / 2 X. 49. 32937. 9.88000800 t 1 / 2 ♈ B. 27. 195. 9.71081089 t 1 / 2 X Cru . 22. 192. 9.61059478 2. Operation . cs . 1 / 2 Z. 72. 85437. Comp. Arith. 0.53012277 ss 1 / 2 X. 49. 32937. 9.81395860 t 1 / 2 ♈ B. 27. 195. 9.71081089 t 1 / 2 Z Cru . 48. 611. 10.05489226 1. Arch. 22. 192. Their Sum is 70.803 the Point of the Ecliptick . cs . ½ Z. 82. 51916. Comp. Arish . 0.88517901 cs ½ X. 59. 00416. 9.71164750 t. ½ ♈ A. 57. 195. 10.19072348 t ▪ ½ Z Cru : 78. 397. 10.68754999 1. Arch — 53. 296. Their Sum 121.693 is the Point of the Ecliptick for the Ascendant . For the Cusp of the Second House . In the Oblique angled Spherical Triangle ♈ T 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . we have given , 1. ♈ T. 144. 39. The half whereof is 72. 195. 2. ♈ T 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . 122. 18374 To find ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . The Angles are the same with those of the Twelfth House . Therefore . 3. T 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 y. 23. 525   s. ½ Z. 80. 49596. Comp. Arith. 0.00601663 s ½ X. 56. 97096. 9.92351651 Their Sum 9.92953314 t ½ ♈ T. 72. 195. 10.49327695 t ½ X Cru . 69. 306. 10.42281009 2. Operation . cs ½ Z 80. 49596. Comp. Arith. 0.78170174 cs ½ X 56. 97096. 9.73628614 Their Sum 10.51798788 t ½ ♈ T. 72. 195. 10.49327695 t ½ Z Cru . 84. 34. 11.01126483 1. Arch. 69. 306. Their Sum is 53.740 is the Point of the Ecliptick for the Second House . For the Cusp of the Third House . In the Oblique angled Spherical Triangle ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , we have , 1. ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . 174. 39. The half whereof is 87. 195. The Angls ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 are the same with those of the Eleventh House . s ½ Z. 72. 85437. Comp. Arith. 0.01977580 s ½ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 49. 32937. 6.88000800 Their Sum 9.89978389 t ½ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . 87. 195. 11.30984054 For the Eleventh House . For the Cusp of the Twelfth House . In the Oblique angled Spherical Triangle ♈ KF , we have given . 1. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 K. 84. 39. The half whereof is . 42. 195. 2. ♈ Kt. 137.46692   3. K ♈ t. 23.525 To find ♈ t. Z. 160.99192 ½ Z. 80.49596 X. 113.94192 ½ X. 56.97096 s ½ Z. 80. 49596. Comp. Arith. 0.00601663 s ½ X. 56. 97096. 9.92351651 t ½ ♈ K. 42. 195. 9.95740882 t ½ X Cru . 37. 625. 9.88694196 2. Operation . cs . ½ Z. 80. 49596. Comp. Arith. 0.78170174 cs ½ X. 56. 97096. 9.73628614 t ½ ♈ K. 42. 195. 9.95740882 t ½ Z Cru . 71. 496. 10.47539670 1. Arch. 37. 625. Their Sum 113.6691 is the Point of the Ecliptick for the Twelfth House . For the Cusp of the Ascendant . In the Oblique angled Spherical Triangle ♈ AG we have , 1. ♈ A. 114. 39. The half whereof is 57. 195. 2. ♈ AZ . 141. 5333. The Complement of HAAE 38. 46667. 3. A 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 y. 23. 525.   Z. 165.05833 ½ Z. 82.51916 X. 118.00833 ½ X. 59.00416 s. ½ Z. 82. 51916. Comp. Arith. 0 . 0037162● s. ½ X. 59. 00416. 9.93313477 t ½ ♈ A. 57. 195. 10.19072348 t ½ X. 53. 296. 10.12757454 2. Operation . t ½ X Cru . 86. 468. 11.20962043 2. Operation . cs ½ Z. 72. 85437. Comp. Arith. 0.53012277 cs ½ X. 49. 32937. 9.81395860 Their Sum 10.34408137 t ½ ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . 87. 195. 11.39984054 t ½ X Cru . 88. 729. 11.65392191 1. Arch. 86. 468. Their Sum 175.197 is the Point of the Ecliptick for the Third House . And thus we have not only erected a Figure for the Time given , but composed a Table for the general erecting of a Figure in that Eatitude ; for by adding together the first and second Numbers in each Proportion for the first , second and third Houses there is composed two Numbers for each House , to each of which the Artificial Tangent of half the Ascension of each House being added , their Aggregates are the Tangents of two Arches , which being added together , do give the distance of the Cusp of the House , from the first Point of Aries , as in the preceding Operations hath been shewed . Only note , That if the Ascension of any House be more than a Semicircle , you must take the Tangent of half the Complement to a whole Circle . And to find the Cusp of the House , you must also take the Complement of the Sum of the Arches added together . The Numbers according to the former Operations which do constitute a Table of Houses for the Latitude of London . 51. 53 are as followeth .   11 and 3 Houses Ascendant 12 and 2 Houses 1. Oper. 9.89978389 9.93685106 9.92953314 2. Oper. 10.34408137 10.59682651 10.51798788 The Six Oriental Houses , by the preceding Operations . The opposite Houses are in the opposite Signs and Degrees . 10 House ♈ 26.311 11 House ♊ 10.803 12 House ♋ 23.691 Ascendant ♌ 11.693 2 House ♏ 3.740 3 House ♏ 25.197 4 House ♎ 26.311 5 House ♐ 10.803 9 House ♑ 23.691 7 House ♒ 11.693 8 House ♓ 3.740 9 House ♓ 25.197 A Figure of the Twelve Coelestial Houses . ASTRONOMY . THE Second Part : OR , AN ACCOUNT OF THE Civil Year , With the Reason of the Difference Between the JULIAN & GREGORIAN Calendars , And the manner of Computing the Places of the SVN and MOON . LONDON , Printed for Thomas Passinger , at the Three Bibles on London-Bridge . 1679. AN INTRODUCTION TO Astronomy . The Second Book . CHAP. I. Of the Year Civil and Astronomical . HAving shewed the Motion of the Primum Mobile , or Doctrine of the Sphere , which I call the Absolute Part of Astronomy ; I come now unto the Comparative , that is , to shew the Motion of the Stars in reference to some certain Distinction of Time. 2. And the Distinction of Time is to be considered either according to Nature , or according to Institution . 3. The Distinction of Time according to Nature , is that space of Time , in which the Planets do finish their Periodical Revolutions from one certain Point in the Zodiack , to the same again , and this in reference to the Sun is called a Year , in reference to the Moon a Month. 4. The Sun doth pass through the Zodiack in 365 Days , 5 Hours , and 49 Minutes . And the Moon doth finish her course in the Zodiack , and return into Conjunction with the Sun , in 29 Days , 12 hours , 44 Minutes , and 4 Seconds . And from the Motion of these two Planets , the Civil Year in every Nation doth receive its Institution . 5. Twelve Moons or Moneths is the measure of the Common Year , in Turkey in every Moneth they have 29 or 30 Days , in the whole Year 354 Days , and in every third Year 355 Days . 6. The Persians and Egyptians do also account 12 Moneths to their Year ; but their moneths are proportioned to the Time of the Suns continuance in every of the Twelve Signs ; in their Year therefore which is Solar , there are always 365 Days , that is eleven Days more than the Lunar Year . 7. And the Iulian Year which is the Account of all Christendom , doth differ from the other in this ; that by reason of the Sun's Excess in Motion above 365 Days , which is 5 Hours , 49 Minutes , it hath a Day intercalated once in 4 Years , and by this intercalation , it is more agreeable to the Motion of the Sun , than the former , and yet there is a considerable difference between them , which hath occasioned the Church of Rome to make some further amendment of the Solar Year , but hath not brought it to that exactness , which might be wished . 8. This intercalation of one Day once in 4 Years , doth occasion the Sunday Letter still to alter till 28 Years be gone about ; The Days of the Week which use to be signed by the seven first Letters in the Alphabet , do not fall alike in every Common Year , but because the Year consisteth of 52 Weeks and one Day , Sunday this Year will fall out upon the next Year's Monday , and so forward for seven years , but every fourth year consisting of 52 weeks and two days , doth occasion the Sunday Letter to alter , till four times seven years , that is till 28 years be gone about . This Revolution is called the Cycle of the Sun , taking its name from the Sunday Letter , of which it sheweth all the Changes that it can have by reason of the Bissextile or Leap-year . To find which of the 28 the present is , add nine to the year of our Lord , ( because this Circle was so far gone about , at the time of Christs Birth ) and divide the whole by 28 , what remaineth is the present year , if nothing remain the Cycle is out , and that you must call the last year of the Cycle , or 28. 9. This Intercalation of one day in four years , doth occasion the Letter F to be twice repeated in February , in which Moneth the day is added , that is , the Letter F is set to the 24 and 25 days of that Moneth , and in such a year S. Matthias day is to be observed upon the 25 day , and the next Sunday doth change or alter his Letter , from which leaping or changing , such a year is called Leap-year , aud the number of days in each Moneth is well expressed by these old Verses . Thirty days hath September , April , June and November . February hath 28 alone , All the rest have thirty and one . But when of Leap-year cometh the Time , Then days hath February twenty and nine . That this year is somewhat too long , is acknowledged by the most skilful Astronomers , as for the number of days in a year the Emperours Mathematicians were in the right , for it is certain , that no year can consist of more than 365 days , but for the odd hours it is as certain that they cannot be fewer than five , nor yet so many as six ; so then the doubt is upon the minutes , 60 whereof do make an hour , a small matter one would think , but how great in the consequence we shall see . The Emperours year being more than 10 minutes greater than the Suns , will in 134 years rise to one whole day , and by this means the Vernal or Spring Equinox , which in Iulius Caesar's time was upon the 24 of March , is now in our time upon the 10 of March , 13 days backward , and somewhat more , and so if it be let alone will go back to the first of March , and first of February , and by degrees more and more backward still . 10. To reform this difference , some of the late Roman Bishops have earnestly endeavoured . And the thing was brought to that perfection it now standeth , by Gregory the Thirteenth , in the year 1582. His Mathematicians , whereof Lilius was the Chief , advised him thus : That considering there had been an Agitation in the Council of Nice somewhat concerned in this matter upon the motion of that Question , about the Celebration of Easter . And that the Fathers of the Assembly , after due deliberation with the Astronomers of that time , had fixed the Vernal Equinox at the 21 of March , and considering also that since that time a difference of ten whole days had past over in the Calendar , that is , that the Vernal Equinox , which began upon the 21 of March , had prevented so much , as to begin in Gregorie's days at the 10 of the same , they advised , that 10 days should be cut off from the Calendar , which was done , and the 10 days taken out of October in the year 1582. as being the moneth of that year in which that Pope was born ; so that when they came to the fifth of the moneth they reckoned the 15 , and so the Equinox was come up to its place again , and happened upon the 21 of March , as at the Council of Nice . But that Lilius should bring back the beginning of the year to the time of the Nicene Council and no further , is to be marvelled at , he should have brought it back to the Emperours own time , where the mistake was first entered , and instead of 10 , cut off 13 days ; however this is the reason why these two Calendars differ the space of 10 days from one another . And thus I have given you an account of the year as it now stands with us in England , and with the rest of the Christian World in respect of the Sun , some other particulars there are between us and them which do depend upon the motion of the Moon , as well as of the Sun , and for the better underderstanding of them , I will also give you a brief account of her revolution . But first I will shew you , how the day of the moneth in any year propounded in one Couutry , may be reduced to its correspondent time in another . 11. Taking therefore the length of the year , to be in several Nations as hath been before declared , if we would find what day of the moneth in one Conntry is correspondent to the day of that moneth given in another , there must be some beginning to every one of these Accounts , and that beginning must be referred to some one , as to the common measure of the rest . 12. The most natural beginning of All Accounts , is the time of the Worlds Creation , but they who could not attain to the Worlds Beginning , have reckoned from their own , as the Romans from the building of Rome , the Greeks from their Olympicks , the Assyrians from Nabonassar , and all Christians from the Birth of Christ : the beginning of which and all other the most notable Epochaes , we have ascertained to their correspondent times in the Julian Period , which Scaliger contrived by the continual Multiplication of those Circles , all in former time of good use , and two of them do yet remain ; the Circles yet in use are those of the Sun and Moon , the one , to wit , the Sun , is a Circle of 28 years , and the Circle of the Moon is 19 , as shall be shewed hereafter . The third Circle which now serves for no other use than the constituting of the Julian Period , is the Roman Indiction , or a Circle of 15 years ; if you multiply 28 the Circle of the Sun , by 19 the Circle of the Moon , the Product is 532 , which being multiplied by 15 , the Circle of the Roman Indiction , the Product is 7980 , the Number of years in the Julian Period : whose admirable condition is to distinguish every year within the whole Circle by a several certain Character , the year of the Sun , Moon , and Indiction being never the same again until the revolution of 7980 years be gone about , the beginning of this Period was 764 Julian years before the most reputed time of the Worlds Creation ; which being premised , we will now by Example shew you how to reduce the years of Forreigners to our Julian years , and the contrary . 1. Example . I desire to know at what time in the Turkish Account , the fifth of Iune in the year of our Lord 1640. doth fall . The Julian years complete are 1648 , and are thus turned into days , by the Table of days in Julian years . 1000 Julian years give days 365250 600 Julian years give days ▪ 219150 40 Julian years give days 14610 8 Years give days 2922 May complete 151 Days 5 The Sum is 602088 Now because the Turkish Account began Iuly 16. Anno Christi . 622. you must convert these years into days also . 600 Julian years give days 219150 20 Years give days 7305 1 Year giveth days 365 Iune complete 181 Days 15 The Sum is 227016 Which being substracted from 602088 There resteth days 375072 900 Turkish years give days 318930 There resteth 56142 150 Turkish years give days 53155 There resteth 02987 8 Turkish years give days 2835 There resteth 152 Giumadi . 4. 148 There resteth 4 Therefore the fifth of Iune 1649. in our English Account doth fall in the year 1058. of Mahomet , or the Turkish Hegira , the fourth day of the moneth Giumadi . 11 2. Example . I desire to know upon what day of our Julian year the 17 day of the moneth in the 1069 year complete of the Persian Account from Ieshagile doth fall . The beginning of this Epocha is from the Epocha of Christ in complete days 230639 1000 Persian years give 365000 60 Years give 21900 9 Years give 3285 Chortal complete 90 Days complete 16 The Sum 620930 1000 Julian years Substracted 365250 There rests 255680 700 Julian years 255675 There rests 5 Therefore it falls out in the Julian year from Christ 1700. the fifth day of Ianuary . He that understands this may by the like method convert the years of other Epochas , into our Julian years and the contrary . The Anticipation of the Gregorian Calendar is more easily obtained , for if you enter the Table with the years of Christ complete , you have the days to be added to the time in the Julian Account , to make it answer to the Gregorian , which will be but ten days difference till the year 1700. and then the difference will be a day more , until the year 1800. and so forward three days difference more in every 400 years to come , unless our year shall be reformed as well as theirs . CHAP. II. Of the Cycle of the Moon , what it is , how placed in the Calendar , and to what purpose . THat the Civil Year in use with us and all Christians , doth consist of 365 days , and every fourth year of 366 , hath been already shewed , with the return of the Sunday Letter in 28 years . In which time the Moon doth finish her course in the Zodiack no less than twelve times , which twelve Moons , or 354 days , do fall short of the Sun's year , eleven days in every common year , and twelve in the Bissextile or Leap-year . And by Observation of Meton an Athenian , it was found out about 432 years before Christ , that the Moon in nineteen years did return to be in Conjunction with the Sun on the self same day , and this Circle of nineteen years is called the Cycle of the Moon , which being written in the Calendar against the day in every Moneth , in which the Moon did change , in Letters of Gold , was also called the Golden Number , or from the excellent use thereof , which was at first , only to find the New Moons in every Moneth for ever , but amongst Christians it serveth for another purpose also , even the finding of the time when the Feast of Easter is to be observed . The New Moons by this Number are thus found . In the first year of the Circle , or when the Golden Number is 1 , where the Number 1 was set in the Calendar in any Moneth , that day is New Moon , in the second Year where you find the golden Number 2 , in the third Year where you find the golden Number 3 , and so forward till the whole Circle be expired ; then you must begin with one again , and run through the whole Circle as before . 2. And the reason why the Calendar begins with the golden Number 3 , not 1 , is this . The Christians in Alexandria had used this Circle of the Moon two Years before the Nicene Council . And in the first of these Years the new Moon next to the Vernal Equinox was upon the 27th Day of the Egyptian month Phamenoth answering to the 23d of our March , against that Day therefore they placed the golden Number 1. And because there are 29 Days and a half from one new Moon to another , they made the distance between the new Moons to be interchangeably 29 and 30 Days , and so they placed the same golden Number against the 26 Day of Phurmuthi the Month following , and against the 26 Day of the Month Pachon and so forward , and upon this ground by the like progression was the golden Number set in the Roman Calendar ; and so the golden Number 1 by their example was set against March 23. April 21. Iune 19. Iuly 19. August 17. September 16. October 15. November 14. December . 13. But then because in the following Year the golden Number was 2. reckoning 30 Days from the 13th of December , the golden Number 2 was set to Innuary 12. February 10. March 12. April 10. May 10. Iune 8. Iuly 8. August 6. September 5. October 4. November 3. December . 2. From whence reckoning 13 Days as before , the golden Number 3 comes in course for the third Year to be set against the first of Ianuary . But that you may know how the golden Number comes to be distributed in the Calendar according to the form in which it now is , you must consider that in 19 Solar Years there are not only 228 Lunar Months or 12 times 19 Lunar Months but 235 for the 11 Days which the common Solar Year doth exceed the Lunar , do in 19 Years arise to 209 Days , out of which there may be appointed 7 Months , 6 whereof will contain 30 Days apiece , and one Month 29 days ; and these 7 Months are called Embolismical Months , because by a kind of injection or interposition they are reckoned in some of the 19 Years . And those Years in which they are reckoned are called Embolismical Years , to distinguish them from the common Years which always contain 354 Days , whereas 6 of these Embolismical Years do each of them contain 384 Days , and the seventh Embolismical Year in which the Month of 29 Days is reckoned , doth contain 383 Days . 3. The Embolismical Years in the Cycle of the Moon are properly these Seven . 3 , 6 , 9 , 11 , 14 , 17 , 19. because in the third Year 11 Days being thrice reckoned do amount to 33 Days , that is one Month of 30 Days and 3 Days over . Again in the sixth Year the 11 Days which the Solar exceed the Lunar , being thrice numbred , do amount to 33 Days . which with the 3 Days formerly reserved do make 36 Days , that is one Month of 30 Days and 6 Days over . Again in the Ninth Year there are also 33 Days , to which the 6 Days reserved being added , there will arise one Month more and 9 Days over . But in the Eleventh Year twice 11 Days being added to the 9 Days reserved , do make 31 Days , that is , one Month of 30 days and one day over , which being added to the supernumerary days in the fourteenth Year do make another Month of 30 Days and 4 Days over , and these being added to the supernumerary Days in the sevententh Year do make another Month of 30 and 7 Days over , and these 7 Days being added to the 22 supernumerary Days in the Ninteenth Year of the Moons Cycle do make another Month of 29 Days . 4. But because there are 6939 Days and 18 Hours in 19 Solar Years , that is , 4 Days 18 Hours more then in the common and Embolismical Lunar Years , in which the excess between the Lunar and the Solar Year is supposed to be no more then 11 Days in each Year , whereas in every fourth Year the excess is one Day more , that is , 12 Days , that is , in 16 Years 4 Days , and in the remaining 3 Years three fourths of a day more . And that the new Moons after 19 Lunar Years or 235 Lunations do not return to the same days again , but want almost 5 days , it is evident that the civil Lunations do not agree with the Astronomical and that there must be yet some kind of intercalation used . 5. Now therefore in distributing the golden Number throughout the Calendar . If the new Moons should interchangeably consist of 30 and 29 days , and so but 228 Lunations in 19 Years ; we might proceed in the same order in which we have begun , and by which as hath been shewed the third Year of the Golden Number falls upon the Calends of Ianuary . But for as much as there are first six Lunations of 30 days apiece and one of 29 days to be interposed , therefore there must be 6 times 2 Lunations together consisting of 30 days and once three Lunations of 29 days . And that respect may be also had to the Bissextile days , although they are not exprest in the Calendar , that Lunation which doth contain the Bissertile day , if it should have been 29 days , it must be 30 , if it should have consisted of 30 days it must consist of 31. 6. And because it was thought convenient , as hath been shewed , to begin with the third Year of the Cycle of the Moon , because the Golden Number 3 is set to the Calends of Ianuary , therefore in this Cycle the Embolismical Years are , 2 , 5 , 8 , 11 , 13 , 16 , 19. But yet that it may appear , that these Years are in effect the same , as if we had begun with the first Year of the Golden Number , save only that the eighth Year instead of the ninth is to be accounted Embolismical , I have added the Table follwing , in which it is apparent that the former Embolismical years do agree with these last mentioned . 7. But as I said before , it was thought more convenient to begin the account from the number 3 set to the Calends of Ianuary , because by so reckoning 30 and 29 days to each Lunation interchangeably , the same Number 3 falls upon Ianuary 31. March 1 , and 31. April 29. May 29. Iune 27. Iuly 27. August 25. September 14. October 23. November 22. December 21. As if the Lunar years were compleated upon the 20 of December there remain just 11 Days , which the Solar years doth exceed the Lunar . 8. And by ranking on and accounting 4 for the Golden Number of the next year , you will find it set on Ianuary 20 , February 18 , March 20 , April 18 , May 18 , Iune 16 , Iuly 16 , August 14 , September 13 , Octob. 12 , Novemb . 11 , Decemb. 10. Cycle of the Moon . Cycle of the Moon . Embolismical Years . Number of Days . 1 3   354 2 4   354 3 5 Embol . 384 4 6   354 5 7   354 6 8 Embol . 384 7 9   354 8 10   354 9 11 Embol . 384 10 12   354         11 13 Embol . 384 12 14   354 13 15   354 14 16 Embol . 384 15 17   354 16 18   354 17 19 Embol . 384 18 1   354 19 2 Embol . 384 9. But in going on , and taking 5 for the Golden Number in the third year , we must remember that that is an Embolismical Year , and therefore that somewhere there must be 2 Months together of 30 days . And for this reason the Golden Number 5 , is set to Ianuary 9 , February 7 , March 9 , April 7 , May 7 , Iune 5 , Iuly 5 , August 3 , September 2 , as also upon the second day of October , and not upon the first , that so there may be 2 Lunations together of 30 , and the same Number 5 is also set to the thirty first of October , to make the Lunation to consist of 29 days , and to the thirtieth of November instead of the twenty ninth , that so a Lunation of 30 may again succeed as it ought . 10. In like manner in the sixth Year , having gone through the fourth and fifth as common years , you may see the Golden Number 8 set to the fifth of April , which should have been upon the fourth , and in the ninth Year the Golden Number 11 is set to the second of February which should have been upon the first . And there is a particular reason , for which these numbers are otherwise placed from the eighth of March to the fifth of April , namely , that all the paschal Lunations may consist of 29 days : For thus from the eighth of March to the sixth of April , to both which days the Golden Number is 16 , there are but 29 days . And from the ninth of March to the seventh of April , to both which days the Golden Number is 5 , there are also 29 days , and so of the rest till you come to the fifth of April , which is the last Paschal Lunation , as the eighth of March is the first , but at any other time of the Year , the length of the Month in the Embolismical Year , may be fixed as you please . 12. And in this manner in the 17 years , in which the lunations of the whole Circle are finished , and in which the Golden Number is 19 , the Month of Iuly is taken at pleasure , to the thirtieth day whereof is set the Golden Number 19 , which should have been upon the thirty first , and the same Number being notwithstanding placed upon the twenty eighth of August , that by the two Lunations of 29 days together , it might be understood , that the seventh Embolismical Month consisting of 29 days is there inserted , instead of a Month of 30 days . In which place the Embolismical or leaping Year of the Moon may plainly be observed for that year is one day less than the rest , which the Moon doth as it were pass over . The which one day is again added to the 29 days of the last Month , that we may by that means come , as in other Years , to the Golden Number , which sheweth the New Moon in Ianuary following . And for this reason the Epact then doth not consist of 11 but of 12 days . And thus you see the reason , for which the Golden Numbers are thus set in the Calendar as here you see . In which we may also observe , that every following Number is made by adding 8 to the Number preceding , and every preceding Number is also made by adding 11 to the Number next following , and casting away 19 when the addition shall exceed it . For Example , if you add 8 to the Golden Number 3 set against the first of Ianuary , it maketh 11 , to which add 8 more and it maketh 19 , to which adding 8 it maketh 27 , from which substracting 19 the remainer is 8 , to which again adding 8 , the sum is 19 , to which adding 8 the sum is 24 , from which deducting 19 the remainer is 5 , and so of the rest . In like manner receding backward , to the 5 add 11 they make 16 , to the 16 add 11 they make 27 , from which deducting 19 the remainer is 8 , to which 11 being added the same is 19 , to which 11 being added the sum is 30 , from which deducting 19 the remainer is 11 , to which 11 being added the sum is 22 , from which deducting 19 the remainer is 3. And by this we may see that every following number will be in use 8 years after the preceding , and every preceding Number will be in use 11 years after the following , that is , the same will return to be in use after 8 Years and 11 , and the other after 11 Years and 8 , or once in 19 years . CHAP. III. Of the Vse of the Golden Number in finding the Feast of Easter . THe Cycle of the Moon or Golden Number is a circle of 19 years , as hath been said already , which being distributed in the Calendar as hath been shewn in the last Chapter , doth shew the day of the New Moon for ever ; though not exactly : But the use for which it was chiefly intended , was to find the Paschal New Moons , that is , those new Moons on which the Feast of Easter and other moveable Feasts depend . To this purpose we must remember , 1. That the vernal Equinox is supposed to be fixed to the twenty first day of March. 2. That the fourteenth day of the Moon on which the Feast of Easter doth depend , can never happen before the Equinox ; though it may fall upon it or upon the day following . 3. That the Feast of Easter is never observed upon the fourteenth day of the Moon , but upon the Sunday following ; so that if the fourteenth day of the Moon be Sunday , the Sunday following is Easter day . 4. That the Feast of Easter may fall upon the fifteenth day of the Moon , or upon any other day unto the twenty first , inclusively . 5. That the Paschal Sunday is discovered by the proper and Dominical Letter for every Year The which may be found as hath been already declared , or by the proper Table for that purpose . Hence it followeth , 1. That the New Moon immediately preceding the Feast of Easter , cannot be before the eighth day of March , for if you suppose it to be upon March 6 , the Moon will be 14 days old March 19 , which is before the Equinox , contrary to the second Rule before given , and upon the seventh day of March there is no Golden Number fixed ; and therefore the Golden Number 16 , which standeth against March 8 , is the first by which the Paschal New Moon may be discovered . 2. It followeth hence , That the last Paschal New Moon cannot happen beyond the fifth day of April , because all the 19 Golden Numbers are expressed from the eighth of March to that day . And if a New Moon should happen upon the sixth of April , there would be two Paschal New Moons that year , one upon the eighth of March and another upon the sixth of April , the same Golden Number 16 being proper to them both , but this is absurd because Easter cannot be observed twice in one year . 3. It followeth hence , That the Feast of Easter can never happen before the twenty second day of March , nor after the twenty fifth day of April : For if the first New Moon be upon the eighth of March , and that the Feast of Easter must be upon the Sunday following the fourteenth day of the Moon ; it is plain that the fourteenth day of the Moon must be March 21 at the soonest : So that supposing the next day to be Sunday , Easter cannot not be before March the twenty second . And because the fourteenth day of the last Moon falleth upon the eighteenth day of April , if that day be Saturday , and the Dominical Letter D , Easter shall be upon the nineteenth day , but if it be Sunday , Easter cannot be till the twenty fifth . 4. It followeth hence , That although there are but 19 days , on which the fourteenth day of the Moon can happen , as there are but 19 Golden Numbers , yet there are 35 days from the twenty second of March to the twenty fifth of April , on which the Feast of Easter may happen , because there is no day within those Limits , but may be the Sunday following the fourteenth day of the Moon . And although the Feast of Easter can never happen upon March 22 , but when the fourteenth day of the Moon is upon the twenty first , and the Sunday Letter D , nor upon the twenty fifth of April , but when the fourteenth day of the Moon is upon April 18 , and the Dominical Letter C. Yet Easter may fall upon March 23 , not only when the fourteenth day of the Moon is upon the twenty second day which is Saturday , but also if it fall upon the twenty first which is Friday . In like manner Easter may fall upon April 24 , not only when the fourteenth day of the Moon is upon the eighteenth day which is Monday , but also if it happen upon the seventeenth being Sunday . And for the same reason it may fall oftner upon other days that are further distant from the said twenty second of March and twenty fifth of April . 5. It followeth hence , That the Feast of Easter may be easily found in any Year propounded : For the Golden Number in any Year being given , if you look the same between the eighth of March and fifth of April both inclusively , and reckon 14 days from that day , which answereth to the Golden Number given , where your account doth end is the fourteenth day of the Moon : Then consider which is the Dominical Letter for that Year , and that which followeth next after the fourteenth day of the Moon is Easter day . Example , In the year 1674 the Golden Number is 3 , and the Sunday Letter D , which being sought in the Calendar between the aforesaid limits , the fourteenth day of the Moon is upon April the thirteenth , and the D next following is April 19. And therefore Easter day that Year is April 19. Otherwise thus . In March after the first C , Look the Prime wherever it be , The third Sunday after Easter day shall be . And if the Prime on Sunday be , Reckon that for one of the Three . 6. Thus the Feast of Easter may be found in the Calendar , and from thence a brief Table shewing the same , may be extracted in this manner . Write in one Column the several Golden Numbers in the Calendar from the eighth of March to the fifth of April , in the same order observing the same distance . In the second Column set the Dominical Letters in number 35 so disposed , as that no Dominical Letter may stand against the Golden Number 16 , but setting the Letter D against the Golden Number 5 , write the rest in this order . E , F , G , A , B , &c. and when you come to the Golden Number 8 , set the Letter C , and there continue the Letters till you come to C again , because when the Golden Number is 16 , which in the Calendar is set to the eighth day of March , is new Moon , and the fourteenth day of that Moon doth fall upon the twenty first , to which the Dominical Letter is C , upon which the Feast of Easter cannot happen ; and therefore in the third Column containing the day in which the Feast of Easter is to be observed , is also void . But in the next place immediately following , to wit , against the letter D is set March 22 , because if the fourteenth day of the Moon shall fall upon the twenty first of March being Saturday , the next day being Sunday , shall be the Feast of Easter . To the Letters following , E , F , G , A , B , &c. are set 23 , 24 , 25 , and so orderly to the last of March , and so forward till you come to the twenty fifth of April , by which Table thus made , the Feast of Easter may be found until the Calendar shall be reformed . For having found the Golden Number in the first Column , the Dominical Letter for the Year next after it , doth shew the Feast of Easter , as in the former Example , the Golden Number is 3 and the Dominicall Letter D , therefore Easter day is upon April 19. The other moveable Feasts are thus found . Advent Sunday is always the nearest Sunday to St. Andrews , whether before or after . Septuagesima Sunday is Nine Weeks before Easter . Sexagesima Sunday is Eight Weeks before Easter . Qainquagesima Sunday is Seven Weeks before Easter . Quadragesima Sunday is Six Weeks before Easter . Rogation Sunday is five Weeks after Easter . Ascension day is Forty Days after Easter . Whitsunday is Seven Weeks after Easter . Trinity Sunday is Eight Weeks after Easter . G. N. D. L. Easter . XVI     V D 22 March   E 23 XIII F 24 II G 25   A 26 X B 27   C 28 XVIII D 29 VII E 30   F 31 XV G 1 April IV A 2   B 3 XII C 4 I D 5   E 6 IX F 7   G 8 XVII A 9 VI B 10   C 11 XIV D 12 III E 13   F 14 XI G 15   A 16 XIX B 17 VIII C 18   D 19   E 20   F 21   G 22   A 23   B 24   C 25 CHAP. IV. Of the Reformation of the Calendar by Pope Gregory the Thirteenth ; and substituting a Cycle of Epacts in the room of the Golden Number . HItherto we have spoken of the Calendar which is in use with us , we will now shew you for what reasons it is alter'd in the Church of Rome , and how the Feast of Easter is by them observed . The Year by the appointment of Iulius Caesar consisting of 365 days 6 hours , whereas the Sun doth finish his course in the Zodiack , in 365 days 5 hours 49 minutes or thereabouts , it cometh to pass that in 134 Years or less , there is a whole day in the Calendar more than there ought ; in 268 years 2 days more ; in 4002 years 3 days : and so since Iulius Caesar's time the vernal Equinox hath gone backward 13 or 14 days , namely from the 24 of March to the tenth . Now because the Equinox was at the time of the Nicene Council upon the twenty first of March , when the time for the observing of Easter was first universally established , they thought it sufficient to bring the Equinox back to that time , by cutting off 10 days in the Calendar as hath been declared , and to prevent any anticipation for the time to come , have appointed , that the Leap-year shall be thrice omitted in every 400 Years to come , and for memory sake , appointed the first omission to be accounted from the Year 1600 , not from 1582 , in which the reformation was made , because it was not only near the time , in which the emendation was begun , but also because the Equinox has not fully made an anticipation of 10 days from the place thereof , at the time of the Nicene Council , which was March 21. The Years then 1700 , 1800 , 1900 , which should have been Bissextile Years , are to he accounted common years , but the Year 2000 must be a Bissextile : In like manner the Years 2100 , 2200 , 2300 , shall be common years , and the Year 2400 Bissextile , and so forward . 2. Again , because it was supposed that the Cycle of the Moon , or Golden Number was so fixed , that the new and full Moons would in every 19 years return to the same days again ; whereas their not returning the same hours , but making an anticipation of one hour 27 minutes or thereabouts , it must needs be that in 17 Cycles or little more than 300 Years , there would be an anticipation of a whole day . And hence it is evident that in 1300 Years since the Nicene Council , the New and Full Moons do happen more than 4 days sooner than the Cycle of the Moon or Golden Number doth demonstrate : Whence also it comes to pass , that the fourteenth day of the Moon by the Cycle is in truth the eighteenth day , and so the Feast of Easter should be observed not from the fifteenth day of the Moon to the twenty first , but from the nineteenth to the twenty fifth . 3. That the Moon therefore being once brought into order , might not make any anticipation for the time to come , it is appointed that a Cycle of 30 Epacts should be placed in the Calendar instead of the Golden Number , answering to every day in the Year ; to shew the New Moons in these days , not only for 300 Years or thereabouts , but that there might be new Epacts without altering the Calendar , to perform the same thing upon other days as need shall require . 4. For the better understanding whereof , to the Calendar in use with us , we have annexed the Gregorian Calendar also : In the first Column whereof you have 30 numbers from 1 to 30 , save only that in the place of 30 you have this Asterisk * , But they begin with the Calends of Ianuary , and we continued and repeated after a Retrograde order in this manner , * 29 , 28 , 27 , &c. and that for this cause especially , that the number being given which sheweth the New Moons in every Month for one Year , you might by numbring 11 upwards exclusively find the number which will shew the New Moons the Year following , to wit , the Number which falleth in the eleventh place . 5. And these Numbers are called Epacts , because they do in order shew those 11 days , which are yearly to be added to the Lunar Year consisting of 354 days , that it may be in conformity with the Solar Year consisting of 365 days . To this purpose , as hath been said concerning the Golden Number , these Epacts being repeated 12 times , and ending upon the twentieth day of December , the same Numbers must be added to the 11 remaining days , which were added to the first 11 days in the Month of Ianuary . 6. And because 12 times 30 do make 360 , whereas from the first of Ianuary to the twentieth of December inclusively , there are but 354 days , you must know that to gain the other six days , the numbers 25 and 24 are in every other Month both placed against one day , namely , to February 5 , April 5 , Iune 3 , August 1 , September 29 , and November 27. But why these two Numbers are chosen rather then any other , and why in these 6 Months the number 25 is sometimes writ to XVI , sometimes to XXV in a common character , and why the number 19 is set to the last day of December in a common Character , shall be declared hereafter . 7. Here only note that this Asterisk * is set instead of the Epact 30 , because the Epact shewing the Number of days which do remain after the Lunation in the Month of December , it may sometimes fall out that 2 Lunations may so end , that the one may require 30 for the Epact , and the other 0 , which would , if both were written , cause some inconveniences , and therefore this * Asterisk is there set , that it might indifferently serve to both . And the Epact 29 is therefore set to the second day of Ianuary , because after the compleat Lunation in the second of December there are 29 days , and for the like reason the Epact 28 is set against the third of Ianuary , because after the compleat Lunation in the third of December there are then 28 days over , and so the rest in order till you come to the thirtieth of Ianuary , where you find the Epact 1. because after the compleat Lunation on the thirtieth day there is only one day over . 8. And besides the shewing of the New Moons in every Month , which is and may be done by the Golden Number , the Epacts have this advantage , that they may be perpetual and keep the same place in the Calendar in all future ages , which can hardly be effected with the Golden Number , for in little more then 700 years , the New Moons do make an anticipation of one day , and then it will be necessary to set the Golden Number one degree backward , and so the Golden Number which at the time of the Nicene Council was set to the first of Ianuary , should in 300 years be set to the last of December , and so of the rest , but the Epacts being once fixed shall not need any such retraction or commutation . For as often as the New Moons do change their day either by Anticipation or by Suppression of the Bissextile year , you shall not need to do any more than to take another rank of 19 Epacts , insteed of those which were before in use . For instance , the Epacts which are and have been in use in the Church of Rome since the year of reformation 1582 , and will continue till the year 1700 , are these 10 following 1. 12. 23. 4. 15. 26. 7. 18. 29. 10. 21. 2. 13. 24. 5. 16. 27. 8. 19. And from the year 1700 the Epacts which will be in use are these . * 11. 22. 3. 14. 25. 6. 17. 28. 9. 20. 1. 12. 23. 4. 15. 26. 7. 18. and shall continue not only to the year 1800 , but from thence until the year 1900 also ; and although in the year 1800 the Bissextile is to be suppressed , yet is there a compensation for that Suppression , by the Moons Anticipation . To make this a little more plain , the motion of the Moon , which doth occasion the change of the Epact , must be more fully considered . CHAP. V. Of the Moons mean Motion , and how the Anticipation of the New Moons may be discovered by the Epacts . THe Moon according to her middle motion doth finish her course in the Zodiack in 29 days , 12 hours 44 minutes , three seconds or thereabout , and therefore a common Lunar year doth consist of 354 days , 8 hours , 48 minutes , 38 seconds and some few thirds , but an Embolismical year doth consist of 383 days , 21 hours , 32 minutes , 41 seconds and somewhat more ; and therefore in 19 years it doth exceed the motion of the Sun 1 hour , 27 minutes , 33 seconds feré . 2. Hence it cometh to pass , that although the New Moons do after 19 years return to the same days ; yet is there an Anticipation of 1 hour , 27 minutes , 33 seconds . And in twice 19 years , that is , in 38 years , there is an Anticipation of 2 hours , 55 minutes , 6 seconds , and after 312 years and a half , there is an Anticipation of one whole day and some few Minutes . And therefore after 312 years no new Moon can happen upon the same day it did 19 years before , but a day sooner . Hence it comes to pass that in the Julian Calendar , in which no regard is had to this Anticipation , the New Moons found out by the Golden Number must needs be erroneous , and from the time of the Nicene Council 4 days after the New Moons by a regular Computation . 3. And hence it follows also , that if the Golden Number , after 312 were upon due consideration removed a day forwarder or nearer the beginning of the Months , they would shew the New Moons for 312 years to come . And being again removed after those years , a day more would by the like reason do the same again . But it was thought more convenient so to dispose 30 Epacts , that they keeping their constant places , 19 of them should perform the work of the Golden Number , until by this means there should be an Anticipation of one day . And when such an Anticipation should happen , those 19 Epacts being let alone , other 19 should be used , which do belong to the preceding day , without making any alteration in the Calendar . 4. And if this Anticipation would do the whole work , nothing were more plain , then to make that commutation of the 19 Epact once in 312 years : but because the detraction of the Bissextile days doth variously interpose and cause the 19 Epacts sometimes to be changed into these that do precede , sometimes into these that follow , sometimes into neither , but to continue still the same ; therefore some Tables are to be made , by which we may know , when the commutation was to be made and into what Epacts . 4. First therefore there was made a Table called Tabula Epactarum Expansa , in this manner . First on the top were placed the 19 Golden Numbers in order , beginning with the Number 3 , which in the old Calendar is placed against the Calends of Ianuary , and under every one of these Golden Numbers there are placed 30 Epacts all constituted from the lowest number in the first rank in which the Epact is 1 , and in that first rank the Golden Number is 3 , the rest from thence towards the right Hand are made by the constant addition of it , and the casting away of 30 , as often as they shall exceed that number , only when you come to the 27 , the Epact under the Golden Number 19 , there must be added 12 instead of 11 , that so the Epact following may be 9 not 8 , for the Reasons already given in this Discourse concerning the Golden Number and Embolismical years . And this rank being thus made , the other Epacts are disposed in their natural order ascending upwards , and the number once again resumed after the Epact 30 or rather this Asterisk * set in the place thereof : only observe that under the Golden Number 12. 13. 14. 15. 16. 17. 18. 19. in the place of XX there is yet 25 in the common Character . And to the Epacts under the Golden Number 19 , 12 must still be added to make that Epact under the Golden Number 1. As was said before concerning the lowest Rank . 5. And on the left hand of these Epacts before those under the Golden Number 3. are set 30 Letters of the Alphabet , 19 in a small Character , and 11 in a great , in which some are passed by , for no other reason save only this , that their similitude with some of the small Letters , should not occasion any mistake in their use , which shall be shewed in its place . 6. Besides this Table there was another Table made which is called Tabula AEquationis Epactarum , in which there is a series of years , in which the Moon , by reason of her mentioned anticipation doth need AEquation , and in which the number of Epacts signed with the letters of the Alphabet , are to be changed ; being otherwise AEquated where it needeth , by the suppression of the Bissextile days . 7. But it supposeth , that it was convenient to suppress the Bissextiles once only in 100 years ; and the Moon to be aequated , or as far as concerns her self , the rank of Epacts to be changed , once only in 300 years , and the 12 years and a half more , to be referred till after the years 2400 , they do amount unto 100 years , and then an aequation to be made : but then it must be made by reason of the interposing this hundred not in the three hundredth but the hundredth year . Moreover this aequation is to be made as in referece to the Moon only , because as the suppression of the Bissextiles intervene , the order of changing the ranks of Epacts is varied , as shall be shewed hereafter . 8. Again this Table supposeth , that seeing the New Moon at the time of the Nicene Council was upon the Calends of Ianuary , the golden Number 3 being there placed , that it would have been the same if the Epact * had been set to the same Calends , that is if the Epacts had been then in use . And therefore at that time the highest or last rank of Epacts was to be used , whose Index is P , and then after 300 years , the lowest or first rank should succeed , whose Index is a , ( for the letters return in a Circle ) and after 300 years more , the following rank whose Index is b and so forward ; but that it is conceived , that the New Moon in the Calends of Ianuary , is more agreeable to the year of Christ 500 , than the time of the Nicene Councel ; and therefore as if the rank of Epacts under the letter l were sutable to the year 500 , it seemed good to make use of that rank under the letter a in the year of Christ 800 , and those under the letter b , in the year 1100 , and those under the letter e in the year 1400. 9. Which being granted , because in the year 1582 , ten days were cut off from the Calendar , we must run backward , or in an inverted order count 10 series , designed , suppose , by the letters b. a. P. N. M. H. G. F. E. D. so that from the year 1582 the series of Epacts whose literal Index is D , is to be used , and this is that rank of Epacts which is now used in the Church of Rome . 10. And therefore as if this Table had its beginning from that year ; the first number in the second column is 1582 , and then in order under it . 1600. 1700. 1800. 1900. 2000. &c. And in the third Column every fourth hundred year is marked for a Bissextile , that is , 1600. 2400. 2800 , &c. and in the fourth Column to every three hundreth ▪ Year is set this Character C , to shew in what year the Moon by her Anticipation of one day , doth need aequation ; but in the year 1800 the double character is set CC , to signify that then another hundred years are gotten by the 12 years and a half reserved , besides and above the other 300 years ; and this character is also set to the years 4300. 6800 , and for the same reason . But in the first Column , or on the left hand of these years are placed the Letters or Indices of those ranks of Epacts in the former Table , which are to be used in those years and when the Letters are charged . Thus against the year 1600 the Letter D is continued , to shew that from that year , to the year 1700 the rank of Epacts is still to be used , which do belong to that Letter . And for as much as the Letter C is set to the year 1700 , it sheweth that that rank of Epacts is then to be used , which do belong thereto , and so of the rest . 11. The reason why these Letters in the first Column are sometimes changed in 100 years , sometimes in 200 , sometimes not in less then 300 Years , and that they are sometimes taken forward , sometimes backward , according to the order of the Alphabet , is because the suppression of the Bissextiles do intervene with the lunar aequation : for if the Bissextile were only to be suppressed , in these 300 or sometimes 400 years , in which the Moon needeth aequation , the rank of Epacts in that case would need no commutation , but would continue the same for ever ; and the golden Number would have been sufficient , if the suppression of the Bissextile , and anticipation of the Moon , did by a perpetual compensation cause the new Moons still to return to the same days : but because the Bissextile is ofttimes suppressed , when the Moon hath no aequation , the Moon hath sometimes an aequation when the Bissextile is not suppressed , sometimes also both are to be done and sometimes neither ; all which varieties may yet be reduced to these three Rules . 1. As often as the Bissextile is suppressed without any aequation of the Moon , then the letter which served to that time shall be changed to the next below it contrary to the order of the Alphabet . And the new Moons shall be removed one day towards the end of the Year . 2. As often as the Moon needeth aequation , without suppression of the Bissextile , then the Letter which was in use to that time shall be changed to the next above it according to the order of the Alphabet , that the New Moons may again return one day towards the beginning of the year . 3. As often as there is a Suppression and an aequation both , or when there is neither , the Letter is not changed at all but that which served for the former Centenary , shall also continue in the succeeding ; because the compensation so made , the New Moons do neither go forward nor backward , but happen in the compass of the same days . 1. And this is enough to shew for what reason the letters are so placed in the Table , as there you see them : for in the year 1600 the Bissextile being neither suppressed , nor the Moon aequated , the letter D used in the former Centenary or in the latter part thereof from the year 1582 , is still the same . In the year 1700 , because there is a suppression , but no aequation , the commutation is made to the Letter C descending . In the Year 1800 , because there is both a suppression and an aequation , the same letter C doth still continue . In the Year 2400 , because there is an aequation and no suppression , there is an ascension to the Letter A. And thus you see not only the construction of this Table , but how it may be continued to any other Year , as long as the World shall last . 12. And by these two Tables we may easily know which rank of the 30 Epacts doth belong to , or is proper for any particular age : for as in our age , that is , from the Year 1600 to the Year 1700 exclusively , that series is proper whose Index is D. Namely , 23 , 4 , 15 , 26 , &c. so in the two Ages following , that is , from the Year 1700 to the Year 1900 exclusively , that series is proper whose Index is C , namely these , 22 , 3 , 14 , 25. and in the three ages following thence , that is from the Year 1900 to the Year 2100 exclusively , that series is proper whose Index is B , namely these , 21 , 2 , 13 , 24 , &c. And so for any other . Hence also it may be known , which of the 19 doth belong to any particular Year , for which no more is necessary , than only to know the Golden Number for the year given , which being sought in the head of the Table , and the Index of that Age in the side , the common Angle , or meeting of these two , will shew you the Epact desired : As in the year 1674 the Golden Number is 3 and the Index D ; therefore in the common Angle I find 23 for the Epact that year , and sheweth the New Moons in every Month thereof . And here it will not be unseasonable to give the reason , for which the Epact 25 not XXV is written under the Golden Numbers 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19. namely , because the ranks of Epacts , which under these greater Numbers hath this Epact 25 , hath also XXIV , it would follow that in these Ages in which any of these Ranks were in use , the New Moon in 19 years will happen twice upon the same days ; in those six Months in which the Epacts XXV and XXIV are set to the same day : Whereas the New Moons do not happen on the same day till 19 years be gone about . To avoid this inconvenience , the Epact 25 not XXV is set under these great numbers , and the Epact 25 is in the Calendar , in these Months set with the Epact XXVI , but in the other Months with the Epact XXV . 14. Hence it cometh to pass , 1. That in these Years the Epacts 25 and XXIV do never meet on the same day . 2. That there is no danger that the Epacts 25 and XXVI should in these 6 Months cause the same inconvenience , seeing that the Epacts 25 and XXVI are never both found in the same Rank . 3. That the Epact 25 may in other Months without inconvenience be set to the same day with the Epact XXVI , because in these there is no danger of their meeting with the Epact XXIV on the same days . 4. That there is no fear that the Epacts XXV and XXIV being set on the same days , should in future Ages cause the same inconvenience , because the Epacts XXV and XXIV are not found together in any of the other Ranks . But that either one or both of them are wanting . Besides , when one of these Epacts is in use , the other is not , and that only which is in use is proper to the day . As in this our Age until the Year 1700 the Epacts in use are those in the rank whose Index is D. In which these two XXIV and XXV are not both found . And in the two following Ages , because the rank of Epacts in use is that whose Index is C , in which there is the Epact XXV , not XXIV , the New Moons are shewed by the Epact XXV not by XXIV . But because in three following Ages , the rank of Epacts in use is that whose Index is B , in which 25 and XXIV are both found , the New Moons are shewed by the Epact XXIV when the golden Number is 6. And by the Epact 25 when the golden Number is 17 , and not by the Epact XXV . 15. And if it be asked why the Epact 19 in the common Character is set with the Epact XX against the last day of December ; know that for the reasons before declared , the last Embolismical Month within the space of 19 years , ought to be but 29 days and not 30 , as the rest are ; and therefore when the Epact 19 doth concur with the golden Number 19 , the last Month or last Lunation beginning the second of December , shall end upon the 30 and not upon the 31 of that Month , and the New Moon should be supposed to happen upon the 31 under the same Epact 19 , that 12 being added to 19 and not 11 , you may have one for the Epact of the year following , which may be found upon the 30 of Ianuary , as if the Lunation of 30 days had been accomplished the Day before . CHAP. VI. How to find the Dominical Letter and Feast of Easter according to the Gregorian account . HAving shewed for what reason , and in what manner the Epacts are substituted in the place of the golden Number , and how the New Moons may be by them found in the Calendar for ever ; I shall now shew you how to find the Feast of Easter and the other moveable Feasts according to the Gregorian or new account ; and to this purpose I must first shew you how to find the Dominical Letter , for that the Cycle of 28 years will not serve the turn , because of the suppression of the Bissextile once in a hundred years , but doth require 7 Cycles of 28 years apeice . The first whereof begins with CB , and endeth in D. The second begins with DC , and endeth in E. The third begins with ED , and endeth in F &c. The first of these Cycles began to be in use 1582 , in which year the dominical Letter according to the Julian account was G , but upon the fifteenth day of October , that Year was changed to C : for the fifth of October being Friday and then called the fifteenth , the Letter A became Friday , B Saturday , and C Sunday , the remaining part of the year , in which the Cycle of the Sun was 23 , and the second after the Bissextile or leap Year , and so making C , which answereth to the fifteenth year of that Circle , to be 23 , the Circle will end at D ; and consequently CB , which in the old account doth belong to the 21 year of the Circle , hath ever since been called the first , and so shall continue until the year 1700 , in which the Bissextile being suppressed , the next Cycle will begin with DC as hath been said already . Under the first rank or order of Dominical Letters are written the years 1582 and 1600 , under the second 1700 , under the third 1800 , under the fourth 1900 and 2000 , under the fifth 2100 , under the sixth 2200 and under the seventh 2300 and 2400. And again under the first Order , 2500 , under the second 2600 , under the third 2700 and 2800 , and so forward as far as you please , always observing the same order , that the 100 Bissextile years may still be joyned with the not Bissextile immediately preceding . 1. And hence it appears , that the seven orders of Dominical Letters , are so many Tables , successively serving all future Generations . For as the first Order serveth from the year 1582 and 1600 to the year 1700 exclusively , and the second Order from thence to the year 1800 exclusively , so shall all the rest in like manner which here are set down , and to be set down at pleasure . And hence the Dominical Letter or Letters may be found for any year propounded , as if it were required to find the dominical Letter for the year 1674 , because the year given is contained in the centenary 1600. I find the Cycle of the Sun by the Rule already given to be 3. In the first order against the number 3 , I find G for the Sunday Letter of that year , in like manner because the year 1750 is contained under the Centenary 1700 , the Cycle of the Sun being 27 , I find in the second rank the Letter D answering to that Number , and that is the Dominical Letter for that year , and so of the rest . 3. Again for as much as the fifth Order is the same with that Table , which serves for the old account , therefore that order will serve the turn for ever where that Calendar is in use , and so this last will be of perpetual use to both the Calendars . 4. Now then to find the time in which the Feast of Easter is to be observed , there is but little to be added to that which hath been already said concerning the Julian Calendar . For the Paschal Limits are the same in both , the difference is only in the Epacts , which here are used instead of the golden Number . 5. For the terms of the Paschal New Moons are always the eighth of March and the fifth of April : but whereas there are 11 days within these Limits to which no golden Number is affixed , there is now one day to which an Epact is not appointed , because there is no day within those Limits , on which in process of time a New Moon may not happen . And the reason for which the two Epacts XXV and XXIV are both set to the fifth of April , is first general , which was shewed before , namly that by doing the same in 5 other Months , the 12 time 30 Epacts might be contracted to the Limits of the lunar Year which consists of 354 days : but there is a particular reason also for it , that the Antients having appointed that all the Paschal lunations should consist of 29 days , it was necessary that some two of the Epacts should be set to one of these days in which the Paschal lunation might happen , the Epacts being 30 in number . And it was thought convenient to choose the last day , to which the Epact XXV belonging , the Epact XXIV should also be set ; and hence by imitation it comes to pass , that these and not other Epacts are set to that day in other Months , in which two Epacts are to be set to the same days . 6. The use of these Epacts in finding the Feast of Easter , is the same with that which hath been shewed concerning the golden Numbers . For the Epact and the Sunday Letter for that year propounded being given , the Feast of Easter may be found in the Calendar after the same manner . Thus in the year 1674 , the Epact is 23 and the Sunday Letter G , and therefore reckoning fourteen days from the eighth of March to which the Epact is set , the Sunday following is March 25 , which is the day on which the Feast of Easter is observed . 7. And hence as hath been shewed in the third Chapter concerning the Julian Calendar , a brief table may be made to shew the feast of Easter and the other moveable Feasts for ever , in which there is no other difference , save only that the Epacts as they are in this new Calendar , are to be used as the golden Numbers are , which stand in the old Calendar . And a Table having the golden Numbers of the old Calendar set in one Column , and the Epacts as they are in the new Calendar set in another , will indifferently shew the movable Feasts in both accounts , as in the Year 1674 , the golden Number is 3 and the Sunday Letter according to the Julian account is D , according to the Gregorian G , and the Epact 23 , and therefore according to this Table our Easter is April 19 , and the other , to wit , the Gregorian , is March 25. The like may be done for any other year past or to come . CHAP. VII . How to reduce Sexagenary numbers into Decimal , and the Contrary . EVery Circle hath antiently , and is yet generally supposed to be divided into 300 degrees , each degree into 60 Minutes , each Minute into 60 Seconds , and so forward as far as need shall require . But this partition is somewhat troublesom in Addition and Subtraction , much more in Multiplication and Division ; and the Tables hitherto contrived to ease that manner of computation , do scarce sufficiently perform the work , for which they are intended . And although the Canon published by the learned H. Gellibrand , in which the Division of the Circle into 360 degrees is retained , but every degree is divided into 100 parts , is much better than the old Sexagenary Canon , yet some are of opinion , that if the Antients had divided the whole circle into 100 or 1000 parts , it would have proved much better then either ; only they think Custome such a Tyrant , that the alteration of it now will not be perhaps so advantagious ; leaving them therefore to injoy their own opinions , they will not I hope be offended if others be of another mind : for their sakes therefore , that do rather like the Decimal way of calculation ▪ Having made a Canon of artificial Signs and Tangents for the degrees and parts of a Circle divided into 100 parts , I shall here also shew you , how to reduce sexagenary Numbers into Decimal , and the contrary , as well in time as motion . 2. The parts of a Circle consisting of 360 degrees , may be reduced into the parts of a circle divided into 100 degrees or parts , by the rule of Three in this manner . As 360 is to 100 , so is any other Number of degrees , in the one , to the correspondent degrees and parts in the other . But if the sexagenary degrees have Minutes and Seconds joyned with them , you must reduce the whole Circle as well as the parts propounded into the least Denomination , and so proceed according to the rule given . Example . Let it be required to convert 125 degrees of the Sexagenary Circle , into their correspondent parts in the Decimal . I say , as 360 is to 100 , so is 125 to 34 , 722222 , &c. that is , 34 degrees and 722222 Parts . 2. Example . Let the Decimal of 238 degrees 47 Minutes be required . In a whole Circle there are 21600 Minutes , and in 238 degrees , there are 14280 Minutes , to which 47 being added the sum is 14327. Now then I say if 21600 give 100 , what shall 14327. The Answ. is 66 , 3287 &c. In like manner if it were required to convert the Hours and Minutes of a Day into decimal Parts , say thus , if 24 Hours give 100 , what shall any other number of Hours give . Thus if the Decimal of 18 hours were required , the answer would be 75 , and the Decimal answering to 16 Hours 30 Minutes is 68 , 75. But if it be required to convert the Decimal Parts of a Circle into its correspondent Parts in Sexagenary . The proportion is ; as 100 is to the Decimal given , so is 360 to the Sexagenary degrees and parts required . Example . Let the Decimal given be 349 722222 , if you multiply this Number given by 360 , the Product will be 1249999992 , that is cutting off 7 Figures , 124 degrees and 9999992 parts of a degree . If Minutes be required , multiply the Decimal parts by 60 , and from the product cut off as many Figures , as were in the Decimal parts given , the rest shall be the Minutes desired . But to avoid this trouble , I have here exhibited two Tables , the one for converting sexagenary degrees and Minutes into Decimals , and the contrary . The other for converting Hours and Minutes into Decimals , and the contrary . The use of which Tables I will explain by example . Let it be required to convert 258 degrees 34′ . 47″ , into the parts of a Circle decimally divided . The Table for this purpose doth consist of two Leaves , the first Leaf is divided into 21 Columns , of which the 1. 3. 5. 7. 9. 11. 13. 15. 17. 19 doth contain the degrees in a sexagenary Circle , the 2. 4. 6. 8. 10. 12. 14. 16. 18 and 20 doth contain the degrees of a Circle Decimally divided , answering to the former , and the last Column doth contain the Decimal parts , to be annexed to the Decimal degrees . Thus the Decimal degrees answering to 26 Sexagenary are 7 , and the parts in the last Column are 22222222 and therefore the degrees and parts answering to 26 Sexagenary degrees are 7. 22222222. In like manner the Decimal of 62 degrees , 17. 22222222. And the Decimal of 258 degrees , 34′ . 47″ , is thus found . The Decimal of 258 degrees is 71.66666666 The Decimal of 34 Minutes is .15747040 The Decimal of 47 seconds is .00362652 Their Sum 71.82776358 is the Decimal of 258 degrees , 34′ . 47″ as was required . In like mauner the Decimal of any Hours and Minutes may be found by the Table for that purpose . Example . Let the Decimal of 7 Hours 28′ be required . The Decimal answering to 7h . is 29.16666667 The Decimal of 28 Minutes is 1.94444444 The Sum 31.11111111 is the Decimal Sought . To find the degrees and Minutes in a sexagenary Circle , answering to the degrees and parts of a Circle Decimally divided , is but the contrary work . As if it were required to find the Degrees and minutes answering to this decimal 71. 02776359 , the Degrees or Integers being sought in the 2. 4. 6 or 8 Columns &c. of the first Leaf of that Table , right against 71. I find 256 and in the last Column these parts 11111111 , which being less than the Decimal given , I proceed till I come to 6666667 , which being the nearest to my number given , I find against these parts under 71. Degrees 258 , so then 258 are the degrees answering to the Decimal given and , To find the Minutes and Seconds from 71.82776359 I Substract the number in the Table 71.66666667 The remainer is 16109692 which being Sought in the next Leaf under the title Minutes , the next leaf is 11747640 And the Minutes 34 , and this number being Subtracted the remainer is 00362652 Which is the Decimal of 47 seconds , and so the degrees and Minutes answering to the Decimal given are 258 degrees 34′ and 47″ , the like may be done for any other . CHAP. VIII . Of the difference of Meridiens . HAving in the first part shewed how the places of the Planets in the Zodiack may be found by observation , and how to reduce the time of an observation made in one Country , to the correspondent time in another , as to the day of the Month , by considering the several measures of the year in several Nations , there is yet onething wanting , which is , by an observation made of a Planets place in one Country to find when the Planet is in that place in reference to another ; as suppose the ☉ by observation was found at Vraniburg to be in ♈ . 3d. 13′ . 14″ . March the fourteenth 1583 at what time was the Sun in the same place at London ? To resolve this and the like questions , the Longitude of places from some certain Meridian must be known ; to which purpose I have here exhibited a Table shewing the difference of Meridians in Hours and Minutes , of most of the eminent places in England from the City of London , and of some places beyond the Seas also . The use whereof is either to reduce the time given under the Meridian of London to some other Meridian , or the time given in some other Meridian to the Meridian of London . 1. If it be required to reduce the time given under the Meridian of London to some other Meridian , seek the place desired in the Catalogue , and the difference of time there found , either add to or subtract from the times given at London , according as the Titles of Addition or Subtraction shew , so will the time be reduced to the Meridian of the other place as was required . Example . The same place at London was in the first Point of ♉ , 6 Hours P. M. and it is required to reduce the same to the Meridian of Vraniburg I therefore seek in Vraniburg in the Catalogue of places , against which I find 50′ with the Letter A annexed , therefore I conclude , that the Sun was that day at Vraniburg in the first point of ♉ , 6 Hours 50′ . P. M. 2. If the time given be under some other Meridian , and it be required to reduce the same to the Meridian of London , you must seek the place given in the Catalogue , and the difference of time there found , contrary to the Title is to be added or subtracted from the time there given . Example . Suppose the place of the Sun had been at Vraniburg , at 6 Hours 50′ . P. M. and I would reduce the same to the Meridian of London ; against Vraniburg as before I find 50′ A. therefore contrary to the Title I Subtract 50′ and the remainder 6 Hours is the time of the Suns place in the Meridian of London . CHAP. IX . Of the Theory of the Sun 's or Earth's Motion . IN the first part of this Treatise we have spoken of the primary Motion of the Planets and Stars , as they are wheeled about in their diurnal motion from East to West , but here we are to shew their own proper motions in their several Orbs from West to East , which we call their second motions . 1. And these Orbs are supposed to be Elliptical , as the ingenious Repler , by the help of Tycho's accurate observations , hath demonstrated in the Motions of Mars and Mercury , and may therefore be conceived to be the Figure in which the rest do move . 2. Here then we are to consider what an Ellipsis is , how it may be drawn , and by what Method the motions of the Planets according to that Figure may be computed . 3. What an Ellipsis is Apollonius Pergaeus in Conicis , Claudius Mydorgius and others have well defined and explained , but here I think it sufficient to tell the Reader , that it is a long Circle , or a circular Line drawn within or without a long Square ; or a circular Line drawn between two Circles of different Diameters . 4. The usual and Mechanical way of drawing this Ellipsis is thus ; first draw a line to that length which you would have the greatest Diameter to be , as the Line AP in Figure 8 , and from the middle of this Line at X , set off with your compasses the Equal distance XM and XH . 5. Then take a piece of thred of the same length with the Diameter AP and fasten one end thereof in the point M and the other in the point H , and with your Pen extend the thred thus fastened to the point A , and from thence towards P keeping the thread stiff upon your Pen , draw a line from A by B to P , the line so drawn shall be half an Ellipsis , and in like manner you may draw the other half from P by D to A. In which because the whole thred is equal to the Diameter AP. therefore the two Lines made by thred in drawing of the Ellipsis , must in every point of the said Ellipsis be also equal to the same Diameter AP. They that desire a demonstration thereof geometrically , may consult Apollonius Pergaeus , Claudius Mydorgius or others , in their treatises of Conical Sections , this is sufficient for our present purpose , and from the equality of these two Lines with the Diameter , a brief Method of calculation of the Planets place in an Ellipsis , is thus Demonstrated by Dr. Ward now Bishop of Salisbury . 6. In this Ellipsis H denotes the place of the Suns Center , to which the true motion of the Planet is referred , M the other Focus whereunto the equal or middle motion is numbred , A the Aphelion where the Planet is farthest distant from the Sun and slowest in motion , P the Perihelion where the Planet is nearest the Sun and slowest in motion . In the points A and P the Line of the mean and true motion do convene , and therefore in either of these places the Planet is from P in aequality , but in all other points the mean and true motion differ , and in D and C is the greatest elliptick AEquation . 8. Now suppose the Planet in B , the line of the middle motion according to this Figure is MB , the line of the true motion HB . The mean Anomaly AMB. The Eliptick aequation or Prosthaphaeresis MBH , which in this Example subtracted from AMB , the remainer AHB is the true Anomaly . And here note that in the right lined Triangle MBH , the side MH is always the same , being the distance of the Foci , the other two sides MB and HB are together equal to AP. Now then if you continue the side MB till BE be equal to BH and draw the line HE , in the right lined Triangle MEH , we have given ME = AD and MH with the Angle EMH , to find the Angles MEH and MHE which in this case are equal , because EB = BH by Contraction , and therefore the double of BEH or BHE = MBH , which is the Angle required . And that which yet remaineth to be done , is the finding the place of the Aphelion , the true Excentricity or distance of the umbilique points , and the stating of the Planets middle motion . CHAP. X. Of the finding of the Suns Apogeon , quantity of Excentricity aend middle motion . THe place of the Suns Apogaeon and quantity of Excentricity may from the observations of our countrey man Mr. Edward Wright be obtained in this manner , in the years 1596 , and 1497 , the Suns entrance into ♈ and ♎ and into the midst of ♉ . ♌ . ♍ . and ♒ were as in the Table following expressed .   1596 1597     D. H. M. D. H. M.   Ianuary . 25. 00.07 24. 05.54 ♒ . 15 March. 9. 18.43 10. 00.37 ♈ . 0 April . 24. 21.47 25. 03.54 ♉ . 15 Iuly . 28. 01.43 28. 09.56 ♌ . 15 September . 12. 13.48 12. 19.15 ♎ . 0 October . 27. 15.23 27. 21.50 ♍ . 15 And hence the Suns continuance in the Northern Semicircle from ♈ to ♎ in the year 1596 being Leap year , was thus found .   d. h. From the 1. of Ianuary to ☉ Entrance ♎ . 256. 13. 48. From the 1. of Iun to ☉ Entrance ♈ 69. 18.43 Their difference . 186. 19.05 In the year 1597 from the 1 of Ianuary to the time of the ☉ Entrance into ♎ . 255. 19.15 To the ☉ entrance into ♈ . 69. 09.37 Their difference is 186. 18.38 And the difference of the Suns continuance in these Arks in the year 1596 and 1597 is 27′ . and therefore the mean time of his continuance in those Arks is days 186. hours 18. minutes 51. seconds 30. And by consequence his continuance in the Southern Semicircle that is from ♎ to ♈ is 178 days . 11 hours , 8 minutes and 30 seconds . In like manner in the year 1596 between his entrance into ♉ 15. and ♍ 15 , there are days 185. 17.36 And in the year 1597 there are days 185. 17.56 And to find the middle motion answering to days 186. hours 18. Minutes 51. seconds 30 I say . As 365 days , 6 hours , the length of the Julian , year is to 360 , the degrees in a Circle . So is 186 days , 18 hours , 51′ . 30″ to 184 degrees . 03′ . 56″ . In like manner the mean motion answering to 185 days , 17 h. 46′ is 183 degrees , 02′ . 09 . Apparent motion from ♈ to ♎ 180. 00.00 Middle motion 184. 03.56 Their Sum 364. 03.56 Half Sum is the Arch. SME 182. 01.58 In 1596 from 15 ♒ to 15 ♌ there are days 185 , hours 01 , minutes 36. In 1597. days 135. hours 4. 02′ . And the mean motion answering thereunto is . 182 d. 30′ . 36″ . Apparent motion from 15 ♉ to 15 ♍ . 180. Middle motion 185. 17. 56. 181. 04.53 Half Sum is 183. 32. 26 From 15 ♒ to 15 ♌ Days . 185. 04 h. 02′ Apparent motion 180. Middle motion 182. 30. 36 Half Sum 181. 15. 18 Now then in Fig. from PGC. 181. 32. 26 deduct NKD 180 , the Remainer is DC+NP . 1. 32. 26. Therefore DC or NP. 46. 13 , whose Sine is HA. And from XPG. 181. 15. 18 deduct TNK 180 , the Remainer is KG+TX 1. 15. 18. Therefore KG or TX 37. 39 , whose Sine is HR . Now then to find the Apogaeon . As HA 46′ . 13″ 5.12851105 To Rad. So HR 37′ . 39″ 15.03948202 To Tang. HAR. 39 d. 10′.04″ 9.91097097 GAM . 45 Apogaeon 95. 49. 56. Hence to find the excentricity AR. As the Sine HAR. 39. 10.04 9.80043756 To Rad. So HR . 37.39 15.03948202 To RA. 1733.99 5.23904446 Or thus , In the Triangle 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 we have given 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . As 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . 37.39 5.03948202 To Rad. So 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . 46. 13. 15.12851105 To Tang. R 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . 50. 49.56 10.08902903 PAS . 45. Apogaeon 95 deg . 49′ . 56″ . as before . Then for the Excentricity RA. As the Sine of R 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . 50. 49. 56 9.88945938 Is to 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . 46′ . 13″ 5.12851105 So is Radius . To RA. 1734.01 5.23905167 And this agreeth with the excentricity , used by Mr. Street in his Astron. Carolina , Pag. 23. But Mr. Wing as well by observation in former ages , as our own , in his Astron. Instaur . Pag. 39. doth find it to be 1788 or 1791. The work by both observations as followeth . 2. And first in the time of Ptolemy , Anno Christi 139 by comparing many observations together , he sets down for the measure nearest truth , the interval between the vernal Equinox and the Tropick of Cancer to be days 93. hours 23. and minutes 03. And from the Vernal to the Autumnal Equinox , days 186. hours 13. and minutes 5.   D. The apparent motion from ♈ to ♎ 90. 36.00 Middle motion for 93 d. 23 h. 3′ . is 92. 36.42 The half Sum is GP 91. 18.21 Apparent motion from ♈ to ♎ 180. 00.00 Middle motion for 186 d. 13 h. 5′ . is 183. 52.03 The half Sum is GEK 181. 56.02 The half of GEK is GE. 90. 58.01 And GP less GE is 00. 20.20 Whos 's Sum is AC 59146.   Again from GEK 181. 56. 02. deduct the Semicircle FED 180. the remainer is the summ DK and FG. 1. 56. 2. and therefore DK = FG. 58′ . 01″ . whose sign is BC. 168755. L is the place of the Aphelion , and AB the Excentricity . Now then in the Triangle ABC . in the Fig. 6 we have given the two sides AC and BC. To find the Angle BAC and the Hypotenuse AB . For which the proportions are . As the side AC . 59146 4.77192538 Is to the Radius . 10.00000000 So is the side BC ▪ 168755 5.22725665 To Tang. BAC . 70. 41. 10. 10.45533127 Secondly for AB . As the Sine of BAC . 70. 41. 10. 9.97484352 Is to the side AB . 168755. 5.22725665 So is the Radius . 10.00000000 To the Hypot . AB . 1788. 10. 5.25241313 Therefore the Aphelion at that time was in II 10. 41. 10. And the excentricity . 1788. 3. Again Anno Christi 1652 the Suns place by observation was found to be as followeth . April . 24. hours . 10. ♉ . 15 October . 27. hours . 7. 10′ ♍ . 15 Ianuary . 24. hours . 11 . 20′ ♒ . 15 Iuly . 27. hours . 16.30 , ♌ . 15 Hence it appeareth that the Sun is running through one Semicircle of the Ecliptick , that is from ♉ 15 to ♍ 15. 185 days 21 hours and 10′ . And through the other Semicircle from ♒ 15 to ♌ 15 , days 184. hours 5. therefore the Suns mean motion , according to the practice in the last example , from ♉ 15 to ♍ 15 is 181. 30. 26. and from ♒ 15 to ♌ 15. 181. 16. 30. Now then in Fig. 7. if we subtract the semicircle of the Orb KMH . 180. from WPV 181. 36. 26. the remainer is the sum of KW and HV 1. 36. 26. the Sine of half thereof 48′ . 13″ is equal to AC . 140252. Again the mean motion of the Sun in his Orb from ♒ 15 to ♉ 15 is the Arch SKP. 181. 16. 30. whose excess above the Semicircle being bisected is 38. 15. whos 's Sine CB. 111345. now then in the Triangle ABC to find the Angle BAC , the proportion is . As the side AC . 140252 5.14690906 Is to the Radius . 10.00000000 So is the Side CB 111345 5.04667072 To Tang. BAC . 38. 36. 21 , 9.89966166 Which being deducted out of the Angle . 69 A ♌ . 45 it leaveth the Angle 69 AL 6. 33. 39. the place of the ☉ Aphelion sought , and this is the quantity which we retain . And for the excentricity BC. As the Sum of BAC . 38. 26. 21 9.79356702 Is to the Radius . 10.00000000 So is the side BC 111345 5.04667072 To the Hypot . AB . 179103 5.25310370 So then Anno Christi . 1652. Aphel . 96. 33.39 Anno Christi . 139. the Aphelion 70. 41.10 Their difference is 25. 52.29 And the difference of time is 1513 Julian years . Hence to find the motion of the Aphelion for 2. years , say I , if 1513 years give 25. 52.29 , what shall one year give , and the answer is 00 d. 01′ 01″ . 33‴ . 56 iv . 44v. that is in Decimal numbers . 0. 00475. 04447. 0555. And the motion for . 1651 years . 7. 84298. 4208862 , which being deducted from the place of the Aphelion Anno Christi . 1652 — 26. 82245. 3703703. The remainer , viz. 18. 97946. 9494841 is the place thereof in the beginning of the Christian AEra , which being reduced is , 68 deg . 19. min. 33. sec. 56. thirds . 4. The Earths middle motion , Aphelion and Excentricity being thus found , we will now shew how the same may be stated to any particular time desired , and this must be done by help of the Sun or Earths place taken by observation . In the 178 year then from the death of Alexander , Mechir the 27 at 11 hours P. M. Hipparcus found in the Meridian of Alexand. that the Sun entered ♈ 0. the which Vernal Equinox happened in the Meridian of London according to Mr. Wings computation at 9 hours 14′ , and the Suns Aphelion then may thus be found . The motion of the Aphelion for one year , was before found to be . 0. 00475. 04447. 0555. therefore the motion thereof for one day is 0. 00001. 501491722. The Christian AEra began in the 4713 year compleat of the Julian Period , in which there are days 1721423. The AEra Alexandri began November the twelfth , in the year 4390 of the Julian Period , in which there are 1603397 days . And from the death of Alexander to the 27 of Mechir 178 , there are days 64781 , therefore from the beginning of the Julian Period , to the 178 year of the AEra Alexandri , there are days 1668178 which being deducted from the days in the Christian AEra , 1721423 , the remainer is 53245 , the number of days between the 178 year after the death of Alexander , Mechir 27 , and the beginning of the Christian AEra . Or thus . From the AEra Alexandri to the AEra Christi there are 323 Julian years , and 51 days , that is 118026 days . And from the AEra Alexandri to the time of the observation , there are 64781 days , which being deducted from the former , the remainer is 53245 as before . Now then if you multiply the motion of the Aphelion for one day , viz. 0. 00001. 3014917 by 53245 , the product is 0. 69297. 9255665 , which being deducted from the place of the Aphelion in the beginning of the Christian AEra , before found . 18. 97946. 9494841. the remainer 18. 28649. 0239176 is the place of the Aphelion at the time of the observation , that is in Sexagenary numbers . deg . 65. 49′ . 53″ . 5. The place of the Aphelion at the time of the observation being thus found to be deg . 65. 49′ . 53″ . The Suns mean Longitude at that time , may be thus computed . In Fig. 8. In the Triangle EMH we have given the side ME 200000 , the side MH 3576 , the double excentricity before found , and the Angle EMH 114. 10′ . 07″ . the complement of the Aphelion to a Semicircle , to find the Angle MEH , for which the proportion is , As the Summ of the sides , is to the difference of the sides , so is the Tangent of the half Summ of the opposite Angles , to the Tangent of half their difference . The side ME. 200000.   The side MH 3576.   Z. Of the sides . 203576. Co. ar . 4.69127343 X. Of the sides . 196424. 5.29321855 Tang. ½ Z Angles . 32′ . 54′ . 56. 9.91111512 Tang. ½ X Angles . 31. 59. 21.   Angle MEH . 0. 55. 35. 9.79560710 The double whereof is the Angle MBH 1. 51. 10. which being Subtracted from 360 the remainer 358. 08. 50. is the estimate middle motion of the Sun , from which subtracting the Aphelion before found , 65. 49. 53. the remainer 292. 18. 57. is the mean Anomaly by which the absolute AEquation may be found according to the former operation . Z. ME+MH . 203576. Co. ar . 4.69127343 X. ME-MH . 196424 5.29321855 Tang. ½ Anom . 56. 09. 28. 10.17359517 Tang. ½ X. 55. 12. 18. 10.15808715 Differ . 00. 57. 10.   Doubled 1. 54. 20 , which added to the middle motion before found gives the ☉ true place ♈ . 00. 3′ . 10″ , which exceeds the observation 3′ . 10″ . therefore I deduct the same from the middle motion before found , and the remainer 358. 05. 50. is the middle motion at the time of the observation of Hipparchus , to which if you add the middle motion of the Sun for 53245 days , or for 323 AEgyptian years 131 days , 280. 46. 08′ the Summ , rejecting the whole Circles , is 278. 51. 48 the Suns mean Longitude in the beginning of the Christian AEra . 6. But one observation is not sufficient , whereby to state the middle motion for any desired Epocha , we will therefore examine the same by another observation made by Albategnius at Aracta in the year of Christ 882 , March : 15. hours 22. 21. but in the Meridian of London at 18 hours . 58′ . The motion of the Aphelion for 881 years , 74 days is 3. 806068653737 , which being added to the place thereof in the beginning of the Christian AEra , the place at the time of the observation will be found to be 22. 785538148578 , that is reduced , Deg. 82. 01′ . 40″ . And hence the AEquation according to the former operations is Deg. 2. 01′ . 16″ which being deducted from a whole Circle , the remainer 357 d. 58′ . 44″ is the estimate middle motion at that time , from which deducting the Aphelion deg . 82. 01. 40. the remainer 275. 57. 04 is the mean anomaly , and the AEquation answering thereto is deg . 2. 02′ . 18″ which being added to the middle motion before found , gives the ☉ place ♈ . 00. 01′ . 02″ which exceeds the observation 01′ . 02″ . therefore deduct the same from the middle motion before found , the remainer 357. 57′ . 22″ is the middle motion of the ☉ at the time of the observation , from which deducting the middle motion for 881 years , 74 days , 18 hours , 58 minutes , viz. 80d. 06′ . 10″ . the remainer 277 deg . 51′ . 12″ . is the ☉ mean Longitude in the beginning of the Christian AEra . By the first observation it is deg . 278. 51′ . 48″ By the second 277. 51. 12 Their difference is 1. 00. 36 He that desires the same to this or any other Epocha , to more exactness , must take the pains to compare the Collection thereof from sundry Observations , with one another , this is sufficient to shew how it is to be found . Here therefore I will only add the measures set down by some of our own Nation , and leave it to the Readers choice to make use of that which pleaseth him best . The ☉ mean Longitude in the beginning of the Christian AEra according to . Vincent Wing is 9. 8d. 00′ . 31″ Tho. Street is 9. 7. 55. 56 Iohn Flamsted is 9. 7. 54. 39 By our first Computation 9. 8. 51. 48 By our second 9. 7. 51. 12 In the Ensuing Tables of the ☉ mean Longitude , we have made use of that measure given by Mr. Flamsted , a little pains will fit the Tables to any other measure . CHAP. XI . Of the quantity of the Tropical and Sydereal Year . THe year Natural or Tropical ( so called from the Greek word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , ( which signifies to turn ) because the year doth still turn or return into it self ) is that part of time in which the ☉ doth finish his course in the Zodiack by coming to the same point from whence it began . 2. That we may determine the true quantity thereof , we must first find the time of the ☉ Ingress into the AEquinoctial Points , about which there is no small difference amongst Astronomers , and therefore an absolute exactness is not to be expected , it is well that we are arrived so near the Truth as we are . Leaving it therefore to the scrutiny of after Ages , to make and compare sundry Observations of the ☉ entrance into the AEquinoctial Points , it shall suffice to shew here how the quantity of the Tropical year may be determined , from these following observations . 3. Albategnius , Anno Christi 882 observed the ☉ entrance into the Autumnal AEquinox at Aracta in Syria to be Sept. 19. 1 hour 15′ in the Morning . But according to Mr. Wings correction in his Astron. Instaur . Page 44 , it was at 1 hour 43′ in the Morning , and therefore according to the ☉ middle motion , the mean time of this Autumnal AEquinox was Sept. 16. 12 h. 14′ . 25″ . that is at London at 8 h. 54′ . 25″ . 4. Again by sundry observations made in the year 1650. the second from Bissextile as that of Albategnius was , the true time of the ☉ ingress into ♎ was found to be Sept. 12. 14 h. 40′ . and therefore his ingress according to his middle motion was Sept. 10. 13 h. 02. 5. Now the interval of these two observations is the time of 768 years , in which space by subtracting the lesser from the greater , I find an anticipation of 5 days , 9 hours , 52′ . 25″ . which divided by 768 giveth in the quotient 10′ . 55″ . 39 which being subtracted for 365 days , 6 hours , the quantity of the Julian year , the true quantity of the Tropical year will be 365 days , 5 hours , 49′ . 04″ . 21‴ . Others from other observations have found it somewhat less , our worthy countryman Mr. Edward Wright takes it to be 365 d. 5 hours . 48′ . Mr. Iohn Flamsted , 5 h. 29′ . Mr. Tho. Street 5 h. 49′ . 01″ . taking therefore the Tropical year to consist of 365 days , 5 hours , 49 Minutes , the Suns mean motion for one day is 0 deg . 59′ . 8″ . 19‴ . 43 iv . 47 v. 21 vi . 29 vii . 23 viii . or in decimal Numbers , the whole Circle being divided into 100 degrees , the ☉ daily motion is 0. 27379. 08048. 11873. 6. The Sydereal or Starry year is found from the Solar by adding the Annual Motion of the eighth Orb or praecession of the AEquinoctial Points thereunto , that praecession being first converted into time . 7. Now the motion of the fixed Stars is found to be about 50″ . in a years time , as Mr. Wing hath collected from the several observations of Timocharis , Hipparchus , Tycho and others ; and to shew the manner of this Collection , I will mention onely two , one in the time of Timocharis , and another in the time of Tycho . 8. Timocharis then as Ptolemy hath it in his Almagist , sets down the Virgins Spike more northwardly than the AEquinoctial , 1 deg . 24′ . the time of this observation is supposed to be about 291 years before Christ , the Latitude 1 deg . 59′ South , and therefore the place of the Star was in ♍ . 21 d. 59′ . And by the observation of Tycho 1601 current , it was in ♎ 18. 16′ . and therefore the motion in one year 50″ , which being divided by 365 days , 6 hours , the quotient is the motion thereof in a days time . 00′ . 8‴ . 12 iv . 48 v. 47 vi . 18 vii . 30 viii . 13 ix . and in decimal Numbers , the motion for a year is 00385. 80246. 91358. The motion for a day . 00001. 05626. 95938. 9. Now the time in which the Sun moveth 50″ , is 20′ . 17″ . 28‴ , therefore the length of the sydereal year is 365 days , 6 hours , 9′ . 17″ . 28‴ . And the Suns mean motion for a day 59′ . 8″ . 19‴ . 43 iv . 47 v. 21 vi . 29 vii . 23 viii . converted into time is 00. 03′ . 56″ . 33‴ . 18 iv . 55 v. 9 vi . 23 vii . 57 viii . which being added to the AEquinoctial day , 24 hours , giveth the mean solar day , 24 hours . 3. ′ 56″ . 33‴ . 18 iv . 55. 9. 23. 57. 10. And the daily motion of the fixed Stars , being converted into time is 32 iv . 51 v. 15 vi . 9 vii . 14 viii . 24 ix . and therefore the AEquinoctial day being 24 hours , the sydereal day is 24 hours , 00′ . 00″ . 00‴ . 32 iv . 51. 15. 9. 14 24. 11. Hence to find the praecession of the AEquinoctial Points , or Longitude of any fixed Star , you must add or subtract the motion thereof , from the time of the observation , to the time given , to or from the place given by observation , and you have your desire . Example . The place of the first Star in Aries found by Tycho in the year 1601 current , was in ♈ . 27 d. 37′ . 00. and I would know the place thereof in the beginning of the Christian AEra . The motion of the fixed Stars for 1600 years , 22 d. 13′ . 20″ Which being deducted from the place found by observ . 27. 37. 00 The remainer . 5. 231. 40 is the place thereof in the beginning of the Christian AEra . 12. Having thus found the ☉ middle motion , the motion of the Aphelion and fixed Stars , with their places , in the beginning of the Christian AEra ; we will now set down the numbers here exhibited AEra Christi . Mr. Wing from the like observations , takes the ☉ motion to be as followeth . The ☉ mean Longitude 9. 8. 00. 31 Place of Aphelion 2. 8. 20. 03 The Anomaly 06. 29. 40. 28 The which in decimal Numbers are The ☉ mean Longitude 77. 22460. 86419 Place of the Aphelion 18. 98171. 29629 The Anomaly 58. 24289. 56790 The mean motions for one year . The ☉ mean Longitude 99. 93364. 37563. 34 The Aphelion 00. 00475. 04447. 05 The ☉ mean Anomaly 99. 92889. 33116. 29 The ☉ mean motions for one day . The ☉ mean Longitude 00. 27379. 08048. 11 The Aphelion 00. 00001. 30149. 17 The mean Anomaly 00. 27377. 77898. 94 And according to these measures are the Tables made shewing the ☉ mean Longitude and Anomaly , for Years , Months , Days and Hours . CHAP. XII . The Suns mean motions otherwise stated . SOme there are in our present age , that will not allow the Aphelion to have any motion , or alteration , but what proceeds from the motion of the fixed Stars , the which as hath been shewed , do move 50 seconds in a year , and hence the place of the first Star in Aries , in the beginning of the Christian AEra was found to be ♈ . 5. 23d. 40. Now then , if from the place of the Aphelion Anno Christi . 1652 as was shewed in the tenth Chapter , deg . 96. 33′ . 39. we deduct the motion of the fixed Stars for that time . 28. 19. 12. the remainer 68. 14. 27 is the constant place of the Aphelion ; but Mr. Street in his Astronomia Carolina Page 23 , makes the constant place of the Aphelion to be 68d. 20. 00 , and the ☉ excentricity 1732. The place of the Sun observed ♈ . 0. 33. 19 The praecession of AEquinox 0. 27. 27. 22 The Earths Sydereal Longitude 5. 03. 05. 57 The place of the Aphelion Subtract 8. 08. 20. 00 The Earths true Anomaly 8. 24. 45. 57 AEquation Subtract 1. 58. 47 The remainer is the Estimate M. Anom . 8. 22. 47. 10 AEquation answering thereto add . 1. 58. 27 The Earths true Anomaly 8. 24. 45. 37 The place of the Aphelion 8. 08. 20. 00 Praecession of the AEquinox 0. 27. 27. 22 Place of the Sun ♈ . 00. 32. 59 But the place by observation ♈ . 00. 33. 19 The difference is 001. 001. 20 Which being added to the mean Anom . 8. 22. 47. 10 The mean Anomaly is 8. 22. 47. 30 The absolute AEquation 1. 58. 27 The true Anomaly 8. 24. 45. 57 Agreeing with observation .   And so the mean Anomaly AEra Christi is 6. 23. 19. 56. But Mr. Flamsted according to whose measure the ensuing Tables are composed , takes the mean Anomaly AEra Christi . to be 6. 24. 07. 091. The place of the Aphelion to be 8 , 08. 23. 50. And so the Praecession of the AEquinox and Aphelion in the beginning of the Christian AEra . 8 , 13. 47. 30. in decimal Numbers . AEra Christi . The Suns mean Anomaly 56. 69976. 85185 The Suns Apogaeon and Praec . AEq. 20. 49768. 51851 The ☉ mean motions for one Year . The ☉ mean Longitude 99. 93364. 37563. 34 The Praecession of AEquin . 00385. 80246. 91 The ☉ mean Anomal . 99. 92978. 57316. 43 The ☉ mean Motions for one Day . The ☉ mean Longitude 00. 27379. 08048. 11 The Praecession of AEqui . 00. 00001. 05699. 30 The ☉ mean Anom . 00. 27378. 02348. 81 CHAP. XIII . How to Calculate the Suns true place by either of the Tables of middle motion . VVRite out the Epocha next before the given time , and severally under that set the motions belonging to the years , months and days compleat , to the hours , scruples , current every one under his like ( only remember that in the Bissextile years after the end of Frebruary the days must be increased by an unite ) then adding all together , the sum shall be the ☉ mean motion for the time given . Example . Let the given time be Anno Christi 1672. February 23. hours 11. 34′ . 54″ . by the Tables of the ☉ mean Longitude and Anomaly , the numbers are as followeth .     M. Longitud . M. Anomal . The Epocha 1660 80. 67440. 53.79815 Years 11 99. 81766. 99.76526 Ianuary   08. 48751. 08.48711 Day . 23 06. 29718. 06.29688 Hours 11 00. 12548. 00.12548   34 00. 00646. 00.00646   54 00. 00017. 00.00017     95. 40886. 68.47951 By the Tables of the Suns mean Anomaly and praecession of the AEquinox , the numbers are these .     Anomaly . Praece . AEqui . The Epocha 1660 53. 76721. 26.90200 Years 11 99. 77520. 00.04243 Ianuary   8. 48718. 00032 Days 23 6. 29694. 00024 Hours 11 0. 12548. 26.94499   34′ .00646 . 68.45882   54″ .00035 . 95.40381 ☉ mean Anomaly   68.45882   There is no great difference between the ☉ mean Longitude and Anomaly found by the Tables of mean Longitude and Anomaly , and that found by the Tables of mean Anomaly and Precession of the AEquinox . The method of finding the Elliptical AEquation is the same in both , we will instance in the latter only , in which the ☉ mean Anomaly is Degrees 68. 45882. And the precession of AEquin . deg . 26. 94499. But because there is no Canon of Sines and Tangents as yet published , suitable to this division of the Circle into an 100 deg . or parts : We must first convert the ☉ mean Anomaly , and prec . of of the AEquin , given , into the degrees and parts of the common Circle : And this may be done either into degrees and decimal parts of a degree , or into deg . and minutes : if it were required to be done into degrees and minutes , the Table here exhibited for that purpose will serve the turn , but if it be required to be done into degrees and decimal parts , I judge the following method to be more convenient . Multiply the degrees and parts given by 36 , the Product , if you cut off one figure more towards the right hand than there are parts in the number given , shall be the degrees and parts of the common Circle . Anomaly . 68. 45882 Praec . AEquinox . 26. 94499 36   36 41075292   16166994 20537646   8983497 Anom . 246. 451752   Prae. AEq. 97. 001964 And if you multiply the parts of these Products , you will convert them into minutes . Otherwise thus . Multiply the degrees and parts given by 6 continually , the second Product , if you cut off one figure more towards the right hand than are parts in the number given , shall be the degrees and parts of the common Circle . The third Product of the parts only shall give minutes , the fourth seconds , and so forward as far as you please . Example . ☉ Mean Anom . 68. 45882 Praec . AEq. 26. 94499 6 6 41075292 16166994 246.451752 97.001964 6 6 27.10512 0.11784 6 6 6.3072 7.0704 And thus the mean Anom . is deg . 246. 451742 or 27′ . 06. The Prec . AEq. 97. 001964. or 00′ . 07″ . Hence to find the Elliptical AEquation in degrees and decimal parts : In Fig. 8. we have given in the right lined plain Triangle EMH , the sides ME , and MH , and the Angle EMH , 66. 451742. the excess of the mean Anomaly above a Semicircle , to find the Angle MEH . The side ME 200000 The side MH 3468 Zcru . 203468 Co. ar . 4.69150389 Xcru . 196532   5.29343327 t frac12 Zangle . 56.774129   10.18374097 t frac12 Xangle . 55.857087   10.16867813 MEH . 0. 917042 the double whereof is the Angle MBH . 1. 834084 or Elliptick AEquation sought , which being added to the mean Anomaly and praecession of the AEquinox , because the Anomaly is more than a Semicircle , the same is the Suns true place . The ☉ mean Anomaly 246.451742 The Praecession of the AEquinox 97.001964 Elliptick AEquation 1.834084 The Suns true place . 345.287790 But because the Elliptick AEquation thus found doth not so exactly agree to observation as is desired , Bullialdus in Chap. 3. of his Book entituled Astronomiae Philolaicae fundamenta clarius explicata , Printed at Paris , 1657. shews how to correct the same by an Angle applied to the Focus of middle motion , subtended by the part of the ordinate line , intercepted between the Ellipsis and the Circle circumscribing it . This Mr. Street maketh use of in his Astronomia Carolina , and this I thought not amiss to add here . XN . GX ∷ OB tang . OEB. OM tang . OEM. And the Angle OEM-OEB = BEM = ETY , the variation to be deducted from the Elliptick AEquation ETH , the Remainer is the absolute AEquation YTS in the first Quadrant . In the second and third Quadrants , the variation or difference between the mean and corrected Anomaly , must be added to the Elliptick AEquation , to find the true and absolute AEquation . For XN . XG . QV. tang . QEV. the comp . m. Anom . QR . t. QER. and the Angle VER = ECO is the variation , and ECO+ECH = OCH is the absolute AEquation sought in the second Quadrant . Again , XN . SG ∷ a D , tang . a ED. a b , tang . aEB . And aEB — aED = DEf the variation = EFO and EfO+EfH = OfH the absolute AEquation sought in the third Quadrant . Lastly , in the fourth Quadrant of mean Anomaly it is . XN . XG ∷ ch . tang . eEH. eg . tang . eFg. and hEg is the variation : And EFH — 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 = 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the absolute AEquation sought in the fourth Quadrant . And to find XN the conjugate Semi-diameter , in the right angled Triangle ENX , we have given , EN = AX and EX the semi-distance of the umbilick points . And Mr. Briggs in Chap. 19. of his Arithm. Logar . hath shewed , that the half Sum of the Logarith . of the sum and difference of the Hypotenuse , and the given leg . shall be the Logarith . of the other leg . Now then EN = AX. 100000     The Leg EX . 1734   Their Sum 101734 5.00745001 Their difference 98266 4.99240328   The Z of the Logarithms , 9.99985329   frac12 ; Z. Logarith . XN . 99983 4.99992664 Now then in the former Example the mean Anomaly is 246 deg . 451741. and the excess above a semicircle is the ang . aED . 66. 451742. Therefore . As XN . 99983 4.99992664 Is to XG . 100000 5.00000000 So is the tang . aED 66.451742 10.36069857 To the tang . aEB 66.455296 10.36077193 aEB — aED = DEf .003544 the variation , which being added to the Elliptick AEquation before found , the absolute AEquation is 1. 837628. and therefore the ☉ true place 345. 291334. that is X. 15. 17. 28. CHAP. XIV . To find the place of the fixed Stars . Example . Let the given time be 1500 , the difference of time is 100 years , and the motion of the fixed Stars for 100 years is 0. 38580. The place of the 1 * in ♈ , 1600 7.67129 Motion for 100 years subtract 0.38580 Place required in the year 1500 7.28549 2. Example . Let the time given be 1674. The place of the first Star in ♈ 1600 was 7.67129 Motion for 60 years is 0.23148 Motion for 14 years is 0.05401 Place required in the year 1674 compl . 7.95678 CHAP. XV. Of the Theory of the Moon , and the finding the place of her Apogaeon , quantity of excentricity and middle motion . THe Moon is a secondary Planet , moving about the Earth , as the Earth and other Planets do about the Sun , and so not only the Earth but the whole System of the Moon , is also carried about the Sun in a year . And hence , according to Hipparchus , there arises a twofold , but according to Tycho a three-fold Inequality in the Moons Motion . The first is Periodical and is to be obtained after the same manner , as was the excentrick AEquation of the Sun or Earth : in order whereunto , we will first shew how the place of her Apogaeon and excentricity may be found . At Bononia in Italy , whose Longitude is 13 degrees Eastward from the Meridian of London , Ricciolus and others observed the apparent times of the middle of three lunar Eclipses to be as followeth . The first 1642. April the 4. at 14 hours and 4 Minutes . The second 1642 , September 27 at 16 hours and 46 minutes . The third 1643. September 17 at 7 hours and 31 Minutes . The equal times reduced to the Meridian of London , with the places of the Sun in these three observations , according to Mr. Street in the 25 Page of his Astronomia Carolina , are thus . Anno Mens . D. h. d. 1642. April 4. 13. 37. ♈ . 25. 6. 54 1642. Septemb. 27. 15. 57 ♎ . 14. 50. 09 1643. Sehtemb . 17. 6. 46 ♎ 4. 20. 20 Hence the place of the Moon in the first observation is in ♎ 25. 6′ . 54. in the second ♈ 14. 50. 9. in the third ♓ 4. 20. 20. Now then in Fig. 10. let the Circle BHDGFE denote the Moons AEquant T the Center of the Earth , the Semidiameters TD , TE and TF the apparent places of the Moon , in the first , second and third observations , C the Center of the Excentrick , CD , CE and CF the Lines of middle motion . From the first observation to the second there are 176 d. 2 h. 20′ The true motion of the Moon is deg . 169. 43. 15″ The motion of the Apogaeon subtract 19. 37. 07 The motion of the true Anomaly is the arch DE 150. 06. 08 The motion of the mean Anomaly DCE 140. 42. 28 From the first observation to the third , there are 530 d. 17 h. 9. The true motion of the Moon is degrees 159. 13. 26 The motion of the Apogaeon subtract 159. 07. 32 The motion of the true Anomaly is the Arch DF 100. 05. 54 The motion of the mean Anomaly DCF 93. 46. 45 And deducting the Arch DGF from the Arch DFE , the remainer is the Arch FE 50. 00. 14 And deducting the Angle DCF from the Angle DCE , the remainer is the Angle FCE 46. 55. 43 Suppose 10.00000000 the Logarithm of DC , continue FC to H , and with the other right Lines compleat the Diagram . 1. In the Triangle DCH we have given the Angle DCH 86. 13. 15. the complement of DCF 93. 46. 45 to a Semicircle . The Angle DHC 50. 02. 57. The half of the Arch DF and the side CD 1000000. To find CH. As the Sine of DHC 50. 02. 57 9.88456640 To the Side DC , so the Sine of HDC 43. 43. 48. 19.83964197 To the Side CA 9.95507557 2 In the Triangle HCE we have given CH as before , the Angle CHE 25. 00. 07. The half of the Arch FE , the Angle HCE 133. 04. 17 the complement of FCE , and by consequence the Angle CEH 21. 55. 36 To find the Side CE. As the Sine of CEH 21. 55. 36 9.57219707 To the Side CH 19.95507557 So is the Sine of CHE 25. 00. 07 9.62597986 To the Sine CE 19.58105543 10.00885836 3. In the Triangle DCE , we have given DC . CE and the Angle DCE 140. 42. 28. whose complement 39. 17. 32 is the Summ of the Angles , to find the Angle CED and DE , As the greater Side CE 10.00885836 Is to the lesser Side DC 10.00000000 So is the Radius 10.00000000 To the tang . of 44. 24. 54 19.99114164 Which subtracted from 45. 2 the remainer is the half . Difference of the acute angles 35. 16.   As the Radius . To the tang . of the com . 35. 16 8.01109962 Is to the tang . of the frac12 ; Z. 19. 38. 46 9.55265735 To the tang . of frac12 ; X. 00. 12. 35 7.56375697 Their Sum 19. 51. 21. is the angle — CDE .   Their difference 19. 26. 11. is the angle CED .   As the Sine of CED . 19. 26. 11. 9.52216126 Is to the Sine of DCE . 140. 42. 28. 9.80159290 So is the Side EC . 10.00000000 To the Side DE. 10.27943164 4. In the Isosceles Triangle DTE we have given the Side DE , the angle DTE 150. 06. 08 whose complement 29. 53. 52 is the Summ of the other two angles , the half whereof is the angle TDE 14. 56. 56 which being subtracted from the angle CDE . 19. 51. 21 the remainer is the angle CDT . 4. 54. 25. As the Sine of DTE 150. 06. 08 Co. ar . 0.30237482 Is to the Sine of DET . 14. 56. 56 9.41154778 So is the Side DE 10.27943164 To the Side DT 9.99335424 5. In the Triangle CDT we have given DC . DT and the angle CDT , to find CTD and CT . As the Side DT 9.99335424 Is to the Side DC 10.00000000 So is the Rad. 10.00000000 To the tang . of 26. 18 10.00664576 Deduct 45. As the Radius . Is to the Sine of the remainer 0. 26. 18. 7.88368672 So is the tang . of the frac12 ; Z angle 87. 32. 57 11.36854996 To the tang . frac12 ; X angle 10. 08. 04 9.25223668 Their Summ 97. 41. 01 is the angle CTD As the Sine of CTD . 97. 41. 01. Co. ar . 0.00391693 Is to the Side DC 10.00000000 So is the Sine of CDT 4. 54. 25 8.93215746 To the Side CT 8.93607439   s. d. The place of the Moon in the first Observation 6. 25. 06. 54 The true Anomaly CTD sub . 3. 07. 41. 01 The place of the Apogaeon 3. 17. 25. 53 ☽ place in the first Observation 6. 25. 06. 54 The AEquation CDT Add. 04. 54. 25 The ☽ mean Longitude 7. 00. 01. 19 From which subtract the place of the Apogeon 3. 27. 25. 53 There rests the mean Anomaly BCD 3. 12. 35. 26 And for the excentricity in such parts , as the Radius of the AEquant is 100000 the Proportion is . DT 9.99335424 CT 8.93607439 100000 5.00000000 8764 3.94272015 And this is the Method for finding the place of the Moons Apogaeon and excentricity . And from these and many other Eclipses as well Solar as Lunar , Mr. Street limits the place of the ☽ Apogaeon to be at the time of the first observation 21′ . 04″ more , and the mean Anomaly 20. 41″ less , and the excentricity 8765 such parts as the Radius of the AEquant is 100000. And by comparing sundry observations both antient and modern , he collects the middle motion of the Moon , from her Apogaeon , to be in the space of four Julian years or 146 days , 53 revolutions , 0 Signes , 7 degrees , 56 minutes , 45 Seconds . And the Apogaeon from the AEquinox 5 Signes , 12 degrees , 46 minutes . And hence the daily motion of her mean Anomaly will be found to be 13 d. 03′ . 53″ . 57‴ . 09 iv . 58 v. 46 vi . Of her Apogaeon 0. 06. 41. 04. 03. 25. 33. And according to these Measures , if you deduct the motion of the ☽ mean Anomaly for 1641 years April 4. hours 13. 37′ , viz. 8. 22. 02. 00. from 3. 121. 35. 26 The remainer is 6. 201. 33. 26 from which abating 20′ . 41″ the ☽ mean Anom . AEra Chr. 6. 20. 12. 45.   In like manner the motion of her Apogaeon for the same time is 6. 05. 311. 57 which being deducted from 3. 17. 25. 57 The remainer is 9. 11. 55. 56 To which if you add 21.04 The Sum 91. 121. 15200 is the place of the ☽ Apogaeon in the beginning of the Christian AEra .   CHAP. XVI . Of the finding of the place and motion of the Moons Nodes . ANno Christi 1652 , March 28 , hour . 22. 16′ , the Sun and Moon being in conjunction , Mr. Street in Page 33 , computes the ☽ true place in the Meridian of London to be in ♈ . 19. 14. 18 with latitude North 46′ . 15″ . And Anno Christi 1654 August 1. hour . 21. 19′ . 30″ was the middle of a Solar Eclipse at London . at which time the Moons true place was found to be in ♌ 18. 58′ . 12″ with North Latitude 32′ . 01″ . 1654 August 1. 21. 19′ . 30″ ☽ place ♌ 18. 58. 12 1652 March 28. 22. 16. 00 ☽ place ♈ 19. 14. 18 From the first observation to the second there are 27 years , 4 months , 5 days , 23 hours 03′ . 30″ . Mean motion of the Nodes in that time , deg . 45. 19. 41 The true motion of the ☽ 119. 43. 54 Their Summ is in Fig. 11. The angle DPB 165. 03. 35 Therefore in the oblique angled Spherical Triangle DPB we have given BP . 89. 13. 45 the complement of the Moons Latitude in the first Observation 2. PD 89. 27. 50 the complement of the Moons Latitude in the second observation , and the angle DPB 165. 03. 35 , whose complement to a Semicircle is DPF 14. 56. 25. The angle PBD is required . 1. Proportion . As the Cotangent of PD 89. 27. 50 9.97114485 Is to the Radius 10.00000000 So is the Cosine of DPF 14. 56. 25 9.98506483 To the tang . of PF 89. 26. 42 12.01191998 BP 89. 13. 45   Their Z is FPB 178. 40. 27. whose complement Is the Arch FG 1. 19. 33. 2. Proportion . As the Sine of FP 89. 26. 42. Co. ar . 0.00002037 Is to the Cotang . of DPF 14. 56. 25 10.57376158 So is the Sine of FG 1. 19. 33 8.36418419 To the Cotang . of FGD 85. 02. 56 8.93796614 FGD = PBD inquired .   And in the right angled Spherical Triangle BA ☊ right angled at A we have given AB 046′ . 15″ the Latitude in the first observation , and the Angle AB ☊ = PBD 85. 02. 56. to find A ☊ the Longitude of the Moon from the ascending Node . As the Cot. of AB ☊ 85. 02. 56 8.93796614 Is to the Radius 10.00000000 So is the Sine of AB 0 . 46′ . 15″ 8.12882290 To the tang . of A ☊ 8. 49. 17 9.19085676 2. To find the Angle A ☊ B. As the tang . of AB 0. 46. 15 8.12886212 Is to the Radius 10.00000000 So is the Sine of A ☊ 8. 49. 17 9.18569718 To the Cotang . of A ☊ B 5. 0. 41 11.05682506 The angle of the ☽ orbite with the Ecliptick   The first observed place of the ☽ ♈ . 19. 14. 18 A ☊ Subtract 8. 49. 17 There rests the true place of the ☊ ♈ . 10. 25. 01 The retrograde motion whereof in 4 Julian years or 2461 days , is by other observations found to be Sign 2. deg . 17. 22′ . 06″ . and therefore the daily motion deg . 0. 03′ . 10″ . 38‴ . 11 iv . 35 v. And the motion thereof for 1651 years , March 28. h. 22. 16′ , viz. Sign 8. deg . 18. 26′ . 58″ being added to the place of the Node before found Sig. 0. 10. 25 : 01. Their Sum is the place thereof in the beginning of the Christian AEra Sign 8. deg . 28. 51′ . 59″ . But the Rudolphin Tables as they are corrected by Mr. Horron and reduced to the Meridian of London , do differ a little from these measures , for according to these Tables , the Moons mean motions are . AEra Christi . The Moons mean Longitude is Sign . 04. deg . 02. 25. 55 The Moons Apogaeon Sign . 09. deg . 13. 46. 59 The Moons mean Anomaly Sign . 06. deg . 18. 38. 56 The Moons Node Retrograde Sign . 08. deg . 28. 33. 16 And according to these measures , the Moons mean motions in decimal Numbers are . AEra Christi . The Moons mean Longitude , deg . 34. 00887.345677 The Moons Apogaeon , deg . 78. 82862.654320 The Moons mean Anomaly , deg . 55. 18024.691357 The Moons Node Retrograde , deg . 74. 69845.679010 The ☽ mean motion for one year . The Moons mean Longitude , deg . 35. 94001. 44893. 1 The Moons Apogeaon , deg . 11. 29551. 126365 The Moons mean Anomaly , deg . 24. 64450. 322566 The Moons Node Retrograde , deg . 05. 36900. 781604 The ☽ mean motion for one day . The Moons mean Longitude , deg 03. 66010. 962873 The Moons Apogaeon , deg . 00. 03094. 660620 The Moons mean Anomaly , deg . 03. 62916. 302253 The Moons Node Retrograde , deg . 00. 01470. 961045 And according to these measures are the Tables made shewing the Moons mean Longitude , Apogaeon , Anomaly , and Node retrograde for Years , Months , Days and Hours . And hence to compute the Moons true place in her Orbit , I shall make use of the Method , which Mr. Horron in his Posthumas works lastly published by Mr. Flamsted , in which from the Rudolphin Tables he sets down these Dimensions . The Moons mean Semidiameter deg . 00. 15′ . 30″ Her mean distance in Semid . of the Earth Deg. 11. 47. 22 The half whereof deg . 5. 53. 41. he adds 45 the whole is deg . 50. 53. 41 Whos 's Artificial cotangent is 9.91000022 And the double thereof makes this standing Numb . 9.82000044   Greatest 6685. 44   The Moons Mean 5523. 69 Excentricity   Least 4361. 94   And her greatest variation 00. 36′ . 27″ . These things premised his directions for computing the Moons place , are as followeth . CHAP. XVII . How to Calculate the Moons true place in her Orbit . TO the given time find the true place of the Sun , or his Longitude from the Vernal AEquinox , as hath been already shewed . 2. From the Tables of the Moons mean motions , write out the Epocha next before the given time , and severally under that set the motions , belonging to the years , months and days compleat , and to the hours and scruples current , every one under his like ( only remember that in the Bissextile years , after the end of February , the days must be increased by one Unite ) then adding them all together , the Summ shall be the Moons mean motions for the time given : But in her Node Retragrade you must leave out the Radix or first number , and the Summ of the remainer being deducted from the Radix , shall be the mean place of her Node required . 3. Deduct the Moons Apogaeon from the ☉ true place , the rest is the annual Augment , the tangent of whose Complement 180 or 360 , being added to the artificial Number given 9. 82000044. the Summ shall be the tangent of an Arch , which being deducted from the said Complement , giveth the Apogaeon AEquation to be added to the mean Apogaeon , in the first and third quadrants of the annual Augment , and Subtracted in the second and fourth , their Summ or difference is the true Apogaeon . 4. The true Apogaeon being Deducted from the ☽ mean Longitude gives the Moons mean Anomaly . 5. Double the annual Augment , and to the Cosine thereof add the Logarithm of 1161. 75. the difference between the Moons mean and extream Excentricity , viz. 3. 06511268 , the Summ shall be the Logarithm of a number which being added to the mean Excentricity , if the double annual Augment be in the first or fourth quadrants ; or Subtracted from it , if in the second or third quadrants ; the Summ or difference shall be the Moons true Excentricity . 6. The Moons true Excentricity being taken for a natural Sine , the Arch answering thereto shall be the ☽ greatest Physical AEquation . 7. To the half of the Moons greatest Physical AEquation add 45 deg . the cotagent of the Summ is the artificial Logarithm of the Excentrick . To the double whereof if you add the tang . of half the mean Anomaly , the Summ shall be the tangent of an Arch , which being added to half the mean Anomaly , shall give the Excentrick Anomaly . 8. To the Logarithm of the Excentrick , add the tangent of half the Excentrick Anomaly , the Summ shall be the tangent of an Arch , whose double shall be the Coequated Anomaly , and the difference between this and the mean Anomaly is the terrestrial Equation , which being added to the Moons mean Longitude , if the mean Anomaly be in the first Semicircle , or Subtracted from it , if in the latter , the Summ or difference shall be the place of the Moon first Equated . 9. From the place of the Moon first Equated , Deduct the true place of the Sun , and double the remainer , and to the Sine of the double add the Sine of the greatest variation 0. 36. 27 , viz. 8. 02541571 , the Summ shall be the Sine of the true variation , at that time , which being added to the Moons place first Equated , when her single distance from the Sun is in the first or third quadrants , or Subtracted when in the second or fourth , the Summ or difference shall be the Moons true place in her Orbit . Example . Let the given time be Anno Christi 1672. Feb. 23. h. 11. 34′ . 54″ at which time the Suns true place is in ♓ 15. 29133 and the Moons middle motions are as followeth .   ☽ Longitude ☽ Apogaeon ☊ Retrograde   1660 13. 36650. 41. 78372. 55.85177   11. 02. 66032. 24. 31246. 59.08943   Ianuary . 13. 46339. 00.95934 .45599   D. 23 84. 18252. .71177 .33832   H. 11 1. 67755. .01418 .00674   34′ .08641 . .00072 .00054   54 .00228 . .00012 .00001   ☽ Longitude 15. 43897. 67.78229 59.89082           95.96094 These Numbers reduced to the Degrees and Parts of the common Circle are for the ☽ mean Longitude . 55.580292 The ☽ Apogaeon . 244.015956 The ☉ true place is 345.29133 The ☽ Apogaeon subtract . 244.01595 The Annual Augment . 101.27538 The Complement whereof is 78.72462 The Tang. of deg . 78. 72462 10.70033391 The standing Number . 9.82000044 The Tang. of deg . 73. 20288 10.52033435 Their difference . 5. 52174 the Apogaeon Equation   Mean Apogaeon 244. 01595   Their difference 238. 49421 is the true Apogaeon .   Secondly . The ☽ mean Longitude . 55.58029 The true Apogaeon subtract . 238.49421 Rests the ☽ mean Anom . correct . 177.08608 Or thus . The ☽ mean Anomaly in the Tables for the time propounded , will be found to be 67. 78221 , which converted into the deg . and parts of the common Circle is 171.56434 To which the Apogaeon Equation being added 5.52174 Their Sum is the mean Anom . correct . 177.08608 And hence it appears that working by the mean Anomaly instead of the mean Longitude , the true Apogaeon Equation must be added to the mean Anomaly , in the second and fourth Quadrants of the ☽ Annual Augment , and subtracted from it in the first and third . Thirdly . The Annual Augment . 101. 27538 being doubled is deg . 202. 55076 , the Cosine of whose excess above 180 , that is the Cosine of 22. 54076 is 9.96545577 The Logarithm of 1161. 75 3.06511268 The Logarithm of 1072. 92 3.03056845 The ☽ mean Excentr . 5523. 69   Their difference 4450. 77 is the ☽ true Excentricity . Which taken as a natural Sine , the Arch answering thereunto Deg. 2. 55094 is the ☽ greatest Physical Equation .   Fourthly . To the half of the Physical Equation . deg . 01. 27547 add 45 degrees , the Sum is deg . 46. 27547 , the Cotangent whereof ; viz. 9. 98080957 is the Logarithm of the Excentrick , the double of which Logarithm is 9.96161914 Tangent frac12 Anomaly corrected 88. 54304 11.59455229 Tang. of deg . 88. 40849 11.55620143 Their Sum deg . 176. 95153 is the excentrick Anomaly .   Fifthly . The Logarithm of the Excentrick is 9.98080957 Tang. frac12 excent . Anom . 88. 475765 11.57505878 Tangent of deg . 88. 407268 11.55586835 The double whereof 176. 814536 is the coequated Anomaly . M. Anomaly correct . 177.086080 Their difference 0. 271544 is the Equation sought to be subst . from ☽ mean Long. 55.580292 The Remainer 55. 308748 is the ☽ place first Equated . Sixthly , From the place of the ☽ first Equated . 55.308748 Deduct the true place of the Sun 345.291330 The Remainer is the Distance of the ☽ à ☉ 70.017418 The double whereof is 140. 034836. The Sine of whose Complement to a Semi-circle , 39. 965164 is 9.80775260 The Sine of the greatest variation 8.02541571 The Sine of the true var. 0. 390206 7.83316831 The ☽ place first Equa . 55. 308748   The ☽ place in Orbit 55. 698954 that is in Sexagenary Numbers . 8. 25. 41. 54.   CHAP. XVIII . To compute the true Latitude of the Moon , and to reduce her place , from her Orbit to the Ecliptick . THe greatest Obliquity of the Moon 's Orb with the Ecliptick or Angle A ☊ B Fig. 11. is by many Observations confirmed to be 5 Degrees just , at the time of the Conjunction or Opposition of the Sun and Moon , but in her Quarters deg . 5. 18′ . Now then then find her Latitude at all times , the said Mr. Horrox refers us to pag. 87. in the Rudolphin Tables , to find from thence the Equation of the Nodes , and Inclination limitis menstrui , in this manner . 1. From the mean place of the Node , deduct the ☉ true place , the Remainer is the distance of the ☉ from the ☊ . with which entring the said Table , he finds the Equation of the Node and Inclination limitis menstrui , which being added to or subtracted from the Nodes mean place according to the title , the Sum or difference is the true place of the Node , which being deducted from the place of the Moon in her Orb , the Remainer shall be the Augment of Latitude or Distance of the Moon from the Node , or Leg A ☊ . 2. With the Augment of Latitude , enter the Table of the Moon 's Latitude , and take thence her Simple and Latitude and Increase answering to it . Then say , as the whole excess of Latitude 18′ , or in Decimals 30. is to the Inclination of the Monethly limit : So is the increase of Latitude to the Part Proportional ; which being added to the simple Latitude , will give you the true Latitude of the Moon . 3. With the same Augment of Latitude , enter the Table of Reduction , and take thence the Reduction and Inclination answering thereto : Then say again , as 18′ . 00″ . or 0. 30. is to the Inclination of the Monethly limit : So is the increase of Reduction , to the Part Proportional ; which being added to the simple Reduction , shall give the true , to be added to , or subtracted from the place of the Moon in the Ecliptick . Example . By the former Chapter , we found the mean motion of the Node to be 95. 96094 , which reduced to the Degrees and Parts of the common Circle is 345.459384 And the Suns true place to be 345.291334 Their difference is the distance ☉ à ☊ . 168050 with which entring the Table , Entituled Tabula AEquationis Nodorum Lunae . I find the Node to need no Equation , and the Inclination limitis menstrui to be deg . 00. 30. The place of the ☽ in her Orbit 55.698954 The Nodes true place , subtract . 345.459384 The Augment of Latitude 70.239570 2. With this Augment of Latitude I enter the Table shewing the Moons simple Latitude , and thereby find her simple Latitude to be Degrees . 04. 70476. North ; And the increase 00.28234 And therefore the Moons true Latitude is deg . 4.98610 3. With the same Augment of Latitude , I enter the Table of Reduction , and thereby find the Reduction to be 00.06955 And the increase of Reduction to be deg . 00.00855 And therefore the whole Reduction to be sub . 00.07810 From the ☽ place in her Orbit 55.69895 The ☽ true place in the Ecliptick 55.62085 That is in Sexagenary Numbers . 8. 25. 37′ . 15″ . CHAP. XIX . To find the Mean Conjunction and Opposition of the Sun and Moon . TO this purpose we have here exhibited a Table shewing the Moons mean motion from the Sun , the construction whereof is this : By the Tables of the Moons mean motions , her mean Longitude AEra Christi is 34.0088734567 The ☉ mean Anomaly . 56.6997085185 Praecession of the AEquinox . 20.4976851851 Their Sum is the ☉ mean longit . AEra a Christi . 77.4973937036 Which being deducted from the ☽ mean longitude , the remainer is the Moons mean 56.8114797531 distance from the Sun , in the beginning of the Christian AEra .   In like manner the Moons mean distance from the Sun in a year or a day is thus found . ☉ Anomaly for a year . 99.9297857316 Praecession of the AEquinox . 0038580246 Their Sum subtract . 99.9336437562 From the ☽ mean Longitude . 35.9400144893 Moons distance from the ☉ . 36.0063707331 Moons distance from the Sun in a days time . ☉ mean Anomaly . 27378.02348 Praecession of the AEquinox . 1.05699 Their Sum subtract . 27379.08047 From the ☽ mean Longitude . 03. 66010.96287 ☽ Daily motion from the ☉ . 03. 38631.88240 And according to these measures are the Tables made , shewing the Moons mean motion from the Sun , by which the mean conjunction of the ☽ and Moon may be thus computed . To the given year and Month gather the middle motions of the Moon from the Sun , and take the complement thereof to a whole Circle , from which subtracting continually the nearest lesser middle motions , the day , hour , and minute enfuing thereto is the mean time of the Conjunction . Example , Anno Christi 1676. I would know the time of the mean Conjunction or New Moon in October . Epocha 1660 32.697283 Years Compl. 15. 50.254463 Septemb. Compl. 24.465038 1. day for Leap-year . 03.386318 Their Sum is the Moons motion from the ☉ . 10.803102 Complement to a whole Circle . 89.196898 Days 26 Subtract . 88.044289 Hours 8. substract . 1.152609 1.128772 Minutes 10 Subtract . 0.023837 0.023516 The Remainer giveth 8″ . .00321 Therefore the mean Conjunction in October , 1676. was the 26 day , 10 min. 8 seconds after 8 at night . And to find the mean opposition . To the complement of the middle motion , add a semicircle , and then subtract the nearest lesser middle motions as before , the day , hour , and minute ensuing thereto , shall be the mean opposition required . Example , Anno Christi , 1676. I desire to know the mean opposition in November . Epocha 1660 32.697283 Years Compl. 15 50.254463 October Compl. 29.440922 1 day for Leap-year . 03.386318 The ☽ mean motion from the ☉ 15.778986 Complement to a whole Circle . 84.221014 To which add a Semicircle . 50. The Sum is 34.221014 Day 10 subtract . 33.863188 Hours 2. .357826 .282193 Minutes 32. .075633 .075251 The Remainer giveth 9 seconds . .000382 Therefore the Full Moon or mean Opposition of the Sun and Moon was November the 10th , Hours 2 , 32′ 09″ . The like may be done for any other . And here I should proceed to shew the manner of finding the true Conjunction or Opposition of the Sun and Moon , but there being no decimal Canon yet extant , suitable to the Tables of middle motions here exhibited , I chuse rather to refer my Reader to Mr. Street's Astronomia Carolina , for instructions in that particular , and what else shall be found wanting in this Subject . AN INTRODUCTION TO Geography , OR , The Fourth Part of COSMOGRAPHY . CHAP. I. Of the Nature and Division of Geography . GEOGRAPHY is a Science concerning the measure and distinction of the Earthly Globe , as it is a Spherical Body composed of Earth and Water , for that both these do together make but one Globe . 2. And hence the parts of Geography are two , the one concerns the Earthy part , and the other the Water . 3. The Earthy part of this Globe is commonly divided into Continents and Islands . 4. A Continent is a great quantity of Land not separated by any Sea from the rest of the World , as the whole Continent of Europe , Asia , and Africa , or the Continents of France , Spain , and Germany . 5. An Island is a part of Earth environed round about with some Sea or other ; as the Isle of Britain with the Ocean , the Isle of Sicily with the Mediterranean , and therefore in Latine it is called Insula , because it is scituate in Salo , in the Sea. 6. Both these are subdivided into Peninsula , Isthmus , Promontorium . 7. Peninsula , quasi pene insula , is a tract of land which being almost encompassed round by water , is joyned to the main land by some little part of Earth . 8. Isthmus is that narrow neck of Land which joyneth the Peninsula to the Continent . 9. Promontorium is a high mountain which shooteth it self into the Sea , the outmost end whereof is called a Cape or Foreland , as the Cape of Good Hope in Africk . 10. The Watry part of this Globe may be also distinguished by diverse Names , as Seas , Rivers , Ponds , Lakes , and such like . 11. And this Terrestrial Globe may be measured either in whole , or in any particular part . 12. The measure of this Earthly Globe in whole , is either in respect of its circumference , ●o its bulk and thickness . 13. For the measuring of the Earths circumference , it is supposed to be compassed with a great Circle , and this Circle in imitation of Astronomers , is divided into 360 degrees or parts , and each degree is supposed to be equal to 15 common German miles , or 60 miles with us in England , and hence the circumference of the Earth is found , by multiplying 360 by 15 , to be 5400 German miles , or multiplying 360 by 60 , the circumference is 21600 English miles . 14. The circumference of the Earth being thus obtained , the Diameter may be found by the common proportion between the Circumference and the Diameter of a Circle , the which according to Archimedes is as 22 to 7 , or according to Van Culen as 1 to 3. 14159. and to bring an Unite in the first place . As the circumference 3. 14159. is to 1 the Diameter , so is 1 the circumference to 318308 the Diameter , which being multiplied by 5400 , the Earths Diameter will be found to be 1718 German miles and 8632 parts , but being multiplied by 21600 , the Diameter will be 6875 English miles , and parts 4528. 15. The measure of the Earth being thus found in respect of its whole circumference and Diameter , that which is next to be considered , is the distinction of it into convenient spaces . 16. And this is either Primary or Secondary . 17. The Primary distinction of the Earthly Globe into convenient spaces , is by Circles considered absolutely in themselves , dividing the Globe into several parts without any reference to one another . Dutch Geographer inclines much to the bringing back the great Meridian to the Fortunate Islands , more particularly to the Peak a Mountain so called from the sharpness in the top , in the Isle Teneriff , which is believed to be the highest Mountain in the World ; therefore the same Iohnson in his greatest Globe of the year 1616 , hath drawn the great Meridian in that place , and it were to be wished , that this might be made the common and unchangeable practice . 25. The Horizon is a great Circle , designing so great a Part of the Earth , as a quick sight can discern in an open field ; it is twofold Rational and Sensible . 26. The Rational Horizon is that which is supposed to pass through the Center of the Earth , and is represented by the wooden Circle in the Frame , as well of the Celestial , as the Terrestrial Globe , this Rational Horizon belongeth more to Astronomy than Geography . 27. The Sensible Horizon is that before defined , the use of it is to discern the divers risings and settings of the Stars , in divers places of the Earth , and why the days are sometimes longer , and sometimes shorter . 28. The great but less principal Circle upon the Terrestrial Globe is the Zodiack , in which the Sun doth always move . This Circle is described upon Globes and Maps for ornament sake , and to discover under what part of the Zodiack the several Nations lie . 29. The lesser Circles are those which do not divide the Terrestial Globe into two equal , but into two unequal Parts , and these by a general name are called Parallels , or Circles aequidistant from the Equinoctial ; of which as many may be drawn , as there can Meridians , namely 180 if but to each degree , but they are usually drawn to every ten Degrees in each Quadrant from the AEquator to the Poles . 30. These Parallels are not of the same Magnitude , but are less and less as they are nearer and nearer to each Pole : and their use is to distinguish the Zones , Climates and Latitudes of all Countries , with the length of the Day and Night ▪ in any Part of the World. 31. Again , a Parallel is either named or unnamed . 32. An unnamed Parallel is that which is drawn with small black Circular Lines . 33. A named Parallel is that which is drawn upon the Globe with a more full ruddy and circular Line : such as are the Tropicks of Cancer and Capricorn , with the Arctick and Antarctick Circles , of which having spoken before in the general description of the Globe , there is no need of adding more concerning them now . CHAP. II. Of the Distinction or Dimension of the Earthly Globe by Zones and Climates . HAving shewed the primary distinction of the Globe into convenient spaces by Circles considered absolutely in themselves , we come now to consider the secondary Dimension or distinction of convenient spaces in the Globe , by the same Circles compared with one another , and by the spaces contained between those Circles . 2. This secundary Dimension or Distinction of the terrestial Globe into Parts , is either a Zone or a Clime . 3. A Zone is a space of the Terrestial Globe included either between two of the lesser nominated Circles , or between one and either Pole. They are in Number five , one over hot , two over cold , and two temperate . 4. The over hot or Torrid Zone , is between the two Tropicks , continually scorched with the presence of the Sun. 5. The two over cold or Frigid Zones , are scituated between the two polar Circles and the very Poles , continually wanting the neighbour hood of the Sun. 6. The two temperate Zones , are one of them between the Tropick of Cancer and the Arctick Circles and the other between the Tropick of Capricorn and the Antarctick Circle , enjoyning an indifferency between Heat and Cold ; so that the parts next the Torrid Zone are the hotter , and the parts next the Frigid Zone are the Colder . 7. The Inhabitants of these Zones , in respect of the diversity of their noon Shadows are divided into three kinds , Amphiscii , Heteroscii and Periscii . Those that inhabit between the two Tropicks are called Amphiscii , because that their noon Shadows are diversly cast , sometimes towards the South as when the Sun is more Northward than their vertical point , and sometimes towards the North , as when the Sun declines Southward from the Zenith . Those that live between the Tropick of Cancer and the Arctick Circle or between the Tropick of Capricorn and the Antarctick Circle are ●alled Heteroscii , because the Shadows at noon are cast one only way , and that either North or South . They that inhabit Northward of the Tropick of Cancer have their Shadows always towards the North , and they that inhabit Southward of the Tropick of Capricorn , have their noon Shadows always towards the South . Those that inhabit between the Poles and the Arctick or Antarctick Circles are called Periscii , because that their Gnomons do cast their Shadows circulary , and the reason hereof is , for that the Sun is carried round about above their Horizon in his whole diurnal revolution . 8. The next secundary Dimension or distinction of the earthy Globe into convenient parts or spaces , is by Climes . 9. And a Clime or Climate is a space of Earth conteined between three Paralells , the middlemo● whereof divideth it into two equal parts , serving for the setting out the length and shortness of the days in every Country . 10. These Climates and the Parallels by which they are conteined are none of them of equal quantity , for the first Clime as also the Parallel beginning at the AEquator is larger than the second , and the second is likewise greater than the third . 11. The Antients reckoned but seven Climates at the first , to which Number there were afterward added two more , so that in the first of these Numbers were comprehended fourteen parallels , but in the latter eighteen . 12. Ptolemy accounted the Paralells 38 each way from the Equator , that is 38 towards the North , and as many towards the South , 24 of which he reckoned by the difference of one quarter of an hour , 4 by the difference of half an hour , 4 by an whole hours difference , and 6 by a Months difference , but now the parallels being reckoned by the difference of a quarter of an hour , the Climates are 24 in Number till you come to the Latitude of 66 degrees 31 Minutes , to which are afterwards added 6 Climates more unto the Pole it self , where the Artificial day is 6 Months in length . 13. The distances of all both Climates and Parallels , together with their Latitudes from the AEquator , and difference of the quantity of the longest days , are here fully exprest in the Table following . A Table of the Climates belonging to the three sorts of Inhabitants . Inhabitants belonging to the several Climes Climes Paralells Length of the Day Poles Elevation Bea of the Clime     0 12.0 0.0     0       4.18     1 12.15 4.18       2 12.30 8.34     1       8.25 Amphiscii   3 12.45 12.43       4 13.0 16.43     2       7.50     5 13.15 20.33       6 13.30 23.10     3       7.3     7 13.45 27.36       8 14.0 30.47     4       6.9     9 14.15 33.45       10 14.30 36.30     5       5.17     11 14.45 39.02       12 15.0 41.22     6       4.30     13 15.15 43.32       14 15.30 45.29     7       3.48     15 15.45 47.20       16 16.0 49.21     8       3.13     17 16.15 50.13       18 16.30 51.58     9       2.44     19 15.45 53.17     Climes Paralells Length of the Days Poles Elevation Breadth of the Clime     20 17.00 54.29     10       2.17 Heteroscii   21 17.15 55.34       22 17.30 56.37     11       2.0     23 17.45 57.34       24 18.00 58.26     12       1.40     25 18.15 59.14       26 18.30 59.59     13       1.26     27 18.45 60.40       28 19.00 61.18     14       1.13     29 19.15 61.53       30 19.30 62.25     15       1.0     31 19.45 62.54       32 20.00 63.22     16       0.52     33 20.15 63.46       34 20.30 64.06     17       0.44     35 20.45 64.30       36 21.00 64.49     18       0.36     37 21.15 65.06       38 21.30 65.21     19       0.29     39 21.45 65.35       40 22.00 65.47     20       0.22     41 22.15 65.57       42 22.30 66.00     21       0.17     43 22.45 66.14   Clime Paralells Length of the Day Poles Elevation Breadth of the Clime     44 23.00 66.20     22       0.11     45 23.15 66.25       46 23.30 66.28     23       0.5     47 23.45 66.30     24 48 24.00 66.31 0.0 Periscii Here the Climates begin to be accounted by Months , from 66. 31 where the day is 24 hours long ; unto the Pole it self , where it is 6 Months in length . 1 67.15 2 69.30 3 73.20 4 78.20 5 84.0 6 90.0 14. Hitherto we have considered the inhabitants of the Earth in respect of the several Zones and Climes into which the whole Globe is divided ; there is yet another distinction behind into which the inhabitants of the Earth are divided in respect of their site and position in reference to one another , and thus the inhabitants of the Earth are divided into the Perioeci , Antoec● and Antipodes . 15. The Perioeci are such as dwell in the same Parallel on the same side of the AEquator , how far distant soever they be East and West , the season of the year and the length of the days being to both alike , only the midnight of the one is the moon to the other . 16. The Antoeci are such as dwell under the same Meridian and in the same Latitude , or Parallel distance from the AEquator , the one Northward and the other Southward , the days in both places being of the same length , but differ in the Seasons of the year , for when it is Summer in the one it is Winter in the other . 17. The Antipodes are such as dwell Feet to Feet , so as a right Line drawn from the one unto the other , passeth from North to South through the Center of the World. These are distant 180 degrees or half the compass of the Earth , they differ in all things , as Seasons of the year , length of days , rising and setting of the Sun and such like . A matter reckoned so ridiculous and impossible in former times , that Boniface Arch-Bishop of Mentz seeing a Treatise concerning these Antipodes written by Virgilius Bishop of Salisburg , and not knowing what damnable Doctrine might be couched under that strange Name , made complaint first to the Duke of Bohemia , and after to Pope Zachary Anno 745 by whom the poor Bishop ( unfortunate only in being learned in such a time of Ignorance ) was condemned of Heresie , but God hath blest this latter age of the World with more understanding , whereby we clearly see those things , which either were unknown , or but blindly guessed at by the Antients . 18. The second part of the Terrestial Globe is the Water which is commonly divided into these parts , or distinguished by these Names , Oceanus , Mare , Fretum , Sinus , Lacus and Flumen . 19. And first Oceanus or the Ocean is that general Collection of all Waters , which encompasseth the Earth on every side . 20. Mare the Sea , is a part of the main Ocean , to which we cannot come but through some Fretum or Strait , as Mare Mediterraneum . And it takes it name first either from the adjacent Shore , as Mare Adriaticum , from the City of Adria ; or secondly from the first discoverer , as Mare Magellanicum , from Magellanus who first found it , or thirdly from some remarkable accident , as Mare Icarium from the drowning of Icarus the Son of Daedalus . 21. Fretum , a Strait is a part of the Ocean penned within some narrow Bounds , and opening a way into some Sea , or out of some Sea into the Ocean , as the Strait of Hellespont , Gibralter , &c. 22. Lacus , a Lake is a great body or collection of Water , which hath no visible Intercourse with the Sea , or influx into it ; as the Lake of Thrasymene in Italy , and Lacus Asphaltites , or the dead Sea in the Land of C●naan . 23. Flumen or Fluvius is a water-course continually running , ( whereby it differs frum Stagnum a standing Pool ) issuing from some Spring or Lake , and emptying it self into some part of the Sea , or some other great River , the mouth or outlet of which is called Ostium . And thus we have gon over those particulars both of Earth and Water , which appertain to this Science of Geography in the general ; We will now proceed to a more particular Consideration of the several parts into which the Terrestial Globe is commonly divided . CHAP. III. Of Europe . THe Terrestial Globe is divided into two parts , known or unknown . 2. The unknown or the parts of the World not fully discovered , are distinguished into North and South , the unknown parts of the World towards the North , are those which lie between the North part of Europe or America and the North Pole ; and the unknown parts of the World toward the South , are those which ly between the South part of America and the South Pole. 3. The known parts of the World were antiently these three , Europe , Asia and Africk , to which in latter ages a fourth hath been added which is called America . 4. Europe is bounded on the North with the Northern Ocean , and on the South with the Mediterranean Sea , on the East with the River Tanais , and on the West with the Western Ocean , and is contained between the Tropick of Cancer , and the Pole Arctick , or 44 degrees as most do say , taking its beginning Southward from Sicily where the Pole is elevated 36 degrees , and is thence continued to 80 degrees of North Latitude , and so the whole Latitude of Europe is in English miles 2640 , but some allow to Europe 45 degrees of Latitude , that is in English miles 2700. 5. The Longitude of Europe is reckoned from the furthest part of Spain and the Atlantick Ocean , to the River Tanais , which some reckon to be 60 Degrees , to one of which Degrees passing through the middle of Europe , they allow fifteen German miles almost , or sixty English , and so the Longitude in German miles is 900 , in English 3600. 6. Europe though the least of all the four Quarters of the World , is yet of most renown amongst us : First , because of the temperature of the Air , and fertility of the Soil : Secondly , from the study of Arts , both ingenuous and mechanical : Thirdly , of the Roman and Greek Monarchies : Fourthly , from the purity and sincerity of the Christian Faith : Fifthly , because we dwell in it , and so give it the first place . 7. Europe may be considered as it stands divided into the Continent and the Islands : the Continent lying all together , containeth these Countries . 1. Spain . 2. France . 3. Germany . 4. Italy , and the Alpes . 5. Belgium . 6. Denmark ▪ 7. Swethland . 8. Russia . 9. Poland . 10. Hungary . 11. Sclavonia , 12. Dacia , and 13. Greece . Of each of which I will give some short account ; as also of the chief Islands as they are dispersed , in the Greek , AEgaean , Cretan and Io●ian Seas , with those in the Adriatick , Mediterranean , and in the British and Northern Ocean . 8. Amongst these I give Spain the first place , as being the most Western Part of all the Continent of Europe environed on all sides with the Sea , except towards France ; from which it is separated by the Pyrenaean Hills : but more particularly , it is bounded upon the North with the Cantabrian , on the West with the Atlantick Ocean , on the South with the Straits of Gibralter , on the East with the Mediterranean , and on the North East with the said Pyren●ean Hills . The Figure of it is compared by Strabo to an Oxes hide spread upon the Ground ; the Neck whereof being that Isthmus which unites it to France . 9. The greatest length hereof , it reckoned at 800 miles , the breadth where it is broadest at 500 , the whole Circumforence 2480 Italian miles : but Mariana measuring the compass of it by the bendings of the Pyrenaean Hills , and the creeks and windings of the Sea , makes the full circuit of it to be 2816 miles of Italian measure . 10. It is situate in the more Southerly Part of the Northern temperate Zone , and almost in the midst of the fourth and sixth Climates ; the longest day being 15 hours and a quarter in length in the most Northern Parts hereof : but in the extream South near to Gibralter not above fourteen , which Situation of this Country , rendreth the Air here very clear and calm , seldom obscured with mists and vapours , and not so much subject to Diseases as the more Northern Regions are . 11. This Continent is subdivided into the Kingdoms of Navarr . 2. Biscay . 3. Guipusco● . 4. Lean and Oviodo . 5. Gallicia . 6. Corduba . 7. Granada . 8. Murcia . 9. Toledo . 10. Castile . 11. Portugal . 12. Valentia . 13. Catalonia . 14. Majorca . And 15. Aragon ; but all of them are now united in the Monarchy of Spain . 12. France according to the present dimensions of it , is bounded on the East with a Branch of the Alpes which divide Dauphine and Piemont , as also with the Countries of Savoy , Switzerland , and some Parts of Germany and the Netherlands . On the West with the Aquitanick Ocean , and a Branch of the Pyrenaean Mountains which divide it from Spain . On the North with the English Ocean , and some Parts of Belgium , and on the South with the rest of the Pyrenaean Mountains , and the Mideterranean . 13. The Figure of it is almost square , each side of the Quadrature being reckoned 600 miles in length , but they that go more exactly to work upon it , make the length thereof to be 660 Italian miles , the breadth 570 , the whole Circumference 2040. It is seated in the Northern temperate Zone , between the middle Parallel of the first Clime , where the longest day is 15 hours , and the middle Parallel of the eighth Clime , where the longest day is 16 hours and a half . 14. The Principal Provinces in this flourishing Country , are . 1. France specially so called . 2. Champagne . 3. Picardy . 4. Normandy . 5. Bretagne . 6. The Estates of Angiou . 7. La Beausio . 8. Nivernois . 9. The Dukedom of Bourbon . 10. Berry . 11. Poictou . 12. Limosin . 13. Piregort . 14. Quercu . 15. Aquitain . 16. Languedoc . 17. Provence . 18. Daulphine . 19. La Bresse . 20. Lionnois . 21. The Dutchy . 22. The County of Burgundy . 23. The Islands in the Aquitanick and Gallick Ocean : Those of most note are these six . 1. Oleron . 2. Re● . 3. Iarsey . 4. Gernsey . 5. Sarke . 6. Aldernay on the shores of Normandy , of which the four last are under the Kings of England . 15. Italy once the Empress of the greatest part of the then known World , is compassed with the Adriatick , Ionian and Tyrrhenian Seas , except it be towards France and Germany , from which it is parted by the Alpes ; so that it is in a manner , a Peninsula , or a Demi-Island . But more particularly it hath on the East the lower part of the Adriatick , and the Ionian Sea , by which it is divided from Greece ; on the West the River Varus , and some part of the Alpes , by which it is parted from France , on the North in some part the Alpes which divide it from Germany ; and on the other , part of the Adriatick , which divides it from Dalmaria ; and on the South the Tyrrhenian and Tuscan Seas , by which it is separated from the main Land of Africa . 16. It containeth in length from Augusta Praetoria , now called Aost , at the foot of the Alpes , unto Otranto in the most Eastern Point of the Kingdom of Naples 1020 miles ; in breadth from the River Varo , which parts it from Provence , to the mouth of the River Arsia in Friuli , where it is broadest , 410 miles ; about Otranto , where it is narrowest not above 25 miles ; and in the middle parts from the mouth of Peseara in the Adriatick or upper Sea to the mouth of Tiber in the Tuscan or lower Sea , 126 miles . The whole compass by Sea reckoning in the windings and turnings of the shore , comes to 3038 miles ; which added to the 410 which it hath by Land , make up in all 3448 miles : but if the Coasts on each side be reckoned by a straight Line , then as Castaldo computes it , it comes to no more than 2550 miles . 17. The whole Country lieth under the first and sixth Climates of the Northern temperate Zone , which it wholly taketh up : so that the longest day in the most Northern Parts is 15 hours and three first parts of an hour ; the longest in the Southern Parts , falling short a full hour of that length . 18. Italy as it stands now is divided into the Kingdoms of Naples , Sicily and Sardinia . 2. The Land or Patrimony of the Church . 3. The great Dukedom of Tuscany . 4. The Common-wealths of Venice , Genoa and Luca. 5. The Estates of Lombardy , that is the Dukedoms of 1. M●llain . 2. Mantua . 3. Modena . 4. Parma . 5. Montferrat , and the Principality of Piedmont . 19. To the Peninsula of Italy belong the Alpes , aridge of Hills , wherewith as with a strong and defensible Rampart Italy is assured against France and Germany . They are said to be five days Journey high , covered continually with Snow , from the whiteness whereof they took this name , it doth contain the Dukedom of Savoy ; the Seigniory of Geneva ; the Country of Wallisland , Switzerland and the Grisons . 20. Belgium , or the Netherlands , is bounded on the East with Westphalin , Gulick , Cleve , and the Land of Triers , Provinces of the higher Germany ; on the West with the main Ocean , which divides it from Britain ; on the North with the River Ems , which parts it from East-Friezeland ; on the South with Picardie and Campagne two French Provinces ; upon the South-East with the Dukedom of Lorrain . 21. It is in compass 1000 Italian or 280 German miles , and is situated in the Northern temperate Zone , under the seventh , eighth and ninth Climates : the longest day in the midst of the seventh Climate where it doth begin , being 16 hours , iu the beginning of the ninth Climate increased to 16 hours 3 quarters , or near 17 hours . 22. It containeth those Provinces which in these later Ages were possessed by the House of Burgundy , that is the Lordship of West-Friezeland , given to the Earls of Holland by Charles the Bald ; the Earldom of Zutphen united unto that of Gelder by Earl Otho of Nassau , and finally the Estate of Groening , Over-Yssel , and some part of Vtrecht , by Charles the Fifth . As it stands now divided between the Spaniards and the States it containeth the Provinces of 1. Flanders . 2. Artois . 3. Hainault . 4. The Bishoprick of Cambray . 5. Namur . 6. Luxemburg . 7. Limbourg . 8. Luyckland , or the Bishoprick of Leige . 9. Brabant . 10. Marquisate . 11. Meohlin . The rest of the Netherlands which have now for sometime withdrawn their obedience from the Kings of Spain , are 1. Holland . 2. Zeland . 3. West-Friezeland . 4. Vtrecht . 5. Over-Yssel . 6. Gelderland . 7. Zutphen . 8. Groening . 23. Germany is bounded on the East with Prussia , Poland , and Hungary ; on the West with France , Switzerland and Belgium ; on the North with the Baltick Seas , the Ocean , and some part of Denmark ; on the South with the Alps which part it from Italy . 24. The length from East to West , that is from the Vistula or Weissel to the Rhine , is estimated at 840 Italian miles , the breadth from North to South , that is from the Ocean to the Town of Brixen in Tyrol , 740 of the same miles . So that the Figure of it being near a Square , it may take up 3160 miles in compass , or thereabouts . Situate in the Northern temperate Zone , between the middle Parallels of the sixth and tenth Climates ; the longest day in the most Southern Parts being 15 hours and an half , and in the most Northern 17 hours and a quarter . 25. The Principal Parts of this great Continent , are 1. Cleveland . 2. The Estates of the three spiritual Electors , Colen , ●●●ntz , and Triers . 3. The Palatinate of the Rhine . 4. Alsatia . 5. Lorrain . 6. Suevia or Schwaben . 7. Bavaria . 8. Austria and its Appendices . 9. The Confederation of Waderaw . 10. Franconia . 11. Wirtenberg . 12. Baden . 13. The Palatinate of Northgoia , or the Upper Palatinate . 14. Bohemia and the Incorporate Provinces . 15. Pomerania . 16. Mecklenburg . 17. The Marquisate of Brandenburg . 18. Saxony , and the Members of it . 19. The Dukedom of Brunswick and Lunenburg . 20. The Lantgravedom of Hassia . 21. Westphalen . 22. East-Friezeland . 26. Denmark or Danemark , reckoning in the Additions of the Dukedom of Holstein , and the great Continent of Norway , with the Isles thereof , now all united and incorporated into one Estate is bounded on the East with the Baltick Sea and some part of Sweden ; on the West with the main Western Ocean ; on the North-East with a part of Sweden ; full North with the main frozen Seas ; and on the South with Germany , from which it is divided on the South-West by the River Albis , and on the South-East by the Trave ; a little Isthmus or neck of Land uniting it to the Continent . 27. It lieth partly in the Northern temperate Zone , and partly within the Arctick Circle ; extending from the middle Parallel of the tenth Clime , or 55 degree of Latitude where it joyneth with Germany , as far as the 71 degree where it hath no other bound but the frozen Ocean ; by which account the longest day in the most Southern Parts is 17 hours and a quarter , but in the Parts extreamly North , they have no Night for two whole Moneths , three Weeks , one Day , and about seven hours ; as on the other side no day for the like quantity of time , when the Sun is most remote from them , in the other Tropick . 28. The whole Body of the Estate consisteth chiefly of three Members . viz. 1. The Dukedom of Holstein ; containing Waggerland , Dilmarsh , Starmaria , and Holstein , especially so called . 2. The Kingdom of Denmark ; comprehending both Iuitlands , part of Scandia , and the Hemodes , or Baltick Islands . 3. The Kingdom of Norway consisting of Norway it self , and the Islands of the Northern Ocean . 29. Swethland is bounded on the East with Muscovy , on the West with the Doferine Hills , which divide it from Norway ; on the North with the great frozen Ocean spoken of before ; on the South with Denmark , Liefland , and the Baltick Sea. 30. It is situate under the same Parallels and Degrees with Norway , that is , from the first Parallel of the 12 Clime , where the Pole is elevated 58 degrees 26 minutes , as far as to the 71 degree of Latitude , by which account the longest day in the Southern Point is but 18 hours , whereas on the farthest North of all the Countrey , they have no Night for almost three whole Moneths together . 31. The whole Kingdom is divided into two Parts , the one lying on the East , the other on the West of the Bay or Gulf of Bodener , being a large and spacious branch of the Baltick Sea , extending from the most Southerly Point of Gothland , as far as to Lapland on the North. According to which Division we have the Provinces of 1. Gothland . 2. Sweden lying on the West side of the Gulph . 3. Lapland shutting it up upon the North. 4. Bodia or Bodden . 5. Finland on the East side thereof . 6. The Sweedish Islands , where it mingleth with the rest of the Baltick Seas . 32. Russia is bounded on the East by Tartary , on the West with Livonia and Finland , from which it is divided by great mountains and the River Poln , on the North by the frozen Ocean , and some part of Lapland , and on the South by Lituania a Province of the Kingdom of Poland , and the Crim Tartar inhabiting on the Banks of Palus Maeotis , and the Euxine Sea. It standeth partly in Europe and partly in Asia , the River Tanais or Don running through it , the common boundary of those great and noted parts of the world . 33. It is scituate North within the Artick Circle so far , that the longest day in Summer will be full six months , whereas the longest day in the southern parts is but 16 hours and an half . 34. It is divided into the Provinces of 1. Moscovy specially so called . 2. Snol●usio , 3. Masaisky , 4. Plesco , 5. Novagrod the great , 6. Corelia , 7. Blarmia , 8. Petzora , 9. Condora , 10 Obdora , 11. Iugria , 12. Severia , 13. Permia , 14. Rozan , 15. Wiathka , 16. Casau , 17. Astracan , 18. Novogordia inferiour , 10. The Morduits or Mordua , 20. Worotime , 21. Tuba , 22. Wolodomir , 23. Duina , 24. the Russian Islands . 35. Poland is bounded on the East with Russia , and the Crim-Tartar , from whom it is parted by the River Borysthenes ; on the West with Germany , on the North with the Baltick Sea and some part of Russia , on the South with the Carpathian Mountains , which divide it from Hungary , Transilvania , and Moldavia . It is of figure round in compass 2600 miles , scituate under the 8 and 12 Climates , so that the longest day in the southern parts is but 16 hours , and about 18 hours in the parts most North. 36. The several Provinces of which this Kingdom doth consist , are 1. Livonia , 2. Samogitia , 3. Lituania , 4. Volkinia , 5. Podolia , 6. Russia nigra , 7. Massovia , 8. Podlassia , 9. Prussia , 10. Pomerellia , 11. Poland specially so called . 37. Hungary is bounded on the East with Transilvania and Walachia , on the West with Sterria , Austria and Moravia , on the North with the Carpathian mountains which divide it from Poland , and on the South with Sclavonia , and some part of Dacia : it extendeth in length from Presburg along the Danow to the borders of Transilvania , for the space of 300 English miles , and 190 of the same miles in breadth . 38. It lieth in the Northern temperate Zone , betwixt the middle parallels of the 7 and 9 Climates , so that the longest Summers day in the Southern parts is but 15 hours and an half , and not above 16 hours in the parts most North. 40. This Country is commonly divided into the upper Hungary and the lower , the upper lying on the North of the River Danow , the lower lying on the South of that River , comprehending all Pannonia inferior and part of Superior , and is now possessed by the King of Hungary and the Great Turk , who is Lord of the most part by Arms and Conquest . 04. Sclavonia is bounded on the East with Servia , Macedonia and Epirus , from which it is parted by the River Drinus , and a line drawn from thence unto the Adriatick , on the West with Carniola in Germany , and Istria in the Seigniory of Venice , from which last it is divided by the River Arsia ; on the North with Hungary , on the South with the Adriatick Sea. 41. It is scituate in the Northern temperate Zone , between the middle Parallels of the sixth and seventh Climates , so that the longest day in Summer is about 15 hours and an half . 42. This Country as it came at last to be divided , between the Kings of Hungary and the State of Venice ; is distinguished into 1. Windischland , 2. Croatia , 3. Bosnia , 4. Dalmatia , 5. Liburnia or Cantado di Zara , and 6. The Sclavonian Islands . 43. Dacia is bounded on the East with the Euxine Sea and some part of Thrace ; on the West with Hungary and Sclavonia ; on the North with Podolia , and some other members of the Realm of Poland , on the South with the rest of Thrace and Macedonia . 44. It lieth on both sides of the Danow fronting all along the upper and the lower Hungary , and some part of Sclavonia ; extended from the 7 Climate to the 10 ; so that the longest Summers day in the most northern parts thereof , is near 17 hours , and in the most southern 15 hours 3 quarters . 45. The several Provinces comprehended under the name of Dacia , are 1. Transilvania , 2. Moldavia , 3. Walachia , 7. Rascia , 5. Servia , 6. Bulgaria , the first four in old Dacia , on the North side of the Danow ; the two last in new Dacia , on the South thereof . 45. Greece in the present Latitude and extent thereof , is bounded on the East with the Propontick , Hellespont , and AEgean Seas , on the West with the Adriatick ; on the North with Mount Haemus which parteth it from Bulgaria , Servia and some part of Illyricum ; and on the South with the Sea - Ionian ; so that it is in a manner a Peninsula or Demi-Island , environed on three sides by the Sea , on the fourth only united to the rest of Europe . 46. It is scituate in the northern temperate Zone , under the fifth and sixth Climates , the longest day being 15 hours . 47. In this Country formerly so famous for learning and government , the several Provinces are 1. Peloponnesus , 2. Achaia , 3. Epirus , 4. Albania , 5. Macedon , 6. Thrace , 7. The Islands of the Propontick ; 8. AEgean , and 9. The Ionian Seas , and 10. finally the Isle of Crete . And thus I have given you a brief description of those Countries which are comprehended in the Continent of Europe ; the Islands in this part of the world are many ; I will mention only some few . These two in the British and Northern Ocean , known by the names of Great Britain and Ireland are the most famous , to which may be added Greenland . In the Mediterranaen Sea you have the Islands of Sicilia , Sardinia , Corsica and Crete , which is now called Candia the greater and the less : As for the other Islands belonging to this part of the world , the Reader may expect a more particular description from them who have or shall write more largely of this subject : This we deem sufficient for our present purpose . Let this then suffice for the description of the first part of the World called Europe . CHAP. IV. Of Asia . ASia is bound on the West with the Mediteranean and AEgaean Seas , the Hellespont , Propontis , Thracian Bosphorus and the Euxine Sea , the Palus Maeotis , the Rivers Tanais and Duina , a Line being drawn from the first of the two said Rivers unto the other , by all which it is parted from Europe ; on the North it hath the main Scythick Ocean ; but on the East the Indian Ocean , and Mare del Eur by which it is separated from America ; on the South the Mediterranean , or that part of it , which is called the Carpathian Sea , washing the shoars of Anatolia , and the main Southern Ocean , passing along the Indian , Persian and Arabian Coasts : and finally on the south-west , the red Sea or Bay of Arabia , by which it is parted from Affrick . Environed on all sides with the Sea , or some Sea like Rivers , except a narrow Isthmus in the south-west , which joyns it to Africk , and the space of ground ( whatsoever it be ) between Duina and Tanais , on the North-west which unites it to Europe . 2. It is situated East and West , from the 52 to the 169 degree of Longitude ; and North and South from the 82 degree of Latitude to the very AEquator ; some of the Islands only lying on the South of that Circle : so that the longest summers day in the southern parts , is but twelve hours , but in the most northern parts hereof almost four whole Months together . 3. This Country hath heretofore been had in special honour ; 1. For the creation of Man , who had his first making in this part of the World. 2. Because in this part of it stood the Garden of Eden , which he had for the first place of his habitation . 3. Because here flourished the four first great Monarchies of the Assyrians , Babylonians , Medes and Persians . 4. Because it was the Scene of almost all the memorable Actions which are recorded by the pen-men of the Scriptures . 5. Because our Saviour Christ was borne here , and here wrought his most divine Miracles , and accomplished the great work of our Redemption . 6. And finally , because from hence all Nations of the World had their first beginning , on the dispersion which was made by the Sons of Noah after their vain attempt at Babel . 4. This part of the World for the better understanding of the Greek and the Roman Stories and the estate of the Assyrian , Babylonian and the Persian Monarchies , to which the holy Scriptures do so much relate , we shall consider as divided into the Regions of 1. Anatolia or Asia minor . 2. Cyprus . 3. Syria . 4. Arabia . 5. Chaldea . 6. Assyria . 7. Mesopotamia . 8. Turcomania . 9. Media . 10. Persia. 11. Tartaria . 12. China . 13. India . and 14. the Oriental Islands . Anatolia or Asia minor . Anatolia or Asia minor , is bounded on the East with the River Euphrates , by which it is parted from the greater Asia ; on the West with the Thracian Bosphorus , Propontis , Hellespont , and the AEgean Sea , by which it is parted from Europe ; on the North with Pontus Euxinus , called also the black Sea , and Mare Maggiore , and on the South by the Rhodian , Lydian and Pamphilian Seas , several parts of the Mediterranean . So that it is a Demi-Island or Peninsula environed on all sides with water , excepting a small Isthmus or Neck of Land extending from the head of Euphrates to the Euxine Sea , by which it is joyned to the rest of Asia . It reacheth from the 51 to the 72 degree of Longitude , and from the 36 to the 45 degree of Latitude , and lyeth almost in the same position with Italy , extending from the middle Parallel of the fourth Clime , to the middle Parallel of the sixth , so that the longest summers day in the Southern Parts , is about 14 hours and a half ; and one hour longer in those parts which lie most towards the North. The Provinces into which it was divided before the Roman Conquest were 1. Bithynia . 2. Pontus . 3. Paphlagonia . 4. Galatia . 5. Cappadocia . 6. Armenia Major & Minor. 7. Phrygia minor . 8. Phrygia major . 9. Mysia the greater and the less . 10. Asia specially so called , comprehending AEolis and Ionia . 11. Lydia . 12. Caria . 13. Lycia . 14. Lycaonia . 15. Pisidia . 16. Pamphylia . 17. Isauria . 18. Cilicia . 19. The Province of the Asian Isles , whereof the most principal are 1. Tenedos . 2. Chios . 3. Samos . 4. Choos . 5. Icaria . 6. Lesbos . 7. Patmos . 8. Claros . 9 Carpathos . 10. Rhodes . Cyprus . Cyprus is situated in the Syrian and Cilician Seas , extended in length from East to West 200 miles , in breadth 60 the whole compass reckoned 550 , distant about 60 miles from the rocky Shores of Cilicia in Asia minor , and about one hundred from the main Land of Syria . It is situated under the fourth Climate , so that the longest day in Summer is no more than 14 hours and a half . Divided by Ptolemy into the 4 provinces of 1. Paphia . 2. Amathasia . 3. Lepathia . 4. Salamine . Syria . Syria is bounded on the East with the River Euphrates by which it is parted from Mesopotamia ; on the West with the Mediterranean Sea ; on the North with Cilicia and Armenia minor , parted from the last by mount Taurus ; and on the South with Palestine , and some parts of Arabia . The length hereof from Mount Taurus to the Edge of Arabia , is said to be 525 Miles ; the breadth from the Mediterranean to the River Euphrates 470 Miles , drawing somewhat near unto a Square . The whole Country was antiently divided into these six parts . 1. Phoenicia . 2. Palestine . 3. Syria specially so called . 4. Comagena . 5. Palmyrene . and Caelosyria , or Syria Cava . Arabia . Arabia hath on the East Chaldaea and the Bay or Gulf of Persia ; on the West Palestine , some part of Egypt , and the whole course of the red Sea , on the North the River Euphrates with some parts of Syria and Palestine , and on the South the main southern Ocean . It is in circuit about 4000 Miles , but of so unequal and heteregeneous Composition , that no general Character can be given of it , and therefore we must look upon it as it stands divided into Arabia Deserta , 2. Arabia Petraea . 3. Arabia Felix and 4. The Arabick Islands . Chaldea . Chaldea is bounded on the East with Susiana a Province of Persia ; on the West with Arabia deserta ; on the North with Mesopotamia ; and on the South with the Persian Bay and the rest of Deserta . Assyria . Assyria is bounded on the East with Media , from which it is parted by the Mountain called Coathras ; on the West with Mesopotamia , from which it is divided by the River Tygris ; on the South with Susiana ; and on the North with some part of Turcomania ; it was antiently divided into six parts . 1. Arraphachitis . 2. Adiabene . 3. Calacine . 4. Aobelites . 5. Apolloniates . Mesopotamia . Mesopotamia is bounded on the East with the River Tygris by which it is parted from Assyria ; on the West with Euphrates which divides it from Comagena a Province of Syria ; on the North with Mount Taurus ; by which it is separated from Armenia major ; and on the South with Chaldea and Arabia deserta from which last it is parted by the bendings of Euphrates also . It was antiently divided into , 1. Anthemasia . 2. Chalcitis . 3. Caulanitis . 4. Acchabene . 5. Ancorabitis and 6. Ingine . Turcomania . Turcomania is bounded on the East with Media and the Caspian Sea ; on the West with the Euxine Sea , Cappadocia and Armenia minor ; on the North with Tartary , and on the South with Mesopotamia and Assyria . A Countrey which consisteth of four Provinces . 1. Armenia major or Turcomania properly and specially so called . 2. Colchis . 3. Iberia . 4. Albania . Media . Media is bounded on the East with Parthia , and some part of Otyrcania , Provinces of the Persian Empire ; on the West with Armenia major , and some part of Assyria ; on the North with the Caspian Sea and those parts of Armenia major , which now pass in the account of Iberia , Georgia ; and on the South with Persia. It is now divided into two Provinces . 1. Atropatia . 2. Media major . Persia. Persia is bounded on the East with India ; on the West with Media , Assyria , and Chaldea ; on the North with Tartary , on the South with the main Ocean . It is divided into the particular Provinces of 1. Susiana . 2. Persis . 3. Ormur . 4. Carmania . 5. Gedrosia . 6. Drangiana . 7. Arachosia . 8. Paropamisus . 9. Aria . 10. Parthia . 11. Hyrcania . 12. Margiana and 13. Bactria . Tartaria . Tartaria is bounded on the East with China , the Oriental Ocean , and the Straits of Anian , by which it is parted from America , on the West with Russia and Podolia , a Province of the Realm of Poland ; on the North with the main Scythick or frozen Ocean ; and on the South with part of China , from which it is separated by a mighty Wall , some part of India , the River Oxus parting it from Bactria and Margiana , two Persian Provinces ; the Caspian Sea which separates it from Media and Hyrcania ; the Caucasian Mountains interposing between it and Turcomania ; and the Euxine Sea which divideth it from Anatolia and Thrace . It reacheth from the 50 degree of Longitude to the 195 which is 145 degrees from West to East ; and from the 40 degree of Northern Latitude , unto the 80 , which is within 10 degrees of the Pole it self , By which accompt it lieth from the beginning of the sixth Clime , where the longest day in Summer is 15 hours , till they cease measuring the Climates , the longest day in the most Northen parts hereof being full six Months , and in the winter half of the Year , the night as long . It is now divided into these five parts . 1. Tartaria Precopensis . 2. Asiatica . 3. Antiqua . 4. Zagathay . 5. Cathay . China . China is bounded on the North with Altay and the Eastern Tartars , from which it is separated by a continued Chain of Hills , part of those of Ararat , and where that chain is broken off or interrupted , with a great wall extended 400 Leagues in length ; on the South partly with Cauchin China a Province of India , partly with the Ocean ; on the East with the oriental Ocean , and on the West with part of India and Cathay . It reacheth from the 130 to the 160 degree of Longitude , and from the Tropick of Cancer to the 53 degree of Latitude ; so that it lieth under all the Climes from the third to the ninth inclusively . The longest summers day in the southern parts being 13 hours and 40 Minutes increased in the most northern parts to 16 hours and 3 quarters . It containeth no fewer than 15 Provinces . 1. Canton . 2. Foquien . 3. Olam . 4. Sisnam 5. Tolenchia . 6. Causay . 7. Minchian . 8. Ochian . 9. Honan . 10. Pagnia . 11. Taitan . 12. Quinchen . 13. Chagnian 14. Susnan . 15. Cunisay . Besides the provinces of Suehuen , the Island of Chorea and the Island of Cheaxan . India . India is bounded on the East with the Oriental Ocean and some part of China ; on the West with the Persian Empire ; on the North with some Branches of Mount Taurus , which divide it from Tartary ; on the South with the Indian Ocean . Extended from 106 to 159 degrees of Longitude , and from the AEquator to the 44th degree of Northern Latitude , by which account it lieth from the beginning of the first to the end of the sixth Clime , the longest Summers day in the southern Parts being 12 hours onely , and in the parts most North 15 hours and a half . The whole Country is divided into two main parts , India intra Gangem , and India extra Gangem . The Oriental Islands . The Oriental Islands are 1. Iapan . 2. The Philippine and Isles adjoyning . 3. The Islands of Bantam . 4. The Moluccoes . 5. Those called Sinda or the Celebes . 6. Iava . 7. Borneo . 8. Sumatra . 9. Ceilan . and 10. others of less note . CHAP. V. Of Africk . AFrick is bounded on the East by the Red Sea , and Bay of Arabia , by which it is parted from Asia ; on the West by the main Atlantick Oceans interposing between it and America ; on the North by the Mediterranean Sea , which divides it from Europe and Anatolia ; and on the South with the AEthiopick Ocean , separating it from Terra Australis incognita or the southern continent , parted from all the rest of the World except Asia only , to which it is joyned by a narrow Isthmus not above 60 miles in length . It is situate for the most part under the Torrid Zones , the AEquator crossing it almost in the midst . It is now commonly divided into these seven parts . 1. AEgypt . 2. Barbary or the Roman Africk . 3. Numidia . 4. Lybia . 5. Terra Nigritarum . 6. AEthiopia superior . and 7. AEthiopia rinferior . AEgypt . AEgypt is bounded on the East with Idumea , and the Bay of Arabia ; on the West with Barbary , Numidia , and part of Lybia ; on the North with the Mediterranean Sea ; on the South with AEthiopia superior , or the Abyssyn Emperor ; it is situate under the second and fifth Climates , so that the longest day in Summer is but thirteen hours and a half . Barbary . Barbary is bounded on the East with Cyrenaica ; on the West with the Atlantick Ocean ; on the North with the Mediterranean Sea , the Straits of Gibralter and some part of the Atlantick also ; on the South with Mount Atlas , by which it is separated from Lybia inferior or the Desarts of Lybia . It is situated under the third and fourth Climates : so that the longest Summers day in the parts most South , amounteth to 13 hours and 3 quarters , and in the most northern parts it is 14 hours and a quarter . This country is now reduced to the Kingdoms of 1. Tunis . 2. Tremesch or Algiers . 3. Fesse and 4. Morocco . Numidia . Numidia is bounded on the East with Egypt , on the West with the Atlantick Ocean ; on the North with Mount Atlas , which parteth it from Barbary and Cyrene ; on the South with Lybia Deserta . Lybia . Lybia is either Interior or Deserta , Libia interior is bounded on the North with Mount Atlas by which it is parted from Barbary and Cyrenaica ; on the East with Lybia Marmarica interposed between it and Egypt , and part of AEthiopia superior , or the Habassine Empire ; on the South with AEthiopia inferior , and the Land of the Negroes ; and on the West with the main Atlantick Ocean . Lybia deserta is bounded on the North with Numidia or Biledulgerid ; on the South with the Land of the Negroes ; and on the West with Gulata another Province of the Negroes interposed between it and the Atlantick . Terra Nigritarum . Terra Nigritarum or the Land of the Negroes is bounded on the East with AEthiopia Superior ; on the West with the Atlantick Ocean ; on the North with Lybia deserta and on the South with the Ethiopick Ocean , and part of AEthiopia Inferior . AEthiopia Superior . AEthiopia Superior is bounded on the East with the Red Sea and the Sinus Barbaricus ; on the West with Lybia Interior , the Realm of Nubia in the Land of the Negroes and part of the Kingdoms of Congo in the other AEthiopia ; on the North with Egypt and Lybia Marmarica , and on the South with the Mountains of the Moon , by which it is parted from the main Body of AEthiopia Inferior . It is situate on both sides of the AEquinoctial , extending from the South Parallel of seven degrees , where it meeteth with some part of the other AEthiopia to the Northern end of the Isle of Meroz situated under the fifth Parallel on the North of that Circle . AEthiopia Inferior . AEthiopia inferior is bounded on the East with the Red Sea ; on the West with the Ethiopick Ocean ; on the North with Terra Nigritarum , and the higher AEthiopia ; and on the South where it endeth , is a point of a Conus , with the main Ocean parting it from the Southern undiscovered Continent . This in Ptolemyes time went under the name of Terra incognita . CHAP. IV. Of America . AMerica the fourth and last part of the World is bounded on the East with the Atlantick Ocean and the Vergivian Seas , by which it is parted from Europe and Africa ; on the West with the Pacifick Ocean , which divides it from Asia ; on the South with some part of Terra Australis incognita , from which it is separated by a long , but narrow Strait , called the Straits of Magellan ; the North bounds of it hither to not so well discovered , as that we can certainly affirm it to be Island or Continent . It is called by some and that most aptly , The new World ; New for the late discovery , and World for the vast greatness of it . The whole is naturally divided into two great Peninsules , whereof that towards the North is called Mexicana . That towards the South hath the name of Peruana : the Isthmus which joyneth these two together is very long , but narrow in some places not above 120 miles from Sea to Sea , in many not above seventeen . The Northern Peninsula called Mexicana , may be most properly divided into the Continent and Islands : The Continent again into the several Provinces of 1. Estotiland , 2. Nova Francia , 3. Virginia , 4. Florida , 5. California , 6. Nova Gallicia , 7. Nova Hispania , 8. Guntimala . The Southern Peninsula called Peruana , taking in some part of the Isthmus , hath on the Continent the Provinces of 1. Castella Aurea , 2. Nova Granada , 3. Peru , 4. Chile , 5. Paraguay , 6. Brasil , 7. Guiana , and 8. Paria . The Islands which belong to both , are dispersed either in the Southern Ocean called Mare del Zur , where there is not any one of Note but those called Los Ladrones and the Islands of Solomon . Or in the Northern Ocean called Mare del Noords , reduced unto the Caribes , Porto-Rico , Hispaniola , Cuba and Iamaica . And thus much concerning the real and known parts of the Terrestrial Globe . CHAP. XV. Of the Description of the Terrestrial Globe by Maps Vniversal and Particular . HItherto we have spoken of the true and real Terrestrial Globe , and of the measure thereof by Circles , Zones , and Climates , as it is usually represented by a Sphere or Globe ; which must be confessed to be the nearest and the most ▪ commensurable to nature : Yet it may also be described upon a plain , in whole or in part many several ways : But those which are most useful and artificial are these two , by Parallelogram and by Planisphere . 2. The description thereof by Parallelogram is thus , the Parallelogram is divided in the midst by a line drawn from North to South , passing by the Azores or Canaries for the great Meridian . Cross to this and at eight Angles , another line is drawn from East to West for the AEquator ; then two parallels to each to comprehend the figure , in the squares whereof there are set down four parts of the world rather than the whole : And this way of description though not exact or near to the natural , hath yet been followed by such as ought still to be accounted excellent , and is the form of our plain Charts , and in places near the AEquinoctial may be used without committing any great error ; because the Meridians about the AEquinoctial are equi-distant , but as they draw up towards the Pole , they do upon the Globe come nearer and nearer together , to shew that their distance is proportionably diminished till it come to a concurrence , and answerably the Parallels as they are deeper in latitude , so they grow less and less with the Sphere ; so that at 60 degrees , the Equinoctial is double to the parallel of Latitude , and so proportionably of the rest . 3. Hence it followeth , that if the picture of the earth be drawn upon a Parallelogram , so that the Meridians be equally distant throughout , and the Parallels equally extended , the Parellel of 60 degrees shall be as great as the line of the AEquator it self is , and he that coasteth about the world in the latitude of 60 degrees , shall have as far to go by this Map , as he that doth it in the AEquator , though the way be but half as long . For the longitude of the Earth in the AEquator it self , is 21600 ; but in the Parallel of 60 but 10800 miles . So two Cities under the same parallel of 60 , shall be of equal Longitude to other two under the Line , and yet the first two shall be but 50 , the other two an hundred miles distant . So two Ships departing from the AEquator at 60 miles distance , and coming up to the Parallel of 60 , shall be thirty miles nearer , and yet each of them keep the same Meridians and sail by this Card upon the very points of the Compass at which they set forth . This was complained of by Martin Cortez and others , and the learned Mercator considering well of it , caused the degrees of the Parallel to increase by a proportion towards the Pole. The Mathematical Generation whereof , Mr. Wright in the second Chapter of his Correction of Errors in Navigation , hath sought by the inscription of a Planisphere into a Concave Cylinder . And this description of the Earth upon a Parallelogram , may indeed be so ordered by Art , as to give a true account of the scituation and distance of the parts , but cannot be fitted to represent the figure of the whole . 4. The description therefore of the whole by Planisphere is much better , because it represents the face of the Earth upon a plain , in its own proper Spherical Figure as upon the Globe it self . This description cannot well be contrived upon so few as one Circle or more than two . Suppose then the Globe to be divided into two equal parts or Hemispheres , which cannot be done but by a great Circle : And therefore it must be done by the AEquator or Meridian ( for the Colure is all one with the Meridian ) the Horizon cannot fix , and the Zodiack hath nothing to do here . 5. Suppose then the Globe to be flatted upon the plain of the AEquator , and you have the first way of projection dividing the Globe into the North and South Hemispheres . In this projection the Pole is the Centre , the AEquator is the Circumference divided into 360 degrees of Longitude , the Paralles are whole Circles , the Meridians are streight lines , the Parallels are Parallels indeed , and the Meridians equi-distantly concur , and therefore all the degrees are equal . After this way of projection , Ptolemy describes that part of the habitable world which was discovered to his time . 6. Suppose the Globe to be flatted upon the plain of the Meridian , and you have the other way of projection ; the AEquator here is a streight line , the great Meridian a whole Circle , in this Section the Meridians do not equi-distantly concur , the Parallels are not Parallels indeed , and therefore the degrees are all unequal . However , this latter way is that which is now most and indeed altogether in use . 7. Particular Maps are but limbs of the Globe , and therefore though they are drawn asunder , yet are they still to be done with that proportion , as a remembring eye may suddenly acknowledge , and joyn them to the whole Body . The Projection is most commonly upon a Parallelogram , in which the Latitude is to be expressed by Paralles from North to South , and the Longtitude by Meridians from West to East at 10 or 15 degrees distance , as you please , and may be drawn either by circle or right Lines ; but if they be right Lines , the Meridians are not to be drawn parallel , but inclining and concurring , to shew the nature of the whole , whereof they are such parts . For the Graduation ; the degrees of Longitude are most commonly divided upon the North and South sides of the Parallelogram ; the degrees of Latitude upon the East and West sides , or otherwise upon the most Eastern or Western Meridian of the Map , within the square . But it hath seemed good to some in these particular descriptions to make no graduation or projection at all ; but to put the matter off to a scale of Miles , and leave the rest to be believed . The difference of Miles in several Countries is great , but it will be enough to know that the Italian and English , are reckoned for all one , and four of these do make a German Mile ; two a French League . The Swedish or Danish Mile consisteth of 5 Miles English and somewhat more . Sixty common English and Italian Miles answer to a degree of a great Circle . Now as the Miles of several Countries do very much differ , so those of the same do not very much agree : and therefore the scales are commonly written upon with Magna , Mediocria and Parva , to shew the difference . In some Maps you shall find the Miles thus hiddenly set down , and the meaning is , that you should measure the Milliaria magna upon the lowermost Line , the Parva upon the uppermost , and the Mediocria upon the middlemost . Scala Milliarium . The use of the Scale is for the measuring the distances of places in the Map , by setting one foot of your Compasses in the little circle representing one place , and the other foot in the like little circle representing another , the Compasses kept at that distance being applied to the Scale , will shew the number of great or middle Miles according as the inhabitants of those places are known to reckon . Soli Deo Gloria . A View of the more Notable Epochae Epochae . Years of the Julian Period . Months The Julian Period 1 Ian. 1 Creation of the World 765 Ian. 1 AEra of the Olympiades 3938 Iuly 8 The building of Rome 4961 Ap. 21 Epochae of Nabonasser 3667 Feb. 26 The beginning of Metons Cyrcle . 4281 Iune 26 The beginning of the periods of Calippus 4384 Iune 28 The Death of Alexander the great 4390 No. 12 AEra of the Caldees 4403 Oct. 15 The AEra of Dionysrus 4429 Mar. 25 The beginning of the Christian AEra falls in the 4713 year of the Julian Period . Years of Christ Month The Dioclesian AEra 284 Aug. 29 The Turkish AEra or Hegyra 622 Iuly 16 The Persian AEra from Iesdagird 632 Iune 16 The AEra from the Persian Sultan 1079 Mar. 14 Days in the Year of Julian Accompt AEgypt and Persian Accompt 1 0 0 0   365 2 5 0   1 0 0 0   365 0 0 0 2 0 0 0   730 5 0 0   2 0 0 0   730 0 0 0 3 0 0 0   1095 7 5 0   3 0 0 0   1095 0 0 0 4 0 0 0   1461 0 0 0   4 0 0 0   1460 0 0 0 5 0 0 0   1826 2 5 0   5 0 0 0   1825 0 0 0 6 0 0 0   2191 5 0 0   6 0 0 0   2190 0 0 0 7 0 0 0   2556 7 5 0   7 0 0 0   2555 0 0 0 8 0 0 0   2922 0 0 0   8 0 0 0   2920 0 0 0 9 0 0 0   3287 2 5 0   9 0 0 0   3285 0 0 0 10 0 0 0   3652 5 0 0   10 0 0 0   3650 0 0 0 Days in Julian Months Days in AEgyptian Months Days in Persian Months Comon Bissex Thoth 30 Pharvadin 30 Ianuary 31 30 Paophi 60 Aripehast 60 February 59 60 Athyr 90 Chortat 90 March 90 91 Chaeae 120 Tirma 120 April 120 121 Tybi 150 Mertat 150 May 151 152 Michir 180 Sachriur 180 Iune 181 182 Phamenoth 210 Macherma 210 Iuly 212 213 Pharmuthi ; 240 Apenina Wahak 245 August 243 244 Pachon 270 September 273 274 Payny 300 Aderma 275 October 304 305 Ephephi 330 Dima 305 November 334 335 Mesori 330 Pechmam 335 December 365 366 Epagomena 365 Aphander 365 Days in Turkish or Arabical Years Days in Turkish Months 1 354   Muharran 30 2 709   Sapher 59 3 .1063   Rabie 1. 89 4 .1417   Rabie 2. 118 5 .1772   Giumadi 1. 148 6 .2126   Giumadi 2. 177 7 .2480   Regeb 207 8 .2835   Sahahen 236 9 .3189   Ramaddan 266 10 .3543   Scheval 295 11 .3898   Dulkadati 325 12 .4252   Dulhajati Dsilhittsche true 354 13 .4607   14 .4961   15 .5315   In anno Abundanti 355 16 .5670   17 .6024     18 .6378     19 .6733     20 .7087     21   7442       22   7796       23   8150       24   8505       25   8859       26   9213       27   9568       28   9922       29   10276       30 0 10631 0     60 0 21262 0     90 0 31893 0     120 0 42524 0     150 0 53155 0     180 0 63786 0     210 0 74417 0     240 0 05048 0     270 0 95679 0     300 0 106310 0       Ianuary February March 1 3 A Circumcis .   D Purificat 3 D   2   B   11 E     E   3 11 C   19 F   11 F   4   D   8 G     G   5 19 E     A   19 A   6 8 F Epiphany 16 B   8 B   7   G   5 C     C   8 16 A     D   16 D   9 5 B   13 E   5 E   10   C   2 F     F   11 13 D     G   13 G   12 2 E   10 A   2 A   13   F     B     B   14 10 G   18 C   10 C   15   A   7 D     D   16 18 B     E   18 E   17 7 C   15 F   7 F   18   D   4 G     G   19 15 E     A   15 A   20 4 F   12 B   4 B   21   G   1 C     C   22 12 A     D   12 D   23 1 B   9 E   1 E   24   C     F     F   25 9 D Conv. S. Paul 17 G S. Matthias 9 G Anunc . 26   E   6 A     A   27 17 F     B   17 B   28 6 G   14 C   6 C   29   A           D   30 14 B         14 E   31 3 C         3 F     April May Iune 1   G   11 B Phil. & Jac.   E   2 11 A     C   19 F   3   B   19 D   8 G   4 19 C   8 E   16 A   5 8 D     F   5 B   6 16 E   16 G     C   7 5 F   5 A   13 D   8   G     B   2 E   9 13 A   14 C     F   10 2 B   2 D   10 G   11   C     E     A S. Barnaby 12 10 D   10 F   18 B   13   E     G   7 C   14 18 F   18 A     D   15 7 G   7 B   15 E   16   A     C   4 F   17 15 B   15 D     G   18 4 C   4 E   12 A   19   D     F   1 B   20 12 E   12 G     C   21 1 F   1 A   9 D   22   G     B     E   23 9 A   9 C   17 F   24   B     D   6 G S. John B. 25 17 C Mark Evang. 17 E     A   26 6 D   6 F   14 B   27   E     G   3 C   28 14 F   14 A     D   29 5 G   3 B   11 E Pet. Ap. 30   A     C     F   31       11 D           Iuly August September 1 19 G   8 C   16 F   2 8 A   16 D   5 G   3   B   5 E     A   4 16 C     F   13 B   5 5 D   13 G   2 C   6   E   2 A     D   7 13 F     B   10 E   8 2 G   10 C     F   9   A     D   18 G   10 10 B   18 E   7 A   11   C   7 F     B   12 18 D     G   15 C   13 7 E   15 A   4 D   14   F   4 B     E   15 15 G     C   12 F   16 4 A   12 D   1 G   17   B   1 E     A   18 12 C     F   9 B   19 1 D   9 G     C   20   E Margaret   A   17 D   21 9 F   17 B   6 E S. Matth 22   G   6 C     F   23 17 A     D   14 G   24 6 B   14 E Barthol . 3 A   25   C   3 F     B   26 14 D   11 G   11 C   27 3 E   19 A   19 D   28   F     B   8 E   29 11 G   8 C     F S. Mich. 30 9 A     D     G   31   B     E           October November December 1 16 A     D All Saints 13 F   2 5 B   13 E All Souls 2 G   3 13 C   2 F     A   4 2 D     G   10 B   5   E   10 A P. Conspir .   C   6 10 F     B   18 D   7   G   18 C   7 E   8 18 A   7 D     F   9 7 B     E   15 G   10   C   15 F   4 A   11 15 D   4 G     B   12 4 E     A   12 C   13   F   12 B   1 D   14 12 G   1 C     E   15 13 A     D   9 F   16   B   9 E     G   17 9 C     F   17 A   18   D Luke Evang. 17 G   6 B   19 17 E   6 A     C   20 6 F     B   14 D   21   G   14 C   3 E S. Thomas 22 14 A   3 D     F   23 3 B     E   11 G   24   C   11 F   19 A   25 11 D   19 G     B Chri. Nat. 26 19 E     A   8 C S. Steph. 27   F   8 B     D S. John 28 8 G Sim. & Jude   C   16 E Innocents 29   A   16 D   5 F   30 16 B   5 E S. Andrew   G   31 5 C         13 A Sylvester   Ianuary February March 1 * A XXIX D * D 2 XXIX B XXVIII E XXIX E 3 XXVIII C XXVII F XXVIII F 4 XXVII D 25. XXVI G XXVII G 5 XXVI E XXV . XXIV A XXVI A 6 25. XXV F XXIII B 25. XXV B 7 XXIV G XXII C XXIV C 8 XXIII A XXI D XXIII D 9 XXII B XX E XXII E 10 XXI C XIX F XXI F 11 XX D XVIII G XX G 12 XIX E XVII A XIX A 13 XVIII F XVI B XVIII B 14 XVII G XV C XVII C 15 XVI A XIV D XVI D 16 XV B XIII E XV E 17 XIV C XII F XIV F 18 XIII D XI G XIII G 19 XII E X A XII A 20 XI F IX B XI B 21 X G VIII C X C 22 IX A VII D IX D 23 VIII B VI E VIII E 24 VII C V F VII F 25 VI D IV G VI G 26 V E III A V A 27 IV F II B IV B 28 III G I C III C 29 II A     II D 30 I B     I E 31 * C     * F   April May Iune 1 XXIX G XXVIII B XXVII E 2 XXVIII A XXVII C 25. XXVI F 3 XXVII B XXVI D XXV . XXIV G 4 25. XXVI C 25. XXV E XXIII A 5 XXV . XXIV D XXIV F XXII B 6 XXIII E XXIII G XXI C 7 XXII F XXII A XX D 8 XXI G XXI B XIX E 9 XX A XX C XVIII F 10 XIX B XIX D XVII G 11 XVIII C XVIII E XVI A 12 XVII D XVII F XV B 13 XVI E XVI G XIV C 14 XV F XV A XIII D 15 XIV G XIV B XII E 16 XIII A XIII C XI F 17 XII B XII D X G 18 XI C XI E IX A 19 X D X F VIII B 20 IX E IX G VII C 21 VIII F VIII A VI D 22 VII G VII B V E 23 VI A VI C IV F 24 V B V D III G 25 IV C IV E II A 26 III D III F I B 27 II E II G * C 28 I F I A XXIX D 29 * G * B XXVIII E 30 XXIX A XXIX C XXVII F 31     XXVIII D       Iuly August September 1 XXVI G XXV . XXIV C XXIII F 2 25. XXV A XXIII D XXII G 3 XXIV B XXII E XXI A 4 XXIII C XXI F XX B 5 XXII D XX G XIX C 6 XXI E XIX A XVIII D 7 XX F XVIII B XVII E 8 XIX G XVII C XVI F 9 XVIII A XVI D XV G 10 XVII B XV E XIV A 11 XVI C XIV F XIII B 12 XV D XIII G XII C 13 XIV E XII A XI D 14 XIII F XI B X E 15 XII G X C IX F 16 XI A IX D VIII G 17 X B VIII E VII A 18 IX C VII F VI B 19 VIII D VI G V C 20 VII E V A IV D 21 VI F IV B III E 22 V G III C II F 23 IV A II D I G 24 III B I E * A 25 II C * F XXIX B 26 I D XXIX G XXVIII C 27 * E XXVIII A XXVII D 28 XXIX F XXVII B 25. XXVI E 29 XXVIII G XXVI C XXV . XXIV F 30 XXVII A 25. XXV D XXIII G 31 25. XXVI B XXIV E       October   November   December   1 XXII A XXI D XX F 2 XXI B XX E XIX G 3 XX C XIX F XVIII A 4 XIX D XVIII G XVII B 5 XVIII E XVII A XVI C 6 XVII F XVI B XV D 7 XVI G XV C XIV E 8 XV A XIV D XIII F 9 XIV B XIII E XII G 10 XIII C XII F XI A 11 XII D XI G X B 12 XI E X A IX C 13 X F IX B VIII D 14 IX G VIII C VII E 15 VIII A VII D VI F 16 VII B VI E V G 17 VI C V F IV A 18 V D IV G III B 19 IV E III A II C 20 III F II B I D 21 II G I C * E 22 I A * D XXIX F 23 * B XXIX E XXVIII G 24 XXIX C XXVIII F XXVII A 25 XXVIII D XXVII G XXVI B 26 XXVII E 25. XXVI A 25. XXV C 27 XXVI F XXV . XXIV B XXIV D 28 25. XXV G XXIII C XXIII E 29 XXIV A XXII D XXII F 30 XXIII B XXI E XXI G 31 XXII C     XX A A Table shewing the Dominical Letter , Golden Number and Epact , according to the Julian account for ever , and in the Gregorian , till the Year 1700.         1672 1 GF CB 1673 2 E A 1674 3 D G 1675 4 C F 1676 5 BA ED 1677 6 G C 1678 7 F B 1679 8 E A 1680 9 DC GF 1681 10 B E 1682 11 A D 1683 12 G C 1684 13 FE BA 1685 14 D G 1686 15 C F 1687 16 B E 1688 17 AG DC 1689 18 F B 1690 19 E A 1691 20 D G 1692 21 CB FE 1693 22 A D 1694 23 G C 1695 24 F B 1696 25 ED AG 1697 26 C F 1698 27 B E 1699 28 A D Year G Julian Gregor .   N Epact Epact 1672 1 11 1 1673 2 22 12 1674 3 3 23 1675 4 14 4 1676 5 25 15 1677 6 6 26 1678 7 17 7 1679 8 28 18 1680 9 9 29 1681 10 20 10 1682 11 1 21 1683 12 12 2 1684 13 23 13 1685 14 4 24 1686 15 15 5 1687 16 26 16 1688 17 7 17 1689 18 18 8 1690 19 29 19 The anticipation of the Gregorian Calender . From 5 October 1582 D. 10 From 24 Feb. 1700 D. 11 From 24 Feb. 1800 D. 12 From 24 Feb. 1900 D. 13 From 24 Feb. 2100 D. 14 From 24 Feb. 2200 D. 15 From 24 Feb. 2320 D. 16     III IV V VI VII VIII 1 P * XI XXII III XIV XXV 2 N XXIX X XXI II XIII XXIV 3 M XXVIII IX XX I XII XXIII 4 H XXVII VIII XIX * XI XXII 5 G XXVI VII XVIII XXIX X XXI 6 F XXV VI XVII XXVIII IX XX 7 E XXIV V XVI XXVII VIII XIX 8 D XXIII IV XV XXVI VII XVIII 9 C XXII III XIV XXV VI XVII 10 B XXI II XIII XXIV V XVI 11 A XX I XII XXIII IV XV 12 u XIX * XI XXII III XIV 13 t XVIII XXIX X XXI II XIII 14 s XVII XXVIII IX XX I XII 15 r XVI XXVII VIII XIX * XI 16 q XV XXVI VII XVIII XXIX X 17 p XIV XXV VI XVII XXVIII IX 18 n XIII XXIV V XVI XXVII VIII 19 m XII XXIII IV XV XXVI VII 20 l XI XXII III XIV XXV VI 21 k X XXI II XIII XXIV V 22 i IX XX I XII XXIII IV 23 h VIII XIX * XI XXII III 24 g VII XVIII XXIX X XXI II 25 f VI XVII XXVIII IX XX I 26 e V XVI XXVII VIII XIX * 27 d IV XV XXVI VII XVIII XXIX 28 c III XIV XXV VI XVII XXVIII 29 b II XIII XXIV V XVI XXVII 30 a I XII XXIII IV XV XXVI IX X XI XII XIII XIV XV VI XVII XXVIII IX XX I XII V XVI XXVII VIII XIX * XI IV XV XXVI VII XVIII XXIX   III XIV XXV VI XVII XXVIII IX II XIII XXIV V XVI XXVII VIII I XII XXIII IV XV XXVI VII * XI XXII III XIV 25 VI XXIX X XXI II XIII XXIV V XXVIII IX XX I XII XXIII IV XXVII VIII XIX * XI XXII III XXVI VII XVIII XXIX X XXI II XXV VI XVII XXVIII IX XX I XXIV V XVI XXVII VIII XIX * XXIII IV XV XXVI VII XVIII XXIX XXII III XIV XXV VI XVII XXVIII XXI II XIII XXIV V XVI XXVI XX I XII XXIII IV XV XXVII XIX * XI XXII III XIV 25 XVIII XXIX X XXI II XIII XXIV XVII XXVIII IX XX I XII XXIII XVI XXVII VIII XIX * XI XXII XV XXVI VII XVIII XXIX X XXI XIV XV VI XVII XXVIII IX XX XIII XXIV V XVI XXVII VIII XIX XII XXIII IV XV XXVI VII XVIII XI XXII III XIV 25 VI XVII X XXI II XIII XXIV V XVI IX XX I XII XXIII IV XV VIII XIX * XI XXII III XIV VII XVIII XIX X XXI II XIII   XVI XVII XVIII XIX I II P XXIII IV XV XXVI VIII XIX N XXII III XIV 25 VII XVIII M XXI II XIII XXIV VI XVII H XX I XII XXIII V XVI G XIX * XI XXII IV XV F XVIII XXIX X XXI III XIV E XVII XXVIII IX XX II XIII D XVI XXVII VIII XIX I XII C XV XXVI VII XVIII * XI B XIV 25 VI XVII XXIX X A XIII XXIV V XVI XXVIII IX u XII XXIII IV XV XXVII VIII t XI XXII III XIV XXVI VII t X XXI II XIII 25 VI r IX XX I XII XXIV V q VIII XIX * XI XXIII IV p VII XVIII XXIX X XXII III n VI XVII XXVIII IX XXI II m V XVI XXVII VIII XX I l IV XV XXVI VII XIX * k III XIV 25 VI XVIII XXIX i II XXIII XXIV V XVII XXVIII h I XII XXIII IV XVI XXVII g * XI XXII III XV XXVI f XXIX X XXI II XIV 25 e XXVIII IX XX I XIII XXIV d XXVII VIII XIX * XII XXIII c XXVI VII XVIII XXIX XI XXII b 25 VI XVII XXVIII X XXI a XXIV V XVI XXVII IX XX Anni Christi . N I     P 320     P 580 Biss.   a 800 Biss. C b 1100 Biss. C c 1400 Biss. C Detract is decem diebus . D 1484     D 1600 Biss.   C 1700     C 1800   CC B 1900     B 2000 Biss.   B 2100   C A 2200     u 2300     A 2409 Biss. C u 2500     t 2600     t 2700   C t 2800 Biss.   s 2900     s 3000   C r 3100     r 3200 Biss.   r 3300   C q 3400     p 3500     Anni Christi . q 3600 Biss. C p 3700     n 3800     n 3900     n 4000 Biss. C m 4100     l 4200     l 4300   CC l 4400 Biss.   k 4500     k 4600   C i 4700     i 4800 Biss.   i 4900   C h 5000     g 5100     h 5200 Biss. C g 5300     f 5400     f 5500   C f 5600 Biss.   e 5700     e 5800   C d 5900     d 6000 Biss.   d 6100   C c 6200     b 6300     c 6400 Biss. C b 6500     A Table shewing the Dominical Letter both in the Julian and the Gregorian account for ever . Cy. ☉ 1 2 3 4 5 6 7 1 C B D C E D F E G F A G B A 2 A B C D E F G 3 G A B C D E F 4 F G A B C D E 5 E D F E G F A G B A C B D C 6 C D E F G A B 7 B C D E F G A 8 A B C D E F G 9 G F A G B A C B D C E D F E 10 E F G A B C D 11 D E F G A B C 12 C D E F G A B 13 B A C B D C E D F E G F A G 14 G A B C D E F 15 F G A B C D E 16 E F G A B C D 17 D C E D F E G F A G B A C B 18 B C D E F G A 19 A B C D E F G 20 G A B C D E F 21 F E G F A G B A C B D C E D 22 D E F G A B C 23 C D E F G A B 24 B C D E F G A 25 A G B A C B D C E D F E G F 26 F G A B C D E 27 E F G A B C D 28 D E F G A B C Anni 1582     1900     2300   1600 1700 1800 2000 2100 2200 2400       2700     3100   Chr. 2500 2600   2900 3000           2800     3200 3300       LXX Ash. East . Asci . Pent. Corp. Christi . Adv. 16 XXIII   Ian. Feb. Mar. Apr. May. May. Nov. 5 XXII d 18 4 22 30 10 21 29   XXI e 19 5 23 Ma. 1 11 22 30 13 XX f 20 6 24 2 12 23 De. 1 2 XIX g 21 7 25 3 13 24 2   XVIII a 22 8 26 4 14 25 3 10 XVII b 23 9 27 5 15 26 No. 27   XVI c 24 10 28 6 16 27 28 18 XV d 25 11 29 7 17 28 29 7 XIV e 26 12 30 8 18 29 30   XIII f 27 13 31 9 19 30 Dec. 1 15 XII g 28 14 Ap. 1 10 20 31 2 4 XI a 29 15 2 11 21 Iun. 1 3   X b 30 16 3 12 22 2 No. 27 12 IX c 31 17 4 13 23 3 28 1 VIII d Feb. 1 18 5 14 24 4 29   VII e 2 19 6 15 25 5 30   VI f 3 20 7 16 26 6 Dec. 1 9 V g 4 21 8 17 27 7 2 17 IV a 5 22 9 18 28 8 3 6 III b 6 23 10 19 29 9 No. 27   II c 7 24 11 20 30 10 28 14 I d 8 25 12 21 31 11 29 3 * e 9 26 13 22 Iun. 1 12 30   XXIX f 10 27 14 23 2 13 Dec. 1 11 XXVIII g 11 28 15 24 3 14 2   XXVII a 12 Ma. 1 16 25 4 15 3 19 25. XXVI b 13 2 17 26 5 16 No. 27 8 XXV . XXIV c 14 3 18 27 6 17 28     d 15 4 19 28 7 18 29     e 16 5 20 29 8 19 30     f 17 6 21 30 9 20 Dec. 1     g 18 7 22 31 10 21 2     a 19 8 23 Iun. 1 11 22 3     b 20 9 24 2 12 23 No. 27     c 21 10 25 3 13 24 28 A Table to convert Sexagenary Degrees and Minutes into Decimals and the contrary . 1 00 37 10 73 20 109 30 145 40 181 50 2   38   74   110   146   182   3   39   75   111   147   183   4 01 40 11 76 21 112 31 148 41 184 51 5   41   77   113   149   185   6   42   78   114   150   186   7   43   79   115   151   187   8 02 44 12 80 22 116 32 152 42 188 52 9   45   81   117   153   189   10   46   82   118   154   190   11 03 47 13 83 23 119 33 155 43 191 53 12   48   84   120   156   192   13   49   85   121   157   193   14   50   86   122   158   194   15 04 51 14 87 24 123 35 159 44 195 54 16   52   88   124   160   196   17   53   89   125   161   197   18 05 54 15 90 25 126 35 162 45 198 55 19   55   91   127   163   199   20   56   92   128   164   200   21   57   93   129   165   201   22 06 58 16 94 26 130 36 166 46 202 56 23   59   95   131   167   203   24   60   96   132   168   204   25   61   97   133   169   205   26 07 62 17 98 27 134 37 170 47 206 57 27   63   99   135   171   207   28   64   100   136   172   208   29 08 65 18 101 28 137 38 173 48 209 58 30   66   102   138   174   210   31   67   103   139   175   211   32   68   104   140   176   212   33 09 69 19 105 29 141 39 177 49 213 59 34   70   106   142   178   214   35   71   107   143   179   215   36 10 72 20 108 30 144 40 180 50 216 60 217 60 253 70 289 80 325 90 277777778 218   254   290   326   555555555 219   255   291   327   833333333 220 61 256 71 292 81 328 91 111111111 221   257   293   329   388888889 222   258   294   330   666666667 223   259   295   331   944444444 224 62 260 72 296 82 332 92 222222222 225   261   297   333   500000000 226   262   298   334   777777778 227 63 263 73 299 83 335 93 055555555 228   264   300   336   333333333 229   265   301   337   511111111 230   266   302   338   888888889 231 64 267 74 303 84 339 94 166666667 232   268   304   340   444444444 233   269   305   341   722222222 234 65 270 75 306 85 342 95 000000000 235   271   307   343   277777778 236   272   308   344   555555555 237   273   309   345   833333333 238 66 274 76 310 86 346 96 111111111 239   275   311   347   388888889 240   276   312   348   666666667 241   277   313   349   944444444 242 67 278 77 314 87 350 97 222222222 243   279   315   351   500000000 244   280   316   352   777777778 245 68 281 78 317 88 353 98 055555555 246   282   318   354   333333333 247   283   319   355   611111111 248   284   320   356   888888889 249 69 285 79 321 89 357 99 166666667 250   286   322   358   444444444 251   287   323   359   722222222 252 70 288 80 324 90 360 100 000000000 A Table to Convert Sexagenary Minutes into Decimals and the contrary .   Minutes Seconds Thirds 1 00462962 00007716 00000128 2 00925925 15432 257 3 01388889 23148 385 4 01851851 30864 515 5 02314814 00038580 00000643 6 02777778 46296 771 7 03240740 54012 900 8 03703703 61728 1028 9 04166667 69444 1157 10 04629629 00077160 00001286 11 05092592 084876 1414 12 05555555 092592 1543 13 06018518 100308 1671 14 06481480 108024 1800 15 06944444 00115740 1929 16 07409407 123450 2057 17 07870370 131172 2186 18 08333333 138889 2314 19 08796296 146604 2443 20 09259259 00154320 2572 21 00722222 162036 2700 22 10185185 169752 2829 23 10648148 177468 2957 24 11111111 185184 3086 25 11574074 00192900 3215 26 12037037 200616 3343 27 12500000 208332 3472 28 12962962 216048 3600 29 13425926 223764 3729 30 13888889 00231481 00003858 31 14351852 00239670 00003986 32 14814814 246913 4115 33 15277777 254629 4243 34 15747040 262345 4372 35 16203703 270061 4581 36 16666666 00277777 00004629 37 17129629 285493 4758 38 17592592 293209 4886 39 18055555 300925 5015 40 18518518 308640 5144 41 18981481 00316356 00005272 42 19444444 324072 5401 43 19907407 331788 5529 44 20370370 339504 5658 45 20833333 347220 5787 46 21296296 00354936 00005915 47 21759259 362652 6044 48 22222222 370●70 6172 49 22685185 378084 6301 50 23148148 385802 6430 51 23611111 00393518 00006558 52 24074074 401234 6687 53 24537037 408950 6815 54 25000000 416666 6944 55 25462963 424382 7073 56 25925926 00432098 00007201 57 26388888 439814 7330 58 26851852 447530 7458 59 27314814 455256 7587 60 27777777 00462962 00007716 A Table Converting Hours and Minutes into Degrees and Minutes of the AEquator , and into   Hours . 1 04.16666667 2 08.33333333 3 12.5 4 16.16666667 5 20.83333333 6 25.0 7 29.16666667 8 33.33333333 9 37.5 10 41.66666667 11 45.83333333 12 50. 13 54.16666667 14 58.33333333 15 62.5 16 66.66606667 17 70.83333333 18 75.00 19 79.16660667 20 83.33333333 21 87.5 22 91.66666667 23 95.83333333 24 100.00000000   Minutes 1 0.06944444 2 0.13888888 3 0.20833333 4 0.27777777 5 0.34722222 6 0.41666666 7 0.48611111 8 0.55555555 9 0.625 10 0.69444444 11 0.76388888 12 0.83333333 13 0.90277777 14 0.97222222 15 1.04166666 16 1.11111111 17 1.18055555 18 1.25 19 1.31944444 20 1.38888888 21 1.45833333 22 1.52777777 23 1.59722222 24 1.66666666 25 1.73611111 26 1.80555555 27 1.875 28 1.94444444 29 2.01388888 30 2.08333333 The Decimal parts of a Day and the contrary . Seconds   Minutes Seconds .00115740 31 2.15277777 .03587963 .00231481 32 2.22222222 .03703704 .00347222 33 2.29166666 .03819444 .00462962 34 2.36111111 .03935185 .00578703 35 2.43055555 .04050926 .00694444 36 2.5 .04166666 .00810184 37 2.56944444 .04282407 .00925925 38 2.63888888 .04398148 .01041660 39 2.70833333 .04513888 .01157405 40 2.77777777 .04629629 .01273148 41 2.84722222 .04745370 .01388888 42 2.91666666 .04861111 .01504630 43 2.98611111 . 0497685● .01620371 44 3.05555555 .05092592 .01736111 45 3.125 .05208333 .01851853 46 3.19444444 .05324074 .01967593 47 3.26388888 .05439814 .02083333 48 3.33333333 .05555555 .02199074 49 3.40277777 .05671296 .02314810 50 3.47222222 .05787037 .02430555 51 3.54166666 .05902777 .02546295 52 3.61111111 .06018518 .02662037 53 3.68055555 . 06134●59 .02777777 54 3.75 .0625 .02893518 55 3.81944444 .06365741 .03009259 56 3.88888888 .06481481 .03125000 57 3.95833333 .06597222 .03240741 58 4.02777777 .06712963 .03356482 59 4.09722222 .06828704 .03472222 60 4.16666666 .06944444 A Catalogue of some of the most eminent Cittes and Towns in England and Ireland wherein is shewed the difference of their Meridian from London , with the hight of the Pole. Names of Citties Differ . Merid. Hight Pole St. Albons 0 1 s 55.55 Barwick 0 6 s 55.49 Bedford 0 2 s 52.18 Bristol 0 11 s 51.32 Boston 0 0 53.2 Cambridge 0 1 a 52.17 Canterbury 0 5 a 51.27 Carlile 0 10 s 54.57 Chester 0 11 s 53.20 Coventry 0 4 s 52.30 Carmarthen 0 17 s 52.2 Chichester 0 3 s 50.56 Colchester 0 5 a 52.4 Darby 0 5 s 53.6 Dublin in Ireland 0 26 s 53.11 Duresm● 0 5 s 54.45 Dartmouth 0 15 s 50.32 Eely 0 1 a 52.20 Grantha● 0 2 s 52.58 Glocester 0 9 s 52.00 Halefax 0 6 s 52.49 Hartford 0 1 s 52.50 Hereford 0 11 s 52.14 Huntington 0 1 s 52.19 Hull 0 1 s 53.58 Lancaster 0 11 s 54.08 Leicester 0 4 s 52.40 Lincoln 0 1 s 53.12 Middle of the Isle of Man 0 17 s 54.22 Nottingham 0 4 s 53.03 Newark 0 3 s 53.02 Newcastle 0 6 s 54.58 N. Luffingham 0 3 s 52.41 Norwich 0 4 a 52.44 Northampton 0 4 s 52.18 Oxford 0 5 s 51.54 Okenham 0 3 s 52.44 Peterborough 0 2 s 52.35 Richmond 0 6 s 54.26 Rochester 0 3 a 51.28 Ross 0 10 s 52.07 St. Michaels Mount in Cornwal 0 23 s 50.38 Stafford 0 8 s 52.55 Stamford 0 2 s 52.41 Shrewsbury 0 11 s 52.48 Tredah in Ireland 0 27 s 53.28 uppingham in Rutland 0 3 s 52.40 Warwick 0 6 s 52.25 Winchester 0 5 s 50.10 Waterford in Ireland 0 27 s 52.22 Worcester 0 9 s 52.20 Yarmouth in Suffolk 0 6 a 52.45 York 0 4 s 54.00 London 0 00 51.32 The Suns mean Longitude and mean Anomaly in AEgyptian Years .   ☉ Mean Longitude ☉ Mean Anomaly 1 99.9336437563 99.9288933116 2 99.8672875126 99.8577866232 3 99.8009312690 99.7866799348 4 99.7345750253 99.7155732465 5 99.6682187816 99.6444665581 6 99.6018625380 99.5733598697 7 99.5355062943 99.5022531814 8 99.4691500506 99.4211464930 9 99.4027938070 99.3600398046 10 99.3364375633 99.2889331162 100 93.3643756334 92.8893311628 1000 33.6437563341 28.8933116289 The Suns Mean Anomaly and Praecession of the AEquinox 8 in . 1 AEgyptian Years . Year . ☉ Mean Anomaly Praecession AEquinox . 1 99.9297857316 00.0038580246 2 99.8595714632 00.0077160493 3 99.7893571949 00.0115740740 4 99.7191429265 00.0154320987 5 99.6489286582 00.0192901234 6 99.5787143898 00.0231481481 7 66.5085001114 00.0270061728 8 99.2978573164 00.0308641975 9 99.3680715847 00.0347222221 10 99.2978573164 00.0385802469 100 92.9785731642 00.3858024691 1000 99.7857316427 03.8580246913 The Suns mean Longitude and mean Anomaly in Julian Years .   ☉ Mean Longitude ☉ Mean Anomaly 1 99.9336437563 99.9288933116 2 99.8672875126 99.8577866232 3 99.8009312689 99.7866799348 B 4 00.008365830 99.9892901234 5 99.9420095864 99.9181834350 6 99.875633427 99.8470767466 7 99.8092970990 99.7759700583 B 8 00.0167316602 99.9785802468 9 99.9503754165 99.9074735584 10 99.8840191728 99.8363668700 11 99.8176629291 99.7652591816 B 12 00.0250974903 99.9678703702 13 99.9587412466 99.8967636818 14 99.8923850029 99.8256569934 15 99.8260287592 99.7545503050 B 16 00.0334633205 99.9571604936 17 99.9671070768 99.8860548052 18 99.9007508331 99.8149481168 19 99.8343945894 99.7438414284 B 20 00.0418291506 99.9164506171 40 00.0836583012 99.8929012342 60 00.1254874518 99.8393518513 80 00.1673166024 99.7858024684 100 00.2091457530 99. 73225308●5 200 00.4182015060 99.4645061710 300 00.6274372590 99.1967592565 400 00.8365830120 98.9290123420 500 01.0457287650 98.6612654275 600 01.2548745180 98.3935185130 700 01. 4640●02710 98.1257715985 The ☉ mean Longitude and Anomaly AEra ☉ mean Longitude ☉ mean Anomaly Chr. 77. 22400.86419 58. 24289.56790 1600 80. 54891.97529 53. 95880.62961 1620 80. 59074.89035 53. 90525.69132 1640 80. 63257.80541 53. 85170.75303 1660 80. 67440.72047 53. 79815.81474 1680 80. 71623.63553 53. 74460.87645 1700 80. 75806.55059 53. 69105.93816 1720 80. 79989.46665 53. 63750.99987 1740 80. 84172.38171 53. 58396.06158 1760 80. 88265.29677 53. 53041.12329   ☉ mean Lon. in Mon. ☉ mean Ano. in Mo. Ianu. 08. 48751.49488 08. 48711.14867 Febr. 16. 15365.74832 16. 15288.96037 Mar. 24. 64117.24320 24. 64000.10904 April 32. 85489.65760 32. 85333.47872 May 41. 34241.15248 41. 34044.62739 Iune 49. 55613.56688 49. 55377.99708 Iuly 58. 04365.06176 58. 04089.14575 Aug. 66. 53116.55664 66. 52800.29442 Sept. 74. 74488.97104 74. 74133.66410 Octo. 83. 23240.46592 85. 22844.81277 Nov. 91. 44612.88032 91. 44178.18245 Dec. 99. 93364.37563 99. 92889.33116 In Anno ●issentili ; post Februarium adde unum diem & unius dies motum . The Suns mean Longitude and mean Anomaly in Days .   ☉ mean Longitude ☉ mean Anomaly 1 0.2737908048 0.2737777898 2 0.5475816096 0.5475555796 3 0.8213724144 0.8213333694 4 1.0951632192 1.0951111592 5 1 . 3●89540240 1.3688889490 6 1.6427448288 1.6426667388 7 1.9165356336 1.9164445286 8 2.1903264384 2.1902223184 9 2.4641172432 2.4640001082 10 2.7379080480 2.7377778980 11 3.0116988528 3.0115556878 12 3.2854896576 3.2853334776 13 3.5592804624 3.5591112674 14 3.8330712672 3.8328890572 15 4.1068620720 4.1066668470 16 4.3806428768 4.3804446368 17 4.6544436816 4.6542224266 18 4.9282344864 4.9280002164 19 5.2020252912 5.2077780062 20 5.4758160960 5.4755557960 21 5.7496069008 5.7493335858 22 6.0233977056 6.0231113756 23 6.2971885104 6.2968891654 24 6.5709793152 6.5706669552 25 6.8447701200 6.8444447450 26 7.1185609248 7.1182225348 27 7.3923517296 7.3920003246 28 7.6661425344 7.6957781144 29 7.9399333392 7.9395559042 30 8.2137241440 8.2133336940 31 8.4875149488 8.4871114838 The Suns mean Longitude and mean Anomaly in Days   ☉ Mean Longitude ☉ Mean Anomaly . 1 0.0114079502 0.0114074079 2 0.0228159004 0.0228148158 3 0.0342238506 0.0342222237 4 0.0456318008 0.0456296316 5 0.0570397510 0.0570370395 6 0.0684477012 0.0684444474 7 0.0798556514 0.0798518553 8 0.0912636016 0.0912592632 9 0.1026715518 0.1026666711 10 0.1140795020 0.1140740790 11 0.1254874522 0.1254814869 12 0.1368954024 0.1368888948 13 0.1483033526 0.1482963027 14 0.1597113028 0.1597037106 15 0.1711192530 0.1711111185 16 0.1825272032 0.1825185264 17 0.1939351534 0.1939259343 18 0.2053431036 0.2053333422 19 0.2167510538 0.2167407501 20 0.2281590040 0.2281481580 21 0.2395669542 0.2395555659 22 0.2509749044 0.2509629738 23 0.2623828546 0.2623703817 24 0.2737777048 0.2737777896 The Suns mean Anomaly and Praecession of the AEquinox . AEra ☉ Anomaly . Praecess . AEquinox Chr. 56. 69976.85185 20. 49768.51851 1600 53. 87323.10751 26. 67052.46907 1620 53. 83789.15687 26. 74768.51845 1640 53. 80255.20623 26. 82484.56783 1660 53. 76721.25559 26. 90200.61721 1680 53. 73187.30495 26. 97916.66659 1700 53.69653 ▪ 35431 27. 05632.71597 1720 53. 66119.40367 27. 13348.76535 1740 53. 65585.45303 27. 21064.81473 1760 53. 59051.50230 27. 28780.86411   ☉ Anomaly in Months Praecess . AEquinox in Months Ianu 08. 48718.72813 0. 00032.76678 Febr. 16. 15303.38579 0. 00062.36258 Mar. 24. 64022.11392 0. 00095.12937 April 32. 85362.81857 0. 00126.83916 May 41. 34081.54670 0. 00159.60594 Iune 49. 55422.25134 0. 00191.31573 Iuly 58. 04140.97947 0. 00224.08251 Aug. 66. 52859.70760 0. 00256.84929 Sept. 74. 74200.41225 0. 00288.55908 Octo. 83. 22919.14038 0. 00321.32587 Nov. 91. 44259.84502 0. 00353.03566 Dec. 99. 92978.57315 0. 00385.80244 The ☉ mean Anomaly , and Praecession of the AEquinox in Julian Years .   ☉ mean Anomaly Praecess . AEquinox 1 99.9297857316 00.0038580246 2 99.8595714612 00.0077160493 3 99.7893571949 00.0115740740 B 4 99.9929231686 00.0154320987 5 99.9227089002 00.0192901233 6 99.8524946318 00.0231481479 7 99.7822803634 00.0270061725 B 8 99.9858463372 00.0308641974 9 99.9156320688 00.0347222220 10 99.8454178004 00.0385802466 11 99.7752035321 00.0424382714 B 12 99.9787695058 00.0462962961 13 99.9085552374 00.0501543207 14 99.8383409690 00.0540123453 15 99.7681266066 00.0578703699 B 16 99.9716926744 00.0617283948 17 99.9014784060 00.0655864194 18 99.8312647376 00.0694444440 19 99.7610498692 00.0733024686 B 20 99.9646158434 00.0771604938 40 99.9292306868 00.1543209876 60 99.8938465302 00.2314814814 80 99.8584623736 00.3086419752 100 99.8270782170 00.3858024690 200 99.6461564340 00.7716049380 300 99.4692346510 01.1574074070 400 99.2923128680 01.5432098760 500 99.1153910850 01.9290123450 600 98.9384693020 02.3148148140 700 98.7615475190 02.7006172830 The Suns mean Anomaly and Praec . of the AEqui . in Days . D ☉ Anomaly Praecess . AEquinox 1 0.2737802348 0.0000105699 2 0.5475604697 0.0000211398 3 0.8213407046 0.0000317097 4 1.0951209395 0.0000422797 5 1.3689011744 0.0000528496 6 1.6426814092 0.0000634195 7 1.9164616441 0.0000739894 8 2.1902418790 0.0000845593 9 2.4640221139 0.0000951292 10 2.7378023488 0.0001056993 11 3.0115825836 0.0001162692 12 3.2853628184 0.0001268391 13 3.5591430532 0.0001374090 14 3.8329232880 0.0001479789 15 4.1067035228 0.0001585488 16 4.3804837576 0.0001691187 17 4.6542639924 0.0001796886 18 4.9280442272 0.0001902585 19 4.2018244620 0.0002008284 20 5.4756046976 0.0002113986 21 5.7493849324 0.0002219685 22 6.0231651672 0.0002325384 23 6.2969454020 0.0002431083 24 6.5707256368 0.0002536782 25 6.8445058716 0.0002642481 26 7.1182861064 0.0002748180 27 7.3920663412 0.0002853879 28 7.6658455766 0.0002959580 29 7.9396258115 0.0003065279 30 8.2134070464 0.0003170979 31 8.4871872813 0.0003276678 The Suns mean Anomaly and Praec . of the AEqui . in Hours D ☉ mean Anomaly Praecess . AEquinox 1 0.0114075097 0.0000004404 2 0.0228150195 08808 3 0.0342225293 13212 4 0.0456300391 17616 5 0.0570375489 22020 6 0.0684450587 0.0000026424 7 0.0798525684 30828 8 0.0912600782 35232 9 0.1026675881 39636 10 0.1140750978 44041 11 0.1254826075 0.0000048445 12 0.1368901174 0.0000052849 13 0.1482976271 57253 14 0.1597051368 61657 15 0.1711126465 66061 16 0.1825201562 70465 17 0.1939276659 74869 18 0.2053351761 0.0000079272 19 0.2167426858 83677 20 0.2281501955 88081 21 0.2395577052 92485 22 0.2509652149 96889 23 0.2623727246 101293 24 0.2737802348 0.0000105698 THE TABLES OF THE MOONS MEAN MOTIONS . The Moons mean Longitude and Apogeon AEra ☽ Mean Longitude ☽ Apogaeon Chr. 34.0088734567 78.8286265432 1600 02.0644290122 63.5892746911 1620 39.1651134566 89.6540895059 1640 76.2658079010 15.7189033207 1660 13.3665023454 41.7837191355 1680 50.4671967898 67.6485339503 1700 87.5675912342 93.9133487651 1620 29.6685801230 19.9781635799 1740 61.7692801230 46.0429783947 1760 98.8699745674 72.1077932095   ☽ Mean Long. in Mon. ☽ Apogaeon in Mont. Ianu. 13.4633984897 00.9593447922 Febr. 15.9464670933 01.8258497658 Mar. 29.4098665830 02.7851945580 April 39.2131554440 03.7135927440 May. 52.6765539337 04.6729375362 Iune 62.4798427947 05.6013357222 Iuly 75.9432412844 06.5606805144 Aug. 89.4066397741 07.5200253066 Sept. 99.2099286451 08.4484234926 Octo. 12.6733271348 09.4077682848 Nov. 22.4766159958 10.3361664708 Dec. 35.9400144893 11.2955112636 The Moons mean Anomaly and Node Retrograde AEra ☽ Mean Anomaly ☽ Node Retrograde Chr. 55.1802469135 74.6984567901 1600 38.4751543211 78.2198302468 1620 49.5110239507 70.7638117283 1640 60.5469035803 63.3077932098 1660 71.5827832099 55.8517746913 1680 82.6186628395 48.3957561728 1700 93.6545424691 40.9397376543 1720 04.6904220987 33.4837191358 1740 15.7263017283 26.0277006173 1760 26.7621813579 18.5716820988   ☽ Mean Ano. in Mon. Node Ret. in Mont. Ianu. 12.5040536975 00.4559979224 Febr. 14.7206183275 00.8678670136 Mar. 27.2246720250 01.3238649360 April 35.4995627000 01.7651532480 May. 48.0036163975 02.2211511704 Iune 56.8785070725 02.6624394824 Iuly 69.3825607700 03.1184374048 Aug. 81.8866144675 03.5744353272 Sept. 90.7615051425 04.0157236392 Octo. 03.2655588400 04.4717215616 Nov. 12.1404495150 04.9130098736 Dec. 24.6445032256 05.3690078260 The Moons mean Motions in Julian Years .   ☽ Mean Longitude ☽ Apogaeon 1 35.9400144893 11.2955112636 2 71.8800289786 22.5910225272 3 07.8200434679 33.8865337908 B 4 47.4201388888 45.2129629629 5 83.3601533781 56.5084742265 6 19.3001678674 67.8039854901 7 55.2401823567 79.0994967537 B 8 94.8402777777 90.4259259258 9 30.7802922670 01●7214371894 10 66.7203067563 13.0169484530 11 02.6603212456 24.3124597166 B 12 42.2604166666 35.6388888888 13 78. ●004311559 46.9344001524 14 14.1404456652 58 . 2299114●60 15 50.0804601545 69. ●2●4226706 B 16 89.6805555555 80.8518518518 17 25.6205700448 91.1473631154 18 61.5605845341 02.4428743790 19 97.5005990234 13.7383856426 B 20 37.1006944404 26 . 0648●48148 40 74.2013888888 52.1296296296 60 11.3020833333 78.1944444444 80 48.4027777777 04.2592592592 100 85.5034722222 30.3240740740 200 71.0069444444 60 . 648●●81●81 300 56.5104166666 90.9722222222 400 42.0138888888 21.2962962962 500 27 . 517361111● 51.6003703700 600 13.0208333333 91.9444444442 700 98.5243055555 12.2685185182 The Moons mean Motions in Julian Years   ☽ Mean Anomaly ☽ Nodes Retrograde 1 24.6445032256 05.3690078260 2 49.2890064512 10.7380156520 3 73.9335096768 16.1070234780 B 4 02.2071759259 21.4912037037 5 26.8516791515 26.7602115297 6 5● . 4951823771 32.1292193557 7 76.1396856027 37.4982271817 B 8 04.4143518518 42.9824074074 9 29.0588550774 48.3514152334 10 53.7033583030 53.7204230594 11 78.3478615286 59.0894308854 B 12 06.6215277777 64.4736111111 13 37.2660310033 69.8426189371 14 55.9105342289 74.2116267631 15 80.5550374545 79.5806345891 B 16 08.8287037037 85.9648148148 17 33.4732069293 91.3338226408 18 58.1177101549 96.7028304668 19 82. ●622133805 02.0718382928 B 20 11 . 0●58796●97 07.4560185185 40 22.0717592594 14.9120370370 60 33.1076388891 22.3680555555 80 44.1435185188 29.8040740740 100 55.1793981487 37.2800925925 200 10.3587062074 74.5601851850 300 65.5381944461 11.8402777775 400 20.7175925948 49.1203703700 500 75.8969907435 86.4004629629 600 31.0763888922 23.6805555555 700 86.2557870409 60.9606481480 The Moons mean Motions in Days . Days ☽ Mean Longitude ☽ Apogaeon 1 03.6601096287 00.0309466062 2 07.3202192574 00.0618932124 3 10.9803288861 00.0928398186 4 14.6404385148 00.1237864248 5 18.3005481435 00.1547330310 6 21.9606577722 00.1856796372 7 25.6207674009 00.2166262434 8 29.2808770296 00.2475728496 9 32.9409866583 00.2785194558 10 36.6010962870 00.3094660620 11 40.2612059157 00.3404126682 12 43.9213155444 00.3713592744 13 47.5814251731 00.4023058806 14 51.2415348018 00.4332524868 15 54.9016444305 00.4641990930 16 58.5617540592 00.4951456992 17 62.2218636879 00.5260923054 18 65.8819733166 00.5570389116 19 69.5420829453 00.5879855178 20 73.2021925740 00.6189321240 21 76.8623022037 00.6498787302 22 80.5224118314 00.6808233364 23 84.1825214601 00.7117719426 24 87.8426310898 00.7427185488 25 91.5027407175 00.7736651550 26 95.1628503462 00.8046117612 27 98.8229599749 00.8355583674 28 02.4830696036 00.8665049736 29 06.1431792323 00.8974515798 30 09.8032888610 00.9283981860 31 13.4633984897 00.9593447922 The Moons mean Motions in Days . Days ☽ Mean Anomaly ☽ Node Retrograde 1 03.6291630225 00.0147096104 2 07.2583260450 00.0294192208 3 10.8874890675 00.0441288312 4 14.5166520900 00.0588384416 5 18.1458151125 00.0735480520 6 21.7749781350 00.0882576624 7 25.4041411575 00.1029672728 8 29.0333041800 00.1176768832 9 32.6624672025 00.1323864936 10 36.2916302250 00.1470961040 11 39.9207932475 00.1618057144 12 43.5499562700 00.1765153248 13 47.1791192925 00.1912249352 14 50.8082823150 00 . 20●9345456 15 54.4374453375 00.2206441560 16 58.0666083600 00.2353537664 17 61.6957713825 00.2500633768 18 65.3249344050 00.2647729872 19 68.9540974275 00.2794825976 20 72.5832604500 00.2941922080 21 76.2124234725 00.3089018184 22 79.8415864950 00.3236114288 23 83.4707495175 00.3383210392 24 87.0999125400 00.3530306496 25 90.7290755625 00.3677402600 26 94.3582385850 00.3824498704 27 97.9874016075 00.3971594808 28 01.6165646300 00.4118690912 29 05.2457276525 00.4265787016 30 08.8748906750 00.4412883120 31 12.5040536975 00.4559979224 The Moons mean Motions in Hours . Hours ☽ Mean Longitude ☽ Apogaeon 1 00.1525045678 00.0012894419 2 00.3050091357 00.0025788838 3 00.4575137035 00.0038683257 4 00.6100182713 00.0041577676 5 00. ●625228391 00.0064172095 6 00.9150274071 00.0077366515 7 01.0675319749 00.0090260934 8 01.2200365427 00.0103155353 9 01.3725411105 00.0116049772 10 01.5250456786 00.0128044192 11 01.6775502464 00.0141838611 12 01.8300548143 00.0154733031 13 01.9825593821 00.0167627450 14 02.1350639499 00.0180521869 15 02.2875685177 00.0193416288 16 02.4400730855 00.0206310707 17 02.5925776533 00.0219205126 18 02.7450822211 00.0232099545 19 02.8975867891 00.0244993964 20 03 . 0500●13560 00.0257888384 21 03.2025959250 00.0270782803 22 03.3551004928 00.0283677222 23 03.5076050607 00.0296571642 24 03.6601096285 00.0309466061 The Moons mean Motions in Hours . Hours ☽ Mean Anomaly ☽ Node Retrograde 1 00.1512151259 00.0006129004 2 00.3024302518 00.0012258008 3 00.4536453778 00.0018387013 4 00.6048605037 00.0024516017 5 00.7560756296 00.0030645021 6 00.9072907556 00.0036774026 7 01.0585058815 00.0042903030 8 01.2097210074 00.0049032034 9 01.3609361333 00.0055161038 10 01.5121512593 00.0061290043 11 01.6633663852 00.0067419047 12 01.8145815112 00.0073548052 13 01.9657066371 00.0079677056 14 01.1170117630 00.0085806060 15 02.2682068889 00.0091935064 16 02.4194420148 00 . 009●064068 17 02.5706571407 00 . 0●04193072 18 02.7218722666 00.0110722076 19 02.8730873926 00.0116451081 20 03 . 9243025●85 00.0122580085 21 03.1755176445 00.0128709090 22 03.3267327704 00.0134838004 23 03.4779478964 00.0140967099 24 03.6291630223 00.0147096103 The Moons mean Motions in Minutes of an Hour M. ☽ M. Long. ☽ Apog . ☽ M. Au. ● Retrog . 1 .0025414 .0000214 .0025202 .0000102 2 .0050828 .0000429 .0050405 .0000204 3 .0076242 .0000643 .0075607 .0000306 4 .0101656 .0000859 .0100810 .0000408 5 .0127070 .0001074 .0126012 .0000510 6 .0152484 .0001288 .0151214 .0000612 7 .0177898 .0001502 .0176416 .0000714 8 .0203312 .0001716 .0201618 .0000816 9 .0228726 .0001930 .0226820 .0000918 10 .0254141 .0002149 .0252025 .0001021 11 .0279555 .0002363 .0277227 .0001123 12 .0304969 .0002577 .0302429 .0001225 13 .0330383 .0002791 .0327631 .0001327 14 .0355797 .0003004 .0352833 .0001429 15 .0381211 .0003218 .0378035 .0001531 16 .0406624 .0003432 .0403237 .0001633 17 .0432038 .0003646 .0428439 .0001735 18 .0457452 .0003860 .0453641 .0001837 19 .0482867 .0004079 .0478843 .0001939 20 .0508284 .0004298 .0504045 .0002041 21 .0533696 .0004512 .0529247 .0002143 22 .0559110 .0004726 .0554449 .0002245 23 .0584524 .0004940 .0579651 .0002347 24 .0609938 .0005154 .0604853 .0002442 25 .0635352 .0005368 .0630055 .0002544 26 .0660766 .0005582 .0655257 .0002642 27 .0686180 .0005795 .0680459 .0002744 28 .0711594 .0006008 .0705661 .0002846 29 .0737008 .0006222 .0730863 .0092948 30 .0762422 .0006437 .0756075 .0003064 The Moons mean Motions in Seconds .   ☽ M. Long. ☽ Apog . ☽ M. Au. ☊ Retrog . 1 0000423 0000003 0000420 0000002 2 0000847 0000007 0000840 0000003 3 0001270 0000010 0001260 0000005 4 0001693 0000013 0001680 0000006 5 0002116 0000016 0002100 0000009 6 0002539 0000019 0002520 0000010 7 0002969 0000022 0002940 0000012 8 0003392 0000025 0003360 0000013 9 0003815 0000028 0003780 0000015 10 0004275 0000035 0004200 0000017 11 0004658 0000038 0004620 0000019 12 0005078 0000041 0005040 0000020 13 0005504 0000044 0005460 0000022 14 0005930 0000047 0005880 0000023 15 0006357 0000050 0006300 0000025 16 0006784 0000053 0006720 0000027 17 0007207 0000056 0007140 0000028 18 0007630 0000059 0007560 0000029 19 0008050 0000062 0007980 0000031 20 0008470 0000065 0008400 0000033 21 0008893 0000068 0008820 0000035 22 0009316 0000071 0009240 0000036 23 0009736 0000074 0009660 0000038 24 0010156 0000077 0010080 0000039 25 0010582 0000080 0010500 0000041 26 0011008 0000083 0010920 0000043 27 0011434 0000086 0011340 0000044 28 0011860 0000089 0011760 0000047 29 0012287 0000092 0012180 0000049 30 0012714 0000095 0012600 0000051 ☉ Sig. o. & . 6 1 & 7 2 & 8 ☉ a AEqu. ☊ Inclin . AEqu. ☊ Inclin . AEqu. ☊ Inclin . a ☊ Addi limetis Addi limitis Addi limitis ☊ 0 0.00000 30000 1.06500 20000 1.08500 15000 30 1 0.00000 30000 1.12888 25722 1.01888 14527 29 2 0.00055 30000 1.19277 25472 0.95305 14055 28 3 0.00194 29972 1.25222 25166 0.88666 13583 27 4 0 . 0041● 29944 1.30833 24888 0.82055 13138 26 5 0.00888 29888 1.36166 24583 0.55333 12666 25 6 0.01472 29833 1.41055 24277 0.68694 12194 24 7 0.02305 29777 1.45666 23972 0.62416 11●22 23 8 0.02416 29722 1.49916 23638 0.56444 11250 22 9 0.04805 29638 1.53666 23305 0.50555 10750 21 10 0.06500 29555 1.58000 22972 0.44666 10250 20 11 0.08555 29444 1.60027 22638 0.38888 09750 19 12 0.10944 29361 1.62527 22277 0.34000 09250 18 13 0.13666 29250 1.64472 219●6 0.28972 08750 17 14 0.16833 29111 1.65771 21●55 0.25083 08250 16 15 0.20250 28972 1.66277 21222 0.20972 07750 15 16 0 . 2411● 28833 1.65805 20833 0.17388 07250 14 17 0.27472 28667 1.64527 20444 0.14138 06750 13 18 0. ●2944 28567 1.62638 20055 0.11305 06250 12 19 0.37916 28361 1.60194 19666 0.08805 05722 11 20 0.43277 28194 1.58222 19279 0.06722 05222 10 21 0.48888 18027 1.53972 18861 0.04916 04694 9 22 0.54833 27833 1.50333 18444 0.03416 04166 8 23 0.60694 27611 1.46222 18027 0.02333 03638 7 24 0.66833 27416 1.41799 17614 0.01500 03138 6 25 0.73555 27104 1.37027 17194 0.00888 02611 5 26 0.79805 26972 1 . 3186● 14750 0.00416 02083 4 27 0 . 8641● 26722 1.26527 16333 0 . 001●4 01555 3 28 0.93083 26500 1.20833 15888 0.00055 01027 2 29 0.99611 26250 1.14750 15444 0.00000 ●0527 1 30 1.06500 26600 1.08500 14000 0.00000 00000 0   Sntract   Subtract .   Subtract .       Sig. 5. & 11 4 & 10 3 & 9   Aug. Sig. o. N. Incr. 1. North Incr. 2. North I ncr .     Sig. 6. S.   7. South   8. South     Lat.   or Exc.   or Exc.   or Exc.     Latit .   Latit .   Latit .     0 0.00000 00000 2.49750 15000 4.32888 26000 30 1 0.08722 00527 2.57277 15444 4.37166 26250 29 2 0.17444 01027 2.64722 15888 4.41361 26500 28 3 0.26166 01555 2.72083 16333 4.45388 26722 27 4 0.34861 02083 2.79361 16416 4.49277 26972 26 5 0.43555 02611 2.86555 17194 4.53055 27194 25 6 0.52222 03138 2.93638 17611 4.56666 27416 24 7 0.60888 03638 3.00666 18027 4.60166 27611 23 8 0.69527 04166 3. ●7583 18444 4.63500 27833 22 9 0.78138 04694 3.14416 18861 4.66722 28027 21 10 0.86722 05222 3.21166 19277 4.69777 28194 20 11 0.95277 05722 3.27805 19666 4.72694 28361 19 12 1.03833 06250 3.34333 20055 4.75472 28527 18 13 1.12333 06750 3.41055 20444 4.78111 28666 17 14 1.10805 07250 3.47111 20833 4.80583 28833 16 15 1.29250 07750 3.53333 21222 4.82916 28972 15 16 1.37666 08250 3.59444 21555 4.85111 29111 14 17 1.46027 08750 3.65472 21916 4.87166 29250 13 18 1.54333 09250 3.71361 22277 4.89055 29361 12 19 1.62611 09750 3.77138 22638 4.90777 29444 11 20 1.70805 10250 3.82833 22972 4.92388 29555 10 21 1.78972 10750 3.88388 23305 4.93833 29638 9 22 1.87111 11250 3.93805 23638 4.95111 29722 8 23 1.95166 11722 3.99138 23972 4.96250 29777 7 24 2.03166 12194 4.04333 24277 4.97250 29833 6 25 2.11083 12666 4.29416 24583 4.98083 29888 5 26 2.18972 13138 4.14361 24888 4.98777 29944 4 27 2.26777 13583 4.19166 25166 4.99301 29972 3 28 2.34500 14055 4.23861 25472 4.99694 29972 2 29 2.42166 14527 4.28444 25722 4.99916 18000 1 30 2.49750 15000 4.32888 26000 5.00000 18000 0   Sig. 11. S.   Sig. 19. S.   9. South       Sig. 5. N.   4 N.   3. North     A Table of the Moons Red. to the El. Subt As Lat. Sig. 0.6   S. 1.7   S. 2.8   As. Lat.     Incr.   Incr.   Incr.     Red.   Red.   Red.     0 .00000 00000 09444 01166 09472 01166 30 1 .00388 00055 09638 01194 09277 01138 29 2 .00750 00111 09805 01222 09055 01111 28 3 .01138 00166 09972 01250 08833 01083 27 4 .01527 00222 10111 01277 08611 01055 26 5 .01888 00250 10250 01277 08388 01027 25 6 .02277 00305 10388 01277 08138 01000 24 7 .02638 00333 10500 01305 07861 00972 23 8 .03000 00361 10583 01305 07611 00944 22 9 .03361 00416 10666 01305 07305 00916 21 10 .03722 00472 10750 01333 07027 00861 20 11 .04083 00527 10805 01333 06722 00833 19 12 .04444 00555 10861 01333 06416 00805 18 13 .04777 00611 10888 01333 06111 00777 17 14 .05111 00638 10916 01361 05805 00722 16 15 .05444 00666 10916 01361 05472 00666 15 16 .05777 00722 10916 01361 05138 00638 14 17 .06111 00777 10862 01361 04805 00611 13 18 .06416 00805 10861 01361 04444 00555 12 19 .06722 00833 10805 0133● 04111 00527 11 20 .07000 00861 10750 01333 03750 00472 10 21 .07305 00916 10694 01305 03388 00416 9 22 .07583 00944 10611 01305 03027 00361 8 23 .07888 00972 10500 01305 02092 00333 7 24 .08111 01000 10388 01277 02611 00305 6 25 .08361 01027 10277 01277 02222 00250 5 26 .08583 01055 10138 01277 01527 00222 4 27 .08823 01083 10000 01250 01138 00166 ●3 28 .09055 01111 09833 01222 00750 00111 2 29 .09250 01138 09638 01194 00388 00055 1 30 .09444 01166 09472 01166 00000 00006 0   11.5   10.4   9.3     A Table shewing the mean Motion of the Moon from the Sun in Years and Months . AEra ☽ à ☉ in Years   ☽ à ☉ in Years Chr. 56.8114797531 1 36.0063707331 1600 21.5206732464 2 72 . 012741466● 1620 58.5795367034 3 08.0191121993 1640 95.6384101604 4 47.4117836215 1660 32.6972836174 5 83.4181543546 1680 69.7561560744 6 19.4245250877 1700 06.8150305314 7 55.4308958208 1720 43.8739039884 8 94.8235672430 1740 80.9027774454 9 40.8298379761 1760 17.9916509024 10 76.8362087092     11 02.8426794423   Motion of the 12 42.2353508645   Moon from the 13 78.2417215976   Sun in Months . 14 14.2480923307     15 50.2544630638     16 89.6471344860 Ian. 04.9758835440 17 25.6535052191 Feb. 99.7928106160 18 61.6598759522 Mar. 04.7686941600 19 97.6662466853 April 06.3582588800 20 37.0589181075     40 74.1178362150 May 11.3341424240 60 11.1767543225 Iune 12.9237071440 80 48.2356724300 Iuly 17.8995906880 100 85.2945905375 Aug. 22.8754742320 200 70.5891810750     300 55.8837716125 Sept. 24.4650389520 400 41.1783621500 Octo. 29.4409224960 500 26.4729526875 Nov. 31.0304872160 600 11.7675432250 Dec. 36.0063707331 700 97.0621337625 A Table shewing the mean Motion of the Moon from the Sun in Days and Hours .   ☽ à ☉ in Days .   ☽ à ☉ in Hours . 1 03.3863188240 1 00.1410966176 2 06.7726376480 2 00.2821932352 3 10.1589564720 3 00.4232898530 4 13.5452752960 4 00.5643864706 5 16.9315941200 5 00.7054830882 6 20.3179129440 6 00.8465797060 7 23.7042317680 7 00. ●876763236 8 27.0905505920 8 01.1287729412 9 30.4768694160 9 01.2698695588 10 33.8631882400 10 01.4109661766 11 37.2495070640 11 01.5520627942 12 47.6358258880 12 01.6931594120 13 44.0221447720 13 01.8342560296 14 47.4084635360 14 01.9753526472 15 50. ●947823600 15 0● . 1164492648 16 54.1811011840 16 02.2575458824 17 57.5674200080 17 02.3986425000 18 60.9537388320 18 02.5397391176 19 64.3400576560 19 02.6808357354 20 67.7263764800 20 02.8219323520 21 71.1126953040 21 02.9630289708 22 74.4990141280 22 03.1041255884 23 77.8853329520 23 03.2452222062 24 81.2716517760 24 03.3863188240 25 84.6579706000     26 88.0442804240     27 91 4306082480     28 94.8169270720     29 98.2032458960     30 01.5895647200     31 04.9758835440     A Table shewing the mean Motion of the Moon from the Sun in Minutes .   ☽ à ☉ in Minutes . 1 00.0023516102 2 00.0047032205 3 00.0070548308 4 00 . 00●4064411 5 00.0117580513 6 00.0141096617 7 00.0164612719 8 00.0188128822 9 00.0211644924 10 00.0235161029 11 00.0258677131 12 00.0262193233 13 00.0305709335 14 00.0329225437 15 00.0352741539 16 00.0376257644 17 00.0399773746 18 00.0423289848 19 00 . 044680●950 20 00.0170322052 21 00.0493838154 22 00.0517354256 23 00 . 0540870●58 24 00.0564386460 25 00.0587902562 26 00.0611418664 27 00.0634934766 28 00.0658450868 29 00.0681966970 30 00.0705483080   ☽ à ☉ in Minutes . 31 00.0728999183 32 00.0752515088 33 00.0776031390 34 00.0799547492 35 00.0823063594 36 00.0846579696 37 00.0870095798 38 00.0893611900 39 00.0917128002 40 00.0940644104 41 00.0964160206 42 00.0997676308 43 00.1011192410 44 00.1034708512 45 00.1058224614 46 00.1081740716 47 00.1105256818 48 00.1128772920 49 00.1152289022 50 00.1175805124 51 00.1199321226 52 00.1222837328 53 00.1246353430 54 00.1269869532 55 00.1293385634 56 00.1316901736 57 00.1340417838 58 00.1363933940 59 00.1387450050 60 00.1410966152 A Table shewing the mean Motion of the Moon from the Sun in Seconds .   ☽ à ☉ in Seconds 1 00.0000391935 2 00.0000783870 3 00.0001175805 4 00.0001567740 5 00.0001959675 6 00.0002351610 7 00.0002743545 8 00.0003135480 9 00.0003527415 10 60.0003919350 11 00.0004811285 12 00.0004703220 13 00.0005995155 14 00.0005487090 15 00.0005879025 16 00 . 00●6270960 17 00.0006662895 18 00.0007954830 19 00.0007446765 20 00.0007838700 21 00.0008230635 22 00.0008622570 23 00.0009014505 24 00.0009406440 25 00 . 0009798●75 26 00.0010190310 27 00.0010582245 28 00.0010974180 29 00.0011366115 30 00.0011758050   ☽ à ☉ in Seconds 31 00.0012149985 32 00.0012541920 33 00.0012933855 34 00.0013325790 35 00.0013717725 36 00.0014109660 37 00.0014501595 38 00.0014893530 39 00.0015285465 40 00.0015677400 41 00.0016069335 42 00.0016461270 43 00.0016853205 44 00.0017245140 45 00.0917637075 46 00.0018029010 47 00.0018420945 48 00.0018812880 49 00.0019204815 50 00.0019596750 51 00 0019988685 52 00.0020380620 53 00.0020772555 54 00.0021164490 55 00.0021556425 56 00.0021948360 57 00.0022340295 58 00.0022732230 59 00.0023124165 60 00.0023516100 A Catalogue of some of the most notable fixed Stars according to the observations of Tycho Brahe , and by him rectified to the beginning of the Year of Mans Redemption , 1601. The Names of the Stars Longit. Latit . The first Star of Aries . 07.671 ♈ 7. 8. N 4 The bright Star in the top of the head of Aries . 00.583 ♉ 9. 57. N 3 The South Eye of Taurus . 01.169 ● 5. 31. S 1 The North Eye of Taurus . 00.801 ● 5. 31. S 1 The bright Star of the Pleiades . 06.620 ♉ 2. 6. S 3 The higher head of Gemini . 04.078 ● 4. 11. N 5 The lower head of Gemini . 04.921 ♋ 10. 2. N 2 The bright foot of Gemini . 01.069 ♋ 6. 38. N 2 In the South Arm of Cancer . 02.238 ♌ 6. 48. S 2 The bright Star in the neck of Leo. 06.662 ♌ 5. 8. S 3 The heart of Leo. 06.745 ♌ ● . 47 . N 2 In the extream of the tail of Leo. 04.458 ♍ 0. 26. N 1 In Virgo's Wing ; Vindemiatrix . 01.217 ♎ 12. 18. N 1 Virgins Spike . 05.074 ♎ 16. 15. N 3 South Ballance . 02.643 ♏ 1. 59. S 1 North Ballance . 03.833 ♏ 0. 26. N 2 The highest in the Forehead of Scorpio . 07.388 ♏ 8. 35. N 2 The Scorpions heart . 01.171 ● 1. 05. N 3 Former of the 3 in the head of Sagittarius . 02.203 ● 4. 27. S 1 Northern in the former horn of Capricorn . 07.861 ● 1. 24. N 4 The left Shoulder of Aquarius . 04.949 ♒ 7. 22. N 3 In the mouth of the South Fish. 03.620 ♓ 8. 42. N 3 The Polar Star or last Star in the ●ail of the lesser Bear.   9. 4. N 5   06.400 ● 66. 02. N 2 The last Star in the tail of the great Bear , 05.888 ♍ 54. 25. N 2 The Tongu● of the Dragon . 05.259 ♍ 76. 17. N 4 Arcturus in the skirt of his Garment . 05.181 ♎ 31. 2. N 1 The bright Star of the North Crown . 01.845 ♏ 44. 23. N 2 The Head of Hercules ▪ 02.921 ● 37. 23. N ● The bright S●●r of the H●rp . 0● . 699 ● 61. 47. N ● The Head of Medusa . 05.727 ♉ 22. 22. N 3 The bright Star in the Goa●s left Shoulder . 04.518 ♊ 22. 50. N 1 The middle of the Serp●nts Neck . 04.583 ♍ 25. 35. N 2 The bright Star in the ●agles Shoulder . 07.264 ♑ 29. 21. N 2 The bright Star in the 〈◊〉 Tail. 02.370 ♒ 29. 8. N 3 The mouth of Pegas●s . 07 . 3●4 ♒ 22. 7. N 3 The head of And●omeda . 0● . 4●0 ♈ ●5 . 42. N 2 In the top of the Triangle . 00.366 ♉ 16. 49. N 4 In the Snout of the Whale . 02.643 ♉ 7. 50. S The bright Star in the Whales Tail. 07.481 ♓ 20. 47. S 2 Bright Shoulder of Orion . 06.444 ♊ 16.06 S 2 Middlemost in the belt of Orion . 04.972 ♊ 24. 33. S 2 The last in the tail of the Har● . 0● . 324 ♊ 38. 26. S 4 The great Dogs mouth Sirius . 02.386 ● 38. 30. S 1 The lesser Dog Procyon . 05.641 ● 1● . 57 . S 2 In the top of the Ships Stern . 01.636 ♌ 43. 18. S 3 Brightest in Hydra's Heart . 06.044 ♌ 22. 24. S 1 FINIS THE CONTENTS OF THE First Part , CONTAINING The Practical Geometry or the Art of Surveying . CHapter 1. Of the Definition and Division of Geometry . Chap. 2. Of Figures in the General , more particularly of a Circle and the Affections thereof . Chap. 3. Of Triangles . Chap. 4. Of Quadrangular and Multangular Figures . Chap. 5. Solid Bodies . Chap. 6. Of the measuring of Lines both Right and Circular Chap. 7. Of the measuring of a Circle . Chap. 8. Of the measuring of plain Triangles . Chap. 9. Of the measuring of Heights and Distances . Chap. 10. Of the taking of Distances . Chap. 11. How to take the Plot of a Field at one Station , &c. Chap. 12. How to take the Plot of a Wood , Park , or other Champian Plane , &c. Chap. 13. The Plot of a Field being taken by an Instrument , how to compute the Content thereof in Acres , Roods , and Perches . Chap. 14. How to take the Plot of mountainous and uneven Ground , &c. Chap. 15. To reduce Statute measure into Customary , and the contrary . Chap. 16 ▪ Of the measuring of solid Bodies . Tables . A Table of Squares . Page . 99 A Table for the Gauging of Wine Vessels . 114 A Table for the Gauging of Beer and Ale Vessels . 120 A Table shewing the third part of the Areas of Circles , in Foot measure and Deoimal parts of a Foot. 132 A Table shewing the third part of the Area of any Circle in Foot measure , not exceeding 10 f. circumf . 136 A Table for the speedy finding of the length or Circumference answering to any Arch in Degrees and Decimal parts . 151 A Common Divisor for the speedy converting of the Table , shewing the Areas of the Segments of a Circle whose Diameter is 2 &c. 154 A Table shewing the Ordinates , Arches , and A rea● of the Segments of a Circle , whose Diameter is 〈◊〉 &c. 156 The Contents of the Second Part of this Treatise , of the Doctrine of the PRIMUM MOBILE . CHap. 1. Of the General Subject of Astronomy . Chap. 2. Of the Distinctions and Affections of Spherical Lines and Arches . Chap. 3. Of the kind and parts of Spherical Triangles , and how to project the same upon the Plane of the Meridian . Chap. 4. Of the solution of Spherical Triangles . Chap. 5. Of such Spherical Problems as are of most general Vse in the Doctrine of the Primum Mobile , &c. The Contents of the Third Part of this Treatise being an Account of the Civil Year with the reason of the difference between the Julian and Gregorian Calendars , and the manner of Computing the Places of the Sun and Moon . CHap. 1. Of the Year Civil and Astronomical . Chap. 2. Of the Cycle of the Moon , what it is , how placed in the Calendar , and to what purpose . Chap. 3. Of the use of the Golden Number in finding the Feast of Easter . Chap. 4. Of the Reformation of the Calendar by Pope Gregory the Thirteenth , &c. Chap. 5. Of the Moons mean Motion and how the Anticipation of the New Moons may be discovered by the Ep●●●ts . Chap. 6. To find the Dominical Letter and Feast of Easter according to the Gregorian Account . Chap. 7. How to reduce Sexagenary Numbers into Decimals , and the contrary . Chap. 8. Of the difference of Meridians . Chap. 9. Of the Theory of the Suns or Earths motion . Chap ▪ 10. Of the finding of the Suns Apogaeon , quantity of Excentricity and middle Motion . Chap. 11. Of the quantity of the tropical and sydereal Year . Chap. 12. Of the Suns mean Motion otherwise stated . Chap. 13. How to calculate the Suns true place by either of the Tables of 〈◊〉 middle Motion . I 〈…〉 Chap. 14. To find the place of the fixed Stars . Chap. 15. Of the Theory of the Moon and the finding the place of her Apogaeon , quantity of Excentricity , and middle motion . Chap. 16. Of the finding of the place and motion of the Moons Nodes . Chap. 17. How to calculate the Moons true place in her Orbs. Chap. 18. To compute the true Latitude of the Moon , and to reduce her place from her Orbit to the Ecliptick . Chap. 19. To find the mean Conjunctions and Opposition of the Sun and Moon ▪ The Fourth Part , or an Introduction to Geography . CHap. 1. Of the Nature and Division of Geography . Chap. 2. Of the Distinction or Dimension of the Earthly Globe by Zones and Climates . Chap. 3. Of Europe . Chap. 4. Of Asia . Chap. 5. Of Africk . Chap. 6. Of America . Chap. 7. Of the description of the Terrestrial Globe , by Maps Vniversal and Particular . A Table of the view of the most notable Epochas . The Iulian Calendar . Page . 461 The Gregorian Calendar . 466 A Table to convert Sexagenary Degrees and Minutes into Decimals and the contrary . 476 A Table converting hours and minutes into degrees and minutes of the AEquator . 480 A Table of the Longitudes and Latitudes of some of the most eminent Cities and Towns in England and Ireland . 482 A Table of the Suns mean Longitude and Anomaly in both AEgyptian and Iulian Years , Months , Days , Hours and Minutes . 484 Tables of the Moons mean motion . 493 A Catalogue of some of the most notable fixed Stars , according to the observation of Tycho Brahe , rectified to the year 1601. 511 Books Printed for and sold by Thomas Passinger at the Three Bibles on the middle of London-Bridge . THe Elements of the Mathematical Art , commonly called Algebra , expounded in four Books by Iohn Kersey , in two Vol. fol. A mirror or Looking-glass for Saints and Sinners , shewing the Justice of God on the one , and his Mercy towards the other , set forth in some thousands of Examples by Sam. Clark , in two Vol. fol. The Mariners Magazine by Capt. Sam. Sturmy , fol. Military and Maritime Discipline in three Books , by Capt. Tho. Kent , fol. Dr. Cudworth's universal Systeme . The Triumphs of Gods Revenge against the Crying and Execrable sin of wilful and premeditated Murther , by Iohn Reynolds , fol. Royal and Practical Chymistry by Oswaldus Crollius and Iohn Hartman , faithfully rendred into English , fol. Practical Navigation by Iohn Seller . Quarto . The History of the Church of Great Britain from the Birth of our Saviour until the Year of our Lord 1667. quarto . The Ecclesiastical History of France from the first plantation of Christianity there unto this time , quarto . The book of Architecture by Andrea Palladio , quarto . The mirror of Architecture or the ground Rules of the Art of Building , by Vincent Scammozi quarto . Trigonometry , on the Doctrine of Triangles , by Rich. Norwood , quarto . Markham's Master-piece Revived , containing all knowledge belonging to the Smith , Farrier , or Horse-Leach , touching the curing of all Diseases in Horses , quarto . Collins Sector on a Quadrant , quarto . The famous History of the destruction of Troy , in three books , quarto . Safeguard of Sailers , quarto . Norwood's Seamans Companion , quarto . Geometrical Seaman , quarto . A plain and familiar Exposition of the Ten Commandments , by Iohn Dod , quarto . The Mariners new Calendar , quarto . The Seamans Calendar , quarto . The Seamans Practice , quarto . The honour of Chivalry do the famous and delectable History of Don Belianus of Greece , quarto . The History of Amadis de Gaul , the fifth part , quarto . The Seamans Dictionary , quarto . The complete Canonier , quarto . Seamans Glass , quarto . Complete Shipwright , quarto . The History of Valentine and Orson , quarto . The Complete Modellist , quarto . The Boat-swains Art , quarto . Pilots Sea-mirror , quarto . The famous History of Montelion Knight of the Oracle , quarto . The History of Palladine of England , quarto . The History of Cleocretron and Clori●ma , quarto . The Arralgnment of lower , idle , froward and unconstant Women , quarto . The pleasant History of Iack of Newb●●y , quarto Philips Mathematical Manual , Octavo . A prospect of Heaven , or a Treatise of the happiness of the Saints in Glory , oct . Etymologicunt parvum , oct . Thesaurus Astrologiae , or an Astrological Treasury by Iohn Gadbury , oct . Gellibrand ' s Epitome , oct . The English Academy or a brief Introduction to the seven Liberal Arts , by Iohn Newton , D. D. oct . The best exercise for Christians in the worst times , by I. H. oct . A seasonable discourse of the right use and abuse of Reason in matters of Religion , oct . The Mariners Compass rectified , oct . Norwood ' s Epitome , oct . Chymical Essays by Iohn Beguinus , oct . A spiritual Antidote against sinful Contagions , by Tho. Doolittle , oct . Monastieon Fevershamiense ; or a description of the Abby of Feversham , oct . Scarborough ' s Spaw , oct . French Schoolmaster , oct . The Poems of Ben. Iohnson , junior , oct . A book of Knowledge in three parts , oct . The Book of Palmestry , oct . Farnaby ' s Epigramms , oct . The Huswifes Companion , and the Husbandmans Guide , oct . Jovial Garland , oct . Cocker ' s Arithmetick , twelves . The Path Way to Health , twelves . Hall ' s Soliloquies , twelves . The Complete Servant Maid , or the young Maidens Tutor , twelves . Newton's Introduction to the Art of Logick , twelves . Newton's Introduction to the Art of Rhetorick , twelves . The Anatomy of Popery , or a Catalogue of Popish errors in Doctrine and corruptions in Worship , twelves . The famous History of the five wise Philosophers , containing the Life of Iehosophat the Hermit . twelves , The exact Constable with his Original and Power in all cases belonging to his Office , twelves . The Complete Academy or a Nursery of Complements , twelves . Heart salve for a wounded Soul , and Eye salve for a blind World , by Tho. Calvert . twelves . Pilgrims Port , or the weary mans rest in the Grave , twelves . Christian Devotion or a manual of Prayers , twelves . The Mariners divine Mate , twelves . At Cherry Garden Stairs on Rotherhith Wall , are taught these Mathematical Sciences , viz. Arithmetick , Algebra , Geometry , Trigonometry , Surveying , Navigation , Dyalling , Astronomy , Gauging , Gunnery and Fortification : The use of the Globes , and other Mathematical Instruments , the projection of the Sphere on any circle , &c. He maketh and selleth all sorts of Mathematical Instruments in Wood and Brass , for Sea and Land , with Books to shew the use of them : Where you may have all sorts of Maps , Plats , Sea-Charts , in Plain and Mercator , on reasonable Terms . By Iames Atkinson . FINIS . 
A51768	----	The sphere of Marcus Manilius made an English poem with annotations and an astronomical appendix / by Edward Sherburne, Esquire. Astronomicon. Liber 1. English Manilius, Marcus. 1675 Approx. 1552 KB of XML-encoded text transcribed from 174 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2004-05 (EEBO-TCP Phase 1). A51768 Wing M432 ESTC R8811 12418069 ocm 12418069 61767 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A51768) Transcribed from: (Early English Books Online ; image set 61767) Images scanned from microfilm: (Early English books, 1641-1700 ; 283:3) The sphere of Marcus Manilius made an English poem with annotations and an astronomical appendix / by Edward Sherburne, Esquire. Astronomicon. Liber 1. English Manilius, Marcus. Sherburne, Edward, Sir, 1618-1702. [18], 68, [2], 221, [9] p., [9] leaves of plates (4 double) : ill. Printed for Nathanael Brooke ..., London : 1675. Translation of the first book of: Astronomicon. "A catalogue of the most eminent astronomers, ancient & modern": p. 6-126, second group of pages. Includes indexes. Following p. 212, figure L, bound and photographed up-side down. Errata on p. [9] at end. Reproduction of original in Huntington Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. 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Understanding these processes should make clear that, while the overall quality of TCP data is very good, some errors will remain and some readable characters will be marked as illegible. Users should bear in mind that in all likelihood such instances will never have been looked at by a TCP editor. The texts were encoded and linked to page images in accordance with level 4 of the TEI in Libraries guidelines. Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Astronomy, Ancient. Astronomy -- Early works to 1800. 2003-11 TCP Assigned for keying and markup 2004-01 Apex CoVantage Keyed and coded from ProQuest page images 2004-02 Mona Logarbo Sampled and proofread 2004-02 Mona Logarbo Text and markup reviewed and edited 2004-04 pfs Batch review (QC) and XML conversion The Mind OF THE FRONTISPIECE . THE Spheres , ( which ever moving are ) imply That Arts , and Learning , if unactive , die . Our Subject's Worth , is by URANIA meant , Our Poet 's , PAN , and MERCURY present , Who sings rough Matter in smooth Verse , t' invite The Ignorant to Learn , the Learn'd Delight . THE SPHERE of M. MANLIVS ▪ made An English POEM . By Edward Sherburne , Esq ▪ CAELIQVE VIAS ET SIDERA MONSTRAT . NATVRAE VNIVERSITAS . VNIVERSITAS INTERPRES . W. Hollar fecit 1673 THE SPHERE OF Marcus Manilius MADE AN ENGLISH POEM : WITH Annotations AND AN ASTRONOMICAL APPENDIX . By EDWARD SHERBURNE , Esquire . LONDON , Printed for Nathanael Brooke , at the Sign of the Angel in Cornhil , near the Royal Exchange , MDCLXXV . HONI ✚ SOIT ✚ QVI ✚ MAL ✚ Y ✚ PENSE . DIEV ET MON DROIT CR royal blazon or coat of arms TO HIS SACRED MAJESTY Charles the II. King OF GREAT BRITAIN , FRANCE and IRELAND , &c. MAY it Please Your Majesty , To Vouchsafe Your Royal View to this Copy ; The Original was by a Great Master , and dedicated to the Great Augustus . Having been long buried by Barbarity , and Ignorance ; It hopes now to rise unto New Life , and Lustre , by the Gracious Aspect of Your Sacred Majesty . The Author now first alters his Native Language , exchanging it for that of Your English Subjects ; Be pleased Great SIR , to afford Him Your Eare , never denied to Strangers , whom Fortune happily casts upon Your Royal , and All-obliging Goodness . He briefly represents the Splendid Oeconomy of the Celestial Spheres , the Pattern of the most Flourishing Empires ; then most Glorious when most conformable to the Heavens . — imitatur Olympum Officiis Augusta Domus — These Rudiments of Astronomy crave Acceptance from Your Majesty , who in Your Late Naval Expeditions , have been pleased to shew Your Self so great a Favourer of that Learning , by encouraging the Noble and Generous Youth of these Nations , to enable themselves thereby , for that Your Service . SIR , It would have seemed an unpardonable Omission , not to have added Your Name to the Constellations , who by your Excellent Virtues justly deserve , and without Question shall in due Time obtain a most Eminent Place among them . But Your Clemency and Moderate Government makes your Subjects to pray , Serus in Coelum redeas , diuque Laetus intersis Populo — Which Blessing upon Your Sacred Self and Us , None more fervently implores , than May it please Your Majesty , Your Majesties most Obedient Subject and Servant , EDW. SHERBURNE . THE PREFACE . THE High Esteem , which the Antient Romans had for Astronomical Learning ; appears even by their Publick Games in the Circus Maximus ; whose Order and Disposition represented that of the Heavens . The Circus being of an Elliptical or Oval Figure ; having twelve Gates or Entries resembling the twelve Signs of the Zodiack . In the Midst an Obelisque , as the Sun : On each side thereof three Metae , denoting the other Six Planets , which in their respective Courses mark out the several Intervals or Spaces , into which the Mundane System is divided . So that the Circensian Games seem not to have been so much , an Exercise of Charioting and Racing , as an Astronomical Cursus ; wherein the People were not only delighted by the Exhibition of corporal Games , but had their * Minds also instructed to apprehend the Course and Order of the Celestial Bodies , which in the Great Circus of the World are continually moving . This Method of inculcating Knowledge with Delight ( though in a different way ) Manilius hath likewise pursued ; who intending to exhibit to the Age wherein he lived the Rudiments of Astronomy , chose to represent the same in a Poetical Dress , that so his Readers might be allured to relish with the greater Gusto the initiating Principles of a Science not easily acquired ; and he thereby gain to himself the Repute which good Poets chiefly affect , of being able at once both to instruct and please . What upon this Accompt he hath delivered in the first of his five Books of Astronomicks , which of it self is a Compleat and entire Poem of the Doctrine of the Sphere ; We have adventured , as well for its Brevity and Politeness , as its Perspicuity and Usefulness , to transfer into our Native Tongue . But some perhaps will demand , Daphni quid Antiquos coelorum suspicis Ortus ? Why , in an Age wherein the learned World is so fruitful in Accurate Productions of this Kind , obtrude We upon the Reader a Piece of less curious and less knowing Antiquity ? This frivolous Objection will easily be obviated and answered , if we shall but duly consider , that it is a design no less commendable for the Industry of this present Age , gratefully to revive the valuable ( but too much obscured and unregarded ) Helps , by which the Wits of former Times have benefitted Posterity ; than it is to labour in the Pursuit of new Discoveries and Inventions ; which many times are rather pretended than real Improvements ; and are ( some of them ) found to be , but the Disguises and Alterations of elder Ingenuity . And we may without derogating or detracting in the least , from the worthy Endeavours of the Learned , modestly affirm , that there are some Particular Notions , touching the Nature of the Heavens and the Celestial Bodies , delivered in the Piece we now publish , which having been revived , and of late dayes reasserted by some of the most eminent Modern Astronomers , have been received with general Applause , and thereby have added no little Honour to their Names . To instance in the following Particulars . First , The Opinion of the Fluidity of the Heavens , against the Aristotelean Hypothesis of Solid Orbs , appears in this Work to have been expresly delivered by Manilius near 1700 years since ; which , by the Noble Tycho , Galilaeo , Scheinerus , and others , hath of late Dayes with all the Acumen of convincing Reason been defended , and demonstrated . Secondly , That the Fixed Stars are not all in the same Concave Superficies of the Heavens , equally distant from the Center of the World , but that they are placed at unequal Distances in the Aethereal Region , some higher , some lower , ( whence the Difference of their apparent Magnitudes and Splendor ) is by the famous Kepler ( Epitom . Astron. l. 1 , ) and other Modern Astronomers lately asserted ; and seems by many to be taken for a Novel Opinion ; which yet in this Piece we find to have been many Ages since , declared by our Author . Thirdly , The Assertion , which by the most knowing Astronomers of these Times is embraced , affirming the Fixed Stars to be of a fiery Nature and Substance , and consequently endued with native and propper Lustre , and that they are ( as Galilaeo terms them ) so many Suns , conform , and like unto this Sun of ours , appears in this very Poem to have been long since maintained by our Manilius . Fourthly , What by help of the Telescope hath been lately detected and demonstrated by Galilaeo , Kepler , and others , that the Galaxie is a Congeries of Numberless small Stars , was by the sole Perspicil of Reason , discovered by the Ancients , and is here by our Author proposed as the most probable Solution of that Phaenomenon . Of the Parts of this Poem , their Distribution and Order , and of our Endeavours in explicating the same both in our Notes and Appendix , We hold it not amiss in this Preliminary Discourse , to give the Reader some Accompt . The Poem begins with a Succinct Indication of the Original and Progress of Arts and Sciences , more particularly of Astronomy , of which last , besides what We have noted in our Marginal Illustrations ; We have added , for the Satisfaction of the more Curious , a Compendious History , continued down to the Age wherein Manilius lived ; together with a Catalogue of the most Eminent Astronomers from the first Parent of all Arts , and Mankind it self , to this Present . It is continued on with a Description of the Mundane System , and of the Celestial Signs and Constellations ; The first of which we have explained according to the various Hypotheses both Antient and Modern ; The latter we have described by the Number of the Stars that compose them , their several Denominations in most of the Learned Languages , and as they are distinguished into prophane and Sacred Figures or Morphoses , according to the different Uranography of the Antient Ethnicks , and some late Christian Astronomers . The Description of the Celestial Circles makes up the next Part of this Poem ; for the better understanding of which , over and above what is explained in the Marginal Notes ; We have added a Cosmographical , Astronomical Synopsis , for the most part according to Mersennus ; to which We have likewise annexed the twelve Propositions of Theodosius de Habitationibus in English. And seeing our Authour hath briefly touched upon the fiery Nature of the Fixed Stars ; We have thought fit in the Appendix to make some further and more curious Enquiries touching their Substance , their Light , Colour and Scintillation , their Number , Figure , Magnitude , Place , and Distance from the Earth , or rather the Sun. In the next Place the Planets are enumerated ; whose several Denominations ( by which they were known and distinguished by the Antients ) We have given in our Notes ; and in the Appendix have further enlarged touching the Nature and Substance of the Sun , his Maculae and Faculae ( which are likewise represented to View in a particular Scheme ) something also being said of his Vertiginous Motion , Magnitude , and Distance : Of the Moon and of her Spots , whereunto we have added the Selenographick Schemes of Hevelius and Grimaldi with their respective Nomenclatures ; and have exhibited a like brief Accompt of the Nature , Substance , Structure , Figure , Magnitude , and Distance of the other Planets . The Poem concludes with a Corollary of fiery Meteors and Comets : These We have in Part explained in our Notes ; and have more fully in the Appendix discoursed of their Names , Kinds , and several Species , their Matter , Place , and Efficient Causes ; adding in the Close a Chronological Historical Table of the most Notable Comets , that have appeared since the Flood to this present . Having in the Illustration of the Whole , observed ( in some Measure ) the Method prescribed by the great * Roman Legislator , which cannot better be expressed than in his own Words . Ita Omnia videntur tradi commodissimè , si primò levi ac simplici Via , deinde diligentiori , atque exactiore Interpretatione Singula tradantur . And seeing it is Customary in publishing Works of this Nature , to premise something touching the Authors : It may justly be expected we should here do the like in reference to MANILIUS his Life , Country , Quality , Studies , Writings , &c. Of this , ( though we are not ignorant , that in a Subject so obscure , and to which Antiquity affords so dim a Light , it will be hard for us either clearly to discern , or certainly to determine ; yet , ) for the Satisfaction of the Curious and Ingenious Reader , We shall in the following Discourse endeavour to give , if not a full , at least a fair and probable Accompt . VVho this Manilius ( whose Name the following Poem bears ) should be ; partly through the Silence of those Authors which are come to our Hands ; partly through the Loss of others , of which the Injury of Time hath deprived us , is left very uncertain . The best means that we can use for the clearing of a Matter so dark and dubious , will be to take a View of Those , who by the Name of Manilius have been recommended to Posterity , as qualified with the Knowledge of good Letters , and among them to consider , which in all rational Appearance may be the Person we look for . Varro in his fourth and sixth Books De Lingua Latinâ , makes mention of one Manlius or Manilius a Poet , out of whose Works he cites these Verses Deli Gemellos Creta Titana Deos Latona pariit , casto complexu Jovis . ( Which Verses may happily be taken out of Chrestus Manlius , whom Gyraldus reports to have written De Deorum Hymnis ) and these Others Cascum duxisse Cascam non mirabile est , Quoniam Canoras conficiebant Nuptias . Or as Jos. Scaliger reads the last Verse Quoniam Charon eas sanciebat Nuptias . But finding no express Evidence ( besides the bare Name ) to prove the Manilius mentioned by Varro , to have written any thing on the Subject of Astronomy , much less to have been the same with the Authour of this Poem ; We shall wave this Authority , and pass on to some others more Explicit and Declarative . Pliny l. 35. c. 17. tells us of one Manilius surnamed Antiochus , who with Publius Mimus and Staberius Eros , was brought to Rome , all three , of Servile Condition , but Persons of good Literature . His Words are These . Pedes Venalium transmare advectorum , Cretà denotare instituerunt Majores ; Talemque Publium ( Syrum , ) Mimicae Scenae Conditorem , & Astrologiae Consobrinum ejus Manilium Antiochum , item Grammatices Staberium Erotem eâdem Nave advectos videre Proavi , i. e. Our Ancestors used to mark with white Lead or Chalk the Feet of such Slaves as were brought over from beyond Sea to be sold. And such an one was Publius ( Syrus ) the Founder of the Mimick Scene , and his Cousin German Manilius Antiochus , of Astrology , and Staberius Eros of Grammer , whom our great Grandfathers saw in that manner brought together in one and the same Ship. This Manilius , Laurentius Bonincontrius ( who near two Ages since commented upon our Authour ) conceives the same with Manilius , who wrote this Astronomical Poem : To confirm which Opinion , he produces the Evidence of a Silver Medal in his Possession , whereon was the Figure of a Man , in an Exotick Habit , with a Sphere placed near his Head , with this Inscription MANILI . the same is affirmed ( sayes Lilius Gyraldus ) by Stephanus Dulcinus ; and the said Gyraldus further assures us that a familiar Friend of his , one Nicholaus Trapolinus , had by him another Medal of the like Stamp and Inscription . But against this Opinion of Bonincontrius , and Gyraldus , Scaliger opposes a double Argument , one , drawn from the seeming inveracity of that supposed Evidence ; No such Medal being at this Day to be found in the Cabinets of any , no not the most curious Antiquaries ; the other from the Reason of Time ; for Manilius Antiochus being brought to Rome ( as Scaliger supposes ) in the beginning of Sylla's Dayes , must needs , if he were the same with the Author of this Poem , have been ( as he reckons ) 120 years old when he began to write ( an ill Age to play the Poet in ) this Piece being written in the later years of Augustus his Reign . But the Author in the Proem of this Work wishes for long life to compleat his intended Poem ; Wherefore ( sayes Scaliger ) certainly he was not then old , who wished he might live to be so . But leaving this Argument at present , to be anon reassumed . We shall go on in our further Enquiry . The same Pliny l. 36. c. 10. speaks of one Manilius a Mathematician , who upon the Obelisque which Augustus erected in the Campus Martius , for finding out the Hours of the Day by the Shadow of the Sun , with the Increase or Decrease of the Dayes and Nights , placed a guilded Ball. Cujus Vertice Umbra colligeretur in seme tipsam , alia Incrementa jaculantem Apice , ratione ( ut ferunt ) à Capite Hominis intellecta , sayes Pliny , who commends the Design , as a Thing worthy of Knowledge , and the Invention of a pregnant Wit. To this Person Scaliger conceives this Work may with fairer Probability be ascribed than to the former ; which Opinion is by divers other learned Persons likewise embraced . The excellently learned Doctor Isaac Vossius conceives yet , that the Manilius Antiochus , and the Manilius Mathematicus , before mentioned are not two distinct Persons , but one and the same under different Titles and Appellations , and the very Author of the Poem we now publish . Whose Particular Sentiments upon this Subject , and Arguments confirming the same , he was pleased not long since to impart to Me , by his most obliging Letter , in Answer to some Queries by Me proposed in one of mine to him , upon Occasion of my intended Publication of this Piece , which for the Readers Satisfaction , I shall here make Publick , though not in his own Words , yet as near as may be in his own Sence . And first in Answer to Scaliger's Argument , drawn from Reason of time , against Manilius Antiochus , upon the Supposition , that Staberius Eros , ( one of the three before-mentioned ) set open his Grammar School in the Time of Sylla , ninety five years before the Death of Augustus ; And that therefore ( according to Scaligers Computation ) Manilius could not probably be less than 120 years old , at the time when this Poem was written . He urges by way of Reply , that Suetonius ( from whom Scaliger takes the Ground of his Argument ) does not say , that Staberius Eros opened his School in Sylla's Time , but that he taught Gratis , the Children of Those , who in Sylla's Time were proscribed . The Words of Suetonius are these . Sunt qui tradunt tantâ eum ( scilicet Staberium ) honestate praeditum , ut temporibus Syllanis Proscriptorum Liberos gratis & sine Mercede ullâ in Disciplinam receperit : How long that was after the Times of Proscription will be needless here to declare ; and that Manilius was not so old as Scaliger conceives , when this Piece was written , may be made out from this , that he was the Cousin German of Publius Syrus , who that he was brought a Young Boy to his Patron , Macrobius affirms ; from whom likewise and from the Verses of Laberius , it may , not obscurely , be collected , that he was but a Youth when he came upon the Stage against Laberius , which was a little before the Death of Julius Caesar , and of Laberius also ; to whom he succeeded on the Mimick Stage in the second Year of the CLXXXIV . Olympiad , that is in the Year of Rome DCCXI . as Eusebius testifies ; And therefore seeing it is manifest that Manilius published this Poem soon after the Varian Defeat , which hapned in the DCCLXII . of Rome ; it is as evident likewise that between the Youth or Adolescence of Manilius , and the Time wherein he writ this Piece , there could not pass above one and fifty years ; and consequently there is no Reason to assign so great an Age to Manilius as Scaliger here does ; since perhaps he was not Seventy years old , when he had finished this his Astronomical Poem . As to what Scaliger subjoyns touching Manilius his Wish for long life , together with a chearful Old Age , and the Inference he thence makes , that he could not reasonably be then thought to be Old , who wished he might live to be so . The Argument is but weak : for Senium is one thing , and Senium Annosum another . Nor does he simply wish Vitam Annosam , but Vitam Annosam quae conjuncta sit cum molli Senecta , which may be wished for even by those who are very old . As for the Name of Antiochus , he seems to have taken it from the famous Philosopher Antiochus Ascalonita , often mentioned by Cicero , Plutarch , Sextus Empiricus , and others ; whose School not only Cicero , but Varro , Brutus , and divers others are said to have frequented , and in all Probability this our Manilius also , as being not only of the same Nation , but happily born in the same Town : ( Ascalon . ) So that it may seem no VVonder if after the manner of those Times , he took upon him the Name of his worthy Tutor and Instructor . For that he was a Syrian is not only manifest from his Consanguinity with Publius Mimus ; but may likewise be collected from the Title , or Inscription of this VVork , which in an antient and excellent Manuscript in the Possession of the said Doctor Vossius , is this : M. MALLII POENI ASTRONOMICON , DIVO OCTAVIO QUIRINO AUG . That the Phaenicians were by the Romans called POENI , is manifest out of Horace , Cicero a pud Nonium , and our Author in this very Poem . He concludes therefore that this our Manilius , or , ( as he is rather pleased to call him ) Manlius , was a Phaenician , and in all Probability Native of the same Town as Antiochus his Tutor , whose Name he assumed . From this Dedication of his VVork to Augustus , by the Name of Quirinus , as the Inscription shews , will appear the Error of those , who imagine the same to have been dedicated to Tiberius or some later Roman Emperor . And the reason of attributing the Name of Quirinus to Augustus may be made clear from the VVords of Suetonius , Censentibus quibusdam Romulum appellari oportere , quasi & ipsum Conditorem Urbis , &c. Dion likewise tells us ; 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . That ( Augustus ) Caesar extreamly desired to be called Romulus , and Joannes Philadelphensis ( scripto de Mensibus , in Aug. ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , &c. Octavianus Son of Octavius was after his great Victories honoured with divers Names ; for by some he was called Quirinus as another Romulus , &c. As to the other Manilius by Pliny stiled Mathematicus ; he conceives , that Titular Distinction to make no Difference in the Person ; but that he is the same with the former ; further adding , Omninò existimo & illum quoque de Nostro Manilio accipi debere . And whereas Salmasius affirms that the Name Manlius ( or Manilius ) is not to be found in that Place of Pliny in any antient Manuscripts , and therefore ought to be expunged out of the Printed Copies ; he makes it appear that Salmasius is extreamly mistaken ; by the Testimony of several antient MS. of . Pliny in his Possession , whereof one is in a Character written above 8 or 900 years since : In all which , the Word Manlius is found though with some small difference in writing of the Name . Nor does he think the Name of Marcus praefixed to Manlius ought to be scrupled at , upon the account that none of the Manlian Family after the CCCLX . Year from the Building of Rome , could or did use that Praenomen , seeing that Prohibition , as Cicero ( in Philip. ) intimates , is only to be understood of the Patrician Race : Now that this Manilius , or ( as he calls him ) Manlius was , before his Manumission , a Slave ; not only the Place of Pliny already cited , but the very Agnomen of Antiochus sufficiently evinces ; for as much as a Greek Agnomen joyned to a Roman Name , is alwayes a most certain Token of a Servile Condition . With this rational Discourse of so incomparable a Person , both my Self and Reader might well rest satisfied ; Did VVe not meet with another Manilius , mentioned by Pliny ( l. 10. c. 2. ) of Senatorian Dignity ; honoured by him with the Character of the most diligent of all the long Robe , and enobled with the greatest Learning without any Teacher . VVho is said first of all the Romans to have written of the Phaenix , That there was never any man that saw it feed , that in Arabia it is Sacred to the Sun ; and ( to omit the mention of some other Particulars ) that it lives 660 years , and that with the Life of this Bird , is consummated the Conversion of the great Year ; In which the Stars return again to their first Points , and give Significations of the same Seasons as at the Beginning . That this Great Year begins about High Noon on the Day , wherein the Sun enters the first Degree of Aries , and was compleated ( as he declares ) when P. Licinius , and M. Cornelius were Consuls , &c. This person ( not taken Notice of by any others that have written touching our Author ) Monsieur Tristan in his Historical Commentaries ( Tom. 1. ) conceives to be the same with our Manilius . The Reasons inducing him to embrace this Opinion , being grounded upon the Concinnity of Time , and Conformity of Study . The Subject here mentioned clearly implying him to have been conversant in the like Astronomical Exercises as our Author , whom not improbably he believes to have made these curious Remarks touching the Phoenix and the Annus Magnus , in the sixth Book of his Astronomicks , which is now lost : though , as Scaliger affirms , extant in the Time of Firmicus , who from thence collected his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Sphaerae Barbaricae , as he did from the fifth Book , yet extant , his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . For , that Manilius wrote of the first Kind as well as of the last mentioned , may appear by these Verses . Quae mihi per proprias Vires sunt cuncta canenda , Quid valeant Ortu , quid quum merguntur in undas ? The Elogy which Pliny gives him , seeming likewise ( as Tristan observes ) to insinuate , besides a particular Respect , a kind of Intimacy and Acquaintance , between this Manilius ( supposed our Author ) and Pliny ; who , as he was a Person very curious might be desirous to be known to him upon the Score of his Eminent Learning ; and happily enjoyed what he desired , about the end of Tiberius his Reign ; at which time Manilius might be far advanced in years , and Pliny a Young Man. I am not yet ignorant , that the Learned Pighius in his Roman Annals , and some other knowing Persons are of Opinion , that this Elogium ought to be applied to Titus Manilius Son of Publius , and Nephew of Marcus Manilius , whom Cicero in Roscio calls Ornatissimum Senatorem : But with the leave of those Learned Persons ; I do not find that among the Characters which Cicero gives him , there is any one of his Learning or Erudition ; for though he sayes he was a most honourable Senator , of a great Age , by Nature pious and Religious , and of a plentiful Fortune , yet he honours him not with any Encomium of his Studies , or of his great Proficiency in all Sciences ; which doubtless he would have done , had he merited eminently in that kind . In all Reason therefore We may conclude the Manilius mentioned by Pliny , to be different from that of Cicero , and with much seeming probability suppose him ( as Tristan does ) to be the same with our Manilius , Author of this Poem , who by Petrus Crinitus de Poet. Latin. is reported ( we wish he had strengthened his Assertion by some Authentick Testimony ) to have been of illustrious Extraction , which adds some further Weight to Mounsieur Tristan his Conjecture . But since this cannot be made out by other Arguments than what are meerly probable , we shall sorbear to determine positively thereupon ; but leave the Reader freely to judge which hath the best Pretence to be entituled to this Work , the Slave or the Senator . As to that Opinion started by Gevartius , that this our Manilius was the same with Manlius Theodorus ( who 400 Years after the Death of Augustus , and of our Author t●…o , was Consul , and Praefectus Praetorio in Illyrium , under the Emperors Theo●… , Honorius and Arcadius , and who by Claudian is celebrated for an excellent 〈◊〉 , Philosopher and Astronomer . ) It is so groundless , and so unworthy the Name of Gevartius , that we shall not spend time in refuting it , since the Reader may find suffici●…nt Evidence against it from the Pen of our Author in this very Poem , without the help of those Arguments , which from thence are drawn by Tristan in his Commentaries before mentioned ( Tom. 1. p. 114 , and 115. ) and Barthius in his elaborate Animadversions upon Claudian ( p. 112. ) The Name of Manilius is no less controverted than his Person ; some affirming it to be Manilius , some Manlius , and others contracting it ( compendio improbo , as Barthius terms it ) into Mallius . But his true Name , ( uncertain whether derived to him by Adoption or Descent ) seems to be MANILIUS , which was the Name of a Roman Family distinct from that of the Manlian , as is apparent , both by the Capitoline Tables , and other Evidences in the Roman Story , of which see Schottus de Famil . Roman . and Glandorpius in his Onomasticon . This Name of Manilius all the Antient Editions in the very Infancy of Printing , give him , and most Manuscripts ; particularly , as Barthius ( in Claudian . ) notes , that of Corpus Christi Colledge in Oxford ; and ( as he adds ) he is so named , with the Addition of the Praenomen , Marcus ; above 600 Years since by Gerbertus Rhemensis Bishop of Ravenna , and afterwards Pope of Rome , in his cxxx . Epistle in these Words . Age ergo , te solo conscio , ex tuis sumptibus fac mihi scribantur , Marcus Manilius de Astrologia , Victorinus de Rhetorica , Demostenes Ophthalmicus , &c. And though some Antient MSS. call him Caius , yet generally all the late printed Copies give him the Name of Marcus Manilius ; Which , as being confirmed by the most prevailing Authority , we admit of . Of his Studies , his own Writings give us the clearest and the best Accompt . By those , ( that is to say his five remaining Books of Astronomicks , for other Writings of his , the learned World is not acquainted with ) he is represented to Us to have been an Excellent Mathematician , Astronomer , Astrologer , a great Humanist , Philosopher , ( and which comprehends all the rest ) an admirable Poet. In Astronomy and Astrology he chiefly followed the Doctrine of the Chaldeans and Aegyptians . In Philosophy , though he was generally conversant in all the different Opinions of the Antients , yet , he more particularly adhered to that of the Stoicks , with which he seems to have been throughly imbu'd ; as may appear by several Instances ; particularly that excellent Proem of his fourth Book ; a Taste of some Part of which , We hold it not amiss to give the Reader . It begins thus . Quid tam sollicitis Vitam consumimus Annis ? Torquemurque metu , caecaque Cupidine rerum ? &c. Why waste We Life in Years of anxious Pain ? With fears tormented , and blind Love of Gain ? Worn old with Cares , not Age ; which in th' Acquest We loose , and with no End of Wishes blest , Act as to live still , yet ne're live indeed : So much more Poor , as our Desires exceed . What We have not We covet ; what We have We count not ; and though Nature little crave , We hoard up Matter for vast Luxury , And purchase Spoyl with Superfluity ; With Gain buy Loss ; as if the End of all Our Wealth , were only to be Prodigal . Lay , Mortals , Lay these Cares , these Follies by ; All govern'd is by changeless Destiny , That rules the World ; and Times long Courses run In a link'd Series , not to be undon . Ev'n in our Births We die ; and our last End Does on our Live's Original depend , &c. Of the Time or Manner of his Death We find Nothing recorded . What Stock of Credit and Esteem he hath left behind him , will best appear by the Censures which the ablest Criticks of these later Ages have given of him , and of his Writings . Some of which for the Reader 's Satisfaction we shall here enumerate . JUDGEMENTS of the Learned on Manilius . We begin with ALDUS MANUTIUS , in his Edition of our Author . Manilius ( sayes he ) was the first of all the Latines who wrote of Astronomy , and therefore , when in many Places of this Work he not a little glories therein , deservedly to be born with ; for it is an Argument of no mean Wit and Industry , to have explained such difficult Matter , so aptly and so clearly in Verse as he hath done ; to have only attempted , though not performed such a Design , being abundantly Praise-worthy and Noble . By ANGELUS POLITIANUS ( in Nutric ) He is stiled Bis Vates , Doubly a Poet ; for describing so excellently in Verse the Babylonian , and Aegyptian Astrology . PETRUS CRINITUS ( De Poet. Latin. ) thus speaks of Him. Marcus Manilius is reputed to have been of Illustrious Extraction ; and flourished at Rome , when Augustus happily swayed the Empire thereof ; and doubtless was most acceptable to so great a Prince for the Eminency of his Learning , and Excellency of his Wit. He employed his Study and Industry chiefly in Mathematical Arts , with so much Proficiency , as he thereby gained from the World no mean Applause of his Ingenuity . ALEXANDER ab ALEXANDRO ( Genial . Dierum l. 2. c. 21. ) speaking of several Authors signalized by Fame for their eminent Skill and Knowledge in Celestial Matters , reckons , among the Greeks , Berosus , Eudoxus , Aristotle , Empedocles and Aratus ; among the Latines , Julius Firmicus and Marcus Manilius . REMBERTUS DODONAEUS ( in Isagog Cosmogr . ) citing the Verses of Manilius proving the Figure of the VVorld to be Spherical , adds this Encomium , As sings that Divine Poet. ADRIANUS TURNEBUS in Adversar . gives him the Title of a Noble Poet , adding withall , that he was an Honour and Ornament even to Poesie it self . LUDOVICUS CARRIO ( emendat . l. 2. ) stiles him a most Grave and Learned Poet. MONSIEUR de MESMES , in his Institutions Astronomiques , written long since in French , calls him , The Gentile Astronomical Poet. The Incomparable JOSEPH SCALIGER ( to whose Learned Labours our Author ows his Second and better Life ) thus writes of him in his Preface to his last Edition of him . As for MANILIUS I cannot say , whether I should rather wish that he had been publickly read in the Schools , or lament that he hath lain hitherto so neglected . A most ingenious Poet , and Polite Author ; having illustrated so Obscure a Subject in such Luculent Verse , and displayed a Matter of it self Morose , in such a pleasing Character . All his Proemial Inductions , His Transitions and Excursions are beyond Censure , than those Nothing can be said more divine , nothing more copious , more weighty or more delightful . Then coming more particularly to the Censure of this Part which We now publish . Certainly ( sayes he ) it is a Piece so useful and advantagious to all Generous Youth , as it ought to prepare their Way to the Elements of Spherical Learning . And again in his Epistle to the Learned Stadius . I exhort all knowing and worthy Professors , that when ever they go about to instruct their Pupils in the first Elements of the Sphere , they would initiate them therein by this first Book of our Author ; for whence ( sayes he ) can they better derive the Principles of that Science , than from this most Disert Poet ; who hath omitted Nothing which may seem pertinent to that purpose . The Learned ISAAC CASAUBON ( Annot. in Strabon . & alibi ) honours him with the Title of a most Elegant Poet. PAULUS MELISSUS in his Encomium upon Scaliger's first Edition of our Author , thus sings of Him. Iove pitying humane Weakness ; gave to Us Th'Inspector of the Stars , Manilius . Who to Rome's Nephews first the Knowledge brought Of Heavens high Orbs , and their hid Motions taught . JOANNES AURATUS upon the same Occasion describes him thus : Manilius , like another Atlas bears , Or an Alcides , on his Head the Spheres FRANCISCUS JUNIUS in the Dedicatory Epistle before his Edition , gives him this following Elogy . Manilius for Gravity of Stile , Propriety of Language , and Usefulness of Argument is to be preferred before many . And again . In my Judgment he expresses all Things briefly , gravely , sweetly , and most commodiously for the Instruction of all that read him . CHRISTOPHERUS SCHEINERUS in his Accurate Work entituled Rosa Ursina , delivers this Censure of him . Marcus Manilius , ( whom some call Caius Manilius ) wrote most elegantly ( much above any Others ) of the fluidity , and Liquidness of the Heavens . That egregious Authour having with extraordinary Clearness , Roundness and Elegancy exprest all things concerning the Heavens and the Celestial Bodies . GASPAR BARTHIUS ( in Adversar . ) gives him the Commendation of a most judicious and ingenious Poet ; and one of the most elegant of the Augustaean Age , and ( in Animadvers . in P. Statium ) adds ; that he was a Poet most consultive in Philosophy . No less Praise is afforded him by JOANNES GLANDORPIUS ( in Onomastic . Roman . ) who gives him the Character of a Noble Mathematician and Poet , and One who first of all the Latines wrote of Astronomy in Verse . JULIUS NIGRONIUS ( de non legend . Libr. Amator . ) reckons him among the most Useful and Instructive Authors . I exhort ( sayes he ) that Young Persons read such Authors as they may peruse without offence to good Manners , such as Persius , Seneca , Silius , Lucan , Claudian and MANILIUS . Of the same Iudgement is ARNOLDUS CLAPMARIUS ( in Nobil . Triennio ) where he thus advises the Generous Young Student . Read , and read o're again Homer with Theocritus and Virgil ; Horace with Pindar ; Lucretius and MANILIUS , with Aratus . The most eminently learned and judicious HUGO GROTIUS In the Preface to the Edition of his own Latine Poems , shews us the Esteem and value he set upon our Author . I acknowledge my self ( sayes he ) to be now and then full of Lucan's Spirit , sometimes above measure studious of MANILIUS . The excellent GERRARD . JO. VOSSIUS ( l. de 4. Artibus Popular . ) speaking of that Part of Philosophy which is comprised under the Title of Grammatica Exegetica . Without this ( saith he ) how can any interpret Lucretius , or Manilius , Parmenides , or Melissus ? who besprinkle their Writings with many things drawn from the inmost Recesses of Philosophy . PAGANINUS GAUDENTIUS sometime Publick Professor of Law and Rhetorick at Pisa , in his Treatise De Initio & Progressu Philosophiae apud Romanos ; ranks him among the Eminent Lights of Learning in the Augustaean Age ; concluding with an Epigram ( which for Brevities sake we forbear here to insert ) in Honour of so great a Poet and Astronomer , as he there stiles him : And in his Obstetrix Literaria thus further Discourses of him . If any shall go about to describe Arts and Sciences in a Poetical Stile , he takes not more from Poetry than the bare versifying Part ; for he then begins to assume from his Subject the Part either of a Philosopher , Astronomer , Physician , or such like , in which kind certainly Empedocles , Lucretius and MANILIUS were more than Poets . BRIETIUS in Syntagmate de Poet. Latin. comparing the Latine Poesie with the different Ages of Man ; makes the virile and perfect State thereof to consist of Virgil , Horace , Ovid , Tibullus , Propertius , and our MANILIUS . Add we to these the Opinion of the most Ingenious Mr. ABRAHAM COWLEY , Who in his Essay of constituting a Colledge for the infusing into Youth , Knowledge and Language at the same time ; conceives the Way to be by breeding them up in Authors or Pieces of Authors that treat of solid and Learned , that is Natural Matters . Among which he commends Virgil's Georgicks , Gratius , Nemesianus and MANILIUS . To accumulate more Encomiums , were superfluous ; Hear himself now speak his own Character . OF The two Hemispheres OF THE STARS . THe One serves for the Northern Constellations ; the Other for the Southern . The Stars are expressed according to their several Magnitudes , as may be seen in the Scale thereof set down in the Southern Hemisphere . And the Constellations are only pricked out , wherein ( with Galluccius ) the Middle Way is taken , betwixt not placing them in any , or representing them in too dark shadowed Figures , as some have done . In the Projection , the Eye is supposed to touch the South Pole , for the projecting of the Northern Hemisphere upon the 〈◊〉 of the Equator , and contrarily for the Southern . So that the Stars are placed in either by the Arches of right Ascension measured upon the Equator , and by their Distances or Declinations from it , set off from a Scale of Double Tangents , which this and All other Stereographical Projections require : Amongst which , I accompt this the most proper and useful to be here placed , because by adding an Index made as above said , and divided as you see one of the Semidiameters done in either Hemisphere , any Star may easily be found either on the Projections or in the Heavens ; And the Way or Course of a New Star or Comet may be traced upon them by any that have but ordinary Skill in the Sphere ; and may serve very well instead of a Celestial Globe ; and being held up before one in the Night , placed according as the Heavens require , will plainly shew the Position at that Time. And are ready , to those that are yet more Curious , by the putting on a particular Horizon , for other several Uses . But yet these Instruments are not true Astroscopes ; there is not any point to place the Eye in , for discerning the Stars in the Heavens as they are placed in the Hemispheres ; for that will require another Polar Projection much like this following , viz. The Eye is to be supposed at the Center of the Sphere , projecting on a Plane touching the Sphere at the Pole Point , in which the right Ascension is measured as before by the Angle at the Pole Point , and the Polar Distances are set off by the Tangents of the said Arks ; On which Supposition an entire Hemisphere cannot be projected ; And this is no other than the Plane of an Equinoctial Dyal , which being placed Erect to the Axis , if the Eye be supposed therein at the Distance of the Radius from the Plane , and if at the Situation of each Star on the Plane . Holes were supposed or made in the Plane ; if the Eye beholds two known Stars shining through their proper Holes , at the same Time it should behold All the rest likewise shining through their Holes , to which their Names being affixed , this Projection becomes an Astroscope to teach Beginners to know the Stars , and will also serve as a Nocturnal for finding the Stars hour , and by Consequence , by Ayd of the Sun 's right Ascension , proper to the Day of the Moneth , the true hour of the Night likewise . The Polar Dyal or Meridional Plane , as Kircher in his Ars Magna Lucis & Umbrae affirms , hath been applied by Griembergerus ; as an Astroscope to teach Tyros how to know the Stars in both Hemispheres , and to find the Hour of the Night by the Rotation of the Plane , affixed as it were to the Handle of a Carpenter's Wimble ; the Axis thereof being conceived to be Parallel to the Axis of the World , and the Eye , at a Knot tyed in a Thread on the said Axis , to be the Center of the Earth , is supposed to behold the Stars shining through their proper Holes as before ; the Distance from the Eye to the Plane being the Radius of the Projection . But neither of these Astroscopes are the same as Schickardus treats of ; His is supposed to be the Surface of a Cone ; In the Circle of the Base whereof conceive a Thread to represent a Diameter ; a Knot in it the Center , a Perpendicular from that Knot to the Side of the Conick Surface the Radius , and a Line passing through the Vertex of the Cone ( which represents the Pole Point ) and the Foot of that Perpendicular to be a Tangent Line each way , in which , the Stars are to be placed according to their Distances from the Pole , counted from the Pole Point , in respect of the Graduation of the said Tangent ; the Arches of right Ascension being measured by the Periphery of the Circle in the Base of the Cone , and this Surface is to be conceived to be directed to the Pole , and that the Eye is at the Knot or Center of the Base of the Cone , beholding two known Stars shining through their Proper Holes , and at the same time it shall likewise behold the rest shining through their respective Holes ; The Rotation of this Figure about an Axis serving as a Nocturnal to give the Hours of the Night . Other Astroscopes there are ; As one , that being rectified and set to the Hour of the Night , the Sight through two Pinnacides shall be directed to that Star to which the Instrument is rectified . Of All which to treat , is not our present Design , and ' therefore shall refer the Reader to the Authors and Composers of such kind of Projections or Astroscopes . map of northern constellations map of southern constellations THE SPHERE OF MARCUS MANILIUS . DIvining a Arts , and Stars b foreknowing Fate , c Varying the divers Turns of Humane State , ( The Work●… of Heav'ns d high Reason ) We bring down In Verse , from Heaven ; and first move e Helicon , And it 's green Groves , with unacquainted Rimes , Offering strange Rites , not known to former Times . Caesar ! thy Countries f Prince and Father ! Thou , To whose g Imperial Laws the World doth bow , Who h merit'st , what was granted to thy Sire , Heaven as a God! do'st this high Song inspire . And now , Heaven i kinder to the Curious grows , And courts in Verse , it 's Treasure to disclose . Fit Task alone for Peaceful Leisure ! Rise We then through yielding Aire , and mount the Skies , There live and range ; Learn all the Signs , and prove How in their k adverse Course the Planets move : To know but which were little ; we will sound The hidden Entrails of this ample Round , Enquire how Stars Creatures beget and sway , Which whilst we sing , l Apollo's self shall play . m Two Altars bright with Flames , we raise ; repair T' a double shrine , prest with the double Care Of Verse and Matter ; on these certain Grounds Raising our Song , concordant Heaven surrounds It's Poet with deep Harmony , and Words Scarce fit for Latian Characters affords . Who to inferiour Earth did first reveal These Gifts of Gods ? Who , what they hid , could steal ? All-ruling Heaven ! What Mortal dar'd so high As spite of Gods , himself to Deifie ? Open the highest Path , the lowest Deep ? Tell how the Stars their bounded Courses keep ? The Force , and Motions of the Signs impart ? n Cyllenius ! Thus first taught'st this sacred Art ; Thou th'inmost Heavens , & utmost Stars mad'st known , That so to Natures Power , not Face alone , Might greater Awe , and Reverence accrue ; And Nations learn what to that God was due , Who did through Seasons , to be known , display The Heavens , and this great Worlds Phaenomena . Nature help'd too ; Her self , Her self improv'd , o And Monarchs ( next to Heaven in power ) first mov'd T' affect these Arts ; who near Sol's rising Beams Fierce Nations tam'd ; whose Lands p Euphrates Streams Divide , and q Nile inundates ; where the Sun Returning , does o're r Negro Cities run . Next , chosen s Priests , who serve from Age to Age At Publick Altars , and with vows ingage Th'indulgent God , whose awful Presence fires Their Zealous Minds with uncorrupt Desires ; He with himself possest them , and made known His t unveil'd Deity unto his own . Such were the Men , who first could apprehend That Humane Fates on wandring Stars depend ; u They to each time apply'd its own Events , And by long Toyl observ'd the Accidents Of many Ages , Birth-days , Lives , what Power Of Fortune govern'd each successive Hour , And what great Changes the least Motions cause . Thus when Heavens various Face , ( the Stars by Laws Of Fate returning in their ordered Course ) Was fully known ; and each Signs proper Force , Experience fram'd thereof an Art ; the Way x Shown by Example ; Which through long Essay , And various Speculation , learn'd from far The tacit Laws of e●…ery ruling Star ; Saw in alternate Course Heaven still move round , And Fate to vary as it's Aspects , found . For before them , rude Man no difference made 'Twixt Natures works , nor things with Reason weigh'd ; Astonish'd at Heavens new disclosed Light , y Now mourn'd the Stars as lost ; now at their Sight As if new-born rejoyc'd : th' uncertain Times Of Day and Night , differing in different Climes , Till then none knew ; nor could the Causes clear z Of shades unlike the Sun far off and near . Yet witty Cunning no a learn'd Arts had found ; Under rude Swains waste lay the untill'd Ground : b Gold then in Desert Mountains lodg'd at Ease , c New Worlds lay hid in unattempted Seas , d To waves and winds to trust their Lives none dar'd , To know themselves and theirs , Men only car'd . But when long Time and Toyl their Wits had whet , And e Want an Edge on Indusiry had set , Then thousand Cares their working Heads possest , Whilst to scape Need , they Sacrifice their Rest ; Conclusions try'd : and whatsoe're f wise Use By oft-repeated Practice did produce Of sure Effect ; the new Experiment Unto the Common Good they gladly lent . Then Barbarous Tongues receiv'd new g Laws , the Earth h Manur'd , to various Fruits gave timely Birth . Bold Seamen the i blind Ocean did invade , k And 'twixt strange Lands procur'd a mutual Trade : Thence Arts of War and Peace in time arose , For Art by Practice propagated , growes . What 's yet more strange , they learnt l the Tongues of Birds , m Entrails t'inspect , n burst Snakes with powerful words ; o Call'd up pale Ghosts , mov'd Hell it self , the p Light Turn'd into Darkness , into Day the Night . Ingenious Industry made All things bend ; Nor put they to their curious Search an End , Till Reason had scal'd Heaven , thence view'd this round , And Nature latent in its Causes found ; Why q Thunder does the suffering Clouds assail ; Why Winters r Snow's more soft than Summers s Hail ; Whence t Earthquakes come , and Subterranean u fires , Why x show'rs descend , what force the y wind inspires . From Error thus she wondring Minds uncharm'd ; z Unsceptred Iove ; the Thunderer disarm'd ; Of Name and Power dispoyl'd him , and assign'd Fire to the Labouring Clouds , Noise to the Wind. These to their proper Causes having brought , Next on the whole Worlds Mass she casts her Thought , Of which the a System in her self she frames , Dispensing to the Signs both b Forms and Names ; Their c Aspects and their Order notes , and saw Heavens changing Face gave fatal changes Law. This is our Muses Theme , as yet d display'd In Verse by None : Propitious Fortune aid The bold Attempt ; with Ease my Life befriend , And to a long and chearful Age extend , That so I sink not with my Subjects weight , But with like care , great Things , and small relate . Now since from Heaven it self our Verse descends , And down to Earth Fates settled Order tends , We first must Natures General State reherse , And draw the Picture of the Universe . Which , whether it from Nothing were deriv'd ; Or ( of Beginning both , and End depriv'd ) Hath e ever been , and ever shall endure ; Or f Chaos severing from the Mass obscure The mixed Principles of things , this bright World teem'd , whilst Darkness took to Hell its Flight ; Or that made up of g Atoms Nature's Frame Exists , and shall resolve into the same Some thousand Ages hence , and almost brought From Nothing , fall again to almost Nought ; Or that the Heavenly Spheres and Globe of Earth , From h Fire , not such blind Matter , drew their Birth , Whose flames in all things dwell , kindled Heav'ns i Eys , And form the glittering Lightning of the Skies ; Or sprung from k Water , which dry Matter soaks , And l ravenous Fire , that would devour it , choaks ; Or unbegot were Earth , Air , Water , Fire , And these m four Limbs make up the God entire , And form this World ; nor will that ought be found Beyond themselves , since All things they compound , Applying Hot to Cold , to Humid Dry , To Heavy Light , which kind n Discordancy The Matrimonial Bands of Nature knits , And Principles for all Production fits ; We can but guess its Birth : obscur'd it lies Beyond the reach of Men and Deities . Yet though its Birth be hid , its Form's disclos'd , And in due Order all its Parts dispos'd ; o Fire up to the Aethereal Confines flew , And a round Wall of Flame 'bout Nature drew , The subtle Air possest the second Place Diffus'd throughout the vast Globes middle space , Whence its hot Neighbour draws cool Nourishment : The third Lot level'd the wide Seas Extent , And in a liquid Plain the Waters spread , Whence hungry Air is by thin Vapours fed ; Prest down b' its p Sediment , Earth lowest fell , Whilst sand-mixt slime contracting did expel The subtler moysture ; which to flight constrain'd Rose by degrees 'till it the surface gain'd , And the more that into pure Water went , The more the q squeez'd out Seas the drain'd Earth pent , Settling in hollow Vales ; whilst Hills thrust out Their Heads from Waves circling the Globe about : This lowest , in the midst is still confin'd , On all parts equally from Heaven disjoyn'd , Secur'd from further falling by its fall , The Middle both and Bottom of this All , In whose r concentring Parts , on every side Bodies Encountring , are to sink deny'd . And did not Earth by its self-Poize suspend , Phoebus , the Stars approaching , could not bend His Course to set , nor set , e're rise again , Nor Phoebe drive through the Aereal plain Her Wave-drench'd s Steeds ; nor t Phosphorus the Light E're usher more , if Hesperus to Night Now in the Middle Earth suspending thus , Not sunk to th Bottom , All is Pervious : For We nor can the rising Stars conceive A u casual Production ; nor believe Of the chang'd Heavens , the oft-renascent State , Sol's frequent Births , and his Quotidian Fate ; Since the Signs always shew the self-same Face , Heav'n keeps one Course , the Sun one constant Race , The Moon in certain , although various , ways , The changes of her Light , and Orb displays . Nature , the Tract which first she made , observes ; Nor e're like an unskilful Novice swerves . Day with eternal Light is carried round , This the times shew , in several Regions found Successively the same ; and we may see Eastward its Rise , its Setting West to be ( The further unto either as we run ) Continued with Heavens Motion , and the Sun. Nor need the Pendent Earth wonder beget , Since the whole World suspends as well as it , Whose x Foot upon no certain Bottom rests , As its swift Course and Circular attests . The radiant Sun suspended runs its Rounds , Never transgressing his Aethereal Bounds . The Moon and Stars in Skies y suspended stray , And Earth by Imitation z hangs as they , Poiz'd in the middle of circumfluent Air : Not flatly stretch'd , but swell'd into a Sphere , Rising alike , and falling every where . This is the Face of Nature ; thus th' Heav'ns roll'd Swiftly about , into a round Figures mould The Sun and Stars ; round is the Moon to sight , And with a swelling Body barrs the Light ; Hence never wholly Lucid is her Ball , When the Sun's Beams on it obliquely fall . A Form eternal , like the Gods alone , In which , Beginning there or End is none ; But like throughout , and every where the same . Such are the Stars , such is the whole Worlds Frame . Hence 't is We see not in all Lands all Signs , b Canopus not till you reach c Aegypt shines , And they d lack Helice , who see his Light , Earth's Tumour hind'ring th'intercepted Sight . The Truth of this Thou Cynthia mayst attest , When dark'ning Shadows thy bright Looks invest , e At once thou dost not all the World amaze , But first the Eastern Nations miss thy Rays ; Then those which under the Mid-Heaven are plac'd ; Next , tow'rd Hesperia fly'st thou , cloudy-fac'd ; Then those who yet more distant have their Seat , Later ( to aid thee ) f brazen Vessels beat . If then the Earth were flat , this sad Defect Of Light , the whole World might at once detect , But since 't is Round , to These first , then to Those , Her Rising self , or setting Delia shows ; For carried Circular , she first attains Th' Ascending Parts , then the Descending gains ; Now climbs this Arch , anon leaves that behind , Whence that the Earth is Round , we clearly find . This is by Men , and Beasts , and g Birds possest , The North Parts Eminent , the South deprest Beneath our Feet ; whose surface seems to be ( It's Breadth deceiving its Declivitie ) Stretch'd to a lengthful Plain ; the large Extent Compos'd of equal Rising and Descent . Hence when Sol's Beams i' th' West our Orient Face There rising Day does sleep from Mortals chace , And when the Light to Labour summons Those , 'T is Night with Us , and Time for our Repose . The watry h Girdle of the Ambient Main , Does either Hemisphere divide , and chain . This Worlds huge Mass fram'd into One Entire Of different Parts , as Earth , Air , Water , Fire , A Power i Divine , whose sacred Influence glides Through all its Limbs , with tacit Reason guides , And mutual Leagues inclines them to contract , That some may k suffer , what the Others act , And the whole Frame ( although diversify'd By various Figures ) be throughout ally'd . Now we the radiant Signs in Order sing ; First those which guirt Heaven with an Oblique Ring , And Phoebus by alternate Courses bear Through the successive Seasons of the Year . Then those whose Course to Heav'n is Opposite , All which may numbred be in a clear Night ; The Laws of Fate depending on their Power . First then of Heav'ns chief Part , its Starry l Tower. The m Princely n Ram glittering in Golden Wool , Wonders to see the backward-rising o Bull With submiss Looks beckon the p Twins ; next whom q Cancer , who after him sees r Leo come ; Him s Virgo follows ; then the t Scales , that weigh In even Ballance equal Night and Day , Draw on the u Scorpion with the fiery Sting , At which the x Centaur his Shaft levelling Seems ready to let f●…y : To these comes on The y Goats contracted Constellation . z Aquarius next pours from his Urn a Flood , Whilst the glad a Fish to the lov'd Waters scud , By Aries touch'd , and make the closing Sign . Now in the Skies near where the bright Bears shine ( Which from Heavens Top on all the Stars look down , Nor know to se●… ; but plac'd on the World's Crown , Though differently , whirle round the Stars and Skies ) Stretch'd through thin Air the b subtle Axis lies , Whose distant Poles the Ballanc'd Fabrick hold ; Round this the Star-imbellish'd Orbs are rowl'd : Whilst yet it self unmov'd through empty Air , And the Earths Globe extends to either Bear. Nor is 't a c solid Substance , or opprest With Weight , though the Worlds d weight upon it rest . But as the Air mov'd in a Circle goes , And on it self , whence first it flow'd , reflows , What e're that is which still the midst doth hold , 'Bout which , ( it self unmov'd ) All else is rowl'd , So subtle it can no way be inclin'd , That by the Name of Axis is design'd . Upon whose Top ( to Mariners distrest Well known , their Guides through Seas ) two bright signs rest . Great e Helice moves in a f greater Bend Mark'd with seven fair Stars , the Greek Pilot's Friend , Small g Cynosure , less both in Light and size , A less Orb holds ; whom yet the Tyrians prize More than the Great ; by This the h Poeni steer Through vast Seas to the Western Hemisphere . These joyn not Fronts , but eithers Head turns to The others Tayl ; pursu'd , as they pursue . Between both which , his large unfolded Spires A i Serpent stretches ; and with winding fires Embracing them , one from the other parts , And from their k Stations sees that neither starts . 'Twixt this , and Heavens Mid-Circle , where the Sun , And six Lights more 'gainst the bright Zodiack run , Rise Stars of different Magnitude and Power , Some near the Pole , some near Heav'ns radiant Tower. Which l temper'd by the disagreeing Air The fruitful Earth for humane use prepare . Next the cold Bears , ( the Cause t' himself best known ) Shines forth a m kneeling Constellation . Behind whose Back n Arctophylax appears , The same Boötes call'd , because yoak'd Steers He seeming drives ; who through the rapid Skies ( Bearing o Arcturus in his Bosome ) hies . On th' other side see the rich p Crown display Its Luminous Gems , bright with a different Ray : Whom the swift y Courser strives t' oretake , his Brest With a refulgent Signature imprest , Which closes in the fair z Andromeda : Kind a Perseus Shoulder lends her Feet a Stay , And joyns t' himself ; but a large Space divides b Deltoton brighter in its Base than sides , So call'd from its Resemblance ; c Cepheus And d Cassiopea made conspicuous Ev'n to her Punishment , seems to deplore Andromeda chain'd to the rocky shore , Fearing the gaping Monster of the Deep ; But Perseus still does his old kindness keep , Comes to her Aid , and of the Gorgon slain Shows the fear'd Head , his Spoyl e the Seers Bane . Close running by the kneeling Bull , behold f Heniochus , who gain'd by skill of old Heav'n and his Name ; as first g four Steeds he drove On flying Wheels , seen , and install'd by Iove . The h Kids next , the Seas barring till the Spring , Then the i Goat , Nurse to the Worlds Infant King , Who from her Teats scal'd Heaven , her Milk , did grow To brandish Lightning , and fear'd Thunder throw , By her own Iove a Constellation made , And for the Heav'n she gave , with Heav'n repay'd . Last view the k Pleiad's and the l Hyades , Both Parts o' th' Bull ; The m Northern Signs are These . Now see the Stars which 'bove the scorcht Earth run Rising beneath the Path-way of the Sun , And those which 'twixt the Tropick are confin'd Of Capricorn , and Pole that is declin'd . Near to the Twins behold n Orion rise With stretch'd Arms almost fathoming the Skies : Nor marching with a less extended Pace . Bright shining Stars his either shoulder grace . Three Lights his Pendant Sword obliquely sign , In his advanced Head three others shine Deep in the Skies immerst ; nor yet less bright , Though such they seem 'cause more remov'd from Sight . Him , as through Heaven he marches , follow All The o starry Legions as their General . Next after whom with rapid Motion bent , ( No Star than that 'gainst Earth more violent ) The fierce p Dog runs ; not one for Heat does rise , Not one for Cold more grievous quits the Skies , The World afflicting with a different Fate : Nor ever fails upon the Sun to waite . Who this from q Taurus Crown first rising see r Ghess thence of Fruits what the s Event may be : What Health , what Quiet may the Year befal : Here War it makes , there Peace does reinstal ; And as it variously returns , doth awe Th' inferiour World ; It 's Aspect is their Law. 'T is strongly credited this owns a Light And runs a Course not than the t Sun 's less bright , But that remov'd from Sight so great a Way It seems to cast a dim and weaker Ray : All other Stars it foyls , none in the Main Is drench'd , or brighter thence ascends again . Next , with the nimble u Hare see x Procyon rise , And then the noble y Argo ; to the Skies From Seas translated which she first did plow ; Once tost with mighty storms , in Heaven fixt now , And deify'd for saving Deities . Close boarding her a glittering z Serpent lies , And by so ordered Lights , seems to present His speckled Bodies scaly Ornament . a Sols Bird , the b Cup dear to the God of Wine , And c Centaure next in a mix'd shape does shine , Half Man , half Horse ; then Heavens bright Temple see , And d Altar consecrate to Victorie , What time th' inraged Earth a Giant Race 'Gainst Heaven produc'd , then Gods besought the Grace Of the e great Gods ; and Iove himself f f So Claudian de Bello Getico , — Ipsumque Iovem , turbante Typhoeo , Sifas est , timuisse ferunt — fear'd too He wanted Power to do , what he could do . When he amaz'd the rising Earth beheld , How ev'n 'gainst Natures self , Nature rebell'd , Saw Mountains heap'd on Mountains to aspire , And Stars from the approaching Hills retire , Charg'd with dire Arms by a g g Applicable to this Place may seem this not common and not unelegant Description of Sidorius Ap●…llinar . in Carm. 9. ad Foeli●…em . N●…n hic Terrigenam loquor Cohortem Admixto magè ●…ividam veneno , Cui praeter Speciem 〈◊〉 c●…rentem A●…gues Corporibus voluminosis , A●…te squammea Cru●…a porrigentes , In a estigia fauce desinebant . Sic ●…ormae triplicis Procax Iuventus , 〈◊〉 Pedem proterens voraci Curs ●…at Capitum stupenda gressu ; Et cum Classica Numinum sonabant , Mex c●…ntrà Tonitrus resibilante And h●…t Superos ciere plantâ . Nec Ph●…egrae legis ampliata rura , Missi dum ●…olitant per Astra M●…ntes , Pindus , Pelion , Ossa , Olympus , Othry●… , Cumsilvis , gregibus f●…ris , Pruinis , S●…xis , fontibus , Oppidis , levati Vi●…rantium spati●…siorum dextrâ . Of th' Earth-born Race is not our Song Who by mix'd Poisons grew more strong ; Their Limbs immeasurably vast ; About whose legs wreath'd Serpents cast , With gaping Jaws which downwards bend , Did like to cloven feet extend . Three-form'd srupendious Race ! that treads Not upon heels , but runs on heads . These when the Gods did sound to fight , Mock'd at their Thunder ; and in spight Kick'd 'gainst the Skies with hissing feet . Nor tell we here how they did meet On P●…legro's Plains , and Mountains hurl'd Against the Bright Lamps of the World ; How Pindus , Pelio●… , Ossa flew Toss'd by their Hands , Olympus too And Othrys with their Woods and Flocks , Wild Beasts , Towns , Fountains , Snows , and Rocks . deformed Birth Issuing from Ruptures of the teeming Earth . No h h The Latine hath H●…stiferum quemquam ; by Barthius ( Adversar . l. 24. c. 10 ) interpreted Hostias ferentem . Servius in prim . Aeneid . Hostiae dicuntur sacrificia quae ab his fiun●… qui in Hostem pergunt . We have therefore chosen to follow Barthius his Interpretation ; Scaliger being here at a loss , who conceives some errour to be in the word H●…stiferum , and would instead thereof read Pestiferum . Victime-Bearers yet the Gods had known , Or that there were Powers Greater than their own ; Then did Heav'ns King this Starry Altar raise , Whose fires ev'n yet with brightest Lustre blaze . Near which the i i This Asterism is by the Greeks call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , by the Latines accordingly Cete and Cetus , Balaena , 〈◊〉 , Leo , or U●…sus Marinus ; by the Arabs ( from the Greek ) Alk●…tus . Ptolomy reckons therein 22 Stars , Bayerus 27. Kepler 25. Of which the bright one in the snout of the Whale is call'd Menkar Alketus , i. e. Rostrum Ceti . That in the Tail , Dan●… Alke●…us , i e. Cauda Ceti , and both these are likewise call'd by th' Arabs , Al Diphdaan , i. e. duo Ranae . There are two also in his hands , ( for this Fish is conceiv'd to be the same with Dagon or Dercet●… , the Syrian Idol ; which was represented in the upper part after a humane shape , in the lower , after that of a Fish , and by the Iews nam'd Adir Dag , i. e. Piseis Magnus ; de quo Seld●…nus de Diis Syris Syntagm . 2. ) and are by the Arabs call'd Al Naaman , or according to Mr. Hyde , Al Naamât , i. e. 〈◊〉 Cameli . The second Star in this Constellation is call'd Caph Al Giedma , i. e. Manus truncata . The 21th Star is call'd Danab Al Ketus Shem●…li , i. e. Ceti Cauda Borealis . The 22th , Danab Al Gienùbi , i. e. Cauda Australis , and Al 〈◊〉 Al Th●…ni , i. e. Rana Secunda . It is seen in the Meridian at Midnight from the beginning of Octo●… to the end of December . Whale raising his scaley Limbs The Whale . In large Wreaths , wallowing on his Belly swims , And gapes as ready just to seize his Prey : As when the same th' k k Of the exposure of And●…omeda to this Sea-Monster , and the Combat betwixt that and Perseus , see the Appendix . The Ground of which Fable may happily arise ; for that the Ship in which she was carried away had for its Ensign , the Whale ; the Story of which see in Photius his Bibliotheca from the Narrations of Conon ; or in regard the Person by whom she was first demanded in Marriage was some Insulary Prince , and exercis'd Piracy , and for that reason compar'd to a Whale or Sea-Monster , of which see Vossius l. 1. de Idololatr . & Scheffer . de Militiâ Navali . l. 1. c. ●… . But not to insist longer upon the Fable ; Divers admit of the exposure of Andromeda to this Sea-Monster as a 〈◊〉 Story ; see the same defended by Bartholom . Barrientus , in Sylv. Annotat. c. 1. from the Testimonies of Stra●… , 〈◊〉 , St. Ierome , Aegesyppus and Pliny ; the last of whom speaking of Ioppa , thus writes : Ioppe Phoenicum , 〈◊〉 〈◊〉 In●…datione ut ferunt , insidet Collem , praejacente Saxo , in quo Vinculorum Andromedae vestigia ostendum . And elsewhere reports that the Bones of this Monster were brought from Ioppe to Rome , and among other 〈◊〉 sights were by Marcus Scaurus in his Aedile-Ship shown to the People , in length forty feet , his Ribs in 〈◊〉 exceeding the tallest Indian Elephants , the thickness of his Back-bone being a foot and half over . Vide Plin. i. 5. ●… . 13. and l. 9. c. 5. expos'd Andromeda To her sad Fate approaching once beheld , Who the forc'd Waves beyond their Shore impell'd . In Heaven's South Part , the l l The Poets fabled this to have been the Fish , which saved Phacetis ( or rather Aphacitis ) the Daughter of Venus , fallen into the Lake Boeth , and for that reason constellated ; by the Arabs called Al Hau●… Al Gienubi , i. e. Piscis Australis ; by Higynus , Piscis solitarius , and by Bassus in Germanicum , Piscis Magnus ; and is said to have spawn'd the other two in the Zodiack . It is made up , according to Ptolemy and Bayerus , of 12 Stars , among which the Bright one in his Mouth is call'd Al Diphda Al Auwal , i. e. Rana prima ; and Al Dalim , i. e. Agger ; and Phom Al Hant , i. e. Os Piscis , commonly but erroneously Phomahant . This glides by the Meridian at Midnight about the midle of August . Fish then from the Wind , The Southern Fish. Call'd Southern , rises ; close to which conjoyn'd In mighty flexures m m This Stream is by Scaliger call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. fusio Aquae , and is different from that which by Vitruvius is call'd fusio Stellarum , ( of which already in the sign Pisces , call'd likewise 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ) and is distinct also from that other starry stream call'd Eridanus , or 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Fluvius Orionis . Manilius here gives to this stream as it were a double Head , making it to flow as well from the Mouth of the Southern Fish , as from the Urn of Aquarius , and to unite in the middle , as is likewise observ'd by Gassendus upon this Place , Tom. 1. l. 2. p. 543. Of the other Southern Constellations , unknown to the Antients , see in the Appendix . starry Rivers run . One of their Heads flows from Aquarius Tun , Whose Waters by communicated Streams Meet in the midst , and mix Sidereal Beams . 'Twixt the Ecliptick and the n n That is the Antartick or Southern Pole , to us invisible , which our Poet imagines to be adorn'd with the like Constellations as the Northern ; and therefore he calls them the latent Bears . latent Bears , Which 'bout the creaking Axis turn the Sphears , Heaven's o o In respect to us , inhabiting the Northern Hemisphere . Not unaptly Sidonius Apollinaris calls the Stars on either side the Zodiack , Exotica Sydera , strange or forreign ; quasi 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Extra Zodiacum ; as is noted by Sirmondus . stranger Orbe with these Stars painted shines , Which Antient Poets call'd the Southern Signs . The rest o' th' World lies under p p That is that part of the Southern Hemisphere to us inconspicuous , being terminated by our Horizon ; for the Antients , as is before noted , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 vocabant , says Scaliger upon this Place . For this Reason by the Eastern People these Southern Constellations are call'd Chadre Teman , i. e. Penetralia Austri , quasi sint in loco Occulto ; as Aben Ezra cited by Mr. Hyde . Water hid , Where unknown Realms , Lands to our Sight forbid , Take from one Sun with us a common Light , The Constellations of the Southern Hemisphere to us inconspicuous . But q q As being to us 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . They having Dextros Ortus & Sinistram Umbram : We Sinistros Ortus & Dextram Umbram . And as Macrobius in Somn. Scip. l. 2. notes , Idem Sol illis & obire dicetur nostro Ortu , & orietur cum nobis occidet . several Shadows , and a different Night . Where Stars sinistral set , and dextral rise , Their Heav'n as ample , nor less bright their Skies , Their Stars as numerous , only thus outvy'd , In that to them Augustus Star's deny'd , Which does our World with Rayes propitious bless ; Earths present , and Heavens future Happiness . That the Extreams which 'bout the neather Pole The Constellations about the Southern Pole ( supposed ) like those about the Northern . Deck'd with bright Stars , though inconspicuous , rowl , The upper Pole's resemble , with r r Our Authour here argues 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , that about the Southern Pole there are , or ought to be the same Constellations , as about the Northern ; which Errour is to be attributed to the Ignorance of the Times wherein he lived , in which that part of the World was altogether unknown to the Romans . But Modern Experience evinces , that there are not only no such Asterisms as the greater and lesser Bear and Dragon ; but also no Stars within many Degrees of that Pole. The nearest to it being a Star in the Tayl of the Hydrus , call'd by the Dutch , the Water Schlang . Vide Ri●…ciol . Tom 1. l. 6. p. 410. Hence Herigon in his Cursus Mathemat . Tom. 1. p. 37. Nulla Coeli pars minoribus & paucioribus Stellis 〈◊〉 quam Austrin●… Circumpolaris , for which Reason it may be stil'd ( as by Seneca in He●…cul . Fure●…e , it is ) De●…ior Polu●… . Signs grac'd Like that ; where Bears with Fronts averse are plac'd , And by one Dragon parted ; we suppose , Induc'd to credit what Example shows , For Reason urges from Analogie , The Parts unseen are like to those we see . These several Stations , by large Skies disjoyn'd ; To all the Constellations are assign'd , The Forms and ●…gines of the several Constellations not corporeal . Yet think not they corporeal Figures are , Or all their Members equal Lustre share ; s s To the same purpose likewise our Poet in the end of his 5th Book , Ipse suas Aether Flammas sufferre nequiret , Totus & accenso Mundus flagraret Olymp●… . Yet this Reason of our Authour Picus Mirandula ( l. 1. in Astrolog . p. 255. ) thinks only worthy of laughter . Mallium ( so he calls Manilius ) nisi esset Poeta , Bone Deus ! quo risu prosequeremur , qui Coelestes illas quas fingit Imagines paucis stellis i●…choatas potius dicit , quam absolutas , Ne pluribus ●…bi ignibus accensis Incendia Mundus flagraret ? But with the leave of that Prince of Learning , our Author is herein ( as to the fiery nature of the Stars ) defended by most of the Antients : Hence in Orpheus , the Sun , Moon and Stars are said to be 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , membra Vulcani : And Cicero in secundo de Natura Deorum , gives this Reason why the Stars are said to be nourished by moisture , ut nihil ferè in●…reat aut admodum paululum , quod A●…rorum Ignis aut Aetheris Flamma c●…umat . Nor wants he the suffrage of divers of the Fathers , Schoolmen and Moderns : In proof of which it may suffice to instance only what the Learned G. V●…ssius hath to this purpose , l 2. Idololatr . c. 39. Unless ( says he ) the Stars be of a fiery Nature , I see no Reason why the Waters should be plac'd above the Heavens , as we are told both by the Writings of Moses and others , they are : But now the Reason is plain , to wit , that by them the exaestuating Fire of the Stars might be repress'd and temper'd , lest by their heat and fervour the whole Heavens should be dissolv'd : The same Reason being rendred by St. Basil , St. Ambrose , Theodoret , Procopius , Damascen , Beda and others . Thus He. Vide etiam Gassendum , Tom. 1. l. 1. p. 502. Heaven could not suffer so intense a Heat , Were no Part voyd , but all with Fire repleat . Some therefore cautious Nature kept from Flame , Lest it should hazard the Coelestial Frame , Only to mark their Figures out content , And Signs by certain Stars to represent , Whose Lights design their shapes ; fire answers fire , Mean to Extream , the Lower to the Higher , It is enough they are not hidden quite . Some Stars the Moon half full show greatest Light , But all the nameless Commons of the Sky Obscur'd by her completed Splendour , fly : The brighter Signs yet nor their Number change , Their rising and setting constant and regular . Nor with less Stars in mixed Motion range , But the same Course ( the better to be known ) And Order , in their Rise and Setting , own . Nor in this World may Ought more wonder raise Than that the Whole Reason , and Laws , obeys , Where Nothing 's crowded , Nothing loosely roves , Or cross to its determin'd Order , moves ; What more confus'd in shew ? yet what in Course More certain ? a clear Reason to inforce Hence the Government of the World by divine Providence is asserted . That this World 's t t Clean●…hes in Cicero de Naturá Deorum l. 2. urging reasons to evince the Belief of a Deity , among others gives this for the last and weight●…st , Aequa●…ilitatem motùs , &c. The Aequability of the Moti●…n and Conversion of the Heavens , Sun , Moon and Stars , their Distinction , Variety , Beauty , Order . The very view of which ( says he ) sufficiently declares them not to be fortuitous or 〈◊〉 : And again , Quid potest esse ●…am ap●…rtum , tamque pe●…spicuum cùm C●…um suspexinius , &c. What can be more evident or perspicuous , when we behold the Heavens and contemplate the Coelestial Bodies , than that there is a Deity , by whose Excellent Providence they are govern'd ? Thus far Cicero , ( with our Authour ) from the bare suggestion of Nature , truly . What follows , where the World it self is said to be a God , is from the mistaken Principles of the Platonists and Stoicks , who ( as before is noted ) make the World to be a God , but a Secondary one ; for that Power which they primarily call God , is by them term'd Ratio & Mens ; by whom they affirm'd the World to be created : So Cicero in Timaeo ; Deus ille Aeternus ( scil . Mens ) hunc perfecte beatum Deum ( scil . Mundum ) procreavit . The World being in their sence the universal Fusion of the first Divine Mind ; for so Chrysippus in Cicero in primo de Natura Deorum describes it : Vim Divinam in Ratione esse positam , & univ●…rsae Naturae Anima atque Mente . Ipsumque Mundum Deum dici & ejus Animae fusionem universam . The Divine Power is seated in Reason , and in the Mind of universal Nature . And this World is said to be a God , and the universal Fusion or Extension of that Mind . Vide etiam Lips ▪ Philosoph . Stoic . l. ●… . Dissert . 8. govern'd by a Deity And is it self a God ; nor casually Together met , as he would once perswade , Who first the VValls of this wide System made u u Democritus , whose follower was Epicurus , as is before noted . There is in Derision of this Opinion an Epigram of Lucilius in the Greek Anthology , l. 2. wherein there is a jocular Comparison between Diophantus , a very little Dwarf , and Epicurus his Atoms , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Of Atoms Epicurus did compose This World , 'cause nothing he thought less than those . Had Diophantus liv'd then , he this All. Had brought from him , for he is yet more small . Or though he held Atoms All else contriv'd , From Him yet sure he Atoms had deriv'd . Of Atoms , and to those resolves again ; Of which , the solid Earth , the floating Main , The fiery Stars , and Aether that creates Infinite Orbs , and others dissipates , Consist : All which revert unto their Springs , And transmutate the various Forms of things . But who can think this World educ'd should be From such blind Grounds without a Deitie ? If Chance did give , Chance rules this All ; Whence are The Signs then in their Course so regular ? Rising by Turns , as if by Laws injoyn'd , None posting on , whilst others stay behind ? The same Stars Summer , the same Winter grace , Day takes , and leaves to Heaven one certain Face . What time Troy's State was by the Greeks undon , x x Respecting this Place in Homer , Iliad . 6. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Ursamque quam & Plaustrum cognomine vocant , Quae ibidem vertitur & Oriona observat . Where 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , answers to Manilius his — Adversis frontibus ibant . These two Constellations being plac'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , in a direct line against one another , as two jealous Princes marking each others Motion , according to Mr. Selden his Observation in his Titles of Honour ( c. 1. ) for the Bear being Princess of the Northern Constellations , observes and looks at Orion Prince of the Southern . Which 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Position of these Constellations Casaubon ( in Strabon . l. 1. ) conceives Manilius to have collected from the only Authority of Homer before cited . Oppos'd did Arctos and Orion run . She the World's Top to circle still content , He facing her , to round th' whole Firmament . The times of obscure Night , were then y y The observation of the time of Night from the rising or position of the Stars was usual among the Antients in the time of the Trojan War , by which they ordered their Watches , as by those they divided the Night . Instances whereof we have in Euripides his Iphigen . in Aulid . and Rhesus . From the later of which take this : 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , &c. Cujus est vigilia ? Quis per vices Succedit mihi primùm ? Iam occidunt signa , & septemgrad●… Pleiades Aetheriae ( oriuntur ) Volat autem Aquila in Medio Cali , &c. The Manner and Method of their Observation is thus deliver'd by Attalus , an Antient Scholiast upon Aratus , as cited by Hipparchus . Since Sun-set is the beginning of Night , and that the Sun is in always one of the 12 Signs ; It is manifest , that knowing in what sign the Sun is , and in what degree thereof , it may be easily told , what sign and what degree will arise in the beginning of Night . For the part of the Zodiack which is Diametrically opposite to that which the Sun is in at his setting , will at the beginning of Night be seen to rise : which being observ'd and known , for as much as every Night six signs arise from the East , it may be told what part of Night answers to their rising , and how much is remaining between that and the rising of the Sun. But the Errours of this ▪ rude observation Hipparchus refutes from the inequality of Time in the Ascensions of the several signs , some of them being less than their Dodecatemoria , others extending beyond ; as for Example : Cancer is much less than the 12th part or division of the Zodiack allotted to it . Virgo takes up some part of Leo and Scorpio . The Southern Fish is almost wholly in the Dodecatemorion of Aquarius : So that their unequal and different rising must needs beget an Errour in the Computation of Time , and consequently the hour of Night cannot thereby be truly determin'd . Vide Hipparch . in Arat. Ph●…nomen . l. 2. & Marcianum Capellam l. 8. c. 24. devin'd From the bright Stars ; Heaven hadits z z The hours as they are now distinguish'd are by some conceiv'd not to have been in use with the Antients ; for certain it is , says Casaubon , ( Animadvers . in Athenaeum , l. 1. c. 1. ) that neither in the time of Plato or Aristotle , nor many years after them , was the Word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 in use among the Greeks , as we n●…w take it : And therefore Pollux reckoning up the Parts , by which the Day and Night were distinguish'd by the Antients , makes no mention thereof ▪ Of this Opinion likewise is Salmasius in Plin. Exercitat . Tom. 1. p. 650. with whom Menagius seems to comply in Observat. ad Laertium . l. 1. p. 44. The contrary , yet , ( viz. that the Day was then by the Greeks divided into Parts Analogical to the hours in use with us , ) with clearer Arguments being defended by Petavius in Uranölog . Dissertat . l. 7. c. 8. And the learned Leo Allatius dé Mensurá Temporum Antiquorum , c. 4. And that among the Iews and other Eastern Nations the division of the day into hours was very antient , if not Coaeval with the first division of Time into Days , Weeks , Moneths or Years , Kircher ( in Oedip. Aegypt . Tom. 2. part . 2. p. 225. ) endeavours to demonstrate . Indeed as to the Romans , Censorinus de Die Natal . c. 23. plainly affirms that the Word Hora was not known among them until 300 Years after the Building of Rome : They dividing the day into two parts only , which they call'd Ortum & Occasum . Afterwards , as Pliny ( l. 7. c. 60. ) witnesses , the Noonstead was added , call'd Meridies , quèd Partes Diei , bifariam tum divisi , discernebat , says Censorinus . These Parts of the Day they call'd Tempestates ; so in the 12 Tables ▪ SOL OCCASUS SUPREMA TEMPESTAS ESTO . The Manner of signifying the time of day was by a Beadle or Cryer at the Command of the Praetor or Consul . Pliny describes it thus : The Consuls Beadle or Cryer standing in the Court , when he beheld the Sun between the Rostra and the Graegostasis pronounced it was Noon . But when the Sun inclined downward from the Column named Moenia , to the Common Gaolor Prison , then he gave warning of the last Quarter of the Day , and so pronounced . Nor had they any other means to know how the Day went , until after the time of the first Punick War. Afterwards they divided the Day ( and so the Night likewise ) into 12 Parts , which they call'd hours , not equal , but varying according to the length or shortness of the Day in Summer or Winter , and therefore call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 seu Temporales . Which Division or Distinction of Time they receiv'd from the Greeks , who deriv'd it from the Aegyptians , as they from the Babylonians , or Chaldaeans according to Herodotus ; The Aegyptians giving to the several hours of the day these particular Names . To the first , Lampé ; to the second , Alexidi ; to the third , Terpsithi ; to the fourth , Phenon ; to the fifth , Erebe ; to the sixth , Diauges ; to the seventh , Proka ; to the eighth , Panphé ; to the ninth , Loitia ; to the tenth , Porphuré ; to the eleventh , Panphout ; to the twelfth , Truphé . Those of the Night had likewise their distinct Denominations ; But Salmasius , who ( in Diatrib . de Antiq. Astrolog . ) gives us these , says , he could never meet with the other . The Chinese antiently , and from them the Turkish Astronomers , divide the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , or natural day into 12 equal parts , each part they call Iagg , answering to our Bihoria , and to every Iagg they apply a particular name from some Creature ; As , to the Chin. Turk . 1. Zeh Cescu . Mus. 2. Iiu. Tut. Bos. 3. Yem . Pars. Pardus . 4. Mau. Tuskan . Lepus . 5. Iin. Lui . Crocodilus . 6. Siz . Yilang . Serpens . 7. Vou. Iunad . Equus . 8. Vi. Kui . Ovis . 9. Shin . Pijin . Simia . 10. You. Daki●…k . Gallina . 11. Su. Eit. Canis . 12. Chai . Tungus . Porcus . Every one of these Iaggs they divide into eight Parts which they call Geh , and may be term'd Scrupula horaria . Again , they divide every day into 10000 Particles , calling each Particle Fenac , which may be interpreted Scrupula Diaria . Vid. Epoch . Celebr . Ulugh Beigh Edit . per Gravium . p. 6. Of the Oeconomical Distribution of the 12 hours of the day among the Romans ; see Martial . lib. 4. Epigr. 8. and the particular explication thereof in Stuckius de Antiqu. Conviv . ( l. 1. c. 11. ) and in Galluccius in Virgilian . Vindicat. ( Aeneid . l. 9. loc . 2. ) The Invention of Sun-Dyals for distinguishing the hours was not known in Rome until the Time of the Tarentine War ; of which see Pliny and Censorinus , as before cited . Among the Greeks it was earlier , being attributed by some to Anaximenes ; by others , to Pherecydes of Syrus , of which Laertius in his life . B●…ebartus in Geogr. Sacr. l. 1. c. 14. makes the Invention much antienter from the Testimony of Homer ( Odyss . ó. ) With the Iews it was 200 Years before the time of Pherecydes , as appears by King Achaz his Dyal . The use of the Clepsydra or water-hour-glass was first invented by Cresibius of Alexandria , who flourished in the time of Ptolomaeus Evergetes ; first brought into use among the Romans by Scipio Nasica , as Vitruvius l. 9. c. 9. The use of Clocks or Watches seems not to be very antient ; there not appearing any mention thereof earlier than in these Verses of Bato the Comick Poet , cited in Atbenaeus , l. 4. — 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . — ut aliquis putet Non Ampuliam Te circumgestare , sed Horologium . Which Bato , Casaubon reckons inter 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Poetas , ( though his Conjecture be severely reprehended by Allatius in his Work before cited ) and believes that Citation to be the only instance that is to be found in any Monument of Antiquity touching that Subject . Hours design'd : Since when how many Kingdoms waste are lay'd ? How many Nations have been Captive made ? a a To this Purpose , Ennius , l. 8. Mortalem summum Fortunarepente Reddidit è summo regno ut famul ' infimus esset . Apposite likewise is that of Iuvenal , Satyr . 7. Servis Regna dabant , Captivis Fata Triumphos . And of Seneca ( Controvers . l. 1. e. 1. ) Mutabilis est Casus ; dederunt victis Terga Victores ; & quos provexerat fortuna , destituit . Quid referam Marium Sexto Consulatis Carthagine Mendicantem , Septimo Imperantem ? Empire and Servitude how oft dissolv'd By Fortunes Power ? and differently revolv'd ? b b Meaning the Roman State and People , which rose from the Ruines and Ashes of subverted Troy ; which may be illustrated by this of Cyprian de Idol . vanitat . Regna non merito accidunt , sed sorts variantur . Imperium antè tenuerunt & Assyrii & Medi & Persae ; E●… Graecos & Aegyptios regn●…sse c●…gnoviinus . Ita vicibus petestatum Romanis quoque ut & caeteris imperandi tempus obvenit . Troy's Ashes now to what a glorious State She reinspires ? c c The Romans bringing upon Greece the same Desolation , which that once brought upon Troy , one of the most flourishing Cities of Asia ; To this place may not impertinently be applyed that Epigram of the Emperour Adrion in the Greek Anthology , l. 1. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Hector thou Blood of Mars ▪ if Words thine Eare Now in the Grave may reach , rise and appear ! See thy fam'd Troy's by a new Race possest , Though not so stout as Thee , valiant at least ; Foyl'd are the Myrmidons ; tell Achilles , These , Thessaly now stoopes to th' Aene●…des . Greece suffers Asia's Fate . 'T were tedious to recount the Ages past , How oft the Sun hath seen the World new cast . All Things by humane Laws created , change : Lands to each other known , in time grow strange : Nations in course of many Years , put on A various Face ; but Heaven wears always one ; Grows not by length of Days , nor wastes with Age , Always in Course , yet faints not in its Stage , d d The Opinion of Xenophane●… ( as before noted ) and of Aristotle ; defended by Averroes , borrowed from Ocellus Lucanus 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Will ever be the same , since such 't was ever ; Other than 't is our e e Not unlike to this is that Argument in St. Peter , Epistol . 2. taken up by the Libertines of that Age , Ex quo Patres dormi●…runt , Omnia sic permanent ab Initio Cre●…nis . But against this unchangeable Durability of the Heavens Seneca declares . Quid Mutationis Periculo exceplum ? Non Terra , non Coelum , &c. What is ex●…pe from the danger of Change ? Not the Earth , not Heaven , not the universal Context of all things guided by the Conduct of God himself ; It shall not always bold this Order ; A Day will come that shall throw it quite out of its Course . Senec. Epistol . 71. Fathers saw it never , Nor shall our Nephews : 't is a God , and knows , Nothing of Change , which Age and Time impose . That the Sun ne'r starts to the North aside , Nor changing Course back to the East does ride , And to strange Lands a new-born Day disclose ; That the Moon always the same f f Appositely Macrobius in Somn. Scip. l. 1. c. 6. Similibus Dispensationibus Hebdomadum , Luna sutluminis vices sempiternd lege variando disponit , and Statius ( Sylv. l. 3. ) Servit & Astrorum velox Chorus , & vaga servit Luna , nec injussae t●…ties redit Orbita Lucis . These Changes of the Moon the Antient Greeks call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and from them the Latines , Phases , sive Apparitiones . The Names of the said Phases or Appearances , especially of the four most notable , are these . The first , ( reckoning her increasing Changes ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Cornicula●…a , about 60 Degrees distant from the Sun. This Phasis is by the Turks and Arabs call'd Nalka , because it resembles the Figure of a Horse-shoe . The second , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Bis●…cta , siu Dimidiata , at 90 Degrees distance . The third , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Gibbosa , sive Dimidio Orbe Major , when distant 120 Degrees . And lastly , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Toti-lunis , when full and in Opposition to the Sun , or 180 Degrees distant , from whence in a contrary Order are reckoned her decreasing Changes . Vide Cleomed . l. 2. c. 3. Vitruvium , l. 9. c. 4 ibidemque Philandrum ; Geminum c. 7. Amian . M●…rcellin . l. 20. Plin. l. 2. c. 14. Ricciolum Tom. 1. l. 4. c. 3. changes shows , The Laws observ'd of her Increase and Wain , That Stars themselves from g g Hence the Stars receive their Denomination . Stellae à stande . Servius ad 1. Georg. from the Authority of Varro . Stelle cadere non possunt , quarum natura est ut stent semper unde & Stellae vocantur : and from him Isidor . l. 3. c. 70. Stellae dictae à stando , quiae fixae stant in Coelo , nec cadunt . And Martianus Capella l. 8. Stellae à stando , Sidera à Considendo . Vide etiam Cassiodorum de Astronomia . falling still sustain , And run in measur'd Courses , seems to Sense No Work of Chance , but Act of Providence . These Signs divided thus by equal space Heavens azure h h Caelum ( says Pliny , from the Testimony of Varro ) haud dubie à Coelati Argumento diximus , from the Variety and Ornament of the several Constellations , ( in varias Coelum laqueantia formas , as Manilius expresses it ) imbellishing the same , as Carving or Fret-work , some curious Roof or Cieling . Hence Turnebus , Coelum ita vocatum alii censent , quòd sit coelatum impressumque variis signis . Vide Turneb . in Varron . de L. L. & in Adversar . l. 20. c. 29. Celing with Gold fret-work Grace , Bove which is i i So says Aristotle in primo de ●… 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , c. 9. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. neque Corpus , neque Locus , neque Vacuum , neque Tempus . But the Stoicks determine otherwise , who though they allow not of any thing corporeal , yet admit of a certain vacuity . In which separate Inanity , or imaginary space ( as both Modern Philosophers and Divines call it ) they fancy the World to suspend . Peremptorily asserted by Lipsius : Cogit●…nti cuicunque ( says he ) aliquid vacui extra Mundum vel invito occurrit : quodetiam Philo Iudaeus palam adstruit , & in Scripturis Abyssum dici contendit . Vid. Lips. Physiolog . Stoic . l. 2. Dissertation . 9. Et Io. Baptist. Port. in Pneumatic . l. 1. c. 3. Nec non Gassendum , Tom. 1. part . 2. p. 186. Vides●… etiam Cleomed . Mete●…r . l. 1. c. 1. Inque illum Balforeum . Et Quonem de Guericke de vacuo spatio , &c. l. 1. c. 35. & l. 2. c. 5 , 6 ▪ &c. Nothing ; there the Worlds height ends , Nor further Natures Publick k k In Allusion to that of Varro : Mundus Domus est Maxima Omnium ; and of Cicero ( in secundo de 〈◊〉 Deorum ) Est enim Mundus quasi communis Deorum atque Hominum Domus . Consonant to which is that of Tertullian : Totus hic Mundus una omnium Domus est ; and of Minucius Foelix ( in Octav. ) Una Domus est Mundus hic Totus . See likewise Lipsius , as before cited , Dissertat . 7. House extends , Which Seas imbraces and the Earths round Ball. All These in mutual Courses rise and fall , As the revolving Skies , here downward bend Beneath th' Horizon , and there reascend . Now to what Compass Heaven's extreamest Round The Dimensions of the Universe . Is stretch'd ; what Limits the bright Zodiack bound , Reason will teach ; to whom there 's nothing hard , From whom by space or Bulk nothing's debarr'd ; To her all stoop ; She sounds the Depths of Night , And Heaven it self is pervious to her Sight . How far the Stars are 'bove the Earth and Main , So great the space is , which two Signs contain , And if the Worlds l l Known is that Demonstration of Archimedes in 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . That the Circumference of every Circle is greater than three times the Diameter thereof by a part less than 1 / 7th and greater than 10 / 70. Hence Manilius cautiously advises of this small difference that is to be made in computing the proportions betwixt the Diameter and Perimeter of the Sphere . See the same Argument in Pliny , l. 2. c. 23. and in Macrobius in Somn. Scip. l. 1. c. 19. Diameter you take , That , with small Difference , will a third Part make Of its Circumference ; Four Signs then , ( so far ) Heavens Zenith and its Nadir distant are ; And twice four added its whole Round compleat . But since i' th' midst Earth hath its Pendant Seat , 'T is two Signs distant from Heaven's Depth or Height . Thus All which 'bove the Earth is reach'd by Sight , Or underneath , by that unseen , extends , Each way the space of two Signs comprehends : And six times that measures the Circle , where Twelve Constellations equal Mansions share . Nor wonder that the self same Signs create Uncertain Births mix'd with much different Fate ; Since Each six rising with their Lights entire , So great a space , and so long time require . It rests , We now th' Aetherial m m Having described the Coelestial Phaenomena and the Dimension of the Universe , Manilius proceeds to the Description of the Coelestial Circles ; differing therein from the Method of Aratus ; who places the Mundane Dimension in the last Place . But this Disposition ( as Scaliger observes ) is only Arbitrary . However he prefers the Method of our Authour before the other . Bounds design , Of the Heavenly Circles . The Circles which the parted Heavens confine , And of the Stars the splendid Order steer . The Artick Polar Circle . n n Whence call'd the Artick Circle 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 — i. e. ab ursá , ( one of the Constellations so named ) being totally compriz'd within it . ) It is likewise call'd Septentrionalis & Borealis , from its Situation , and contains within it the Northern Frigid Zone , and terminates the Temperate . It is doubly to be considered , either according to the Modern , or Antient Hypothesis ; According to the Moderns , It is a lesser Circle Parallel to the Aequator , passing about the Axis of the World by the Northern Pole of the Ecliptick : According to the Antient it is described a Circle passing about the Axis of the World , by the Intersection of the Horizon and Meridian , of an Indefinite Magnitude , in respect to the several Situations of divers Regions more or less Northerly posited , of which Chalcidius ( in Timaeum Platonis ) Circuli vicini Polis , i. e. Septentrionalis & huic diversus Antarticus neque Magnitudine neque Positione solidati sunt ; sed pro differentia Regionum Aquilom●…ae itemque Australis , apud quosdam Majores , apud alios Minores putantur . See Scaliger upon this Place , Geminus , and upon him Petavius in Uranolog . Gassendus , Tom. 1. l. 3. p. 591. Pincierus in Parerg. Otii Marp . l. 2. c. 13. and Grotius in Arati Phaenomen . One tow'rd the North sustains the shining Bear , And from the Pole o o The Antient Greeks divided the Sphere into sixty Parts ( whereof one was equal to six of the Common Division of 360 ▪ Degrees ) This manner of Division our Authour ( as following Eudoxus and Hipparchus ) here makes use of , though hereafter in describing the Zodiack he takes up the Common way of dividing a Sphere or Circle into 360 Parts or Degrees ; which shews the same to have been also usual with the Antients at least about his Time. According to the first Division our Authour here makes the Artick Polar Circle to be distant from the Pole six of those sixty Parts , making thirty six Degrees according to the later Division ; which yet cannot be understood of the Roman Horizon , wherein Manilius then wrote ; but is to be applyed to that of Cnidus or Rhodes , according to the Doctrine of Eudoxus and Hipparchus , whom Manilius here follows , as is rightly observ'd by Scaliger upon this Place , and Gassendus , as before cited . And generally the rest of the Greeks gave the like Situation of this Circle in the Athenian Horizon , and by a Catachresis , universally in any other Part of Greece . This being here premis'd and observ'd , the Reader will the better understand the following Measures and Descriptions which our Authour uses in the position of the Coelestial Circles . six Parts of Heaven retires , The other touching p p That is the Tropick of Cancer . The Tropicks being so call'd from the Word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which signifies Conversion or turning ; because the Sun , when it comes at those Circles , turns back to the Aequator again , nor ever goes beyond those Bounds either to the North or South . Hence the Aegyptians , as is noted by Clemens Alexandrinus ( l. 5. Stromat . ) Hieroglyphically decyphered the Tropicks under the Figure of two Dogs , as if they were Guards deputed by Nature to keep in and restrain the Sun from running beyond his Bounds . The first among the Greeks , who found out these Tropicks , is said to be Thales , the Milesian , of which he wrote a particular Treatise according to the Testimony of Eudemus , cited by Laertius . Cancer's utmost Fires , The Summer Tropick , or Tropick of Cancer . ( Where Phoebus consummates his Light and stay , Bearing through q q Not unlike is that of Nemesianus , — Postquam Phoebus candentem fervidus Axem Contigerit ; tardasque vias , Cancrique Morantis Sidus inest — Where Ulitius gives the Reason of that Epithete Morantis , quia Incrementa Dierum tardè adeo consummantur & 〈◊〉 , ut vix percipi possit , & quasi sistatur Sol ▪ whence the Solstice . The Explication whereof cannot be better given than in the Words of Iulius Scaliger in Problemat . Gellian . Is Circulus quem Sol quotidie signat , non est Circulus ▪ sed mag●…s quaedam Spira . Neque enim Revolutionis finis , eodēm committitur , unde initium habuerat : Major enim Distantiae est à puncto , unde digressus est , ad punctum ad quem Horae 24 eum perduxere , ubi propior fit iis signis quae propius ad Aequinoctium accedunt , propter obliquitatem . Itaque cum tendit ad Solstitia propter lineae prope rectitudinem , vix vari●… , ideo Solstitia dicta . That Circle which the Sun by its dayly Motion describes , is not a Circle , but rather a Spiral Line . For the end of its Revolution is not terminated in the point , whence ▪ it began . It s Distance from that Point whence he digrest , unto that to which he is brought by the Revolution of 24 houres , being greater when he is nearer those Signs which ▪ are ●…ighest to the Aequinoctial by reason of the Obliquity of his Course . But when he approaches the Solstitial Points by reason of the almost directness of the said Line , there appears no variation of his Course , whence it is call'd the Solstice . tedious Rounds the tardy Day ) Does from the Season , and r r This Tropick is call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Tropicus Aestivus , from the Heat of Summer , which We in the Northern Hemisphere enjoy , when the Sun is near that Circle . It is describ'd a l●…sser Circle Parallel to the Aequator , whose distance from thence i●… equal to the Sun 's greatest Declination or the Obliquity of the Zodiack , which it touches in the first point of Cancer . It s Office is on one side to terminate the Torrid Zone , on the other , the Northern Temperate one , and to make the Summer Solstice and longest day Northward , and the Winter Solstice , or shortest Day Southward . Mid-Summers heat Derive its Name ; and to the Sun's Race set Th' extreamest Bound : which s s That is 30 Degrees according to the usual and received Division ; see the like Distribution , as to the Distances of these Parallel Circles , in Ge●…inus conform to this of Manilius , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . p. 19. five Parts of the whole Declines the Circle of the Northern Pole. The t t This Circle is call'd by the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , by the Latines , Aequidialis , Aequinoctialis , Aequator and Cingulum Mundi ; Mariners commonly call it the Line : It is one of the greater Circles of the Sphere , whose Poles are the same with the Poles of the World , from either of which it is equally distant , dividing the Calestial Globe into the Northern and Southern Hemisphere . It is describ'd , according to Clavins ( in Sacrobose . ) by an Imaginary Line draewn from the Center of the World and extended to the first Point either of Aries or Libra , and thence carried about by the Diurnal Revolution of the Primum Mobile . In this the Sun being posited ( which happens twice every Year , when he enters the first Degrees of Aries and Libra ) it makes the Days and Nights even . Third , which the World 's middle Region holds , The Aequator or Aequinoct●…at Circle . Olympus with a mighty Bend infolds , On either Hand viewing the Pole ; the Way , In which the Sun makes even Night and Day . When by the Springs and Autumn's Points he glides , And Heaven i' th' midst by equal Parts divides . This from the Solstice u u That is four Parts of 60 , according to the Antient Division , or 24 of 360 according to the later and commonly received . four Degrees retreits ; The Winter Tropick , or Tropick of Capricorn . The next beyond nam'd from the x x This is called the Trospick of Capricorn , and is decrib'd a smaller Circle Parallel to the Aequator , whose Distance from thence is equal to the Sun 's greatest Declination , and touches the Ecliptick in the first Point of Capricorn ; on one side bounding the Torrid Southern Zone ; on the other , the Southern Temperate one ; making the Winter Solstice or shortest Day Northward , and the Summer Solstice and longest Day Southward . Winter , sets The utmost Bound to the Sun 's backward flight , Obliquely rend'ring us his y y For this reason says Macrobius ( Saturnal . l. 1. c. 21. ) the Aegyptians represented the Statue of the Sun with his Head shaven on one side , and long Hair on the other . By the first intimating the time of the Winter Solstice , cum velut abrasis Incrementis , angustâ manente Exstantiâ , ad Minimum Diei Sol pervenerit Spatium . By the later , the Summer Solstice , or his full grown Splendour , to which he arrives by Degrees , emerging from those straits of Light in his abode in this Winter Tropick : or to express it in Macrobius his own Words , Ex quibus latebris vel Angustiis , rursus emergens , ad aestivum Hemisphaerium enascens , in Augmenta porrigitur . niggard Light By a short Course ; but long o're Those He stays , Whose Lands are warm'd by his directer Rays ; The z z Of this We have given the reason and explication , in the Note upon the Tropick of Cancer , and shall here only add , that the Antient Aegyptians when they would express the Course of the Sun in his Solstice , signified the same by the Hieroglyphick of two feet fasined together ; ( as represented by Pierius , l. 5. c. 41. and Casalius de Veter . Aegypt . rit . c. 20. ) Intimating thereby the slowness of his Motion , or rather Stationary Condition , to which I know not whether our Authour in this place may allude , when he says , Vixque dies transit — As if the feet of the Day were fetter'd . slow-pac'd Day there hardly passing round . This from th' Aequator four Degrees is found . One Circle more yet rests , whose a a The Antartick Polas Circle . Site inclines Tow'rd the South Pole , and Southern Bears confines , Rang'd from the Winter Tropick five Degrees , And near its Pole , as the North's far from his . Thus Heaven in two divided , Pole from Pole , Does by that double Summ measure the Whole , ( f ) The Antartick or Southern Polar Circle ; which is describ'd a smaller Circle , Parallel to the Aequator , passing about the Axis of the World by the Southern Pole of the Ecliptick , comprehending the frigid Southern Zone , and terminating the temperate ; and is call'd the Antartick Polar Circle , in opposition to the Artick , before describ'd , to which it is equal . And by b b The four Parallel lesser Circles before described , that is to say , the two Tropicks , and two Polar Circles , mark out the Heavens into five Zones , which by the Latines are called Fasciae , Cinguli , Plagae ; and by Cicero , Maculae and Orae . That included between the two Tropicks , is called the Torrid Zone , which Polybius divided into two , parted by the Aequator ; but he is not followed therein by any . The two included between the Tropicks and the Polar Circles , are called the temperate ; the other two included within the Polar Circles , are call'd the Frigid Zones . Of these Thales is said to have been the Inventor , though Posidonius cited by Strabo without ground ascribes it to Parmenides . five Bounds distinguish'd into c c The Distinction of the Zones not sufficing the Antients to mark out the various Position and Situation of several Regions on either side of the Aequator ; They added divers other Parallel Circles , which they called Climates . A Climate being a little Zone included between two Circles , parallel to the Aequator , or between the Aequator and one Circle parallel thereunto , mutually distant from one another by the Arch of a Meridian , answerable to an half hours difference , by which the longest day of the Year under one Parallel varies from the longest Day of the Year under another . They are call'd Climata , quasi Inclinamenta , as it were deflexious from a right Position of Sphere , or so many st●…ps and degrees , mounting from the Aequator towards the Poles . The Antients reckon'd only seven , which they distinguish'd by the Names of the Places over o●… through which they passed : Viz. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , &c. i. e. Per Meroen●…per Syenen●…per Alexandriam , per Rhodum , per Romam , per Pontum , per Boristhenem . But Modern Astronomers and Geographers reckon 48. that is to say ; from the Aequator on each side , to either of the Polar Circles 24. At which the Climates end ; the longest day there exceeding the ordinary Horary Measure , unless by a kind of Analogy We reckon Moneths and half Moneths for hours and half hours . Those Climates are again by the Moderns subdivided by drawing in the Middle of each Climate another Parallel Line , dividing the same into two smaller Zones , which by a Peculiar name are term'd Parallels : Of which , the more remote from the Aequator hath the longest Day of the Year differing from that nearer to it by the space of ¼ of an hour . These are in number double to the Climates . Vide Weigel . Method . Sphaeric . l. 1. Sect. 1. Cap. 3. Climes , Marks out the Difference of Place and Times . Which ( Parallels ) One Course with Heaven partake , And equal Rise with that and Setting make , Since in th' Aethereal Texture they observe Their stated Distance , and thence never swerve . Passing a-cross by either Pole d d These are the Coluri , which are two great Circles , cutting each other at right Angles in the Poles of the World. Whereof one passes by the Aequinoctial , the other by the Solstitial Points of the Zodiack . They are called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Mutili , because in our oblique Position of Sphere , they never entirely appear above the Horizon , either at once or by Successive Conversion . two more There are , which intersect all Those before , And themselves too ; concurring in th' Extreams Of the Worlds Axis at right-angled Scheams , Which mark the Seasons out , and Heaven beside Into four Quarters equally divide . Of these , through highest Heaven its Course e e The Colurus Aequinoctiorum is describ'd a great Circle of the Sphere , passing by the Poles of the World , and cutting the Aequator at right Angles in the two Equinoctial Points or first Degrees of Aries and Libra , whose Poles are in the first Points of Cancer and Capricorn , or otherwise whose Poles are 90 Degrees distant from the first Points of Aries and Libra . one steers Colurus Aequinoctiorum . Parting the Serpents Tayl and undrench'd Bears , And Tips of Scorpio's Claws , born through Mid-skies , Of Hydra cutting the Extremities And Middle of the Southern Centaur , then Concurring in the Adverse Pole , agen Returns by the huge Whale : whose Scaly Chine , Bright Trigon , and the Bounds the Ram confine It marks ; then by Cepheïs Waste doth run , Her Mothers Head , and ends where it begun . By th' midst of this , the Worlds Extremitie , And the Fore-feet and Neck of Helice , Colurus Solstitiocum . ( Which first of all when Sol withdraws his Light With seven fair Stars illuminates the Night ) The f f The Colurus 〈◊〉 is a great Circle , passing by the Poles of the World and Poles of the Zodiack , cutting both the Aequator and Ecliptick at right Angles in the So●…al Points or first Degrees of Cancer and Capricorn , and hath its proper Poles in the first Degrees of Aries and Libra . To these two Circles are to be applyed this Vulgar Dis●…ch : Haec duo Solstitium faciunt Cancer , Capricornus , Sed N●…ies ae●…uant Aries & Libra Diebus . other runs ; the Crab and Twins divides , By the fierce Dog and Argo's steerage glides ; Then cross the formers travers'd Signs is born By the South Pole ; Thee touching Capricorn ! Parting the Eagle from its Starry Fires By the Lyre running , and the Dragons Spires ; Then cuts the less Bears Tayl and hinder Feet , And makes its End with its Beginning meet . The Seasons thus have fixt within these Rounds , Their Everlasting Seats and changeless Bounds . These two are moveable : Whereof one Bend The Meridian . Does through Mid-Heaven from g g The Meridian Circle , by the Greeks call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , by the Latines , Meridianus , and by Astronomers Li●…a M●…dii Coeli , and M●…ii D●…i , Cus●…is Re●…alis , Cardo R●…ius , and M●…aium Coeli . It is describ'd a great Circle , passing by the Poles of the World , and the Zenith and N●…dir Points , and hath its proper Poles in the Aequinoctial Points of East and West , though Scaliger upon this place ( defended therein by the Learned Mr. Isaac Vossius Not. in Me●…am . ) will have the Poles of every Meridian to be the Poles of the World. It is call'd Meridian , because when the Center of the Sun reaches it , it is Noon or Mid-day , to all such as are directly under that Circle , when the Sun is above the Horizon . Helice ascend , The Day distinguishes , the sixth Hour tries , And at just distance East and West descries , Changing the Signs by turns , still as we run , Or tow'rd the rising or the setting Sun , Cutting Heavens hightith ' midst ; and with Earth's Place , Varies the Skies Position , and Times Race . h h The Reason thus rendred by Macrobius in Som. Scip. l. I. c. 15. Quia Globosuas Terrae Habitationes omnium aequales sibi esse non patitur ; non eadem Pa●…s Coeli omnium verticem despicit . Et ideo unus omnibus Meridianus esse non poterit : sed singulis Gentibus super verticem suum pr●…prius Meridianus eff●…citur : and therefore the Meridian is distinguished into the General and Particular ; the General being one and always the same ; the Particular , on the contrary , mutable and diverse , according to the change and diversity of Place , either Eastward or Westward , and may be imagined as numerous as there are vertical Points . Vide Bartschium in Planisphaer . Stellat . c. 2. All have not one Meridian ; th' Hours fly round : When first we see Sol rise from th' Eastern Sound , 'T is their sixth Hour by his i i St●…ler in his Commentary upon Proclus , conceives that Manilius here by the Golden Orb , means the Meridian Circle , and imagines it to deserve that Title , because the Island Taprobana , being as he says , in Meridiem exposita , is famous for its plenty of Gold and Silver . A ridiculous Interpretation ; for aureus Orbis is not to be understood of the Meridian Circle ; but of the Globe of the Sun , coming to and pressing upon the Meridian . gold Orb then prest ; Such theirs , when he to us sets in the West . These two k k This Place hath exercis'd and foil'd the Wits of the greatest Criticks ; the Verse in the Latine is this , Nos primam , & summam sextam numeramus utramque . S●…aliger interpreting Primam & summam for one and the same hour ; quia summâ horâ Noctis ( i. e. duodecima says he ) confecta , incipit 〈◊〉 , as the Athenians us'd to term the last day of the Moneth 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , The Old and the New. But this is far from the 〈◊〉 of Manilius . Gassendus endeavouring to mend the matter , instead of primam & summam , conceives it ought to be read Im●…m & Summam , ab 〈◊〉 inter Imam & Summam Antithesin ( says he , ) by Im●…m understanding the Hour of Midnight , by Summam that of Mid-day ; but this is yet wide from the Mark. Salmasius undertaking to put a better sence upon the words than the former , is himself grav●…l'd ; for thus he expounds this and the 3 foregoing Verses . Cum Sol oritur Romanis , &c. when the Sun ( says he ) rises at Rome , it is their first Hour of the Day , but to the Indians their sixth , or Noon ; and again when it is Noon to the Romans , it is Sun set to the Indians or their last Hour of the Day ; so either of these Hours , viz. the first and the 〈◊〉 says he ) by reason of the Diversity of Meridians is reckon'd for the sixth hour ; which Interpretation reaches not the meaning of 〈◊〉 ; being justly reprov'd by Pe●…avius , in Vranol●…g . l. 7. who thus expounds both this and the three foregoing Ver●…s . 〈◊〉 est says he ) Manilium , Tractum illum terrarum & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , ubi tum degebat , in medio ponere , & quae utrinque distant 〈◊〉 〈◊〉 〈◊〉 longitu●… 90 , cum Habitatione suâ conferre . Qui ad Ortum siti sunt Eoos appellare , qui ad Oc●…asum , Hesperi●…s , &c. Hence he infers , when the Sun seems to rise at Rome , it is in the Meridian of those that are posited 90 Degrees Eastward from thence ; and again , when the Sun at Rome seems to set , it makes the like sixth Hour or Noon to those so posited Westward : Either of which sixth 〈◊〉 ●…r N●…ontides to those Eastward or Westward , they at Rome count not their sixth Hour , but name the one , the first , the 〈◊〉 , the last Hour of their Day . This Exposition of Petavius ( whereunto our Interpretation is consonant ) speaks the 〈◊〉 of the words , which I held my self oblig'd thus to clear , lest the Authority of the other great Persons might be objected against us , or impo●…e upon the Reader . sixth Hours we count our first , and last , When from th' Extreams of Light l l By Reason of the obliquity and depression of the Suns light at Morning and Evening , the Air likewise being then coolest in regard of the chill Briezes usually stirring . Hence the Evening in Genesis 3. ver . 8. is call'd Ru●…h , i. e. spiritus seu ventus Diei ; and what by the 〈◊〉 is there rendred 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , or the Evening , is by others rendred 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. adspiritum seuventum Diei . Vide Salmas . in Epictet . et Simplic . p. 125. chill Beams are cast . The m m This Circle is call'd Horizon , from the Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . coming from the Verb 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which signifies to bound , or terminate , for which reason it is by the Latines called Finiens and Fini●…or , because it bounds the sight . It is divided into the Rational ( which is likewise call'd the Natural and Astronomical ) and the Sensible ( which is likewise call'd the Physical , Apparent and Artificial : ) the Rational Horizon is describ'd a great Circle of the Sphere , whose Poles are the Zenith and Nadir Points , ( though Scaliger with the approbation of Mr. Isaac Vossius makes the Poles of every Horizon to be as well the Ae-quinoctial Points of East and West ) dividing the Globe equally into the upper and lower Hemisphere . The Sensible Horizon is describ'd a smaller Circle , parallel to the Rational , dividing the Sphere into two unequal Segments , of which the uppermost is the least . This though in respect to any one particular place , it be immoveable , yet generally it is to be conceiv'd mutable , forasmuch as when we change any Place upon the Earth , we likewise change the Horizon . others Bound if thou desir'st to know , The Horizon . Look round about far as thy sight will go , What e're Earths Surface with Heavens Verge doth close , And the divided Hemispheres compose ; Couches in Seas the Stars and thence doth send ; Rounding the travers'd Earth with a slight Bend ; That , shifting Place about the World still flies , Now more and more unto the South applies , Now to the North again as much inclines , Now runs against , now with the n n The Latine hath — Mota sub Astra . Which Salmasius ( in Plin. Exercitat . p. 661 ) Criticizing upon this Place , will needs read muta sub Astra . Interpreting muta Astra 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. not apparent ; and by those words conceives our Authour implies the Antartick Pole , to us invisible . But as Petavius says , mutum esse praestat , quàm talia dicere ; for M●…nilius by — Mota sub Astra , means only the shifting of the Horizon East or West , either against or with the Course of the Stars , as Petavius rightly expounds those Words . Per Mota Astra ( says he ) Orientem atque Occidentem breviter elegantérque designat Manilius . Vide illum , Uranolog . l. 7. c. 14. moved Signs . But wheresoe're its wandring Course it steers , As now to this , then to that Part it bears , It changes still ; a new Arch always making ; For leaving now this Heav'n , then that forsaking , One half 't will still disclose , or hide , and sign With varying Limits which the Sight confine . This is terrestrial , 'cause the Earth it rounds , And call'd Horizon , 'cause the sight it bounds . To these two others add , obliquely born , Whereof the o o That is the Zodiack ; by Ptolomy call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Circulus Animalium ; because parted into 12. Signs , resembling men and other living Creatures . The Iewish Astronomers give it several other Denominations , as Galgal Hammazzaloth , i. e. Orbis Signorum , and Ighul Hammatzaloth , i. e. Circulus Signorum , and Ophun Hammazzaloth , i. e. Rota Signorum ; and Ezor Hammazzaloth , ie . Zona Signorum . The Syrians call it Chudronûtho de Malûshe , i. e. Circulus Signorum , and the Arabs Phelek Al Burugi , i. e. Orbis Signorum . By the Latines it is call'd Signifer , and by the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and is describ'd ●… Circle or rather a Fascia or Zone obliquely passing from East to West by the Aequinoctial and Solstitial Points , parted in the midst by the Ecliptick , which divides it into two Parts , the one Northern the other Southern , which are terminated by the Circumferences of two imaginary Circles less than one of the great Ones , distant so far from the Ecliptick , as is the greatest Latitude of any Planet from then●…e ; The Invention of this Circle is by some ascrib'd to Pythagoras , by others , to Oenopides the Chian , by some again , to Anaximander the Milesian . Vide Plutarch . de Placit . Philosoph . & Plin. l. 2. c. 8. one twelve radiant Signs adorn , The Zodi●…k . Through which the Sun runs his Career of Light , And the Moon follows in her Coach of Night , And five Stars more 'gainst Heavens swift Course advance Their p p Meaning the Primary and proper Motion of the Planets from the West to East ; for their Secundary or Diurnal Motion from East to West is not their own , but that of the Primum Mobile , by which they are violently carried about contrary to their own Course . Which double Motion of the Planets is elegantly thus describ'd by Germanicus in Arataeis : Omnibus his gemini Motus , quorum alter ab ipsis N●…scitur , & proprios ostendit sydere Nisus , ( Tunc Mundum subeunt lentopede ) concitus Alter Invi●…os rapit , & Coeli circumrotat Orbem . All these have double Motions ; one their own , By which their proper Tendency is shown , That 's a slow March ; th' other 's swift , and bears Them running Counter , back with the rapt Spheres . oppositely Nature-guided Dance . On whose Top Cancer , Base the Goat resides , Twice through th' Aequator runs it , twice divides At Libra and the Ram ; whose sloping Bend Obliquely by three Circles does extend ; Not hid ; nor , as the rest ( discern'd alone By mental view ) q q Though our Authour here speaking Poetically , make the Zodrack a visible Circle , because the 12 Signs moving in it are visible ; yet properly speaking as it is taken for a Fascia or Zone , it is but 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , perceivable only by Reason . And therefore Geminus in Isagog . says rightly , that of all the Circles in the Heavens , only the via Lactea is perceivable by sense , the rest being no otherwise discernible than by the Eye of Reason . to mental view is shown ; But shines a glittering r r Hence by the Arabs call'd Al Mintaca and Nitac , i. e. Baltheus , and by the Iewish Astrologers , Ch●…hebh Ephadath Haggalgal , i. e. Opus Phrygionarium , or Limbus Textilis , according to Scaliger . Why this Circle above any of the rest is called Baltheus seu Cingulum ( from the like denomination of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 given to it by the Greeks ) take from Ulitius in Nemes . p. 341. Ideo veteres Zodiacum Baltheum dixerunt Astrologi , quia obliquus Meridianum secat . And before him Balforeus ( in Libr. 1. Cleomed . ) Zodiacus Appellationem Bal●…hei , ( quem etiamnum b●…die transversum gestamus ) apud Manilium meruit . Et omnino haec forma Balthei , à dextro humero ad latus sinistrum per medium Corpus obliquè ducti , Zodiaci Situm optimè exprimit . Belt with bright Stars grac'd , And girdles with its golden Fires Heavens Waste . Degrees three hundred and thrice twenty counts Its Circles Round ; its Breadth to s s Sacroboscus ( says Rieciolus Tom. 1. l. 1. p. 19. in Schol. ) and Clavius upon him , give to the Zodiack 12 Degrees of Latitude , because for the most part the Planets recede not from the Ecliptick above 6 Degrees on either side . But Regiomontanus extends the Latitude thereof to 16. others otherwise . For Kepler gives 7 Degrees of Northern Latitude to Mars ; to Venus in her greatest Evagation 10 , or according to Argol ( Pandos . Sphaer . c. 29 ) 9 degr . — 3′ . So that the Total Latitude of the Zodiack according to Modern Observation is extended to no less than 20 Degrees . twelve amounts : Within which measur'd Limits is confin'd The Planet's Motion , variously inclin'd . The t t The Galaxie , or Milky way , by the Greeks call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , by the Latines Circulus lacteus , and Orbis lacteus . By the Arabs according to Scaliger , Tarick Al lubbana , i. e. Via lactea ; according to Kirker , Almegiret or rather Magierra , i. e. Tractatrix , and Tarick Al Tibn , i. e. Via straminis ; and to the same sence by the Aethiopians , Chasara ' tsamangadu . ( Isis according to the Aegyptian Fable in her flight from Typhon scattering bundles of fired straw to retard his pursuit , whence the Original of that Name ) In Syriack it is called Shevil Tévno ; by the Persians , Rah Kahkeshân , i. e. Via Paleamtrahens ; the Turks call it Samân Ughrisi , i. e. Pal●…am rapiens . In the Coptick Tongue it is called Pinóiten Tépitoc , i. e. Via straminis ; others call it Viam Romae , and Viam Sancti Iacobi . The Turks , Hâgjiler Yuli , i. e. Via festum Agentium , or the way of Pilgrims to Mecha ; by the Aegyptian Astrologers call'd Porta Mansionum Lunae . It is a great Circle having for Center the Center of the World , or rather an oblique Conspicuous Zone , of a different Breadth or Latitude , being no where broader than 10 Degrees , and in some places not exceeding 6 or 7. in some stretching to 8 or 9. Where its Course is not divided . From this Circle , as Pliny ( l. 18. ●… . 29. ) reports , the Antients believ'd all Plants received their Milky Juice or Nourishment ; and hence perhaps is that Arabick Name of Um Al Sama , i. e. Mater Coeli , ( quasi ejus lactatrix ) Nor less famous for the strange Productions , which Modern Eperience hath observed therein ; it being found the Store-house from whence have issued all the new Phaenomena's that have hapned either in this or the precedent Age. other , carried tow'rd the opposed Bears Galaxia or the Milkie Way . Its Course close by the Artick Circle steers , And by inverted Cassiopea tends ; Thence by the Swan obliquely it descends The Summer Tropick , and Iove's Bird divides , Then cross th' Aequator and the Zodiack glides 'Twixt Scorpio's burning Tail , and the left Part Of Sagittarius , near the fiery Dart ; Then by the other Centaure's Legs and Feet Winding , remounts the Skies ( again to meet ) By Argo's Topsail and Heaven's middle Sphere , Passing the Twins t' o'retake the Charioteer ; Thence Cassiopea seeking Thee does run , O're Perseus Head , and ends where it begun . Three middle Circles and the Zodiack too Twice passing , and by that as oft past through . Nor needs it to be sought ; its obvious Course It self illustrates , and the sight doth force ; For in the azure skies its candid Way Shines like the dawning Morn , or closing Day ; And as by often passing o're some Green , An even Path , parting the Mead , is seen ; Or as a Ship plowing the Seas smooth Plain , Of foaming Bubbles leaves a silver Train : So shines its milky Path in the dark Night , Parting the blew Skies with its numerous Light. And as through Clouds the Rainbow does extend , So on Olympus Height shows its white Bend , And Mortals fills with Wonder , whilst they spy New Lights unknown Flames darting through the sky . The sacred Causes humane Breasts enquire , Whether the Heavenly u u The Opinion of Diodorus , who conceiv'd the via lactea to be a Coelestial fire , of a dense and compacted Nature , shewing it self through the Clefts of the starting and dividing Hemispheres , as Macrobius in Somn. Scip. ( l. 1. c. 15. ) expresses it , Ignem densatae concretaeque naturae , in unam curvi Limitis Semitam Discretione Mundanae fabricae coacervante concretum . Hence says Gassendus we may observe Genium Stoicae Providentiae . They calculating the Destruction of the World to commence from the Breach or loosening of the Commissures of the closed Globe . To which doubtless Manilius here alludes . Vide Gassend . Tom. 1. l. 1. p. 506 , 507. Segments there retire Various Opinions concerning the Galaxie . ( The whole Mass shrinking ) and the parting Frame Through cleaving Chinks admits the stranger flame ? Astonishment must sure their Senses reach To see the Worlds wounds , and Heavens gaping breach ! Or meets Heaven here ? and this white cloud appears x x The fancy of Theophrastus , that great Philosopher , who declar'd the Galaxie to be no other than the soldering and knitting together of the Hemispheres . So Macrobius delivers it , Lacteum dixit esse Compagem , quâ de duobus Hemisphaeriis Coeli Sphaera solidata est ; & ubi O●…ae convenerint notabilem Claritatem videri . Vide illum loco ●…oitat . The Cement of the close-wedg'd Hemispheres ? Or seems that old Opinion of more sway That the Sun's y y Oen●…pides Chius ( according to Achilles Tatius in Arat. Phaenomen . ) affirmed that this Circle was antiently the Course of the Sun ; till frighted from that Tract by Thyestes his bloody Banquet , he chose this he now holds in the Zodiack , but left behind him the Impression of his former Course . Of which ridiculous Opinion was likewise Metrodorus , and some other Pythagoreans , whereof Plutarch in Placit . Philosoph . l. 3. c. 1. Horses here once ran astray , And a new Path mark'd in their straggling flight Of scorched Skies , and Stars adusted Light , Changing to paler white Heavens azure Face , And with the burnt Worlds Ashes strew'd the Place ? Fame likewise from old Time to us succeeds How z z See Ovid Metamorphos . l. 2. and Plutarch loco citat . Phaëton driving his Fathers Steeds Through radiant Signs , and with a wounding Eye Viewing th' approached Beauties of the Sky , ( Whilst in his Chariot proud he childlike plays , And things yet greater than his Sire essays ) Left the known Path , and a rough Tract imprest In the smooth Skies , whilst wand'ring Flames infest Th' affrighted Signs , not brooking the loose Course Of th' erring Chariot and ill-guided Horse . Hence the whole World became a fiery spoyl , And burning Cities made Earths funeral Pile ; When from the hurried Chariot Lightning fled , And scattered Blazes all the Skies o'respred ; By whose approach new Stars enkindled were , Which still as Marks of that sad Chance appear . Nor must that gentler Rumour be supprest , How a a Eratosthenes as cited by Ac●…iller Tatius in Arati Phaenomen . is reputed the Father of this Fable , in his Book entituled 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Partitio ( or rather 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Asterismi ) which is by Achilles Tatius thus related . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , &c. Hercules being an Infant sucking at Juno's breast , and too hardly pressing the Nipple , she suddainly withdrew it , and spilt the milk , which form'd this Circle in the Heavens . The like ( says he ) is reported by the same Eratosthenes of Mercury's sucking Iuno . Milk once flowing from fair Iuno's Breast , Stain'd the Coelestial Pavement ; from whence came This Milky Path , its Cause shown in its Name . Or is 't a b b This is the true Cause of the G●…laxie ; which long since by Conjecture and probable Reason was asserted by Democritus , as Plutarch ( in Placitis Philosoph . ) attests . But since the Invention of the Telescope , clearly demonstrated by Galilaeo , Kepler , and others . Crowd of Stars crowning the Night ? A candid Diadem of condens'd Light ? Or c c The antient Ethnicks believed the condensed light of the Milky way to proceed from the Crowd and multitude of valiant , wise , and Pious Souls inhabiting that Circle . Hence Macrobius in Somn. Scipionis . Rursus filium Pater , ut in Deos Piu●… , nt in homines Iustus esset , hortatus Praemium adjecit , Ostendens Lacteum Circulum , virtutibus debitum , & Beatorum Coetu r●…fertum . Believ'd no less even by Christians , ( as is manifest by that Prayer of Ausonius in Ephemeride : Pande viam quá me post vincula Corporis aegri , In sublime feram ; puri quá lactea Coeli Semita ventesae superat vag a lumina Lunae : Quá Proceres abiére Pii . — ) Of the Original of which Errour La Cerda ( in Virgil. Bucolic . Eclog. 5. ) from the Authority of Philo ( 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ) gives this Reason . In the highest Heavens ( says Philo ) are most pure Souls , which the Greek Philosophers call Heroes ; Moses from their Office , Angels . Whence it may appear that the Heathens having some dark Notion of the Angels , called them by the Names o●… their Heroes , and fixed them here . Vide etiam Turneb . Adversar . l. 13. c. 2. valiant Souls freed from corporeal Gives Believ'd antiently the Sea●… of Heroick Souls . Thither repair and lead Aetherial Lives ? There the d d Agamem●…on and 〈◊〉 the Sons of Atreus , Kings of Mycenae and Sparta , and Generals of the Grecian Forces against the Trojans . Atrides , there th' Aeacides , Fierce f f Son of Tydeus and Deiphile , King of Ae●…olia , one of the most valiant Commanders of the Greeks against the Tr●…jans . Diomede ; He , who through Lands and Seas ( e ) 〈◊〉 The Grand-child of Ae●…cus by Pel●…us and The●…is , the most signal of the Greeks in the Trojan War , and Pyr●…bus or 〈◊〉 his Son. His Triumphs over conquer'd Nature rear'd , g g That Epithete being peculiar to him , who is likewise call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , ob mu●…tiformem prudentiae varietatem , says Coelius Rhodigin . l. 14. c. 18. and Polyeides à perspicaci solertiâ rerúmque prudentia , as Ianus Parrhasius Syllog . 4. Epistol . 39. The Mythology of Ulysses ( by which is chiefly denoted Wisdom , quae invicta per omnia pericula intrepidè pertransit ) See in Natalis Comes l. 9. c. 1. Subtle Ulysses , We believe inspher'd . There Nestor's thron'd among the Grecian Peers , Crown'd with h h — Senectâ Ins●…gnem Triplici — Says the Original in an indefinite sence , by Senecta expressing what Homer ( Ili●…d . 1. ) calls 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. aetatem . seu aevum . Hence Nevius in Alceste ( as cited by Aulus Gellius ) calls Nestor Trisech-senem , and by Horace he is stil'd Senex●…ter Aevo functus . But there is much difference among the Antients about the extent of this 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Aetas ; the same being diversly interpreted by divers . Herodicus , as cited by Censorinus de Die Natal . c. 171. stretches it no further than to 25 years . Zenon and Heraclitus to 30 , with whom consents Artemidorus Oneirocrit . l. 2. c. 75 according to which Computation Porphyrius ( in libro de Homericis Quaestionibus ) and Eustathius determine of the longevity of Nestor . Others inlarge it , making 3 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 equal to 100 years . So Herodotus l. 2. and Clemens Alexandrinus Stromat . l. 1. p. 335. But taken in its greatest extent , a 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Aetas amounts to no less than 100 years , as appears by Genes . c. 15. v. 13 and 16. and according to this Computation most of the Latines sum up the Age of Nestor . So Ovid in the person of Nestor : — Vixi Annos bis Centum , nune tertia vivitur aetas . In which sence Tibullus , Propertius and Iuvenal are to be taken , when they say of Nestor that he liv'd terna and tri●… Saecul●… , and so we have adventured to interpret 〈◊〉 Senect●…m . Vide Francisc. Floridum Sabinum . Lect. sub●…isiv . l. 2. c. 3. a triple Century of years . i i M●…mnon the Son of Aurora by Tithon , who came to the succour of Troy with 20 Thousand Foot , and 200 Chariots , being sent ( according to Diod●…rus Siculus , l. 2. ) by Teutamo , King of the Assyrians , slain by Achilles , or rather by the Treachery of the 〈◊〉 , famous for the yearly combat performed at his Monument by the Fowls called Aves Memnoniae , raised from his Ashes , as it were in an Annual Parentation to his Memory . Of which see Ovid Metamorphos . l. 13. Pliny l. 10. c. 26. Solinus , and his Exercitator Salmasius Tom. 2 p. 870. and 871. Nor less signal for his Statue at Thebes in Aegypt after the fashion of a man sitting , of an entire black Marble , the upper part being broken off from the seat by some Earth-quake , as both Strabo and Pausanius , eye-witnesses , report ; which every day at the Sun rising , or as Phil●…stratus says , when touched by the Sun-Beams , rendred a sound not unlike that of a Harp or Lute . Chearful at the Suns approach , at his deparure or setting , sad . Strabo yet doubting whether the Musical sound proceeded from that Cause , or from some Artif●…ce , within the Basis of the Statue , or from some of the Company or by-standers . Vide Strab●…nem l. 17 : The Satyrist Iuvenal ( Satyr . 1. ) ascribes it to Magick . Dimidio Magicae resonant ubi Memnone chordae . See likewise Coelius Rhodiginus Antiqu. lect . libr. 22. c. 5. and Scho●…tus in Ortel . Tabul . Aurora's Black Son , He who k k Sarpedon King of Lycia , Son of Iupiter and Europa , according to Herod●…tus and 〈◊〉 Sicu●…us ; but as Homer will , of Iupiter and Laodamia ; slain in the defence of the Trojans against the Greeks by Patroclus , of whom Iupiter in Virgil , — Occidit unà Sarpedon mea Progenies — Who is said to have mourned his loss with tears of blood , as Homer Iliad 16. Ausonius bestowing upon him this Epitaph . Sarpedon Lycius , geni●…us Iove , Numine Patris Sperabam Coelum , sed teg or hoc tumulo , Sanguineis fletus lachrymis , beu ferrea fata ! E●… 〈◊〉 luctum qui probibere potest ? I Lycia's King , Iove's Son , who thought to gain Heaven by my Birth , Sarpedon , here lie slain : Wept for with bloody Tears ; dire fate ! must he Know grief , who souls from grief can only free ? Lycia sway'd Iove's Royal Issue ; and Thou l l 〈◊〉 . Daughter of Mars , according to Diodorus Siculus ( l. 2. ) whence by our Poet , stil'd M●…vortia Virgo ; and by Calaber , l. I. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Empress of the Amazons●… , signal for her valour against the Greeks in the defence of Ili●…m , falling at length by the destroying hand of Achilles , which see in Calaber . 〈◊〉 . Martial Maid ! The Kings whom Asia did or Greece beget , Or m m To the same purpose Mela. l. 2. c. 3. Macedonum Populi centum quinquaginta u●…bes inhabitant , quarum Pella & Maxima & Illustris . Alumni efficiunt ; Philippus Graeciae Domitor , Alexander eti●…m Asiae . It was seated upon a Lake , not far from the Sea , into which run the two Rivers , Axius , now called Bardari or Vardari , and by some Vistrizz●… , and Ludias , now Castoro . The Greeks at this day call it 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Paru●… Palatia , where are dayly dig'd up Marbles with Antient Inscriptions , and the foundations of Princely Buildings , in the Place , where the Inhabitants believe the Pallace of Philip and Alexander stood , as the learned Lucas 〈◊〉 ( in Annotat. in Or●…elium ) from the Authority of Critopulus reports . By the Romans it was called Colonia Iulia Augusta , being made a Colony either by Augustus Caesar , or some other of the Roman Emperours , as the curiously diligent Spanhemius proves from the Testimony of Antient Medails , in Dissertat . de Prae●…t . & usu Numism Dissert . 9. Vide etiam Pa●…in in Num. Imper. Rom. p. 195 and 370. By the Turks it is at this day call'd Ieniza , or Ienizza , which in their Language signifies a New Town . Pella justly greatest in the Great . There those whom Wisdom hath exalted , shine ; Just n n The Athenian Law g●…r , who deserv'd that Epithete , ●…is 〈◊〉 M●…deramine Legibus ; for the Justice and Equity of his Laws ; as Ammianus Marcellinus ( l. 22. ) attest●… ▪ who further adds that the Model of his Laws , Romano quoque Iu●…i maximum addidit Firmamentum , added also to the Roman State the greatest Foundation . For the Rom●…s as Li●…y ( l. 3. ) writes , agreeing concerning Laws in General , but differing about the Law-giver , sent Embassadors to Athens , Sp. 〈◊〉 A●…bus , A. Manlius , and P. Sulpitius Camerinus , commanding them to transcribe the renowned Laws of Solon : which transferr'd out of the Books of Solon , the Decemviri expounded in the 12 Tables , as Aurel. Victor . de Viris Illustr . Solon , stout o o The famous Spartan Legislator ; who to ennoble his Laws pretended he received them from Apollo , as Cicero ( de Divi●… . l. 1. ) or according to Lucian ( in Astrolog . ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , deriv'd from his skill in Astronomy ; He contemperating his Laws according to the Course and Influence of the Celestial Bodies . Hence one of his Laws was , that the Spartans should never go forth to War before the full of the Moon . But rather according to the Scholiast of Thucydides ( in l. 2. ) really comp●…l'd out of the Laws of the Cretans and Aegyptians . See besides Plutarch ( in vita Lycurgi ) the learned Io. Meu●…sius Miscellan . Lacenic . l. 2. c. 5. Lycurgus , the p p That Epithete being given him for the excellency of his Stile , Manners , and Philosophy ; of which Cicero in Tusculan . l. 9. Credamus Panaetio ( speaking of Plato ) quem omnibus l●…cis Divinum , quem Sapientissimum , quem Homerum Philosophorum appellat ; nay he sticks not elsewhere to call him Philosophorum Deum . By Numenius in Clemens Alexandrinus ( Stromat . l. 1. ) he is stil'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Moses Articissans . Vide etiam Suidam in voce 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Divine Plato , and q q Socrates the Instructor of Plato . He who made him such ; whose Doom Justlier r r The unjust Condemnation of Socrates brought a General Calumny upon Athens . Hear Socrates in defence of himself in Xenophons Apologie 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , &c. That I die unjustly will not trouble me . It is not a reproach to me , but i●… th●…se that condemn'd me . Nor brought it only a Calumny , but a Calamity likewise ; for as Eunaplus ( in Aedesio ) observes , from thence forward the Athenians did nothing considerable , but the City by degrees decay'd , and with it all Greece . condemns his Athens : He s s Scaliger by Persidis Victor ( in the Original ) understands Xerxes the Persian Monarch ; so likewise Tanaquil Faber ( not . in Lucret. ) who instead of Victor would read Rector . We rather conceive Themistocles to be here meant , Authour of that signal Defeat given to Xerxes his Naval Forces , before Salamis , wherein was the strength of all Persia , ( of which in Herodotus , l. 8. ) For what had timorous Xerxes to do among the valiant Heroes ? The Verse in the Latine is thus commonly read , Persidis & Victor strârat qui Classibus aequor . Gronovius ( in Di●…trib . ad S●…atii Sylv. ) instead of qui , reads quae , which gives us clearly the sence of the Verse according to our Interpretation . by whom Persia was foyl'd , which strow'd with Fleets the Main , And Roman Worthies , the more numerous Train . There 's all their t t Festus ( in breviari●… ) Regnaverunt Romae per annos 243. Reges numero septem , &c. Romulus the first , who Reigned 37 years , ( then the Senate for one year ) Numa P●…mpilus 43. Tullus Hostilius 32. Ancus Marcus 24. Priscus Tarquinius 38. Servius Tullius 44 ▪ & Tarquinius Superbus 25. in the last of which years he was expell'd by Brutus and his Faction . Kings but the Proud Tarquin ; there u u The Story of the 3 Curiatii and the 3 Horatii Brethren , the first Albans , the other Romans , ( who when the two Armies under the Command of Metius Suffetius , General of the Albans , and Tullus Hostilius King of the Romans were ready to joyn , upon Parl●…y , were chosen out on both sides to end the quarrel by Combate ) is sufficiently known , recorded by Livius , l. 1. Dionys. Halicarnass . l. 3. Lucius Florus l. 1. c. 3. Aurel. Victor de viris Illustr . and others . One of the Horatii only surviving the Duel , to which Manilius elsewhere alludes . l. 2. Nulla Acies tantum vicit ; pendebat ab uno Roma viro — No Battle ever was so fought ; Rome's state Depended upon one man's single Fate . Th' Horatii , who their Sides sole Army were ; x x So Sidenius Apollinaris in Carmine de Narbone , — Trunco Mutius eminet lacerto . Than whom none is more celebrious in the Roman Stories ; his daring Attempt compriz'd in this Epigram in Catalect . Veter . P●…t . Lictor●…m p●…o Regen●…eans nunc Mutius ultro Sacrific●… propriam c●…ncremat igne Manum . Miratur Porsenna virum , poenámque relaxans Maxime cum obs●…ssis soederà Victor in●… . Plus flammis P●…triae confert quàm for tibus Armis , Una d●…mans Bellum funere dextra suo . Stead of the King his Lictor Mutius slew , Then makes his Hand in Flames its Errour rue . Porsenna wonders ; does his Pains release , And Victor with th' e'en vanquish'd makes a Peace . More to his Country , than stout Arms and Swords , By its self Ruine one Brave Hand affords . Rewarded ▪ by the Senate with the Ground where Porsenna pitch'd his Pavilion and Camp ; call'd from thence Mutia Prata ; and honour'd with a Statue ; which seems too great a Reward for an Act of Desperate Assasination , ( for it is censur'd no other by Tertullian in Apologet. ) and derogatory from the Roman Magnanimity to encourage or recompence such an Attempt against a free Prince , waging a fair and lawful War. But Paganinus Gaudentius excuses the Roman Senate , as rewarding the 〈◊〉 , not Intention of his Act. Vide ●…um de ' Fatti del Grand . Alessandro . See likewise Alberic . Gentilis arguing upon this Act of Scaevola's Pr●… & C●…n . l. 1. & 2. de Armis Roman . Scaevola glorying in his Arms stump ; then , y y A Roman Virgin , one of the Hostages ( amongst others of her Sex ) in Porsenna's Camp , who one Night deceiving her Keepers lead her Fellows within the shot and darts of the Enemies to take the Tiber and swim to Rome for their Liberty : For which Fact admir'd even by Porsenna , who extoll'd Rome as happy not only in breeding Men of Valour , but Virgins of like Bravery ; The Romans perpetuating her Memory by a Brazen Equestral Statue at the Head of the via sacra : under which , as Aldus Manutius ( in Cicer. Offic. l. ●… . ) affirms , were these Verses engraven ▪ VOS ETENIM JUVENES ANIMUM GERITIS MULIEBRE ILLA VIRAGO VIRI — Paul Merula conceiving Ennius to be the Authour of those Verses in 4 Annal. and to be the very Encomium which Porsenna gave of her daring spirit . This Statue Dionys. Halicarnass . l. 5. reports to have been destroyed by the firing of the Neighbouring Houses before his Time. See likewise Livy l. 1. Plutarch in Vita Poplicolae Valer. Max. l. 3. c. 2. and Pliny l. 34. c. 6. who yet from the Authority of Annius Faecialis reports it was not Claelia but Valeria , the Daughter of Publicola that was so honoured . But it were Injury to deprive this Lady of her Antient Merit , whose Story affords such Romantique Divertisement to our Modern Ladies . Claelia although a Maid more Brave than Men. z z Horatius Cocles , so called for having formerly lost one of his eyes in a Combat ; renowned ▪ 〈◊〉 his Valour in singly defending the Sublician Bridge against a whole Troop of the Thuscans , until the Bridge ( as he direct●… ) was cut down behind him , who then , armed as he was , threw himself into the Tiber , crying out , Veniat si quis vult sic euntem sequi ; and swam safe ( notwithstanding a multitude of Darts and Javelins thrown after him ) to Rome : yet Polybius ( l. 6. ) expresly affirms him to have perished in the Attempt . However it was , he is said for this eminent piece of service to have been by the Romans rewarded with as much ground , as could be ploughed in one day , and honoured with a Statue in the Comitium with a Civick Wreath or Mural Crown . Which Statue of his coming after to be stricken with Thunder ; The Romans consulting the Etrurian South-sayers about the Omen , were by them ( out of Malice to such a Monument of exemplary valour performed against them ) perswaded to take the Statue from the Place , where it stood , and to set it in some obscure low ground , where the Sun might not shine upon it . This being performed , and the People understanding at whose instance it was done ; the South-sayers were called before them and examined ; who confessing their perfidious intent , were condemned and executed , and the Statue planted in a higher Place , in the Area of Vulcan's Temple , which proved happy and successful to the Commonwealth . Upon this Occasion grew that Common Proverb ( expressing the sence of that Greek Verse in Hesiod 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Malum Consilium Consultori Pessimum ▪ ) . To be taken up and sung by the Young People and Children of Rome , as Aulus Gellius , from the Authority of the Annales Maximi and Verrius Flaccus his memorable Stories , relates . l. 4. c. 5. Cocles with Romes Walls crown'd which he maintain'd , And He who by a Crows Assistance gain'd Both Spoyls and Name , a a Marcus Valerius , who when Camillus , the younger , pursued the Reliques of the Galli Senones , being then a Tribune o●… Colonel , undertook the Combate with the Giant-like General of the Gauls , who dared the stoutest of all the Roman Army to a single Encounter . In the Conflict a Crow is said to have pearched upon Marcus Valerius his Helmet , and to have assaulted the face of his Enemy , wounding him with his Beak and Tallons , and buffeting him with his wings , by which Assistance he vanquished and slew the Gaul , and from thence gain'd the Surname of Corvinus ; rewarded beside with a Donativē of ten Oxen , and a Crown of Gold ; as Livy l. 7. c. 36. reports . Which Story of the Crow the learned Vossius ( Idololatr . l. 1. c. 27. ) conceives to be fabulous , and will have it to be only a Figure of a Crow upon his Crest or Helmet , according to the Custom of the Antients who adorn'd their Casques with the Effigies of several Birds and Beásts . Against which his Conjecture we shall only oppose these Words of Aulus Gellius l. 9. c. 11. de M. Valerio , qui Corvinus appellatus est , ob Auxilium Propugnationémque Corvi Alitis , haud Quisquam est Nobilium Scriptorum qui secùs dixerit . Augustus Caesar erecting a Statue to Corvinus in the Portico of his Forum , as the said Gellius affirms Rei Pugnaeque Monumentum . Nor seems it more incredible than what is reported of Alexander the Great , while he fought in the Battle at Arbela against Darius , that an Eagle all the while hovered over his Helmet , nor left him , till he had obtained the Victory ; touching which see Quintus Curtius l. 4. c. 15. Of this Corvinus ▪ Plutarch ( in Mario ) reports , that like him there was none , upon whom the Roman People conferred so many Magistracies , nor any , whose Suits or Petitions they answered with such readiness . He was six times Consul , as often Praetor , and as many times Aedile , once Censor , and twice Dictator . Vide Pighii Annal. Rom. Corvinus ! on whose Crest Phoebus does in his black-plum'd Emblem rest . b b A most signal Example of Loyal Magnanimity , who being by L. Apuleius Tribune of the People , accused as though he had unjustly divided the Veientine Spoyls , and a day appointed for him to answer ; not brooking such an Affront , before the day of hearing came , betook himself to a voluntary Exile ; upon whom in his absence the inraged People imposed a heavy Fine . In the interim the Gaules besieging the Capitol and ravaging the Country about , as far as Ardea , whither Camillus had retired himself ; He ( notwithstanding the Injury done him by his ungrateful Country men ) perswades the Ardeates to take up Arms against the Gauls , fights and defeats them ; whereupon by the remainder ▪ of the Roman Army , which after the Overthrow at Allia were escaped to Veii , he was chosen General , and by a Decree of the Senate call'd home from Banishment , and though absent made Dictator ; yet would he not return , till all Acts touching his Magistracy and Restitution were solemnly past by the People . Seven Moneths had the Capitol been besieg'd , and at last , capitulated to give the Gauls a vast summ of Gold to quit the siege ; at which instant Camillus arrives with his Army , commands the mony not to be paid , saying his Country was to be freed by Steel , not Gold ; and thereupon charges the Gauls within the Ruins of the City , defeats them , pursues them in their flight in the Gabine way , and makes so general a slaughter of them , that hardly any escaped to carry home news of their Overthrow . For this and other his eminent services to his Country ( among which that of hindring the People from quitting Rome for Veii , is to be reckon'd , whereby , as Victor says , & Oppidum Civibus & Cives Oppido reddidit ) he was thought worthy to be stil'd the second Founder of Rome , and call'd by the name of Romulus : Of which see Li●…y . l. c. Cassiodorus in Chronic. Eutropius libr. 1. and Aurel. Victor . de Vir. Illust. c. 23. He was 6 times Tribune , 4 times triumph'd , was once Censor , 5 times Dictator , and thrice Interregent . Camillus too , who Heaven with Iove may claim , Whom saving Rome , We may Rome's Founder name . The Generous c c Lucius Iunius , Son of Marcus Iunius by Tarquinia ; the Sister of Tarquinius Superbus , to avoid the Tyranny of the King his Uncle , who had put to death his Brother Marcus , seigned himself to be a Fool , and thereby gain'd the Surname of B●…utus ; notorious for expelling the Regal Power , and the whole Family of the Tarquins out of Rome , and introducing the Government of Consuls ; of which he was the first , and for a time the sole , notwithstanding his Colleague Collatinus ; to which Virgil alludes Consulis Imperium hic primus , saevasque secures Accipiet : — He was honoured by the Romans with a Brazen Statue , plac'd in the Capitol among those of their Kings with his sword drawn as Plutarch in his life , being s●…ain by Aruns , Son of Tarquinius ( as he by Brutus singly encountring one another ) for whom the Roman Ladies and Matrons kept a solemn mourning , during the space of one whole year , as for their Publique Father and Avenger of the violated Chastity of their Sex. See Livy l. 2. Brutus her Infranchiser , d d The Papyrii Father and Son were signaliz'd by their Triumphs over the Samuites , Lucanians , Tarentines and Brutians , who all joyn'd with Pyrrhus against the Romans . The Father was twice Dictator , five times Consul , and thrice triumph'd over the Samnites ; whom Livy doubts not to compare with Alexander the Great , and reckons him the fittest General to have opposed him , had he after the Conquest of Asia turn'd his Arms upon the Romans : Of which Livy l. 9. c. 16. But the Papyrius here meant , is the Son ; who with Sp. Carvilius triumph'd over the Samnites , Lucanians , Tarentines and Brutians ; having compell'd Milo , the Prefect of King Pyrrbus , to deliver up Tarentum ; which he dismantled and spoyled of all its strength by Sea and Land : by which Victory he put an end to the most desperate War , which ( till then ) the Roman People had ever been engag'd in . The Memory of this Victory and Triumph is preserv'd in some silver Coins ; On one side of which is the armed head of Rome , with the Rostrum or Beak of a Ship , thereby signifying the increase of Naval Power to the Romans by the Conquest of Tarentum ▪ On the Reverse the Figure of Victory in a Chariot drawn by four Horses , implying the Advantage and Superiority , which 〈◊〉 Victory gave them by Land. The Inscription this . L. PAPYRI . L. F. SP. N. CURSOR . See Vinand . Pighii Annal. Rom. Tom. 1. p. 447. Papyrius , who reveng'd the Pyrrhick War ; Stayd e e Manius Curius Dentatus ; so call'd for that he was born with teeth : by Valerius Maximus stil'd , the most exact Rule of Roman Frugality and perfect Pattern of Fortitude , famous for his exemplary Abstinence , and his refusal of a vast sum of Gold presented him by the Embassadours of the Samnites , saying he held it more honourable to command over those that were rich , than to be rich himself ; nor less ennobled by his many Victories and Triumphs over the Samnites , Sabins , Brutians , Appulians , Lucanians , and the defeat and expulsion of King Pyrrbus out of Italy , making good the Character he gave of himself , that he was neither to be corrupted by money , nor vanquish'd by Arms. See more of him in Cicero , ( in Cato . M. ) Valerius Maximus l. 4. c. 3. & Aurel. Vict. de Vir. Illustr . c. 35. Curius , and f f C. Fabricius Luscinus , of whom Valerius Maximus says , that in Honour and Authority he was greater than any Roman Citizen of his time ; but in estate as mean as the poorest ; who yet when sollicited by Pyrrhus with the offer of the fourth part of his Kingdom to become his Friend , refused with scorn so great a Bribe . No less exemplary for his Justice ; for when Pyrrhus his Physician offer'd him in hopes of reward to poyson his Prince ; Fabricius was so far from accepting the Offer , that he discovered the treachery to Pyrrhus , and sent back the Traytour , bound , to receive the just recompence of his villany : whereupon Pyrrhus is said to break out into this expression , That it was harder to draw Fabricius from Honesty , than the Sun from his Course . See ( besides Seneca Epist. 120. ) Valerius Maximus , l. 4. c. 3. Aurel. Victor . de Vir. Illustr . c. 39. and Eutropius in Brev. Histor. R●…m . To which I shall only add what I find mentioned by Seguinus in select . Numismat . touching an antient silver Meddaile , having on one side the head of Iuno , with this title , MONETA ; on the Reverse the several instruments of Coyning , with this Inscription , SALUTARIS ; which Coyn the said Seguinus conceives was stamp'd in honour , and as a Memorial of this great General . The occasion this ; When the Romans ( as Suidas in voce 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 reports ) were in the War against Pyrrhus impoverished , they were by Iuno , whom they consulted by sacrifice , told , That if they wag'd War with the Arms of Justice , they should not want mony : which Admonition Fabricius observing , gained to himself the honour of Equity and Justice , as well as Valour and Conduct , and by those means obtain'd a glorious Victory , which brought with it a vast Treasure to the Roman People , and so rendred MONETAM taken in which sence you will , SALUTAREM to the Commonwealth . Fabricius , a stern Pair ! g g Marcus Claudius Marcellus , of whom thus briefly the Triumphal Tables . M. CLAUDIUS . M. F. M. N. MARCELLUS . ANNO. P. R. C. D XXXI . COS. DE. GALLIS . INSUBRIBUS . ET . GERMANIS . K. MART. ISQUE . OPIMA . SPOLIA . RETULIT . DUCE . HOSTIUM . VIRDOMARO . AD. CLASTIDIUM . INTERFECTO . M. CLAUDIUS ( M. F. M. N. ) MARCELLUS CONSUL IN THE D XXXI . YEAR AFTER THE BUILDING OF ROME , TRIUMPH'D OVER THE GALLI INSUBRES , AND GERMANS IN THE KALENDS OF MARCH , AND BARE RICH SPOILES FROM VIRDOMARUS , GENERAL OF THE GAULS , WHOM HE SLEW AT CLASTIDIUM . To this Ausonius alludes ( in Monosyllab . ) Tertia ●…pima dedit spoliatus Aremoricus Lars . Lars being there no proper Name , but Title , signifying as much as Prince . See Scaliger in Propert. p. 237. Aurelius Victor de 〈◊〉 〈◊〉 . adds , that he first taught the Roman Souldiers how to make a Retreat , without turning their Backs , and at Nola made it appear that Hannibal was vincible ; he took the City of Syracuse after a 3 years siege ; and when denied by the Senate through the calumny of his Enemies a Triumph at Rome , he of his own accord and at his own expence triumph'd at Mount Alb●…nus : being the fifth time Consul , he was slam , over-reach'd by the treachery , rather than valour of Hannibal : See more of him in Virgil lib Ae●…neid . 6. Propertius l. 4. Eleg. 11. Livy l. 27. c. 16 ▪ and Plutarch in his life , call'd by Hannibal , the sword of Rome . Marcellus , who the third h h These the Romans call'd ●…pima 〈◊〉 , quasi optima , ampla , magnifica vel honorifica , in which sence by Plutarch ( in vita Mar●… ) call'd TIMIA , according to whom the conditions requisite to those spoils were ; First , that they were to be taken by the General of one Army from that of another ; Secondly , that they were to be taken in Battle ; Thirdly , in Prima Aci●… , in the first Part o●… Front of the Battle , to which Livy adds a fourth , That they were to be born or carried to Iupiter Feretrius by the Victor General , whence Iupiter according to Propertius ( l. 4. Eleg. 11. ) had that Title of Feretrius . See this noted by La Cerda in 6. 〈◊〉 . Aeneid . by Alexander ab Alex. Genial . D●…erum l. 1. c. 14. and Ianus Rutgersius Var. Lect. l. 4. c. 7. The first that ever won the●…e Spoils and Triumph'd was Romulus , having slain Acron , General of the Ceninenses . rich Trophies bare And i i Of him thus Livy , l. 4. C●…rn ▪ Cossus eximi●… pulchritudin●… corporis , Animo & viribus Par. And the Triumphal Tables , AULUS . CORNELIUS . ( M. F. SER. N. ) COSSUS . ANNO. POST . R. C. CCCXXV . COS. DE. VEIENTIBUS . IS QUE . SPOLIA . OPIMA . RETULIT . DUCE . HOSTIUM . LARTE . TOLUMNIO . AD. FIDENAS . INTERFECTO . AULUS CORNELIUS ( M. F. SER. N. ) COSSUS BEING CONSUL IN THE YEAR CCCXXV . AFTER THE BUILDING OF ROME , TRIUMPH'D OVER THE VEIENTINES , AND BARE RICH SPOILS FROM PRINCE TOLUMNIUS GENERAL OF THE ENEMIES , SLAIN BY HIM AT FIDENAE . Of which Ovid briefly in this Pentameter , as cited by Priscian , Larte ferox caeso Cossus opima tulit , &c. See likewise Propertius l. 4. Eleg. 11. Livy l. 4. Valer. Max. l. 3. c. 2. Aurel. Victor . de Viris Illustr . and Servins in Octav Virgil. Aereid . Cossus Second , from Kings spoyl'd of Life . The k k Of the Decii ( Father and Son ) devoting themselves to a voluntary death for the Good of their Contrey , the Roman Stories are full : See Livy more particularly , l. 8. and l. 10. Hence Lucan l. 6. calls them Lustrales bellis Animae — As if they had been propitiatory sacrifices for the welfare of the Roman Legions in time of hazard , concerning which Valerius Maximus , l. 5. c. 6. Dignosci arduum est utrum Romana Civitas utilius habuerit Decios vivos , an amiserit : quoniam vita corum ne vinceretur obstitit , mors fecit ut vinceret . I shall only add what is not commonly taken notice of , that there were not two only , but three of this Name and Family , who devoted themselves as sacrifices for the good of their Country ; of which thus Cicero in Tusculan .. Quaestion . l. 1. Simors timere●…ur , non cum Latinis decertans Pater Decius , cum E●…ruscis filius , cum Pyrrho Nepos , se hostium telis obtulissent . Decii in their Vows at noble strife , In Honours equal ; l l Quintus Fabius Maximus Verrucosus call'd the Buckler and Shield of Rome , as Marcellus the Sword ; who as Ennius says , cunctando Romanam restituit Rem ; or as L. Florus more nearly to the sence of our Authour : Novam de Hannibale Victoriam commentus est non velle pugnare . Hence the Proverb , Romanus sedendo vincit . Propertius likewise , l. 3. Eleg. 3. stiling his wary and delatory prosecution of the War Victrices Moras : Of whose Actions ( so generally noted in the Roman Stories ) we cannot give a better Summary than what is contained in this following Antient Inscription on a Marble found long since at Aretium , as Marlianus reports , and extant at Florence in the House of Petrus Victorius , as Panvinius in his Fasti affirms . Q. F. MAXIMUS . DICTATOR . BIS . COS. V. CENSOR . INTERREX : II. AED . CUR . Q. II. TRIBUN . MIL. II. PONTIFEX . AUGUR . PRIMO . CONSULATU . LIGURES . SUBEGIT . EX . IIS . TRIUMPHAVIT . TERTIO . ET . QUARTO . ANNIBALEM . COMPLURIBUS . VICTORIIS . FEROCEM . SUBSEQUENDO . COERCUIT . DICTATOR . MAGISTRO . EQUITUM . MINUCIO . QUOIUS . POPULUS . IMPERIUM . CUM . DICTATORIS . IMPERIO . AEQUAVERAT . ET . EXERCITUI . PROFLIGATO . SUBVENIT . ET . EO . NOMINE . AB . EXERCITU . MINUCI . ANO. PATER . APPELLATUS . EST. CONSUL . QUINTUM . TARENTUM . CEPIT . TRIUMPHAVIT . DUX . AETATIS . SUAE . CAUTISSIMUS . ET . REI . MILITARIS . PERITISSIMUS . HABITUS . EST. PRINCEPS . IN. SENATUM . DUOBUS . LUSTRIS . LECTUS . EST. QUINTUS FABIUS MAXIMUS TWICE DICTATOR , FIVE TIMES CONSUL , TWICE CENSOR , AND INTERREX , AND TWICE AEDILE OF THE CHAIR ; TRIBUNE OF THE SOULDIERS , HIGH PRIEST AND AUGUR . IN HIS FIRST CONSULATE HE SUBDU'D THE LIGURIANS AND TRIUMPH'D OVER THEM . IN HIS THIRD AND FOURTH HE REPREST AND RESTRAIN'D HANNIBAL RAGING WITH MANY VICTORIES BY CLOSELY FOLLOWING HIM : BEING DICTATOR , HE RELIEV'D MINUCIUS MASTER OF THE CAVALRY ( WHOSE COMMAND THE PEOPLE HAD EQUAL'D WITH THAT OF THE DICTATOR ) AND HIS DISCOMFITED ARMY . AND FOR THAT CAUSE WAS BY THE MINUCIAN . ARMY CALL'D FATHER . IN HIS FIFTH CONSULATE HE TOOK TARENTUM AND TRIUMPH'D , ACCOUNTED THE MOST WARY CAPTAIN OF HIS AGE , AND THE MOST EXPERT IN ALL MILITARY AFFAIRS , ELECTED PRINCE OF THE SENATE FOR TWO LUSTRES . See likewise Antonius Augustinus , Dialog . 10th , and Pighii Annal. Roman . Tom. 2. p. 132. and Paul Merula in Commentar ▪ ad Ennii Annal. l. 8. p. 467. Fabius , Romes Defence , In War unconquer'd , by the War's suspence . m m M●…rcus Livius Salinator , Consul with Claudius Ne●…o in the 546th year after the building of Rome , triumphed for the overthrow of Asdrubal the Brother of Annibal , who came into Italy with a great Army intending to joyn with that of his Brothers , which ( if effected ) had prov'd the Ruine of the Roman State. But Nero , who attended the motion of Annibal in Apulia , secretly upon notice of Asdrubal's Arrival , not far from Sena or Senogallia , ( where Livius was encamped ) taking with him 7000 Foot and 1000 Horse of the choisest of his Camp , left the rest to face Hannibal , and marching with incredible speed , joyn'd his Forces with those of his Fellow Consul , who together defeated the whole Army of Asdrubal and slew him in the Battle . Nero returning to his Camp before Hannibal understood any thing of his departure , or heard news of his Brothers defeat : The first notice whereof Nero himself gave him by causing Asdrubal's head ( which he had brought with him ) to be cast before the Camp of Hannibal ; which he seeing cryed out , That the Fortune of Carthage was overthrown . Of this Meritorious Act of Nero's , thus Horace , Carm. l. 4. Od. 4. Quid debeas â Roma Neronibus Testis Metaurum Flumen , & Asdrubal Devictus , & pulcher fugatis Ille dies Latio tenebris . What Rome thou ow'st to Nero's Name Metaurus and slain Asdrubal proclaim , And that bright Day , Which chac'd from Latium Night away . Livius the Victor of slain Asdruball , With Nero the joynt Authour of his Fall. n n Of these Scipio's the one was Publius Cornelius Scipio , who being Pro-Consul of Africa in the second Punick War drew Hannibal from Italy to the Defence of his own Country , whom he defeated and brought the Carthaginians to sue for Peace and acknowledge themselves tributary to the State of Rome ; for which he triumphed , being call'd Scipio Africanus Major : The other , the Son of Aemilius Paulus Macedonicus , adopted into the Cornelian Family by the Son of Afri●…anus Major , and call'd Publius Cornelius Scipio Aemilianus , who took and utterly destroyed Carthage in the third and last Punick War , and reduced Africa into the Form of a Roman Province , for which he triumphed and gained the Sir-name of Africanus Minor , samed for his Justice and Military Science ; whence is that Adagial Encomium , Scipione Iustior , & Militarior : in Tertull. 〈◊〉 . c. 2. These Virgil in 6 Aeneid . calls — Geminos duo Fulmina belli Scipiadas , Cladem Lybiae — Of whom likewise Lucius Florus says , Fatale Africae Nomen Scipionum videbatur . See more of them in Livy , Velleius Paterculus , Orosius , Appian . de Bello Civil . Lucius Florus , Aurelius Victor , & Eutropius . The Scipio's unto Carthage both one Fate : o o Vel●…eius Paterculus , l. 2. speaking of Pompey designed General in the War against the Pyrates , says , it was voted by Decree of the People and Senate , that Cn. Pompeius ad eos opprimendos mitteretur , essetque ei Imperium aequum in omnibus Provinciis cum Proconsulibus usque ad Quinquagesimum Miliarium à Mari. Quo. S. C. paene totius Terrarum Orbis Imperium uni viro deferebatur : Confirmed by Plutarch in Pomp. and further asserted by some Antient Coins , stamped in honour of the said Pompey , with this Inscription : MAGNUS . IMPERATOR . And on the Reverse of some others ( in token of his Dominion by Sea and Land ) a Scepter figur'd erect between a Dolphin and an Eagle . See Fulv. Ursin. in famil . Pomp. p. 204. Pompey , 'fore Caesar Prince of Rome's great State , And the aw'd World , which p p Commemorated by Albinus the Poet ( not the Historian ) in his Poem of the Gests of Pompey the Great , out of which Priscian l. 7. cites these Verses . Ille cui ternis Capitolia celsa Triumphis Sponte Deûm patuêre , cui freta nulla repostos Abscondêre Sinus , non tutae Moenibus Urbes . In which Verses are celebrated the three Triumphs of Pompey ; the first from Africa over King Iarbas ; the second from Spain over Sertorius ; the last from Asia over Mithridates and the Pyrates . See Popma in Schol. in Fragment . Historie . But what is to be chiefly noted , these Triumphs were permitted to Pompey contrary to the Express Decrees of the Roman State , before he had undergone any Magistracy , being only a private Knight ; which Privilege none before him ever injoyed . But it was in a Time quo silebant inter A●…ma Leges . Of the stupendious Splendour and Luxury of these Triumphs , especially of the last , see particularly Pliny l. 37. c. 2. thrice his Triumphs sung , And q q Marcus Tullius Cice●…o ; of whom it were lost Labour to speak , save in a Language equal to his own . And therefore I shall only salute him , as Pliny does l. 7. c. 30. Salve Primus omnium Pater Patriae appellate . Primus in Toga Triumphum , Linguaeque L●…uream merite ; & facundiae Lati●…rúmque literarum Parens ; atque ( ut Dictator Caesar Hostis quondam Tuus de ie s●…ipsit ) Omnium Triumphorum L●…uream ad●…pte Majorem , quanto plus est Ingenii Romani Terminos in tantum promovisse , quàm Imperii . ( i. e. ) Hail Thou who of all Men wert first saluted Father of thy Country , who first deservedst a Triumph in thy long Robe , and a Laurel Garland for thy Language . The only Father of Eloquence , and Latian Learning ; and ( as Caesar Dictator sometimes thine Enemy hath written of thee ) honoured with a Crown so much more glorious than those of other Tri●…mphs , by how much nobler it is to have enlarged the Bounds of Roman Wit than those of its Empire . Tullius worthy Heaven for his sweet Toung . There the great r r Of the Claudian Name there were two Families , one Patrician the other Plebeian . Of the first , were the several Surnames of the Pulchri , Centhones , N●…rones , Regillenses Crassini , Cae●…i , Crassi , Caudices , Hortatores , Rufi , Sabini , C●…nini . Of the latter , which yet was more signal than the first , were those of the Marcelli , Aesernini , Aselli , Cliti●… , Flaminii . All descended from Regillus a Town of the Sabines , whose Chief was Atta Tatius Clausus , who about the sixth year after the Expulsion of Tarquinius Superbus came to Rome , and was admitted into the Patrician Order ; changing his Name into Appius Claudius . Of the Original of which Family thus Virgil ( Aeneid . 7. ) more Poetically , than truly ( for he alludes to this very Appius Claudius ) Ecce Sabinorum prisco de sanguine , Magnum Agmen agens Clausus , Magnique ipse Agminis instar , Claudia nunc à Quo diffunditur & Tribus , & Gens Per Latium — See Clausus of old Sabine blood , who brings A Mighty Troop , himself as Great ; whence springs The Claudiam Tribe , and Family , now spred Through Latium — Plutarch derives them from Sparta , and makes them to have been part of a Lacedaemonian Colony planted in Italy : This Family in the Time of Tiberius ( who was of the same Race , and whom perhaps the Poet in this Place flatters , as being the designed Heir to Augustus ) was signaliz'd with 28 Consulates , 5 Dictatorships , 7 Censorships , as many Triumphs , and 2 Ovations ; as Suetonius in Tiberio witnesses . See more in Antonius Augustinus de Familiis Roman . and Andreas Schottus in his Idaea Rom. Histor. ad Pighii Annal. Claudian Progeny does shine , And all the Worthies of th' s s The Aemilian Family some derive from Mamercus the Son of Pythagoras the Philosopher call'd ' 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 from his Affability and singular Humanity , as Plutarch in Numa , and in the life of Paulus Aemilius , and Festus in voce Aemil. attest . Others , as the same Festus notes , deduce it from Ascanius who had two Sons Iülus and Aemylus , the later of whom is supposed to have given the Origine to that Name and Family . It was one of the most celebrious in all Rome , and honour'd even from the first times of the Roman Liberty until the Empire of Augustus , with the most signal Magistracies of that State. It was of Patrician Degree , and distinguished into 5 Principal Surnames , of the Barbulae , Lepidi , Mamercini , Papi , and Pauli : To these Onuphrius adds the Buae , Liviani , Marci , Porcini , and Privernates ; to whom likewise are to be added the Regilli and Scauri . See all these with their several Honours and Performances enumerated by Antonius Augustinus de Fami●… . Rom. and Pighius in Annal. Aemilian Line ; t t The Metelli were the Noblest Branch of the Caecilian Family ; which though it were Originally Plebeian , rose yet to the greatest Honours which the Roman Commonwealth could afford : Nineteen of which Name in the space of 280 years were signaliz'd with 4 Chief Priesthoods , 2 Dictatorships , 3 Presidentships of the Senate , 7 Censorships , 9 Triumphs , 20 Consulships , and 2 Masterships of the Cavalry . The most famous of the Metelli , were Metellus Maced●…nicus , so call'd from his Conquest of Macedonia , whose saying it was That he would burn his shirt if he thought it could know his Designs or Counsels . Metellus Numidicus so call'd from his Triumph over Iugurth King of Numidia , and Metellus Pius who gain'd that Surname by his assiduous Supplication and Intercession for the recalling of his Father from Banishment , which at last he effected : See Aurel. Victor de Viris Illustr . & Valer. Maximus . The Name ( notwithstanding its great Nobility ) seems to be deriv'd from some servile Military Employment , touching which thus Festus in voce Metell . Metelli dicuntur in re Militari quasi Mercenarii . Attius Annal. 17. Calones , Famulique , Metellique , Caculaeque . A quo Genere Hominum Caeciliae Familiae Cognomen putatur dictum . See more of this Family in Antonius Augustinus , and Schottus ad Pighii Annal. as likewise Ursinus in Numism . Gentis Caecil . Vide etiam de Origine hujus Nominis Meurs . Exercit. Critie . part . 2. p. 108. Metelli , signal for their Noble Name ; u u Marcus Porcius Cato call'd Uticensis from Utica the Place of his Death , and Minor , to distinguish him from Cato Major or Censorinus , thus character'd in Velleius Paterculus . Per omnia Ingenio Diis quàm Hominibus propior : Omnibus humanis vitiis immunis , semper fortunam in sua Potestate habuit . The great Assertor of the Roman Liberty in time of the Civil wars between Pompey and Caesar ; chosing rather to dy in freedom by his own Hand , than to fall a Captive into those of the Conqueror . Of whose resolute and Heroick Death , see Seneca l. de Providentia , and almost every where else . And particularly Dion Cassius l. 43. This is further observable of him , that though he himself chose rather to dy , than to submit to Caesar , yet at his Death he perswaded his Son to do so , giving for it this Reason ; That he having always liv'd in Liberty and a free State , could not in his old Age be brought to change that manner of life , and subject himself to a servile condition ; but for his Son , he being born and having lived in other Times , he advised him to comply with the Fortune that should be offered him . See Dion Cassius loco citato : Which Reason is likewise hinted at by Cicero in primo de Offi●… . Caeteris forsitan vitio datum esset , si se interemisse●…t , propterea quod eorum vita lenior , & mores fuerunt faciliores : Catoni autem cum incredibilem tribuisset Natura Gravitatem , eamque ipse perpetuâ Constantiâ corroboravisset , semperque in proposito , suscept●…que consilio permansisse●… ; moriendum potius , quàm Tyranni vultus aspiciendus fuit . Manilius elsewhere ( l. 4. ) calls him — Invictum devictâ Morte Catonem . Cato , who Fortune ev'n in Death o'rcame ; x x Marcus Vipsanius Agrippa though of a mean Family , by his Merits and Valour attained to that eminent Degree , as to be Second in the Empire under Augustus , and to become his Son in Law : Of which thus Taci●…us in primo Annal ▪ Marcum Agrippam ignobilem loco , bonum Militiae & Victoriae S●…cium geminatis Consulatibus extulit ; mox defuncto Marcello , Generum sumpsit . Vell●…ius Paterculus giving this further Elogy of him , That he was Virtutis Nobilissimae , Labore , Vigiliâ , periculo invictus , parendique , sed uni , scientissimus , aliis sanè imperandi cupidus ; & per omnia extra dilationes posi●…us , consultisque facta conjungens . To whom Augustus may justly be said to owe the Establishment of his Throne aud Empire by those 2 Memorable Victories gain'd by his Conduct and Valour , over Sextus Pompeius near Sicily , and Marcus Antonius near Actium , for which he merited a Naval Crown . Yet this great Statesman , and Souldier , the latter of which he was even born as Manilius here intimates , ( for we read with Scaliger upon his last and better thoughts — Matrisque sub Armis , not Martis , by Armis understanding Armos , i. e. Ulnas , not Arma ; as if sub ipsa Matre cum lacte imbibisset Militarem Scientiam : Though we cannot but here acknowledge the Interpretation of Spanhemius ( in Dissertat . de Numism . ) to be very ingenious , who understands by Matris , Patriae , seu Romae belligerantis , that Title of Mater being often by the Antients apply'd to Rome ) was of that equal and moderate Temper , that he never advis'd Augustus to any Actions but those of Humanity , Honour , and Publick Utility ; the Glory whereof he never arrogated to himself nor made of the great Honours and high Charges conferred upon him , any Advantages to his own private Gain and Pleasure , but converted and applyed them wholly to the profit of his Prince and Country . Indelible Characters of an excellent Subject and Patriot ▪ Agrippa , Souldier from his Mothers Brest ; ( y y Meaning Iulius Caesar , of whom 〈◊〉 P●…rculus ( l. 2. ) Nobilissimá Iuliorum genitus Familiâ , & qu●…d inter omnes Antiqu●…ssimos constabat , ab Anchise ac Venere duceus Genus . The Iulian Family taking its Name from ●…lus the Son of Aeneas , and Grand-Child of Venus ; whence Virgil ( Aeneid . l. 1. ) Niscetur pul●…râ Trojanus Origine Caesar Iu●…ius , à Magno demissum Nomen Iulo. Confirm'd by Livy l. 1. Strabo l. 19. Appian de belio Civil . l. 2. and the Testimony of Caesar himself , in his Funeral Oration upon Iulia the Wife of Caius Marius , his Aunt ; as recorded by Sue●…onius , where he thus speaks . Amitae Meae Iuliae Maternum Genus ab Regibus orium , Paternum cum Diis Immortalibus conjunctum est . Nam ab Anco Marcio sunt Reges , quo Nomine fuit Ma●…er . A Venere Iulii , cujus Gentis Familia est Nostra . Hence the Title of VENUS GENETRIX on the Roman Coyns stamped in Honour of Iulius and Augustus ; and this Inscription mentioned in Gruterus : VENERI GENETRICI D. JULI . IN MEMORIAM GENTIS JULIAE &c. See more to this purpose in Ursinus in Famil . Iul. And as to the Pretence of its Original see the same discussed by the 〈◊〉 B chartus in his Particular Tract entituled , Num Aeneas unquam fuerit in Italia . ) Venus her Iulian Offspring , repossest Of Heaven , whence first descended ; which now proves The Rule of great ( z z 〈◊〉 here questions Manilius for giving to Augustus , a share in the Government of Heaven before he 〈◊〉 thither . Quare dicit Coelum regi ab Augusto quod nondum tenebat ? Hoc mortuo melius conveniebat ( says 〈◊〉 〈◊〉 that Illustrious Critick might have remembred , That Augustus was even in his life time ( such was the 〈◊〉 Adulation of those Times ) reputed and honoured as a God , and had his Priests , Altars , Sacrifices , and 〈◊〉 as is manifest by those Altars with their Inscriptions erected to him at Lyons and Narbon : To which 〈◊〉 ●…udes ( Epist. l. 2. ) where he says that Augustus had that Praeeminence above either Romulus , Bacchus , 〈◊〉 or Pollux , who were not honoured as Deities till after their Deaths . For this Reason Manilius while yet 〈◊〉 gives him a share in the Celestial Government , as another Iupiter . And hence Philippus in that flattering but 〈◊〉 Epigram of his ( in Antholog . l. 1. ) upon occasion of a Laurel springing out of an Altar dedicated to Au●… at Arragon in Spaine , calls him 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , JOVEM AENEADEM . Nor did Augustus ' think 〈◊〉 〈◊〉 himself , as may appear by his facetious and yet tar●… Answer to the Arragonians who told him of that Pro●…y of the Laurel , or rather Palm , as Quintilian relates it : Apparet ( inquit ) quàm s●…pe accendatis . It is a sign 〈◊〉 he ) how often you kindle fire there ; taxing them thereby of Negligence in his Worship : For if they had fre●…ntly sacrificed , the Laurel or Palm could not have grown there . And that he had equal share with Iove him●… in the Vows and Addresses of Suppliants appears by this Antient Inscription found near Nismes in France : SANCTITATI JOVIS ET AUGUSTI SACRUM LUCILIUS CESTTI FIL. &c. 〈◊〉 which Gruterus ( in Inscript . ) and Guiranus ( in Explicat . Num. Nemaus . ) But of the servile and Idolatrous Adula●… of the Antients , and particularly of the Athenians and Romans towards their living Kings and Emperours ; see ●…aeus Deipn●…soph . l. 6. c. 14 and 15. and the learned Casaubon thereupon . ) Augustus joyn'd with Iove's ; Who'mong the Deathless Deities inroll'd , His Father and Quirinus doth behold . More high th' Immortal Gods have fix'd their Seat , Next whom , is This , with Godlike Men repleat . But of the Stars e're we the Laws rehearse , And fatal Changes , We the Universe Must first compleat ; and shew what does dispence Throughout the Whole , or Light , or Influence . ( a a Having finished the Description of the fixed Stars and their several Asterisms , together with the Doctrine of 〈◊〉 ●…stial Circles : The Poet to compleat his Work , adds a brief mention of the several Planets according to their 〈◊〉 and Position ; and then subjoyns ( as a Close to the Whole ) a short Enumeration of Comets , and other fie●… 〈◊〉 . Of the Planets the first is ) Some Stars there are which 'gainst the World's Course bend , The Seven Planets . And wand'ring 'twixt the Earth and Heaven suspend . As ( b b Saturn ; by the Greeks call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 from the slow time of his motion ; by Plato in Timae●… 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Apparens ; as being of all the Planets the least obscur'd under the Sun's Beams ; by others 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; and by Plutarch ( in facie Lunae ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. N●…ctis Custos . In a fragment of an Antient Astronomical Poem ( cited by Scaliger in Ausonian . Lect. ) stil'd Pollucis Pr●…les ; which by Fulgentius is thus explained . Saturn ( says he ) is called the Son of Pollux , sive à pollendo , sive à pollucibilitate , i. e. humanitate . In Hebrew this Planet is call'd Schabtai , i. e. Saturatio seu Quies . The Arabs call it Zohalo from Zahala , which signifies abscedere , recedere , vel discedere , quòd multùm retrogradus sit , says the Learned Doctour Pocock ( Not. in Carm. Tograi . ) By the Chaldeans it is called Caun , by the Egyptians Rephan , i. e. Deus Temporis , and ( according to Achilles Tatius ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Nemesis Stella ; by Astrologers term'd Infortuna Major . ) Saturn , ( c c This Planet is in Hebrew called Cochab Tzedeck , i. e. Stella Iustitiae & Aequitatis ; by the Greeks , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; by Plato in Timaeo , Phaëton from its brightness ; by the Latines , Iupiter , i. e. Iuvans Pater ; by the Aegyptians , Picheus , i. e. Deus vitae , answering to the Greek , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; by Achilles Tatius ( in Isagog . ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Osiridis Stella ; by Hesychius , Molobobar , or rather ( as Vossius Idololatr . l. 2. conceives the word ought to be read ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . In the Phrygian Tongue Mazeus , ( si fides Hesychio , says Mr. Selden . ) In the Chaldee , Taus ; in Arabick , El Mes●…icri . The Antient Germans called this Planet T●…ranis , or Taran . Astrologers entitle him by that of Fortuna Major : Which they have from the Iews who call this Planet by the Name of Mazal Tob , i. e. Sidus bonum , seu fortuna bona . And therefore among them it was usual in the Marriage Ceremony for the Bridegroom to deliver to the Bride a Ring in which was inscrib'd MAZAL TOB. This Star in their Opinion conducing much to Fertility , and the Propagation of Children . As Mr. Selden ( from the Authority of Munster ) de Diis Syris , Synt●…gm . primo . ) Iove , ( d d Mars , call'd likewise by the Latines , Gradivus , seems to be derived from the Hebrew , Maratz , which signifies strong and powerful ; or from Mechares , destroying , ( as the often cited G. Vossius de Idololatr . l. 2. ) call'd also in Hebrew , Ma●…dim , from his Colour resembling Blood. In Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 from his fiery light , as also 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Thuras , quasi Thra●…um Deus , according to Bochartus his Interpretation ( Phaleg . l. 3. c. 2. ) By the Aegyptians called Mel●…ch , i. e. Deus Destructionis , and ( according to Vet●…ius Valens , as cited by Mr. Selden de Diis Syris Syntagm . primo ) Artes , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , as being the Destroyer of Life ; and according to Pliny and Achilles Tatius 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Herculis Stella ; by the Emissaeans , and those of Edessa styl'd Azizus , whom they believ'd to be 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Assessor Solis ( as Iulian the Apostate in his Encomiastick Oration upon the Sun ; ) by the Chaldeans call'd Ari●…z , i. e. praevalidus ; by the Arabs , El Marigh , i. e. Sanguinolentus . Astrologers stile him Infortuna Minor. ) Mars , ( e e This glorious Luminary is in Hebrew call'd Cham●…h , or Schemash from his Heat , or Adon Schemez , i. e. Dominus Sol ; by the Phoenicians , Baal Schemaim , i. e. Dominus Coeli ; in Chaldee , Schemso ; in Arabick , El Schems ; by the Greeks , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 quasi 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Lux vitae ; whence the Latine , Phoebus ; call'd likewise Titan and Apollo , Cor Coeli , Oculus Iovis , & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Oculus Aetheris . By the Aegyptians styl'd Potiris , i. e. Deus Sanctus , and Osyris from his vital and kindly Heat , as on the contrary Typhon and Seth from his violent and destructive fervor , call'd by them likewise Horus ; by the Persians call'd Mi●…hra , i. e. Dominus sive Dynasta ; by the Arabs antiently Urotalt , i. e. Lucis Deus , and Dusares , or Dai Us●…r , i. e. Deus perlustrans , as S●…bedius de Diis German . interprets those Names ; by the Syrians according to Macrobius call'd Adad , or as Scaliger and Mr. Selden would rather have it , Ahad , or Elhad , i. e. Unus , or as Pontanus ( Not. in Macrob. ) Badad , i. e. Solus , Unicus . ) Phoebus , ( f f Mercury is in Hebrew call'd Cochau , or Cochab , i. e. Stella fulgens , and Choteb , i. e. Scriba seu literatus , and Margim●… , i. e. Negotiator , and Merkolis , whence some derive the Name Mercury , though Arnobius l. 3. says he is so call'd by the Latines , quasi Medicurrius , from his Office as Messenger between the Gods and Men. In the Astronomical Fragment before cited he is called Semo , quia ferein infimis collocatus ( says Scaliger in Auson . Lect. ) as those Deities were likewise call'd S●…mmes , qui infimi censebantur , being Majores Hominibus , Minores Diis , as Fulgentius expounds the Word ; by the Phoenicians call'd Sumes , i. e. Minister says Bochar●…us ( Phaleg . l. 1. c. 2. ) call'd by them likewise Adared . By the Chaldeans , N●…bu ; and as Hesychius says , S●…ehez ; which some make the same with Sesach . He is likewise by the Emissaeans and Edessaeans call'd M●…mimus , They Holding him to be one of the Suns 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Assessors , as Azizus or Mars was another , according to the Testimony of Iulian before cited . By Astrologers he is stil'd Fortuna per Aspectum , or ( according to Apulcius de Mundo ) Communis Stella , as participating of the Nature of the Star , with which he is in Conjunction , good with the good , bad with the bad . Hence the Authour of the Fragment after Censorinus de Die Natal . Stella Mercurii fit similis illi quam videt . ) Maia's Son , Plac'd under these 'twixt ( g g Venus in Hebrew is call'd Nogah , i. e. Lux. The Name Venus coming from the Hebrew Word Benot , by the change of the first and last Letters ; as Mr. Selden de Diis Syris Syntagm . 2. c. 7. and Vossius Idololatr . l. 2. c. 22. derive it . By the Greeks call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Phosphorus , seu Lucifer , when she is the Morning Star , as 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Hesperus , Vesper , and Vesperugo , when she is the Evening Star ; by Timaeus Locrus call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Iunonis Astrum . The Aegyptians call her Suroth ; the Chaldeans , Spharphara , and Astaroth ; by the Arabs named Elzahareth and Chabar , i. e. Magna . ) Venus and the ( h h This Planet or Luminary is in Hebrew call'd Lebanah or Laneah from its white Colour ; by the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , from the renewing of its Light. She is by them likewise honoured with the Title of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , as Gaulmin . notis in Psellum ( 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . ) By the Latines , Luna , quasi Lucuna or Lucina , the middle Syllable being cast away , as Isidor . ( Origin . l. 8. ) and before him Cicero ( de Natur. Deorum l. 2. ) Luna à Lucendo , eadem enim Lucina . Or as V●…ssius ( Idololatr . l. 2. ) derives it from an Oriental Original , Luna potius à Lon , i. e. pernoctavit , and Metaleptically , quie●…it : In regard as the Sun is President of the Days Labour , so the Moon is Surintendent of the Nights Rest and Quiet : By the Egyptian Copies call'd Isis Pcochos Act●…phcom , i. e. Domina Maris & humidorum ; by the Chaldeans , Scha●…ro ; by the Persians , Anai●…is ; by the Arabs , Alkamer , and Abilat , and Alitta ; by the Indians ador'd under the Name of Schendra . ) Moon . Others there are too of less usual kind ; For Suddain Flames streaming through Skies We find , And Times more rare have Comets seen to blaze Comets and ●…iery M●…teors . ( i i According to the Vulgar Belief , who conceive Comets to be fore-runners of great Troubles and Commotions ; by which Manilius here signalizes their Exstinction . ) And loose midst mighty stirs their threatning Rays . Whither as k k Alluding to the opinion of those who hold Comets to be generated of Elementary Matter , that is of Exhalation and Vapour ; the first from the Earth hot and dry ; the other from the Water , hot , moist and unctuous , carried by their Lightness above the Aiery Region , where compacted they are by Motion of the superiour Orbs set on fire . Of which Opinion is Aristotle and his followers , and ( differing only as to place ) Galilaeo 〈◊〉 , Guiduceius , and some others . See Gassendus Tom. 1. part . 2. p. 702. and Ricciolus in Almagest . Nov. Tom. 1. l. 8. and Fromond . Meteorolog . l. 3. Earth transpires its Native fumes , Those humid Spirits the hot Air consumes , Their Original . When a long Drouth from Clouds hath clear'd the Sky And Heav'n by the Sun's scorching Beams grows dry ; Whence fitting Aliment is snatch'd by Fire , And Matter like to Tinder flames acquire . And since the Principles which Air compose Are not gross Bodies , but like Smoke that flows , The fiery Substance is not permanent , But with the Comet , l l Touching the Duration of Comets , Pliny ( l. 2. c. 25. ) makes the shortest to be Septem Dierum , the longest Oct●…ginta , or rather ( as Muretus conceives the Text of Pliny ought to be read ) C. & Oct●…ginta , a 180 Days ; which Emendation Tycho Brahe Progymn . l. 1. p. 273 ( though Scaliger seem to disallow it ) approves of . And so long Seneca ( Natural . quaest . l. 7. ) affirms the duration of one seen in the beginning of Nero's Reign . Iosephus de Bello Iudaico l. 7. reports one to have continued a wh●…le year a little before the Destruction of Ierusalem in the form of that which is called Xiphias , or the Sword Comet . But this Tycho conceives to have been supernatural and extraordinary ; so that the longest Duration of Comets ( their ordinary not extending to half that space ) seems not to be above six Moneths : Of which co●…tinuance we find in History only three . The first that of Nero's beforementioned in the year of Christ 64. the second in the year 603. not long before the appearrance of the Impostor Mahomet ; and the last in the year 1240. observed by Albertus Magnus . soon as kindled , spent . Else , if its Rise and Fall were not so nigh , We should another Day in Night descry , And the couch'd Sun , when from the watery Deep Return'd , would the whole World surprize in sleep . Then since the arid Vapour is not us'd To be alike attracted , or diffus'd ; Hence m m The Word Comet though when strictly taken it signifies Stellam Crinitam , and Sidus Cincinnatum ; yet in a larger sence it is us'd as a common and general Name for all sorts of fiery Meteors : Of which Pliny ( l. 2. c. 25. ) reckons twelve several Spec●…es : Viz. Cometa , Pogonias , Acontias , Xiphias , Disceus , Pithetes , Ceratias , Lampas , Hippeus , Argenticomus , Hircus , Longchites , seu Hast●… . Divers of which are by our Poet here enumerated ; whose Explanation we shall give in the following Notes ; and shall only add the Distinction which is made by a Reverend and Learned Authour upon this Subject , who will have such Meteors to be peculiarly called Comets , as are super-Lunary , and have ( as he says ) . proprium Aetherium , Geometricum motum , qualis esse solet Planetarum ; to the others he gives the Name 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , as having some Resemblance with , but differing as to their Motion , Place , and other Affections , from Comets properly so called ; their Birth and existence being within the sublunary Sphere . Vide D. Setb . Wardi Praelect . de Cometis . several Shapes to Meteors are assign'd , Their several kinds . As in dark Nights their suddain Births they find . For now ( like long hairs flowing from some head ) The Flame is in dishevell'd n n These kind of Meteors are by the Greeks properly called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Stellae Crinitae , seu Cincinnatae , as is before noted ; whose blaze rises upward , above the Head or Body of the Comet , whence Pliny calls them 〈◊〉 modo in vertice Hispidas : But when the Cheveleure is round about equally diffused , then the Comet is called Rosa. Tresses spred ; Cometa or Stella Cincinnata . Then what a fiery Peruke first appear'd , Assumes the Figure of a blazing o o Thence called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Barbata , from the Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Barba , which the Vulgar distinguish not from that which is called Caudata , as Fromondus observes , l. 3. c. 4. That difference being caused only by its Respect to the Sun , for if it appear in the Morning before the Sun-rise it seems bearded , the Blaze tending in Anteriora , before the Sun , Westward ; but if it appear in the Evening the Sun being set , then it seems Caudata , the Train flowing from behind the Sun , Eastward : But it is more properly said to be Barbata , when the Head or Body of the Comet is above , and the Train or Stream underneath flow●…ng downward 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 More Barbae , in opposition to that which is called Crinita , whose Hair or Bash is above the Head of the Comet . See Stobaeus Eclog Physic. l. 1. And Suidas in voce 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Beard . Pogonias or Stella Barbata . Sometimes 'twixt equal-bounded Sides it flows , And a square p p This Com●… or Meteor is called in English a Beam or Post ; in Latine , Trabs ; in Greek , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Igni●…a Trabs . When extended to an extraordinary length , it was by the Greeks likewise called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Via ▪ as A●…istotle Meteorolog . l. 1. c. 6. affi●…ms . Pliny ( l. 2. c. 26 ▪ ) reports such a one to have appeared at what time the Lacedemonians ( vanqu●…shed in Fight at Sea ) lost the Empire of Greece ; and Charimand●…r in his Book of Comets , as cited by Seneca ( Natur. Quaest. l. 7. ) rela●…s the like Meteor of unusual Brightness and Greatness to have been observed by Anaxagoras , for many days continuance . Callisthenes likewise affirms such a one to have appeared a little before Buris and Helice were swallowed up in the Sea : The difference between a Trabs and Columna is this : The first is of an oblong Form in a down lying Posture , the latter appears in an erected Figure . Vide Fromond . Meteor . l. 2. c. 5. Post , or a round Pillar shows , Doki●… or Trabs . Like a big-bellied q q Call'd therefore by the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Dolium , and thence by the Latines , Pithetes , thus described by Pliny ( l. 2. c. 25. ) Pithetes Doliorum cernitur Figurā in C●…ncavo fumidae Lucis , i. e. Pithetes is seen in the form of a Barrel or Tun , within the Concave of a fumid or smoaky Light ; which according to Seneca ( Natural . Quaest. l. 7. ) vel fertur , vel in uno loco flagrat . And to this kind is to be reduced the Meteor called Tenaculum , sub ciner●…o fumo Luridum , says Ricciolus Almag . Nov. Tom. 1. l. 8. Tun now its swoln Beams Pithetes ▪ Dilate , and then contract to narrower Streams , Like little r r Known by the Name of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , from the Resemblance it bears to a small Lock or Curle of Hair , which in Greek is 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; in Latine , Cincinnulus . Locks which in small Curles are ti'd , Bostruchias . Now like fir'd s s Manilius here describes these kind of Meteors by the Periphrasis of Hirta M●…ssis : They are commonly called Stipulae Ardentes , resembling the firing of Straw or Stubble in the Fields . Which appear ( as Aristotle says ) when the Exhalation that causes them is extended to a considerable breadth and length . sheafs , now like branch'd t t Called therefore Lampadias , imitating burning Lamps or Torches , which Manilius here divides into ●…issus Ram●…sos , branched sprayes , and are not seen but in their Fall. Of these kinds Pliny ( l. 2. c. 26. ) reports one to have appeared at Noon in sight of all the Roman People , at what time Caesar Germanicus exhibited a Prize or Spectacle of Fencers . He makes of them a double difference ; the first called Lampades , Lamps or Torches , which burn only at the Tops , though they draw a long fuming Train after them . The other called Bolides ( commonly englished Lances ) burning through the whole Extent or Length of their Train : Of which last sort ( says he ) there were some seen in the Calamity o●… 〈◊〉 when that City was sack'd . lamps descri'd , Stipulae Ardentes . Now falling u u Anaxagoras would have these kind of Meteors to be sparkles falling from the fiery Region . By Eunapius in Ae●…es . they are called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Effluentiae seu Trajectiones quaedam Stellarum ; by Aristotle 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , discursus , seu Stellae fluxus ; By the Arabs called Shihâb : which ( as I find in the Commentator upon Ulugh ●…eight Tables ) is expounded , Stella quae nocte incedit sicu●… Ignis ; and Stella Daemones pellens ; for the Antient Arabs and Ea●…ern People fancy'd falling Stars to be fiery Darts lanc'd from Heaven against the Devils or evil Spirits of the Aire , as is likewise observed by the Learned Golius ( notis in Alferganum . p. 65. ) But Fromondus ( Meteor . l. 2. c. 3. ) according to the Doctrine of Aristotle describes them to be a fiery Exhalation expulsed out of a Cloud , having the Resemblance of a true Star falling . They are conceived to come from the same Cause and Origine as Lightning , though they are not attended by Thunder , at least as to us perceivable ; Bearing the same Proportion to Lightning , as the firing of a Musquet does to that of a Canon . For as at a great distance we may see the Fire of a Musquet , but scarce hear its Noise ; but of a Canon within the same distance we may both see the Fire and hear the Noise : So by reason of the Exility of the Exhalation we hear not the Noyse when these falling Stars break from a Cloud , as we do Thunder when ushered by Lightning . Fromondus compares these Meteors to ou●… kind of Fireworks called Rockets ( though their Motions be different , the one being forced upward the other downward ) which run in a Train and fall in the manner of Stars . And therefore Pliny calls them Scintillas & Discursus Stellarum ; Ptolomy , Trajectiones ; both which our Poet expresses when he says they shoot and sparkle . Stars seem to shoot every where , Lampadias . Stella Cadens . When wandring Lights do sparkle in the Aire . And darted Flames swift x x Call'd in Greek ▪ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and from thence in the Latine Acontiae , which as Pliny says Iaculi m●…do vibrantur 〈◊〉 significatu . Of which the Emperour Titus , or ( as some will ) Tiberius , is said to have written an excellent Poem . This Meteor when it appears in a shorter form is called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Ensis Gladius , seu Pugio , the Head or Body of the Comet representing the Hilt , the Ray or Iubar , the Blade of a Sword , and appears of all others the most Pale . Arrows imitate , Acontiae . When the dry Train runs in a narrow Strait , For every Thing does mixed Fire infold ; That dwells in pregnant Clouds which Thunder mold , Pierces Earths Veins ; Heavens Terrors counterfeits From Aetna's Caves ; in Springs cold Water heats ; Lurks in hard Flints , and in green Bark finds Room , When Woods by their ( y y To this Accident Vitruvius ( l 2. c. 1. ) ascribes the Original of our Culmary Fire ; where he says , Ab Tempest●… & ventis densae crebri●…ibus A●…bores agitatae , & inter se 〈◊〉 Ramos , Ignem ex●…itaverunt . Which being observ'd by the Antients , they from thence derived their 〈◊〉 , by rubbing one stick against another , until being heated they catched Fire , which they fed by dry Leaves , and such like combu●…ible Fuel . This Part says Turnebus ( no●…is in Theophrast , de Igne ) was by them called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. F●…cus , or according to the Scholiast of Apollonius 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Strator . Which we may compare with our Tindar . The other parts which were the sticks the●… called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Terebrum ▪ and served instead of our Flint and Steel . The Trees most subject to this manner of taking Fire , are reckoned the Fig-Tree , Laurel , Oake and Ilex , the Tile-Tree , Ivy and Vine , but especially the Laurel . Coneparius de Atramentis c. 13. reckons up these several ways of generating and kindling Fire . Propagatione , Putredine , Coitione , Antispasi , Frictione , & Percussione . Which he reduces to these three kinds , Propagation , Coition , and Motion . In which the rest are included ; for Putredo , and Antispasis kindle fire by compelling the dispersed Heat to unite together , and therefore fall under the head of Coition , as Friction and Percussion under that of Motion . ) Collision flames assume ; So fertile every Matter is in fire . Nor suddain Flames breaking through Skies admire , Nor frequent Coruscations by Earths hot Exhaling Vapours in the Aire begot , Which the swift-feeding Flame pursues or flies ; Since trembling Lightning darted through the Skies , Thou mayst behold in midst of falling Rain , And Thunder through forc'd Clouds its way constrain : Whether from ( z z He resumes his former Arguments touching the Original of Comets , and begins with that of the Peripateticks , asserting ( as is before noted ) Comets to come from a sulphureous unctuous ignescent matter exhaling from the Earth and Sea , &c. Vide Aristotel . Meteor . l. 1. c. 7. and 10. ) fiery Seeds inclos'd in Earth , Their Causes farther enquired into . And thence emitted , Comets draw their Birth , Or Nature did those fading Lights design As ( a a The Opinion of Anaxagoras and Democritus ; who held Comets to be the Coapparition of wandring Stars or Planets , which when they approach near each other seem mutually to touch , and to become as it were all one ; or as Plutarch expresses it , A Conjunction of divers Stars meeting with their Lights together ; or according to Laertius , a Concourse of Planets emitting Flames . O●… which Opinion likewise was Zeno in Seneca Natural . Quaest. l. 7. c. 19. Our Zeno ( says he ) was of the Opinion of these who judged the Stars to concurr , and intermingle their Rays , and by that Society of Light to beget the Image of a long Star ; which Coll●…cency from the Conjunction of the Rays of divers Stars or Planets Manilius here calls Subjuncta Sidera . ) sub-united Stars in Heaven to shine , Or the ( b b The Chaldeans ( as Stobaeus Eclog. Physic. c. 3. delivers their Opinion ) held that there were other Planets besides those ordinarily observed , which are sometimes inconspicuous , in regard they move at a great distance above us . But now and then appear when they come nearer to the Earth , and run a lower Course ; at which time by those who know them not to be Stars , they are called Comets . Again , they seem to disappear and vanish , when they retire back into the Depth or Profundity of the Aetherial Region : As Fishes cease to be discerned when they sink down into the Bottom of the Sea. Of which Opinion likewise Seneca reckons Apollonius Mindius ; who held these to be aeterna Naturae Opera ; Or , to use Pli●…y's Words , esse Sydera Perpetua , suoque ambitu ire , sed non nisi relicta à sole cerni . Whence by Manilius they are said sometimes to be involved , sometimes dismissed by the Sun. See Ricciolus in Almagest . Nov. Tom. ●… . l. 8. and Gassendus Tom. 1. l. 5. c. 1. ) Sun 's rapid Course these Meteors rears And draws t' himself , his flames involving theirs , And now dismisses ; Like ( c c Mercury ; who because he makes a●… almost equal Course with the Sun , and ascends not ( as Aristotle says ) to any great Height above the Horizon , is therefore seldom seen . ) Cyllenius Light , Or fair ( d d Venus ; so called from her Mother Dione ; Daughter of Tethys and Oceanus : Whence that of Theocritus ( Eidyll . 15. ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Dionaea Cypris : And of Virgil. Aeneid . 3. Sacra Dionaea Matri — ) Dione's Star , Usher to Night ; Which often shine , as oft the sight delude , ( Hiding themselves ) and then again are view'd : Or God in Pity to our humane State , Sends these as ( e e The Belief of the Illiterate ; asserted lik●…wise by the Learned of divers Ages . Several of the Antient Fathers maintaining the Opinion , That Comets are made by the immediate Act and Power of God , and designed for the Terrour , D●…ruction , or 〈◊〉 at ●…ast , of the offending World , especially of Princes . 〈◊〉 of which Opinion are ●…koned Tertullian , Nicephorus , D●…scen ; and Saint A●… . Vide ●…lum A●…st . N●…v . Tem. 2. l. 8. Petit Disser●…ac . sur les C●…es , where he discourses against that Opinion ; and L'escaloperius in Ciceron . de N●…tur . Deorum , moderating the Assertion of Damascen ▪ who 〈◊〉 Comets to be sent by God as the p●…culiar ●…orerunning Signs of the Death of Kings and Potentates . ) Nuncio's of ensuing Fate , Never did Heav'n with these fires vainly burn ; Deluded Swains their blasted Labours mourn , Their Cala●… Effects . And the tir'd Husband-man to fruitless Toyl Compels his Oxen in a barren Soyl : Or the lethiferous Fire their Bodies kills , Wasting their Marrows out with lingring Ills , People consumes , whole Towns depopulates , Whilst flaming ( f f By burning of the Dead , which was customary with most Nations amongst the Antients ; especially with the Athenians , and the Greeks in general , for so says the Scholiast of Thucydides ( l. 2. ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . It was established by Law among the Athenians , and all the Greeks . The Ground 〈◊〉 Reason thereof proceeding from their Opinion , that what was Divine and Immortal in Man , was by that hery V●…iculum carried up to Heaven , and what ever was Terrestrial and Mortal , subsided in the Ashes . They did by that Means likewise as they conceived ( according to the Testimony of Psiny l. 7. c. 54. ) avoyd the 〈◊〉 of the Aire by the Putrefaction of buried Carkasses ; but especially the Injury or Ignominy which might be do●…e to the Bodies of the Dead , by taking them out of the Grave ere consumed . For which reason the Tyrant Sylla ordered his Corps to be burned , lest he might be served in the same kind as he before had served his Enemy ●…ius Marius ; whose Body he caused to be digged up and thrown into the River Aniene , ( now Teverone ) as Cacero in secundo de Legibus , and Plutarch in his Life testifies . This Custom of burning the Dead ceasing among the Romans about the Time of Maximinus the Tyrant , or not long before : It being hard to point out the Precise Time : Seeming to be abolished by the contrary Custom of the Iews and Christians , especially by the Prevalence of the lat●…er . Vide Kirkmanum de funere Rom. l. 1. c. 2. & Meursium de sunere , necnon Vales. Not. in Euseb. Histor. Ecclesi●…st ▪ l. 9. c. 8. ) Piles conclude the publick Fates . Through ( g g The Athenian Territories : so called either from Erectheus the Son of Vulcan and Minerva , Daughter of 〈◊〉 , or Cranaus , or from Erectheus Son of Pandion . Diodorus Siculus ( Bibliothec. l. 1. ) makes him to have b●… by Birth an Egyptian , and that in time of a general Famine , he brought great store of Corn from Egypt to Athens , and for that signal Benefit , was by the Athenians made their King. Herodotus ●… l. 8. ) calls him Earth-born , 〈◊〉 he says that in the Castle of Athens there was the Temple 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , of Erectheus the Earth-born ; alluding perhaps to the fabulous occasion of his Birth ( of which Apoliodorus Bibliothec. l. 3. ) Or in regard of the incertainty of his Parentage ; whence those whose Original was not known were by the Antients reputed 〈◊〉 filii . Vide Casaubon . in 6. Satyr . Persii upon these Words Terrae est jam 〈◊〉 — Eusebius in Chronic. makes him Brother to Perseus , but erroneously : Vide Scalig●…r . Animadvers . in Euseb. and 〈◊〉 de regno Attico l. 2. c. 1. and 7. ) Erecthean Lands as that ( h h He alludes to that Memorable Plague at Athens , which hapned in the beginning of the Peloponnesi●…n War ▪ of which Lucretius l. 6. — Mortifer Aestus Finibus in Cecropis funestos reddidit Agros , Vastavitque Vias , ex●…ausit Civibus Urben●… . Accurately described by Thucydides ( l. 2. ) and thence paraphrased in English Verse after the Pindarick Way , by 〈◊〉 excellent Pen of Doctor Spratt ; who for that Reason merits with Thucydides himself ( in 〈◊〉 . 〈◊〉 . ) to be stiled — Tyrannus Atticae Febris — ) Plague stray'd , i i I●… . 〈◊〉 in his particular Treause de Fo●…tuna 〈◊〉 , c. ●…o conceives the Epithete Antiquae to be here given to Athens by 〈◊〉 for distinction sake , because ( as he would have it ) that C●…ty in Man●…ius his Time ( whom he ●…iles as falsely as incons●…lerately 〈◊〉 〈◊〉 Scriptorem ) was call'd N●…vae A●…henae . This he would seem to make out from the Authority of this following In●… in Gruter●… , extant at Millan ; cited likewise by Scaliger in 5. de Emendatione Tempor . & in Animadvers . in Euseb. ad Numer . MMCXLVII . IMP. CAESAR . T. AELIUS HADRIANUS ANTONINUS AUG . PIUS . COS. III. TRIB . POT . II. P. P. AQUAEDUCTUM IN NOVIS ATHENIS COEPTUM A DIVO HADRIANO PATRE SUO , CONSUMMAVIT . DEDICAVITQ . But against this his Opinion we oppose the better Judgment of Salmasius ; who ( in Not. in Aelium Spartianum ) makes it 〈◊〉 that the Grecian Athens was never call'd N●…vae Athenae . But that that Part of it which was re-edified by Hadrian , was expresly call'd 〈◊〉 ; as is clear from the Testimony of Spartianus . Besides , Quis credat Inscriptionem Latinam in Urbe Grae●… suisse posi●…am , says Salmas●…us ? Or what Relation had the Works or Structures at Athens in Greece , to Millan in 〈◊〉 ? Quid 〈◊〉 cum Athenis ? Says S●…aliger Animadvers . in Euseb. With fairer Probability therefore conclude we ( as Salm●…sius does ) that the Novae Athenae mentioned in the foregoing Inscription was a Town so called in Liguria a Region of Italy ( which comprizes part of the Dutchy of Millan ) whereof Stephanus de Urbibus ; and that Manisius by that Epithere means no more than to set out a Matter of fact of great Antiquity without any reference to the Novel Conceit , or Nominal Dis●…inction , which 〈◊〉 fancies . Old Athens waste by k k Tan●…quil Fa●…er in his Notes upon the sixth Book of 〈◊〉 by way of Collation cites these two Verses of Manilius , thus read in the Original . Qualis Erect●…eos Pestis populata Colonos Extulit Antiquas per sunera Pacis Athenas . Which Verses he undertakes to correct or amend , but trul●…er to corrupt after this manner . Qualis Ereth●…os olim populata Col●…nos Extulit Antiquas per funera , Pestis Athenas . He confessing that he made that Alteration for this Reason , Because he never yet saw any that could understand the meaning of 〈◊〉 P●…is . But that nimble Critick might have forborn the exposing of his own or others Ignorance in that Point , and have left M●…nilius his Elegancies unbl●…mished by so rude an Interpolation ; who ingeniously uses the expression of funera P●…eis , or Peaceful funerals in Opposition to ( cruen●…a funera , or funera Belli ) those occasioned by the Sword. For as Thu●…ydides observes , the Athenians were at once doubly afflicted , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , H●…minibus inter 〈◊〉 m●…rientibus , Terrque extrà vastatâ . Which Place his Scholiast illustrates by applying this Verse of H●…mers . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Siquidem simul Bellumque domat & Pestis Achivos . Now the Mortality occasioned by the Plague , Manilius here describes by the Periphrasis of funera Pacis ; which had brought upon Athens , unconflicted by any Enemy within , a greater Destruction than the bloody Effects of War had done upon its Territories without . peaceful Funerals lay'd , When each contracted others Death ; whilst Art No Cure could find , nor Prayers no help impart ; Care to the Sick , and Funerals to the Dead , Ev'n l l Tears were a main part of Funeral Exequies , whence that of Servius in Virgil. Sine fle●…u non est Sepultura . The want of them being reckoned as unfortunate as the Deprivation of Funeral it self . Virgil ( in 11. Aeneid . ) joyns them as alike 〈◊〉 . N●… Animae viles , inhuma●…a , infletaque Turba . And O●…id ( Metamorph. 11. ) brings in the drowned C●…yx appearing , and thus speaking to his Hal●…yone : Surge , age , d●… Lacrym●…s , Lugu●…riaque indue , nec Me 〈◊〉 sub inania 〈◊〉 . Rise , weep , and put on black , nor undeplor'd , For pity , send Me to the S●…ygian Ford. G. S. The Antients believing the Dead to be comforted and delighted with the Tears of their surviving Friends . And upon this Ground it is that We meet so frequently in the Antient Epitaphs with LACRIMAS POSUIT , and CUM LACRIMIS POSUIT , and LACRIMIS ET OPOBALSAMO UDUM CONDIDIT , and TUMULUM LACRIMIS , PLENUM DEDIT . Of which Gutherius ( l. 1. de Iure Manium ) affords the Examples . Wherefore not unfitly does Manilius here , by the Defect of so mean and ordinary an Obsequie , aggravate the Miseries of a 〈◊〉 Mortality , by which Mankind is deprived of all the Resentments and Benefits of commiserating Humanity . Tears were wanting : Those no Mourners shed . The wearied Flame did from its Office cease , And Heaps of m m Thuryliles delivers the same historically . Some ( says he ) when one Body was burning , brought another , and casting it upon it went their Way . Leaving the Reliques of one fired Carkass to burn another . For as Dr. Sp●…at ingeniously paraphrases upon that part of the Story , The Woods gave Funeral Piles no more , The Dead the very ●…ire dev●…ur . A sadder kind of Funeral than that which Virgil ( Ae●…eid . 11. ) gives to the slaughtered Latines , for they had yet Wood to burn them . Caetera confusaeque ingentem Caedis Acervum Nec Numero , nec Honore cremant — Upon which last Words Gutherius observes , Nec Numero nec Honore cembusti dicuntur , qui confuso Lignorum Acervo , lento dabantur Igni , multis Corporibus simul congestis . And this by Macrobius , is called Tumultuarium funus , only used in calamitous Accidents . In which kind of promiscuous Funeral it is noted by Macrobius that it was usual to every ten Mens Bodies to add one Womans to make them burn the better . He gives the Reason likewise ; Quòd Muliebre Corpus juvabat ardentes Viros , non Caloris erat , sed Pinguis Carnis & Oleo similis . Vide Macrob. Saturn . l. 7. c. 7. fir'd Bones burnt dead Carkasses ; Whilst to so great a People scarce an Heir Remain'd . Such Woes dire Comets oft declare . They bring with them the Worlds n n Manilius here will have Comets to be the Ushers of the Worlds general Conflagration . Which Opinion seems to be grounded upon this supposition , That the Aether by reason of the long Consumption of its humid Aliment shall be then fitted for such fiery Productions ; at which time likewise the Sun and Stars having wasted all the Elementary Supplies , shall reduce the World into Flames . Being the Opinion of the Stoicks , especially of Zeno , Cleanthes , Chrysippus , and ( but doubtingly ) of Panaetius ; of which Cicero in secundo de Natura Deorum : Though the Doctrine be as antient as Heraclitus , Empedocles , and Hyppasus the Metapontine . Yet was it not by them believed that this Conflagration should bring with it a total , substantial Destruction , but rather a purifying Renovation of the World : For so Cicero delivers their Opinion where he says , Ad extremum Omnis Mundus ignescet . Ita relinqui nihil praeter Ignem ; à quo rursum animante ac Deo Renovatio Mundi fie●… , atque idem Ornatus orietur . Christian Philosophy likewise declaring not only the Worlds 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Conflagration ; but its 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Res●…itution . See Lipsius in Stoic . Phil. Dissertac . 22 , and 23. Delrius in Commentar . ad Octav. Senec. p. 533. Gassendus Tom. 1. Syntagm . Philosoph . part . 2. p. 178. and L'escaloperius in Ciceron . de Natur. Deorum . l. 2. Sect. 118. last Funeral Fire , In which sick Nature one Day must expire . Suppos'd to occasion the Worlds General Conflagration . Wars they proclaim too , Tumults to arise , And open Arms from secret Treacheries . So when the Nations late from Faith withdrew , When the fierce Germans our great o o Divers , and some eminently learned ( among whom is Sleydan de 4. Imper. Stadius in L. Florum , and the excellent Gassendus in vitae Epicuri ) conceive the Quintilius Varus here mentioned to be the same with that Quintilius Varus , of whose Death Horace in that consolatory Ode of his to Virgil ( Carm. l. 1. Od. 24. ) But since it is evident that Quintilius Varus who was General of the Roman Legions in Germany was not slain till twenty eight years after the Death of Virgil ( to whom that Ode is directed ) Virgil dying in the DCCXXXIV year of Rome , and Varus not till DCCLXII year of the same ( at which time neither Virgil nor Horace were living ) It must be against all Reason and Chronology to imagine him the same with that Quintilius Varus whom Horace there bewails . He being justlier conceiv'd to be the same with him mentioned by Eusebius in Chronic. in these Words . Olymp. CLXXXIX . Quintilius Cremonensis Virgilii & Horatii familiaris , moritur . Servius likewise stiling him 〈◊〉 Vir●… gilii , and therefore Horace makes this Particular Application of his Loss to Virgil. Multis ille quidem flebilis occidit , Nulli flebilior quàm Tibi Virgili . See Torrentius in his Notes upon that Ode , and Tanaquil Faber expresly discussing this Point . ( Epistol . 46. l. 2. ) But the Quintilius Varus here meant , was the Son of Sextus Quintilius Varus , who ( together with A●…ius Varus ) warred against Iul. Caesar , as we find in his Commentaries de bello Civili l. 2. and was flain afterwards in the Battle with Brutus and Cassius against Augustus by the Hand of his Freeman , Quem id facere ●…egerat cum se Insignibus Honorum velasset , as Velleius Paterculus l. 2. c. 71. relates . Whose Fate his Son followed though in a different Cause , Quippe , ( to use Paterculus his Words ) Paterni , Avitique Exempli Successor , se ipse transfixit . He was before the Generalship of the Army in Germany , Prefect of Syria ; Quam , Pauper , Divitem ingressus , Dive●… , Pauperem reliquit , as the same Velleius Paterculus testifies l. 2. c. 117. Varus slew , And Fields in p p Of this s●…d defeat of Quinti●… Varus , and the Roman Legions by the Germans under the Conduct of Arminius , ( occasioned by Varus his overweening confidence , who in the midst of an Em●…my Country , undertook to rule by the bare Formalities of Law , a fierce and warlike People whom the Power of the Sword could not ter●… or subdue . ) See Strabo l. 7. 〈◊〉 Paterculus l. 2. Lucius Florus l. 4. c. 12. Tacitus Annal. l. 1. 〈◊〉 in August . ) and Dion Cassius l. 56. A Disaster so resented by A●…uius that it brought him almost to despair ; who often in Passion knocking his Head against the wall would cry out , Quintili Vari , redde Legiones . Quintilius Varus , restore M●… my Leg●…ons ! The Place of this defeat Cluverius ( in Antiqu. German . l. 3. ) will have to be near the Town of Dietmel , antiently Th●…utoburgium ; for thus ( from the forenamed Authorities ) he describes Varus his March as he was train'd by the subtlety of Armini●…s from his Camp at Alizon , now Esen , towards the Borders of the Cherusci . First p●…ssing through the utm●…st Bounds of the Marsi towards a Town which now is called Teuten Meyer , he came to the Woody Hills , where is the Castle at this Day called Falkenberg : In the Vallies beneath which runs the River vulgarly called Beerlebeker Be●…k so named from the Town Beerlebek ' ; then entring the confines of the Cherusci , he was there between the said Mountains , and the Town of Theutmel or Dietmel , set upon , and his whole Army defeated and slain . Otho Frisingensis l. 3. reports this Defeat to have been given within the Territories of Ausburg near a Place where there is a Hill by some said to be raised by the heaped up Bones of the slaughtered Romans , and therefore called Perleich , quod ibi Legiones perierint : But that gross Errour is refuted by Velserus l. 1. Rerum August . Vindel. Ber●… in Sueton. affirms the Place where this Defeat was given , to be at this Day by the Germans in Memory of their Victory called 〈◊〉 , near the Town Horn in Westphalia , not far from Dietmel aforesaid . But one Place or Time was not sufficient to comprize so signal a Disaster , for the Fight ( or slaughter rather ) was continued for three days . The first Days Conflict was near the Head of Luppia , now called Lips-spring ; the second Days Discomfiture was carried more remote from thence toward the Castle of Falkenberg ; the third and final Defeat was in the Fields ( from their Victory by the Germans called 〈◊〉 ) between Horn and Dietmel before mentioned . Vide Monument . Paderbornens . p. 35. Blood of three whole Legions drown'd , Through all the Skies such Ominous Lights were found ; As if with Those warr'd Nature ; and 'gainst Ours , Threatning an End to All ; oppos'd her Powers . Nor wonder Men and States such Mischiefs grieve , The fault 's at Home ; We will not Heav'n believe . Oft Civil Wars , and Kindred Arms they raise , Nor more did Heaven with such fires ever blaze , Than when fierce Leaders joyning bloody hands Rang'd on q q He refers to the Civil Wars raised by Brutus and Cossius , who on th●…se Plains fought a desperate Battle against Augustus Caesar , wherein they both perished together with the Roman Liberty : Of which see Livy Epitom . l. 124. Plutarch ( in the Lives of Marcus Antonius and Brutus ) Lucius Florus , l. 4. c. 6. and Appian de Bellis Civilibus l. 4. These Plains were so called from the Town Philippi , heretofore called Bunomos or Bunomia , Datus and Crenides ; the last name being given it from the many Springs there rising , but afterwards renamed from Philip the Father of Alexander its Reedifier , particularly described by Appian ( loco citato ) a Place fatal to the Roman Common Wealth ; by most conceived the same with the Pharsalian Plains where Pompey received his last and fatal overthrow ; but erroneously . For those were in Thessaly near the River Pharsalus ; these in Thrace or the utmost Limits of Macedonia not far from the River Strimon . Vide Bunonem in Cluver . Introduct . Geograph . l. 4. c. 8. However the Poets generally , and Virgil himself , with our Manilius confounds them with the Pharsalian Plains ; as in this Verse in 1. Georgic . Romanas Acies iterum videre Philippi : And in complyance with that Vulgar Opinion Cabellavius in this following Epigram upon the present Subject . Pharsa●…s Ausonias frangit rursum Hasta Secures , 〈◊〉 rursum Aemathio Pulvere Roma cadit . Cred●… suum Macetum Tellus imitatu●… Alumnum : Hic Orbem , 〈◊〉 Vrbem vici●… & Orbis Heram . Once more Pharsalia routs Ausonian Bands , And Rome once more falls on Aemathian Sands . The Land sure imitates her great Son ; He The whole world vanquish'd ; the worlds Empress she . Philippick Plains confederate Bands . The Roman Souldiers on Sands yet scarce dry , Trampled fresh Reliques of Mortality . Empire , It self with its own Strength assayl'd , But Great Augustus ( Iulius-like ) r r The Memory of this Victory , which seems chiefly to be attributed to the Valour of the Praetorian Cohorts , is preserved in some an●…nt Medails , on one side whereof is the Figure of Victory standing upon a Globe , holding forth in her right Hand a Laurel Wreath with this Inscription , VICT. AUG . On the Reverse three Military Ensigns with this Inscription , COHOR . PRAET. PHIL. See Goltzius , Occo , and Patin in Numism . Imp. Rom. prevail'd . Yet ends not there : the s s The Battle of Actium was one of the most signal that ever was fought at Sea ; upon whose Success depended no less than the Empire of the whole World. The Chiefs interessed were Augustus Caesar , and Mark Anthony , abetted with all the Strength of the East and West . Plutarch reckons on Mark Antonies side no less than eleven Kings engaged , whereof six were personally present in the Action . The Battle being denominated from the Town of Actium in Epirus seated upon a Promontory of the same Name , at present call'd Capo Figalo at the Mouth of the 〈◊〉 Golf , known at this Day by the Name of Golfo de Larta ; near to which on the third of September in the 723. year after the building of Rome , ( as Brietius computes it ) the Engagement hapned . Augustus his Fle●… consisting of 400 stout Men of War , Mark Antonies being double that Number , and of much greater Burden . But by the Valour and Conduct of Agrippa the Victory after a long and dubious Dispute rested on Augustus his side ; Cleopatra first flying , and after her Antony shamefully following . See Virgil , Aeneid . l. 8. Horace Od. 37. l. 1. and Epod. 9. Plutarch in the life of Mark Antony , and particularly Fournie●… in the fifth Book of his Hydrographie , where he treats de la Puissance Navale des Anciens . p. 217 , and 218. Actian Battle 's fought ; When Armies as a fatal t t So by Sidonius Apolinaris ( in Panegyr . ad Majorian . ) the Army which Mark Anthony and Cleopatra brought against Augustus is called Dotalis Turba in this Verse , Dum venit à Phario dotalis Turba Canopo . For Anthony had promised to Cleopatra , by the help of that Army to give her the Roman Empire for her Dowry ; consirm'd by Propertius l. 3. Eleg. 11. Conjugis obscoeni Pretium Romana poposcit Moenia — And Lucius Florus l. 4. c. 11. Mulier Aegyptiaca ab ebrio Imperatore Pretium Libidinis , Romanum Imperium pe●…is , & promis●… Antonius , to which Albinovanus ( speaking of M●…aenas ) alludes . Hic modò Miles erat , ne posset Foemina Romam Dotalem stupri , turpis , habere sui . And the Authour of this Epigram ( in Catalect . Veter . Poet. ) Venerat Eoum quatiens Antonius Orbem Et conjuncta suis Parthlea Belia gerens , Dotalemque petens Romam Cleopatra Canopo , &c. Dowry brought , Once more engag'd for the Worlds glorious Prize , And sought at Sea , a Ruler of the Skies ; When Fleets did on a Womans Sway depend : u u Manilius here calls them Isiaca Sistra , the Sistrum being a kind of Musical Instrument or Crepitaculum used in the Sacrifices of Isis to whom it was sacred ; reputed to have been her Invention , and thence so named according to Isidor , or from the Greek Word , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. quatio , because it was shaken ( when play'd on ) crispante Bracchio , as Apuleius ( l. 1. Metamorph. ) describes it . It was made in form of a Racquet , of Iron , Brass , Silver , and , sometimes , of Gold ; through the Rim , Webb , or Border thereof was put several small Rods , of the same Metal with the Sistrum , on which were hung divers Rings , which , when shaken by the Handle , made a kind of gingling Noise . The Greek Poet Hedylus in an Epigram of his cited by Athenaeus , seems to derive the Invention of the Sistrum from the murmuring Sound which Milus makes passing through the Clifts and rocky Places ; touching which , see Casaubon , Animadvers . in Athenaeum , l. 11. c. 13. It is by Scaliger ( in C pam Virgil. ) and Salmasius ( in Flav. Vopisc ) confounded with the Crotalum , but erroneously , as observed by Pignorius ( de 〈◊〉 , p. 8●… . ) where the Differences are clearly stated from their contrary Figures . It was the peculiar Instrument of Aegypt : That Land being by the Prophet Esay ( c. 8. v. 1. ) according to the Interpretation of 〈◊〉 ( in G●…ogr . Sacr. l. 4. c. 2. ) called Terra C●…mbali O●…arum , i. e. Cymbali Marginati The Land of Timbrels with Rims or Borders ( to distinguish them from the Timbrels of other Countries ) and not as our English Translation reads it , the Land shadowing with Wings . Isidore yet affirms the Amazons to have used this sort of Timbrel in their Wars instead of Trumpets , as well as the Aegyptians ; and gives the Reason , 〈◊〉 〈◊〉 ejus erat Mulier ( namely Isis. ) Kirker likewise ( in Arte Magna Conson . & Disson . l. 2. ) reports the Iewish Timbrel 〈◊〉 〈◊〉 call Thoph , to have been of the same Fashion with , and made in Imitation of the Aegyptian Sistrum ; And that 〈◊〉 〈◊〉 Virgins used it in their Solemn Dances , as he proves by the Examples of Moses his Sister , and I●…phte's Daughter : 〈◊〉 thereof being yet continued in Palestine as he affirms from the Testimony of credible Witnesses , the Figure whereof 〈◊〉 〈◊〉 us correspondent to that of the Aegyptian Sistrum ; of which see more in Plutarch , ( l. de Iside & Osyride ) 〈◊〉 〈◊〉 〈◊〉 his particular Tract entitled Isiacus seu de Sistro , Dempster in Paralipom . ad Rosin . l. 2. Pierius Hieroglyp●… . l. 4. c. 6 , and 7. 〈◊〉 ●…da in 8. Aeneid . ad Vers. 696. and Kirker in Oedip. Aegypt . Tom. 1. & alibi . Nile's Timbrels 'gainst Rome's x x Tristan in his Historical Commentaries ( Tom. 1. p. 82. ) conceives by the Thunder here mentioned , some Tempest of Thunder , which he observes to have been always favourable and auspicious to Augustus , and instances particularly ( from Appian ) in the Conflict against Sextus Pompeius ; imagining the like propitious Accident to have happened in this against Mark Anthony and Cleopatra . But his Conjecture is without Ground : for the Poet intends no more in this Place than to set forth the Engagement between the Forces of Augustus under the Protection of Iupite●… Capitolinus or Tonans , the Roman Deity ; and those of Anthony and Cleopatra under the Protection of Isis , the Aegyptian Goddess . Hence that in Catalect . Vet. Poet. — Capitolino Sistra minata Iovi . And Propertius speaking of Cleopatra Lady General in the Battle of Actium , Ausa Iovi nostro latrantem opponere Anubim . Consonant to which is that of Lucan . l. 10. Terruit Illa suo , si fas , Capitolia S●…stro . Thunder durst contend . There yet remain'd the y y He calls it the Servile War , because the Forces of Sextus Pompeius were compos'd of Slaves and Prisoners which he had pick'd up to manage his Py●…atick War. ●…o this Lucan alludes l. 1. Accedant fatis , & quas premit aspera , Classes , Le●…cas , & a●…denti Servilia Bella sub Aetna . See Laurentius Abstemius Sylloge 4. V●…r . Annotat. . servile War behind ; When with his Countries Foes young Pompey joyn'd , Harrass'd those Seas his Father did defend . But this suffice the Fates ; now let Wars end ; And Adamantine Fetters Discord bind , To close Restraint eternally confin'd . Whilst Father of his Country z z Manilius ( as is well observed by Spanhemius ( in Dissertat . de Numism . ) alludes in this Place not unappositely to the Title of INVICTUS usually given to the Roman Emperors . Of whom perhaps Augustus was the first that enjoyed it . In after Times we find it frequent . Hence in the Coyns of Septimius Severus INVICTO IMPERATORI , and of Geta SEVERI INVICTI AUG . P. FIL. and of Alexander Severus INVICTUS AUG . So likewise in these Antient Inscriptions within the Territories of Verona collected by Panvinius : IMP. CAES. M. AUR. CLAUDIO P. F. INVICTO AUG . and IMP. CAES. M. AUR. MAXENTIO P. F. INVICTO AUG . Rome likewise being frequently honoured with the same Attribute , as in the Coyns of Constantinus , Priscus Attalus , Alexander the Tyrant , and Athalaricus , where we find the Inscriptions of ROMA INVICTA , and ROMA INVICTA ●…TERNA . Of which in Goltzius , Occo , Tristan , and Patin . ne're o'recome , Augustus lives ; such too beneath him , Rome . And when a God she to a Heavenly Throne Resigns Him up ; else in the World seek None . FINIS . APPENDIX . INtending the subsequent Appendix as a further Illustration of the Precedent Poem , I find my self obliged to follow the same Method which our Author himself hath laid down , and to trace him in his own steps , through the main Design of his Work ; in the very Front whereof appears , as it were lightly delineated , The ORIGINAL and PROGRESS of ASTRONOMY . Of which ere we begin to speak , it will berequisite to give some Account of its NAME . It is derived 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ▪ because it teaches the Laws and Rules whereby the Motions of the Stars are regulated and determined ▪ being anciently , by a Promiscuous Community of Denomination , called also Astrology : For what is , by Plato , call'd ASTRONOMY , is , by Aristotle and others , term'd ASTROLOGY . Thus a Thales is said first among the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , to Astrologize , who never treated of the Iudiciary Art : So to Pherecydes they gave the Title of Astrologer , though he was absolutely an Astronomer ; and the Astronomical Treatise of Phocus the Samian , which some have ascribed to Thales , bears the Inscription of Nautical Astrology . On the contrary , our Manilius inscribes his Poem , which treats ( all but the First Book ) of Iudiciary Astrology , ASTRONOMICON . But this Synonymy in after-times ceased : For this Celestial Science , known anciently in Greece by that Part of it only , which was properly call'd Meteorologick , as considering the Motions of the Stars with the Reasons thereof , came , in succeeding Ages , to receive the Addition of another Part , call'd Apotelesmatick , which teaches to divine and prognosticate from the Site and Aspects of the fixed Stars and Planets , their Influence as to the Production of future Events . And when this last became transplanted into Greece , and had there taken Root , there was given to it ( as a peculiar and distinctive Appellation ) the Name of Astrology , there being reserved to the former only that of Astronomy ; which is properly understood , and so described to be , That Science which contemplates the Motion , Distance , Colour , Light , Order , Place , Magnitude , and the like Adjuncts of the fixed Stars and Planets , without any respect to the Iudiciary Part. As Astronomy , so its Professors were doubly distinguished . Plato , in Epinomide , differences them by the Titles of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . By the first , he means those who observe the Rising and Setting of the Stars , in Order to the Prognostication of the Seasons of the Year , and Temperature of the Air ; these he calls Astronomers , according to Hesiod : by the later , he understands those , whose study is particularly confin'd to the Theory of the Planets . As to its ORIGINAL , we cannot reasonably refer it to a better Parent than Admiration . So says * Gassendus , Originem ipsi fecit Admiratio . For our Forefathers admiring the Splendour , Variety , Multitude and Magnitude of the Stars , together with their constant and regular Motion , transferred their Admiration into Observation , and that in process of time into Tables , or Parapegmata , for the Information of Posterity . And upon this Ground we may , with * Ricciolus , affirm Astronomy to be as ancient almost as the Stars themselves , and that it was first ( with other divinely infused Arts ) reduced to Experiment and Practice by Adam himself , and by his Posterity perpetuated , as we find by * Iosephus , who writes that Seth , having been instructed therein by Adam , and understanding that the World was twice to perish , once by Deluge , afterward by a general Conflagration , reduc'd this Art to an Epitome , and inscrib'd it on two Pillars ; the one of Brick , against the Violence of Fire ; the other of Stone , against the Inundation of Waters : One of which ( that is the Pillar of Stone ) he affirms to have been extant in his Time , in a Place call'd Syrias or Seirath * conceived to be the Land bordering upon Mount Ephraim , not far from Iericho . Astronomy being thus brought into the World , was cultivated and improved by the following Patriarchs , who , by reason of their long lives , had the Opportunity of observing and noting many Astral Revolutions . To which end chiefly ( according to the Opinion of some of the Jewish * Doctors ) the Prolongation of their Lives was by divine Providence in a manner miraculously extended . Among whom , in this Science the most celebrated is Enoch , whose Books upon this Subiect are said to be extant at this Day ; whence Tertullian and Origen produce several Citations . But to what Extent of Improvement this Science was brought before the Flood is uncertain . This only from the Testimony of Origen , citing the Books of Enoch before mentioned , appears , That the Stars were then reduced into Asterisms , under peculiar and distinct Denominations : Touching which Names the said Enoch wrote many secret and mysterious things . And Scripture makes it manifest , that the Year then , as now it is , was computed by 〈◊〉 Revolutions of the Moon , to one of the Sun 's through the Zodiack . For in Genesis , it is said , that Noah entred into the Ark the 17. Day of the 2. Moneth ; there is likewise express mention of the 7. and the 10. Moneth ; and that on the 27. Day of the 2. Moneth of the Year following , Noah went out of the Ark. Whence we may infer , that the Patriarchs had then the knowledge , as well of the Sun's Course as of the Moons , with their Periods , and in probability of the other Planets . And that the Opinion of those , who conceive the Year , before the Flood , to have been only Menstrual , deserves to be exploded , as most absurd and ridiculous . After the Flood , and the Dispersion of Mankind over the face of the Earth , the Study of Astronomy began to be improved by several Nations , who doubtless had derived the Knowledge thereof from Noah and his Posterity . So that it may seem no wonder , if at one and the same Time divers Persons in divers Regions applied themselves to the Observation and Study of this Astral Science . Hence arises among several Nations the Contest for the Glory and Honour of its Invention . But seeing it is clear beyond all Controversie , that Mankind issued and dispersed themselves out of Asia into Africk , Europe , and other parts of the World , the Glory thereof ought in the first Place to be attributed to the Asiaticks ; and among them chiefly to the Babylonians , Chaldeans and Bactrians . Among whom are principally celebrated Evahdnes , Belus , Zoroaster , and his Successor Otanes ; as likewise Cidenas , Naburian , Sudinus and Seleucus the Chaldean ; before whom yet is to be reckoned the Patriarch Abraham , and his Father Thare , as great Improvers of those Inventions , which had been handed down to them from their Forefathers , and the Sons of Noah . From the Assyrians and Chaldeans it came in the next Place to the Egyptians , brought thither by the Patriarch Abraham , as * Eusebius proves , from the Authority of Iosephus , Eupolemus , Artapanus , Melo and others , as cited by Alexander Polyhistor ; though Eupolemus seem to infer , that Abraham first taught the same to the Phenicians , before his Descent into Egypt . There are others yet who attribute the Honour of its Invention to the Egyptians , before the Chaldeans , conceiving that Tradition of Abraham's instructing the Egyptian Priests to be inconsistent with Reason ; since Abraham's * Stay in Egypt ( however Artapanus report it to have been 20 years ) seems not to have been above 3 Moneths ; most of which time was spent in Fears , Jealousies , and Dangers , which in all Probability would not permit him to communicate , at leisure and with freedom , the Mysteries of that sublime Science . They add further , that the Egyptians were so far from receiving the Knowledge of Astronomy from the Chaldeans , that on the Contrary , they affirm the Chaldeans to have been first instructed therein by the Egyptians . To prove which they produce the Testimonies of * Diodorus Siculus , and a Hyginus ; The former writing that Babylon was a Colony of the Egyptians , founded by Belus , Son of Libya , who therein instituted a College of Priests , who were to contemplate the S●…ars in the same manner as those in Egypt : The later reporting , that one Evahdnes is said to have come from beyond the Seas into Chaldea , and there to have taught Astronomy . But it seems strange , if this Science were known to the Egyptians , before the Babylonians and Chaldeans , that yet the Egyptian Observations should be so much later than those of the Babylonians ; for we find scarce any of the Egyptians to precede the Time of Alexander the Great his Death , than which even those of the Greeks are earlier ; whereas the Observations of the Babylonians appear to have been made almost 2000 years before that Time. Others there are who would rob both the Chaldeans and Egyptians of this Honour , and assign the Invention thereof to the Ethiopians ; of which Opinion is Lucian , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . But this Assertion seems to want much of Validity , as being opposed by the general Stream of Tradition , and that long before Lucian's Time. Nor wants Africa , besides the Egyptians , and Ethiopians , other Pretenders to the Invention of Astronomy ; particularly the Mauritanians , who are said to have been instructed therein , by Atlas ( the Son of Libya ) their King. From the several Nations before mentioned Astronomy seems to have been divided anciently into Three Principal Sects , that is to say , the Assyrian , comprehending the Babylonian and Chaldaick , the Egyptian , and the Atlantick : of which last yet the Greeks and Romans made no reckoning , for among them were only enumerated these 3 Sects , the Chaldaick , Egyptian and Grecian ; the Original and Progress of which last comes next to be described . To pass by the fabulous Age , touching which there is nothing certain , we shall only confine our Discourse to the Historical , which began with the Olympiads . Nor do any Monuments of this Later inform us , that the Greeks had made any considerable Advance in Astronomy , before the Death of Alexander the Great . For , excepting some few Observations of Eclipses , made by Thales and Anaxagoras , the rest of the Greeks imployed their Studies no further , than in nothing the Rising and Setting of the fixed Stars , and accommodating the Cycles of the Sun and Moon to the Constitution of the Civil Year ; to which end they observed the Solstices and Equinoxes : Oenopides , Cleostratus , Harpalus , Democritus , Meton , Euctemon , or Eudoxus , having not delivered to us any thing of the proper Motion of the fixed Stars , or their certain Distances from one another , nor yet ( says Ricciolus ) of the Revolutions of the Planets , or the Periods determining the Apocatastasis of the Moons Anomaly and Latitude . And yet such was their Self-conceit and Presumption , as confidently to affirm , that Astronomy ow'd its Invention to them , and particularly to the Rhodians , from whom they will have the Egyptians to have receiv'd it , as Diodorus Siculus reports in the story of the Heliadae . Others of them ascribe its Original to their Poet Orpheus . But these assertions savouring too much of the Fable , perswade us rather to conclude with the Opinion of those , who maintain Astronomy to have been first brought into Greece by Thales the Milesian , who derived it from the Egyptians . From him it was improv'd by Anaximander , Anaximenes , Anaxagoras , Democritus , Empedocles , Euctemon , Meton , Eudoxus , and others of the Athenian School , till the Time of Alexander the Great his founding the City of Alexandria in Egypt . After which the Ptolemies , his Successors , erecting there an Academy for all manner of Studies , the Grecian Astronomy made its Retreat thither , and under those Princes flourished in equal Glory with the Egyptian . From thence we hear of the famous Names of Autolychus , Calippus , Timochares , Aristyllus , Eratosthenes , Conon , Hipparchus , Sosigenes , Theon Senior , Ptolemy , Paulus Alexandrinus , Theon Alexandrinus , and his Daughter , the Excellent , but Unfortunate , Hypatia . Among the Romans it was long before it gain'd Acquaintance , or Professors . For though * Dion Prusieus affirm the Italians to have been instructed by the Pythagoreans , and that in Probability the Doctrine of Philolaus , Timaeus , Archytas and others ( the fame of whose Learning invited even Plato himself to make a voyage into Italy ) could not be concealed from the curious and ingenious Spirits of Rome : Yet that Martial City being more addicted to Arms than Arts , slowly entertained , these kind of speculative Studies . And therefore ( to pass by the rude Essays of Numa Pompilius ) we find in the Roman Stories no Mention of any Persons considerably knowing therein , before Cains Sulpicius Gallus , who was Legate to Aemilius Paulus in the War against Perses King of Macedon , who first among them published a Discourse of Eclipses . After him we hear of Lucius Taruntius , Nigidius Figulus , Varro , and Cicero , who applied themselves to the Study of Astronomy ; But to none of the Latines is that Science so much indebted as to their Great Dictator C. Iulius Caesar , who — media inter Praelia semper Stellarum , Coelique Plagis , Superisque vacabat . He with the assistance of Sosigenes , the Egyptian , reduced the Roman Year to the Course of the Sun , which we yet retain , and wrote , in Greek , of the Stars . From him Mathematical Arts , and particularly Astronomy , began to flourish among them ; his Nephew and Successor Augustus , by his Example encouraging the same . In whose Reign our Manilius wrote this his Astronomical Poem . And thus having clearly and concisely , to Manilius his Time , deduced the History of Astronomy from its Original , I conceive it may serve as a competent Illustration of his Proemial , but brief Indication of the first Rise , Authors , and Promoters thereof . To continue the Progress thereof down to these Times in the same Series of Discourse would perhaps be both tedious and unsatisfactory . I have therefore chosen for the better Information ( and it may be Delectation ) of the more Inquisitive and Ingenious Lovers of these Studies , to collect a Catalogue of the most Eminent Astronomers , as well Antient as Modern , their Works and Writings , according to the Succession of Time from the first Birth of Astronomy to this present , whereby the Curious Reader may perceive , when , how , and by whom it hath been improved to that Degree of Perfection wherein it now stands . A CATALOGUE Of the most Eminent ASTRONOMERS , Ancient & Modern . ASTRONOMERS before our SAVIOUR's Nativity . ADAM , the first Authour of Astronomy , as of all other Arts and Sciences , according to Suidas ; 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Hujus sunt omnia inventa omnésque Doctrinae . That he particularly instructed Seth in this Astral Science , and that by writing , is the opinion of the Iewish and Arabian Doctours , and , among them , expressly of Gelaldinus Arabs , cited by Kircher in Obelisc . Pamphil. pag. 5. the Book which goes under the title of Liber Creationis , being own'd for his , and commented upon , as such , by Rabbi Abraham , and Rabbi Ioseph Ben Uziel ; but how far to be credited , see Bangus , Exercit. Literar . pag. 4. SETH , the son of Adam , inscrib'd on two Pillars , one of Brick , the other of Stone , the Theory of this Celestial Science , received from his Father , and afterwards by that means perpetuated by Cainan , Mahaliel , Iared , &c. unto Enoch . ENOCH , the seventh from Adam , wrote of Astronomy , and particularly of the Number and Names of the Stars , and their secret Vertues ; the Book reported to be yet extant in the Territories of the Queen of Sheba , as Vossius , De Scientiis Mathemat . affirms . CHAM , the son of Noah , by some conceived the same with the first Zoroaster , by others taken for Menes , or Osyris the first King of Egypt , is famed for his skill in Astronomy , which yet he is said to have contaminated by the addition of divers Magical arts . NEBROCH , or NEMBROTH , or NIMROD , the son of Ch●… , the son of Cham , and the first King of Babylon , is reported to have writ some things in Astronomy and Astrology , as Simler affirms in Biblioth . Gesner . BELUS the Assyrian , King of Babylon , by Pliny ( l. 6. c. 26. ) stiled The Inventor of the Science of the Stars , to whom Semiramis his Daughter erected a Temple in the middle of Babylon , of an exceeding Height , by the Help whereof the Chaldeans , who addicted themselves there to Contemplation of the Stars , did exactly observe their risings and settings : of which Diodor. Sicul. l. 2. ABRAHAM the Patriarch , instructed by the Posterity of Noah , ( from whom he was the tenth , as Noah was from Adam ) taught this Knowledge to the Phoenicians and Egyptians , as Eusebius attests . He is said to have inscribed on two Pillars ( as Seth before had done ) whatever related to the Astronomical Science , as Ranzovius from the Authority of Marianus Scotus affirms in Catalog . Astronom . ZOROASTER , called PERSO-MEDUS , the first of the Magi , and a most knowing Astrologer , besides four Books , De Naturâ , left five others of Predictions , Ex inspectione Stellarum , as Suidas testifies in Voce 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which yet by G. Vossius are supposed not to be authentick , De Scient . Mathemat . p. 371. COELUS , the most ancient of the Ethnick Gods , by the Greeks called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which name he acquired by his continual Observations of the Heavenly Bodies . His sons were Saturn , Hyperion , Iapetus , &c. HYPERION , the son of Coelus , is said to have demonstrated the Course of the Sun and Moon , and thence the people took occasion to call his Son , Helius , and his Daughter , Selene , as Diod. Sicul. l. 3. affirms . MOSES , by Extraction a Chaldean , by Birth and Education an Egyptian , the Great Legislator of the Iews , and first truly Divine Philosopher , is not to be omitted in this Catalogue of Astronomers ; for Philo Iudaeus , in his life ( l. 1. ) affirms , That he received from the Assyrians the Chaldaick Learning of the Stars , and Knowledge of the Heavens ; In which likewise he improved himself from the Doctrines of the Egyptians , chiefly addicted to Mathematical Studies . ATLAS , King of Mauritania , inventor of the Sphere , and therefore by the Poets feigned to have supported Heaven . PROMETHEUS , Brother to Atlas , instructed the Assyrians in Astronomy , making his Observations on Mount Caucasus , with that assiduous care and sollicitous study , as gave occasion to the Fable of his being tortured by a Vultur feeding on his Liver . HERMES , called likewise THEUT or THOTH , and MERCURIUS TRISMEGISTUS , a great Propagator of Astronomy among the Egyptians . Something bearing his name was printed at Norimberg 1532. His Books called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 did treat 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , as we find in Eusebius ; and Iamblicus , ( out of Chaeremon ) speaks of other his Writings upon the same subject . ENDYMION , a curious Observer of the Moon 's motion : which on Mount Latmus he used to contemplate , and for that cause was fabled to have been her Paramour . BELLEROPHON , Son of Glaucus , Prince of Corinth , who is fabled to have backed Pegasus the winged Horse , and soared up to Heaven , is by Lucian , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , reputed a great Astronomer ; for thus he writes of him . I believe not at all ( says he ) the Story of his winged Horse . But this I conceive of him , that he being much addicted to Astronomical Contemplations , and conversant in the Observation of the Stars ( 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ) was carried up to Heaven not by a Horse , but by his Mind . CEPHEUS , King of Ethiopia , a Royal Promoter , and Advancer of Astronomical Studies , of whom we have already made mention in our Notes upon the Constellations . HERCULES , called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , or Musarum ductor , to distinguish him from the other Hercules , was so well learned in the Doctrine of the Sphere , that he is therefore feigned to have eased Atlas of his burthen ; whence Ovid , Hercule supposito Sydera fulsit Atlas . ATREUS , Brother to Thyestes , King of the Argives was , according to the testimomy of Lucian , ( 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ) an excellent Astronomer . For when the Argives by publick consent had decreed , That the Kingdom should be given to him of the two who should manifest himself the most learned in the knowledge of the Heavens ; Thyestes is thereupon said to have made known to them the Constellation in the Zodiack called Aries . But Atreus discovered to them the course of the Sun , with his various rising and setting , demonstrating his Motion to be contrary to that of the Heavens ; Whereupon they elected him to be their King. PALAMEDES found out many Observables concerning the Stars , their Measures , Distances , and Motions , as we find exprest in Sophocles . SOLOMON , King of Israel , besides his other divinely infused knowledge , was excellently skilled in the course of the Heavens , and order of the Stars , as it is said of him , Wisdom , chap. 7. v. 19. NUMA POMPILIUS , second King of the Romans , first Authour of the Roman year , which he so disposed ( to the end the Lunar might agree with the Solar year that every four years there was an Intercalation of 45 Days , which he divided and adjusted after this manner , adding to the first 2 years 22 Days , and inserting in the latter 2 years 23 Days . Vid. G. Voss. de Scient . Math. NECEPSO , though but a petty Prince of some part of the lower Egypt , was one of the greatest Instauratours of Astronomy in that Nation , and brought into practice and publick use , whatever Thoth , or the first Mercury had invented , or Siphoas , Son of Vulcan , the second Mercury had deposited in writing in the private Archives of their Temples . In which Writings of Mercury were contained ( besides Hieroglyphicks and other sacred Ceremonies ) Cosmography , Geography , the course of the Sun and Moon , and of the other five Planets ; as Clem. Alex. Strom. l. 6. testifies . PETOSYRIS , an Egyptian Priest , and Philosopher , wrote , according to the testimony of Suidas , of Astrology , collected out of the Sacred Books of the Egyptians , which he dedicated to Necepso , one of the Egyptian Kings immediately before mentioned , yet extant ( as Simler , in Biblioth . Gesneriana , affirms ) in Biblioth . Carpensi & Sancti Angeli . PHOCUS SAMIUS wrote de Astrologia Nautica , as Diog. Laertius testifies . This Phocus is conceived to be the same to whom Solon inscribed a Poem , as Plutarch writes . THALES , the Milesian , one of the Greek Sages , first Introducer of Astronomy among the Greeks . He first observed the apparent Diameter of the Sun to be the 7●…0 th part of the Orb in which he moves ; first found out , or at least denominated the Constellation of the Lesser Bear , and first foretold Eclipses , particularly that memorable one , happening in the time of the Battle between Halyaties King of Lydia , and Astyages King of Media , recorded by Herodotus . He first divided the Celestial Sphere into five Zones , and composed two Treatises , the one of the Trepicks , the other of the Aequinoctials , therein asserting the obliquity of the Zodiack , and distinguishing the Seasons of the year ; and measured the height of the Egyptian Pyramids by their shadows . OENOPIDES , the Chian , is highly commended by Plato , Proclus , and Theon Smyrnaeus , for his eminent Knowledge in Astronomy ; Eudemus asserting him to have first found out the Obliquity of the Zodiack . Aelian , in his Various Histories ( lib. 10. c. 7. ) reports , that he set up a Brass-Table at the Olympicks , having written thereon the Astronomy of LIX . years ; within which Term or space he comprized the Great Year , or the Annus magnus vertens . ANAXIMANDER , Country man , Companion , Kinsman , and Disciple to Thales , first asserted the Moon to receive light from the Sun , yet withall affirming that she hath a light of her own , but very thin . He first erected a Gnomon at Sparta , to discover by the shadow of the Sun the times of the Solstices and Equinoxes . The invention of the Zodiack's Obliquity , is likewise attributed to him . HYSTASPES Son of Arsames , or Arsa●…es , King of Persia , and Father of Darius ; of whom thus , Ammianus Marcellinus ; ( l. 24. ) Hystaspes was a most Wise Person , who boldly penetrating into the Inner Parts of upper India , came to a woody Desert , whose calm Silence was possest by those high 〈◊〉 the Brach 〈◊〉 . Of these he learnt the Discordant Concord of the Motions of the St●…rs , and ●…f Heaven ▪ and of pure Rites of Sacrifice , which , returning into Persia , he contributed as 〈◊〉 Addition and complement to Magick . CLEOSTRATUS , the Tenedian , is said first to have studied the Parts , or Division of the Zodiack , and noted the Commencement of the Sign Aries and Sagittary . He invented a Luni-Solar Cycle , consisting of eight Solar years , thence called Octaëteris , in lieu of the Tetraëteris , which the Greeks before used , touching which see Ricciolus Almagest . l. 4. c. 19. ANAXIMENES of Miletus , Friend , Disciple , and Successour to Anaximander , first demonstrated the Eclipse of the Moon to be by the Earth's Interposition between Her and the Sun , and maintained the Stars to move , not only above , but about the Earth . HARPALUS corrected the Octaëteris of Cleostratus , according to whose opinion , at the expiration of every ninth year , the New Moon returned again at the same hour , unto the same point of the Heavens , in which it was nine years before ▪ But this Cycle , proving erroneous , was afterwards corrected by Me●…on . PYTHAGORAS , the Samian , travelled into Egypt and Chaldaea , to improve himself in the study of Philosophy and Astronomy . He first discovered , that Lucifer and Hesperus ( believed before to be two several Stars ) were but one and the same , being the Planet Venus . The invention of the Zodiack's Obliquity is likewise ascribed to him . He first gave to the World the name 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , from the order and beauty of all things comprehended in it ; asserting the same to be made according to musical proportion ; and the seven Planets to have an harmonious motion and Intervals correspondent to musical Diastemes . He held the Sun ( by him and his followers termed the fiery Globe of Unity ) to be seated in the midst of the Universe , and the Earth to move about it . ALCMAEON , of Crotona , son of Perithus , Disciple to Pythagoras , a Physician and Physiologist , asserted that the Planets held an opposite course to that of the fixed Stars , as Plutarch affirms , Plac. Philosoph . l. 2. c. 16. ANAXAGORAS CLAZOMENIUS , Disciple to Anaximenes , held the Moon to be a dark Body enlightned by the Sun , and to be habitable , having Plains , Hills , and Waters , as the Earth hath . DEMOCRITUS , of Abdera , Disciple to Anaxagoras & Leucippus , wrote of the Sun and the Moon and the other Planets , of the Annus Magnus , and Astronomical Prognosticks . Of which Pliny , Hist. Nat. lib. 18. cap. 35. and the Scholiast upon Apollonii Argon . lib. 2. cites him 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Laertius mentions his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , sive 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . EMPEDOCLES , who studied under Parmenides , Pythagoras , & Anaxagoras , wrote ( besides his other Pieces of Philosophy ) of the Sphere , in Verse , yet extant ; though the same , by some , be ascribed , not to him , but to Demetrius Triclinius . TIMAEUS LOCRUS , a Pythagorean Philosopher , wrote de Naturâ Mun●… ▪ from which Piece Plato borrowed the greatest part of his Dialogue entituled 〈◊〉 , in the beginning whereof he commends Timaeus , as most knowing and 〈◊〉 Astronomy . METON , an Athenian Astronomer , observed , with Euctemon , the Solstices , and instead of Cleostratus's Octaeteris , introduced a Novendecennial Cycle , called Meton's Cycle , or the Golden Number . HIPPOCRATES wrote of judging of Diseases by the Rules of Astronomy , which by Gesner is said to have been published by Ioannes Ganivettus , at Lyons , in the year 1508. an imperfect MS. Copy whereof is now extant in Gonvil and Caius College in Cambridge . EUCTEMON observed , at Athens , the Solstices 108 years before the death of ▪ Alexander the Great ; see more of him in Pliny , Hist. lib. 18. PHILOLAUS , of Croton , a Pythagorean Philosopher , maintained the opinion of the Earth's motion about the Sun. Of which sentiment was likewise Seleucus , Cleanthes Samius , Leucippus , and Ecphantus , as also HERACLIDES PONTICUS ; who wrote ( as we find it cited by Chalcidius , in Timaeum ) of the Planetary Spheres , or Circles , conceived by M●…ursius , to be that Piece of his , which bears the Title 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which he inscribed to Democritus , as Laertius affirms in his Life . There is also another 〈◊〉 mentioned by the same Laertius , who writ De Astrologia . PLATO , the Divine Athenian Philosopher , travelled into Egypt , under pr●…tence of selling Oyl , but indeed to fetch from thence a far more noble Merchandise , Astronomy ; informing himself by their Priests of the Celestial motions ; and hath , in his Timaeus , Epinomis , and other his Dialogues , left sufficient testimonies of his improved knowledge , treating therein of several Parts of Astronomy , and particularly of the Celestial System . THEAETETUS ATHENIENSIS , Disciple to Socrates , and a familiar Friend of Plato's , a Philosopher and Astrologer , as Suidas affirms , who yet gives us no account of any Writings of his in Astronomy . HERMES AEGYPTIUS , Disciple to Plato , writ De Sole ; De Imaginibus Martis ; De Imaginibus Iovis ; De Imaginibus Saturni ; De Septem Annulis Planetarum ; De Medicinis & Conjunctionibus Planetarum . To him likewise is attributed the Book , De duodecim Herbis duodecim Signis attributis , & aliis her●…is septem Stellis dicatis ; as Simler . in Biblioth . Gesner . ARCHYTAS TARENTINUS , a noble Pythagorean Philosopher , Mathematician , and Cosmographer , whom Horace calls — Maris ac Terrae , numeróque carentis Arenae Mensorem . — He wrote several Works ( though none of them have been so happy as to escape the injury of Time ) both Physical , Moral , and Mathematical ; particularly ( to instance only what is pertinent to our subject ) a Tractate , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , De Universo , cited by Simplicius in Aristot. Categ . as noted by Meursius , in Hesych . De viris illustribus . HELICON CYZICENUS , a familiar Friend of Plato's , and an eminent Astronomer , who having foretold to Dionysius the Tyrant an Eclipse of the Sun ( which hapned at Athens 3 0 Sept. feria 6 ta hora 9. ¼ post mediam Noctem ) was , for that , rewarded by him with a Talent of Silver . PHILOSOPHUS , one of Plato's Disciples , so called by his proper name , wrote of Eclipses , of the distance and magnitude of the Sun , Moon , the Earth , and the other Planets , as also of Lightnings , and several other Pieces , mentioned by Suidas . Gesner is of opinion , his name might be corrupted , and that it ought to be read Philippus Opuntius . EUDOXUS CNIDIUS , the Son of Aeschines , instructed by Archytas , in Geometry ; in Physick , by Philistio , the Sicilian ; in Philosophy , by Plato ; travelled into Egypt , and of the Priests there learned the proper motions of the Planets , which he first communicated to his Countrymen the Greeks . He wrote De Mundo , De Coelestibus , De Phaenomenis , Astrological Fasti , with Prognosticks . He reformed the Octa●…teris of Harpalus , and introduced a new one of his own ; of which yet others make Dositheus the Authour . He wrote likewise an Astronomical Poem , as Suidas affirms . But his two most celebrated Pieces were his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 seu Speculum , & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , sive Apparentium , as Hipparchus ( in Arataeis ▪ ) witnessess . He is reported to have been so greatly enflamed with the love of Astronomy , that he usually professed he would willingly ( as the Poets fable of Phaeton ) perish by the scorching beams of the Sun , provided he might first approach so near it , as clearly to discern its Figure and Magnitude . G. Voss. XENOCRATES CHALCEDONIUS , a Platonick Philosopher , writ , among divers other Works , one Book , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , De Intervallis , and six Books , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , De his quae circa Astrologiam versantur , as Laertius in his Life . There is likewise a Piece under h is Name , De Influentia Planetarum in Corpora ; mentioned by Iac. Phil. Thomasinus among the MS. of Io. Rhodius ( in Bibliothec. Patavin . ) DEMOPHILUS , son of Ephorus , according to Gesner , writ certain Pieces , called Astronomica ; And his Apotelesmata , as Labbeé reports , are in the French King's Library . CALIPPUS CYZICENUS , an eminent Philosopher , of whose Systeme of the Celestial Sphere Aristotle makes mention , in his Metaphysicks . He was Authour of a Luni-Solar Cycle of LXXVI . years , consisting of four Metonick Cycles reformed . ARISTOTLE , besides his other learned Works in Philosophy , hath left several testimonies of his study in Astronomy , particularly in his Book De Coelo . He left likewise a Book entitled 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , as Diog. Laertius testifies in his life . There is likewise a Treatise under his Name , De Astrologia Navali , extant in MS. in Bibliothec . Sancti Ioannis in Viridario Patav. as Thomasinus in Bibliothec. Patavin . attests . THEOPHRASTUS , of Evessus in Lesbos , a great Philosopher , Disciple and Successour to Aristotle in the Lycaeum , wrote six Books of Astrological History , and particularly of Democritus's Astrology . EUDEMUS of Rhodes , one of Aristotle's Disciples , in emulation of Theophrastus , wrote likewise some Astrological Histories , in which he described the Lives and Inventions of divers Astrologers and Astronomers , together with the Original and Progress of Astronomy , as Clemens Alexandrinus , and Laertius affirm ; and from them Ionsius , lib. 1. cap. 15. De Script . Histor. Philosoph . ARISTYLLUS was Contemporary with Calippus , and , together with Timochares , observed the Declinations of the Fixed Stars mentioned by Ptolemy in Magn. Construct . as also in the Greek Prolegomena to Aratus , where we find several others of the name famous for Astronomy . AUTOLYCHUS PRYTANAEUS , Tutour to Arcesilaus , left two Books , yet extant ; the one , De Sphaera Mobili , the other , Of the Rising and Setting of the Fixed Stars , some parts whereof are translated by G. Valla. The former published by Mersennus according to the Translation of Maurolycus , and the Propositions illustrated , in Synops. Mathemat . TIMOCHARES the Astronomer , ( as may be collected out of Ptolemy's Almagest . lib. 7. c. 2 , & 3. ) observed the Fixed Stars , and particularly , one of the eight Stars in the Constellation of Lyra ; mentioned by Theon upon Aratus . MANETHO , an Egyptian Priest at Heliopolis , and Notarius Sacrorum Penetralium per Aegyptum , writ Physiologica Apotelesmatica , in Verse , and other Astronomical Pieces , as Suidas attests , and may be proved from this Verse of 〈◊〉 . — Arati numeros , & picta Manethonis Astra . His Apotelesmaticks are reported to be yet extant in the Florentine Library , by Simler . in Biblioth . Gesner . ERACUS ASTRONOMUS is said to have written something in Astronomy , about the time of Ptolemaeus Philadelphus , as Gesner testifies . ARISTARCHUS SAMIUS , following the Opinion of Pythagoras and Philolaus , maintained the Earth to move about the Sun. He wrote a particular Treatise of the Distances and Magnitudes of the Sun and Moon , yet extant , translated and commented upon by Commandinus , with some Explications of Pappus Alexandrinus , and animadverted by Mr. Forster , in his Miscellanies . There is another Piece which goes under his Name , of the Mundane Systeme , its parts , and motions , published in Latine by Robervalle , and Mersennus in his Mathematical Synopsis . But the same , by Menagius , ( in Diog. Laert. ) and Descartes , in his Epistles , is censured as a supposititious Piece of Robervalle's , and not the genuine Work of Aristarchus . ARATUS SOLENSIS , at the Command of Antigonus Gonatas , turned into a Greek Poem the Phaenomena of Eudoxus , translated into Latine Verse by Cicero , Germanicus Caesar , and Avienus , and commented upon , by the several Commentatours hereafter mentioned , as they are cited at the end of the Prolegomena in the Edition of Iunta , in folio . AGESIANAX , ALEXANDER AETOLUS , by Strabo likewise reckoned , inter Homeri Interpretes . ALEXANDER EPHESIUS , ( of whom hereafter more particularly . ) ANTIGONUS GRAMMATICUS , APOLLONIUS GRAMMATICUS , APOLLONIUS GEOMETRA , ARISTARCUS GRAMMATICUS , ARISTARCHUS SAMIUS , ARISTOPHANES , ARISTYLLUS GEOMETRA Major , ARISTYLLUS GEOMETRA Minor , ATTALUS RHODIUS , BOETHUS , CALLIMACHUS CYRENAEUS , CALLISTRATUS TENEDIUS , CRATES , DIDYMUS GNIDIUS , DIDYMUS PONEROS , five Laboriosus . DIODOTUS , perhaps the same with him mentioned by Alexander Aphrodisaeus in the first Book of his Commentaries in Meteor . Aristot. by whom he is stiled a most learned Astrologer . EVAENETUS , HELIODORUS STOICUS , HERMIPPUS , NUMENIUS GRAMMATICUS , PARMENIDES , PARMENISCUS GRAMMATICUS , mentioned by Hyginus and Pliny . PYRRHUS MAGNESIUS , SMINTHES , THALES , TIMOTHEUS , ZENO . There are some few others who have likewise commented upon Aratus , the Mention of whom the Reader will find elsewhere in this Catalogue . ERATOSTHENES , a Native of Cyrene , succeeded DEMETRIUS PHALEREUS in the charge of the Alexandrian Library . He wrote 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , being a Comment on the several Asterisms of Aratus , lately printed ; ( perhaps the same with that Piece which is cited under the Title of Astronomica , by Suidas , Plutarch . de Placit . Philosoph . Hipparchus , Ptolemy , and Proclus in Timaeum ) Of the Zones , and of the measure of the Terrestrial Globe . He caused likewise several Armillae , and other Mathematical Instruments to be placed in a publick Portico , at Alexandria , for observation of the Celestial Motions . He was a most skilful Geometer , and writ a Treatise de Medietatibus , mentioned by Pappus in his Mathematical Collections , not now extant . BEROSUS , the Chalaean , of whom Iosephus ( l. 1. Antiqu. Iudaic. c. 8. & in l. 1. contra Appian . ) writes , that he was , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , &c. Most celebrious among those conversant in the study of Astronomy , and the Philosophy of the Chaldeans , of which he published Books among the Grecians . He flourished in the time of Antiochus Soter , and hath left it recorded , that , among the Chaldeans , he observed Astronomical Ephemerides of 480. years , inscribed on baked Bricks or Tyles . He is said likewise to have invented divers kinds of Sun-Dyals , and , for the certainty of his Predictions , to have been rewarded by the Athenians with a Statue , having a golden Tongue in its mouth . APOLLONIUS MYNDIUS , by Seneca ( Natur. Quaest. lib. 7. ) stiled peritissimus inspiciendorum naturalium , travelled into Chaldea , to be instructed in Astronomy , and wrote particularly , De Cometis . EPIGENES BYZANTINUS , Contemporary and Partner in Study and Travels with Apollonius , by Pliny ( lib. 7. c. 56. ) joyned with Berosus and Critodemus , and reputed to have been an Authour of equal credit with the best , hath left it recorded , that , among the Babylonians , there were found Ephemerides , containing the Observation of the Stars , for the space of 780. years , inscribed in Brick and Tiles . He wrote likewise , as Seneca affirms , Of Comets . ARCHIMEDES of Syracuse , famous , besides his other Mathematical Works , for his admirable artificial Sphere of Glass , wherein the Motions of the Sun , Moon , and the other Planets were represented , to the astonishment of the Beholders , celebrated by Claudian in a particular Epigram . In his Book entituled 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ( sen Arenarius ) he examines divers Astronomical Hypotheses as to the Distances of the fixed Stars , of the Diameters of the Earth , Sun , Moon , and other Planets , according to the opinions of Aristarchus Samius , Eudoxus , and others of the Ancient Astronomers , being commented upon by Paschasius Hammel , Rivaltus , and Mersennus . The Lemmata of Archimedes recovered out of the Rubbidge of Antiquity were published in M r. Forster's Miscellanies , as likewise by Borellius at the end of the three latter Books of Apollonius . CONON , an excellent Geometrician and Astronomer collected divers Observations made by the Chaldeans , of the Solar and Lunar Eclipses , wrote six Books of Astrology , ( not now extant ) and invented the Constellation called Coma Berenices . Celebrated he is by Pliny and Hyginus : C. SULPITIUS GALLUS , a Roman Tribune , by his skill in Astronomy , much encouraged the Roman Army in the War against Perses . For when the Souldiers were terrified with the Eclipse of the Moon , by his Oration to them he made it appear , that what they apprehended as a Prodigy , was only the effect of a natural Cause , describing to them the Reasons of the Eclipse ; and so animated the drooping Army with fresh courage , to the attaining of a glorious Victory . HIPPARCHUS , ( by the Arabs and Eastern Writers called Abrachys ) whom some make a Native of Nice , a City in Bithynia ; others , a Rhodian , Prince of Astronomers in his time . He wrote a Catalogue of the fixed Stars , several Observations of the Aequinoxes , mentioned by Ptolemy ; of the Moon 's monthly motion , according to Latitude ; A Collection of divers Observations of the Chaldeans , touching Eclipses , by him examined and compared . Chalcidius , in Timaeum , cites a Book of his , De Secessibus atque Intervall is Solis & 〈◊〉 ; which Me●…rsius ( Not. in Chalcid . ) conceives to be the same mentioned by Poppus ( in 5. Syntax . Ptol●… . ) under the title 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. De Magnitudinibus & Distantiis . He hath left likewise ( yet extant ) three Books , by way of Comment upon Aratus , in which he shows Aratus to have taken all from Eudoxus , and to have followed him even in his Errours ; first published from a Manuscript in the Medicaean Library by Petrus Victorius , and since in Greek and Latine , by Dionysius Petavius in Uranolog . NIGIDIUS FIGULUS wrote a Comment , De Sphaera Graecanica & Barbarica , mentioned by Servius , in Georg. Virgil , whence the Commentatour in Germanici Arat. cites divers particulars . L. TARUNTIUS FIRMANUS a familiar Friend of Varro's , and a great Astronomer . He calculated the Nativity of Romulus , and the Horoscope of Rome's foundation , and wrote , in Greek , of the Stars . He is mentioned by Cicero and Plutarch , though with some small variety in the writing of his name . MARCUS VARRO , the most learned of his time among the Romans , wrote of Astronomy , of which Cassiodorus makes mention , in Mathem . Discipl . GEMINUS , a Native of Rhodes , wrote an Isagoge in Meteora , and in Arati Phaenomena ; out of which Proclus's Sphere is for the most part compiled , published by Petavius , in Uranolog . POSIDONIUS APAMENSIS SYRUS , a Stoical Philosopher , Disciple , and Successour to Panaetius , observed , at Rhodes , the Star Canopus . He is commended by Cicero , for an Artificial Sphere , by him made , representing the motions of all the Planets . Laërtius mentions a Book of his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , De Meteoris ; and another 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . And Labbeé , in his Catalogue of Manuscripts , mentions another Piece of his , Of the Original of Comets , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , extant in the French King's Library . M. TULLIUS CICERO translated the Phaenomena of Aratus into Latine Verse . THEODOSIUS TRIPOLITA signalized his name by his three Books Sphaericorum , and his twelve Propositions , De Habitationibus , both published by Mersennus , in his Synopsis Mathemat . He wrote likewise De Diebus & Noctibus : and Sceptica capita Astrologica , as cited by Laertius . JULIUS CAESAR , first of the Roman Emperours , according to the testimony of Pliny , wrote of Astronomy in Greek ; Macrobius affirming likewise , that he left several not unlearned Books of the motions of the Stars , which he derived from the Doctrine of the Egyptians . SOSIGENES , a famous Astronomer of Alexandria , whose assistance Iulius Caesar made use of , in reforming the Roman year , and reducing it to the course of the Sun , which we yet retain . Of this Argument he writ three Discourses , as Pliny witnesseth , lib. 18. c. 25. DIONYSIUS AFER , called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Geographus , wrote a Greek Poem ▪ De situ Orbis . He was sent , by Augustus , before his adopted son Caius , into the East , the better to describe to him those Regions and Provinces . ALEXANDER EPHESIUS , surnamed LYCHNUS , wrore besides his Historical Pieces , an Astronomical Poem of the Heavens , and another of the Description of the Parts of the Earth . He is mentioned by Strabo , lib. 14. and therefore cannot be less ancient than these times . He wrote likewise a Comment , in Arati Phaenomena . P. OVIDIUS NASO , the most Ingenious of the Latine Poets , besides that he translated Aratus his Phaenomena into Verse , which is lost ; hath leftfix Books , De Fastis Romanorum , yet extant , being a Calendar , describing their Year , Moneths , Festival Days ; together with the rising , and setting of the several Constellations , and the most noted of the fixed Stars ; dedicated by him first to Augustus , afterwards revised in his Exile , and addressed to Germanicus Caesar. STRABO , the Geographer , hath left us the Description of the World in seventeen Books , wherein there are divers Astronomical Disquisitions . ARTEMIDORUS COSMOGRAPHUS was Contempora●…y 〈◊〉 Strabo , and wrote upon the same Subject . MARCUS MANILIUS wrote five Books of Astronomicks , ( 〈◊〉 Heroicis non contemnendis , sayes Ricciolus , in Chron. Astronom . ) which he dedicated to Augustus Caesar , wherein he comprehended as well the Astronomy , as the Astrology , of the Ancients , according to the Doctrine of the Chaldaeans and Egyptians ; the first of which five Books , treating of the Sphere , is the Subject of our present Undertaking . The few following Authours , not being reducible to the certain time wherein they flourished , either before or after our Saviour's Nativity , are , for want of authentick Testimony , in this place , ambiguously inserted . BOLUS MENDESIUS , a Pythagorean Philosopher , wrote ( among other things ) de Signis ex Sole & Luna , & Ursa , & Lucerna , & Arcu Coelesti , as Suidas testifies in voce 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . LASBAS BABYLONIUS wrote of Astronomy , in a Book entituled Selech , cited by Iohannes Camaterus , in Opere Astrologico , especially in the Chapter De Canonibus Astrorum , & Sorte Fortunae ; extant in Manuscript , in the hands of my worthy Friend , M r. Thomas Gale. ZEUCHRUS , or TEUCHRUS , or TEUCER BABYLONIUS , by Scaliger , in Manilium , and Salmasius , De Annis Climactericis , stiled an ancient Authour , wrote , De Decanis Signorum ; some Fragments of his , according to Labbeé , being extant in the French King's Library . ALBU-BATUR is , by Iunctinus , placed in the Catalogue of Astronomers about the 500. year before Christ ; he writ De Nativitatibus , Printed at Noremberg by Iohannes Petreius , in the Year 1540 , but wanting good Authority to confirm the Time wherein he flourished , We have rather inserted him in this Place . PAPYRIUS FABIANUS , is mentioned by Pliny in several places of his Natural History , out of whose Works he has made frequent Citations , upon several arguments and occasions , being by him stiled Astrologus & Physicus , upon which score we have given him a place in this Catalogue . DOROTHEUS SIDONIUS wrote an Apotelesmatick Poem , as ci●…ed by Athen●…us , of which little or nothing is now extant , except what is pre●…ed in the Excerpta , mentioned in Labbeé's Bibliotheca . Simler ( in Biblioth . Ges●… ) will have Manilius to have followed aud imitated him , in his Astronomical Poem ; S●…aliger , ( in Manilium ) and Vossius , affirming the like to have been done by Omar , Messalah , and Alchabitius in their Astrological Tractates . Iulius Firmicus gives this Character of him , that he was Vir prudentissimus qui Apotelesmata veri●… & disertissimis versibus scripsit . I find likewise in Iames's Eclog. Oxon. Cant. a P●…ce under the name of Dorotheus , De esse Solis in Domibus Planetarum . But whether that Authour be the same with this Dorotheus , is altogether uncertain . CRITON NAXIUS writ an Octaeteris , which some ( sayes Suidas ) will have to be that of Eudoxus . Gesner writes thus of him ; Ha●…a dubio est Criton Astronomus , cujus Plinius meminit , lib. 18. c. 31. ANTIMACHUS HELIOPOLITANUS Aegyptius is by Suidas said to have written 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Mundi fabricationem , in a Poem of 3780. Verses . SPORUS NICENUS wrote a Comment upon Aratus's Phaenomena . He is mentioned in the Isagoge of Leontius Mechanicus . LEONTIUS MECHANICUS wrote 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Printed , inter Astronomica Veterum Scripta Isagogica Graeca & Latina , Ex Officinà St. Andraeana , 1589. DIONYSIUS CORINTHIUS writ a Treatise of Meteorologicks , 〈◊〉 Suidas affirms . LASUS MAGNES , in the Life of Aratus , MONOPHANTUS , by Thèon , upon Aratus , and PHILIPPUS , by Hipparchus , in his Exegesis , are mentioned for Astronomers ; as is likewise MNESISTRATUS , by Censorinus . ANTIOCHUS wrote in Greek Thesauri Apotelesmatum , distinguished into 107. Chapters , extant at Rome in the Vaticane Library , as Simler , in Bibl. Gesner ▪ affirms . He is mentioned more than once by Firmicus . DOSITHEUS ASTROLOGUS is mentioned by Pliny , lib. 18. c. 31. to have written Of the Rising and Setting of the Stars . JULIANUS LAODICENSIS PHILOSOPHUS , wrote 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , as Gesner affirms . BELINUS , a Greek Authour , seemeth to have written on this Argument , as the Title of his Book , De judiciis Futurorum , and De Imaginibus , imply . See Gesner , and something of him now extant in his Majesty's Library at St. Iames's . GEZ , perhaps GESSIUS , a Greek Authour , wrote Libros Imaginum , Et De Stationibus , Et De Imaginibus Veneris , as Gesner testifies ; if yet those Treatise●… may not be Philological , rather than Astrological . APOMASARIS Apotelesmata , with some other Authours of that kind , are extant in the Vaticane Library , and in that of Ausburg , as Simler affirms , in Biblioth ▪ Gesner . HELICONIUS , according to the testimony of Suidas , writ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . i. e. De Syderum & Tempestatum Effectis , Et De Aeris Signis . DEMETRIUS TRICLINIUS writ De Schematismis Lunae , & Macula in ejus facie , extant in the French King's Library ; to whom is likewise ascribed that Greek Poem , De Sphaera , attributed to Empedocles , and for such translated into Latine , and published by Q. Sept. Florens Christianus . Simler in Bibl. Gesner . asc●…ibes to him another Work , under the Title of Inventum Astronomicum , written in Greek . POLEMON ATHENIENSIS , supposed the same with Him who was Disciple to Xeno●…rates , writ a Book de Interpretatione Naturae Signorum , translated into ●…atine by Nicholaus Petreius Cor●…yraeus , and Printed at Venice , apud Gryphium 1552. cum al●…is quibusdam , as Simler , in Epitome Bibl. Gesner . testifies . EUTHYMIUS writ , in Greek , a Synopsis of Astronomy , or as Simler entitles it , De Sphaera , extant in the French King's Library . DION NICAENUS writ De Septem Planetis . GIAPHAR ASTROLOGUS wrote a Book which he entituled Major Introductorius . He wrote likewise a Book of Commentaries , and another , of Experiments , mentioned by Gesner . CAUDAS ASTROLOGUS wrote Nine Books de Annulis Astronomicis , a Book de Tribus figuris Spirituum , and another de figura Almandal . as Simler , from the Authority of Guil. Pastregicus , de Originibus Rerum , affirms . ASTRONOMERS after our SAVIOUR's Nativity . MODERATUS COLUMELLA , De Re Rustica , hath left an Astrological Calendar ; with Prognosticks . THRASYLLUS , Native of Mendes , a City of Egypt , multarum Artium scientiam professus ( sayes the old Scholiast of Iuvenal ) prostremò se dedit Platonicae Sectae , ac deinde Mathesi , quâ praecipuè viguit apud Tiberium . By Mathesi , is to be understood chiefly Astronomy , or rather Astrology , according to the Doctrine of the Chald●…ns , in which he instructed Tiberius . He wrote likewise Of Musick ; out of which Porphyry , upon Ptolemy's Harmonica , and Theon Smyrnaeus cite some Pieces . See more of him in Paganinus Gaudentius , De Philosophia apud Romanos , cap. 54. and V●…ssius de Histor. Graec. l 4. c. 16. TIBERIUS CAESAR , the Emperour , was skilful in Astronomy and Astrology , instructed therein by Thrasyllus , quem ut Sapientiae Professorem contubernio adm●…verat , sayes Suetenius , especially during his recess or exile at Rhodes . He had the luck to predict many future Events , particularly to foretel , by inspecting Galba's Nativity , that he should one day be Emperour ; which he declared ( Galba being then but a Youth ) in these words , Et tu , Galba , quandoque degustabis Imperium , as Tacitus relates it , though Suetonius and others apply it to Augustus . He is also reported to have had always by him the Genitures of all his Nobility , and that according as he found his own or the Kingdom 's Horoscope to be well or ill looked upon by theirs , so he let them stand , or cut them off by Legislative Astrology ; to use the expression of the famous M r. Gregory . GERMANICUS CAESAR , that excellent Prince , translated 〈◊〉 h●… Phaenomena into Latine Verse yet extant . CHAEREMON , a Philosopher of the Stoical Sect , by birth an Egypti●… . Master to Dionysius Alexandrinus ; wrote of the Egyptian Astrology , as we find by the mention made of him in Iamblichus , De Mysteriis , Aegypt . although both the Latine Translatours mistook his Name . He wrote also De Cometis , as Origen and Seneca testifie , the latter of whom calls him Charimander , and not Chaeremon , which G. Vossius conceives to be a mistake in the Text. He is mentioned by Strabo ( ●…ib . 17. ) to have attended Aelius Gallus in a Voyage from Alexandria up into Egypt , whence we may conclude him to have flourished , about the latter end of Augustus , or beginning of Tiberius's Reign . DIONYSIUS AREOPAGITA may justly be admitted into the number of Astronomers , since it is reported of him , that , at Helipolis in Egypt , together with Apollophanes , he observed that miraculous Defection of the Sun , at the time of our Saviour's Passion : Whereupon he broke out into this Exclamation , Aut Deus Naturae patitur , aut Mundi machina dissolvitur . He was afterwards converted to the Christian Faith , for which he died a Venerable Martyr , being aged above one hundred years . JULIUS HYGINUS , whom some would have to be the Freed-man of Augustus , others , with more probability , of Severus and Antoninus , or of Iulia Severa the Empress , wrote the Astronomicum Poeticum , De Mundi & Sphaerae partibus , and the Fables of the several Asterisms , yet extant . SENECA , the Philosopher , occasionally intermingles in divers of his Writings several Astronomical Dissertations , and , in the seventh Book of his Natural Questions , hath expresly written of Comets . ANDROMACHUS CRETENSIS was Physician to Nero , and about the latter end of his Reign wrote ( as it is affirmed by Lucas Gauricus , and Clavius , in Sacroboscum ) the first of any touching the Theory of the Planets ; His Writing●… are much commended by Galen . PLINY the Elder , in the second Book of his Natural History , hath written many things touching the Celestial Bodies . JARCHAS Prince of the Brachmannes was a famous Astronomer according to the Testimony of St. Ierome ad Paulinum , whose Words are These , Apoll●… ( whether the Magician as vulgarly reputed , or the Philosopher according to the Tr●…dition of the Pythagoreans ) went to the Brachmannes that he might hear Jarchas fitting on a Throne of Gold , and discoursing of the daily Revolution and Motion of the Stars . Damis likewise reports that the said Iarchas gave to Apollonius seven Rings inscribed with the Names of the seven Planets , which he was to wear successively every Day One. See Rantzov . in Catalog . Astrol. APOLLONIUS TYANAEUS wrote four Books , de Divinatione Astrologica , as Philostratus relates in his Life , though none of them be now extant . PLUTARCHUS CHAERONENSIS , in his Book , De facie in Or●…e Lunae , and in his Work , De Placitis Philosophorum , hath shown himself studious and skilful in Astronomy . MENELAUS , a most eminent Mathematician and Astronomer , was an Observer of the Stars for a long time , both at Rhodes and at Rome . He hath left Three Books Sphaericorum , published by Mersennus , in his Synopsis Mathemat . AGRIPPA , the Mathematician , observed ( as it is reported by Ptolemy 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . ) the Conjunction of the Moon with the Pleiades , happening Anno Nabonassar . 840. Nov. 29. ASCLETARION was an Astrologer in the time of Domitian , whose fate he had predicted ; for which being questioned and avowing the Prediction , he was asked by the Emperour what his own fate would be ? To which he confidently reply'd , that he should be torn in pieces by Dogs . Whereupon Domitian commanded that he should be immediately slain , and carefully buried , that the vanity of his Art might appear : But a sudden and violent tempest happening at the enterment of him , his body was deserted , and the Dogs came and tore it in pieces . See Sueton. in Domit. HADRIANUS the Emperour was singularly well skill'd in Astronomy , and particularly in Judiciary Astrology , according to the Testimony of Aelius Spartianus in his Life , who affirms that he used yearly in the Evening of the Calends of Ianuary to calculate what ever should happen to him for the whole year following . And in the Life of Verus , His Successour , he gives us this further Testimony , which take in his own Words : Fuisse Adrianum peritum Matheseôs , Marius Maximus usque adeò demonstrat , ut eum dicat cuncta de se scîsse , sic , ut omnium dierum usque ad horam mortis futuros actus antè perscripserit . AQUILA PONTICUS was a learned Mathematician of Synope , first a Christian , but afterwards , by the Church , for his too great adherence to Judiciary Astrology , excommunicated ; whereupon he became a Iewish Proselyte , and translated the Old Testament ( though not very sincerely ) into Greek . THEON ALEXANDRINUS Senior ( whom some would have to be the same with that Theon Smyrnaeus , who wrote in Mathematica Platonis , published by Bulialdus ) made several Observations of the Planet Venus in the sixteenth year of the Emperour Hadrian , mentioned by Ptolemy cap. 10. Almagest . In the Library at Ausbourg , there is extant a Tractate of his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . PHLEGON TRALLIANUS , the Freed-man of Hadrian the Emperour , among other his Works , wrote De Olympiadibus , in which , according to the testimonies of Origen and Eusebius , he made a Chronological remark on the obscuration of the Sun , which happened at the time of our Saviour's Passion . CLAUDIUS PTOLEMAEUS a Native of Pelusium , descended as some would have it of the Royal Race of the Ptolemies Kings of Egypt ; The Prince in his Time of Astronomers , Geographers , and Astrologers ; His Principal Works being eight Books of Geography , thirteen Books , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , commonly called Almagestum ; 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , seu Quadripartita Syntaxis de judiciis Astrorum ; And Parapegma de Apparentiis & Significationibus Inerrantium Stellarum , de Analemmate , &c. there are likewise ascribed to him 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. faciles & expediti , upon which Theon Alexandrinus Iun. is reported to have commented , or rather ( as Golius in Alferganum from the Authority of Keusian Gilaeus notes ) to have composed himself , and to have given them the Title of Canones Ptolemaici , because computed according to the Hypotheses of Ptolemy . SEXTUS EMPIRICUS , Nephew to Plutarch the Philosopher , in his Hypotyp . Pyrrhon . writes sharply against Iudiciary Astrology . HEPHAESTION THEBANUS wrote de Configurationibus Stellarum , as cited by Salmasius , De Annis Climactericis , and others . Of whom divers Excerpta , De duodecim Zodiaci Signis & eorum Effectibus , are published by Camerarius , in Greek and Latine , amongst his Astrological Collections Printed at Norimberg . Of this Authour also three Books 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 are , by Simler , affirmed to be yet extant , in Bibliotheca Strozzae . CLAUDIUS GALENUS Native of Pergamus in Asia , the most famous Physician of his time , in which Function he served three Roman Emperours , Adrianus , Lucius Verus , and Antoninus Pius . That he was learned in Astronomy and Astrology appears by his Books , de Diebus Decretoriis , his Epid. and his Mathemat . His Father likewise being well skilled therein , for thus ( according to the Testimony of Antonius Fumanellus cited by Rantzovius in Catalog . Astronom . ) he writes of Him. Pater Meus Optimus fuit Mathematicus , Exercitatus quandoque in Geometria , Arithmetica , Architectura , & Astronomia . APULEIUS ( if the Piece bearing his name be genuine ) wrote De Sphaera , now extant , with other Astronomical Tractates , amongst the Manuscripts in the Library at Westminster , and in that of Nicholaus Trivisanus of Padua , as cited by Thomasinus in Bibliothec. Patavin . under this Title , Sphaera Apuleii Platonici . LUCIAN the Philosopher , a Native of Samosata ( at this Day Scempsat ) a City in Syria , in the Province of Comagene , the facete Authour of the Ingenious Dialogues , wrote a Particular Treatise of Astrology , or Astronomy , setting forth it 's Original , Antiquity , and Excellency . In which Dissertation , and in his Saturnalia , Bourdelotius affirms he hath inserted many things taken from our Manilius . ANDRUZAGAR , an Arabian Astrologer , is said to have flourished about this time , by Iunctinus , in his Catalogue . CENSORINUS , in his Book de Die Natali , hath written divers things touching the Harmonical Systeme of the Heavens . ANATOLIUS ALEXANDRINUS , Bishop of Laodicea , in Syria , is mentioned by St. Hierome in his Book De Scriptoribus Ecclesiasticis , to have been well skilled in Astronomy . RABBI ADDA , about the end of Dioclesian's , or beginning of Constantius's Reign , composed an Hebrew Calendar , and Rules for finding out the Tekupha's , or revolution of the Equinoxes . JULIUS MATERNUS FIRMICUS , a Sicilian , about this time wrote eight Books Astronomicôn , containing Astrological Precepts , which , like an ungrateful Plagiary , he transcribed for the most part out of Manilius , without making the least mention of his name . VETTIUS VALENS , of Antioch , by some called Vestius Valens , a famous Astronomer , or rather Astrologer of the same time , who calculated , for Constantine the Great , the fate of New Rome's Foundation , as L. Taruntius had done that of Old Rome ; by G. Vossius conceived to be the same with him , of whose Works some Pieces are published by Ioachimus Camerarius , In Astrologicis Veterum opusculis , Edit . Norimberg . Anno 1532. His Anthologia is now intended for the Press , at Paris , by the care , as I am informed , of Mons. Huetius . PORPHYRIUS , a famous Platonist , but bitter Enemy to Christianity , wrote an Isagoge of Astronomy in three Books , as Suidas testifies . His Isagoge to Ptolemy's Apotelesmatice , is also here to be mentioned ; Printed at Basil. MARIUS VICTORINUS AFER , Master to St. Ierome , among many other Works translated Porphyrius his Astronomical Isagoge , into Latine , yet extant with the Comment of Boetius thereupon , as Gesner affirms . THEON ALEXANDRINUS Iunior , a Philosopher , contemporary to Pappus , and an excellent Mathematician . He observed an Eclipse of the Sun in the year of Nabonassar 1112. and besides other Mathematical Tractates , wrote ( according to Suidas ) De ortu Caniculae , Canonem expeditum in Ptolemaeum , a Commentary in parvum Astrolabium , and upon Ptolemy's Almagest , in eleven Books first published at Basile , by Ioachimus Camerarius , according to the Greek Manuscript , brought into Italy by Cardinal Bessarion , and from thence into Germany , by Regiomontanus ; as also upon Aratus's Phaenomena , this last lately Printed at the Theater in Oxford ; but upon no account so famous , as that of being Father to the excellent HYPATIA . ABYDAS ASTRONOMUS is mentioned by Epiphanius ; against whom Bardesanes the Syrian ( in his Book de fato ) writ , who flourished in the time of Antoninus Verus . PAULUS ALEXANDRINUS wrote an Astronomical Isagoge , or Introduction ; perhaps the same whom G. Vossius calls Paulus the Philosopher , who wrote likewise Apotelesmatica , sive , de Effectibus Syderum , Published by Rantzovius . MACROBIUS-AMBROSIUS-AURELIUS-THEODOSIUS , Consul of Rome , born at Parma , contemporary with Symmachus , wrote two Books , De Somnio Scipion●…s , wherein he handles divers Astronomical Arguments , as he does likewise in his Saturnalia . CLEOMEDES , a learned Astronomer and Philosopher of the Stoical Sect , wrote two Books 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. De Contemplatione Orbium Coelestium , first published , in Greek , by Conradus Neobarius , afterwards translated into Latine , by 〈◊〉 Valla , and commented upon by Robertus Balforeus , Printed at Bourde●… ●…05 . 4 o. SEXTUS AVIENUS RUFUS , an elegant Poet , by birth a Spaniard , 〈◊〉 the Phaenomena of Aratus into Latine Heroick Verse , and likewise paraphrased Dionysius Afer , De Situ Orbis , and wrote , in Iambicks , De Oris Maritimis . FLAVIUS MANLIUS , or MANLIUS THEODORUS , Consul of Rome is celebrated for his great Erudition , having written several Pieces both in Philosophy and Mathematicks , particularly in Astronomy , as may appear by that elegant Panegyrick Poem written in praise of him , by Claudian ; whence we have taken these following Verses to shew his Indeavours on that Subject . — Elementa doces , sempérque fluentis Materiae causas ; quae vis animaverit Astra , Implêritque choros : quo vivit Machina Motu . Sidera cur septem retrò nitantur in Ortus Obluctata Polo , variisque meatibus idem Arbiter , an geminae convertant Aethera Mentes . But the Injury of Time hath not left us any Remains of these his curious and learned Labours . PAPPUS ALEXANDRINUS , besides other his Mathematical Works , wrote a Comment upon Ptolemy's Almagest , and in his sixth Book of Mathematical Collections hath left some Explications , In Aristarchum Samium , De Magnitudinibus & Distantiis Solis & Lunae , yet extant , and translated by Commandinus ; published at Pesaro , 1572. and likewise to be found in M r. Foster's Miscellanies . HYPATIA , Daughter to Theon Alexandrinus Iunior , and Wife to Isidorus the Philosopher , which name she her self more justly merited , as being eminently learned in the Mathematicks and Philosophy , which she publickly professed and taught , till by the barbarous Christians , or Monsters rather , of Alexandria , out of meer envy for her admirable skill in Astronomy , and other Mathematical Learning , she was most inhumanely murthered and torn to pieces , in the very Cathedral Church . She wrote ( besides a Comment upon Diophantus , and another upon Apollonius's Conicks ) an Astronomical Canon , as both Hesychius and Suidas affirm . About this Time flourished two Aegyptian Monks ; ANIANUS , who , after the Example of Eusebius , writ a Chronological Work ; and PANODORUS , who to his skill in Chronology added the Knowledge of Astronomy . Out of the Fragments of which last Syncellus hath excerpted many things , as Scaliger likewise , in his Eusebian Animadversions . SYNESIUS , first a Heathen Philosopher , afterwards a Christian , and Bishop of Cyrene , writ , among other his Works , De Instrumentis Astronomicis , being a Discourse occasioned by his presenting Paeonius with an Astrolabe , and is extant in his Majesty's Library at St. Iames's . There are also extant divers Epistles of his to the before mentioned Hypatia , with this direction , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . AETIUS AMIDENUS ( Comes & Medicus , sayes Ricciolus ) wrote Hemerologium , De Significationibus Stellarum , translated first out of Greek into Latine , by Cornarius , and since published by Petavius , Uranolog . pag. 421. S. CYRILLUS , Bishop of Alexandria ; besides other Works of his , wrote De Cyclo Paschali , mentioned by Sigebertus Gemblacensis , in Chron. BACHARIUS MACCAEUS , a Britain , Disciple of St. Patrick , Published a Book , De Prognosticis Nativitatum , according to Balaeus . S. PROSPER AQUITANUS , Bishop of Rhegium , composed a Paschal Cycle , consisting of 532. years . VICTORINUS AQUITANUS , whom G. Vossius conceives to be more truly called Victorius , composed a Paschal Cycle , being by Pope Hilarius , for his eminent skill in Astronomy , invited to Rome , to undertake the correction of the Calendar . Yet his Paschal Cycle seems to have been not long after reformed by Victor , Bishop of Capua , who likewise wrote on the same Subject . THEODORET , Bishop of Cyrus , is by Iunctinus , in his Catalogue , put into the number of Astronomers , as also by Ricciolus , in Chron. part . 2. MAUGANTIUS , a Britain by extraction , a famous Philosopher , and Mathematician , in the time of Vortigerne , to whom he was principal Physician , as Geoffry of Monmouth reports . He studied in the City of Chester , in which at that time Astronomy , and all other Arts flourished , and , from the diligent observation of the course of the Stars , and Planets , became more eminently learned in Astrology , than any of his time . He calculated the prodigious conception of Merlin , and wrote De Magia Naturali . AMBROSIUS MERLINUS , a Britain , in the time of King Vortigern , was famous for his admirable skill in Astronomy and Astrology , of whom Balaeus thus writes ; Merlinus in Urbe Legionum ( Caerlleon ) studiis diligenter in●…ubuit , & eruditis Artibus & literis operam dedit , Magiae potissimùm Naturali . Unde Astronomiae tandem peritissimus futura praedixit multa , quibus sequenti saeculo mirabilem se praebuit . He wrote a particular Treatise of a certain Comet , which appeared in his time , as Balaeus testifies , and a Book of obscure Predictions translated into Latine by Geoffry Monmouth , as Gesner affirms . CARPUS ANTIOCHENUS wrote 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Rei Astronomicae libros ; of which Proclus , in primum Euclidis , mak●…s mention . To him Mr. Selden ascribes the Books commonly entituled Ptolemaei Centiloqutum . Vid. Selden . de Diis Syr. Syntagm . 1. seu de Teraphim . CASSIODORUS , a Person of Consular dignity , and honoured with the most eminent Charges of State in the time of Anastasius the Emperour and Theodoricus King of the Goths , afterwards a Recluse in the Monastery of Cassina , wrote , amongst other things , Of Astronomy , & De Computo Ecclesiastico . SIMPLICIUS , a Native of Phrygia , an eminent Platonick Philosopher , and excellent Commentator upon Aristotle , De Coelo , merits to be here mentioned . MARIANUS , Marci Causidici F. wrote a Metaphrasis of Aratus , in MCCCXL . Iambicks . He lived in the time of Anastasius the Emperour . See Simler in Bibl. Gesner . THIUS ATHENIENSIS wrote seven Books of Observations of the mean Motions of the Stars , so much the more acceptable ( sayes G. Vossius de Scient . Mathem . ) in regard that from Ptolemy's time unto that of Albategnius , there are not any Observations of the Celestial motions extant . These , transcribed from a Manuscript in the King of France's Library , were first published by Bulialdus , at Paris , Anno 1645. PROCLUS LYCIUS , a Platonick Philosopher , surnamed DIADOCHUS , Disciple to Magnus Syrianus , taught for a long time at Athens , and writ a Comment upon the first Book of Euclid ; Of the Sphere , ( being for the most part an Epitome of Geminus ; ) Of the Astrolabe and Astronomical Hypotheses , ( being a Compendium of Ptolemy's Almagest . ) There was another Proclus surnamed Siccensis , who was Master , or Tutor , to M. Antoninus the Emperour , confounded by some with this Proclus Diadochus ; but without all reason . For Diadochus flourished not till the Reign of Anastasius , being 300. years after Siccensis . Ricciolus conceives this Proclus Diadochus to be the same with Proclus the famous Mathematician , who as Zonaras ( part . 3. Annal. ) reports , made , in imitation of Archimedes , Burning-Glasses , with which he fired Vitalianus his Fleet , at the Siege of Constantinople , and was employed by Anastasius the Emperour , as Interpreter of his Dreams . MARINUS NEAPOLITANUS , Disciple to Proclus Diadochus , wrote , Praevia ad Phaenomena , and Phaenoménôn Librum singularem , sayes Voss. de Scient . Math. p 166. who yet doubteth whether this be not another Marinus , who writ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , ad Euclidem . JOANNNES LAURENTIUS PHILADELPHENSIS LYDUS , wrote in the time of Iustinian the Emperour , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , de Mensibus , with other Mathematical Tractates , mentioned by Photius , and Suidas , yet extant in MS. in the Library of my honoured and most learned Friend , M r. Isaac Vossius . DIODORUS MONACHUS , Bishop of Tarsus in Cilicia , wrote ( according to Suidas ) contra Astrologos & Fatum ; he put forth likewise a Book de Sphaera , & septem Zonis , of the Annual Progress of the Stars , and of the Sphere of Hipparchus . DIONYSIUS EXIGUUS , by birth a Scythian , but a Roman Abbot , wrote a Paschal Cycle , or rather corrected that of Victorinus , or Victorius , as Victorius had done that of Theophilus , and he , that of Cyrillus . This Computus , or Cycle was observed by the Latine Church , until the correction of the Calendar by Pope Gregory XIII . From this Dionysius , the Christians first learnt to reckon their years , from the Nativity of our Saviour , thence called Aera Dionysiana ; whereas before , they reckoned , from the Persecution of Dioclesian . TRIBONIANUS SIDETES , a Civil Lawyer in the time of Iustinian the Emperour , wrote a Comment upon Ptolemy's Canon , in Verse . He published likewise Concentum Mundanae & Harmonicae Dispositionis ; and another Book , de Planetarum domiciliis , as likewise de Mensium Permutatione , and some other Pieces ; of which Suidas . PHILIPPUS MEDMAEUS , so called from Medme , a Town of Italy , by Stephanus , in Voce Medme , stil'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which G. Vossius conceives ought to be read , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . for he wrote de Ventis , as they are foreseen or predicted , from the Position of the Stars , or Constitution of the Heavens . He also flourished in the time of Iustinian the Emperour . PHILOPONUS , surnamed Grammaticus , deserves here to be recorded for his Comment in Astrolabium planum , sive de usu Astrolabii , written in Greek , yet extant in New Colledge , Oxford , and ( as Simler in Bibl. Gesner . adds ) in the French King's Library . BUZUR-GIUMHUR , an ancient Persian Authour , being one of the Counsellours and Courtiers of Nushirvân King of Persia ( in the 42. year of whose Reign Mahomet the false Prophet was born ) wrote De Quaestionibus Astrologicis . MARTIANUS FELIX MINAEUS CAPELLA , in his Work , entituled , De Nuptiis Mercurii cum Philologiâ , wrote of Geometry , Arithmetick , Musick , and Astronomy . ISIDORUS , Bishop of Hispalis , or Sevit , in Spain , Son to Severianus , Duke of Carthage , in his Book , De Originibus , hath inserted a Compendium , or Epitome of all the Mathematicks ; and in his Book , De Mundo ; with the like brevity treated of the Sphere . The Astronomical Poem , ( of which the Fragment is published by Pythaeus among the Ancient Latine Poets by him set forth ) under the Name of Fulgentius , is by Pythaeus conceiv'd to belong to Isidore , at the End of whose Works it is commonly inserted without any other Name to it ; if yet ( as Pythaeus adds from the Conjecture of a certain Learned Person ) it may not rather be ascribed to Varro Atacinus . HEMOALDUS , an English man , surnamed PROVIDUS , between whom and Venerable Bede there was great familiarity , to whom he addressed his Book De Rebus Mathematicis , yet extant , as Bede , on the other side , did an Epistle to him , De Ratione Quadrantis Anni , sive , de Bissexto . THEODORUS MELITENIOTAS , Magnus Sacellarius Magnae Ecclesiae Constantinopolitanae , wrote of Astronomy , and particularly upon Ptolemy's Astronomical Syntaxis , or Almagest ; the Proem of which Work from a MS. out of the Library of Mr. Isaac Vossius , Bulialdus lately published , at the end of his learned Comment , upon Ptolemy's 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . BEDA , commonly called Venerable Bede , was renouned for his knowledge and study of Astronomy , amongst whose Works there is yet extant , De Argumentis Lunae , De Ephemeride , De Embolismis , De Circulo Decennovennuali , De Cyclo Paschali , De Circulis Sphaerae & Polis , De Planetis & Signis Coelestibus , De Astrolabio , & De Aequinoctio Vernali . ADELMUS DUROTELLUS , seu BLADUNIUS ( i. e. MALMESBURIENSIS ) Son of Kenred , and Grandchild of Ina , King of the West-Saxons . Bishop of Sherburne , ( now translated to Salisbury ) wrote De Cyclo Paschali , contra Britannos , and De Astrologia , as Balaeus affirms . FLACCUS ALBINUS , sive ALCUINUS , an English-man , born in York shire , Scholar to Venerable Bede , and Tutour to Charlemaigne , to whom he was sent upon an Embassie by Off a King of the Mercians , and , for his exquisite Learning , invited by Charlemaigne , to continue with him in France ; which he did ; perswading that Prince to erect the University of Paris . He was excellently well skilled in all the Parts of the Mathematicks , which he publickly taught ; and wrote De Septem Artibus Liberalibus , and De Astrologia , as Vossius , De Scient . Mathemat . testifies . CHARLEMAIGNE , King of France , and Emperour , instructed by Alcuinus aforesaid , became excellently well skilled in the Mathematicks , particularly in Astronomy , insomuch that he wrote Ephemerides , and was extremely delighted in making observations of the Stars . He gave names to the Moneths of the Year , and to the Winds , in High-Dutch , which continue to this Day . He was , by a King of Persia his Contemporary , upon the knowledge he had of his affection to Astronomical Studies , presented with a Piece of Clock-work , showing the motion of ●…he Planets ; which the Emperour being then at Paderborne , in Westphalia , received with no less admiration than pleasure . Vid. Voss. De Scient . Mathem . c. 35. JOHANNES CAMATERUS , Chamberlain to the Emperour Porphyrogeneta , writ De Genethliis , & Syderum positione , & Astrologiam Chaldaicam , in Verse , now in the Possession of my Learned Friend Mr. Tho. Gale. ALMAEON , whom some call ALMAMON , the deservedly renouned Califfe of Babylon , ( as Mr. Graves stiles him in his Pyramidograph . ) fifty years before the time of Albategnius , observed the greatest Declination of the Sun to have been 23° . ( according to Elancanus and Herigone ) or 23° . and 35′ . ( according to Ricciolus , from the authority of Alfraganus . ) He first commanded Ptolemy's 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 to be translated into Arabick ; which Translation gave that Work the corrupt , but now common name of Almagest . He found by observation and measuring in the Plains of Singar , that one Degree of a great Circle on the Earth is equal to 56. miles . His Astronomical Designs were so acceptable to the Genius of that Nation , that in the Times succeeding , no less than Thirty Kings are said to have emulated his Example ; as is observed by Golius ( notis in Alfergan . ) EGMUNDUS , surnamed ASTROLOGUS , is by Ricciolus put also into the Catalogue of Astronomers about this Time. MESSHALA ARABS , sive MESSAHULACH , signalized his Name by his Book De Receptionibus , & De Conjunctionibus Planetarum , & De Revolutionibus Annorum Mundi . He wrote likewise , De Elementis & Orbibus Coelestibus ; a third Book , De Ratione Circuli & Stellarum Operationibus ; and another , De Compositione & Utilitate Astrolabii : The first Printed at Venice , Anno 1493. with P●…olemy's Quadripartitum ; The second , at Norimberg , by Montanus and Neuberus ; The third , at Basil , by Hervagius , Anno 1533. And the fourth and last , by Henricus Petri , in Appendice Margaritae Philosophicae . LEO PHILOSOPHUS writ something in Astrology , yet extant in the French King's Library , as Labbeé testifies , in Catal. MS. ALBATEGNIUS or trulier ALBATTANIUS ARACENSIS , called likewise MAHUMETES TINEU , vel MAHUMETES ARACENSIS , or ( but mistakenly ) ARACTENSIS , from the City of Arrac , commonly , but corruptly , called Aracta , in Syria , Son of Geber Auchan , Son of Cruen , Prince of Syria , made diligent observations of the Stars , both at Arrac and Antioch : And finding that Ptolemy's Canons in his time dissented much from the course of the Heavens , he made new Tables of his own . He wrote a Book De Scientia Stellarum , first translated out of Arabick into Latine , by Plato Tiburtinus , and illustrated with Annotations , by Io. Regiomontanus . He observed the Sun's greatest Declination to be 23° . 35′ . and the first Star of Aries to be 18° . 2′ . in Longitude from the Equinoctial Point . His Observations were Printed at Norimberg . His Book De Numeris & Scientia Stellarum , according to a Transcript thereof , taken by Lucas Valerius ( Publick Professour of Mathematicks at Rome ) out of the Vati●…an Library , was reprinted more correctly in Latine at Bologna in the year 1645. and dedicated by Bernardinus Ugulottus to Ferdinand the second Grand Duke of Tuscany . ACHILLES TATIUS wrote a Book De Sphaera , as Suidas affirms , part of which G. Vossius conceives to be his Commentary in Aratum , Published in Greek and Latine , by Petavius , in Uranolog . MOHAMMED IBN ZACHARIAE AL RAZI wrote many Books in several Sciences , and among the rest , a Particular Astronomical Treatise , as I find it mentioned in the Catalogue of Golius his Manuscripts . He died in the year of the Hegira 320. of Christ 932. ABDORRAHMAN AL-SUPHI , commonly ( but corruptly ) called AZOPHI , or ELZUPHI , or EBENNOZOPHIM , an Arabian Astronomer , Authour of the Persian Tables , in which , sayes ricciolus , Stellarum Schemata & loca ordinata sunt . The Work transcribed by his Son , with the Delineation of the Celestial Signs in Miniature by the same hand , is extant among the Manuscripts of Iacobus Golius . ALFRAGANUS MAHUMEDES , or AMETUS , or AHEMED , or MUHAMED , the Son of Amet , called Alfraganus , or rather Alferganus , from the City Fergana , in the Province of Sogdiana . He wrote Elementa Astronomica , compiled chiefly out of Ptolemy , which by Rabbi Iacob Antolius were turned into Hebrew , and by Iohannes Hispalensis , in the year 1142 translated out of Arabick into Latine , but lately published in Arabick and Latine , by the famous Iacobus Golius , with learned Notes , which yet he lived not to compleat . He writ likewise de Astrolabii Descriptione & Usu , and a Book of Dialing , as Golius in his Notes asserts . G. Pastregicus mentions another Treatise of Alfraganus , entitled De Aggregationibus Stellarum . V. Simler . Bibl. Gesner . HALI BEN RAGEL is about this time , by Ricciolus , inserted into the number of Astronomers . ARZAHEL ALA BEN writ Tables and Canons of the Motions of the Celestial Bodies , preserved in MS. in the Library of Merton Colledge in Oxford , and in that of Caius and Gonvil in Cambridge , according to Iamesius Eclog. Oxon. Cant. Whether the same with Arzahel Hispanus ( of whom in the next Century ) we leave to be considered . ALI IBNO'L HOZEIN , a Persian , wrote of the Theory of the Planets , as Abul Pharagius in Hist. Dynast . witnesses , and De Demonstratione Planisphaerii , as Hottinger , in Smegm . Orient . ALFARABIUS Arabs , stiled by Blancanus , Astronomus celebris , called likewise ABUNASR , according to Abul Pharagius , in Histor. Dynast . under whose Name Simler , in Bibl. Gesner . affirms , there is extant a Piece entitled de Compositione Astrolabii . ETHEL WOLDUS WENTANUS , of the Race of the West-Saxon Kings , sometime Abbot of Abington , afterwards Bishop of Winchester , wrote , among other Works of different Subjects , a Treatise de Planetis , & de Climatibus Mundi , as Balaeus affirms . MUHAMMED IB'N AHMED ALBIROUNI , a Persian Astronomer , wrote De modo mensurandi Altitudinem Stellarum ; as also an Explication of the use of the Astrolabe , extant amongst the Manuscripts of Iacobus Golius . IB'N JUNES , or JOUNIS , an Egyptian , wrote Astronomical Tables , together with a History of Various Observations , and the reason of Calculating the Celestial Motions ; which he dedicated to Hakein , perhaps Elhacain King of Egypt , who flourished about the year 373. of the Hegira , of Christ , 996. ABBO FLORIACENSIS , so called as being Abbot of the Monastery of Fleury , in Burgundy , a French man , Native of Orleans , among other Works , wrote De Motibus Stellarum , De Planetarum cursu , & Demonstrationes Astronomicae . CAMPANUS NOVARIENSIS , an eminent Astrologer and Astronomer . He found a peculiar way of erecting a Celestial Scheme , by division of the prime vertical Circle , which way Gazulus followed . He wrote , besides Theoricas Planetarum , De Sphaera , & De Computo ; Another Piece , de Compositione Astrolabii ; and a Calendar . Simler mentions another Piece of his entitled Breviloquium duodecim Signorum Zodiaci , which he sayes in his Time was extant , apud M. Dresserum in MS. ABU-ALI-IBN SINA , commonly called AVICENNA , a famous Physician , whose life is exactly written and prefixed to Plempius's Translation of the second Books of Avicen's Canon Medicinae , and of whom an excellent account is given in Abul Pharagius his History of the Dynasties . He writ De Astronomia & Chronologia , mentioned amongst the Manuscripts of Iacobus Golius . He was born in the year of the Hegira 370. and died in the year 428. which are the years of Christ , 980. and 1036. IB'N HAITEM wrote touching the motion of the Center of the Moon 's Epicycle ; Of the difference of the Solar and Lunar Year ; Of the Dimensions of the Earth , Sun , and Moon ; And De Motu Circulari : As also touching the exact method of taking the Elevation of the Pole. He died at Grand-Cairo about the Year of Christ , 1038. HERMANNUS CONTRACTUS a Monk , but of noble Extraction , as being Son of Wolferad , Earl of Varinge in Suaben , ( which Surname of Contractus he gained à membrorum contractione , as G. Vossius affirms ) wrote three Books De Compositione Astrolabii , and one De Utilitate Astrolabii . He wrote likewise another De Eclipsibus , and translated the Works of several Arabian Astronomers into Latine . ISAACIUS ARGYRUS MONACHUS wrote de Cyclis Solis & Lunae , and de Computo Ecclesiastico ; which last Petavius hath published in Greek and Latine , in Uranolog . His Astronomical Tractates are said to be kept in MS. in the Library at Auspurg ; and what other Mathematical Pieces he wrote , will appear in Simler's Epitome of Gesner's Bibliotheca . OLIVERIUS MALMESBURIENSIS , by some called ELMERUS , wrote Astrologorum Dogmata quaedam , and another Book , De Signis Planetarum ; as Balaeus testifies . GULIELMUS , Abbas Coenobii Hirsaugiensis , in the Diocess of Spires , composed Three Books Rerum Philosophicarum , & Astronomicarum ; Printed at Basile , 1431. ARZACHEL HISPANUS , an Arabian by extraction , 190. years after Albategnius , observed the greatest Declination of the Sun to be 23° . 34′ . Some make him a Native of Toledo , being called likewise Abraham Elzara Keel . Georgius Ioachimus Rheticus , in the Preface to his Ephemerides , makes him to be the Authour Toletanarum Tabularum , and that he left 402. Observations , touching the Sun 's Apogaeum . Vid. Ricciol . in Chronol . Astron. ROBERTUS LORRAINE , so called by the English , by reason he was Originally a Lorrainer , Profest and taught both in the Schools of France and Belgia , Philosophy , Rhetorick , and Mathematicks , for which Reason he was well esteemed by William the Conquerour , and advanced to the Bishoprick of Hereford ; He wrote de Stellarum Motibus , Tabulae Mathematicae , & de Lunari Computo . See Balaeus . ALHAZEN ARABS , wrote , besides seven Books of Opticks , one De Crepusculis , in which , sayes Blancanus , Aeris suprema maltitudinem acutissimè rimatur . Fredericus Risner published and illustrated his Works with a Comment and Sculps , and makes mention of three other Signal Arabians of the same name , as Ricciolus ( Chronic. Astron. ) affirms . GEBER HISPALENSIS ARABS , explained Ptolemy's Almagest , in nine Books , first Printed at Norimberg by Petreius , Anno 1533. together with Petrus Apianus , his Scheme or Instrument of the Primum mobile . In the beginning of which Work he treats of Spherical Triangles , as far as requisite to Astronomical Calculations ; from whence , ( sayes Mersennus , in Synops. Mathemat . ) Purbacchius and Regiomontanus excerpted many things in their Epitome of Ptolemy's Almagest . His chief study was to amend what he found defective in Ptolemy . However Copernicus stiles him Ptolemaei Calumniatorem . ALKINDUS , a Philosopher and Astrologer , wrote , much about this time , a Piece entitled , De Temporum mutationibus : And about the Year 1235. Iacobus Alkindus wrote , among other things , De Radiis Stellarum , yet extant in France . See Labbeé's Bibliotheca . RABBI ABRAHAM wrote de Sphaera , sayes Blancanus , from the Authority of Christmannus in Alfraganum . ATHELARDUS , Bathoniensis Coenobii Monachus , Philosophus , Astronomus , Rhetor , ac Poeta non vulgariter eruditus ( sayes Balaeus Cent. 2. ) leaving England , out of a desire to enrich himself by the Acquisition of Forreign ( especially the Eastern ) Learning , travelled into the Oriental Parts , and having made a Peregrination through Egypt and Arabia , and in a great measure satisfied his curious and learned Appetite , he returned into his own Country , and published , among other Works of his , a Treatise of Ezychiafarim , of the seven Planets , by him translated out of Arabick ; he wrote likewise a Book de septem Artibus Liberalibus , and another , de Astrolabio . RICHARDUS , Monachus Eboracensis , wrote upon Arzahel's Tables , now extant in the Publick Library at Oxford . ALMAEON ALMANSORIUS , in the year 1140. observed the greatest Declination of the Sun to be 23° . 33′ . His Aphorisms , Propositions , or Astrological Sentences , Hervagius published in the year 1530. together with Iulius Firmicus . This Almaeon , Vossius conceives to be different from Almaeon King of the Arabs , of whom before . JOANNES HISPALENSIS first translated into Latine , Alfraganus , as Blancanus , from Christmannus , and from them both Vossius , de Scient . Mathem . c. 35. affirm . He likewise translated Alcabicius his Isagoge ad Magisterium Iudiciorum Astron. He writ likewise Epitome totius Astrologiae , first Printed at Norimberg 1548. with Ioachimus Hellerus his Preface , contra Astrologiae Adversarios , as Simler . Bibl. Gesner . hath noted . RODOLPHUS BRUGENSIS , a Mathematician of Tholouze , translated into Latine , and Published Ptolemy's Planisphere , which he dedicated to his Master , Theodoricus Platonicus , ( as Gesner testifies ) Printed together with Aratus , by Valderus , at Bafile , 1536. ALPETRAGIUS , an Astronomer of Marocco , as Ricciolus affirms . He wrote Theorica Physica , translated out of Latine by Calo Calonymus Parthenopaeus , and likewise , De Astrologia , sayes Vossius , who conceives him to be the same with him mentioned in Summa Alberti Magni . He observed the Declination of the Sun to be the same with that of Almaeon . ABRAHAM ABEN-EZRA , or , according to others , AVEN-HESRE , a great Astronomer and Philosopher , wrote a Book entitled Mispatho Hamazzaloth , i. e. De Iudiciis Signorum ; and another , called Ta●…min , i. e. Rationum Astronomicarum ; and a third , De Luminaribus & Diebus Criticis , sayes Ricciolus . This last was revised and published at Rome by Angelus Blondus , as Vossius , in Addend ad L. de Scient . Mathemat . affirms . There is likewise extant under his name , a Book , amongst the Manuscripts of Iacobus Golius , entitled , De Anni magnitudine , and Indorum Astronomia . MANUEL COMNENUS , Emperour of Constantinople , wrote several Astronomical Tractates , yet preserved in the Vatican Library ; as Simler . in Bibl. Gesner . testifies . JOHANNES DE HEXHAM , so called from the place of his Nativity ; a Town in-the Bishoprick of Durham , a Benedictine Monk , wrote , among other things , De Signis . & Cometis . RABBI MOSES BEN-MAIMON , commonly , from the initial Letters of his Name , called Rambam , among many other Works , writ De Astrologia , sive Siderum Viribus & Effectis , first published in Hebrew , afterwards translated into Latine , by Ioannes Isaac Levita Germanus , Professour of the Hebrew Tongue in the University of Colen , and there Printed by Maternus Cholinus , in the Year 1555. AVERROES , an Arabian Physician of Corduba , for his diligence in commenting upon all the Works of Aristotle , called Commentator Magnus , and simply Commentator , reduced Ptolemy's Almagest into an Epitome . SIMEON , Monk of Durham , wrote De Cometa , & Combustione London , & aliis injuriis , as I find it cited by Iames's Eclog. Oxon. Cant. who affirms the same to be extant in Benet ▪ Colledge Library in Cambridge . Balaeus sayes of him , that he was Vir suo saeculo in multis Scientiis eleganter instructus , praesertim Mathematicis . ALBUMAZAR , otherwise called ABU-ASSAR , and JAPHAR , wrote Eight Books De Magnis Conjunctionibus , & Annorum Revolutionibus , and is reported to have observed a Comet , in his time , to have been above the Orb of Venus . He wrote likewise Introductio in Astronomiam , Printed in the Year 1489. ROGERUS HEREFORDIENSIS , of whom Balaeus sayes , That he was , Astrorum Peritus , & Metallorum Indagator Maximus , wrote In Artem Iudiciariam ; Theoricam Planetarum ; De Ortu & Occasu Signorum , and Collectaneum Annorum Planet . CLEMENS LANTHONIENSIS , so called from the Town of Lanthony near Gloucester , an Augustine Fryer , wrote , among other things , De Orbibus Astrologicis , and flourished about the same time . HUMENIUS AEGYPTIUS , about this time , wrote Astronomical Tables , which Christmannus , in Alferganum , affirms to be yet extant in the Palatine ( now the Vaticane ) Library , as also in the Publick Library at Oxford . DANIEL MORLEY , so named from the place of his birth , a Town in Norfolk , out of his great inclination to promote and advance Mathematical Learning , having sometime studied in the University of Oxon , travelled to Toledo , in Spain , to instruct himself in the Language and Learning of the Arabians , which there chiefly flourished , and , after his return home , wrote De Inferiori Mundo , One Book ; Another , De Superiori Mundo ; and a Third , entitled , Principia Mathematices . OMAR ASTROLOGUS , or HOAMAR or HOMAR , Son of Belnal Fargardian , a Native of Tyberias , wrote Three Books Of Nativities , published by Hervagius , together with Firmicus , 1532. HALY ABEN RODOHAM , an Arabian , or according to G. Vossius , an Egyptian , wrote a Commentary upon Ptolemy's Centiloquium and Quadripartitum , Published by Octavianus Scotus , at Venice , together with other Arabian Astrologers . He wrote likewise De Radiorum Projectionibus , and Three Nativities , whereof one his own , annexed to his other Works . This very Year he observed a Comet in the fifteenth Degree of Scorpio ; of which more in the History of Comets . LEOPOLDUS DE AUSTRIA , Son of the Duke of Austria , Episcopus Frisingensis , writ Ten Tracts , De Astrorum Scientia , Printed at Augsbourg , 1489. GILBERTUS LEGLEY , Philosophus & Mathematicus suae Aetatis non vulgaris ( sayes Balaeus ) wrote Compendium in Astronomia , & in Prognostica Hippocratis . He was Physician in Ordinary to Hubert , Archbishop of Canterbury . JOANNES AEGIDIUS , vel de SANCTO AEGIDIO , born at St. Albans , Philosophus Summus , Physician to Philip King of France , Professour of Physick and Philosophy , both in the University of Paris and Montpelier ; He wrote Prognostica Futurorum , and another Book , de Materia Coeli . Balaeus , de Scriptor Brit. ALEXANDER DE VILLLA DEI , Dolensis , wrote of the Sphere . He published likewise a Book of Arithmetick , and Computum Ecclesiasticum ; as G. Vossius , De Scient Math. affirms . GEORGIUS MEDICUS CHRYSOCOCCA , writ De Inventione Feriae , and an Exposition Syntaxeos Persarum , with several Tables Mediorum Motuum , published by Bulialdus , at the end of his Astronomia Philolaica . RABBI IASAAC HAZAN , i. e. Cantor , as being Chaunter to the Iewish Synagogue at Toledo , was one of the Principal Compilers of the Alphonsine Tables . ALBERTUS MAGNUS , Bishop of Ratisbon , one of the most learned Persons of his Age , among other the various Monuments of his Wit and Learning , wrote De Sphaera , De Astris , De Astronomia , and Speculum Astronomicum ; as Simler . in Bibl. Gesner . ROBERTUS LINCOLNIENSIS , Bishop of Lincoln , commonly called Grossa Testa , in English , Grouthead , writ a Compendium of the Sphere , Published first by Lucas Gauricus , 1531. He wrote likewise De Coelo & Mundo , De Sphaera Coelesti , Theoricam Planetarum , and In Astrologiam , as Balaeus affirms . ROGERUS BACON , a Franciscan Fryer of Oxford , a most acute Philosopher and admirable Mathematician , insomuch that he was reputed , but falsely , a Necromancer . Out of whose vast number of Books written upon several subjects , by which he hath eternized his name , we shall select only what is proper to our purpose , as they are enumerated by Balaeus . He wrote a particular Treatise , De Utilitate Astronomiae ; Introductio in Astrologiam ; De Coelo & Mundo ; De Cosmographia ; De Radiis Solaribus ; De Locis Stellarum ; De Aspectibus Lunae ; Et Prognostica ex Siderum cursu , with other Pieces of Opticks very considerable in that Age. ALBUASSIN , or ALBOAZEN HALY , Son of Aben Ragel , wrote De Stellarum Fixarum motu ac locis ( according to Ricciolus , Chron. Astron. ) as also De Iudiciis & Fatis Astrorum , translated at the command of Alphonsus King of Castile , out of Arabick into Spanish , by Iudas Ben Musce , and out of Spanish into Latine , by Aegidius de Thebaldis , of Parma , Printed at Basile 1550. He writ likewise another Book Signalium Astronomiae , as Simler . in Bibl. Gesner . affirms . JOHANNES DE SACRO BOSCO , an English man , born at Hallifax , anciently called Holy-wood , from which he took his name . After some time of study at Oxford , he became a Doctour of the University of Paris , and compiled , out of Ptolemy , Albategnius , Alfraganus , and others of the Ancients ; his Four Books De Sphaera , commented upon by Vinetus , Iunctinus , Clavius , Barocius , and divers others . And though Barocius hath detected and published no less than 84. Errours in that Work of Sacroboscus , yet it still keeps up its credit in the Schools , as a Classick Piece . ALPHONSUS x. King of Castile and Leon , having sent for the most learned among the Moors , Arabs , and Iews , began the Instauration of Astronomical Tables , which in the Year 1252. he first published , having , in Books , Instruments , and other Necessaries , relating to that Work , expended no less than four hundred thousand Crowns . These Tables , from his Name called Alphonsine , being defective , grounded partly upon Cabalistick Figments , he afterwards ( viz. Anno 1256. ) Published more correct . He observed in the Year 1250. the first Star of Aries , to have been distant from the Equinoctial Point 23° . 40′ . as Blancanus reports . Ricciolus affirms , that Egnatius Dante 's , in the fourth Part of his Astrolabe , reports , that he saw a Book of all the Alphonsine Instruments , translated out of Arabick into Spanish , and thence into Latine . PROFATIUS , a Iew , about this time , applyed his study to the Observation of the Stars . He writ Tables of the Motion of the Eighth Sphere , as Balaeus affirms , and found the Sun 's greatest Declination to be 23° . 32′ . His Almanack Perpetuum is now extant in several of our Libraries . JOHANNES PECKHAM , a Franciscan Fryer , and Archbishop of Canterbury , wrote among other learned Works of his , De Sphaera , and Theoricam Planetarum . VITELLIO THURINGO-POLONUS , an excellent Mathematician , wrote Ten Books 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. of the nature , reason , and projection of Visual rayes , &c. commonly called Perspective ; Printed first at Norimberg by Petreius , Anno 1535. and afterwards reprinted , and adorned with Figures , by Frederick Risner , at Basile , 1572. a Work subservient to Astronomy . — ODINTON , a Benedictine Monk in the Abbey of Evesham , and an English man , Scholar to Profatius the Iew and of Iewish Extraction , endeavoured to vindicate his Name from Oblivion by his Book , De Motibus Planetarum , and De Mutatione Aeris ; as Balaeus affirms . COGIA ▪ NASIR EDDIN . TUSAEUS , wrote Astronomical Tables , which he dedicated to Ile-Chan , Prince of the Tartars , and a Treatise of the Astrolabe , in twenty Chapters , as I find mentioned in the Catalogue of Golius's Manuscripts . He died in the year of the Hegira 675. of Christ , 1276. KOTBODDINUS SHIRAZITA , wrote a Book entitled Donum Regium seu Universae Astronomiae Syntagma . He was contemporary with Nasir Eddin Tusaeus . THEBIT BEN CHORA , i. e. the Son of Chora , by Profession a Iew , and according to ●…eland , born in England , though others make him a Native of Spain , first introduced the motion of Trepidation in the Eighth Sphere ( by some called Motus Accessus & Recessus ) from North to South ; and observed the Sun's greatest Declination to be 23° . 33′ . He wrote likewise De significationibus Planetarum ; De Capite & Cauda Draconis ; Demonstrationes in Almagestum , and Additiones in Sphaerica Menelai , as they are particularized by Balaeus . There are mentioned likewise other Treatises of his Writing , as Practica Planetarum ; Ganones Astronomici , and De Prognosticatione Temporum , said to be extant in his Majesties Library at St. Iames's . GUIDO BONATUS FORO-JULIENSIS , wrote Theoricae Planetarum , Published at Venice , 1506. He wrote likewise , De Astrologia Iudiciaria . HENRICUS BATEN of Mechlin , Dr. in Theology , Chancellour of the University of Paris , and Chaunter and Canon of Liege , Published a Book , De Erroribus Tabularum Alphonsinarum , as Ricciolus affirms , in Catal. Astronom . MICHAEL SCOTUS , surnamed Mathematicus , for his eminent skill in that kind of Learning , by Balaeus stiled , Eximius Physicorum Motuum , Cursúsque Siderei Indagator , Published a Comment , super Authorem Sphaerae ; Four Books , De Constitutione Mundi ; Two Books , De Coelo & Mundo ; Imagines Astronomicae ; And Dogmata Astrologorum ; De Signis Planetarum , l. 1. De Natura Solis & Lunae , l. 1. Printed at Venice 1546. He wrote likewise other Opera Astrologica , of which the MS. is extant in the Bodleian Library . GULIELMUS DE SANCTO GODIALDO gained about this time the honour and repute of an able Astronomer , that is , as G. Vossius notes , twenty years and more after the Publication of the Alphonsine Tables . PETRUS DACIUS , or DE DACIA , as G. Vossius , from the Authority of Trithemius , calls him , Published Astronomical Tables , extant in MS. in the Library of Benet-Colledge in Cambridge . He wrote likewise , De Calculo , sive Computo ; and set forth a Calendar . ISAAC ISRAELITA , wrote a Book entitled Iessod Holam , i. e. De Fundamento Mundi ; in which he often takes occasion to treat of the Motion of the Eighth Sphere . PETRUS ▪ DE APONO , called likewise CONCILIATOR , Ob Librum , quo Veterum Medicorum Scripta conciliat , ( sayes G. Vossius , de Scient . Mathemat . ) wrote De Astrolabio Plano , Published at Venice , 1502. NICHOLAUS TRIVET , a Dominican Frier , Son of Sir Thomas Trivet Knight , one of the Judges of the Courts of Common Law in Edward the Third's time , among other learned Works , wrote De Astronomia . JOHANNES BACONTHORP , a Carmel●…e Fryer in the Monastery of Blackney , in Norfolk , reputed one of the most learned of his time , stiled Doctor Resolutus , wrote four Books , De Coelo & Mundo ; One , De Sphaera Iudiciali ; and another , De Astrorum Scientiis . NICHOLAUS OCKHAM , a Franciscan Fryer , in Coenobia Oxoniensi , Praelector Publicus ( sayes Balaeus ) wrote , De Latitudine Oppositionum , and another Book , entitled , Astrologi Iudicium . ISMAEL ABULFEDA , Sultan of Syria , Assyria , and Persia , an illustrious Cosmographer , and Geographer , whose Tables the learned Mr. Graves published in the year 1650. in Arabick and Latine . CICHUS ASCULANUS , Dr. of Physick , Philosopher , and Publick Professour of Astronomy at Bologna , was accused for a Necromancer , and burnt at Florence ( being LXX . years of age ) Anno 1328. RICHARDUS WALLINGFORD , so called from the Town of Wallingford , where he was born ; Son of a Blacksmith ; after some time of Study in Oxford , betook himself to a Monastick life , in the Abby of St. Alban , whereof he had the Honour to be Abbot . He was excellently well skilled in Arithmetick , Astronomy , and Geometry . He caused to be made a famous Clock or Horologe , for the use of the Monastery , being ( according to the Words of Leland ) a miraculous Fabrick , sive quis Cursum Solis seu Lunae , seu fixa Sidera notet , sive iterum Maris Incrementa & Decrementa , seu Lineas unà cum figuris ac Demonstrationibus , ad infinitum penè variis , consideret . For the better Explanation of which Curious Piece , and the orderly regulating thereof ; he published Canons or Rules , in a particular Treatise , which he entitled Albion . Alluding something to the Name of the Monastery ; But thereby chiefly expressing this sence or meaning , in English , All by One , i. e. Omnia per Unum , as Balaeus reports . He wrote besides his forementioned Canones in Albionem ; a Book ; De Iudiciis Astronomicis ; and another , De Rebus Astronomicis . JOHANNES DANK , a Native of Saxony , writ Canones Eclipsales , Canones Tabularum , & De Astrolabio , as Gesner testifies . GUALTERUS CATTON , an English Fryer in the Convent of Cordeliers at Norwich , a learned Theologue and Philosopher , published a Treatise Adversus Astrologos . RABBI LEVI , eminent in all kind of Learning , and particularly in Astronomy , wrote a Book called Milhamot-Hessem , i. e. Defensionem Dei. JOHANNES BARWICK , by some ( but corruptly ) called BRENLANTIUS , surnamed likewise BRITANNUS , a learned English Franciscan Fryer , published several Books , De Astrologorum Praenotionibus ; in which he impugnes Judiciary Astrology . ROBERTUS HOLCOTH , a Dominican Fryer , of Northampton , of whom Balaeus sayes , that he was penè infinitae lectionis Homo , atque ingenii solidissimi , wrote De Effectibus Stellarum ; and another Treatise , De Motibus Stellarum , as G. Vossius affirms , out of Possevinus . GAUFREDUS DE MELDIS , published a Treatise , entitled Iudicium Stellae Comatae Anno Dom. 1330. and of two other Comets , which appeared in the years 1337. and 1338. preserved yet in Manuscripts in the Library of Pembroke Colledge in Cambridge . See Iames , Eclog. Oxon. Cant. RABBI DAVID ABUDERKEM , writ a Treatise , entitled , Ordo Intercalationis . JOHANNES MANDOVICH , sometime Fellow of Merton Colledge in Oxford , a learned Physician and Astronomer , published Astronomical Tables . JOANNES ESTWOOD , or ESTWED , or ESCHU●…D of Ashenden , sometimes Fellow of Merton Colledge in Oxford , highly commended by Io. Picus Count of Mirandula , wrote a Book , which he entitled Iudiciale Astronomicum , sive Summa Iudicialis . He published likewise Elucidarium Planetarum , Tabulae Planetarum , and Canons of their Utility and Practice ; of the Conjunction of Saturn and Mars in Cancer 1357. and of the Conjunction of Saturn and Iupiter , & de Signis Conjunctionum . His Iudiciale Astronomicum sive Summa Anglicana , or Iudicialis , vel de Accidentibus Mundi ( for those several Titles it bears ) was Printed at Venice in the year 1442. and is yet extant in MS. in the Publick Library at Oxford , and in that of Oriel Colledge . It was afterward Printed at Venice in the year 1489. and elegantly for that Age , at the Charge of a Patrician , for the Honour of whose Name ( because Noblemen in those Dayes would be at the charge of Printing of good Books ) I will subscribe what follows , as I received it from my very deserving and ingenious Friend , Mr. Francis Bernard , in whose Possession the said Book ( among other curious ones with which he is stored ) now is . Summa Anglicana Iohannis Eschuid , Opus factum est tum Diligentiâ , tum Impensâ Francisci Bolani Patritii Veneti , Viri certè bonarum Artium studiosi , Clarissimi quondam Oratoris Candiani ; Nec defuit Impressoris Iohannis Lucilii Santritter Herbronensis Germani maxima Lucubratio , maximus Labor , & Diligentia . NICHOLAUS CABASILAS , a Grecian , Archbishop of Thessalonica , wrote a Comment upon Ptolemy's Almagest . JOANNES ELIGERUS of Gondersleven , a German , writ de Compositione Astrolabii ; de Utilitate Astrolabii ; de Utilitate Quadrantis ; Two Books de Magnete , and One de Astrogemetro ; and several other Pieces , as Simler in Bibl. Gesner . affirms . JOHANNES DE SAXONIA , and JOHANNES DE LIGNERIIS , both Germane Astronomers , and Contemporaries . The latter put forth Canones Primi Mobilis , together with Tables , and a Book De Sphaera . He is reckoned by Petrus Cirvellus Daiocensis , in his Preface in Sphaeram Mundi , to have been one of the four most celebrious Astronomers , that had flourished between the times of Alphonsus and Purbacchius ; as cited by Vossius in Addend . ad Scient . Mathemat . GUILELMUS GRIZAUNT , an English man , Fellow of Merton Colledge in Oxford , and Dr. of Physick , leaving England , setled at Marseilles in France , where he dyed in much Esteem for his Knowledge and Practice in Physick , leaving behind him a Son of his own Name ; who was first Abbot of the Canons Regular at Marseilles , afterward Pope of Rome , by the Name of Urban the Fifth : Of the Issue of his Brain , I find these following , mentioned by Balaeus , relating to our Purpose . Speculum Astrologiae ; De Magnitudine Solis ; De Qualitatibus Astrorum ; De Significationibus Eorundem . JOHANNES KILLINGWORTH , Fellow of Merton Colledge in Oxford ; wrote De Iudicio Astronomiae ; Canones & Tabulae Astronomicae ; De Crepusculis ; & De Nubium Ascensionibus . NICEPHORUS GREGORAS writ De Astrolabio , extant in the King's Library at St. Iames's . Gesner mentions another Piece of his , De Calumniatoribus Astronomi●… , & De Astronomia . Andreas Cellarius , in Praeloquio Harmon . Macrocosm . reports that in the 27 th year of his Age he applied himself to Andronicus Palaeologus , Emperour of Constantinople , offering to him Reasons for the Emendation of the Roman Calendar . LUDOVICUS CAERLION , so called from the Town of Caerlion in Wales , where he was born , a learned Theologue and Physician , wrote De Eclipsi Solis & Lunae ; Tabulae Eclipsium Solis & Lunae , secundum Diametros Richardi Wallingfordi , now extant in his Majesty's Library at St. Iames's ; Canones Eclipsium ; De Tabulis Umbrarum ; and Fragmenta Astronomica . IB'N SHATER DAMASCENUS , stiled by Mr. Graves , Sedulus Coeli Siderúmque Inspector , by many Observations made at Damascus , found the Obliquity of the Zodiack to be 23° . 31′ . He wrote likewise Canons , and universal Precepts of Astronomy , and Of Astronomical Instruments , and their use ; as likewise De extruendis Coeli Thematibus , as cited by Hottinger , Smegm . Orient . His Tables are extant in the Publick Library , at Oxford . JOHANNES BOCCACIUS is about this time numbred among Astronomers by Gualterus , in Chronico , as cited by Ricciolus , in Catalog . Astron. THEOPHRASTUS PARACELSUS , besides his many other Works in Physick and Chymistry , hath left some Astronomical and Astrological Fragments , published by Gerardus Dornus , together with his Book , De Meteoris & Tribus Principiis : He writ De Astronomia Magna , & Astronomiae Magnae Compendium , Printed in the year 1584. RICHARDUS LAVINGHAM , of Suffolk , Professour of Mathematicks , Philosophy , and Theology in the University of Oxford , composed a Book , De Planetarum Distantia ; Compendium Meteororum , in four Books , and two Books , De Coelo & Mundo . He was killed in that Popular Tumult ; wherein Simon Sudbury , Archbishop of Canterbury , was murthered . SIMON BREDON , or BRIDON , alias BIRIDANIUS , born at Winchcomb in Gloucester-shire ; Fellow of Merton Colledge in Oxford , Dr. of Physick , and Professour of Astronomy , wrote , according to Balaeus , Two Books In Demonstrationes Almagesti ; One , In quaedam Capita Ptolemaei ; De Rebus Astronomicis ; Aequationes Planetarum ; De Latitudine Planetarum ; Super Introductorio Alcabitii ; Astronomia Calculatoria ; and Astronomia Iudiciaria . His Book De Aequationibus Planetarum , is yet extant in Manuscript , in the Library of Peter-House in Cambridge . NICHOLAUS DE LYNN , so named from the Town where he was born , in Norfolk , a Carmelite Fryer , Astrologorum sui Temporis in Anglia celeberrimus ac maximus , sayes Balaeus : He wrote Canones Tabularum ; De Natura Zodiaci ; De Planetarum Domibus ; De Sphaera Iudiciali ; Astrologorum Dogmata ; De Figuris & Signis ; De Mundi Revolutione ; De Usu Astrolabii , De Eclipsi Solis ; De Astrorum Iudiciis ; & de Variis Genituris . BLASIUS PELACANIS , or ( as the Italians write him ) BIAGIO PELACANO , of Parma , by Alberto Leandro ( in Descript. Ital. ) stiled an Excellent Philosopher and Astronomer ; left ( sayes Simler from the Authority of Iovius ) Quaestiones Subtilissimae , in Astronomia & Optica . He taught at Pavy under Io. Galeazzo first Duke of Millain ; His Book being yet extant in MS ▪ in the Medicean Library . LEO Emperour of Constantinople , Son of Basilius Macedo was very learned in Mathematicks . His Tactica , sive de Acie ordinanda , are yet extant , Printed at Basile , 1554. And some MSS. of his are in the French King's Library , entitled Logarica ( an Obsolete Word instead of Logistica ) and are supposed to contain some Astronomical Computations , and an Exercise upon Diophantus . HENRICUS DE HASSIA , a Germane , Professour of Theology and Astronomy at Vienna , having shewn his Knowledge in the latter , in his Comment upon Genesis , lib. 1. and in Theoricis Planetarum , as Ricciolus affirms . JOHANNES CHYLMARK , Fellow of Merton Colledge in Oxford , Mathematicus insigniter doctus , as Balaeus characters him , published a small Treatise , De Accidentiis Planetarum . JOHANNES SOMER , a Franciscan Fryer , in the Convent of that Order at Bridgewater , wrote Calendarii Castigationes ; Tertium Calendarii ; Astrorum Canones ; and De Quantitate Anni . RICHARD the Second , King of England , wrote something in Astronomy or Astrology , now extant in his Majesty's Library at St. Iames's . JOANNES DE LINERIIS , or DE LINARIIS , Siculus , wrote Canones primi Mobilis , of which mention is made by Zacutus in his Tables . He wrote likewise Canones Quadrantis compositivi & operativi ; which Pieces of his are extant in MS. in the Library of Nicholaus Trivisanus of Padua , as I find in Thomasinus his Bibliothec. Patavin . GERARDUS CREMONENSIS translated Geber , out of Arabick into Latine , and put forth Theoricae Planetarum ; but such as are severely censured by Io. Regiomontanus . JOHANNES DE EGMUNDA , Professour of Astronomy at Vienna , Published Tables , De Motibus Planetarum , & de Luminarium Eclipsibus , calculated for the Meridian of Vienna . He wrote likewise De Astrolabio , together with other Works , which are said to be yet extant in the Library at Vienna . GALFRIDUS CHAUCER , a learned Knight , and Prince of English Poets , Cui Veneres debet Patria lingua suas , to use Leland's Encomium of him , merits a place in this Catalogue , for his Book of the Astrolabe , which he composed for the use and instruction of his Son. JOHANNES WALTERUS , Scholar , at first , in the Colledge of Winchester , afterwards , Fellow of New-Colledge in Oxford , where he chiefly applied himself to Mathematical Studies , and published Tabulae Aequationis Domorum , and Tabulae Ascensionum Universalium , as they are cited by Balaeus . GULIELMUS BATECUMB , alias BADECON , Professour of Mathematicks in the University of Oxford , wrote De Sphaera Concava ; De fabrica & usu ejusdem ; De operatione Astrolabit , and D●… Sphaera Solida . He is said to have flourished in the Reign of King Henry V. by G. Vossius ; and by Balaeus he is ranged among the Authours of this time . PETRUS ALIACENSIS , Cardinal and Bishop of Cambray , and Chancellour of the University of Paris , wrote , besides his other Theological Works , Quaestiones in Sphaeram Sacrobosci ; De Reformatione Calendarii ; and another Tractate , entitled , Concordia Theologiae & Astronomiae . JOHANNES GERSON , Chancellour of the University of Paris , put forth at Lyons , Trilogium Astrologiae Theologizatae ; or as G. Vossius mends the Title , Trilogium Astrologiae ad Theologiae Trutinam expensae . PROSDOCIMUS DE BELDEMANDO of Padua , some time before Io. Baptista Capuanus , Published a Comment in Sphaeram Sacrobosci , which Lucas Gauricus caused to be Printed in the year 1531. He writ likewise Canones Operativi & Compositivi Astrolabii , and Canones de Motibus corporum Coelestium , written in the year 1434. Whereof a MS. transcribed by Candus Master of Arts and Doctour of Physick , Nephew to the said Beldemandus , is extant in Bibliotheca Candorum , as Thomasinus affirms in Bibliothe●… . Patavin . GEORGIUS TRAPEZUNTIUS , born in Creet , but taking his name from Trapezond , a City in Cappadocia , translated into Latine , Ptolemy's Almagest ; to which he added , of his own , an Isagoge , together with a Comment . He commented likewise upon Ptolemy's Centiloquium , and wrote a Book , De Antisciis ; and another with this Title , Cur Astrologorum judicia plerunque fallant ? as Voss. de Scient . Mathemat . affirms . ULUGH BEIG , Nephew to the Great Tamerlane , put forth most exact Astronomical Tables in Arabick , of the Longitude , and Latitude of the Fixed Stars , calculated for the Meridian of Samarcand . To which were added the Commentary of Ali ▪ Cushgi . But the said Tables , collated with Three Persian Manuscripts in the Bodleian Library , about the year 1665. were translated into Latine , and Printed with the Arabick at Oxford , by Doctour Hyde , Keeper of the said Library , to which he added his own most learned Commentary , together with Mohammedes Tizinus his Tables , of the Declination and Ascension of the Fixed Stars , in Arabick and Latine . ALI CUSHGI wrote Astronomica , extant among the Manuscripts of Iacobus Golius : He flourished in the time of Ulugh Beig , to whom he was assistant in composing his Tables . KADI ZADA , or as the Persians pronounce it , KAZI ZADE , whose name more fully expressed is MULANA SALAH EDDIN MUSA , surnamed Cadi-Zadi Rumaeus , was one of the Assistants to Ulugh Beig , in calculating his Astronomical Tables . MULANA GIJATH EDDIN GIEMSHID Published a Piece , by him entitled Scala Coeli ; or Of the Distances and Magnitudes of the Celestia●… Bodies . He was likewise an Assistant to Ulugh Beig . JOHANNES GAZULUS , of Ragusa , a great Astronomer and Astrologer , flourished about this time ; of him Simler writes , that Nescio quid Astronomicum scripsit ; He is named by Ioannes Regiomontanus , in his Tables of Directions ; and what he writ was a Method of the erecting a Celestial Figure or Scheme , which is now called the Way of Campanus and Gazulus . HUMPHREY , Duke of Gloucester , surnamed The Good , Son of Henry the Fourth , King of England , Nobilitatis omnis , atque Eruditionis Phoenix planè Unicus , as he is stiled by Balaeus , was a great Lover of Astronomical and Astrological Learning , and set forth Tables of Directions , of his own Composing . GEORGIUS THEMISTUS PLETHO CONSTANTINOPOLITANUS composed a Book , entitled , De Mensium ac Annorum Ordine●… Dierúmque Recensione . NICHOLAUS CUSANUS , born at Cusa , a Town seated upon the Moselle , in the Diocess of Treves , known by the title of Cardinal of St. Peter's ad Vincula , a most subtile Divine , Philosopher and Mathematician , wrote ( besides other his Works , not relating to our Subject ) De emendatione Calendarii ; and De Stellarum Fixarum Canone . GEORGIUS PURBACCHIUS , so called from the Town of Peurbach ( the Place of his birth ) in the Confines of Bavaria and Austria , was publick Professour of Mathematicks both at Ferrara and Vienna , and a great Instauratour of Astronomy . His first Essayes were several Tractates of Dyalling , with Tables fitted for the variety of Climates ; a Small Piece , with a Table thereto , of the Sun's Altitude ; Astrolabial Canons ( as Gassendus terms them ) with a Table of Parallels , proportioned to every Degree of the Equinoctial . The making and use of Solid Spheres , or Globes , especially the Celestial , to which he added a New Table of all the Fixed Stars ▪ with their augmentation of Longitude , from Ptolemy's time , to his own . But his chiefest Work ( after his Theory of the Planets , and Tables of Eclipses ) by which he intended to signalize his Name , was the Reducing of Ptolemy's Almagest into a correct Epitome , or Compendium , being chiefly encouraged thereunto by Cardinal Bessarion , which he lived not to complete , but left the same , by Testament , to be fulfilled by his Scholar Iohannes Regiomontanus . JOHANNES FUSOR , or FUSORIUS , contemporary with Purbacchius , published Tables of Sines and Chords ; and by command of Charles VII . King of France , made Observations for the better composing of new Tables of the Celestial Motions , as Gassendus , in the Life of Purbacchius , testifies , extant in MS. in the Library of Nicholaus Trivisanus of Padua , as Thomasinus in Bibliothec. Patavin . affirms . GUILELMUS BOTONER , an English Knight , noble by Extraction , but much more ennobled by his Learning , as well in History , Physick , as Mathematicks , Published with other Works , upon several Subjects , a Book , De Astrologiae Valore . JOHANNES JOVIANUS PONTANUS , a Neapolitane , acquired no little honour and esteem , by his Astronomical Studies and Writings . He translated into Latine , Ptolemy's Centiloquium , and published it with an Exposition or Comment thereupon , and wrote XIV . Books , De Rebus Coelestibus , and Five others , in elegant Latine Verse , entitled , Urania , sive , De Stellis ; and One other , in Verse , De Meteoris . MICHAEL SCOTUS , a diligent Observer of the Stars , at the desire of the Emperour Frederick the Third , put forth , ( about this Time ) Quaestiones in Sphaeram Ioh. de Sacro Bosco , as Ricciolus , Chronol . Astronom . affirms ; which certainly is a great mistake : for Frederick the Third came to the Empire much earlier , and was deposed in the year 1323. Scotus flourishing according to Balaeus in the year 1290. about which time the Reader will find him already inserted in this Catalogue . JOHANNES MULLERUS , commonly called JOHANNES REGIOMONTANUS , or DE MONTE REGIO ; from Cunisberg a Town in Franconia , where he was born , Disciple to Purbacchius , finished the Epitome ( begun by his Master ) of Ptolemy's Almagest . He published likewise Tables of Directions and Eclipses , and first of all in that Age set forth Astronomical Ephemerides , of many years duration , Printed at Augsburg 1488. He wrote likewise De Theoricis Planetarum , & De Cometis , and published a Treatise De Triangulis , Printed at Basile in folio , by Daniel Santbech , and is still a Book of good accompt , as containing in it divers extraordinary Cases about plain Triangles . He assisted Sixtus IV. ( by whom he was honourably to that end invited ) in the emendation of the Iulian Calendar , though he lived not to perfect what he had begun . He dedicated his Tables of the Primum Mobile , to Matthias Corvinus , King of Hungary , who not only rewarded him with 800. Hungarian Crowns , but also made him his dayly Guest , for some time , at his Table , justly deserving to be honoured by Posterity , as the great Advancer of all Mathematical Learning , especially of Astronomy , as well by his own Labours , as the publishing in Print , at Norimberg , the most eminent Authours among the Ancients in that Science ; particularly our Manilius , Ptolemy , Theon , Proclus , Menelaus , Theodorus , Firmicus , Hyginus , and others , to the number of Thirty at least . He observed the Sun's greatest Declination to be 23° . 30′ . He died , as some write , at the 33 d. or , as others , at the 40 th . year of his Age , not without the suspicion of being poysoned by the Sons of Georgius Trapezuntius , the envious opposers of his merits , and lies buried at Rome , in the Pantheon . See more of him in Gassendus , who writ his Life . JOHANNES BLANCHINUS , was , as Blancanus affirms , of Ferrara , but more truly , as Ricciolus , of Bologna , and composed Astronomical Tables , which he dedicated to the Emperour Frederick the Third , to whom he was both well known and acceptable . These Tables , with new ones of his own , and more correct Canons , and several Additions , were by Lucas Gauricus published at Venice , 1526. EBERHARDUS SCHLUSINGERUS of Gasmanstorfe in Franconia , Doctour of Physick at Zurick , writ a Treatise of Comets , and of their Significations ; particularly of a Comet which appeared at Zurick in the year 1472. He writ likewise an Introduction to Astrology , chiefly relating to Medical Elections . BESSARION , by birth a Grecian , Cardinal of the Roman Church , and Patriarck of Constantinople , a great Favourer of Astronomical Studies : He left ( among other his various and learned Works ) a small Tractate , whereof the Manuscript is extant in the Emperour's Library at Vienna , entitled Methodus cognoscendi quot horis , singulis Noctibus Luna fulgeat ; as the same is cited by Simler in Biblioth , Gesner . ABRAHAM ZAGUT , or ZACUTI , was first publick Professour of Astronomy at Carthage , afterwards at Salamanca , of whom Ricciolus affirms , that he was Astronomiae consultissimus . Vossius sayes he was Astrologer to Emanuel King of Portugal . He wrote Fasti , sive Almanach perpetuum omnium coeli Motuum , Printed at Venice 1502. In the Preface of which Work he makes mention of Abenverga , a Iew , his Astronomical Tables , but without giving any account of the Time wherein he flourished . In the year 1474. he observed the Star called Spica Virginis to be in the 17° . 10′ . of Libra , as Ricciolus from the Authority of Augustinus Riccius affirms . His Almanach Perpetuum sive Ephemerides were calculated for Salamanca , the Radix they began from was the year 1472. but the Places of the Planets were taken from Regiomontanus his Ephemerides ; his first part ( which whether ever Printed is uncertain ) beginning from that year . He writ the Preface to the Bishop of Salamanca , ( who he was doth not appear ) Ioannes Michael Germanus made the Problems before it , Alphonsus de Corduba Hispalensis made a Canon of the Equation of Venus , and discourses a little of the Errours of Zacutus . In the same Book one Octavius Sfortiades Episcopus Aretinus , sayes , that Marcus Antonius Grimanus Patricius Venetus , Iuntae Calcographiae imprimendam tradidit Novam Tabellam , utpote Supplementum Aequationis Veneris in 30 Revolutionibus , quam suae Celsitudini Abraham Zacutus ex Damasco destinaverat paululum antequam Diem clauderet Novissimum . Gauricus ( being but a young Man ) corrected and put out the Book at Venice Anno 1515. JOANNES ODDI , of Padua , by Ia. Phil. Thomasinus ( in Bibl. Patav. ) stiled Physicus , & Astronomus ( upon the Score of which last , We give him place in this Catalogue ) wrote a Book which he dedicated to Frederick Duke of Urbine , de Impressionibus Elementorum , de Copia rerum , & Pretio , de Bello , de Religione , de Principibus , de Civitatibus ; which I conceive to be some Astrological Discourse , or Prognostick , extant in MS. in the Library of Hippolytus Oddi of Padua Knight of St. Mark. JOHANNES BAPTISTA CAPUANUS SIPONTINUS , De Manfredonia , and as Ricciolus affirms , Canon Regular of the Church of Lateran , while he was a secular Person ▪ his name was Franciscus Capuanus , and he was publick Professour of Astronomy at Padua , at which time he wrote an Exposition , In Sphaeram Sacrobosci . Being afterwards made a Bishop he revised it , and dedicated it to his Fellow-Canons , sometime his Auditours . He wrote likewise In Theoricas Purbacchii , Computus Ecclesiasticus , and a Book , De Compositione Quadrantis . ANDALO of Genua , a most excellent Mathematician , wrote of the Astrolabe , Printed at Ferrara 1475. THEODORUS GAZA wrote in Greek , De Mensibus , & De Anno , in which sayes Ricciolus , Astronomiae non inscium se ostendit ; Published by Petavius , in Uranolog . CHRISTIANUS MOLITOR , of Clagenfurt , was , as Ricciolus affirms , Astronomus insignis , and wrote , at Vienna , Opuscula Astrologica , which , according to the testimony of Vossius , apud Doctos in magno pretio habentur . NICHOLAUS ORESMIUS wrote a particular Treatise , by way of Commentary , against the Superstition of Iudiciary Astrology . He is cited by Iohannes Picus Mirandula , by the name of Nicholaus Orem , to have written a Book , De Proportionibus Proportionum , as Simler in Biblioth . Gesner attests . ALEXANDER ACHILLINUS , of Bologna , Professour of Philosophy , wrote De Orbibus Coelestibus . ALCHABITIUS , or ALCABITIUS , called likewise ABDILAZUS , an Arabian , composed an Isagoge , or Introduction , Ad scrutanda Astrorum judicia , and writ De Planetarum Conjunctionibus . Ricciolus affirms he wrote four Tractates , in which he comprized the Elements of Astrology , commented upon by Naiboda . Iohannes Hispalensis first translated him into Latine , Printed at Venice in the year 1491. and 1521. together with the exposition of Ioannes de Saxonia , and the Emendations of Antonius de Fantis , Doctour of Physick at Trevigi in Italy . He wrote likewise of Opticks , of which see Vossius , De Scient . Mathemat . There is a MS. Treatise in the Bodleian Library , entitled Introductio ad Iudicia Astronom . under the Name of Algabicus ; I know not whether mistaken for Alchabitius . MARCILIUS FICINUS , an eminent Florentine Physician , Philosopher , and Astronomer , who both in his Notes In Timaeum Platonis , and other his Dialogues , discourses learnedly , as occasion requires , upon several Astronomical Subjects , having likewise put forth an Apology , De Medicina Astrologiae ▪ jungenda ; a Disputation Contra Iudicia Astrologorum ; and a Book , De Sole & Lumine . In his Book , De vita coelitùs comparanda , he shews himself very Learned in Astrology , though he writ against the Astrologasters . JOHANNES KENT , alias KAYLEG , Native of Caermarden in South-Wales , a Great Philosopher , Botanist , and Mathematician , of which Studies he was Professour in the University of Cambridge , put forth Astronomical Tables . JOANNES ANGELUS put forth Opus Astrolabii Plani cum Tabulis , Printed August . Vindel. 1488. JOHANNES ERGHOM , of York , an Augustine Fryar , having , at Oxford , professed Logick , Natural Philosophy and Theology , gained to himself the repute of an eminent Scholar , and put forth a Book of Astrological Calculations . JOHANNES PICUS , Count of Mirandula , Ingeniorum Phoenix , as some have stiled him , besides other Works of exquisite and profound Learning , wrote Twelve Books Against Iudiciary Astrology . NICHOLAUS COMES DE COMITIBUS , a Noble Italian , wrote a Tractate , De Motu & Recessu Octavae Sphaerae , extant in MS. among those of Nicholaus Trivisanus of Padua , recorded by Iac. Phil. Thomasinus in Bibliothec. Patavin . PONTICUS VIRMIUS , alias VIRUNNIUS , Native of Trevigi in Italy , Professour of Philosophy , writ , besides many other Works upon different Subjects , a Commentary In Sphaeram Iohannis Sacrobosci . JACOBUS SCHONHEINTZ , Professour of Mathematicks and Philosophy , in Academia Herbipoli , writ an Apology in vindication of Astrology , against Io. Picus Count of Mirandula . DOMINICUS MARIA NOVARAS FERRARIENSIS , Professour of Astronomy in Bologna , and Master to Copernicus , is said to have observed the Sun's greatest Declination to have been 23° . 29′ . He was a great Promoter of Astronomical Observations , both by his teaching and practice . BERNARDUS WALTHERUS , of Norimberg , Disciple to Regiomontanus , and a Continuatour of his Observations , wh●…ch with his own were published , first at Norimberg ; afterwards together with the Hassian and Tychonick , by Willebrodus Snellius . He was a great Observer of the Stars , and partly from the Authority of Alhazen and Vitellio , partly by his own experience , made it appear of how great moment the Doctrine of Refractions is , in relation to the Stars , when near the Horizon . HERMOLAUS BARBARUS , a Noble Patrician of Venice , and Patriarch of Aquileia , besides his other eminent Works , both in Historical and Critical Learning , writ a Book , De convenientia Astronomiae & Medicinae . CHRISTOPHORUS COLUMBUS , a Native of Genua , by Blancanus stiled Argonautarum Princeps , trusting to his skill in Astronomy and Geography , by a high and daring , yet a happy and successful undertaking , discovered , to the Old , a New World. JOHANNES ABIOSUS , of Naples , Doctour of Physick , and Professour of Mathematicks , writ Dialogues in defence of Iudiciary Astrology , in which he predicts many Schismes and future Changes to happen in the Church . He dedicated his Books to Alphonsus King of Sicily . JOANNES LUCILIUS SANTRITTER HEILBRONNENSIS , reduced the Alphonsine Tables into a most easie Order and Method , to which he added Tables of his own , with Rules or Canons ▪ thereunto . He writ likewise a Book of the Judgements of Nativities , Printed at his own Shop in Venice , 1494. JOANNES ANGELUS BAVARUS , of Aichen , put forth a Correction of the Romane Calendar , a Plain Astrolabe , a Treatise of Nativities , and of unequal Hours in each Climate of the World , as also Ephemerides , and various Prognosticks , Printed at Venice in the year 1494. He died in the year 1512. at which time he was about finishing Purbacchius's Table , of the Equations of the Planets Motions . LAURENTIUS BONINCONTRIUS MINIATENSIS , writ Three Books , De Rebus Coelestibus , in Heroick Verse , Printed by Robert Winter , at Basile , in the year 1540. with the accession of divers Observations of the Eclipses of the Sun and Moon , made by Philippus Melancthon , Iohannes Stigelius , M. Acontius , Ioachimus Camerarius , and Georgius Aemilius . He was the first that wrote a Comment upon Manilius's Astronomica , Printed both at Bologna , and at Basile . JACOBUS FABER , besides his Arithmetical Epitome of Boetius , and his Comment upon Iordanus Nemorarius , wrote also a Commentary , In Sphaeram Sacrobosci . RAPHAEL VOLATERRANUS , a Chronologer and Cosmographer , who in the third Tome of his XXXVIII . Books Urbanorum Commentariorum , collected ( as himself affirms ) out of more than a thousand Greek and Latine Authours , hath written , De Philologia , sive Artium Rudimentis , in which those of Astronomy are included . LUCIUS BELLANTIUS , of Siena , wrote Twenty Questions touching the truth of Astrology , and Twelve Books in defence of Astrology , against Picus Mirandula , Printed at Florence and Basile . To which are annexed the Dialogues of Gabriel Pirovanus , De Veritate Astrologiae . CONRADUS COCUS WIMPINAE DE BUCHONIA , Professour of Theology at Francfort , and Leipsick , writ , among divers other Tractates , six Books De Corporibus Coelestibus , as Simler testifies . STEPHANUS ROSINUS of Ausbourg , Professour of Philosophy , Batchelour of Divinity , and Canon , at Vienna , taught Astronomy there , and published Tables of the Declinations of the fixed Stars , with Prognosticks . JOHANNES MANTZ , of Plabeim , a famous Theologue , and Astronomer , in his time , wrote Prognostica ex Stellis . ANDREAS STIBORIUS , a Bohemian , Canon and Professour of Mathematicks at Vienna , a most acute Astronomer . He composed an Epitome of Ptolomy's Almagest , Albategnius , and Geber ; wrote five Books touching Shadows ; a Book of Astronomical Instruments , of the first and second Mobile , with his own Canons , and those of the Ancients ; an Introduction in sensilem Astronomiam ; a Book of Mathematical Authours ; and of the Primum Mobile divided into four parts , and handled Geometricè , Arithmeticè , Exemplariter , & Instrumentaliter . See more of him in Vossius , de Scient . Mathemat . MARCUS BENEVENTANUS , a Celestine-Monk , wrote upon Thebit , De Octava Sphaera . He likewise corrected Ptolemy's Planisphere , and together with Iohannes Cota of Verona , Scipio Carteromachus , of Pistoia , and Cornelius Benig●…us , of Viterbo , sedulam navavit operam in Geographia Ptolemaei corrigenda , sayes G. Voss. De Scient . Mathemat . BARTHOLOMAEUS VESPUCIUS , a Florentine , publick Professour of Astronomy in the University of Padua , where he drew many into admiration of his Learning . He commented in Sphaeram Sacrobosci , and put forth an Oration , in Laudem Quadrivii , sive , Quatuor Disciplinarum Mathematicarum , chiefly of Astrology . JOHANNES GANIVETUS , of the Order of Minime Fryars at Vienna , put forth a small Astronomical Treatise , beginning with these words , Quod Coeli enarrant , &c. To which he added an Abbreviation of Aben-Ezra , De Luminaribus & Diebus Criticis , with the Astrology of Hippocrates , as Gesner affirms , Printed at Lyons , in the year 1508. JOHANNES EZLER , of Mentz , published a Piece entitled Speculum Astronomicum , in which he treats of the Causes of the Errours in Astrology proceeding from the neglect of the Equation of Time. He put forth likewise the Theory of the Planets , and of the Eighth Sphere ; Printed at Basil , by Henricus Petri , 1509. Unà cum Theoricis Purbacchii . JACOBUS LOCHER , PHILOMUSUS GERMANUS , wrote among other things , a Treatise De Cometa , mentioned by Simler . in Bibl. Gesner . AUGUSTINUS RICCIUS , of Casal , wrote a learned Treatise , Of the Motion of the Eighth Sphere , in which he professes to have learnt Astronomy of Abraham Zaguti , at Carthage and Salamanca . He wrote likewise an Epistle touching the Authours of Astronomy , wherein he shews the same to have come originally from the Hebrews . In which Work of his ( sayes Simler . in Bibl. Gesner . ) are contained Platonica quaedam & antiqua Magiae Dogmata . JOHANNES VERNERUS , of Norimberg , Successour to Ioh. Regiomontanus , and Bernardus Walterus , commented upon Ptolemy's Geography , wrote De motu Octavae Sphaerae , and published Astronomical Tables . In the year 1514. he observed the Sun's greatest Declination to have been 23° . 28′ . and the distance of the first Star in Aries , from the Equinoctial Point , 26° . LUDOVICUS VITALIS , a Bolognian Astronomer , flourished about this time , as Ricciolus ( Chronolog . Astronom . ) affirms , though without any mention of his Works . JOHANNES HEREMITA , of Ferrara , is by Ricciolus in Chronic. Astronom . stiled Geometra & Astronomus non vulgaris , but he gives no particular account of his Works or Writings . PAULUS MIDDLEBURGENSIS , Bishop of Fossombrone , or Forum Sempronii , wrote XIV . Books of the Emendation of the Calendar and Observation of Easter , in which Work he not only treats of the Romane Account , but also of the Iewish , Egyptian , and Arabian Years , having therein designed the exact Doctrine of all Times . He wrote likewise XIX . Books of the Year and Day of our Saviour's Nativity and Passion , and other Pieces of like Argument , Voss. de Scient . Mathemat . He writ Prognosticon ostendens Anno Dom. 1524. Nullum neque Universale neque Particulare Diluvium futurum . Forum Sempronii 1523. JOANNES STOEFLERUS JUSTINGENSIS , Professour of Mathematicks at Tubingue , wrote a Treatise De fabrica & usu Astrolabii . He likewise composed Ephemerides , Calendarium Romanum Magnum , dedicated to Maximilian the Emperour , and Astronomical Tables , and wrote a large Commentary in Sphaeram Procli . His Death , or the occasion thereof at least , was very remarkable ( if the Story be true . ) Having found by calculation , that upon a certain Day his life was like to be endangered by some ruinous accident , and the day being come , to divert his thoughts from the apprehension of the danger threatning him , he invites some Friends of his into his Study , where , after discourse , entring into some dispute , he , to decide the controversie reaches for a Book , but the Shelf on which it stood being loose came down with all the Books upon him , and with its fall so bruised him , that he died soon after of the hurt , Voss. in Addend . ad Scient . Mathemat . But the whole Story of his Death , of which some make Calvisius the Authour , is false by the Testimony of Io. Rudolphus Camerarius Genitur . 69. Centur. 2. who had it from Andreas Ruttellius his Auditour ; for he died of the Plague at Blabira Febr. 16. 1531. in the 78 th year of his Age , happening ( according to Calculation if you will believe it ) from the Direction of ☉ to ♂ . ALBERTUS PIGHIUS , besides his other learned Historical Works , wrote of the Observation of the Solstices and Equinoxes ; Of the Restitution , or Emendation of the Calendar , and a Defence of Astrology , against some Prognosticatours of his Time , particularly an Apology against the New Astronomy of Marcus Beneventanus , a Celestine-Monk , traducing the Opinions of all Modern Astronomers , touching the motion of the Eighth Sphere . JOHANNES HASFURT VIRDUNGUS , a Germane Astronomer , set forth Tables , ( by him entitled Tabulae Resolutae ) for supputation of the Celestial Motions , Printed at Norimberg by Iohannes Petreius , in the year 1542. He published likewise in the year 1521. Prognosticon , upon the stupendious Conjunction of the Planets , which was to happen in the year 1524. following ; with some other Prognosticks of his , written in High-Dutch , as Gesner . affirms . He writ likewise Novam Medicinae Methodum quâ ex Mathematica ratione curandi rationem ostendit , Printed Helingae & Hagenoae 1532. and set out afterwards with a Commentary by Ioannes Paulus Galluccius Venet. 1580 : GEORGIUS COLLIMITIUS TANNESLETTERUS was Scholar to Andreas Stiborius , as Gesner affirms . He writ De Applicatione Astrologiae ad Medicinam ; De Natura & Proprietatibus Planetarum , out of Haly , Firmicus , and Alchabitius , and some other Tracts upon those Arguments , Printed at Basil , 1524. MOHAMMED IBNO'L ATTAR , published Astronomical Tables of the Motions of the Planets , calculated for the Longitude of Damascus ; written in the year of the Hegira 930. and of Christ 1523. and preserved in Manuscript in the Publick Library at Oxford . ALBERTUS BRUDZEVIUS , Professour of Mathematicks in the University of Cracovia , was the first Master and Instructour of Copernicus in Astronomy , as we find it mentioned by Gassendus , in the life of Copernicus . PETRUS APPIANUS , of Leipsick , called in the Germane Tongue , Binewilt , Professour of Mathematicks at Ingolstadt , ( in intimate favour with the Emperour Charles the Fifth , who not only invited him to his Court , but also honoured him with Knighthood ) wrote a Book of Cosmography , revised and augmented by Gemma Frisius , together with Observations of several Eclipses . He put forth likewise an Instrument , or Table of the Primum Mobile , with 100 Problems thereupon ; and another Piece entituled Opus Caesareum , in which , to use Ricciolus's Expression , Rotulis & Automatis ingeniosissimis docet expedire omnia ferè Problemata Astronomica . Of his several other Works , not proper to this place , see Vossius , De Scient . Mathemat . FRANCISCUS SARZOSUS of Xelsa in Arragon , wrote two Books in Aequator●…m Planetarum Alphonsinae Hypothesi superstructum , as Ricciol . affirms , Chron. Astronom . Part. 2. JOHANNES VOGELLINUS was Disciple to Ioh. Regiomontanus , and made Observations on the Comets appearing in the years 1527. and 1532. PETRUS CIRVELLUS , besides his Cursus Mathem . Artium , Published a Treatise De Correctione Calendarii , Printed Compl. 1528. HENRICUS BAERSIUS , alias , VEKENSTYL , a Mathematician and Printer to the University of Lovaine , put forth , but not under his own Name , Tabulae perpetuae Longitudinum & Latitudinum Planetarum , calculated for the Meridian of Lovaine . And under his own name he likewise set forth a Book , De Compositione & Usu Decretorii Planetarum ; and another , De Compositione & Usu Quadrantis . OTHO BRUNFELSIUS , Doctour of Physick at Mentz , totius 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , cultor , a great Student likewise in Divinity and the Sacred Scriptures , out of which he endeavoured to refute Iudiciary Astrology . He prefixed likewise to the Edition of Firmicus , Printed by Hervagius , and dedicated to him by Nicholaus Prucnerus , a small Treatise not unuseful to young Beginners , De Definitionibus & Terminis Astrologiae . JOANNES FERNELIUS of Ambois , a famous French Physician , and as eminent a Geometrician and Astronomer , wrote besides other his Learned Works , a particular Treatise , entituled , Cosmotheoria , in which he explains the Motions , Site , Magnitude and Theory of the Celestial Bodies ; and another Piece , called Monalosphaerium . JOHANNES CARIO , besides his Chronological Work , left , as Vossius terms them , Practicas Astrologicas , nec non Ephemerides , beginning with the year 1536 , and ending in the year 1550. JACOBUS MILICHIUS , Professour of Mathematicks at Wittemberg , and Tutour to Erasmus Reinholdus , wrote a Commentary upon the Second Book of Plinius Secundus , the Subject whereof is chiefly Astronomical . ORONTIUS FINAEUS , of Dauphiné , Regius Professor of Mathematicks at Paris , wrote De Sphaera ; Of Cosmography ; Of the Theory of the Planets ; Astronomical Canons , or Problems of the Primum Mobile ; Of the difference of Longitude , to be found by the Moon ; and several other Pieces ; which ( as Blancanus advises ) ought to be read cum Antidoto Petri Nonnii de Erroribus Orontii . HIERONYMUS FRACASTORIUS , a Native of Verona , an excellent Poet , Physician , Philosopher , and Astronomer , Published a Book De Orbibus Excentricis & Homocentricis , which he dedicated to Pope Paul III. SEBASTIANUS MUNSTERUS was famous for two things , as Vossius affirms , to wit , Hebraeis Literis , & Mathesi . As to what concerns our purpose , he wrote Notes , In Geographiam Ptolemaei , & Universalem Cosmographiam , and of Dyalling ; as also Organum Uranicum , wherein the Theories of the Planets , and their Motions were computed for an hundred years and more . He was also Authour of the Canones super novo Luminarium Instrumento . JOACHIMUS FORTIUS RINGELBERGIUS of Antwerp , writ De Horoscopo , De Tempore , De Cosmographia , and Three Books of Astrological Institutions . JOHANNES ROBINUS , in English , Robins , was a great Astrologer , and put forth a Book , De Portentosis Cometis , dedicated by him to King Henry VIII . which Balaeus calls , Opus valde Lucidum , now extant in Manuscript , in the hands of Mr. Thomas Gale. SIMON GRYNAEUS , Native of Viring , a Town in Suevia , or Suaben , merited eminently in all kind of Learning , particularly by publishing , in Greek , the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 of Ptolemy , to which he added a Preface of his own touching the use thereof , Dedicated to King Henry the Eighth of England , Printed at Basil , 1538. HENRICUS GLAREANUS , a Geographer , Chronologer , Musician , and Physician , Native of Glarona , commonly called Glarys , a Town in Swisserland , put forth a Book De Geographia , induced chiefly thereunto , as he pretends in his Preface , because he found the Sphere of Proclus to be too concise , and only fitted to the Horizon of Greece , and erroneous , as to the Description of some Circles ; and Sacroboscus in his Parallels and Climates , mutilous and defective . He published likewise other Pieces , both in Astrology and Cosmography , being ( according to the testimony of G. Vossius ) Vir undequaque doctissimus . ACHILLES P. GASSARUS of Lindaw , by Gesner stiled Medicus & Mathematicus praestantissimus , put forth a Chronology from the beginning of the World to the year of Christ 1532. He published likewise a Mathematical Table , entituled , Sciaterion Pedarium , Printed at Zurick . JODOCUS CLITCHTHOVEUS NEOPORTICENSIS , writ a Comment upon Iacobus Faber his Theory of the Planets . GEORGIUS PRUCNER , of Ruspach , left behind him ( sayes Simler in Bibl. Gesner . ) very fair and exquisite Astronomical Instruments , and several Books collected by him , in Astrorum Scientia , yet preserved at Vienna , in Bibliotheca Facultatis Artium . JACOBUS CEPORINUS of Zurick , eminently learned in the Hebrew , Greek , and Latine Languages , put forth a Commentary upon Dionysius his Periegesis , and Aratus his Astronomicon , Printed at Basil , by Wolphius , in the year before mentioned , as Gesner testifies . LUDOVICUS DE RIGIIS , published Astrological Aphorisms , addressed to the Patriarch of Constantinople , Printed at Norimberg , in the year 1535. together with Ptolemy's Tetrabiblos . JOHANNES STIGELIUS , Native of Gota , a City in the Province of Thuringen , in Germany , an ingenious Poet and Mathematician , Professour at Wittemberg and Iena , put forth Prognosticks upon the Eclipse of the Moon happening in the year 1536 , as likewise others upon one of the Sun in the year following , and upon one of the Moon , and another of the Sun , in the year 1551. JACOBUS KAEBELIUS , besides an Arithmetical Treatise , Published another of the Astrolabe , in High-Dutch , which was Printed afterwards in Latine , at Paris . JACOBUS ZIGLERUS , of Landaw , a City in the Province of Vasgow , in the lower Alsatia , set forth Constructionem Solidae Sphaerae , Printed at Basil , by Valderus , together with Aratus and his Scholiast , in the year 1536. He wrote likewise Scholia in Procli Lycii Sphaeram ; and De Canonica per Sphaeram operatione ; and De Hemicyclio Berosi , mentioned by Vitruvius , l. 9. c. 9. He published likewise a Comment upon the Second Book of Pliny's Natural History ; in which he explains the most obscure , especially Astronomical , Places therein . NICHOLAUS COPERNICUS , by Bulialdus , not without reason , stiled Vir absolutae subtilitatis , a Native of Thorne in Prussia , and Canon of the Church of Frawenburg , the Cathedral of Warmerlandt , Scholar to Dominicus Maria , of Ferrara , to whom he was Assistant in making his Astronomical Observations at Bologna ; and Professour of the Mathematicks at Rome , honoured at his Publick Lectures with the Assembly of the most Illustrious Persons in that City , whence returning into his own Country , he wholly applyed himself to the study and instauration of Astronomy , finding the Sun's greatest Declination to be 23° . 28′ . The year before his Death , at the instance of the Cardinals , Schomberg , and Ghisi , he published his Noble Work , De Revolutionibus Orbium Coelestium , in Six Books , in which he not only revived , but most happily united , and formed into an Hypothesis of his own , the several Opinions of Philolaus , Heraclides Ponticus , and Ecphantus Pythagoreus . For according to the opinion of Philolaus , he made the Earth to move about the Sun , as the Center , whence its Annual Motion . ; And with Heraclides and Ecphantus , he likewise gave it a Motion like that of a Wheel about its own Axis , whence its Diurnal Motion ; an Hypothesis so near the Truth , that like that when persecuted , maugre all Opposition , Per damna , per caedes , ab ipso Sumit opes animúmque ferro ; As Ricciolus ( though a Dissenter from it ) observes . ANDREAS OSIANDER took not only care in publishing the first Edition of Copernicus his Book De Revolutionibus , but condescended to be Overseer of the Press , while it was Printing , to which he added a brief Preface of his own , therein chiefly endeavouring , because of the seeming Novelty of the Opinion , to perswade the Reader , to look upon it as an assumed Hypothesis , rather than an asserted Tenet . To which purpose , about that time was published this Distich , Quid tum si mihi Terra movetur , Solque quiescit Et Coelum ? Constat Calculus inde Mihi . Of which Gassendus , in Vitâ Copernici . JOHANNES SCHONERUS , a Native of Carolostadt , Professour of Mathematicks at Norimberg , put forth Astronomical Tables for their perspicuity called Resolutae , and a Book De usu Globi Stelliferi , De Compositione Clobi Coelestis , De Usu Globi Terrestris & de Compositione Ejusdem ; as also another Piece , called Aequatorium Astronomicum ; Libellus de Distantiis Locorum per Instrumentum & numeros investigandis ; De Compositione Torqueti ; In Constructionem & Usum Rectanguli sive Radii Astronomici Annotationes ; Horarii Cylindri Canones ; Planisphaerium seu Meteoroscopium ; Organum Uranicum ; Instrumentum Impedimentorum Lunae . All Printed at Norimberg in fol. 1551. GEORGIUS VALLA , an Italian , Native of Piacenza ; among other his Learned Works , wrote a Treatise in four Books De tota Astrologia , In which , Fabrica Ususque Astrolabii exaratur , & quae Signorum in exhibendis Medicaminibus sit habenda Observatio . He writ likewise a Commentary in Almagestum & Quadripartitum Ptolemaei , and translated out of Greek into Latine , Proclus Diadochus his Hypotyposes Astronomicarum Positionum , and Cleomedes de Contemplatione Orbium Coelestium . V. Simler . in Biblioth . Gesner . JOHANNES BAPTISTA AMICUS COSENTINUS , wrote De motu Coelestium , juxta Principia Peripatetica , Published in the year 1532. PETRUS PITATUS , of Verona , wrote Isagogen ad Ephemerides , and De novo Calendario instituendo , which he addressed to Pope Paul III. He wrote likewise an Explication of the Rising and Setting , of the Fixed Stars , Printed at Basil , 1568. JOHANNES LUCIDUS SAMOSATHEUS , about this time put forth his learned Chronological Labours , non sine Eruditae Caveae Applausu , sayes G. Vossius ; in which are contained Emendationes Temporum ab Orbe condito , with Canons in perpetuam Temporum Tabulam ; Of the true Day of our Saviour's Passion ; And an Epitome of the Emendation of the Romane Calendar , Printed at Venice by Iunta , 1537. BONETTUS a Iew , put forth a small Treatise De Annulo sive Instrumento Astronomico , Printed at Marpurg 1537. SYMPHORIANUS CAMPEGIUS ( alias CHAMPERIUS ) Eques Auratus Lugdunensis , a French-man , among other Learned Works of his in Physick and Philosophy , put forth several Mathematical Treatises , and particularly One of Astronomy , Printed by Henricus Petrus , at Basil 1537. JOHANNES GIGAS STAINFORTENSIS , Published Enchiridion Sphaericum , seu Systema Cosmographicum compendiosum . He wrote likewise , according to the Testimony of Simler in Bibl. Gesner , an Elegy upon two notable Eclipses of the Moon , which happened in the year 1538. Whereof the former was on the fourteenth of May , the latter on the sixth of November . His Enchiridion Sphaericum was Printed at Oxford in the year 1664. MAURUS FLORENTINUS , first , a Monk , of the Order of the Humiliati , afterwards , of the Fraternity of the Servants of the Blessed Virgin , of whom Gerardus Vossius sayes , That he was most learned in the Latine , Greek , and Hebrew Tongues , and excellently well skilled in Cosmography , and other Sciences , Published in his own Language ( the Italian ) divers Pieces , as his Annotations in Sphaeram Sacrobosci ; and ( besides his Sphaera Theologica & Christiana ) Sphaera Platonica , which he dedicated to Cosmo de Medicis . He wrote likewise De Arte Navigatoria ; and an Epitome of Musick . GASPAR BORNERUS , Professour of Phylosophy at Leipsick , among other Tractates , put forth a Book , De Stellis . JOHANNES PENA , a French-man , Regius Professor of Mathematicks in the University of Paris , translated Euclid's Opticks into Latine ; to which he prefixed an Encomium of Opticks , wherein ( to use Gesner's Words ) there are Iucundissimae Disceptationes & imprimis arduae , touching the Epicycles , Excentricks , Apsides , Apogaeums , and Perigaeum's of the Planets , as likewise of their Parallaxes ; together with ingenious Arguments concerning the Earths Rest or Motion , drawn from the Principles of that Art. He first maintained the Heavens to consist of no other Substance than that diffused through the Aery Region , and discovered some Comets to have been above the Moon ; as Gassendus , in the life of Tycho , observes . JOHANNES PIERIUS VALERIANUS , the noble Authour of Hieroglyphicks , wrote and dedicated to Cardinal Alexander Farneze , being but yet young and much addicted to Astronomical Studies , an elegant Compendium Of the Sphere . PETRUS CATENA a Venetian , Doctour in Theology and Professour of Mathematicks at Padua , about the same time with Pierius , wrote upon the same Subject of the Sphere ; and other Mathematical Peeces . JULIANUS RISTORIUS DE PRATO , a Carmelite Fryar , Doctour in Theology , and an eminent Astronomer , Tutour to Iunctinus , by whom , in his Preface to his Tabulae Resolutae , he is reported to have observed the Planets for several years , viz. from the year 1536. to 1542. PAULUS CRUSIUS published a Treatise , wherein he sets forth the Doctrine of the Sun's Revolutions , and Tables of the mean Conversions of ●…ime , and of the Sun's motion , in Annis Tropicis & Sideriis . ANGELUS FORTIUS Doctour of Physick , is by Gesner , in Biblioth . reckoned as an eminent Astrologer . ANTONIUS DE MONTULMO , Doctour of Arts and Physick , published a Book De judiciis Nativitatum , illustrated with the additions of Io. Monteregi●…s ; Printed at Norimberg , 1540. JOHANNES MASSAEUS , put forth twenty Books of Chronology , from the beginning of the World to the year now mentioned , to which he prefixed a fourfold Calendar , to wit , the Egyptian , Hebrew , Macedonick , and Roman . Voss. De Scient . Mathemat . FRANCISCUS MAUROLYCUS , Abbot of Messena in Sicily , whom Ricciolus calls Siciliae Lumen clarissimum , wrote three Books of Cosmography , intended as a Comment upon Ptolemy's Almagest . To him we are beholding for Theodosius's Sphaerica , and those of Menelaus , which he first of all published . He put forth a Piece , De Lineis Horariis , Fabricam Astrolabii , and divers other Works , mentioned in the beginning of his Cosmography . He was the first that wrote of Secant Lines , as Blancanus affirms . He left likewise behind him a Posthume Work , entituled , De Lumine & Umbra , and many Treatises unprinted , as appears at the End of his Opus●…ula , and though it be beside our Argument , yet in regard it is not well known , we think fit to mention that Alphonsus Borellius published in Sicily about 1656. the Comment of Maurolycus on the first four Books of Apollonius his Conicks , with two more of the said Authours , of which if there were Copies they would be grateful to Students , and more acceptable than that of Commandinus , in which the Text and Comment lie dispersed , which Inconvenience is avoyded in that of Maurolycus ; the said Borellius is likewise now about publishing Maurolycus his Archimedes at Rome . JOHANNES ANTONIUS DELPHINUS , of Casal , Provincial of the Franciscan Order , wrote , and dedicated to Camillus Palaeottus , a Senator of Bologna ; a Book , De Caelestibus Globis , & Motibus , full of Erudition , as Ricciolus affirms . PHILIPPUS MELANCTHON , among other the numerous Volumes by him published , set forth Tabula de Mensibus Graecorum , & Descriptiones Eclipsium Solis & Lunae , annis jam aliquot visarum , usque ad Annum 1540. and translated out of Greek into Latine , Ptolemy's four Books , De Syderum effectionibus . V. Simler . AUGUSTINUS NIPHUS PHILOTHEUS SUESSANUS , who by his great Learning gained to himself the Title of Philosophus Magnus , among other the various Works by him published , writ ( as to our purpose ) a particular Treatise , De figuris Stellarum Helionoricis , in two Books ; Another , De Diebus Criticis , seu Decretoriis ; a third , De falsa Diluvii Prognosticatione quae ex conventu omnium Planetarum ( qui in Piscibus contingeret anno 1524. ) divulgata est , in three Books , addressed to the Emperour Charles the Fifth . He wrote likewise Eruditiones in Apotelesmata Ptolemaei , & Annotationes in Librum secundum Ejusdem Quadripartiti , mentioned , wi●…h the rest , by Simler , in Bibl. Gesner . JACOBUS PELETARIUS , a French man , besides his Geometrical Works , wrote De Constitutione Horoscopi . He published likewise Astronomical Tables , ●…and a Compendium of Astronomical Fractions ; as also of the Sun's place , and ▪ that of the Moon , in the Zodiack . ERASMUS OSWALDUS SKREKENFUSIUS , of Austria , Disciple , according to Ricciolus , to Henricus Glareanus , according to Vossius , to Se●…stianus Munsterus , Professor , at Freiburg in Brisgaw , of the Hebrew Tongue and Mathematicks , wrote a Comment in Sphaeram Sacrobosci , Annotations on 〈◊〉 Almagest , put forth a Book De Primo Mobili , and of the Theory of the Plan●… ▪ Another De Gentium Calendariis , and translated , out of Hebrew into Latine , the Sphere of Rabbi Abraham Cai. JOACHINUS CAMERARIUS , of Bamberg , a Town in Franconia , put forth , at Norimberg , in the year 1532. several Greek Astrological Authours , by him translated into Latine , as 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , sive , Rationem Orbis Solaris ; likewise , Excerpta ex Hephaestione Thebano , De Duodecim Signis & eorum effectis , also 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Quid Stellae Erraticae , sive Quinque Planetae , in unoquoque Zodiaci Signo significent . These Pieces he set forth in Greek and Latine . And in Latine only , he published a Fragment of the first Book of Vettius Valens , his Florida ; and in Greek only Mercurius Irismegistus his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Medicationes rationibus Astrologicis convenientes . In the year 1535 ▪ he set forth , at Norimberg , in Verse , Tùm Phaenomena , sive Siderum ac Stellarum Historiolam , tùm Prognostica . And in the year 1541. he published the two first Books of Ptolemy , De Iudiciis Astrologicis , by him translated into Latine , and illustrated with Annotations . We are obliged to him likewise , for the first publication of Theon Alexandrinus , his eleven Books of Commentaries upon Ptolemy's Almagest , which he caused to be Printed at Basil , by Walderus , from a MS. of Cardinal Bessarion's , brought into Germany by Regiomontanus . See more of this eminently learned Person , in G. Vossius , L. de Scient . Mathemat . RAINERUS GEMMA FRIZIUS , Physician and Professor of Mathematicks at Lovaine , put forth a Book of the use of the Globe , and the Astronomical Ring ; De Principiis Astronomiae & Cosmographiae ; De Astrolabio Catholico , &c ▪ He left his Son Cornelius Gemma , his Successour in the Professor's Place . JOANNES GUIDO wrote , De Observat. Temporis Astrorum , Printed at Paris 1543. CLAUDIUS MARIUS ARETIUS a Patrician of Syracuse , and Historiographer to the King of Spain , wrote a Comment , by way of Dialogue , upon this Verse of Virgil's . Defectus Lunae varios , Solisque labores . BUCHARDUS MITHOBIUS , wrote a Piece entituled Compositi●…●…li Astronomici , Printed together with the Treatise of Iohannes Driander , De Annul●… Astronomicis ; as Simler affirms . MICHAEL ANGELUS BLONDUS , Doctour of Physick , w●…ote and dedicated to Pope Paul III. a Book De Diebus Criticis ; and to Rudolphus Cardinal of Carpegna another , De Anticipatione Stellarum fixarum cu●… 〈◊〉 significationibus . COELIUS CALCAGNINUS , among the various Works by him published , set forth a Paraphrase on the three Books of Aristotle's Meteors ; A Commentation , Quod Coelum stet , Terra moveatur ; De Mensibus , & De Re Nautica ▪ See more of him in Simler . Bibl. Gesner . GEORGIUS PILANDER published a Book De Annulo Astronomico , aut Sphaerico . POMPILIUS AZALUS writ De omnibus Rebus naturalibus quae continentur in Mundo , viz. De Coelestibus , de Terrestribus , & Mathematicis , Printed at Venice in Folio ; as Simler in Bibl. Gesner . testifies . JOHANNES STADIUS , Professour of the Mathematicks and History , first , at Paris , afterwards at Lovaine , put forth among other his Mathematical Works , Ephemerides , which he entituled Tabulae Bergenses , in honour of Robertus à Bergis , Bishop of Liege . He put forth likewise other Ephemerides , from the year 1654. to the year 1606. with an Isagoge in Astronomiam & Astrologiam . He left Tabulas aequabilis & apparentis Motus Coelestium Corporum , as G. Vossius stiles them , and Prognostica Stellarum fixarum , cum Tabulis , in the beginning whereof he hath prefixed the History of Astronomy . NICHOLAUS SOPHIANUS CORCYRAEUS , wrote in Greek of the Astrolabe , and by Gesner is said to have flourished about this Time. VICTORINUS STRIGELIUS of Kaufbeurn , a Town in Suaben , published , at Wittemberg , an Epitome of the Doctrine of the Primum Mobile , illustrated with Demonstrations . He was Scholar to Melancthon . AUGERIUS FERRERIUS of Tholouse , Doctor of Physick , whom Scaliger the Father entirely loved and consulted in all his learned Designs , writ , as I find mentioned in Gesner Castigationes Practicae , & De Diebus Decretoriis secundum Pithagoricam Observationem . JOHANNES MERCURIUS MORSHEIMERUS , put forth at Heidelberg , a Dissertation of the Name of Astronomy , it 's Division and Causes ; to which he adjoyned a Table of the Species of ●…ontinued Quantity , serving only for the use of young Beginners . He professes himself to have been Scholar to Melancthon . JOACHIMUS HELLERUS corrected and published several Astrological Authors , before which he prefixed Prefaces of his own , at Norimberg . ANDREAS GERARDUS HYPERIUS , Professor of Divinity in the University of Marpurg , writ , besides other various Tractates , Geometrica , Optica , Cosmographica quaedam , as Simler affirms , in Bibl. Gesner . ERASMUS REYNOLDUS , Native of Salfieldt , a Town in Thuringe , a Province in the Upper Saxony , Son to Iohannes Reynoldus , and Scholar to Iacobus Milichius , was Professor of Mathematicks in the University at Wittemberg , and wrote a most learned Commentary on Purbacchius's Theory of the Planets . He composed likewise , and dedicated to Albert , Marquess of Brandeburg , and Duke of Prussia , Astronomical Tables , according to the Hypothesis of Copernicus , which he called Prutenick Tables , in honour of the said Prince , as also Tables of Directions . He endeavoured likewise to illustrate and establish Chronology from the Eclipses of the Luminaries , and the great Conjunctions of the Planets ; but his Death prevented the finishing of that Work. He had also a Son , called after his own Name , an eminent Mathematician and Physician , who wrote upon the new Star in Cassiopaea , as Tycho Brahe testifies ; Progymnasm . Tom. 1. ARIEL BICHARDUS put forth a Collection of Questions , In Sphaeram Iohannis De Sacro Bosco , which he dedicated to his Godfather , Antonius Mullerus , sayes Ricciolus , in Part. 2. Chronic. Astronom . JOHANNES ROIAS wrote , and dedicated to the Emperour Charles the Fifth , certain Commentaries upon the Astrolabe or Planisphere . JOHANNES MARIA TOLOSAS , of the Order of the Predicants , wrote something of the Sun 's greatest Declination . He published likewise a short Correction of the Roman Calendar , touching the due celebration of Easter . JOHANNES BAVARUS , Medicus & Mathematicus , put forth Ephemerides , beginning in the year 1551. and ending in the year 1560. This Bavarus , is different from Iohannes Angelus Bavarus , mentioned in the year 1494. GEORGIUS JOACHIMUS RHETICUS , Disciple to Copernicus , and Professor of Mathematicks in the University of Wittemberg , where he interpreted and explained Alfraganus . But hearing of the new Hypothesis of Copernicus , he quitted his Professor's place , and went to Copernicus , whom he ceased not to exhort to perfect his Work , De Revolutionibus , which after his death he made publick , illustrating his Hypothesis by a particular narration , which he dedicated to Iohannes Schonerus , published by Maestlinus , and annexed to Kepler his Mysterium Cosmographicum , in the year 1621. He likewise set forth Ephemerides , according to the Doctrine of Copernicus , until the year 1551. What other Astronomical or Astrological Works he had either perfected or designed , will appear by his Epistle written to Petrus Ramus . LUCAS GAURICUS , a Neopolitan , first , Professor of Mathematicks at Ferrara , afterwards Bishop of Civita Reale , corrected the ▪ Alphonsine Tables , as also those of Regiomontanus , and Blanchinus , and published Tables of his own of the Primum Mobile , commonly called Tables of Directions , and Laurentius Bonincontriu ▪ s his Book , De Rebus Coelestibus , and Zacutus his Tables , together with Astrological Precepts and Problems . He illustrated with Annotations Ptolemy's Almagest , put forth a learned Dissertation touching the miraculous Defect of the Sun at the time of our Saviour's Passion , and composed a new Ecclesiastical Calendar , compiled out of the Sacred Scriptures , and Ancient Synods , which last was Printed at Venice 1552. at which time like wise he published at Venice a Book called Tractatus Astrologicus , wherein are many Astrological Judgments on the Nativities of the most eminent Persons of his Time. V. Simler . Bibl. Gesner . TOBIAS MARMORARIUS , a Florentine , and Monk of the Cistertian Order , Vir Mathesios studiis egregiè excultus , as Vossius sayes of him , wrote yearly Prognosticks , of the Seasons of the year , and future Events . ANTONIUS MYZALDUS writ Phaenomena , sive , Tempestatum Signa , quatuor Aphorismorum Sectiunculis Methodicè concinnata ; Cometographia ; Aesculapii & Uraniae Conjugium ; Planetologia ; Three Books of the Sphere , illustrated with Figures and Demonstrations ; Zodi●…cus , sive duodecim Signorum Coeli Hortulus , Libris tribus concinnatus ; Planetarum Collegium , and some other Tractates of like Argument , as Simler , in Bibl ▪ Gesner . JACOBUS HOMELIUS is , about this time , reckoned , by Ricciolus , in the Catalogue of Astronomers , but without any mention of his Works . There was also one Iohannes Homelius , who wrote concerning the New Star in Cassiopea , and is mentioned by Ticho Brahe , in Progymn . Tom. 1. JOANNES STABIUS , of Austria , Poet Laureat , Cosmographer , and Historiographer , to the Emperour Maximilian the First , Professor of Mathematicks at Vienna , wrote a Piece entituled Horoscopicum Universale ; and several other Works , mentioned by his Scholar Georgius Collimitius , in Gesner's Bibliotheca , Tom. 1. PAULUS EBERUS KYTZINGENSIS , put forth Calendarium Historicum , in the Preface to which he treats , De ejus Utilitate , & de Mensium apud diversas Gentes varietate . See more of him in Gesner's Bibliotheca . GASPAR PEUCERUS , Son-in-Law to Philip Melancthon , wrote of the Doctrine of the Celestial Circles , and the Primum Mobile , and De praecipuis Divinationum generibus , and among them , De Praedictionibus Astronomicis , as it is affirmed by Vossius , De Scient . Mathemat . He wrote also Hypotheses Astronomicas , seu Theorias Planetarum , ex Ptolem●…i & aliorum Veterum Doctrinâ , ad Observationes Copernici , & Canones Motuum ab eo conditos , accommodatas , Printed , as Draudius affirms , at Wittemberg , 1572. JOHANNES SCHRAETERUS VINARIENSIS , published , at Vienna in Austria , Astrological Tables , designing to gain himself , a repute by his predictions ; of whom see Gesner's Biblioth . HIEREMIAS BROTHEIEL , put forth various Prognosticks mentioned by Simler . in Addit . Bibl. Gesner . ANDREAS PERLACHIUS of Stiria , Doctor of Physick and Professor of Mathematicks in the University at Vienna , set forth , as Gesner stiles them , G●…mentaria Ephemeridum , ita conscripta , ut quisque absque Praeceptore , ex sola Lectione integram inde Artem consequi possit , Printed by Aegidius Aquila at Vienna 1551. FRANCISCUS RAPALDUS , Doctor of Physick at Bruges in Flanders , wrote against Astrology as altogether useless to a Physician , to whom Petrus Haschardus , of Lisle , a Chirurgeon , replied in a Discourse by him entituled , Clipeum Astrologicum . ROBERTUS RECORD , a Learned Doctor of Physick , and an excellent Mathematician , descended of a generous Family in Wales , illustrated by his learned Labours , Cosmography , Geometry , Musick and Astronomy . He published Cosmographiae Isagogen , wrote a Book , De Arte faciendi Horologium ; and another , De usu Globorum , & de statu Temporum . All which with several others he writ in the English Tongue . PETRUS NONIUS , a Portuguez , Professor of Mathematicks in the Colledge at Conimbra , wrote ' De Crepusculis ; De Erratis Orontii ; Astronomical Problems , and Rules for Observation , together with Annotations in Theoricas Purbacchii , commendable , sayes Vossius , not only for their Acumen and Perspicuity , but for discovering divers things omitted , and detecting several Errors committed by others . HIERONYMUS CARDANUS , a Native of Milan , Professor of Physick and Mathematicks at Bologna , commented upon Ptolemy's Quadripartitum , De Iudiciis Astrorum , and put forth several other Tracts , as 1. De Supplimento Almanach . 2. De Restitutione Temporum , & Motuum Coelestium . 3. De Iudiciis Geniturarum . 4. De Revolutionibus . 5. De Exemplis Centum Geniturarum . Aphorismi Astronomici : Not to mention his many other Works , not relating to our purpose . LEVINUS LEMNIUS , Medicus Zirizaeus , writ three elegant Tractates , in the first whereof he treats of Astrology , shewing the verity or falsity of that Art , in which , sayes Gesner , multae amoenissimaeque causae explicantur , and particularly the Original of the Proverb , Quartâ Lunânati . MICHAEL NOSTRADAMUS , Physician to Henry II. Francis II. and Charles IX . Kings of France , is famous for the several Centuries of Prophetical Prognostications extant under his Name ( lately Englished with large Annotations ) which in his Epistle Dedicatory of some part of them to Henry II. he affirms to have calculated by Astronomical Doctrine . But whether he were a greater Trifler or Astronomer , is by some questioned ; but especially by Iodelé an ingenious French Poet , who hath bestowed on him this Distich ; NOSTRA DAMUS cum falsa damus , nam fallere nostrum est , Et cum falsa damus , nil nisi NOSTRA DAMUS . NICHOLAUS SIMUS , Professor of Mathematicks in the Univertsiy of Bologna , set forth the Theories of the Planets , reduced to a Compendium , illustrated with divers Sculps and Figures . He put forth likewise Ephemerides for 15. years , calculated for the Meridian of Bologna , with Canons expounding the use of the said Ephemerides . MARCUS FRITSCHIUS LAUBANUS HEXAPOLENSIS , wrote a Book De Meteoris , with a Catalogue of Prodigies and Ostents ; Printed at Norimberg , 1555. as Gesner attests . ANDREAS SCHONERUS , Son of Iohannes Schonerus of Carolostadt , published Tables of the Primum Mobile , according to the Fundamentals of Regiomontanus . HADRIANUS JUNIUS HORNANUS , for his Learning merited to be stiled , Alterum ab Erasmo Hollandiae Lumen . He published a Commentary , De Anno & Mensibus , likewise Fastorum Liber sive 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , rerum Memorabilium qualibet Anni die actarum apud Hebraeos , Graecos , Romanos , gentesque exteras , also Calendarium Syllabicum , so called , because the dayes of the year , Vocabulorum Syllabis respondeant ; besides these he put forth Fasti Caesariani & Calendarium . These as he writ them were from hand to hand presented to Edward the Sixth King of England , afterwards being enlarged and corrected , dedicated to his Sister Queen Mary . See more of him in Meursius in Athen. Batav . and G. Vossius de Scient . Mathemat . p. 398. JOANNES GARCAEUS , a Brandeburgher wrote a Piece entituled Methodus Astrologiae , illustrated with 400. Genitures , as Ricciolus affirms . To which Vossius adds , that he put forth , at Wittemberg , a Commentary consisting of XXII . Propositions , in which he comprizes the Doctrine of erecting a Celestial Scheme , and computing the Motions of the Planets . Draudius sayes , he put forth a small Treatise , De Tempore , sive De Ortu & Occasu Stellarum , & De usu Globi Coelestis , Printed at Wittemberg 1565. He was Scholar to Gaspar Peucerus . JOSEPHUS ZARLINUS , a Native of Fossa Clodia ( commonly called da Chioggia ) an excellent Musician , who in his Institutioni Harmoniche , published in Italian , treats likewise of the Harmonick System of the Spheres . RODOLPHUS BATTINGIUS , a Friezlander , published Methodum Astrolabii , according to Vossius , De Scient . Math. CORNELIUS VALERIUS VETERAQUINAS , Successor to Petrus Nonnius at Lovaine , in Collegio Trilingui , put forth an Encyclopaedia , in which he treats of the Sphere , and the Elements of Astronomy , and Geography , succinctly and elegantly . JEAN PIERRE DE MESMES , a French Gentleman , writ in his own Language , Astronomical Institutions , Printed at Paris , in folio , 1557. CONRADUS DASYPODIUS , Professor of Mathematicks at Strasbourg , put forth Astronomical Precepts , and wrote a brief Treatise of Comets and their Effects , famous for being Author of the Astronomical Horologe set up in the Great Church at Strasbourg , the Description whereof he published in the year 1578. GULIELMUS XYLANDER , Successour to Iacobus Mycillus in the Greek Professor's place at Heidelberg , a Person of good repute for his Philosophical and Mathematical Studies , among other Tractates of the later kind , put forth a small Treatise , De usu Globi & Planisperii , Printed at Heidelberg . DANIEL BARBARUS , a noble Venetian , and Patriarch of Aquileia , hath sufficiently manifested his excellent knowledge in all Parts of the Mathematicks , and particularly in Astronomy , by his learned Commentary upon Vitruvius his ninth and tenth Books . JOHANNES TEMPORARIUS wrote an Astronomical Treatise , which he entituled Organum Astronomicum , grounded upon the Prutenick Tables , in which the whole Work of Astronomical Calculation is contracted to two Operations , to wit , only Addition and Substraction . All Proportional Scruples are laid aside , in the search after which much time is fruitlesly spent . The true Precession of the Equinox , which by the Alphonsine Astronomers is called the Motion of the Auges of the fixed Stars , is exposed to view for some Ages to come . The places as well of the Planets as the fixed Stars are with little or no trouble found for any time given . The Conjunctions and Defects of the Luminaries , with their Quantities and Durations , are most exquisitely defined , not only ●…n one Climate , but in any Parallel whatsoever . The Parallaxes , whose invention gives trouble to the most experienced Artists , are by a wonderful compendious way found out and cleared , as to Latitude and Longitude , without the trouble of Calculation . Whence any one may frame to himself Ephemerides without any pains or labour . The Original Manuscript of which Work is at present in the possession of my worthy Friend , George Wharton Esquire . PHILIPPUS FANTONIUS , a Florentine Monk , afterwards Abbot of Camaldolat , published a Book in Italian , of the reason of reducing the Year , to its true Form and Measure ; of whom G. Vossius sayes , that he was Matheseos Scientia egregius , which he publickly professed in the Academy at Pisa. See more of him in Simler . Bibl. Gesner . CYPRIANUS LEOVITIUS , of the Leonitian Family in Bohemia , Mathematician to Otho-Henry , Prince Palatine of the Rhine , put forth Astronomical Observations , with Astrological Prognosticks , upon the new Star in Cassiopaea . He likewise accurately described ( to render Vossius's words ) several Eclipses from the year 1556. to the year 1606. and published Ephemerides , and several other Works , mentioned by Simlerus , in his Bibliotheca Gesneriana , among the rest , Brevis & perspicua Ratio judicandi Genituras ex Physicis Causis & vera Experientia extracta , &c. to which is prefixed Admonitio de vero & licito Astrologiae usu per Hieronymum Wolphium , Printed at London 1558. Of Him Tycho Brahe ( in Progymnasm . l. 1. ) writes at large , adding withall , that , Pleraque ipsius Manuscripta opera , ad supputationes Astronomicas , praesertim primi Mobilis Tabulas copiosiores & faciliores reddendas facientia ; Augustae in Fuggeorum Bibliotheca non sine harum A●…ium promovendarum Incommodo , detinentur . JOHANNES DRIANDER , Doctor of Physick , and Professor of Mathematicks , which he illustrated by his learned Writings , particularly by his Book of the various Composition of Sun-Dyals ; by his Description of a nocturnal Instrument , for taking the hour of the Night from the inspection of the Stars ; Astrolabial Canons , and the Explication of the Quadrant ; with several other Astronomical Inventions ; as it is testified by the excellent Thuanus , and Draudius in Bibl ▪ Classica . GEORGIUS BUCHANANUS , that learned Scotch-man , hath written Five Books of the Sphere , in a Latine Poem ; to which Iohannes Pincierus hath added a Supplement of the fourth and fifth Books , and Arguments to them all . RABBI ORI , filius Simeonis , a Iew of Palaestine , put forth Calendarium Palaestinorum , & omnium Iudaeorum , computed for forty years , first Printed at Venice , in Hebrew , afterwards translated into Latine , and illustrated with Annotations by Iacobus Christmannus ; and published at Francfort , 1594. FEDERICUS COMMANDINUS of Urbino , optimè meritus , si quisquam alius , de Mathematicis , sayes Blancanus . For besides the many other excellent Monuments of Greek Learning , which we owe to his happy Traduction , we are beholding to him for Aristarchus Samius , De Magnitudinibus & Distantiis Solis a●… Lunae , which he illustrated by a Comment of his own . He put forth likewise Ptolemy's Analemma , and wrote De Lineis Horariis . MICHAEL BEUTHERUS , Native of Carolostadt in Westphalia , not far distant from Wurstburgh , Scholar to Erasmus Reinholdus , afterwards Professor of Poetry , History , and Mathematicks ; in the University of Gripswaldt , in the Dukedom of Pomerania , read at Paris publick Lectures , De Annorum Supputatione . He wrote De Globo Astronomico ; De Circulis ; Of the Correction of the Gregorian Calendar ; Of the seventy weeks in Daniel ; Of the time of the World's Creation , and the day of our Saviour's Passion . He was Library-Keeper to Otho-Henry , Prince Palatine of the Rhine , and of his Council in Ecclesiastical Affairs , and restored to the same Charges afterwards by Frederick the Third . ELIAS VINETUS , Professor at Bourdeaux , besides his Notes on Pomponius Mela , De situ Orbis , wrote a Commentary in Sphaeram Sacrobosci ; for which he justly merits a room in this Astronomical Catalogue . JOHANNES HONTERUS CORONENSIS , of Cronstadt ( in Transylvania ) anciently called Zarmigethusa , writ Four Books , in Verse , De Rudimentis Cosmographiae , which he adorned with several Land-Tables or Maps . To which he adjoyned , in Prose , a Treatise of the Principles of Astronomy and Geography . PETRUS RAMUS , first Disciple to Orontius Finaeus , afterwards Regius Professor of Mathematicks in the University of Paris , besides his Two Books of Arithmetick , and XXVII . of Geometry , put forth XXXII . Scholarum Mathematicarum , in the first of which he treats of many things relating to the Rise and Advancement of Astronomy . MICHAEL NEANDER , è valle Ioachimica , put forth Elementa Doctrinae Sphaericae , & Materiam Computi Astronomici , as Ricciolus affirms in Chronolog . Astron. DANIEL SANTBECH , of Nimmeghen , put forth , according to Ricciolus , Praeclara Problemata Astronomica & Geometrica , in VII . Sectiones distributa : In the first whereof he treats of several Observations of the Phaenomena of the Sun , Moon , and fixed Stars ; In the second , he exhibits Canons of the Primum Mobile , extracted from the Tables of Regiomontanus ; The third is of the Reasons of Gnomons and Shadows . The other Four are upon Geometrical Subjects . JOSEPHUS MOLETIUS Professor of Mathematicks at Padua , besides his Comment upon Ptolemy's Geography , composed out of the Prutenick Tables , others , which he called Tabulae Gregorianae ; for which by the Senate of Venice , he was rewarded with 200. Ducats , and promised by Pope Gregory XIII . for the continuation of them 300. Crowns more . He published likewise Introductio ad Ephemerides , Printed together with the Ephemerides of Iosephus Scala , of Sicily , in the year 1589. LUCILLUS PHILALTHAEUS , Doctor of Physick , wrote as Ricciolus terms them , Luculentos Commentarios , upon Aristotle , De Coelo . LEONARDUS DIGGES , of a generous Family in Kent , besides his Stratiotices , and his Mathematical Discourse of Geometrical Solids , wrote an Astronomical Prognostication , then Printed . ALEXANDER PICOLOMINAEUS , of Siena , wrote Four Books , De Sphaera Mundi ; as also a Treatise of the Fixed Stars in Italian , in which Language he likewise published another , of the Theory of the Planets , and dedicated the same to Cosmus de Medicis ; and farther another , De Magnitudine Terrae & Aquae ; all rendred into Latine by Nicholaus Stupanus , and Printed at Basil , 1568. SAMUEL SYDEROCRATES wrote De usu Partium Coeli , in Commendationem Astronomiae , Printed at Strasbourg , as Draudius affirms , 1567. TITUS à POPMA , a Friezlander , wrote Tabellas in Sphaeram , & Elementa Astronomiae . EDO HILDERICUS writ a small Treatise entituled Logistice Astronomica , Printed at Wittenberg 1568. mentioned by Simler , in Bibl. Gesner . CHRISTIANUS VURSTISIUS , of Basil , Professor of Mathematicks in the University of Zurich , wrote learned Questions in Theoricas Purbacchii ; whereto he prefixed an Introduction of his own , Printed at Basil , by Henricus Petri , 1586. ABRAHAMUS ORTELIUS , of Antwerp , Geographer to Philip II ▪ King of Spain , most deservedly challenges a place in this Catalogue , especially for that great Work of his , Theatrum Orbis Terrarum , with it's Parergon , and his Thesaurus Geographicus . GERARDUS MERCATOR , a Native of Rupelmonde in Flanders , made several Mathematical Instruments for the Emperour Charles the Fifth , particularly a Globe , in which was comprized the Constitution of the Planets , and the Celestial Signs and Constellations . He likewise made for the said Emperour two other Globes ; the one Celestial of Chrystal , the other Terrestrial , of Wood. He put forth a Cronology from the beginning of the World to the year 1568. exactly composed and calculated , as well from Eclipses , and other Astronomical Observations of all Times , as from the Sacred Scriptures , and other Authentick Authors , highly commended by Onuphrius Panvinius . Not to mention his other Geographical Works . HUGO , sive HUO HELTILIUS , of Groeningen , in Friezland , wrote in Spanish of the Planisphere . HENRICUS BRUCAEUS of Alost in Flanders , Doctor of Physick and Professor of Mathematicks at Rome and Rostoch , put forth Three Books of the Primum Mobile , and the Institutions of the Sphere , of whom Vossius , De Scient . Math. gives an ample Account . FRANCISCUS BAROCCIUS , a Patrician of Venice , wrote ( besides his other Works in Mechanicks and Geometry ) Four Books of Cosmography , in the Preface to which he detects no less than LXXXIV . Errors of Io. de Sacrobosco , and his Followers . JOANNES LALAMANTIUS , of Antun in Burgundy , a Physician published a Tractate entituled , Collatio Rationis Anni exterarum ferè Omnium & Praecipuarum Gentium cum Romano Anno , Printed at Geneva apud Crispinum 1571. 8 o. ADAMUS URSINUS , of Norimberg , wrote Prognosticks upon the new Star in Cassiopaea , touching which , see Tycho , Progymn . Tom. 1. ANDREAS NOLTHIUS , of Embeck , wrote concerning the Star in Cassiopaea about the same time as the Landtgrave of Hesse , as is likewise noted by Tycho , Progymnas . Tom. 1. BARTHOLOMAEUS RASACHERUS , Professor of Mathematicks at Vienna , wrote also touching the Star in Cassiopaea . CORNELIUS GEMMA , of Lovaine , wrote likewise upon the same Subject : So also did CORNELIUS FRANGIPANUS , whose Censure see in Tycho Brahe , Progymnas . Tom. 1. HIERONYMUS MUNOSIUS , Professor of the Hebrew Tongue and Mathematicks in the University of Valentia , and Physician to the Emperor Maximilian the Second , put forth his Observations upon the New Star in Cassiopaea . ELIAS CAMERARIUS , Professor of Mathematicks at Francfort , upon Oder , wrote De Nova Stella Cassiopaeae . GUL●…ELMUS POSTELLUS , Native of Barenton , a Town in Normandy , about this time put forth his Cosmography , sive , De Universitate , and wrote , De Nova Stella Cassiopaeae . JOHANNES d ee , Doctor of Physick and an excellent Mathematician ( besides other his learned Works , whereby he hath honoured our Nation , not pertinent to our present purpose ) wrote , upon occasion of the New Star in Cassiopaea , a small Treatise , by him entituled Parallacticae Commentationis & Praxeos nucleus , highly commended by Tycho Brahe , in Progymnasm . Tom. 1. He published in the year 1558. a Treatise entituled , De Praestantioribus quibusdam Naturae Virtutibus , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , containing several curious Astronomical and Astrological Aphorisms ; In the Preface to which Piece , he makes mention of the several Astronomical Tractates following , by him intended for the Publick , but whether ever yet Printed is uncertain ; as first , De Planetarum , inerrantium Stellarum , Nubiumque à Centro Terrae Distantiis , & Stellarum omnium veris inveniendis Magnitudinibus in two Books , De praecipua Perspectivae Parte , quae de Radiorum Fractione tractat , in three Books , De Caelestis Globi amplissimis Commoditatibus , in two Books , De Nova Navigationum Ratione , in two Books , and one Book , De Annuli Astronomici multiplici usu , divided into a hundred Chapters , besides some other Mathematical Pieces , among which , his Apology for Fryar Bacon . A farther Account of the Works and Writings of this Stupendious Person the Reader may happily e're long meet with in his Life ; intended to be written ( if Providence second his Design ) by my worthy Friend Elias Ashmole Esquire , whose singular Affection to Astronomical and Astrological Studies may justly entitle him to a Place in this Catalogue . PAULUS HAINZELIUS , Consul of Ausbourg , diligently observed , at Gegginge , near the City of Ausbourg aforesaid , the motions of the Stars and Planets , using in his Observations a Quadrant of fourteen Cubits , as Ricciolus , in Chronol . Astron. affirms . His Prayses and Commendations may be seen in Tycho Brahe , Progymn . Tom. 1. PAULUS FABRITIUS , a Mathematician and Physician to the Emperour of Germany , wrote De Nova Stella Cassiopaeae 1572. THEODORUS GRAMINEUS , Professor of Mathematicks at Colen , published a Prolix and tedious Commentary , or ( as Tycho more truly terms it ) Commentum , upon the New Star in Cassiopaea . MICHAEL MAESTLINUS GOEPINGENSIS , at first Parish-Priest , or Curate of a little Town called Bachnang , afterwards Professor of Mathematicks in the Universities of Heidelberg , and Tubinge , and Master or Tutor to Kepler , wrote De Stella Nova Cassiopaeae , and of the Comet which appeared in the year 1576. as also Ephemerides according to the Prutenick Tables , and Additions to the first Narration of Rheticus , with an Appendix ; De Dimensionibus Orbium Coelestium , according to the Opinion of Copernicus . He published likewise Theses De Eclipsibus , and an Epitome of Astronomy , and wrote against the Gregorian Calendar , in which he was opposed by Clavius ; yet happy in this , that he was not only Master to the learned Kepler , but first Motor to the famous Galilaeo ( addicted before that time entirely to Aristotle and Ptolemy ) of his embracing the Copernican Hypothesis , perswaded thereunto by the force of his Arguments , which in a Publick Lecture upon that Subject he used at the time of his being in Italy . GELLIUS SASSERIDES , a Dane , of Copenhagen , was one of those who assisted the noble Tycho Brahe in his Celestial Observations ; some of whose Epistles are extant in Maginus , De Directionibus . JOHANNES HECKIUS , of Daventer , Doctor of Physick , wrote a small Treatise upon the New Star in Cassiopaea , termed by Ricciolus , Opus non inelegans . TYCHO BRAHE , descended of an illustrious Family among the Danes , as being eldest Son to Otto Brahe , Lord of Knudsthorp , in the Island Schonen , not far from Elzinbourg , who was Son of another Tycho , Son of Axilius Brahe , Lord of the said Place ; the Hipparchus of his Age , who even from his Childhood being addicted to Astronomical Studies , though diverted from them by the Advice of his Friends and morose humour of his Tutour , grew by his own Ingenuity and Industry without any Instructor , so great a Proficient therein , that in the time of his Minority , and without the help of other Instruments , than a small Globe little bigger than a Man's Fist , and a large pair of Compasses , with which by applying his Eye to the Head of the Compasses , and opening the shanks thereof , he used by stealth to take the Distances of the Stars , he made a shift to detect divers considerable Errors , both in the Alphonsine and Prutenick Tables . At length by his Studies and Travels , having consummated his Knowledge in Astronomy . He was by Frederick the Second King of Denmark ( at what time he resolved to make his Retreat into Switzerland , the better to apply himself entirely to the Contemplation of the Stars ) invited to fix his Studies at Home , and to honour his own Country with his Learned Labours and Observations . To which end the King gave him the Island Huena , commonly called Ween , between Scania and Zeland , in the Baltick Sound , as a Place for his Retirement and Studies . Where causing to be built a Stately Pallace , to which he gave the Name of Uranoburgum , procuring most costly and exquisite Instruments for observing , and calling to his Assistance the most learned Astronomers of that Age , he happily began and made his glorious Progress in the Instauration of Astronomy . In which Work he is said to have expended no less than two hundred thousand Crowns . And as Copernicus had corrected many things in Ptolemy , so did Tycho no less in Copernicus . So that from thence the Learned World began to look upon only three chief Sects of Astronomers , whereof the Tychonick was the mean and middle between the Pythagorean or Copernican , and the Aristolean or Ptolemaick . Of his Works there are published Astronomiae Instauratae Progymnasmata , in three Parts ; whereof the first treats of the Restitution of the Sun's Motion , as also of the Moon 's , and the fixed Stars ; chiefly of the new Star which appeared in the Constellation of Cassiopaea , 1572. The second of several new Phaenomena's of the Aetherial World , more particularly of the Comet which appeared in the year 1577. The third and last contains his Astronomical Epistles to divers Persons . There is extant likewise a Book of his entituled Astronomiae Instauratae Mechanica , dedicated by him to the Emperor Rudolphus the Second , describing the several stupendious and costly Instruments , by him used in his Astronomical Instauration . To these is to be added his Historia Coelestis , being a Collection of twenty years Observations preserved in MS. by three mighty Emperors , Rudolph the Second , Ferdinand the Second , and Ferdinand the Third , and lately by Command of his Imperial Majesty Leopold , made publick at Ausburg . Which said Observations are ushered by a Liber Prolegomen●… , compendiously representing the Observations made from the time of the Infancy of Astronomy unto that of it's Restauration by the Illustrous Tycho , reduced into 7. Class . containing the Babylonian Observations , the Grecian , the Alexandrian , the Syro-Persian , the Norimbergian , the Borussian , and mixt Observations from the year 1529. to the year 1582. After which begin the Tychonick Observations in twenty Books , containing as many Annual Observations ending in the year 1601. which was the last of Tycho's life : A correct Copy of these Observations ( transcribed from the Original , by Erasmus Bartholinus ) being now likewise in the Press at Paris . See more of him , in his life , written by the excellent Gassendus , in six Books . PETRUS BEAUSARDUS , Doctor of Physick , and Regius Professor of Mathematicks in the University of Lovain , wrote of the Astronomical Ring , or the Armilla . THADDAEUS HAGGECIUS of Haic , Disciple to Ioachimus Camerarius , and Physician to the Emperour Maximilian the Second , put forth a Piece , entituled Dialexis , touching the New Star in Cassiopaea , whose several Arguments see reported and examined by Tycho , Progymn . Tom. 1. JOHANNES RASEH , at Munichen , wrote De Cometarum Significationibus , about the year 1573. About the same time GEORGIUS BUSCHIUS , Pictor & Astronomus Erfordiensis , as Ricciolus stiles him , wrote of the Star which appeared in Cassiopaea . And ANTONIUS SANTUTIUS , Professor of Mathematicks at Pisa , wrote De Cometis , in which he treats of the same Star. WOLFANGUS SCHULERUS , Professor of Mathematicks in the University of Wittemberg , wrote upon the same Subject , in answer to Caspar Peucerus , the Younger , his Proposals touching the said New Star. FRANCISCUS BORDINUS , of Correggio , Doctor of Arts and Physick , and Publick Professor of Mathematicks in the University of Bologna , published Chilias Quaestionum & Responsorum Mathematicorum ad cognitionem Universi pertinentium , divided into three Parts ; the first treating of Geometry , the second of Geography , and the last in a more ample manner of Astronomy , Printed at Bologna . JACOBUS SCHOL , of Strasbourg , Doctor of Physick , set forth a Book , wherein he reduces Theses aliquot rei Medicae simplicioris , Integritati Astronomicae . He published likewise a Book , De brevi applicatione Astrologiae ad Medicinam ; with Canons of their conveniency and agreement ; Extant in the King's Library at St. Iames's . JOHANNES FRANCISCUS OFFUSIUS , wrote De Divina Astrorum Facultate , in Larvatam Astrologiam , Printed at Paris , in the year 1574. HERMANNUS WITTEKINDUS , Professor of Mathematicks at Heidelberg , published a small Tractate , De Sphera Mundi , & Temporis Ratione apud Christianos , Printed at Newstadt , in the year 1590. He put forth also a Piece entituled , Conformatio Horologiorum in superficiebus planis utcunque sitis ; with a Horological Quadrant , Printed at Heidelberg . ADAMUS à BODENSTEIN , Son of Andreas , Doctor of Physick , at Basil , writ De Herbis duodecim Zodiaci signis dicatis , as Simler affirms , in Bibl. Gesner . LUDOVICUS LAVATERUS , of Zurich , besides his Book , De Spectris , Lemuribus , & magnis atque insolitis fragoribus , variisque Praesagitionibus , quae plerunque Hominum magnas clades , mutationésque Imperiorum praecedunt , wrote a large Catalogue of Comets , published at Zurich , by Gesner . ANDREAS ROSA SINGFURDENSIS MEDICUS , in his Prognostick , published 1574. made some Observations upon the Star in Cassiopaea . JOSIAS SIMLERUS , Author of the Epitome of Gesner's Bibliotheca , put forth two Books , De Principiis Astronomiae . FRANCISCUS JUNCTINUS , a Florentine , Doctor in Theology , Professor of Philosophy and Astronomy , put forth Speculum Astrologicum , Tabulis Astronomicis , & multiplici eruditione refertum , according to the Judgement of Ricciolus ; and wrote accurate Commentaries in Sphaeram Sacrobosci , as Vossius calls them . He left likewise two Treatises , Ad judicandum De Revolutionibus Astrorum ; and a large Commentary upon Ptolemy's Quadripartite , with a Catalogue of the most famous Persons of his Time , and some Ages before him , Printed together in folio . GODESCALCUS EBERBACHIUS , wrote of the Eclipse of the Moon , which happened in December 1573. with a brief Prognostick thereupon according to the Doctrine of Ptolemy . He published likewise the Reason of another Eclipse of the Moon , which happened in the year 1576. demonstrated Geometrically , and Printed at Erford , as Draudius affirms . SIXTUS SENENSIS , of the Order of Preaching Fryars , put forth , by way of Comment , upon the Scripture , one Book of Geographical ; another of Astronomical Questions . EGNATIUS DANTE 's , of Perugio , a Dominican , and publick Professor of Mathematicks in the University of Bologna , wrote of the use of the Astrolabe , and the making of Astronomical Instruments , and reduced Astronomy , with other Mathematical Sciences , into a Compendium . He erected a Gnomon , in the Church of St. Petronio at Bologna , for observing the Sun's Declination , and Equinoctial Armillae in the Church-wall of St. Maria Novella at Florence , for the observation of the Equinox . He first published the Optick Fragments of Heliodorus Larissaeus in Italian , in which there is something Astronomical ; of which , another Edition hath been published in Greek and Latine , at Paris in 1657. by Erasmus Bartholinus in 4 o. and lately at Cambridge another in 8 o. Greek and Latine , ad Hetrus●…i Codicis fidem , ex Bibliotheca Fr. Lindenbrogii , Printed at the end of the Opucsula Mythologica Ethica & Physica , set forth by Mr. Tho. Gale , 1670. THOMAS BLEBELIUS , wrote of the Sphere , and of the first Rudiments of Astronomy , Printed at Wittemberg in the year 1576. BARTHOLOMAEUS SCULTETUS GORLICIENSIS , wrote of the Comet which appeared in the year 1557. Astronomicè & Astrologicè ; of which see Tycho's censure , lib. 2. p. 175. JOHANNES MARIA FIORNOVELLUS , of Ferrara , upon occasion of the Comet appearing in the year 1577. Published a small , but learned Treatise , De Cometis . GUID ' UBALDUS , or GUIDUS UBALDUS , a Noble Italian Marquess , of the Family DE MONTE , besides other Signal Monuments of his great Skill in Mathematicks , especially in Mechanicks , set forth a Treatise of the Astrolabe and Perspective , and left behind him ( being a Posthume Work ) divers Astronomical Problems , as Ricciolus in Catalog . Astron. and Vossius , De Scient . Mathemat . testifie . NICHOLAUS WINKLERUS of Hall , or Hala , in Suabe , commonly called Schwabishe Hall , to distinguish it from a Town of the same Name in Saxony , wrote a small Piece , wherein he proposes to demonstrate the Parallax and distance of the former Comet from the Center of the Earth ; but censured by Tycho , to be a work full of enormous absurdities . JOHANNES PRAETORIUS JOACHIMICUS , wrote likewise upon the Comet appearing 1577. and occasionally upon the New Star in Cassiopaea happening not long before ; of which Tycho , in Progymnas . Tom. 1. HELIZAEUS ROESLINUS , Published a Treatise entituled Theoria Coelestium 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , in which ( sayes Draudius in Bibl. Classica ) from the Phaenomena of divers Comets , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , quaedam afferuntur de Novis cujusdam Miraculi Tertiae Sphaerae Circulis , Polis , & Axi ; Printed at Strasbourg 1578. He assumed to himself , as Raimarus Dithmarsus had done , the Invention of the Tychonick System , to which he added the ( exploded ) Solidity of the Celestial Orbs , as Gassendus , in vita Tychon . testifies . PAULUS CRUSIUS COBURGENSIS , put forth a Treatise , De Doctrina Revolutionum Solis , cum Tabulis Mediarum Conversionum Temporis , & Motuum Solis in Annis Tropicis & Sidereis , Printed at Iena 1567. and another , De Epochis seu Aeris , Printed at Basil in 8 o. 1578. GEORGIUS CAESIUS , put forth a Catalogue , according to the Series of Time , of all the Comets which appeared from the Flood , until the year 1579. Printed at Norimberg the same year . ANDREAS DUDITIUS , wrote a small Comment , De Cometarum significationibus ; to which is adjoyned the Opinion of Thomas Erastus , Printed at Basil 1579. ALKAS CURIACUS , in the year of Hegira 950. and of Christ 1580. writ Tables , or Computus Astronomicus , now extant in the Publick Library at Oxford . VALENTINUS NAIBODA , Professor of Mathematicks at Colen and Padua , wrote Three Books of Astronomical Institutions , and put forth an enarration of the Elements of Astrology , collected out of Alchabitius , and other Authors . He was found dead in his House , at Padua transfixed with many wounds , having predicted that he should die by the Sword. Vide Ricciol . in Append. ad Tom. prim . Almagest . Nov. & Campanellae Astrolog . MARCUS ALBERTUS LONICERUS , wrote of the Theory of the Celestial Motions , according to the Hypothesis of Copernicus , Printed at Colen , 1583. JOHANNES BAPTISTA CARELLUS , of Piacenza , wrote Ephemerides , together with a Treatise or Introduction to Astrology ; as Ricciol . in Astron. Chron. affirms . MAURITIUS BRESSIUS , put forth Four Books , Metrices Astronomicae , Printed at Paris , 1581. MATTHAEUS RICCIUS , Native of Macerata , a Town in Italy , a Iesuit , famous as well for his Travels into the East - Indies and China , as for his eminent Skill in the Mathematicks . To ingratiate himself with the Chineses , he is said to have Composed a Cosmographical Map , of an Oval Form , in which he ordered the Kingdom of China to be placed at large in the midst , and the other Kingdoms and Territories about the skirts thereof in little , the better to humour that proud conceited Nation . He wrote likewise , in the Chinese Tongue , a Cosmographical Table , which he illustrated with a Comment , together with Cosmographical and Astrological Rules , and divers other things for the benefit of that Nation . ALOYSIUS LILIUS ; of Verona , Doctor of Physick , by Blancanus stiled , Alter nostri aevi Sosigenes , whose assistance Gregory XIII . made use of in correcting and reforming the Iulian Calendar . He invented a perpetual Cycle of the Moon , and established the immutable and fixed seats of the Aequinoxes . THOMAS ERASTUS , an eminent Philosopher and Physician , writ some thing upon the Subject of Astrology , or rather against the Iudiciary Part , Quam validis Argumentis confutavit , sayes the excellent Thuanus , in Histor. ad Ann. 1583. ▪ SIXTUS ab HEMINGA , called likewise by Vossius , Simon ab Heminga , a Native of Friezland , of a Noble Family , Doctor of Physick , and an excellent Astronomer , in his Youth much addicted to Judiciary Astrology , but afterwards having detected the falsity of that vain Study by his inspection into the Genitures of thirty most eminent Persons , he put forth a Book in confutation thereof ; wherein he chiefly oppugns Cyprianus Leovitius , Hieronymus Cardanus , and Lucas Gauricus . JOHANNES PADUANUS , wrote of the various Composition and use of Sun-Dials , together with a Method , or Tables for supputation of the Hours , according to the several Regions of the World , and distinguishing the Places of the Stars ; Printed at Venice and Verona , in the years 1582. and 1583. as Draudius affirms . ALBERTUS LEONINUS , sive LEUWIUS , a Groenwood , Native of Utrecht , of a generous Family , Doctor of the Civil Law , and eminently learned in the Mathematicks , put forth the Theory of the Celestial Motions , according to the Doctrine of Copernicus . In which he likewise treats of the true Quantity of the Tropical year , and of the Reason of the Reformation , or Restitution of the Civil year . In the same Work likewise he gives an Introduction to Astronomy , Geography , and Horography . He wrote also against Judiciary Astrology . REMBERTUS DODONAEUS , Published a Cosmographical Institution of the Sphere , comprehending the Principles of Astronomy and Geography ; Printed at Antwerp , 1584. JOANNES BAPTISTA BENEDICTUS , a Noble Venetian , invited from Parma to Turin , by the Duke of Savoy , in the year 1566. to answer several Questions proposed in Arithmetick , Geometry , Astronomy , Opticks , and Musick , to which he endeavoured to give satisfaction and solution , by his learned Epistles , published in the year 1585. He was an Excellent Geometer and ▪ Tutor to Clavius . NICHODEMUS FRISCHLINUS , wrote Five Books , De Astronomicae Artis cum Doctrinâ Coelesti , & Naturali Philosophiâ congruentiâ , Printed at Francfori , in the year 1586. SALOMON PLEPPIUS , wrote a new Explication of the Motion of the utmost Heaven , called the Prime Mover , Printed in the year 1587. HENRICUS DECIMATOR , put forth a small Treatise , as well of the Fixed Stars as Planets , serving not only for the use of Astronomers , but also Poets ; Printed at Magdeburg , 1587. JOSEPHUS SCALA , a Sicilian , composed Ephemerides , continuing from the year of Christ , 1589. to the year 1600. JOSEPHUS AURIA , a Neopolitane , whom Blancanus commends , as if he were another Commandinus , for his learned Labours , in translating divers of the Ancient Greek Mathematicians , in particular ( and to our purpose ) Autolycus De Sphaera Mobili , Euclidis Phaenomena , & Theodosius Tripolita , De Habitationibus , & De Diebus & Noctibus . CHRISTOPHORUS ROTHMANNUS , was Mathematician to the Illustrious William , Landtgrave of Hesse . He made his Celestial Observations at Cassels , at the same time , as Tycho did his at Uranoburg ; and besides his accurate Piece upon the Comet which appeared in the year 1585. There are extant in the first Tome of Tycho Brahe's Epistles , divers Letters of his to Tycho , with Tycho Brahe's Answers to him , touching several Controversies in Astronomy . SIMON STEVINUS , of Bruges , Mathematician to Maurice ▪ Prince of Aurange , put forth , among other Works of his , Theories of the Planets , and Tables of the Celestial Motions , in Three Books . DAVID WOLKENSTEIN VRATISLAVIENSIS , a Silesian , writ an accurate Description of the Astronomical Horologe at Strasbourg , where he was Professor of Mathematicks , extant in Manuscript in the hands of my worthy Friend , Mr. Thomas Gale , JACOBUS CHRISTMANNUS , Publick Professor of Mathematicks , and the learned Languages at Heidelberg , translated into Latine , out of a Manuscript in the Elector Palatine's Library , Alfraganus's Chronological and Astronomical Elements , which he supplied and illustrated with various Scholia ; to which he annexed a Comment , wherein he explained the Roman , Egyptian , Arabian , Persian , Syriac , and Hebrew Calendar . He put forth likewise divers Solar Observations , therein explicating the true Motion of the Sun in the Zodiack , accommodating the Doctrine of Triangles to the apparent motion of the Heavens . He wrote likewise of the Theory of the Moon , grounded upon a new Hypothesis , for finding out the Moon 's true place in the Zodiack ; and several other Pieces , as well in Astronomy and Chronology , as in Geometry . JOHANNES BAPTISTA PORTA , a Noble Neapolitane , published an Interpretation of the first Book of Ptolemy's Almagest with the Commentary of Theon thereupon ; not to mention his twenty Books of Natural Magick , Printed in most of the Europaean Languages . He writ also an Excellent Book of Opticks , and of Celestial Physiognomy . FRANCISCUS VIETA , a French-man , Native of Fontenay , whom Ricciolus entitles Gallicanae Matheseos insigne decus , besides his many other excellent Works in Geometry , and other Parts of the Mathematicks . He exhibited to Pope Clement VIII . a new form of the Gregorian Calendar , to which he added perpetual Canons , and an Explication thereof against Clavius , whom he accused to have Deformed the true Lilian Reformation , by not rightly understanding the Reason of it ; touching which Controversie Thuanus , in the 129 th Book of his History , writes more particularly . But the Work of his chiefly pertinent to our Subject , and whose Loss cannot be sufficiently deplored , was his Harmonicon Coeleste , which being communicated to Mersennus , was , by some perfidious Acquaintance of that honest-minded Person , surreptitiously taken from him , and irrecoverably lost or suppressed , to the unspeakable detriment of the Letter'd World. Vide Buliald . Prolegom . in Astron. Phil. The learned Golius had it , and Sir Alexander Hume from hence imparted another Copy ; both which , 't is feared , are lost , there being no Impression made thereof , and Golius being since dead , his Collections ( whereof he had many in Arabick ) are said to be dispersed , and ( which is to be pitied ) carried back by a Iew into Turkey . JANUS DOUZA , the Learned Son of as Learned a Father , sometim●… Tutor to Henry Frederick , Prince of Orange , and the first Keeper of the Publick Library in the University of Leyden . Published among other his Writings , Rerum Coelestium Libri , & De Umbra , sive Umbrae Encomium , Printed at Leiden apud Raphelengium 1590. 8 o. JOHANNES BUSAEUS NOVIOMA GENSIS , of the Society of Iesus , wrote an Apologetical Disputation in behalf of the Gregorian Calendar , against Iacobus Herbrandus , a Divine of Tubingue ; of whom more in Ribadeneira , lib. De Scriptor . Soc. Iesu. GULIELMUS ADOLPHUS SCRIBONIUS , wrote a Spherical Institution , published together with Zacharias Parthenius his Notes , at Francfort , 1591. PETRUS RYFF , wrote concerning the Sphere , as also touching the Principles of Astronomy and Geography , Published in the year 1591. THOMAS DIGGES , Son of Leonard Digges , before mentioned , of whom Tycho Brahe ( Progymnasm . l. 1. ) gives this Elogy , that he was ( ●…nerosi Stemmatis Vir , & Eximius Mathematicus ; wrote a Book entituled , Alae & S●…alae Mathematicae , being a Treatise about calculating Parallaxes , Printed 1573. He published likewise his Pantometria , and some other Mathematical Tractates in the year 1591. ANTONIUS LUPICINUS , an Italian , writ ( in that Language ) D●…lle Verghe Astronomiche , Printed at Florence 1591. GEORGIUS BACHMANNUS , put forth an Epitome of the Doctrine of the Primum Mobile ; comprehending a brief exposition of all the Celestial Circles and Appearances ; to which is added a small Treatise , De Doctrina Sphaerica , Printed at Wittemberg , 1591. HENRICUS RANTZOVIUS , a Noble Dane , and Viceroy in the Dutchy of Schleswick , Holsatia , and Ditmars , put forth Calendarium , Romanum , Oeconomicum , Ecclesiasticum , Astronomicum , & fere perpetuum ; and an Astrological Treatise , collected out of the most ancient and best Authors of Judiciary Astrology ; Printed at Francfort , by Wechelius ; also Locorum Hylegi●…lium ad quodvis Tempus datum Directiones . He writ also a Catalogue of Emperours , Princes , and other Illustrious Persons , who had either affected , promoted , or studied Astrology ; A Treatise , De Veritate Astrologica , and another , De Annis Climactericis , &c. Printed at Leipsick 1584. JOANNES PAULUS GALLUCIUS , Published Theatrum Mundi & Temporis , Printed at Venice 1589. Likewise Speculum Uranicum , there Printed in the year 1593. And Della Fabrica & Uso di diversi Stromenti di Astronomia & Cosmographia , Printed in the year 1597. Also , De Figura Coelesti erigenda , with some other Tractates of like Nature . FEDERICUS BONAVENTURA , wrote , De Affectionibus Meteorologicis ; De vero Ortu & Occasu Siderum ; De Stellarum significationibus , &c. Printed at Venice , 1594. He hath written also upon Theophrastus De Ventis , and upon Ptolemy De Siderum Ortu & Occasu , and in his Book , De Octomestri Partu , shews himself not ill affected to Astrology . GULIELMUS HARTGILL , an English-man put forth Tabulae Astronomicae Universales , Printed at London 1594 and Reprinted 16 with Additions by Iohn Gadbury of London . BERNARDINUS BALDUS , Disciple to Federicus Commandinus , of whom Vossius gives this Charecter , that he was Vir non solum Mathesios universae peritissimus , sed etiam , ( ut Germanicam , Gallicam , & Slavonicam Linguam omittam ) Latinè , Graecè , Hebraicè , Chaldaicè , & Arabicè Doctissimus . Not to mention his many curious Works in other Parts of the Mathematicks , well known to the Learned ; We shall only insist on what more nearly relates to our present Subject ; as his five Books , Novae Gnomonices , Horologium universale , & de Firmamento . He writ likewise upon the Phaenomena of Aratus ; and hath composed a History of the Lives of all the famous Mathematicians from Thales Milesius to Commandinus , with a Chronology of the Times wherein they flourished , and their several Eulogies . Of which , if we may judge ( as of Hercules by his Foot ) by that Life he hath written of Hero , already published with his Belopoica . We cannot but conclude them worthy of that Honour which they yet want , that is , a speedy Publication to the view of the Learned World. And if the Manuscript now in possession of some of his Family , or a Copy thereof may be obtained ; we may have then hopes that er'e long the Work will be communicated to the Curious of this Nation . GERARDUS RUPELMUND ANUS , set forth a Book , which he entituled Atlas , or Cosmographical Meditations , De fabrica Mundi , & fabricati figura ; Printed at Duisberg , in the year 1595. according to Draudius , whom I conceive to be the same with Mercator . JOSEPHUS ACOSTA , in the year 1597. published the use of an Instrument , called a Cylinder , together with Astronomical Tables ; Printed at Colen . GULIELMUS , Landtgrave of Hassia , merits an Elogium beyond what can be here given , for his assiduous Observations for many years of the Celestial Bodies ; to which end , at Cassells , he erected an Observatory , with excellent Instruments , calling to his assistance two eminent Artists , Christophorus Rothmannus , and Iustus Byrgius . His Observations were published at Leyden , in the year 1618. by Willebrodus Snellius , and are in part mentioned by Tycho , as well in his Epistles , as in the second Tome of his Progymnasm . A signal example to all Princely and Heroick Minds , to undertake the promoting and advancing of this truly Noble and Celestial Science . NICHOLAUS RAIMARUS DITHMARSUS URSUS , one of Tycho Brahe's Scholars , published a Piece under the Title of Astronomical Hypotheses , with a Defence thereof , Printed at Prague , 1597. In which he endeavours to prove himself Author , or at least first Reviver of the pretended Brahean Hypothesis , which he will have to be ancient , ascribing the same to Apollonius Pergaeus , as its first Inventor , ingratefully seeking to deprive Tycho of the due honour thereof . But he is answered by Tycho , who hath vindicated and asserted his own right . JOSEPHUS SCALIGER , the Great Prince or Monarch of Universal Learning . As to what concerns our present Subject , his elaborate Work , De Emendatione Temporum , his exquisite Animadversions on Eusebius , with his Canon Isagogicus Chronologiae , and his accurate Comment upon Manilius's Astronomicks , sufficiently evidence his admirable knowledge , as well in Astronomy , as in other the Mathematical Learning of the Ancients ; whom , if we may trust the Judgment of the incomparable Vieta , he alone , above all others , perfectly understood , as the same is reported by the Learned Casaubon , Epist. 586. He wrote likewise Cyclometrica , Et Diatriba De Aequinoctiorum Anticipatione . FEDERICUS SAMINIATUS , published Astronomical Tables , at Anwerp , in the year 1599. 4 o. CHRISTOPHORUS FEMILLUS , put forth Synoptical Tables , for finding out the true place of the Planets , derived from the Prutenick Tables ; together with the Investigation of the Festival Dayes of either Calendar , Printed at Wittemberg , 1599. MELCHIOR JOESTELIUS , published Observations of an Eclipse of the Moon , happening in the year 1599. for his Skill in Astronomy well esteemed by Tycho Brahe , with whom he lived sometime a Domestick , and to whom he was an Assistant in his Astronomical Observations . SIBRANDUS à SICCAMA , wrote , De Veteri Anno Romano Antitheses , and Fasti Calendar . Having Successively deduced this Astronomical Catalogue thus far ; I hold it fit , before I proceed to the next Century , to insert in this Place the Names of divers Jewish , Persian , Arabian , and some other Astronomers , whose Times are Dubious , and uncertain ( at least to me ) of whom yet Mention is made in Simler ; Hottinger's Smegm . Orient . Abul-Pharagius his Dynasties ; James his Eclog. Oxon-Cant . Labbee , and the Catalogue of Golius his Manuscripts , &c. DANIEL surnamed SAPIENS , wrote an Astronomical Tractate in Syriack , extant in the publick Library at Oxford . RABBI JACOB BEN-MACHIR , wrote De Quadrante Astrolabii , Vestimentum Lucis , & Iter Stellarum . R. JEHUDA BAR BARZILEI , wrote a Book , teaching the supputation of Times , according to the Celestial motions . R. ISAAC BEN LATAPH , an eminent Philosopher , wrote of the Figure of the World. R. ABRAZARTH , a learned Astrologer , mentioned by Gesner , from the authority of Pastregicus , lib. De rerum Inventoribus . R. AB RUSAK , a great Astronomer , mentioned by Gesner . R. ABRAHAM , an eminent Astronomer wrote a Treatise entituled , Liber Intercalationis ; as also another , called Intercalatio Annorum ; De Solstitiis & Aequinoctiis ; De Lunae motu , & Mensibus , & totius Calendarii ratione . Quaere whether the same with R. Abraham , who wrote De Sphaera , mentioned by Christmannus in Alfraganum , of whom already , ad annum 1115. R. ISAASCHAR BEN SUSAN , writ a Treatise entituled , Correctio vel Ordinatio Calendarii . R. ISAAC ALCHADEB , published a Work entituled , Via Strata , De Calendario , De Festis , &c. R. SALOMON , writ a Treatise , entituled Sex Alae ; as also another , under the title of Talmid . Ephemerides , comprehended in six Tables , as Hottinger , in Smeg●… . Orient . There is likewise a Treatise under his Name , called Tabula Lunae , extant in MS. in the Library of Marcus Mantua Benavidius of Padua , mentioned by Thomasinus in Bibl. Patav. ALGAZEL ABUHAMAD , a Iewish Philosopher and Astronomer , writ in Hebrew , a Book , De Luminibus , entituled Haoroth , as the same is cited by Ricciolus , in Catalog . Astron. JOSEPHUS CHALDAEUS , wrote De Planetis , as testifies Habede-Iesu in his Catalogue of Chaldeé Ecclesiastick Writers , Printed at Rome . R. SIMCHA , Disciple to R. Solomon , put forth an Astronomical Treatise . KUSIANUS or KEUXIAN GILAEUS , composed Universal Astronomical Tables , with Demonstrations of their Canons . He is cited by Golius in Alferganum . ABU-SEHEL , published a Treatise touching the Demonstration of the Planisphere . ABDORRACHMAN of Damascus , wrote Tabulae 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , sive Resolutiones ex Tabulis Ulug Beigi , brought by the learned Golius from Constantinople . He wrote likewise , De Astrothesia , Imaginum formis variisque Nominibus . IBN-JAHIA ABBASIDES AFER , published a Treatise , of the Doubts and Errors of Astronomers , and of the Astrolabe . IBN-OMAR SOPHY , wrote of Horology , or Dialling . ABU-SHUKER AFRICANUS , wrote of the Theory of the Planets , demonstrated and amended , according to the newest and latest Observations . MAHUMEDES CHARIKAEUS , put forth a System of the Doctrine of the Sphere . GEORGIANUS , wrote a Treatise of the Orbe or Circle called Aequans , and of the Obliquity , Inclination , or Reflection of Epicycles . ABI ZELTUS DANITA , an Andaluzian , put forth an Astrological Treatise . ABU MESUD , wrote De Corporum Coelestium Contemplatione , mentioned in Golius his Catalogue MS. IB'N SINA , wrote touching the best Instruments , for making of Celestial Observations , perhaps the same with Avicenna . ALKASRANUS ; MAHMOUD IB'N MESAUD ASSIJTARI ; IBRAHIM IB'N ALI ALABASHI ALGJMDE ; OMMAR ALFARESKOURI ; ALI IB'N ALHAZEN IB'N IBRAHIM IB'N MAHAMMED IB'N ALHUMAM ; HAKIM ALMUGJAREITI ; CHALIN ALFAKI ; IB'N SARCALI ; SJAHAB ADDIN ; ALI ALHAZEN IB'N ALI IB'N MUHAMMED IB'N IBRAHIM ALMERWAZI ; all Arabian and Persian Authors , wrote upon the Subject of Astronomy , and are mentioned in Iacobus Golius his Catalogue of Manuscripts , to which may be added HELVENOR Astrologus , and GERGIRO De Significatione Planetarum , mentioned by Simler . ABI'L ASSAKER ABDOL AZIZ IB'N KOBERSI , wrote an Astronomical Introduction , mentioned in the foresaid Catalogue of Golius . OMAD EDDIN ALBOCHARI , an Arabian , wrote a Treatise of the Figure and Motion of the Moon and Mercury . ABU'L ALI ALMARASKOSJI , wrote a most accurate Treatise of the use of the Astrolabe . ALCAJIM put forth very exquisite Astronomical Tables . MUHAMMED IB'N ALI CHAR ARMIOUNI , put forth an Astronomical Institution , touching the supputation of Time and the motion of the Sun. There is also among the same Manuscripts of Golius an anonymous Treatise , in the Persian Language , Of the Figures and Motion of the Stars , together with a Latine Version thereof by JUSTUS RAPHELENGIUS . ABEN MERGIOUR , wrote Virtutes Oppositionum & Conjunctionum Saturni & Iovis juxta Sententias Antiquorum , mentioned in the Catalogue of Golius his Manuscripts . NEDAMENIN , wrote a Treatise , De variis Annorum formis , & Rebus Coelestibus . TEILESANUS published Astronomical Canons . SIDIN SHERIFFUS , wrote Elementa Astronomica , perhaps the same with Ali Escheriff , who put forth likewise Tabulae expeditae Motuum Coelestium , extant among Golius his MS. JOHANNES LEBDEBENHAZER , writ De Iudiciis Astrorum , said to be in his Majesties Library at St. Iames's . JARDAGIRD ALEXANDRINUS , otherwise called CHILVENUZ , wrote De Scientia Annorum Arabum , the Manuscript whereof is extant in Caius Colledge at Cambridge . THOMAS , De Iudiciis Astrorum , a Manuscript extant in the Library of Merton Colledge at Oxford , and in that of Gonvil and Caius Colledge in Cambridge . HELIODORUS LARISSAEUS , writ Optica , & De Septem Planetis , his Opticks lately Printed at Cambridge . HERACLIDES his Apotelesmata , are by Labbeé said to be in Bibliotheca Cardinal Carpens . and that of the French King. AEGIDIUS ROMANUS , wrote a Treatise De essentia , motu , & significatione Cometarum ; extant in MS. in the Publick Library , as also in that of Pembroke-Hall , at Cambridge . PETRUS LEMONIENSIS , a Canon of the Cathedral of York , wrote a Piece entituled , Iudicium De Stella Cometa , extant in MS. in the Publick Library at Cambridge . CHRISTIANUS ROLIANUS , put forth totius Orbis Generalis Descriptio , & Sphaera , extant in the French King's Library . BERNARDUS SYLVESTRIS , wrote a Treatise entituled Megacosmus , seu De Majori Mundo ; as also of Cosmography , a MS. whereof is extant in Benet-Colledge in Cambridge . JACOBUS ZALESE ; wrote De Dierum Aequationibus contra Propositiones Bartholomaei De Valentia , extant in MS. in the Library of Nicolaus Trevisanus of Padua , and mentioned by Thomasinus in Bibl. Patavin . JOHANNES DE INERIIS , a Picard , of the Dlocese of Amiens , wrote a Treatise , entituled Canones super magnum Almanach omnium Planetarum , calculated for the Meridian of Paris , of which a Manuscript is in Caius and Gonvil . Coll. ARCANDAM , or ARCANDUM , and ALCANDRINUS , ( as some name him ) writa Book . De Veritatibus & Praedictionibus Astrologiae , Printed at Paris in the year 1542. 8 o. Published by Richard Roussat Canon of Lingon . HABASH MERWAZENSIS , wrote three Books of Astronomical Tables ; the first composed according to the Rules Send Hend ; the second called Montahen , i. e. approved by experience ; the last , Tabularum minorum , entituled Alshah , as Abulpharagius , in Histor. Dynast . ABDALLA EB'N SAHEL EB'N NUBACHT , wrote likewise upon the same Subject . ALEXANDER , an Astronomer , wrote De Influentia Planetarum in Herbas , extant in MS. in the Library of Io. Rhodius of Padua , of which Thomasinus in Bibliothec . Patavin . MAHOMED AL-BUZIANI , besides several Books , which he set forth in Arithmetick , composed a Treatise which he entituled Almagestum , sive Systema Astronomicum ; as Abulpharagius attests . MOSES EB'N MAIMON of Corduba , a Iew , together with Yuseph Eb'n Yahya , corrected the Astronomy of Eb'n Aphla Hispanus ; as the same Abulpharagius affirms . ANDALIUS DE NIGRIS , wrote De Sphaera , in Theorias Planetarum , Planisphaerium Ptolemei , and Astrolabium , mentioned by Thomasinus in Bibliothec. Patavin . yet extant among the MS. of Nicolaus Trivisanus . GHAMINAEUS , an Arabian Astrologer , wrote in Arabick , of Astrology , with a twofold Prolix Commentary in the Moorish Character , a Book commended by Scaliger , and remaining in the Library at Leyden , among the Manuscripts by him bequeathed to that University ; as Hottinger affirms in Append. Smegmat . Orient . ABENHAM writ De Astronomia , now extant in MS. in the Cottonian Library . JOANNES LAURATIUS , or LAURENTIUS DE FUNDIS , wrote De Sphaera , & Theorica Planetarum , extant in MS. in the Library of Io. Rhodius of Padua , of which Thomasinus in Bibliothec. Patavin . AVIENUS , or as others , ABIENUS wrote a Tract , De Cometis , as Simler in Bibl. Gesner . affirms . MICHAEL HAVEMAN put forth a Treatise entituled Astraea ; in qua de Hypothesibus Astrosophorum disseritur . AMBROSIUS LACHER , according to the Testimony of Ge●…ner , writ quaedam De Astronomia , who makes no mention of the Time wherein he flourished , nor of the particular Subject he wrote upon . HENRICUS DOPELSTIN , or TOPELSTEIN , Doctor of Physick wrote a Book , De Iudiciis Astrorum , mentioned by Simler in Bibl. Gesner . JOHANNES ZINERIS , is mentioned by Gesner among the Astronomers , and he farther affirms , that his Astronomical Tables are extant , but assigns not the time wherein he flourished . ALACENUS , a Mathematician , an ancient English Author , of whom Balaeus writes , that he deserved Astrologi Peritissimi nomen , wrote Of Perspective , and De Ascensione Nubium Of the time wherein he flourished no Author , we can meet withal , gives any account . ARNOLDUS DE VILLA NOVA , wrote Compendium Astrologiae ad Utilitatem Medicorum ; extant in MS. in the Library of the Canons of St. Io. Lateran of Padua . See Thomasinus in Bibliothec. Patavin . ALDILAZITH ASTROLOGUS , writ a Book entituled Archibia , as Gesner , from the authority of Gulielmus Pastregicus ( L. De Inventoribus rerum ) assirms ; Printed at Venice , in the year 1547. by Nicholaus Bascorinus . MASLEM , an Astronomer , translated Ptolemy's Planispaerium out of the Greek , into the Arabian Tongue , as Rudolphus Brugensis relates in the Preface of his Latine Translation of the same Work. MORIENTES , a certain Greek Author , writ De Zonis & Climatibus Mundi , extant , as the Author Luminis Animae affirms , in his Preface , adding that it was by him translated out of Greek into Latine . See Simler . in Bibl. Gesner . RAYMYRUS GADITANUS , wrote a Treatise , which he entituled , Divinatio Sideralis , mentioned by Gesner . STANTONIUS , an expert English Mathematician , wrote In Canones Tabularum Arzahelis , as Leland and Gesner affirm . TRECHINDUS , an Astronomer and Astrologer , is often mentioned by Haly Aben-Ragel , as Simler testifies in Bibl. Gesner . ZAHEL , sive ZAEL , or ZEEL BEBIS , an Arabian Astrologer , writ De Interrogationibus ; De Electionibus ; De Temporum Significationibus in Iudiciis ; Printed at Venice 1493. together with Ptolemy's Quadripartitum ; vid. Gesner's Biblioth . There is also under his name a Treatise , entituled De Revolutionibus Annorum Mundi , extant in Manuscript , in the Publick Library at Cambridge , and in that of Pembroke-Hall . MAHUMED BEN MALUD , wrote learned Commentaries on the Book of Tap Phatis Scihajah de Astronomia , extant in the Vatican Library , of which mention is made by Labbeé in Bibliothec. MS. NECTARIUS , Bishop of Hydrusa , turned the Book called Laxeuterion ( treating of Astrological Predictions according to the Chaldaick Doctrine ) into Greek , now extant in the Library of Trinity Colledge in Cambridge , and in that of the French King. Scaliger ( L. 1. Epist. 67. ) gives to that Piece likewise the Name of Raboulion , and the Publisher of the Florentine Library makes an Author of it ; citing him by the Name of Laxeuterius Pythagoricus , sive Rabolius . GULIELMUS READ , sometime Fellow of Merton-Colledge in Oxford , ( to the Library whereof he liberally contributed ) afterwards Bishop of Chichester , writ Tables of the mean motions of the Planets , and Canons of those Tables , extant in the Publick Library at Oxford . HALPERICUS , wrote a Treatise De Arte calculatoria , extant in Manuscript in Caius-Colledge in Cambridge . JACOBUS ZALES , wrote De Dierum Aequationibus contrà Propositiones Bartholomaei de Valentia , as cited by Ia. Phil. Thomasinus , inter MS. Nicolai Trivisani , biblioth . Patav. BERNARDUS DE TRYLLIA , a Dominican Fryar , and a Spaniard wrote Quaestiones super Totam Astrologiam ; as cited by Simler in Bibl. Gesner . There is a Book entituled , NOVEM IUDICUM IN ASTRONOMIA , said to be sent by the Soldan of Babylon to Frederick the German Emperor ; Printed in the year 1509. and extant in his Majesty's Library at St. Iames's , and in the Bodleian at Oxford . Proceed we now in our former Order and Method to the ASTRONOMERS flourishing in the Seventeenth Century , in which the first Author appearing is CHRISTOPHORUS CLAVIUS , of Bamberg , a Iesuit , Scholar to Io. Baptista Benedictus , and Master to Blancanus , and Griembergerus , a most profound Mathematician and Astronomer . The Works whereby he hath signalized his Name upon the Subject of Astronomy , are these : His Commentary in Sphaeram Sacrobosci , & in Sphaerica Theodosii ; De Forma & Usu Astrolabii ; His Apology for the Gregorian Calendar , against the two Oppugners thereof , Michael Maestlinus , and Ioseph Scaliger , and his Problemata Astronomica , Printed at Rome 1599. HUGO GROTIUS , the great Ornament of Learning , and of his Country , put forth Aratus his Phaenomena , & Diosemeia , in Greek , with Cicero , Germanicus Caesar , and Avienus their Translations thereof , with Cuts of the several Constellations ; to which he added his own learned Notes , and the names of the Stars , in Hebrew , Arabick , Greek , and Latine , Printed in the year 1600. THEODOSIUS RUBEUS Published Diarum Universale perpetuum , for finding out the Quantity of the Day or Night in any Part of the World , together with the Rising and Setting of the Sun , according to the Italick , Babylonian , and Astronomical Hours . CHERUBINUS SAND●…LINUS , is likewise numbred amongst the Astronomers of this Time , as having written something upon the same Subject with the former . HENRICUS SAMERIUS , of Luxemburg , a Iesuit , stiled by Ricciolus , Egregius Temporum Supputator , Published a Chronology from the beginning of the World to the time of our Saviour's Nativity , and is by Ricciolus inserted in his Catalogue of Astronomers . JOHN CHAMBER , Prebendary of Windsor , and Fellow of Eaton-Colledge , put forth a Treatise against Iudicial Astrology , together with the Encomium or Praise of Astronomy , made by him some years before , upon Occasion of his Publick Lectures on Ptolemy's Almagest in the University of Oxford , Printed in Latine and English 1601. 4 o. London . ABRAHAMUS ROCHENBACKIUS , at Wittenberg , wrote De Cometis , of which he published a Catalogue . NATHANIEL TORPORLEY , an English man born in Shropshire , set forth a Treatise , entituled Diclides Coelo-Metricae , seu Valvae Astronomicae Universales , in two Books , Printed at London . The first shewing the Composition of Astronomical Tables , with their Application , as to Directions ; comprized in a new Universal and most easie Method . The second teaching to calculate the Prostaphaereses of the Planets Motions , without the Subdititious Aid of Proportional Scruples ; and setting forth the Doctrine of Spherical Triangles most fully and easily ; the whole Artifice being reduced to Six Words in a Tractable Order , represented in the Form or Figure of a Mitre . He was sometime Amanuensis to the famous Vieta , and merits commendation for the Legacy he bequeathed of many choice Books toward furnishing the Library at Sion ▪ Colledge London . ANTONIUS GREVENSTEIN put forth a Supputation of all the Eclipses which happened from the year of Christ 1593. to this year 1601. together with the Tract of Proclus Diadochus , touching the signification of Eclipses , Printed at Breme , by Bernardus Petri. JOHANNES BAYERUS RHEINANUS , Doctor of the Civil Law , and an eminent Astronomer , exhibited elegant Schemes of all the Stars and Celestial Constellations , with their several Situations , according to the Descriptions of Hipparchus , Ptolemy , Alphonsus , and Copernicus , reduced to the Scale of Truth by Tycho Brahe , together with their distinct Denominations in Latine , Greek , Arabick , Chaldee , Persian . Sir CHRISTOPHER HEYDON Knight , a Person of great Worth and Learning , wrote a Defence of Iudicial Astrology , in Answer to the Treatise of Chambers published against it , a Work full of no common Reading , and carried on with no mean Arguments , Printed at Cambridge 1603. 4 o. THOMAS LYDYAT , an English man , in the year 1605. Published a Book entituled Praelectio Astronomica , De Natura Coeli & Elementorum ; and the same year another Piece , De variis Annorum formis , &c. cum refutatione Anni Novitii Gregoriani . In the year 1607. he writ Defensio Tractatus de variis Annorum Formis , praesertim Antiquissima & Optima , contra Iosephi Scaligeri Obtrectationem , Unà cum Examine Ejus Canonum Chronologiae Isagogicorum . Another Book called Solis & Lunae Periodus Eruditae Antiquitati Appellatus ANNUS MAGNUS constans Octodesexcentis Annis vertentibus , Printed at London 1620. Epistola Astronomica ad D. H. Savilium Equit. Auratum de Anni Solaris Mensura pro Confirmatione Periodi Octodesexcentenariae Solis & Lunae , 8 o. Lond. 1621. BALTHAZAR CAPRA Published at Padua , a Book entituled Tyrocinia Astronomica . ADRIANUS ROMANUS Published in the year 1591. a Book entituled Ouranographia , sive de Coelorum Numero & Ordine , Printed at Antwerp . He set forth likewise in the year 1595. Theoria Calendariorum in five Parts , Printed at Wirteberg . 4 o. And in the year 1602. Universae Mathesis Idaea , Printed Herbipol . In the year 1606. he published Speculum Astronomicum , wherein he represented the Motions of the Primum Mobile , Printed at Lovaine , 4 o. See more of him in Andreas Desselius his Bibliotheca Belgica . JOANNES RUDOLPHUS CAMERARIUS , a learned Physician , and descended from the Great Ioachimus , a good Astronomer , though he chiefly applied himself to Astrological Studies , Published a Century of Genitures , wherein he spoke of the violent Death of Henry the Fourth King of France , and in 1610. published another Century with Iudgments thereupon . JOHANNES TALENTONIUS , besides his Thesaurus Rerum Reconditarum , published a Treatise , of which Draudius gives this Character , that it was , De Supremae Sphaerae loco Disceptatio gravissima . HENRICUS LINDOUGHT , of Brussels , Doctor of Physick , and Professor of Philosophy , set forth a Book which he called , Speculum Astrologiae , being an Introduction in Scientiam Genethliacam , sive Physicam Iudiciariam ; in which he endeavours to distinguish between the vanity and the verity of Astrology ; Printed at Francfort , with a Preface of Gothardus Arthurus of Dantzick , De Astrologiae praestantia & utilitate , in the year 1608. BERNARDINUS SALINUS , a Iesuit , wrote among other things , De variis Problematibus Astronomicis ; which with other his Works are preserved in the Iesuits Library at Genua . GEORGIUS HENISCHIUS , Doctor of Physick , and Professor of Mathematicks at Ausbourg , put forth Proclus De Sphaera , in Greek and Latine , which he illustrated , ( to use Ricciolus's expression ) with an egregious Commentary . JOHANNES BASSANTINUS , a Scotch-man , published a Treatise of Astronomy , in French , though he scarce understood that Language , much less Latine or Greek , and yet , In Astronomia ita excelluit , ut inter primos Aetatis suae habitus sit , sayes Ioannes Tornaesius , who translated that Work of his into Latine , and published the same at Geneva . DAVID ORIGANUS , born at Glatz , a Town in Silesia , Professor of Mathematicks at Francfort upon Oder , set forth New Ephemerides , in Three Tomes , continuing from the year 1595. to the year 1654. with a most ample Preliminary Introduction , in which are explained the Grounds or Principles of Chronology , Astronomy , and Astrology . JOANNES ANTONIUS MAGINUS , of Padua , Professor of Mathematicks in that University ; as also at Bologna , was Author of the several Works hereafter mentioned : Ephemerides , according to the Prutenick Tables for fifty years . Tables Secundorum Mobilium Coelestium . New Theories of the Planets , according to the Copernican Hypothesis . Tables of the Primum Mobile , or of Directions . De Astrologica ratione & usu Dierum Criticorum ; as also ( though he was a severe Impugner of the common Judiciary Astrology ) De legitimo Astrologiae in Medicina usu . He commented upon Galen De Diebus Decretoriis , in the Astrological Part , Printed at Venice 1607. He wrote likwise a Book against Scaliger's Diatriba , De Aequinoctiorum Processione , and several other Pieces in Cosmography , and Geography , being stiled by Ricciolus , Insignis Astronomus & Cosmographus . BARTHOLOMAEUS KECKERMANNUS wrote among other things Systemata Astronomiae , and Problemata Nautica , Printed at Hannov. 1610. JOHANNES FABRICIUS put forth a Treatise entituled , De Maculis in Sole , & Modo Eductionis Specierum Visibilium , Dubitatio , Printed at Witteberg . 4 o. 1611. NICHOLAUS MULLERUS , of Bruges , Doctor of Physick , and chief Moderator of the School at Leovard , afterwards Publick Professor of Mathematicks in the University at Groningen , put forth hi●… Tabulae Frisicae Lunae-Solares Quadruplices , Printed at Alcmaire ; which Title he gave them , because composed in Friezland , and fitted to the Meridian of Leovard , containing the Calculation of the Conjunctions and Eclipses of the Sun and Moon , in Four Parts , according to the Ptolemaick , Alphonsine , Copernican , and Brahaean Astronomy ; together with an Introduction and Appendix thereunto ; represented by Vossius to be Opus omnino eruditum atque accuratum . He published likewise Solis totidem Tabulae , wherein he proves the Iewish year to be Luni-Solaris , that of the Turks merè Lunaris , Printed at Groning . 1630. He set forth also Calendarium vetus Romanum cum Methodo Paschali emendata . JOSEPHUS LANGIUS , Professor of the Greek Tongue and Mathematicks in the Arch-Duke's Academy at Friburg in Brisgaw , put forth a Work entituled , Elementale Mathematicum , in which , besides Vulgar Arithmetick , Geometry and Geography , he treats De Logistice-Astronomica , Astronomica Sphaerica , & Theorica Planetarum . Which Work Isaac Habrechtus not only enlarged , but also explained with Annotations , and illustrated with Figures , causing the same to be Printed at Strasbourg . CHRISTOPHORUS GRIEMBERGERUS , a Iesuit , native of Hale in Tiroll , at first Scholar to Clavius , afterwards his Successor in the Mathematical Chair in the Roman Colledge , put forth a Catalogue of the Longitudes and Latitudes of the Fixed Stars according to the Ancients , compared with the Modern ; together with a new Perspective of the Heavens . He wrote likewise a Book , De Speculo Ustorio Elliptico , and a new Invention of delineating all sorts of hours ; as also a Treatise for the describing of all manner of Astrolabes , in which Argument Clavius acknowledged the assistance of this his Scholar . What is found Geometrical in Villalpandus of Solomon's Temple , Claudius Rickardus , and others ascribe to Griembergerus , of whose worth and commendation Bettinus , in Aerario , hath made a Digression , Philip Alegambe , in his Catalogue of Iesuit-Writers affirming , that he left Elementa Conica , and other Geometrical Pieces , not proper for this place . JOANNES PAULUS RESENIUS put forth Initia Geometrica , Arithmetica , Astronomica , Printed at Wittemberg 1612. 8 o. JULIUS CAESAR LA GALLA Published a Discourse touching the New Phaenomena discovered in the Moon by the help of the Telescope . OCTAVIUS PISANUS Published in a very large but thin foli●… , a T●…atise entituled Astrologia , seu Motus & Loca Syderum . In which Astrology , or ●…ather Astronomy is reduced to Method , and Ocular Demonstration by the Means of a Planisphere , and an Instrument which he calls Sphaera Materialis & Instrumentalis . Whose ●…se is exprest by several Chartaceous Instruments exquisitely cut and printed ; the whole grounded upon the Ptolemaick Hypotheses ; the Industry , Labour and Pains of which costly Design ( if you will take his own Word for it ) he conceives may be reputed Archimedis Laboribus non Dissimiles . He dedicated his Works to Cosmus the Second Duke of Florence , being printed at Antwerp ex Officina Roberti Brunea●… . JOHANNES NEPERUS , Lord of Merkinstone in Scotland , Inventor of Logarithms , or Artificial Numbers , which , by bare Substraction or Addition , perform the Rule of Three , and by a wonderful facility of operation , resolve as well Plain , as Spherical Triangles , an incredible help to Astronomical Calculations , and for that respect alone , meriting a place in this Catalogue , and eternal Commendations . PETRUS LAURENBERGIUS is mentioned by G. Vossius , to have published at Hamborough a Book , entituled Amphilychus , being a Dissertation of the Nature of Twilights . JOSEPHUS BLANCANUS , of Bologna , a Iesuit , Professor of Mathematicks at Parma , wrote ( besides his Book , In Loca Mathematica Aristotelis , & De Natura Mathematicarum , and his Chronology of Mathematicians ) a Book De Sphaera Mundi , according to the 〈◊〉 and most recent Observations , with an Introduction to Geography , and an Apparatus ad Mathematicas Artes. He wrote likew●…e De Echometria , and another 〈◊〉 , entituled , Instrumentum Horologiorum , first published by Ricciolus ▪ ( his Scholar . ) GALILAEUS GALILAEI , the most excellent Philosopher and Mathematician of his Time , was Son of Vincentius Galilaeus , a Gentleman of Florence , whose Ancestors for many Descents had the Honour to be reckoned among the Patricii of that City ; to which Name of Galilaeus Authors usually add that of Linceus , from a famous Academy of Noble and Ingenuous Persons , calling themselves the Lyncei ( instituted by the Illustrious Prince , and Generous Maecenas Angelo Caesi , Duke of Aqua Sparta ) of which he was a Member and singular Ornament . The Works and Writings , by which he hath eternized his Name are many , both in Philosophy and Mathematicks ; of which , such as are Pertinent to our Purpose , we shall briefly enumerate . He first applied the Belgick Perspective Glass , by him meliorated , to Celestial Objects , by which he discovered that Iupiter was invironed with four smaller Stars or Planets , commonly called his Guards or Satellites ; to whom in Honour of his Prince and Patron , the Grand Duke of Thuscany , he gave the Names of Sidera Medicaea . By that he likewise discovered the different Phases of Saturn appearing now round , now in an oblong form , with two Handles or Ansae : That Venus , like the Moon , had her waining , and increasing ; and that the Moon 's Supersicies was like that of the Earth rising with Mountains , and deprest into Vallies and Seas ; that the Fountain of Light the Sun had its Spots , by which likewise he evinced that the Sun had a Circular Motion about its own Axis . That the Via Lactea was a Congeries of numberless Lights or small Stars ; and that the nebulous Stars , as that in the Head of Orion , and that in the Praesepe , or Manger of the Aselli , are composed of such . For which admirable Inventions , and many more , altogether unknown to the Ancients , he merits eternal Honour , especially for having communicated them to Posterity , and so excellently and clearly demonstrated them by his learned Writings ; particularly by his Nuncius Sidereus , and its Continuation , by his History and Demonstration of the Solar Spots , in three Letters to Marcus Velserus , by his Letters to Signore Alfonso Antonini , touching La Titubatione Lunare . To which is to be added his Systema Cosmicum , asserting the Copernican Hypothesis , with his Defence thereof in Answer to the Objections brought from Scriptures , Fathers , and School-men , written first in Italian , and addressed to Katherine of Lorrain , Grand Dutchess of Thuscany , and since published in Latin and Italian together . Not to mention his many other exquisite Tractates in Philosophy , Geometry , and other the most abstruse Parts of Mathematicks , as not immediately relating to our Subject . A farther Account of his Inventions or Discoveries is to be had in his life , published , by his Scholar Signore Viviani , which we have not yet seen . RUDOLPHUS GOCLENIUS , Doctor of Physick , and Professor in the University of Marpurg , published in the present year 1615. his Urania , with her two Daughters , Astronomy and Astrology . He likewise put forth a Cosmographical Treatise , seu Sphaerae Mundi Descriptionis Rudimenta , Printed at Cologne 1605. JOHANNES MICRAELLIUS Published a Manuduction to the use of the Celestial and Terrestrial Globe , &c. as Vossius affirms . DAVID FABRICIUS , a Friezlander , Professor of Astronomy , wrote Prognosticks of the years 1615 , 1616 , and 1617. mentioned by Kepler in his Ephemerides . DOMINIQUE JAQUINOT , a French-man , writ in his own Language of the Use of the Astrolabe , together with a small Treatise of the Sphere , Printed at Paris . FRANCISCUS AGUILONIUS , a Iesuit of Brussels , was Professor of Philosophy at Doway , and of Theology at Antwerp , and one of the first that introduced Mathematical Studies into Flanders . How far ( though not directly & ex professo ) he contributed to Astronomy , may appear by his six Books of Opticks , and his Excellent Treatise of Projections of the Sphere . REDEMPTUS BARANZANUS , of Serravalle , Professor , at Annesium , in Savoy , of Natural Philosophy and Astronomy . He wrote a Book entituled , Uranoscopia , sive Universa Coelorum Doctrina . EMANUEL DIAZ , a Iesuit , at Cochine in India , observed the Comet , which appeared in the year 1618. and set forth a Treatise against the Opinion of those , who conceive Comets to be sublunary and elementary Bodies . JOHANNES LEUTECHOMIUS , a Lorrainer , of the Society of Iesus , wrote Hilaria Mathematica , De Horologiis , & De Cometa . CAROLUS PISO , a French man , wrote in his own Language , Speculum Cometae , Anno 1618. WILLEBRODUS SNELLIUS , à Royen , Son of Radolphus Snellius , published , besides divers other Mathematical Treatises , Eratosthenes Batavus , sive De mensura Terrae ; and Tiphys Batavus , sive Histiodromice . He wrote likewise of the Comet which appeared in the year 1618. and published the Hessian and Bohemian Observations , with his own Notes thereupon ; together with the Observations of Regiomontanus and Waltherus . HORATIUS GRASSUS , a Iesuit , Native of Savona , sometime Professor of Mathematicks in the Iesuits Colledge at Rome , put forth an Astronomical Disputation , touching Three Comets in the year 1618. And a Book , entituled Libra Astronomica & Philosophica , wherein he undertakes to weigh and censure the Opinion of Galileo , concerning Comets . CAMILLUS GLORIOSUS , Professor of Mathematicks at Padua , wrote learnedly in a Treatise entituled Dissertatio Astronomico-Physica de Cometis , and in another Piece , entituled , Responsio ad Controversias de Cometis Peripateticas , and in some other things written against Claramontius and Licetus . BENJAMIN URSINUS , Mathematician to the Elector of Brandenburg , put forth a new Canon of Logarithms and Trigonometry ; of which Work Crugerus gives this Character , that it is Opus aestimationis immensae . JOANNES DEKERIUS , a Iesuit , Native of Haesbruch , in Flanders , Professor of Philosophy sometime at Doway , and of Divinity at Lovaine , and Chancellour of Gratz , wrote Theorems , touching the year of our Saviour's Birth and Passion ; and Chronological Tables from the taking of Ierusalem by Pompey , to its final eversion by Titus ; and several other Chronological Works not published . ALEXANDER DE ANGELIS , of Spoleto , a Iesuit , Professor of Theology , and Prefect . of the Schools in the Roman Colledge , wrote Five Books , In Astrologos Conjectores . LIBERTUS FROIDMONT , sive FROMONDUS , vindicated his Name from Oblivion , by his Dissertation upon the Comet which appeared in the year 1618. He writ likewise a Book entituled Anti-Aristarchus , sive De Orbe Terrae immobili , against Philippus Lansbergius ; as also a Reply , entituled Vesta , sive Anti-Aristarchi Vindex , in answer to Lansbergius . DAVID HERLICIUS , lately Doctor of Physick at Stetin in Pomerania , hath published many things relating to Astronomy and Astrology in the German Tongue . In the Latin there is nothing of his come to my Notice more than his Prognosticon Astrologicum for the year 1619. which is done with so much Skill and Pains , that it shews ●…e does not write like one of your Common Prognosticators . JOHANNES BAPTISTA CYSATUS , a Iesuit of Lucerne in Switzerland , and Professor of Mathematicks in the University of Ingolstadt , published Mathematica Astronomica , upon the occasion of the Comet which appeared in the year 1618. VINCISLAUS PANTALEO , a Iesuit of Austria , travelled into China , and put forth the several Observations made by those of that Society in the East-Indies , upon the Comets appearing in the year 1618. SIMON MARIUS wrote a Book , of the Satellites of Iupiter , to which he gave the title of Mundus Iovialis , as Ricciolus affirms , in Chronic. Astronom . JOHANNES TARDE , Canon of the Cathedral Church of Sarlat , in Aquitaine , wrote a Treatise , by him entituled Bourbonia Sidera , in which he endeavours to prove , that the Solar Spots are Planets , moving by a proper and regular Motion about the Sun , and not inherent in the Body thereof , as the Telescopes represent . To which Work are subjoyned Optical Demonstrations teaching the way of making those Instruments fit to discover Objects more distinctly at a great distance . He wrote another Treatise of the Use of the Magnetical Quadrant , by which he resolves divers Astronomical Problems . MICHAEL ZANARDUS put forth a Tractate containing Universum Coeleste ; wherein he disputes and concludes , De omnibus & singulis , quae ad Naturam Coelestium Sphaerarum , ab Empyraeousque ad Sphaeram Elementorum faciunt , Printed at Colen . CHRISTOPHORUS LONGOMONTANUS , Son of Severinus Longomontanus , a Dane , Assistant to Tycho Brahe in his Celestial Observations , for the space of eight years together ; afterwards Professor of Mathematicks in the University of Copenhagen . The Work , by which he signalized his Name , was his Astrologia Danica ; the first part whereof treats , in Two Books , of the Doctrine of the Sphere ; and the latter , in as many of the Theory of the Planets , according to the threefold Hypotheses of Ptolemy , Copernicus , and Tycho Brahe , together with an Appendix of Adscititious Phaenomena , as New Stars , and Comets . JOANNES KEPLERUS WITTEMBER GICUS , Disciple to Maestlinus , and Principal Mathematician to three Emperours , Matthias , Rudolphus , and Ferdinand the Second , stiled by Ricciolus , Sagacissimi & ardentissimi Vir Ingenii , & Astronomicarum Subtilitatum scrutator acutissimus . In the year 1596. he put forth his Prodromus Dissertationum Cosmographicarum , seu Mysterium Cosmographicum : In the year 1604. Paralipomena ad Vitellionem , seu Astronomiae Pars Optica . In which he gives Directions for using of Instruments in making of Observations . In the year 1605. De Nova Stella Serpentarii . In the year 1609. he published Astronomica Nova , seu Physica Coelestis , cum Commentariis Stellae Martis , ex Observationibus Tychonis ; in which , according to the Judgment of the knowing Mr. Flamstead , he hath so well considered the Motions of that Star , and ordered his Numbers so well , that though his method of Calculation be troublesome , no Tables answer his Appearances and Transits by Fixed Stars half so well as his . In the year 1610. he set forth Dissertatio cum Nuncio Sydereo Galilaei . In the year 1616. he published Ephemerides Nova , cum Fundamentis earum , from the year 1617. to the year 1620. In the year 1618. he set forth the three first Books of his Epitome Astronomiae Copernicanae ; and in the year 1619. Five Books De Harmonia Mundi , and three Books De Cometis . In the year 1621. he reprinted his Mysterium Cosmographicum , illustrated with Annotations ; and the year following , he published the IV. V. and VI. Books of his Epitome Astronomiae Copernicanae . In the year 1625. he set forth , in vindication of Tycho Brahe , against Scipio Claramontius , a Treatise , entituled , Hyperaspistes , cum Appendice ex Trutinatore Galilaei , and in the year 1627. Tabulae Rudolphinae Tychonicis Observationibus superstructae . In which Work he had spent no less than 26. years study . The Appendix which is added to the first Tome of Tycho's Progymnasmata , is likewise his . He writ also Eclogae Chronologicae , a Book , De vero nati Christi Anno , Stereometria & Trigonometria Logarithmetica . The first in somethings censured by Guldinus in Centrobaricis . There is extant a Posthume Piece of his , called Somnium , sive Lunaris Astronomia , which whilst he endeavoured to publish at Zeigan in Silesia , he died , as did also his Son-in-Law Iacobus Bartschius , prosecuting , at the same place , the same Design . But it was afterwards happily compassed , by his own Son Ludovicus Kepler , and we could have wished he had done the like by other the Learned Remains of his incomparable Parent . But 't is hoped that Defect will be now supplied , and made good by the Care and Industry of the Learned Hevelius , into whose Hands all the Remains of that Admirable Person are at last happily fallen . And among them all his Epistles written ( upon the Subject of Astronomy , and other Mathematical Arguments ) to divers Eminent and Learned Persons , together with their Answers ; more Particularly his Book entituled Hipparchus , containing ( according to the Testimony of Hevelius , Praefat. Machin . Coelest . ) plurimùm Laboris , ac Ingenii Acuminis ; though wanting in many Places the finishing Hand of the Author , upon which yet , in his other Works he seems to set a very valuable esteem . The Publication whereof , the studious in Astronomy earnestly expect . THOMAS CAMPANELLA , a Calabrian ; of the Order of Preaching Fryars , put forth seven Books Astrologicorum , in which Astrology , separated from Iewish and Arabian Superstitions , is Physiologically handled . He set forth likewise four Books De sensu Rerum , & Magia , in the third of which . he treats of the Heavens , and the Celestial Bodies . GEORGIUS SCHOMBERGERUS , Professor of Mathematicks in the University of Freiburg in Brisgaw , a Iesuit , put forth a Book , entituled Sol illustratus , wherein he treats of the several Accidents of the Sun , of the Solar Stars , and of the liquidity of the Heavens . He published likewise a Century of Optical Problems , and a new way of Dialling , as well by direct , refracted , as reflected Rayes . SIMEON PARTLICIUS put forth Astronomici Apologetici Pars prior , Printed in 8 o. 1623. as I find in Iames his Appendix to the Catalogue of the Bodleian Library . JOHANNES ADAMUS , a German , of the Society of the Iesuits , travelled into China , and in the Language of that Country wrote a Table of all the Stars . He put forth likewise a Treatise , De Calculo Eclipsis Lunae , in the year 1624. HENRICUS BRIGGIUS , Savilian Professor of Geometry in the University of Oxford , pursuing what Nepier had invented and begun , put forth two Books of Logarithms , after a more commodious Method ; the first , entituled Arithmetica Logarithmetica ; the other Trigonometria Britannica ; the former shewing the Construction of Logarithmetical Tables ; the latter , the Construction of the Tables of Sines , Tangents and Secants , and the Doctrine of Triangles , to the great advantage of Astronomy , and Astronomical Operations . Mr. EDWARD WRIGHT , Contemporary with Mr. Briggs before mentioned , having spent sometime in Cambridge , and being naturally addicted to Mathematical Studies , was perswaded to accompany , and went along with the Right Honourable George Earle of Cumberland , in his Expedition to the Azores , in the year 1589. on purpose to add the Practice of Navigation to the Theory ; and in the year 1599. he published his Book called the Errors in Navigation . A most excellent Work for the true describing a Sea-Chart ; which Invention of his , Gerardus Mercator published without owning the Author . Before the Publication of this Work , in the year 1594 , 1595 , and 1596. He , by a large Quadrant of six foot Radius , made Observation of the Sun's Meridian Altitude , and thereby not only left the best Theory of the Sun's Motion at that Time , but new made exquisite Tables , for the Sun's Declination . He held Intelligence with the most Able Artists abroad , and being chosen Tutor in the Mathematicks to Prince Henry , he , by the help of some German Workmen , caused to be made for that hopeful Prince , a large Sphere with curious Movements , which by the help of Spring-Work , not only represented the Motion of the whole Celestial Sphere , but shewed likewise the Particular Systems of the Sun and Moon , and their Circular Motions , together with their Places , and possibilities of eclipsing each other . There is in it a Work by Wheel and Pinion for a Motion of 17100 years , certainly effected , if the Sphere should be so long kept in Motion . This Sphere , though thus made at a great Expence of Mony and ingenious Industry , was in the late Times of Devastation , cast aside among other Rubbidge , and had been utterly lost and destroyed , had it not in the year 1646. been found out by Sir Ionas Moore Knight , my worthy Friend , and at his great cost and charge restored to its Pristine Perfection , remaining now at his House in the Tower , among other Mathematical Instruments and Curiosities in his Possession . Besides the Book of the Errors in Navigation before mentioned , the said Mr. Wright writ a Book of the Use of the Sphere ; a Piece of Dialling , and a Book of Navigation , called the Haven finding Art ; in all which he hath shewn himself not only a Sedulous , but a Knowing Astronomer . MARTINUS HORTENSIUS , of Delpht in Holland , Professor of Mathematicks at Amsterdam , Companion and Adjutor to Philippus Lansbergius , in his Astronomical Studies , and no mean Observator of the Stars , undertook to answer something which Kepler had inserted in the Preface to his Ephemerides , and put forth a Dissertation , De Mercurio sub Sole viso , & Venere invisâ ; which he addressed to Gassendus , who had written upon the same Subject . ROBERTUS HUGHES Professor of Mathematicks in Gresham-Colledge London , set forth a Treatise of the Use of the Celestial and Terrestial Globes , illustrated with Figures and Annotations , by Iohannes Isaac Pontanus , Professor of Philosophy at Harderwick in Gelderland . ANDREAS ZERGOL , Native of Sancta Cruce in Carniola , a Iesuit , Professor of Mathematicks and Theology at Gratz in Styria , put forth Chronological Theorems , of the year of our Saviour's Nativity and Passion . CAROLUS ANTONIUS MANZINUS , Professor of Philosophy at Bologna , a learned Mathematician , put forth Tables of the Primum Mobile , cum nova Arte dirigendi , with a compendious Method of Directions . He writ likewise of the Theory of the Planets ; and was , at the time Ricciolus published his Almagest ; a diligent Observer of the Celestial Motions . D. HENRION , Professor of Mathematicks at Paris , put forth in French the Problems of Regiomontanus touching the Use and Practise of his Tables of Directions , to which he added large Annotations and Explications of his own , together with Regiomontanus his Tables , by him corrected and augmented . In the Preface to which Work he hath laid down the Doctrine of Spherical Triangles : He set forth in French Theodosius his Sphericks , published a Treatise of the Use of the Globes , and Compass of Proportion , of Cosmography , and a Canon Manuel des Sinus , &c. besides his Mathematical Collections , and Euclid's Elements . JULIUS SCHILLERIUS , of Ausburg , Dr. of the Laws , put forth Coelum Stellatum Christianum , reducing the fabulous Morphoses of the several Constellations , and changing their Profane Names into those of Christian Saints and Martyrs ; Bayerus adding thereto a new and more accurate Uranometria . ALBERTUS CURTIUS , a Iesuit , Native of Munichen in Bavaria , proposed in the year 1627. a New System of Heaven to be disputed on at Dining ; whose ingenuity in the Theory of the Moon , his Aemulator Kepler not only admired , but commended , in his Rudolphine Tables , c. 25. ADRIANUS ULACK , of Gouda , challenges a place in this Catalogue , for his Chiliads of Logarithms , resolving , by an admirable Compendium , Astronomical , Geometrical , and Arithmetical Problems . JACOBUS ROSIUS BIBERACENSIS put forth Ephemerides , or a General Calendar Astronomical and Astrological , in which the rising and setting of the Stars , with their several Effects for every Day of the Moneth are set forth ; A Work collected out of Ancient and Modern Authors , with no mean Industry , as G. Vossius sayes of it . He stiles himself Mathematician , and Publick Imperial Notary , which Office he executed at Biennae , or Biel , a Town in Switzerland . GULIELMUS JANSONSIUS CAESIUS , alias BLAEU , of Amsterdam , an Excellent Artist , as well for his Geographical Tables , as his Celestial Globes and Spheres , whereof he was the first Composer , according to the Copernican System ; of which G. Vossius affirms the World not to have seen the like since Archimedes's . time . He likewise put forth a twofold Astronomical Institution , according to the Ptolemaick and Copernican Hypothesis , which being written in his own Language , was translated into Latin by Martinus Horten●…ius . JACOBUS BARTSCHIUS of Lauban , a City in the upper Lusa●…ia o●… Lausnitz , a Province adjoyning to Bohemia , now under the Dominion of the Duke of Saxe , Doctor of Physick , and Son-in-Law to the famous Kepler , set forth Uran●…burgum Strasburgicum sive Motuum Coelestium Ephemeris , Printed at ●… eipsick in the year 1629. He published likewise Planisphaerium Stellatum seu vice-globus Coelestis in Plano Delineatus . He wrote also another Treatise , De Indice Astronomico cum se●…tem Rotulis Planetarum aliisque figuris , imprimis Phases Lunares , Eclipses , & apparentes Planetarum Magnitud●…es adumbrantes , Printed at Norimberg in 4 o , 1661. CAROLUS MALAPERTIUS , a Flemming of Montz , and a Iesuit , Professor of Mathematicks at Doway , among other his Mathematical Works , put forth a small Piece , De Maculis Solaribus , which he stiled Sidera Austriaca . LE SIEUR BOULENGER , a French-man , Reader in Ordinary to the late King of France , hath written a Treatise , in his own Language , of the Sphere , in four Books , to which he hath added a fifth , touching the use thereof ; the third Edition whereof was Printed at Paris , 1648. CHRISTOPHORUS SCHEINERUS , of the Society of Iesus , a Native of Mundeilhen in Swaben , Professor , sometime of the Hebrew Tongue and Mathematicks at Fribourg and Ingolstadt , afterwards Rector of the Colledge of Nisse or Nissa in Silesia , observed , about the same time with Galilaeo , the Spots in the Sun. The most Eminent Pieces by which he hath signalized his Name , are these ; Oculus , seu Fundamentum Opticum ; Sol Ellipticus , Disquisitiones Mathematicae , De Controversiis & Novitatibus Astronomicis , Apelles post Tabulam ; and lastly Rosa Ursina , in which he hath so excellently and learnedly written of the Solar Spots , that , according to the Judgment of Des Cartes and Hevelius , nothing can be expected in that kind more satisfactory . DIONYSIUS PETAVIUS , Native of Orleans in France , of the Society of Iesus , the Varro of our Age , as Ricciolus stiles him , hath not only merited much by his Studies in Theology , but in Chronology likewise , and the Reason of Times , and particularly in Astronomy ; as his two Volumes , the one , De Doctrina Temporum , the other Rationarium Temporum , and his Uranologium sufficiently evidence . JOANNES BAPTISTA MORINUS , Regius Professor of Mathematicks at Paris , put forth several Astronomical Tractates ; as first , Nova Mundi Sublunaris Anatomia ; Another with this Title , Famosi Problematis De Telluris Motu vel Quiete , hactenus optata Solutio . A third was entituled , Arae Telluris fractae , written in opposition to Gassendus's Book , De Motu impresso à Motore Translato . Three Books of the Doctrine of the Sphere . Tabulae Rudolphinae ad accuratum & facile Compendium redactae , to which is annexed a Compendium of Trigonometry , Plain and Spherical . Constructio Figurae Coelestis ; Nova Dirigendi Methodus ; Et de Planetarum Revolutionibus tàm Mundanis , quàm Genethliacis . He published a Book in French called Remarques Astrologiques , being a Commentary on Ptolemy's Centiloquium . He put forth likewise Nine Books of Longitude , under the title of Astronomia à Fundamentis integrè & exactè restituta . To which is to be added his long-studied Work , entituled , Astrologia Gallica , published after his death . HENRICUS PHILIPPI , a Iesuit , Professor of Philosophy and Theology at Gratz , Vienna and Prague , of whom Ricciolus reports , that Plurimis Operibus , Chronologiam Universam , praesertim sacram , illustravit . The Works by him put forth are , first , Chronological Questions , for reconciling the Iulian years of our Lord , and those of Nabonassar , with the Iewish Aera : Likewise Chronological Questions , touching the year of our Saviour's Birth and Passion ; in the first of which is explained the Roman Calendar , with the Epacts , Calends , Ides , Nones , and Beginnings of the Moneths , as well of the Greeks , Syro-Chaldeans , and Aegyptians ; as also of the Feriae , Cycles of the Sun and Moon , and of Indictions , &c. G. Voss. ADAMUS TANNERUS , a Iesuit of Inspruck , Professor of Mathematicks at Munichen , Ingolstadt , and Vienna , wrote a most learned dissertation De Caelo ; as also another Piece , entituled Astrologia Sacra . PHILIPPUS LANSBERGIUS , of Gaunt , put forth at Middleburgh , Tables of the Celestial Motions , fitted to the Meridian of Goese ; together with a Thesaurus of Observations , and the Theory of the Planets . He put forth also Progymnasmata ▪ Astronomiae restitutae , and three Books Uranometriae . Whereto may be added his Commentationes in Motum Diurnum & Annuum , grounded partly on his own , partly upon Martinus Hortensius's Observations . JACOBUS LANSBERGIUS , Doctor of Physick , wrote an Apology for Philippus Lansbergius his Commentary In Motum Diurnum & Annuum Terrae , against Fromondus . MELCHIOR INCHOFER , a Iesuit , sometime Professor of Mathematicks , Philosophy , and Theology , at Messina in Sicily , wrote a Treatise entituled , Tractatus Syllepticus De Statione Terrae , & Motu Solis , secundum Sacram Scripturam , & SS . Patres : And an Examen Thematum Coelestium variorum Astronomorum usque ad Tychonem ; the Reason of calculating Eclipses , and of the Theory of the Planets ; these three last published not under his own Name , but that of Academicus Vertumnius . EVERARDUS WELPERUS , of Strasbourgh , put forth a Compendium of Astronomy , as well Spherical as Theorical , collected out of various Authors , from whom ( says G. Voss. ) much more might have been expected , had he not been opprest by a low and necessitous Fortune . PETRUS CRUGERUS , Professor of Mathematicks at Dantzick , and Master to Hevelius , besides his Logarithmical Tables , undertook to write Astronomia Dantiscana , which yet he lived not to finish , as his Scholar Hevelius testifies . He wrote likewise another Piece , entituled Uranodromus Cometicus . ANDREAS ARZET , a Iesuit of Constance , put forth a Mathematical Clavis , and diligently observed the Stars , as Ricciolus affirms , as long as either his Occasions or the Gout would permit ; many of whose Observations , especially about Eclipses , he freely communicated to Ricciolus . BONA VENTURA CAVALLERIUS , Iesuatus Mediolanensis , Disciple to the Excellent Galilaeo , and Primary-Professor of Mathematicks in the University of Bologna , put forth Directorium Generale Uranometricum , Practica Astrologia , and a Century of Mathematical ( and among them Astronomical ) Problem●… a Person of an acute Wit and Judgment , and by Ricciolus acknowledged to have been no mean Assistant and Promotor of his Astronomical Studies . He w●… Trigonometria , wherein are some Astronomical Problems more exquisitly demonstrated than are else where to be met with . PAULUS GULDINUS , Native of S. Gal , of the Society of Iesu●… , taught Philosophy and Mathematicks at Rome , Gratz and Vienna . He wrote in defence of the Roman Calendar , against Sethus Calvisius ; in which Work he also opposes Scaliger's Diatriba , De Aequinoctiorum Praecessione . He also published a Geographical Problem , touching the difference in numbring the dayes , between those that sail hence to the New World , and those that inhabit there . Not to mention his Centrobarica , and other Geometrical Pieces , of which Ricciolus in Chronolog●… Astronom . HUGO SEMPILIUS , by Birth a Scotch-man , by Profession a Iesuit in the Colledge at Madrid , writ twelve Books De Mathematicis Disciplinis . In the three ▪ last of which he treats distinctly , De Astronomia , De Astrologia , & De Calendario , Printed at Antwerp in folio in the year 1635. and dedicated to Philip the Fourth King of Spain . In the End of which Work he hath annexed several Catalogues of Mathematical Authors , and among them of Astronomers and Astrologers , but giving no more of them than their bare Names . NATHANIEL CARPENTER , sometimes Fellow of Exeter-Colledge in Oxford , put forth Geography Delineated-in two Books ; in the first of which ( containing the Spherical Part ) among other things , he treats of the Magnetical Affections and Motion of the Earth , of its Site and Proportion in respect of the Heavens ; of the Longitudes and Latitudes of Places , and their several Wayes of Invention . In the second ( containing the Topical Part ) he treats likewise among other things of the Adjuncts of Place in relation to the Heavens , either Northward , Southward , Eastward , Westward , with the Differences of the respective Hemispheres . ; and several other things worthy the Knowledge of a young Student in Astronomy , Printed at Oxford 1635.4 o. Upon the same Accompt may be here inserted Varinius his Geography , being much after the same Method , and a very useful Piece , especially since lately reprinted at Cambridge , with the Addition of the several Schemes wanting in the former Edition .. JOHANNES PHOCYLLIDES HOLWARDA wrote an Epitome Astronomiae Reformatae , and a succinct Examen of Lanbergius's Astronomy . ABDIAS TREW , Professor of Mathematicks at Nuremberg , Astronomiae partem Sphaericam accurata ibidem Methodo consignabat , sayes G. Vossius , L. De Scient . Mathemat . to which is to be added his Nucleus Astrologiae correctae , written in High Dutch , and Printed at Norimberg 1651.4 o. and his Tota Mathesis there likewise Printed in the year 1657.4 o. JACOBUS HUMIUS , a Scotch-man , Professor of Mathematicks at Paris , liath published , besides divers other Mathematical Pieces , a Treatise of the Sphere , according to the Hypotheses of Ptolemy and Copernicus ; and another , of the Theory of the Planets , according to the Doctrine of Ptolemy , both written in French. ANDREAS ARGOLUS ; Professor of Mathematicks in the University of Padua , put forth Ephemerides , continuing from the year 1630. to the year 1700. and another Work , entituled Pandosium Sphaericum . He writ likewise De Diebus Criticis , De Decubitu Aegrorum , with above a hundred Genitures of Popes , Cardinals and Princes . Also a Piece of Genethliacal Astrology called Ptolemaeus Parvus Arabibus junctus . Tables of oblique Ascensions , and the whole Art of Direction , he calls it Tabulae Primi Mobilis ; some Astrologick Aphorisms , and others , under the Title of Astrologia Aphoristica . FORTUNIUS LICETUS , of Genua , an eminent Philosopher , among other his learned Works , put forth a Treatise De Novis Astris & De Cometis . Item , Controversiae . De Cometis , De Motu & Parallaxi Cometarum ; of the Comet seen in the years 1642. and 1643. De Lucidis in Sublimi ; De Regulari Motu Planetarum ; De Lunae subobscuurâ luce , prope Conjunctiones , & in Eclipsibus observatâ ; De Terrae unico Centro Motûs , &c. CAROLUS GONTRANUS , Doctor of Sorbonne , and General of the Oratorian Order , put forth a small Piece , Pro Astrologia , sed sana , as Ricciol . in Chronol . Astron. affirms . BALTHAZAR GONRADUS , a Iesuit , born at Nisse , Professor of Philosophy and Mathematicks at Olmutz , the Metropolis of Moravia , published a New Reason of Cosmographical Tables , Described in a right Angled Cone , whose Basis is the Aequator ; and made some Observations of Eclipses , which he communicated to Ricciolus . HADRIANUS METIUS , of Alcmaire , wrote learnedly of the Use of the Globe , saies Ricciolus , and in the first Book of his Geometry resolves divers Astronomical Problems , Geometrically and Arithmetically . He published likewise his Primum Mobile , wherein he treats De Sphaera , Planisphaerio , sive Astrolabio , &c. His Brother Iacobus Metius being one of the first Inventors of the Telescope . G. Voss. Doctor JOHN WILKINS , sometimes Warden of Wadham Colledge in Oxford , afterward Bishop of Chester , wrote about the year 1638. Two Tractates , in one indeavouring to prove the Moon a World , in the other the Earth a Planet , without putting his Name to either of them ; yet they were so well known to be his , that Langrenus in his Map of the Moon ( dedicated to the King of Spain ) names one of the Spots of his Selenographick Map after his Name . He highly promoted the Study and Perfecting of Astronomy both at Oxford , whilst he was Warden , and at London whilst he was Bishop , and Fellow of the Royal Society ; he died in November 1672. NICOLAUS CABAEUS , a Native of Ferrara , of the Society of Iesus , Professor of Philosophy at Parma , besides his Magnetick Philosophy , wrote a Comment In Aristotelis Meteora , and other Pieces of abstruse Learning , wherein he treats of many things well deserving the Knowledge of an Astronomer or Cosmographer , especially touching Comets , the Galaxie , &c. He died at Genua , where also with great applause he had publickly taught and professed Mathematicks . NICHOLAUS CAUSSINUS , a Iesuit , Native of Troyes in France , wrote a particular Treatise De Domo Dei , that is , of the Heavens , and the Celestial Bodies , wherein he learnedly and acutely argues against the Professors of Judiciary Astrology . JOHANNES ANTONIUS ROFFENUS , of Bologna , Disciple to Maginus , and an eminent Astronomer and Astrologer , whom Ricciolus affirms to have published many Astrological Discourses , but gives not the particulars thereof . GULIELMUS SCHICKARDUS , Professor of the Oriental Languages and Astronomy at Tubinge , put forth a little Piece , entituled Astroscopium , with a Synoptical Table , for the easier investigation of the Places of the Planets . He published likewise a Dissertation , addressed to Gassendus , De Mercurio sub Sole viso , with other Celestial Observations , and particularly touching Eclipses . His Astroscopium was published by Iohannes Ruffius , at Nordling in the year 1655. WILLIAM MILBOURN Master of Arts , Curate at Brancespeth near Dunham , aged about forty years , was very knowing in Arithmetick , particularly in Algebra ( having in the year 1628. extracted the Root of this Equation , 1,000 = aaaaa − aaaa − 4aaa + 3aa + 3a . before he had seen Hariott's Praxis ) and in Geometry . But his greatest Labours were in Astronomy , and in his Observation of the Stars , he used a good Cross Staff , and a Sextans of five foot Radius , he discovered the weakness of Lansbergius his Astronomy , and verified Kepler's Tables , which he turned into Decimals , and made Tables after Kepler's subsidiary way ( pag. 97. Tab. Rudolph . ) which were sent to his Brother Mr. Milbourn a Stationer in London , to be Printed ; but never passed the Press , being yet preserved in MS. in the hands of Sir Ionas Moore Knight . All his Observations and other Papers , &c. were most unhappily lost , by the coming in of the Scots , in the year 1639. HIEREMIAS HORROX , born at Toxteth , a small Village near Liverpoole in ●…ancashire , after some time of Study at Emanuel Colledge in Cambridge , about the year 1633. first applied himself to Astronomical Observations , having by his industry considerably advanced that Science ; as first by his excellent Tractate of Venus discovered in the Sun , an Observation which never had been made by any before , published by the famous Hevelius , together with his own Mercurius in Sole visus , and illustrated with his accurate Annotations . His other Posthume Works , or rather his imperfect Papers were lately digested and published , by the great care and labour of that learned Mathematician , Doctor Iohn Wallis , Savilian Professor of Geometry in the University of Oxford . Wherein he first asserts and promotes the Keplerian Astronomy , against the Hypotheses of Lansbergius , which he proves to be inconsistent among themselves ; not agreeable with former Observations exactly made ; nor the Precepts of them well demonstrated . He likewise disputes of the Celestial Bodies and their Motions , and answers the Cavils of Hortensius against Ty●…ho ; gives a new Theory of the Moon , to which are added the Lunar Numbers of Mr. Flamstead . There are also Extracts of several Letters of his to his Friend and Associate in Study Mr. Crabtree , upon divers Astronomical Subjects , with a Catalogue of Astronomical Observations made by the said Horrox , without allowance of the Excentricity of the Eye , which he afterwards castigated by a correction fairly written with his own hand . WILLIAM CRABTREE , a Clothier of Broughton near Manchester , in Lancashire , was a diligent Observer of the Stars , as appears by his Observations printed by Doctor Wallis 1673. in the Edition of Mr Horrox his Works , which amount not to the tenth part of what he had made . He converted Kepler's Rudolphine Tables into Decimals , for his own use whereof there is now a MS. Copy remaining with the said Sir Ionas Moore . Mr. Horrox and this Mr. Crabtree died in the year 1641. having about a year before had the happy accquaintance of the most incomparable and ingenious Gentleman , WILLIAM GASCOYGNE of Middleton in the County of York Esquire , who for some years before , had taken much pains in Astronomical Observations , and invented wayes to grind Glasses . He was the first that used two convex Glasses ; had at that time a Tube that drew out fifteen foot in length , of his own working . The Object-glass was a Meniscus . He invented wayes to measure small Angles by the Prospect-Glass to a second ; and had he lived , he had certainly brought great perfection to Telescopes . Mr. Crabtree taking a Journey into York shire in the year 1639. writ thence to Mr. Horrox , as followeth . The first thing Mr. Gascoygne shewed me was a large Telescope amplified and adorned with new Inventions of his own , whereby he can take the Diameters of the Sun or Moon , or any small Angle in the Heavens , or upon the Earth most exactly through the Glass to a second . A device much desired , but little expected , &c. In the year 1641. Mr. Gascoygne writ to Mr. Crab-tree , that he questioned not to provide an Instrument to take at once the Distances of three Points in the Periphery of the Earth's shade of the Moon , the Diameters of the Planets , &c. But he and all his excellent Inventions and Labours were lost by his Death , which was in his late Majesty's Service , in the Fight at Marston Moore . These Four , were Lights of the first Magnitude , in the Northern Hemisphere , who were happily brought to the Acquaintance of one another by the means of Christopher Townley of Carr in Lancoshire Esquire , who stuck not for any cost o●… labour to promote as well Astronomical as other Mathematical Studies by a diligent Correspondence kept and maintained with the learned Professors in those Sciences , ; upon which Account he was very dear to All the Four ; and for which Reason , as for the Particular respect I owe him , he merits to be named in thi●… Catalògue . The others that follow , though they were not so conspicuous as the former , were yet of considerable Lustre , and afforded no mean Influence towards carrying on the Work of Astronomy in those Parts . In the first Place , Sir JONAS MOORE Knight , Surveyor General of His Majesty's Ordnance , my Worthy Friend and Collegue , born at Whitebee , in Lancashire , by his diligent endeavours , contributed not a little to the advancement of the Astronomical Design , so well begun and prosecuted by the much deserving Persons before mentioned . He turned Bulialdus his Tables into Decimals , after Mr. Milbourn's Method , and writ of the Sphere , and its several Projections ; which Work he hath now by him , though it were to be wished , he would rather , by the publication thereof , afford the ingenious Lovers of these Studies an opportunity at once of witnessing , and receiving the benefit of his Labours . GEORGE WHARTON Esquire , born at Kirby-Kendal in the County of Westmerland , my ancient kind Friend , and now Treasurer and Pay-master to the Office of His Majesty's Ordnance , complying with the incitements of the said Mr. William Milbourn , addicted himself very assiduously to the Calculation and Observation of the Celestial Motions ; till the late Rebellious Times , deprived him of his Liberty ; and since that , the frequent Accesses of the Gout , have taken from him , the opportunity of prosecuting those Studies with that Assiduity as formerly . Mr. JEREMIAH SHACKERLEY a great Pains-taker in calculating and comparing several Observations , he writ Tabulae Britannicae grounded chiefly upon the Theories and Observations of Mr. Horrox , which were Printed in 8 o. about the year 1647. he dyed in the East-Indies . Mr. NATHAN PIGHELLS , a very diligent Observer , &c. to whom may be added some others , which for Brevities sake I here omit . All which Examples may serve as very inducive Arguments to perswade the learned Doctor Wallis to be of another Opinion than that , which ( I presume through want of due Information ) he declared in his Preface to Mr. Horrox his Works , where he saith ; ●…atendum est paucissimos tunc Dierum in Anglia , partibus saltem Borealibus , Studiis illis Animum sedulo applicuisse ; when as it is more than probable , that if some of the Persons before mentioned had not been overtaken by too untimely Death , others of them by the fatal Calamities of the late horrid Rebellion , Astronomy had by their Labours been most considerably advanced . And I question whether so many Able Artists were to be met with again at the same time , in any one Province in England , beside . FRANCISCUS MONTEBRUNUS , a Noble Genouese , and Doctor of the Civil and Canon Laws , composed out of Lansbergius's Tables , Ephemerides , calculated for the Meridian of Bologna , commencing in the year 1641. and ending in the year 1660. JOHANNES GEORGIUS HERVARTUS , of Howenburgh , Doctor in the Laws , set forth a new kind of Chronology , grounded upon the Calculation of Eclipses ; which yet both Petavius and Ricciolus have undertaken to refute . EMANUEL PORTUS set forth a Treatise , entituled Dipluranologia , giving an account of the going back of the Sun in the time of Hezekias , and of the standing still of the Luminaries in the time of Ioshua ; Printed at Padua in the year 1642. ANTONIUS DEUSINGIUS writ a Dissertation De vero Systemate Mundi , Printed at Amsterdam in the year 1643. In which the Copernican System is reformed ; and those numberless Orbs in that of Ptolemy , by which human Apprehension is so distracted , are quite taken away . GEORGIUS FOURNERIUS , a Iesuit , Professor of Mathematicks at Paris , published about this time his famed Piece of Hydrography ; out of which saies Ricciolus , Doctrina profundior hauritur , quàm Mare ipsum , quod Monumento adeo nobili illustravit . Of his skill in observing the Celestial Phoenomena , especially Eclipses , Ricciolus gives ample testimony . PETRUS HERIGONUS , Professor of Mathematicks at Paris , wrote a Cursus Mathematicus , in several Tomes ; in the Fourth of which he treats De Sphaera Mundi , and De usu Mappae Geographic●… ; and in the Fifth , of the Theory of the Planets . JOHANNES SELDENUS sometime the Great Dictator of Learning in this Nation , besides his other Works of admirable value , hath gained no mean Esteem by his Dissertation De Anno Civili , & Calendario Veteris Ecclesiae seu Reipublicae Iudaicae , Printed at London by Richard Bishop 1644. 4 o. MICHAEL FLORENTIUS LANGRENUS , Cosmographer and Mathematician to Philip IV. King of Spain , wrote a Treatise of the Observation of the Longitude by Sea and Land , from the Obscuration , or Illumination of the Spots of the Moon . To which end he designed a New Selenography , under the Title of Selenographia Langreniana , sive Lumina Austriaca Philippica ; of whom see more in Ricciolus , Chron. Astronom . JOHANNES GREGORY , Native of Amersham in Buckinghamshire , and sometime Chaplain of Christ-Church in Oxford , merits a place in this Catalogue , for his learned Tractates De Aeris & Epochis , and his Description and Use of the Terrestial Globe , and of Charts and Mapps , published in his Posthume Works , among other Pieces of exquisite erudition , and some Astronomical and Astrological Discourses in his Annotations upon the Scripture , in which he shews no Vulgar Learning . GEORGIUS POLACCUS , a Venetian , set forth Anticopernicum Catholicum , in which he maintains the Stability of the Earth , and the Sun's motion . ALBERTUS LINEMANUS of Prussia , Professor of Mathematicks in the Academy of Konningsberg , put forth a small Tract of Astronomical Observations , especially of Eclipses , to which he gave the Title of Memoria Saecularis , as Ricciolus affirms . JACOBUS GRANDAMICUS , a Iesuit , put forth a Treatise , entituled Nova Demonstratio Immobilitatis Terrae petita ex virtute Magnetica , Printed at La Fleche in France 4 o. He writ likewise a Treatise of the Nature , Motion , and Effects of the Comet , which appeared in the year 1665. mentioned in the Iournal des Seavants . EMANUEL MAIGNANUS , a Fryar of the Order of St. Francis de Paula , put forth an excellent Piece , under the Title of Perspectivae 〈◊〉 ; in the First and Fourth Book whereof , he treats of many things touching Refractions , Scitu digna & Astronomis Utilia , sayes Ricciolus . LAURENTIUS EICHSTADIUS , Doctor of Physick , Native of Stetin , in Pomerania , and Professor of Mathematicks at Dantzick , reckoned by Bulialdus , ( in Prologo Astro Philol. ) among the most eminent Astronomers of his Time , put forth among other his Works Paedia Astrologica , and Ephemerides of thirty years , ending in the year 1665. to which he added a Compendious Canon of Logarithms and Mesologarithms ; together with Tables of the Primum Mobile , Calculation of Eclipses , and the like . He likewise published Tabulae Harmonicae Coelestium Motuum , tum Primi , tum Secundorum , chiefly grounded upon the Observations and Hypotheses of Tycho Brahe . Likewise a Century of Astrologick Aphorisms . MARINUS MERSENNUS , a French-man , a Minime Fryar , of the Order of St. Francis de Paula , hath , in his learned Comment upon Genesis , added many curious Astronomical Observations ; and in his Mathematical Synopsis , not only by his own Industry , but also by the publication of others learned Labours , hath much contributed to the advancement of Astronomy . PETRUS GASSENDUS , Dean of the Cathedral Church of Digne in Provence , and Regius Professor of Mathematicks in the University of Paris , the learned Restorer and Vindicator of the Epicurean Philosophy , among other the eternal Monuments of his Erudition , hath left divers Astronomical Tractates ; as first , four Epistles , De apparente Magnitudine Solis humilis & sublimis ; three , De Motu impresso à Motore translato , wherein he defends the Copernican ▪ Hypothesis , of the Earth's motion ; another De ●…arheliis , seu Solibus quatuor spuriis Romae circa verum visis , Anno 1629. He put forth also , about the time of his admission into the Mathematical Chair at Paris , an Astronomical Institution , Printed lately at London , with the addition of Kepler's Dioptricks ; and hath left , among other his Works , a Volume of Celestial Observations , which from the year 1621. to the year 1655. he made with assiduous care and accurate speculation . A Treatise also entituled , Mercurius in Sole visus & Venus invisa , Printed at Paris in the year 1631. His Judgment about nine pretended Satellites of Iupiter , in Answer to Rheita . Solstitialis Altitudo Massiliensis , seu Proportio Gnomonis ad Solstitialem Umbram observata Massiliae , 1636. in an Epistle to Vendelinus . The Lives of Purbacchius and Regiomontanus , as likewise those of Copernicus and Tycho Brahe , the most illustrious Astronomers of their Times ; and a Compendious Exposition of the Roman Calendar . Besides the Life of the incomparable Peireskius ; and his Epistles to divers eminent and learned Persons , wherein he frequently treats , upon occasion given , of Astronomical Subjects . RENATUS DES CARTES , Native of La Hay en Touraine , a Town on the Confines of Poicton in France , of a Generous Extraction ( his Father having been President of the Parliament at Rennes in Britanny ) one of the most Signal Philosophers and Mathematicians , which this last , or ( happily ) former Ages have produced . Who having given new Life and Light to Philosophy ; added likewise no mean Lustre to Mathematical Arts , and particularly to that of Astronomy . For in the third Part of his Principles of Philosophy , ( the Subject whereof is De Mun●… Aspectabili . ) He treats of the Distances and Magnitudes of the Sun , Moon , and the other Planets ; examins the several Hypotheses of Ptolemy , Copernicus , and Ty●… Brahe , Discourses of the Maculae and faculae Solares , of Comets , and their several Phaenomena , of the Moon , her various Phases , and different Motions , with divers other Particulars relating to Astronomy ; to which likewise he contributed in his Dioptricks by his curious Inventions for the more exact polishing of Glasses , and bringing Telescopes to a greater Perfection , for the Contemplation and Observation of the Celestial Bodies . Of which Subject likewise he sometimes treats in his Epistles , particularly in the 67 th Epistle of his Second Tome ( to Mersennus ) the Argument whereof is , De Astrorum Observatione , & utilitate quae indè capi potest . See more of this Excellent Person in the brief Summary of his Life drawn by the accurate Pen of Lipstorpius in his Specim . Philosoph . Cartes ; and in that written by Petrus Borellius , wherein he gives a particular Catalogue of all his Works and Writings . ANTONIUS MARIA SCHYRLAEUS DE REITHA , a Capucine Fryar , & Astronomus non ignobilis , according to Ricciolus , wrote an Astronomical Treatise , entituled Oculus Enoch & Eliae , seu Radius Sydereomysticus , Printed in the year 1645. ISMAEL BULIALDUS , Son of Ismael Bulialdus , and Native of Loudun , a Town in the Province of Poictou in France , by Ricciolus stiled , Astronomus profundae indaginis , hath highly merited , as well by his publication of several ancient Mathematical and Astronomical Authors ( some of whom we have already mentioned ) as by his own most learned Labours , having first published his Dissertation , entituled Philolaus , sive De vero Systemate Mundi . Afterwards in the year 1645. he set forth his Astronomia Philolaica , grounded upon the Hypothesis of the Earth's motion , and the Elliptical Orbit described by the Planets motion about a Cone ; illustrated with solid Demonstrations , to which he hath added Tables , by him entituled Tabulae Philolaicae , in which the motions of Saturn , Iupiter , and Mercury are more accurately represented than in the Rudolphine Tables , being for the most part much easier than those , a Work , sayes Ricciolus , Omnibus Astronomiae studiosis , sed non sine attentione , legendum . He likewise published about the year 1666. Monita duo ad Astronomos ; the first , touching a New Star , in the Neck of the Whale , appearing at some times , at others , disappearing ; the other , touching a cloudy Star in the Northern part of Andromeda's Girdle , not discovered by any of the Ancients , sometimes appearing , and sometimes not . Which Phaenomena he recommends to the Observation of all curious Astronomers . FRANCISCO GENERINI set forth in Italian the Design of a Moving Globe , composed by him , to demonstrate the diurnal and annual motion of the Moon , together with the inequality of dayes ; to which is annexed a Discourse of Natural and Artificial Houres , declaring the meaning of the said Author touching the said Invention , and an account of many other Operations to be wrought by the said Globe , besides those before mentioned , Printed at Florence , in 4 o. 1645. JOHANNES BAINBRIDGE , sometime Savilian Professor of Astronomy in the University of Oxford , writ a Treatise , of the Dog-Star , and of the Canicular dayes , ( published by Mr. Graves , together with a Demonstration of the Heliacal Rising of Sirius , or the Dog-Star , for the Parallel of the Lower Egypt ) Printed at Oxford in the year , 1648. He writ likewise of the Comet in 1618. and published Procli Sphaera , with Ptolemy's Chronological Canon . ATHANASIUS KIRCHERUS , a Iesuit , Native of Buchon , within the Territories of the Abbot of Fulda , in Germany , sometime Professor of the Oriental Languages ( in which , by Ricciolus , he is said to be ad stuporem usque peritus ) as also of Mathematicks at Wirtsberg , and Avignon , afterwards Ordinary Professor of Mathematicks in the Iesuits Colledge at Rome , hath in most of his Works treated largely upon the Subject of Astronomy ; as in his Oedipus Aegyptiacus , where he displayes Systematica Mundorum , sive de Mundo , Mundorúmque varietate ex mente Aegyptiorum ; De Astrologia Aegyptiorum & Chaldaeorum Hieroglyphica ; and more particularly in his Musurgia , where he treats De Coelorum Symphonismo ; De admiranda Mundanorum Corporum ad invicem proportione ; De particulari Symphonismo Planetarum ; De Choro Ioviali ; De Choro Solari & Martio ; De Harmonia Stellarum Fixarum ; In his Book De Magnete , where he fully handles the Subject of Magnetick Astronomy , under the several Heads of Sphaera Magnetica , Uranographia Sciotherico-Magnetica , and Horologiographia Magnetica ; In his Book entituled Ars magna Lucis & Umbrae ; wherein besides his various Horography he treats De Astrolabiographia , & Geographia Gnomonica , Gnomonica Physico-Astrologica ; De Arte Anacamptica , sive Astronomia Reflexa ; De Arte Anaclastica , sive Astronomia Refracta , & De Cosmometria Gnomonica , hoc est , De Mundi Lucumbris Dimensione , &c. as also in his Itinerarium Ecstaticum Coeleste , in which to express him in his own words , Mundi Opificium , i. e. Caelestis Expansi , Siderúmque tàm errantium quàm fixorum natura , vires , proprietates , singulorumque compositio & structura , ab infimo Telluris Globo usque ad ultima Mundi confinia perfecti Raptus Integumentum explorata novà Hypothesi exponitur ad veritatem , Printed at Rome 1656. JOHANNES DE EPIERES , Doctor of Divinity and Grand Prior of the Monastery of Aquicintinum , put forth an Universal Calendar , wherein he proposes an easie Method for finding out the Golden Number , Epact , Dominical Letter , Moveable Feasts , and Indictions , for any year proposed , and promises a larger Work under the Title of Astronomia Aquicinctina , which whether ever published , does not yet appear to me . DIRK REMBRANTZ , in his Netherlandish Astronomy , treats of Planet-Wisers , and gives the Reader an Eclipsigraphia , shewing when an Eclipse of the Sun happens , what and how great a part of the Earth will be obscured thereby . ROBERTUS DUDLEY , an English-man , known abroad , especially in Italy , by the pretended Title of Duke of Northumberland , published three Volumes in folio , entituled Arcano del Mare , in which are Sea-Charts , Directions for the building of Galleys , and a Description of many Planetary Instruments . SAMUEL FOSTER , a learned Professor of Astronomy in Gresham-Colledge , contrived several ingenious Planetary Instruments , published afterwards in his Posthumous Miscellanies . SILVIO PHILOMANTIO , an Italian , under that feigned Name , and in that Language put forth Ruota Planetaria , which Ricciolus ascribes to Bonaventura Cavallerio . PHILIPPUS LABBEE , a learned French Iesuit , Native of Bourges en Berry , put forth , in his own Language , L'Abbregé de la Sphere , being a compendious Treatise of the Sphere , reduced by an easie and short Method into XII . Chapters , with some important Advertisements thereupon , Printed in the year 1647. JACOBUS USSERIUS , the late most learned and Reverend Archbishop of Armagh , published a Dissertation of the Macedonian and Asiatick Solar year , together with a Parapegma of Greek Astronomers , accommodated to the Reasons of the Macedonian and Iulian years ; Vide Voss. L. De Scient . Mathemat . GOTHOFREDUS WENDELINUS , Canon of the Collegiate Church of Conde in Flanders , published Idaea Atlanticarum Tabularum , grounded upon the Observations of divers Eclipses . He set forth likewise Lampas Arcanorum Coelestium , and wrote upon several other Astronomical Subjects , as may appear by his Epistles to Gassendus , and those of Gassendus to him , published in his Works . AEGIDIUS MATROPTUS composed something of the Sphere , & Machinationem conversionibus Secundorum Mobilium repraesentandis , commended by Gassendus , in his Epistles . CLAUDIUS SALMASIUS having signalized his Name by divers learned Works , hath also endeavoured to give honour thereto by his Diatribes De Annis Climactericis , & De Antiqua Astrologia , Printed at Leiden 1648. He hath interspersed likewise in his Plinian Exercitations sundry Astronomical Arguments , and some Critical Observations upon Manilius , but such as are now and then severely met with by Petavius in Uranolog . Mr. WILLIAM OUGHTRED , a learned Divine , and most eminent Mathematician ; famous for his Clavis Mathematicae ; at the End whereof is a Treatise of Dialling , which is an Astronomical Subject . He was likewise the Author of the Circles of Proportion , where ( not to mention the Double Horizontal Dial ) there is a Treatise of Navigation , besides divers Astronomical Propositions . He likewise published a Treatise of Trigonometry , being the first Author that demonstrated two Proportions for finding both the Angles , at the Base of an oblique Spherical Triangle , at two Operations , when two Sides with the Angle are given . PHILIPPUS FINELLA wrote in Italian Planetaria Physionomia , Printed at Naples 1649. 4 o. SCIPIO CLARAMONTIUS , of Caesena , a Knight , and formerly Professor of Philosophy in the University of Pisa , a most expert Mathematician , put forth many learned Pieces , among which the chief are these ; Anti-Tycho , in defence of the Sublunary Place of Comets , with its Apology , and Supplement ; but answered by Kepler , in his Hyperaspistes . Of three New Stars , against the Opinion of Tycho Brahe , which is yet defended by Galilaeo , in his Mundane System ; And XVI . Books De Universo Anno , published in the year 1644 as also a particular Treatise , De Phasibus Lunae , Geometrically demonstrated ; and another entituled Anti-Philolaus . He wrote also against the truth of Telescopes , asserting that the Earth cannot reflect a Light to the Moon ; but is answered by Zucchius , in his Opticks . MARIUS BETTINUS , a Native of Bologna , of the Society of Iesus , Professor of Moral Philosophy and Mathematicks at Parma , among other his Works , published Apiarium , seu Paradoxa universae Philosophiae Mathematicae , in the Eighth Book whereof he treats chiefly touching matters Astronomical ; which Subject he also handles in his Aerarium Mathematicum . He writ likewise in Vindication of himself , being accused by Ricciolus , of committing many Errors in Astronomy , a thin folio Book published in Latin. JOHANNES MARCUS MARCI , Counsellor and Physician to the Emperor Ferdinand the Third , and primary Professor of Physick in the University of Prague , wrote , among other Physico-Mathematical Tractates , a Particular Treatise , De Longitudine , seu Differentia inter duos Meridianos , unà cum Motu vero Lunae . inveniendo ad tempus datae Observationis , Printed at Prague in the year 1650. 8 o. JOHANNES GRAVES sometime Savilian Professor of Astronomy in the University of Oxford ; A Person who as well by his Forraign Travels , as his learned Labours , hath gained to himself an unperishing Reputation ; as his Pyramidegraphia , & de Pede & Denario Romano sufficiently testifie , and as to our present Subject , his Discourse or Demonstration of the Heliacal rising of Sirius , or the Dog-star for the Parallel of the Lower Egypt , published together with Doctor Bambridge his Canicularia likewise evinces ; to which is subjoyned out of Ulugh Beigh the Longitudes and Latitudes of the chiefest of the fixed Stars . He published likewise in Arabick and Latin , Epochae Celebriores Astronomis , Historicis , Chronologis Chataiorum , Syro-Graecorum , Arabum , Persarum , Chorasmiorum Usitatae , ex Traditione Ulugh Beigh , together with Abul Feda's Geographical Tables , both which Pieces he illustrated with his learned Notes . In like manner he set forth Astronomica Shah Cholgii Persae unà cum Hypothesibus Planetarum , to which likewise he subjoyned the Geographical Tables of Nassir Eddinus the Persian , and of Ulugh Beigh . And from whom the learned World might justly have expected yet greater things , had not Death by a too hasty End of his Life , put a stop to the Course of his Ingenious Studies . LEO ALLATIUS , a Graecian , of the Isle of of Chios , lately Keeper of the Vatican Library at Rome , a Person most eminently learned , hath published ( among other his various Works of most profound and diffusive Reading ) an Exercitation , proper to our present Subject , entituled , Mensura Temporum Antiquorum , & praecipuè Graecorum . He likewise designed another Treatise , under the Title of Historia Astrologica , and Three Books De Magnete , as I find in the Catalogue of his Works , as well already Printed , as to be Published , set forth by Bartoldus Nihusius ; but whether the two last have yet passed the Press , is to me uncertain . He translated the Paraphrase of Proclus Diadochus upon Ptolemie's Quadripartite , and caused it to be elegantly Printed . JOHANNES BECHET put forth a new Theory of the Planets Geometrically demonstrated , by Concentrick and Excentrick Circles , Printed at Paris . MARIA CUNITIA , Daughter to Henricus Cunitius Doctor of Physick , by Birth a Silesian , highly meriting for her excellent Skill in Languages , and History , more especially for her admirable Knowledge ( like another Hypatia ) in Mathematical Learning , particularly in Astronomy and Astrology ; of which she hath given Signal Testimony by her Exquisite and curious Work , entituled Urania Propitia , wherein she hath set forth Astronomical Tables , of wonderful facility and exactness , grounded upon Kepler's Hypotheses , and satisfying the Celestial Phaenomenae by a most easie and Compendious way of Calculation ; expressing and performing by explicite Numbers , what the Rudolphine Tables contain implicitely in Logarithmical Numbers , and thence require to be effected . Dedicated by her Self and Husband , Elias à Leonibus , to Ferdinand the Third Emperor of Germany , and Printed in fol. ( Bicini Silesiorum ) 1650. in Latin and High Dutch. JOHANNES GARIBUS writ De Phaenomenis Ostentis , from the year 1641. to the year 1650. VINCENTIUS MUTUS , of Majorca , a most expert Astronomer , and sedulous Observer of the Stars , hath added honour to his Name by his signal Work , De Sole Alphonsino . JOHANNES DRIENES , of Dieppe , a Iesuit , and Professor of Mathematicks at Paris , wrote Tabulae Canorienses , seu Doctrina Luminarium . NICOLAUS ZUCCHIUS , Native of Parma , of the Society of Iesus , was an eminent Philosopher and Divine . He , at Rome , assisted Scheinerus in his Observations of the Solar Spots ; having published his Philosophia Optica , in which he treats of Refractions , and Celestial appearances by the Telescope . JOANNES BAPTISTA RICCIOLUS , of Ferrara , a Learned Iesuit , sometime Professor of Rhetorick and Poetry , then of Philosophy and School-Divinity , partly at Parma , partly at Bologna ; but being chiefly addicticted to Geographical , Chronological , and Astronomical Studies , hath ennobled his Name by his excellent Work , entituled Almagestum Novum , divided into three Tomes ; in the first whereof he treats of the Sphere , of the Sun and Moon , and their Eclipses , of the fixed Stars , of the lesser Planets ; of Comets and New Stars , of the several Mundane Systems , &c. In the second , he handles Trigonometry , or the Doctrine of Plain and Spherical Triangles , promises a Treatise of Astronomical Instruments , and the Optical part of Astronomy ; ( which yet he never published ) of Latitude and Longitude , and Hydrography , the Reason of Times , with a Chronological Epitome confirmed by Astronomical Characters . In the third he comprehends Observations of the Sun , Moon , Eclipses , of the fixed Stars and lesser Planets , with Precepts and Tables , Primi & Secundorum Mobilium , and other Astronomical Tables . He put forth likewise another Work , entituled Astronomia Reformata ; the design of which is ( considering the various Hypotheses of several Astronomers , and the difficulty thence arising of concluding any thing certain ) by comparing together all the best Observations , and examining what they have most certain in them , to reform upon that measure the Principles of Astronomy . Not to mention his Chronology , Published likewise by him , in folio . FRANCISCUS MARIA GRIMALDI of an Illustrious Family , a Iesuit of Bologna , partly by his joynt Indeavours and Observations with Ricciolus , partly by his own Inventions and Discoveries , hath greatly illustrated and improved Astronomy . The chiefest of his joynt Observations are these , De Quantitate Crepusculi , De Dimensione Ambitus Terrae , De Solis Distantia per Dichotomiam Lunae , De Solis Diametro apparenti , De Obliquitate Eclipticae seu maxima Solis Declinatione , De Altitudine Lunarium Montium , De Parallaxibus Lunae , De Diametro Apparenti Lunae , De Fixarum Distantiis inter se , De earum Ascensione recta & Declinatione , De Venere falcata , De Iovis Fasciis ac earum Parallelismo cum Aequatore , De Diametris apparentibus Planetarum Minorum ; & Fixarum . Those of his proper Invention are these ; his Problema aemulum Aristarchi pro Distantia Solis ; Opinio de Lunae Maculis ; Modus observandi Parallaxes . His Selenographia , his Industrious and Select Observations of the Motions of the Moons Spots , and his Detection of Hevelius his double Error touching the Moon 's Libration : All which with several others , are mentioned in the first Tome of Ricciolus his Almagest : He writ likewise a Treatise , De Lumine , Coloribus & Iride , mentioned in the Iournal des Scavans , Tom. 3. p. 175. JOHANNES WENDELINUS writ De Hora Passionis & Triduo Mortis Christi , Printed at Leipick in the year 1651. HONORATUS DE MEYNIER , a French-man , besides his Paradoxes ( wherein he maintains , that Experience ought to precede Science , and Theorical Learning to be acquired by Practice ) put forth a small Treatise of the Sphere . PETRUS COURCIER , a French Iesuit , put forth a Treatise , entituled Astronomia Practica , containing Practical Observations of the Celestial Motions by certain Astrolabes ; by which the Places and Motions of any Star may easily , at any time be known . DANIEL LIPSTORPIUS , Professor of Philosophy , and the Liberal Sciences at Lubeck , put forth a Treatise , entituled Copernicus Redivivus seu de vero Systemate Mundi , wherein his Design is , not by new Astronomical Calculations , or Geometrical Demonstrations to confirm and establish the Copernican Hypothesis , but by rational , explanatory , and Physico-Astronomical Arguments to lead the Lovers of Truth to an easie and clear understanding of what is delivered by Copernicus , Galilaeo , Longomontanus , Kepler , Bulialdus , in their more diffusive Writings ; answering all the Objections of the Adversary Party , and clearing what ever may seem difficult in the Doctrine proposed by the Assertors of that Hypothesis , and that chiefly to this End , ( to use his own Words ) Ut Stabilitâ & suppositâ Nova hac Mundi Dispositione Copernicanâ , Verissimâ & Solidissimâ , Omnes promiscuè ad veram Philosophandi Rationem & Nobilissima Cartesiana Monumenta legenda invitentur . Of which he gives the Specimina in a particular Tractate explained 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Philosophandi Ratione ; whereunto is annexed an Appendix , in which there are divers Arguments relating to Astronomical Hypotheses of no vulgar strain . MONSIEUR P. PETIT , Surintendant of the Fortifications of his most Christian Majesty Lewis XIV . published , in his own Language , a Dissertation touching Comets , and particular Observations of the Comets appearing in the year 1654. &c. And upon the Eclipse of the Sun , which happened in the same year , 1654. Of the Exact Method of taking the Diameters of the Planets in a Letter to Monsieur Auzout mentioned in the Iournal des Scavants . The Reverend Doctor SETH WARD , sometime Savilian Professor of Astronomy in the University of Oxford , afterwards Bishop of Excester , and at present Lord Bishop of Salisbury , and Chancellour of the most noble Order of the Garter , hath honoured and illustrated Astronomy by his learned Labours , having published first , his Prelection De Cometis , wherein the Nature of Comets is discoursed of , a new Theory of them proposed , and the History of a late Comet , which appeared between the 19 th . and the 30 th . of December , 1652. declared . He put forth likewise a brief Inquision into the Grounds of Bulialdus his Philolaical Astronomy , wherein is detected Bulialdus's Error , in the Method of the Calculating the double Inequality of the Planets Motion , Geometrically evinced . But the Work , by which he hath chiefly ( on this Subject ) signalized his Name , is his Astronomia Geometrica , wherein a Method is proposed of Geometrically resolving the Astronomy of the Primary Planets , either Elliptical or Circular . And having mentioned this learned Prelate , we cannot but here subjoyn his worthy Friend , Sir PAUL NEILE Knight , one of the Gentlemen Ushers of His Majesty's Privy Chamber ; who , by his Liberal Expences , great Ingenuity , vigilant Observations , excellent Erudition , and Indefatigable Study ( for I cannot speak him better than by repeating this Signal Character already given him ) hath exceedingly contributed toward the Advancement of Astronomy . To which may be added his exquisite Skill in fitting and ordering of Glasses for Telescopes , thereby discovering many new Phaenomena hitherto unknown to others ; his not contenting himself with the exact Knowledge of the ancient Systems and Hypotheses , but indeavouring a Plus ultrae by moulding and framing New Ones of his own for the future Benefit ( as is hoped ) and Improvement of Astronomy ; if at least he shall be pleased by the Publication of these and other his worthy Indeavours in this kind , to do himself that Honour , which cannot be given him by this Imperfect Commemoration . LEONARDUS DU LIRIS , a French-man , and a Recollect-Fryar , put forth in the year 1655. in his own Language , a Treatise entituled Ephemeride Maritime , calculated for the Observation of the Latitude and Longitude at Sea , with a new Method of perpetuating the Ephemeris of the Sun , by which , at all times , his Declination may be exactly found . To which is added the Invention of an Instrument , termed La Spire Solaire , for finding out , at any hour of the day , by the Sun-beams , the Height of the Equator , and the Elevation of the Pole. Doctor JOHN PELL , sometime Professor of Mathematicks in the Colledge at Breda , and before that , in the Colledge at Amsterdam , where his learned Collegue Ger. Io. Vossius ( as he testifies , De Scientiis Matth. c. 10. ) heard him with Admiration read his Publick Lectures upon Diophantus ; by whom likewise he is stiled a Person of various Erudition , and a most acute Mathematician ; published his Refutation of Longomontanus his Quadratures of the Circle , in which he hath a Digression or Exercise , showing the Errors or Failings of the greatest Part of Astronomers for want of better Knowledge in Geometry . He published likewise a little Anonymous Exercitation concerning Easter . And he would further extreamly oblige the Learned World , by making good what he propounds in his Idea of Mathematicks , viz. by laying down such a Method , as by that , in an orderly way to deduce not only all that ever is to be found in our Antecessors Writings , and whatsoever they may seem to have thought on , but also all the Mathematical Inventions , Theorems , Problems or Precepts , that it is possible for the working Wits of our Successors to light upon ; and that in one certain unchanged Order from the first Seeds of Mathematicks to their highest and noblest Applications , as well as to the meanest and most Ordinary . See his Idea of Mathematicks , Printed at the end of Durie's and Hartlib's Reformed School , in 12 o. JOHANNES CARAMUEL LOBKOWITZ , Bishop of Campagna and Satrianum , in the Kingdom of Naples , hath written largely through the whole course of the Mathematicks , particularly , as to our purpose , the several Tractates following ; Pandoxium Physico-Ethicum , in three Tomes , in the second whereof , besides Philosophy , Physick , and the Law , he treats of Astronomy . Solis & Artis Adulteria , in which he treats of Dialling . Coelestes Metamorphoses , wherein he resolves the Circular Theories of the Planets into other Forms . Mathesis Biceps , Vetus , & Nova , in two Volumes , fol. wherein among other various Mathematical Subjects , he handles Astronomical Trigonometry , and gives a particular Treatise , which he entitles Interim-Astronomicum , comprizing the Theory of the Planets in three Parts ; the first describing the same by Circles ; the second , by Perpendicular Oscillations ; the third , by right Lines . To which , by way of Appendix are added three Tractates ; the first exhibiting most easie Tables of the Celestial Motions , as well of the Planets as of the fixed Stars ; the next , teaching the composing of Ephemerides , and demonstrating that an Astronomer may attain to the exact knowledge of the Planets Places , both as to Longitude and Latitude , without Calculation ; the last shewing to delineate upon a Plane , by a pair of Compasses only , the Eclipses of either the Sun or Moon ; thereby ( at least as pretended ) freeing Astronomers from the tedious trouble of Supputation . GEORGIUS HILARIUS , a Dane , published Praecepta Doctrinae Sphaericae , Printed at Copenhagen , 1656. JOHANNES BAPTISTA HODIERNA , a Sicilian , and Mathematician to the Duke of Palma , first of any , published Theories of the Satellites of Iupiter . He writ likewise De admirandis Phasibus in Sole & Lunâ visis ponderationes Opticae , Physicae , & Astronomicae ; Protei Coelestis vertigines , seu Saturni Systema ; Il Microcosmo del Sole ; Rerum Coelestium peculiares Observationes ; De Magnitudinibus Stellarum inerrantium Visis ; Il Coelo Stellato distinto in cento Mappe , O Tavole , doue con faciltà si insegna à conoscer tutte le Costellationi stellificati nel Firmamento . He published some other pretty Tractates in Italian , among which some thing erroneous in a Treatise of his , wherein he makes the Earth bigger than all the other Planets , the Sun only excepted . JOHANNES NEWTON D. D. and at present one of His Majesty's Chaplains , set forth a Treatise entituled Astronomia Britannica , exhibiting the Doctrine of the Sphere , and Theory of the Planets decimally by Trigonometry , and by Tables according to the Copernican System , as it is illustrated by Bullialdus . He published likewise a Mathematical Institution , shewing the Construction and Use of the Natural and Artificial Sines , Tangents , and Secants , in Decimal Numbers , and also of the Table of Logarithms , in the general Solution of any Triangle , whether Plain or Spherical ; with their particular Application in Astronomy , Dialling , and Navigation . BLASIUS FRANCISCUS COMES PAGANUS writ , among other Mathematical Tractates ( as his Fortifications and Geometrical Theorems . ) Of the Theory of the Planets , with very neat Tables upon the Foundation of the Rudolphine , in which all the Motions of the Celestial Bodies ( to use his own terms ) are ranged within the limits of pure Geometry ; Printed at Paris , in the year 1657. He published likewise a Book of Spherical Triangles , as also Astrologie Naturelle ; all in French ; he writ likewise a little Discourse of the Longitude , and promises Geographical Tables . ERHARDUS WEIGELIUS Professor of Philosophy and Mathematicks in the University of Iena , put forth Astronomia Sphaerica , digested into the Method of Euclid , and Astronomical Exercitations , De Motu & Tempore . He wrote likewise Cosmologia , a Treatise succinctly handling the Principles of Astronomy , Geography , the Use of the Globe . And is Author of divers Mechanical Engines and Instruments , serving to the Use and Advancement of Astronomy , as his Pancosmus , being a large Engine or Machine , capable to receive a Man on Horse-back , representing the whole Mundane System , together with the Motions of the Celestial Spheres , Stars , and Planets ; Astrodicticum Majus , being another great Machine , able to receive at once 200 Observers , and so fitted with Dioptrick Instruments , that the several Observers may at one instant take the view of one and the same Star. Astrodicticum Minus , a Rule to be applied to the Celestial Globe for the pointing out of any Star aimed at , as likewise Goniometrum , Horographum , Topometrum , Globus Hydrostaticus , and Astrocosmus , being the Names of several Engines and Instruments ( among others ) by him invented for Astronomical Uses , which for Brevities sake we forbear to explain , particular mention and description of them being made at the end of the third Volume of the Miscellanea Medico-Physica Academiae Naturae Curiosorum German . Printed 1673. GABRIEL DULLENDIUS put forth Astronomical Tables , to which he gave the title of Tabulae Ambianenses , seu , Theoriae Planetarum , tàm in forma Tychonica quàm-Copernicana , per unicam cujusque Ellipsim ex proprio Centro Descriptam , Plano-Geometrica Delineatio ; Printed at Paris in 4 o. 1658. CHRISTIANUS HUGENIUS ( Son of Constantinus Hugenius of Zulichem ) a Gentleman of great Worth and Reputation for his singular Knowledge in all manner of polite Literature , especially in the Mathematicks , as not only his excellent Book of Pendulums , and some Essayes in Dioptricks , but what relates more nearly to our present Subject , his Systema Saturnium sive de Causis mirandorum Saturni Phaenomenôn , & Comite ejus Planetâ novo , sufficiently declare . In which Work are detected the various Phases of that Celestial Proteus , shewing that his Brachia or Ansae are no other than a Luminous Annulus or Ring about the Body of that Planet , every way alike distant from it , whose Plane●… keeps in a certain and constant inclination to the Ecliptick , appearing ( according to its diversity of Aspect ) now like a large Ellipsis , now like a more contracted one , at other times like a streight Line ; discovering likewise a Lunula or small Planet to move about Saturn , and to finish its Course in sixteen dayes , and that Saturn in a less space of Time turns about his own Axis , carrying about with him the whole Aetherial Body or Matter interjected between him and the said Satellite or Planet , together with the said Annulus , in a Motion not much slower than his own . Printed by Adrian Ulacq at the Hague 1659. To which is to be added his Brevis ejusdem Systematis Assertio , Printed at the Hague 1660. Mr. VINCENT WING born at North Luffenham in the County of Rutland , a very Industrious Mathematician and Astronomer ; as the several Works , by him published , declare , of which we shall mention only such as relate to our present Design , as his Urania Practica , or Practical Astronomy , published by Him , and Mr. William Leiburn , about the year 1649. wherein ( contrary to his Later Sentiments ) is asserted the Earth's Stability : Against which Mr. Ieremy Shakerley writ ; to which Mr. Wing replied in a small Treatise entituled Ens fictum Shakerlaei . About the year 1652. He published his Harmonicon Coeleste , therein asserting , contrary to his former Opinion , The Earth's Mobility . He put forth likewise Astronomia Instaurata in four Parts ; and Ephemerides of the Celestial Motions , for twenty years , with an Introduction to the Knowledge of all Mundane Alterations ; also Examen Astronomiae Carolinae . Having likewise left two Posthume Works , viz. Astronomia Britannica , Printed in fol. in Latin , and Computatio Catholica , published about a year after his Death , which was in September 1668. See more of him in the Remarks on his Life and Death , published by Mr. Gadbury . GASPAR SCHOTTUS REGISCURIANUS , a Iesuit , sometime Professor of Mathematicks in the Iesuits Colledge at Palermo , in Sicily , afterwards at Wirtsberg in Franconia , set forth Cursus Mathematicus , sive absolut a omnium Mathematicarum Disciplinarum Encyclopaedia , in 28 Books . In the seventh , eighth and ninth of which Books he treats of Astronomy ; the first comprizing Astronomia Elementaris , or the Description of the Sphere , the Celestial Circles , &c. the next handling Astronomia Theorica , the Theory of the Planets ; the third Astronomia Practica , resolving divers Astronomical Problems , as well Organically as Geometrically . The whole Work Printed in folio , at Wirtsberg 1661. He published likewise Kircher's Iter Ecstaticum Coeleste , adorned and augmented with several Prelusions , Scholia's and Schemes , and promises the Edition of a greater Work by him entituled Mundus Mirabilis , which whether it were ever finished or published I know not . THOMAS STREET Student in Astronomy and Mathematicks , put forth a New easie Geometrical and Harmonious Theory of the Celestial Motions , under the Title of ASTRONOMIA CAROLINA , with Astronomical Tables , and their Uses , exhibiting most plain and easie Examples of finding the true Places , of the fixed Stars and Planets , and the Eclipes of the Luminaries at all times ; the several Calculations therein being compared with all the best and most certain Observations both Ancient and Modern . In which likewise more particularly is asserted the Verity of the Equation of Time for the inequality of Natural Dayes , and the near Agreement of the Lunar Theory ( therein proposed ) to the Phaenomenon , whence the Science of the Longitude , or Difference of Meridians as well at Sea as Land , may be far more truly obtained than formerly it hath been , Printed at London 1661. 4 o. To which he added an Appendix in the year 1664. and in 1667. put forth Memorial Verses on the Ecclesiastical and Civil Calendar , with an Epitome of the Heavenly Motions . He is now about publishing Planetary Instruments . PLACIDUS DE TITIS of Perugio , Professor of Astronomy in the University of Pavy , in Italy , put forth Ephemerides of the Celestial Motions , beginning in the year 1661. and continued to the end of the year 1675. calculated according to the Lansbergian Hypotheses , for the Longitude of 35° . together with a Treatise of the Efficient , Proximate , and Remote Causes of the Transmutation of the Elements , with a Method of erecting a Celestial Scheme or Figure , and some Observations upon Earth-Quakes , Printed at Pavy 1661. Mr. LAURENCE ROOK , first Astronomy and then Geometry Professor of Gresham Colledge , and Fellow of the Royal Society ; had begun to make exact Observations of the Immersions and Emersions of the Satellites of Iapiter , besides many others of other Celestial Bodies , but was snatched away from his Studies and Labours in th●… year 1662. shortly after the Establishment of the Royal Society , whose Institution he had zealously promoted , and it was a Deplorable Accident in his Death ( as is noted by the ingenious Authour of the History of the Royal Society ) that he deceased the very Night , which he had for some years expected , wherein to finish his accurate Observations on the said Satellites . His Loss was regretted by all that knew his Extraordinary Worth both for Knowledge , and Probity ; deservedly celebrated by that excellent Prelate the now Lord Bishop of Sarum , Doctor Seth Ward , ( at the Time of Mr Rook's Decease Lord Bishop of Exon ) by this Sepulcral Monument . M. S. Hìc subtùs sive dormit , sive contemplatur , Qui jamdiu Animo metitus est Quicquid aut Vita aut Mors habet , Vir Cl. LAURENTIUS ROOK è Cantio Oriundus , In Collegio Greshamensi Astronomiae primò , deìn Geometriae Professor , Utriusque Ornamentum , & Spes Maxima , Quem altissima Indoles , Artesque Omnifariae , Mores pellucidi , & ad amussim probi , Consuetudo facilis & accommoda , Bonis , Doctisque Omnibus fecere Commendatissimum . Vir totus Teres , & sui Plenus , Cui Virtus & Pietas , & summa Ratio Desideria Metusque omnes sub pedibus dabant . Ne se penitus seculo subducere mortuus possit Qui iniquissima Modestiâ vixerat , SETHUS WARD Episcopus Exoniensis Sodalis , & Symmystae desideratissimi Longas suavesque Amicitias , Hoc Saxo prosecutus est . Obiit Iunii 27 o. A. D. MDCLXII Aetat . XL. There is extant in the Philosophical Transactions N o. 22. p. 388. his Method for observing the Eclipses of the Moon free from the common Inconveniencies . His Astronomical Papers are ( if I am not misinformed ) in the Hands of the above mentioned Lord Bishop of Sarum , who will doubtless take care of seeing them digested and published . ANDREAS CELLARIUS PALATINUS , Scholae Hornanae in Hollandia Boreali Rector , set forth a large Work in folio with this Title , Harmonia Macrocosmica , seu Atlas Universalis , & Novus , totius Universi Creati Cosmographiam Generalem exhibens . In qua Omnium totius Mundi Orbium Harmonica Constructio secundum diversas Diversorum Authorum Opiniones ; Ut & Uranometria , seu totius Orbis Coelestis , ac Planetarum Theoriae , &c. ob oculos ponuntur ; Printed at Amsterdam , with curious Sculps , and dedicated to his present Majesty Charles the Second . JOHANNES HECKERUS , of Dantzick , set forth Ephemerides of the Celestial Motions , beginning in the year 1666. and continued to the year 1680. calculated for the Meridian of Uranoburgum , from the correct Observations of the Noble Tycho Brahe , the Physical Hypotheses of Kepler , and the Rudolphine Tables . To which he prefixed an Introduction , Printed at Dantzick , 1662. Having gained good Repute among the most nice and skilful Astronomers . CORNELIUS MALVASIA , Marquess of Bismantua , and General of the Artillery to the Duke of Modena , set forth Ephemerides of the Celestial Motions , by him stiled Ephemerides Novissimae , calculated according to the Hypothesis of Philippus Lansbergius , for the Longitude of Modena , being 34° . 5′ . beginning in the year 1661. and ending with the year 1666. together with the Author 's own Observations of Saturn , Iupiter , Mars , Venus , the Sun and Moon for the year 1662. reduced to Calculation , wherein he shews the Excess or Defects of the Lansbergian Tables . To which are added Ephemerides of the Sun , and Tables of Refractions , according to the latest Hypotheses of the famous Cassini , at present Regius Professor of Mathematicks at Paris . JACOBUS GREGORY , a Scotch-man , Professor of Mathematicks in the University of St. Andrew's in Scotland , put forth his Optica Promota , Printed at London , in the year 1663. in which Work there are divers difficult useful Problems relating to Astronomy . The same Author hath prepared a Treatise of Dioptricks and Astronomy , which may supply and doubtless much exceed a second Edition of the forementioned Optica Promota . NICHOLAUS MERCATOR published a Piece entituled Hypothesis Astronomica nova ; Printed at London , in a thin folio , in the year 1664. And two Diatribes De Emendatione Annua ; and hath prepared for the Press a Treatise of Astronomy , in which his design is to render Astronomy Geometrical . He hath likewise prepared for the Press , at Cambridge , an Astronomical Institution or Introduction resembling that of Gassendus , but much more to the Purpose , as not only discovering the several Theories of the Planets , but leading a Tyro to the Calculation of their Places , upon the Principal Hypotheses both Ancient and Modern . FRANCISCUS LEVERA a Roman , put forth Prodromus Universae Astronomiae Restitutae de Anni Solaris & Siderei ac Dierum Magnitudine in Omni Aevo , & de reliquis Periodis , Motibus & Circulationibus Solaribus admirandis adhuc incognitis , ac etiam Sideriis , ab Authore exploratis , & inventis , ac plenè dilucidatis , per Demonstrationes Arithmeticas , aliasque plures Probationes ; with the Radixes , and divers Tables of the said Motions , calculated for the Longitude of Rome , with a new Method of Supputation . He put forth likewise a Treatise , De Inerrantium Stellarum Viribus & Excellentia , with a Table of their Declinations and right Ascensions , &c. Printed At Rome by Angelo Bernabo . SAVINIUS MUTUS put forth a Treatise by way of Dialogue , in which he replies to two Letters , the one of Ricciolus , the other of Cassini , written against the aforesaid Prodromus of Levera ; wherein the Doctrine and Use of the said Prodromus is asserted , Printed at Rome , Typis Angeli Bernabo 1664. PETRUS PALATIUS BRIXIENSIS published Novae Ephemerides Motuum Solis ab Anno 1664. usque ad Annum 1670. calculated for the Longitude of Rome according to Levera's Tables , Printed at Rome in fol. 1664. Typis Angeli Bernabo . SAMUEL DANTFORTH , Master of Arts , set forth an Astronomical Description of the Comet in 1664. as it appeared in New-England ; Printed at Cambridge there . PIETRO MARIA MUTOLO , published at Pisa a small Tractate of the Motion and Place of the Comet which appeared in December 1664. shewing that the said Comet was above the Moon , it having been found without a sensible Parallax . For the observing of which he shews an easie way , which needs no Quadrants or Sextants curiously made ; nor a precise taking of the Meridian Altitudes , nor the Situation of the Comet in the Zodiack ; nor the noting of the Precise Time of the Observation ; nor lastly , needs to fear to be prejudiced by the Consideration of the various refractions ; for as much as he works not by the way of taking several Altitudes from the Horizon ; but by observing the Position of the Comet among some neighbouring fixed Stars ; for the doing of which , he employed only a Simple Thread stretched out by an Arch , to make it Evident whether this Comet had a sensible Parallax or no. See Philos. Transact . N o. 53. p. 1070. ANTONIUS FRANCISCUS PAYEN , an eminent Mathematician and Astronomer , hath published all or most of the several Treatises ensuing . Paradoxon Astronomicon , De Tabularum Omnium à Coelo dissensu ; Aenigma Astronomicum , Adulterium Solis & Lunae ; Emblema Astronomicum , Sol Larvatus ; Monopolion Coeleste , Conjunctio Saturni & Iovis 1663. Et alia Conjunctio Saturni & Martis 1666. Tabulas omnes enormiter fallens ; Selenelion , ou Apparition Luni Solaire observée en l' Isle de Gorgonne , le 16. Iuin 1666. Eclipse du Soleil , observée à Paris , l●… 1. Iuillet , 1666. Specula Parisiensis Astronomica ; De Tabularum Motibus ad Observationum trutinam observandis ; Nova Dissertatio adversus Astrologiam Gallicam , cum Mantissa Astronomica , De Plagio Morini circa Doctrinam Longitudinum Indicata unica Possibili Methodo Universali . He writ likewise these following Treatises , by him intended for the Press , viz. Sportula Ecliptica Compendiaria , cum Appendice Praeceptorum supputandi Selenelii Phases , Durationem & Digitos Lunae deficientis in ortu visibili ; Paradoxa Physico-Astronomica Spiralis Systematis Prodroma , circa naturam Atmosphaerae & causarum Physicarum Astronomica Phaenomena alterantium ; Catacrisis Cometica , statuens Cometoidas inter Meteora sublunaria , Cometas verò inter superlunaria , viamque non Linealem vel Circularem , aut Conicam , sed spiralem & flexuosam Meteoris Coelestibus propriam , variis Observationibus comprobatam ; Ecloge Prostaphaeretica , De Quadruplice Aequatione Astronomica temporis Meridianorum Centri & Orbis Planetarum , cum novis ad Calculum Locorum Planetarum & Eclipsium tabulis , exulatâ cruciformi parte proportionali . Upon the occasion of an Eclipse of the Moon happening near Sun-set , in Iuly 1666. both Luminaries appearing visibly above the Horizon , elevated by Refractions , the Author published his Treatise entituled Selenelion , from whence this account was taken , which being about six or seven years since , and divers of these Tractats then extant , as appears by the Iournal S●…avans , it is probable the rest , or most of them are since published . The Right Honourable the Late EARL OF SANDWICH , even in the midst of his weighty State Negotiations was pleased sometime to imploy himself in making considerable Observations both Astronomical and Physiological , and to communicate the same to the Royal Society ; as his Observation of an E●…lipse of the Sun , Iune 22. 1666. at Madrid ; the Sun's Height in the Solstice ; also the Latitude of Madrid ; esteeming by the Sun's Altitude in the Solstice , and by other Meridian Altitudes ; the Latitude of Madrid to be 40 Degrees , 10 Minutes , which differs considerably from that assigned by others ; the General Chart of Europe , giving to it 41° . 30′ . the General Map of Spain 40° . 27′ . A large Provincial Map of Castile 40° . 38′ . He likewise made some Observations of the Immersions of the Satellites of Iupiter , and on December 25 th . old style 1666. observed at Madrid a great Halo about the Moon , the Semidiameter whereof was about 23° . 30′ . Aldebaran being just in the North-East Part of the Circle , and the two Horns of Aries just enclosed by the South-West of the Circle , the Moon being in the Center : and about five or six years before , viz. Nov. 21. old stile 1661. an hour after Sun-set , he observed a great Halo about the Moon , of the same Semidiameter , at Tangier , the Moon being very near the same Place . See Phil. Transact . N o. 21. p. 390. ERASMIUS BARTHOLINUS , a Dane writ on the Comets which appeared in the years 1664. and 1665. He put forth like wise Astronomical Considerations of the great Conjunction of Saturn and Iupiter , happening in the year 1663. Printed at Copenhagen . He published likewise Heliodorus Larissaeus his Optical Fragments in Greek and Latin , with his Learned Animad versions thereupon , Printed at Paris by Cramoisy 1657. 4 o. JOHANNES ALPHONSUS BORELLIUS , published a Treatise of the Satellites of Iupiter , about fitting Theories to their Motions , and some Contestations , about the nature of that curve Line , that is described by the falling of a Stone from the Earth's surface to its Center , supposing the Earth's motion . PETRUS GALTRUCHIUS , of Orleans , a Iesuit , put forth ( to use his own Terms ) Clara , Brevis , & Accurata Institutio Mathematicae totius , in gratiam studiosae Iuventutis adornata . In which among the rest he treats De Sphaera Mundi , De Astronomia & De Principiis cognitionum Caelestium , De Chronologia , & Cnomonica , Printed lately at Cambridge . HIERONYMUS VITALIS , of the Order of the Regulars commonly called Theatins of Capua , put forth Lexicon Mathematicum , Astronomicum , Geometricum , containing a Collection , and Explication of all Things relating to either of those Parts of the Mathematicks , more especially as to Astronomy , with a brief Consideration , and Declaration of divers new Theorems , and a Dilucidation of several exotick Terms therein used . Printed at Paris 1668. ANDREAS TACQUET , a Iesuit , sometime Professor of Mathematicks in the Roman Colledge , put forth , in his Works , entituled Opera Mathematica , Eight Books of Astronomy , in which he explains the whole Doctrine of that Science , in such a gradual Scientifick Order , that a Student , without the aid of a Master , may learn the whole by his own Study , not formerly attained by the best Instructions . He therein likewise argues against Ricciolus his Opinion , touching the Farth's rest , from the Descent of heavy Bodies ; and shews that the Eclipses of the Sun may be calculated without the aid of Parallax , and that the Sun's Parallax , as to the determination of Celestial Motions , may be safely neglected . He rejects also the sensible inequality of the Solar or Tropical Years , and the irregularity of the Obliquity of the Ecliptick , of the Procession of the Equinoxes and Excentricity . To the end of which Eight Books are annexed Propositions for twenty eight Cases of Sphaerical Trigonometry . PIETRO M. CAVINA of Fienza , in Italy , published in the Language of that Country , Congietture Physico-Astronomiche della Natura dell Universo , Printed at Faenza 1669. in 4 o. Which Conjectures were raised by the Author upon some Observations made about the fixed Stars at Faenza ; the whole Tractate consisting of three Parts , Considerations , Observations , and Reflections . In the first , he considers the unreasonableness of the Aristotelean Opinon , touching the Ingenera●…ility , and Incorruptibility of the Celestial Bodies ; whence he proceeds to the second Part containing the Observations themselves ; whereby he affirms to have found considerable Changes in divers of the fixed Stars , from what Baye●…s , and others have remarked of them as to Magnitude and Number , instancing in Ursa Major and Minor , in the Dragon , Cepheus , Bootes , Corona Septentrionalis , Hercules , Lyra , Cygnus , Cassiopaea , Perseus , and the Via Lactea . From which he deduceth these Conjectures ; First , that the Heaven of the sixed Stars is liquid ; Secondly , that it is generable and corruptible ; Thirdly , that the Motion of the Earth is ( as he fancies ) improbable ; Fourthly , that the Changes and Variations of the fixed Stars , are Effects of the Sun , from which ( he conceives ) they are but moderately distant ; Fifthly , that those Stars are of a Matter easily Dissipable and like unto Lamps which for want of Aliment are extinguished , and by Accession of Aliment are magnified ; Sixthly , that all the fixed Stars are in the Concave Superficies of their Heavens ; with some other ( such like ) Conjectures : Of which see further in Phil. Transact . N o. 65. p. 2112 and p. 2113. FRANCISCUS TRAVAGINI , an eminent Venetian Philosopher put forth a Tractate entituled Physica Disquisitio super Observationibus à Se factis Tempore ultimorum Terrae Motuum , seu Gyri Terrae Diurni Indicium . In which ( from the Observations by him made in some late Earthquakes , especially in the last about Ragusa ) he affirms , that he noted , besides a Subsulting Perpendicular Motion , a Concomitant Lateral Vibration of the Earth from West to East , whence he conceive●… it may validly be inferred that the Earth hath a progressive Motion from West to East . See Phil. Transactions N o. 6. p. 1084. and 1085. The Tractate itself was Printed at Leyden in Holland 1669. in 4 o. AEGIDIUS STRAUCH , Publick Professor of History and Philosophy in the University of Wittemberg , besides his Breviarium Chronologicum , set forth a small Treatise entituled , Astrognosia , Synopticè & Methodicè , in usum Academi●…um adornata . To which are added Schemes of the several Asterisms cut in Brass , Printed at Wittemberg , in the year 1669. JOHANNES OTT , of Schafhuysen , an Helvetian , in a small Treatise of Vision , Printed at Heidelberg , in the year 1670. asserts this Thesis ; Motus Medius Siderum Astronomorum est figmentum , in rei natura non existens , neque in Hypothes●… Elliptica super altero focorum peragitur ; Quocirca computi Astronomica Geometrica accuratio , in Problemate adhuc nondum determinato sita est ; viz. Datum Circulum ex Puncto extra Centrum dato , in data ratione secare ; & quamvis ope Cycloidis construi suo modo possit , attamen cum Punctum , per quod Perpendicularis ad Axes ducitur , indeterminatum sit , etiam ipsa Sectio indeterminata manet , ejus tamen Problematis Solutionem ex supposito Tetragonismo tam accuratè D. Stephanus Spleissius Gymnasii Scaph Rector , & Astronomus Subtilssimus expediit , quam certae sunt Sinu●… Tabulae , quarum accuratio ad Astronomicum Calculum abundè sufficit . But if Spleissius solve the Problem no otherwise than by tentative work , by ayd of a Table of Sines ( and Arks ) he hath done no more than what was well known here . But however , without the use of any Tables , the Problem is solved by Mr. Iames Gregory , Professor of Mathematicks in the University of St. Andrews in Scotland ; as I am informed by the Ingenious and Industrious Promoter of Mathematical Studies , Mr. Iohn Collins . GABRIEL MOUTONUS published Observations of the apparent Diameters of the Sun and Moon , and of the Meridian Altitudes of the Sun , and some few of the fixed Stars ; together with a Table of the Sun's Declinations , calculated to each prime scruple of a Degree . To which is annexed a brief Dissertation of the Inequality of Natural Dayes , and of the Equation of Time , with a new Idaea of Geometrical Measures ; and a new Method of communicating and preserving them , for the future , without any alteration . JOHANNES CHRISTOPHORUS STURMIUS , Professor of Mathematicks and Natural Philosophy in the University of Altdorf in Franconia , published a brief Treatise in folio , entituled , Scientia Cosmica , sive Astronomia tam Theorica quam Sphaerica , paucis Tabulis in usum Incipientium comprehensa , Printed at Altdorf in the year 1670. JOHANNES HEVELIUS , Consul of Dantzick , an Excellent Mathematician and Astronomer , hath ennobled his Name by several curious and learned Works ; as his Selenographia , or Description of the Moon , containing an accurate Delineation of the several Spots therein visible , and of the various Motions , Changes , and Appearances discovered by the Telescope , as well in that as in the Sun , and other Planets . His Cometographia , representing the whole Nature of Comets , their Situation , Parallaxes , Distances , diverse Appearances , and admirable Motions ; with a History of all the Comets , from the beginning of the World to this present , either noted by Historians , or observed by Philosophers or Astronomers ; both the said Works being enriched with exquisite Sculps of his own Graving . To these is to be added his Treatise of Mercury discovered in the Sun at Dantzick in the year 1661. May 3. stilo novo , with the History of a New Star appearing in the Neck of Cetus , and another in the Beak of Cycnus , and his Illustration of our Countryman Horrox his Tractate upon Venus seen in the Sun , in the year 1639. on the 24 th of November , old style ; being the Noblest , and since the beginning of the World till then , unpractised Observation ; with a Discourse of some rare Paraselenae , and Parhelii , by him discovered at Dantzick ; as likewise two Epistles to Ricciolus , De Lunae motu Libratorio in certas Tabulas redacto , and other Astronomical Pieces , whereof mention is made in the Philosophical Transactions . He put forth this present year 1673. The first Part of his Machina Coelestis , containing an accurate Delineation and Description of all the Astronomical Instruments by him used in his Celestial Observations fairly cut in Brass ; the Construction of Telescopes , and Direction for the most commodious Way of managing those of Extraordinary Length ; with the Reason of grinding Glasses of an Hyperbolical Form. He promises likewise Prodromus Astronomiae cum Integro fixarum Catalago , atque Globis Coelestibus reformatis ; As likewise the latter Part of his Machina Coelestis ( of which that published is but the first Book ) containing the second , third , and fourth Books ; the second comprizing all his Celestial Observations , as well of Eclipses , as of the Occultations of the Planets and fixed Stars from the Year 1630. to this Present ; the third shewing his Observations of the Meridian Altitudes of the Sun , and of the Equinoxes and Solstices from the year 1632. hitherto ; as likewise special Observations of every Planet ; the fourth and last exhibiting a Catalogue or Index of the Distances of the fixed Stars taken by his great Brass Sextants and Octants ; together with those noted by the Landt-Grave of Hesse , Tycho , Gassendus , and Ricciolus . All which are now in the Press , and will e're long ( 't is hoped ) come to Publick View . PIETRO MENGOLI an Italian ; Prior of Sancta Maddalena , and Reader of Mechanicks , in the Bolognan Academy ; published among other ingenious Pieces in the Mathematicks , a small Quarto Treatise in Italian , entituled Refra●…tioni , & Parallasse del Sole . In which , besides his Observations and Tables of the said Refractions , Parallaxes , Declinations of the several Points of the Ecliptick , and right Ascensions ; these several following Conclusions , are by him undertaken to be demonstrated , viz. First , The Sun 's Horizontal Refraction to be 1′ . 58″ . 6‴ . Secondly , The Estival Horizontal Parallax thereof 38″ . 49‴ . Thirdly , It 's Hibernal Horizontal Parallax 40″ . 4‴ . Fourthly , The Height of the Pole at Santo Petronio in Bologna in the beginning of the year 1656. to have been 44° . 28′ . 56″ . Fifthly , The Height of the Pole at Uraniburgh in the beginning of the year 1582 , to have been 55° . 53′ . 27″ . Lastly , The Obliquity of the Ecliptick , or the Sun 's greatest Declination to be 23° . 28′ . 24″ . LE PERE CHERUBIN a Capuchin Fryar in the Convent of that Order in Orleans , put forth a large and elegant Volume in French , entituled La Dioptrique Oculaire ; the Ocular Dioptrick , concerning the Theory , Use , and Mechanism of Telescopes , divided into three Principal Parts ; the first contai●… 〈◊〉 Doctrine of Opticks , and Dioptricks , or of simple Vision Direct , and that 〈◊〉 〈◊〉 made by Rays refracted ; the second delivering the Theory of the Telescope in 〈◊〉 kinds , which is ushered in by a History of the Invention , and Antiquity of Telescopes , and by a Discourse concerning the Difference of the Antient Glasses from the Modern . The third and last Part , being doubly divided into the Positive and Mechanical : The Positive teaching the actual Construction of Telescopes , and their Uses in the Observations of Celestial Objects : The Mechanical shewing the way of polishing and forming all sorts of Glasses that serve for Telescopes ; giving likewise an Account of many excellent Discoveries that by their means have been made by Modern Astronomers . The Work adorned with most curious and elegant Cuts , and Printed in an answerable Letter in folio at Paris 1671. OTTO DE GUERRICK , Councellor to the Elector of Brandenburg , and Consul of the City of Magdeburg , or Meydburg , put forth Experimenta nova Magdeburgica , De vacuo spatio , in which he occasionally treats of the several Mundane Systems , of the Planets , and of the Fixed Stars , their Magnitudes and Distances , Printed at Amsterdam in folio 1672. Doctor JOHN WALLIS Savilian Professor of Geometry in Oxford , Fellow of the Royal Society , and Chaplain to His Majesty , famous for his many learned Mathematical Works , as his two Volumes of Arithmetick , the latter whereof is entituled Arithmetica Infinitorum , his Commercium Epistolicum , his Tract De Cycloide , his Treatises of Mechanicks , & De Calculo Centri Gravitatis , at the latter end of Arithmetica Infinitorum , is a Scheme and a Narrative concerning an Eclipse of the Sun 2. August 1654 by him observed at Oxford ; to whom likewise we are beholding for his Care in digesting and publishing Mr. Horrox and Crabtrec's Astronomical Remains . He hath likewise a learned desirable Treatise of Angular Sections ready for the Press , a due Knowledge of which Doctrine cannot but conduce much to the facilitating of difficult Sphaerical Problems , and consequently to the Advancement of Astronomy . AEGIDIUS DE GOTTIGNIES the Scholar of the eminent Geometer Gregory of St. Vincent ; is the Author of a Treatise of Dioptricks concerning the Foundation , Construction , and Use of Telescopes in order to Astronomical Observations , as also of Microscopes . The Treatise ( written in Latin ) is common in MS. in Italy : whereof a Copy came over lately into England , and here meets with the Applause of the learned , which we hope will e're long be translated and published in English. Sir CHRISTOPHER WRENN Knight , sometime Astronomy Professor in Gresham Colledge , afterwards Savilian Professor of Astronomy in the University of Oxford , and now Surveyor General of His Majesty's Works and Buildings , is here deservedly to be remembred ; whose learned Labours , and curious Discoveries both in Philosophy and Mathematicks , being already recorded by the excellent Pen of the Ingenious Author of the History of the Royal Society , I shall from thence collect such Particulars as are pertinent to our present purpose , and whose mention may give Honour to this Catologue . He hath invented many Wayes to make Astronomical Observations more accurate and easie , hath fitted and hung Quadrants , Sextants , and Radii more commodiously than formerly , hath made two Telescopes to open with a joynt like a Sector , by which observers may infallibly take Distances to half a Minute , hath added many Sorts of Retes skrews , and other Devices to Telescopes for taking small Distances , and apparent Diameters to Seconds . He hath added much to the Theory of Dioptricks ; much to the Manufacture it self of grinding good Glasses : He hath made constant Observations on Saturn , and a Theory of that Planet truly answering all Observations , and that before the Printed Discourse of Mr. Hugenius on that Subject appeared He hath essayed to make a true Selenography by Measure ; the World having nothing yet but Pictures , rather than Surveys or Maps of the Moon . He hath stated the Theory of the Moon 's Libration as far as Observations could carry him . Hath composed a Lunar Globe , representing not only the Spots and various degrees of Whiteness upon the Surface , but the Hills Eminencies and Cavities moulded in solid Work ; the Globe thus fashioned into a true model of the Moon , as you turn it to the Light , represents all the menstrual Phases with the variety of Appearances that happen from the Shadows of the Mountains and Valleys . Hath made Maps of the Pleiades and other Telescopical Stars , and proposed Methods to determine the great Doubt of the Earth's motion or rest , by the small Stars about the Pole to be seen in large Telescopes ; which few Instances may serve in part ( at present ) to shew his exquisite Skill and Indeavours in Astronomy , until such Time as he shall please on that Score further to oblige the World by other excellent Productions of his great Industry and Learning . Doctor ISAAC BARROW , formerly Geometry Professor in Gresham Colledge , afterwards Lucasian Professor of Mathematicks in the University of Cambridge , and now Master of Trinity Colledge there ; hath lately published eighteen Optick Lectures ; Theodosius his Sphericks , and hath other Lectures concerning the Projections of the Sphere , ready for the Press . All which conduce much to the Advancement of Astronomy , as his Geometrical Lectures already published , together with his Apollonius , and Archimedes ready to come forth , besides others which we hope may follow , do to the Advancement of Geometry ; which not to mention ( though somewhat beside our Purpose ) were very Injurious to a Person that hath so much enriched the Commonwealth of Learning . Mr. ROBERT HOOK the Learned and Ingenious Curator of the Royal Society , and Professor of Geometry in Gresham Colledge , exceedingly well versed , as in all Mathematical and Mechanical , so particularly in Astronomical Knowledge . He was the first that discovered in the year 1664. ( May the ninth ) a permanent Spot in the biggest of the three obscurer Belts of Iupiter , and by observing it for some Hours together , found that within two hours after , the said Spot hadmoved from East to West , about half the length of the Diameter of Iupiter . See Philosophical Transactions , N o. 1. p. 3. and N o. 8. p. 143. which Discovery of a Permanent Spot in Iupiter was since confirmed by that famous Astronomer Cassini , of which see Phil. Trans . N o. 8. p. 143. and N o. 10. p. 171. The same Mr. Hook discovered in the Month of February and March , Anno ( 1665 / 6 ) in the face of Mars several Maculae or spotted Parts changing their Place , and not returning to the same Position 'till the next ensuing Night , near about the same time : See Ph. Transact . N o. 11. p. 198. and N o. 14. p. 239. He also made divers considerable Observations concerning the Planet Iupiter , his apparent Diameter , the various Degrees of Light in the Parts of his Phasis , his several Belts , &c. See Phil. Transact . N o. 14. p. 245. 246. where also are to be found his Observations of the Body of Saturn , his Shape , Ring of a brighter Light than that of his Body , and some black Lines crossing the Ring and others crossing the Body . The same was the Proposer of that Method ( inserted in N o. 9. p. 151. of the Phil. Transactions ) directing how a Correspondency may be setled for the finding out the true Distance of the Sun and Moon from the Earth by the Parallaxes observed under or near the same Meridian . Nor is to be passed by what contrivances he hath made of measuring the Diameters of the Planets to the exactness of a Second by the help of a Telescope , as also of taking the Position and Distance of the small fixed Stars one from another , or from any of the less bright Planets , if the Distance be not above two or three Degrees . See N o. 25. of the Phil. Transact . p. 459. He published his Micrographia in the year 1664. wherein amongst other Astronomical Matters , he hath explained the Reason of the Redness , Oval Figure , and Undulation of the Sun and and Moon , and the twinckling of the Stars by a new Property of the Air called by him Inflection , differing from Refraction and Reflection . He hath mentioned several wayes of improving Telescopes ; he hath given two Specimina of the Discovery of a fifteen Foot Glass among the smaller Stars ; one , by a Description of the Pleiades , and the second by a Declination of one small spot in the Moon described by Hevelius and Ricciolus . He hath made many Astronomical Instruments , by which an Angle may be taken to the Exactness of 1 / 10 part of a Minute . He in the year 1670. detected the Parallax of the Orb of the Earth amongst the fixed Stars by observing the Transits of several Stars near our Zenith , and comparing the Measures so found . He first observed the Stars with a Telescope at the the same time that the Sun shone above the Horizon and into the Room where the Observation was made ; of which see more in his Excellent Attempt to prove the Motion of the Earth lately published . Doctor WALTER POPE Professor of Astronomy in Gresham Colledge ▪ the Successor of Sir Christopher Wrenn and Mr. Rook ; with whom he hath spent much Time in observing the Motions and Appearances of the Heavens ; the Result of which he hath delivered in his Astronomical Lectures there read , which 't is hoped he may be prevailed with to make publick hereafter . Mr. JOHN GOAD , late of St. Iohn's in Oxford , hath an Elaborate Treatise now in the Press , entituled Astro-Meteorologica , i. e. Aphorisms Physical and Astrological in two Parts : The first whereof inquires into the Natures of the Planets , Sun , Moon , &c. The second observes the Nature also of the fixed Stars in their several Asterisms , as they are clearly found to be joynt Producers of the Meteors below , Storms , Tempests , &c. The whole Discourse founded on sacred Authority , Reason , and the Experience of twenty years last past . RICHARD TOWNLEY of Townley in Lancashire Esquire ( whom for Honours sake I here mention ) Nephew to the before named Christopher Townley ; hath , among other his much commendable Indeavours in the Mathematicks , perfected the Instrument of Mr. Gascoyns before-mentioned ▪ , now called a Micrometer , and fitted it that any small Angle may be taken by his Tube to a Second . Having for some years past been a diligent Observer of the Satellites about Iupiter , whose Motions he hath reduced to Exactness of Rule and Order . He is an Excellent Arithmetician and Geometer , and from whom great Things may justly be expected . MONSIEUR ADRIAN AUZOUR , a very ingenious and candid Philosopher and Astronomer of Paris , Fellow of the Royal Society of London , published his Ephemerides concerning the Motion of the two Comets which appeared Anno 1664 / 5 ) and of which he predicted the Places , through which they should pass , and where they should cease to appear , after he had seen them but four or five times . The same Person entertains hopes that a Motion of Comets exactly observed may in time clear that grand Question , whether the Earth moves or not . He also hath taken Notice , by making Reflections upon former Comets , that more of them enter into our System by the Sign of Libra , and about the Spica Virginis , than by all the other Parts of the Heavens : See the Phil. Transact . N o. 1. p. 3. N o. 2. p. 18 , 19. N o. 3. p. 36 , 39. And being very well versed in Opticks and Dioptricks , he hath given us the Proportions of the Apertures of Telescopes , and reduced them to Tables ibid. N o. 4. p. 55. as he hath also delivered a Means to illuminate an Object in what Proportion one pleaseth ibid. N o. 4. p. 68. And we doubt not , but he will upon his Return out of Italy where he hath spent some years of late , impart to the World as well the Astronomical as other the learned Observations , he-hath there made . SIGNOR GIOVANNI DOMINICO CASSINI a deservedly Famous Astronomer of Italy ; now entertained by His most Christian Majesty in the Royal Observatory at Paris , and withall a Member of the Royal Society of London ; doth continually oblige the learned World by his excellent and most important Astronomical Observations , of which there are recorded in the Phil. Transact . First , that of the permanent Spot in Iupiter arguing the Rotation of that Planet about it's Axis ; Secondly , those of the Shadows cast by the Satellites of Iupiter upon his Disque , and Ephemerides of their Motions . Thirdly , those of the Spots in Mars arguing the Conversion of that Planet also about it's Axis . Fourthly , those of the Spots in Venus evincing the Revolution of that Body likewise about it's Axis , as well as that of Iupiter and Mars . Fifthly , those of the Spots in the Sun. Sixthly , those of the change of Saturns Figure . Seventhly , those of some new Stars discovered by him , and especially of the two new Planets about Saturn . Of all which , see the Phil. Transact . N o. 4. p. 75. N o. 8. p. 143. N o. 10. p. 171. N o. 12. p. 209. N o. 14. p. 242. N o. 32. p. 615. N o. 78. p. 2201. N o. 78. p. 2250. N o. 78. p. 3020 , 3024. N o. 102. p. 4039. N o. 92. p. 5175. To which add his Calculations for the Eclipses of the Satellites of Iupiter for Anno 1671. in N o. 74. p. 2238. Neither ought we to pass by his three excellent Letters concerning the Hypothesis of the Sun's Motions and his Doctrine of Refraction , of which an Account is given in N o. 84. p. 5001. What other Observations and Discoveries he hath made concerning the Heavens , we hope he will in due time likewise publish . SIGNOR GEMINIANO MONTANARI the learned Professor of Mathematicks at Bologna hath taken particular Care and Pains in acquainting us with the Total Disappearance of divers Stars that appeared formerly ▪ and intends to write upon this Argument a Book to be entituled Firmamentum Instabile . See Philosoph . Transact . N o , 73. p. 2202. and N o. 89. p. 5125. Where 't is intimated that this Author doubts not but to make it out to the Assertors of the Incorruptibility of the Visible Heavens , that even in the Stars anciently described there are observed such Changes as would be sufficient to make Aristotle himself , if alive , change his Opinion in this Point . Mr. JO. FLAMSTED of Derby , an Industrious and accurate Astronomer , and Observer of the Heavens ; hath of late endeavoured to advance Astronomy , by publishing yearly his Calculations of the more notable Celestial Appearances conspicuous in these Parts ; of which see the Phil. Transactions N o. 55. p. 1099. N o. 66. p. 2029. N o. 77. p. 2297. N o. 79. p. 3061. N o. 89. p. 5118. To which may be added his Observations of the Transits of Iupiter and Mars near certain fixed Stars , N o. 82. p. 4036. N o. 86. p. 5034. As also those for determining the Inclination of Iupiter to the Ecliptick , N o. 94. p. 6033. together with those lately described in a Letter of his to Signor Cassini , that were made by Him after a New and exquisite Way , about the farthest Elongations of the Medicean Stars from the Centre of Iupiter , and others concerning the Diameters of the Planets and their Distances from the fixed Stars , as also the Parallax of Mars , N o. 96. p. 6094. which Communications were with much Applause received by the said Signor Cassini , Witness his Answer , which we hope will also be published e're long , together with the sequel of more Letters lately exchanged between these two eminent Astronomers . Mr. EDWARD BERNARD Successor to Sir Christopher Wrenn , in the Savilian Professor's Place of Astronomy in the University of Oxford , merits here a due Remembrance ; from whom , besides those future Improvements Astronomy is like to receive by his learned Lectures , and Observations ; we are incouraged to expect the Publication of the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , or ( as Pappus terms it ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , of the Alexandrian School , restored to it's Pristine Splendor , being a Book so called by way of Distinction from Ptolemy's Almagest , commonly by the Alexandrians call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which two Books were the only or at least the chief Astronomical Pieces usually read in that University . The first whereof consists of nine Books , containing Theodosii Sphaerica , ( with Euclids Opticks and Phaenomena ) in three Books . Theodosius de Habitationibus , & de Diebus & Noctibus in two Books . Autolycus de Sphaera Mota , & de Ortu & Occasu siderum inerrantium in two Books , Aristarchus Samius de Magnitudinibus & Distantiis Solis & Lunae , & Hypsicles ▪ his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 sive de Ascensionibus . Which nine Books collected into one Volume , and remaining in several Libraries in Italy and France , were by Sir Henry Savile , partly in Print , partly in MS. given to the University of Oxford , and now hope for New Life from this learned Persons Hand , who intends ( as I am informed ) further to oblige the learned World by publishing the three remaining Books of Apollonius Pergaeus from the MS. Copies of Beni Musa , and Aldelmelech , with the Annotations of Eutocius upon one of them , whereas the Copy used in the Version of Abraham Ecchellensis , and illustrated with the learned Annotations of Alphonsus Borellius seems to be a Stream from a more impure Fountain : and this Supplement is to be subjoyned to the first four Books put forth , or ready to be put forth by the most Learned and Reverend Doctor Isaac Barrow . Mr. ISAAC NEWTON Lucasian Professor of Mathematicks in the University of Cambridge , and Fellow of Trinity Colledge , hath lately published his reflecting Telescope ; New Theories of Light and Colours ; hath ●…ready for the Press a Treatise of Dioptricks , and divers Astronomical Exercises , which are to be subjoyned to Mr. Nicholas Mercator's Epitome of Astronomy , and to be Printed at Cambridge . From him besides is to be expected a New General Analytical Method by infinite Series for the Quadrature of Curvilinear Figures , the finding of their Centers of Gravity , their Round Solids , and the Surfaces thereof , the straitning of curved Lines ; so that giving an Ordinate in any Figure as well such as Des Cartes calls Geometrical , as others , to find , the Length of the Arch Line , and the Converse ; Such an Invention , to wit , but in one particular Figure the Circle , the Learned Snellius thinks transcendent to any thing yet published ; and how much conducing to the Benefit of Astronomy , and the Mathematical Sciences in General , such an Universal Method is , I leave others , together with my self to admire , and earnectly expect . Mr. JOHN COLLINS Accomptant , and a Member of the Royal Society , published in the year 1658. his Treatise entituled The Sector on a Quadrant , in which there are very curious Prints of two great Quadrants , and of two small Quadrants with particular Projections on them , serving for the Latitude of London ; Albeit by Aid of other Lines each of those Quadrants is rendred Universal for Astronomical Use , as , finding the Hour and Azimuth , and all other Spherical Proportions ; The Author 's chief Design in publishing such Prints , was to shew the World that the said Prints might be pasted on Copper or Brass , and so varnished , as to be rendred preservable from Dirt , or sullying , and sold at a cheap Rate , as now they are . In 1659. he published his Treatise of Navigation , entituled the Mariners Plain Scale new Plained . In which , besides Projections of the Sphere , there are Constructions for many Astronomical Problems , and Spherical Proportions . The Book hath found good Acceptance , and is now like to become a Common Theme to the Scholars of Christ's Hospital London , whereof forty ( by His Majesty's Bounty , and to His Immortal Renown in Establishing a Lecturer to instruct them ) are constantly to be taught Navigation , and e're long 't is to be hoped the Author will reprint the same with considerable Additions . The same year he published a Treatise of Geometrical Dyalling , of good Esteem , both for the Newness and easiness of Method in situating the Requisites , and drawing the Hour-Lines . In which there being Spherical Proportions , and some Astronomical Problems , it deserves to be remembred in this Catalogue . In the year 1667. he published in the Philosophical Transactions the Solution of a Problem concerning Time , to wit , about the Iulian Period , with divers Perpetual Almanacks in single Verses ; a Chronological Problem , and divers other Things since , in the said Transactions , which we mention not , as being irrelative to the Sphere or Astronomy ( viz. concerning Merchants Accompts , compound Interest , and Annuities , &c. ) We should be injurious to him , if we did not farther inlarge , by telling the World how much it is obliged for his Pains in exciting the Learned to publish their Works , and in acting the Part of an Ingenious Obstetrix at the Press , in correcting and in drawing of Schemes ; So that he hath been Instrumental in furnishing the World with the many learned Mathematical Books here lately published ( for which , his chief Reward hitherto hath been to obtain from the Learned the Title of Mersennus Anglicanus ) and many more may be expected , if moderate Encouragements towards Printing such Works , and Leisure for such an Affair be not impeded through the necessary Avocations for a livelyhood , and though it be besides my Design , yet I cannot but digress in giving him and others like minded ( which are very rare to be found ) their due commendations , in promoting the laudable Design of getting Learned Men to impart their Labours to be Printed ; and exciting others to encourage the same , as being of singular Use and advantage to the Republick of Learning ; through the want whereof many Learned Mens Works of much worth have been lost , suppressed or long delayed . As those of Maurolycus , Abbot of Messina , a large Catalogue whereof is to be seen at the End of his Opuscula , but by the Care of the learned Mathematician Alphonsus Borellius some of them have been published in this Age , ninety years after the Author's Death ; as his Apollonius at Messina in 1656. containing the substance of the four first Books of the Apollonius of Commandinus , and two more Additional Books of Maurolycus , and all in less Room , and at a much cheaper price . And now by the like Diligence the said Borellius is publishing Maurolycus his Archimedes in Latin , reputed a Good one , after we have been long tired with the Common Latin bad one . Through want of such care the many learned Works of Vernalion of Naples , Master to Iosephus Auria , have not hitherto come to light , as his Commentaries upon all Archimedes , Apollonius , Serenus , Euclid , Ptolemaeus , and divers others of the Ancients ; which is much to be lamented ; seeing he was , according to the Testimony of the said Auria , Vir , Divinitate quadam Ingenii Ornatus . Nor those of the learned Bernardinus Baldus , Abbot of Guastalla , mentioned at the End of his Comment on Aristotle's Mechanicks , amongst which are two Volums of the Lives of Mathematicians , whereof Bartholinus in his Preface to the Edition of the Optick Fragments of Heliodorus Larissaeus , Printed at Paris 1657. gives an honourable Elogium . Varenius could find no Stationer or Printer in Holland to undertake his Treatise of Conicks and curved Lines . See the Preface to his History of Iapan . If Sir Charles Cavendish deceased , Brother to the present Duke of Newcastle , had not ( as 't is credibly reported ) given liberally toward the Printing of Mydorgius his four first Books of Conicks , they had never come to publick view ; the four last , as likewise those of Paschal the Younger , yet remaining unprinted upon the same Accompt , of whom Mersennus gives this Censure , quòd Unicâ Propositione Universalissimâ , quadringentis Corrolariis armatā , totum Apollonium complexus est . The Manuscript as yet remaining unprinted ( as I am informed ) in the Hands , or at the Disposal of Monsieur Du Prez a Bookseller in Paris ; the want whereof is the most considerable in regard the Author ( besides the ordinary method ) treats of the Conick Sections , as projected from lesser Circles of the Sphere - Erasmius Bartholinus well known by his Additions to the second Volume of Des Cartes , as it is commonly termed ; could find none to undertake the Printing of De Beaunes Treatise De Angulo solido , and other Treatises both of that Authors , and his own . Iungius his Phoranomicks , and Treatise De locis Planis , &c. and other Algebraical Tractates ; have remained at Hamborough above ten years since the Author's Death unprinted , for want of due Encouragement : Albeit a Iesuit , who writes his Life , makes him , although a Physician , equal in Mathematical Knowledge to Des Cartes . On the like Reasons we may conceive we want the many learned Algebraical Works of our famous Countryman Mr. Thomas Harriot , ( and of Mr. Warner , into whose Hands they fell ) who is esteemed by some of the most knowing Persons alive to have been much Superiour to all that ever writ ; and , that equivalent to what of his might have been forty or fifty years since known , is not readily to be expected . For want of the like Encouragement , we have lost that most excellent Piece of the incomparable Vieta , his Harmonicon Coeleste ; as likewise the Remains of Alexander Anderson the Scot , as his Conicks , Stereometria Solidorum , & Triangul . Sphaerie . the want whereof Guldinus much bewails and excites the ingenious to enquire after them . On the same Accompt the Remains of Griembergerus , as his Conicks , Dialling , and Projections of the Sphere have not come to light ; and for the very same Reason the second Tome of Galilaeus in English doth , and is like to remain , unprinted . With the like Remora in France , have met the Works of the Excellent Monsieur Fermat , viz. Euclidis Porismata restituta ; his Treatise De Locis Planis Solidis Linearibus & ad Superficiem , and his Treatise De Contactibus Sphaericis . As also the Remains of the much knowing Lalovera , as his Geometrical Dictionary ▪ sive Explieatio vocum Geometricarum , four Books Problematum Illustrium , four Books Problematum Physico-Mathematicorum , and a Collection of Letters between him and the learned , containing the Solution of many Problems of great Curiosity and Difficulty , which seeing they are not like to get Printed there , they have written over to know if they would be undertaken here ; promising to send the MS. Copies . And having hinted thus much at the Instance of this Ingenious and Industrious Person , to the Curious , and Generously learned ; I come now again further to acquaint the Reader , that we have more particularly obtained from him an Accompt of two of his own Designs , relative to the Sphere and Astronomy . The one of Geometrical Dialling , whereby reflex Dyalling is rendred Geometrical , and reduced to a Method of Calculation ; so that if a Glass were placed at Random , and ●…ines drawn on the Plain by chance , by either Method , Points might be found in the said Lines which joyned should be the Hour Lines ; and the like when the Gl●…ss is so placed , that the Hour Lines may be drawn in that Part of the Room which is most capable of them ; and as a Corollary of this Doctrine a Dial for any Latitude may be suddainly divided from a Line of Tangents parallel to any Line proposed , and that without any Calculation for the Horary Divisions . The other a Treatise of Projections of the Sphere , and concerning Spherical Trigonometry ; in which many extraordinary Cases will be solved ; those Proportions mentioned before in the Narrative concerning Mr. William Oughtred , several wayes more easily demonstrated , and all Spherical Triangles measured by a new Method ( not by him formerly insisted on ) after the manner of Plain Triangles ; all which perchance may be handled in some little Tractates concerning the Use of Prints of several other Instruments designed to be cut , pasted , and varnished , as before mentioned ; viz. the Analemma , the double Horizontal Dial , the Logarithmical Serpentine Line , Prints of Logarithmical Rulers ; whereof if there be three , they may be so placed as to lie still all Day , and as fast as the Hight of the Sun is given , shall find either the Hour or Azimuth universally by bare Inspection . The hasty Collection , and uncorrect transcribing of the foregoing CATALOGUE , hath occasioned the omission of some considerable Persons , and Authors , which should therein have been inserted in their Proper Times , and Places , The Reader therefore is desired to take Notice of them as We have here set them down ( according to Order of Time ) in the following SUPPLEMENT . FOHIUS the first Emperor of China , was greatly addicted to the Study of Astronomy , and first ( of all the Chineses ) reduced the Motions of the Celestial Bodies into Tables , as Martinius in his History of China affirms . TANAUS chief Minister of State to Hoantgius the third Emperor of China , contemporary with Methusalem ( as Martinius in his History of China reports ) composed a Solar Cycle of sixty years , which the Chineses use at this Day . YUMCHINIUS another chief Minister of State to the former Emperor about the 28 th year of his Reign , first of all observed the Pole and the Stars about it , and composed a Sphere or Globe representing that of the Heavens . CHUENHIOUS the Fifth Emperor of the Chineses was the first who published a Calendar for the common Use of his Subjects . He wrote likewise Ephemerides of the five Planets , which he saw at one time all in Conjunction , upon the same Day that he observed a Conjunction of the Sun and Moon ( which Day he ordered to be observed as the first Day of the Year ) in the Sign or Constellation Xe , which is now reckoned from the eighteenth Degree of Pisces to the fourth of Aries . This Admirable Conjunction of the Planets , is perhaps the same with that which the European Chronologers affirm to have hapned in the Time of Noah sayes Martinius in his History of China , p. 33. ANDUBARIUS a certain Indian of the Race of Arphaxad is said to have flourished near the Time of the Building of the Tower of Babel , and to have been very knowing in Astronomy , and first of all to have taught the same to the Indians , as the Chronicon Alexandrinum attests . JAUS the seventh Emperor of China , whom Kepler ( in Commentatiune . in Epistolium R. Patr. Terrentii ex Sinar . Regn. Miss . ) supposes the same with Ion , or Iavan , or Iaon Son of Iaphet , is reported to have been extreamly addicted to Astronomical Observations , and to have corrected the Chinese Calendar ; to have caused divers Instruments to be made for observing the Motions of the Celestial Bodies , and to have exactly noted the Winter Solstice , which the Chinese Writers affirm to have then been in the first Degree of the Sign or Constellation Hiu , which at present is about the first Degree of Aquarius . V. Martin . Histor. Sinic . p. 25. XUNUS the Eighth Emperour of China , caused to be made out of the Gold and Jewels of his Imperial Treasury a Sphere of Admirable Workmanship , shewing the Motion of the seven Planets , each of which were represented by a precious Stone resembling their respective Natures , in the midst of which was a large Jewel placed representing the Earth . See Martinius Histor. Sinic . CHUMKANG the Fourth Emperor of China , of the Family of Hia , about a year after Noah's Death , observed a Memorable Eclipse of the Sun to have hapned in the Sign or Constellation called Fang , which now ( sayes Martinius ) is about the 28 th Degree of Scorpio ; he put to Death the Astronomers of that Time for their Negligence in not observing the same . CHEUCUNGUS a great Astronomer and Mathematician among the Chineses caused to be made an Ample Instrument or Rule erected perpendicularly upon a large Plain of Brass , and divided into certain Parts , upon the Superficies of which Plain was likewise a Line drawn divided into several Parts , by which Instrument he used to take the Meridian Altitude of the Sun , as likewise the Elevation of the Pole , and made other such kind of Observations . The said Instrúment being still preserved in the City Tengfang , where likewise is yet standing a Tower , on which he used to make his Observations , called Quensing Tai , or the Starry Specula , as Martinius in his Atlas attests . By which several Instances it may appear , that the Chineses of all the Asiaticks , have seemingly the most Reason to claim Precedence and Priority in Point of Antiquity as to the Study of Astronomy and Celestial Observations , even before the Egyptians and Chaldeans themselves : If any Credit may be given to the Histories and Chronologies of that Nation . GERYON a famous Trojan Augur , Companion to Brutus or Britus at his first Entrance into this Island , as Pitsaeus ( from the Authority of Ponticus Virunnius ) affirms , wrote , among other things De Astronmia . PERDIX a Britain , surnamed PRAESAGUS , by Pitsaeus stiled Mathematicus Insignis , atque Observatione Stellarum ac Coelestium Corporum supra quam dici potest Curiosus . Of his Writings I find no other mention than of one Book of Predictions . HESIODUS ASCRAEUS a Poet supposed contemporary with Homer , by Ioseph Scaliger stiled the most Ancient Astrologer , and Theologue of the Greeks . ( A Specimen of his Astrology , yet remaining in his Poem entituled 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , of his Theology , in that entituled 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ) merits a Place in this Catalogue ; and therefore , being omitted by the oversight of the Transcriber in his due Place ; we have inserted him in this Supplement . DEMOCRITUS besides what we have already mentioned , is said to have written the several Works following relative to our present Subject , although no Remains of them be now left ; as his Magnus Diacosmus , and Parvus Diacosmus , in which he not only treated of the Fabrick of this Visible World ; but of other Worlds , which he held to be innumerable ; De Sideribus Vagis seu Planetis , which he asserted to be more than the Seaven commonly observed and taken notice of ; which Assertion of his , Modern Experience hath since confirmed Phanae Causae , i. e. De Sole vel Apparentiis , wherein he took Cognizance of the Solar Maculae , or Spots , as Magnenus ( in his life ) affirms ; for Phana or Phanes is the same with the Sun , so called quòd maximè appareat ; of which Macrobius . Certamen C●…epsydrae , which Magne●… stiles a most subtle Piece , because he thereby examined the Motion of the Hea●…ns , and made as it were a commensuration , or Comparison of Motion and Time , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , sive Poli Descriptio , qua voce nihil aliud intelligitur , sayes Salmasius Exercit. Plin. p. 740 ) quam 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Descriptio ; for these Ancient Sorts of ●…ials , if we may relie upon Salmasius his Authority , were called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , à rotunda Poli Forma , cujus Medio Gnomon infigebatur . ORONIUS a Britain , surnamed MODESTUS is by Pitsaeus from the Authority of Ponticus Virunnius about this time affirmed to have flourished ; of whom he thus writes ; Dicunt eum in Astronomia & in Poesi Plenidium superasse . ( Plenidius was a learned British Philosopher , of the same time ) He writ both in Greek and Latin several Works , among them divers Poems , not now extant . PROTAGORAS ASTROLOGUS ( not the same with Protagor●… the Philosopher of Adbera ) is celebrated by Euphorion Chaleidensis ( who was Keeper of the famous Library of Antiochus Magnus King of Syria , and a great Historian and Poet ) in an Epicedium which he wrote upon his Death , mentioned by Diogenes Laertius in the Life of Protagoras Abderit . HYPSICLES of Alexandria in Egypt , Disciple to the great Isidorus , flourished in the Reign of Ptolemaeus Physion . He writ De Dodecaedri & Icosaedri in eadem Sphaera Descriptorum comparatione atque inter se Proportione , as likewise a Treatise entituled 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , sive de Ascensionibus , or as some MS. entitle it , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 this last published in Greek and Latin , by Iacobus Mentelius , Printed at Paris by Cramoisy , together with Heliodorus Larissaeus his Opticks , 1657. in 4 o. ATHELSTAN King of England was learned in Astronomy , and among other Writings , of which he was Author , wrote one Book De Rebus Astrologicis , as Pitsaeus testifies . MICHAEL PSELLUS of Constantinople , is by some conceived to be Author of those Astronomical Pieces ascribed to Enthymius , of whom before among the Authors of uncertain Times ( who perhaps is the same with Euthymius Zygabenus Monachus , who was in a manner Contemporary with Psellus ) viz. Synopsis Astronomiae . De Sphaera ; & Quod Rotunda sit Terra . AVERROES , besides what he wrote upon Ptolemy's Almagest already mentioned ; writ likewise Astrologica translated into Hebrew by R. Iacob Ben Samson extant in the French King's Library . See Labbée Bibliothec. MS. NICHOLAS TREVET , already mentioned in the Catalogue at this year , wrote besides what is there exprest ) Canones de Conjunctionibus , Oppositionibus & Eclipsibus Solis & Lunae ; as they are cited by Pitsaeus . GEORGIUS MEDICUS CHRYSOCOCCA , is by us already mentioned in the year 1240. But Scaliger ( l. 1. Epist. 80. ) places him in the year 1346. at which time he published his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , sive 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , at Tibena Chasariae , quae Regio erat in finibus Imperii Trapezuntici in the longitude of 72° . according to the said Scaliger , whose Authority we willingly submit to . ROGERUS SWINSETTUS , or rather Swineshead , vulgarly ( but erroneously ) Suisset ; surnamed for his Eminent Skill in Algebra , Calculator , Fellow of Merton Colledge in Oxford , afterwards , Monk of the Cistertian Order , a most subtle Mathematician ; of whom the great Master of Subtlety , Iul. Caesar Scaliger ( Exercitat . 324. ) thus wrtes , pene Modum excessit Ingenii humani . And ( Exercitat . 340. ) gives this further Elogy of him , Dignus profectò quem neque Senium Senem faceret , neque Naturae Lex vitâ privaret , nisi meliorem Vitam apparasset . He wrote two Books De Coelo & Mundo , one Book entituled Descriptiones Motuum Coel. stium , said to be extant in MS. in the Library of Caius and Gonvile Colledge in Cambridge . He put forth likewise Ephemerides and Calculationes Astronomieae , this last said to have been Printed by Iohannes de Cypro at Padua . Vide Pitsaeum . GUALTERUS BRITHUS , or BRITTE , an English-man , Fellow of Merton Colledge Oxon ; of whom Leland sayes , Celebre sibi Nomen acquisivit maximè quod Astrorum Motus & Corporum Coelestium Naturas , Proprietates , Affectiones , curi●…sissima Sedulitate scrutatus fuerit . He writ Theoremata Planetarum , & de Rebus Mathematicis , &c. Vide Pitsaeum . JOANNES DE SACRO FONTE ; Anglicè HOLYBROOK , an English man born in Surrey , reduced Alphonsus his Astronomical Tables into a clear and easie Method , and published Tabulae Novae Mediorum Motuum & Aequationis Dierum ; according to the Testimony of Leland very accurately computed . He put forth likewise Canones Astronomici , said by Pitsaeus to be extant in the Publick Library at Oxford . ALBERTUS DE PRUSA POLONUS writ a Book of Commentaries upon Peurbachius his Theory of the Planets , and another upon Regiomontanus his Ephemerides , and some other Pieces , as Simler in Epitom . Gesner . attests . JOANNES PENA , besides what is already mentioned of him , published Theodosius his Sphaerica in Greek and Latin , with Explanations and Notes , Printed at Paris 1558. in 8 o. FRANCISCUS SANCTIUS BROCENSIS , a Spaniard , Professor of Rhet●…ck and the Learned Languages in the University of Salamanca , pu●… forth ( among other Works ) a Treatise De Sphaera Mundi , collected out of various Authors , of which mention is made by Peregrinus in his Bibliotheca Hispaniae p. 578. JOANNES MENA CORDUBENSIS , a learned Spanish Poet is about thi●… time ( by the said Author Bibliothecae Hispan . ) reported to have written in Latin , De Planetis , which Ferdinandus Pintianus , the worthy Commentator upon Pliny , in his younger dayes translated into Spanish . JOANNES BENEDICTUS , besides what we have already mentioned wrote De Gnomonum , Umbrarumque Solarium Usu , Printed Augustae Taurin . 1574. SEBASTIANUS VERRO HELVETIUS wrote ten Books Physicorum , in the second whereof he treats particularly of Astronomy , Printed at London 1590. in 8 o. JOSEPHUS AURIA over and above the Works by him published , and of which we have already spoken ; promises the publication of the two Books of Autolycus de Ortu & Occasu Siderum Inerrantium , which , whether he ever performed I yet know not . To PETRUS RYFFE his Elementa Sphaerae Mundi sive Cosmographiae , is added a Treatise De Structura & Usu Planisperii , by Ludovicus Lucius of Bafile ; and there Printed 1598. in 8 o. NICHOLAUS RAIMARUS published in the year 1588. before he put forth his Astronomical Hypotheses ( already mentioned ) a Treatise entituled Fundamentum Astronomicum , i. e. Nova Doctrina Sinuum & Triangulorum ; to which among other things is adjoyned Hypotheses Novae ac Verae Motuum Corporum Mundanorum . ASCANIUS MARTINENGUS Brixianus , Canonicorum Lateranensium Generalis Abbas , is by Ricciolus about this Time inserted in the Catalogue of Astronomers ; of whom he thus writes ; Praeter Ea quae in Glossa Magna de Coelo & Sideribus à Deo conditis , eruditissimè vulgavit Anno circiter 1600. scripsit etiam Geographiam Terrae Sanctae , & Chronologiam insignem adornavit . Doctor HOOD Publick Professor of Astronomy and Mathematicks in London , published two Celestial Hemispheres projected upon the Poles of the Ecliptick , and laid down in two large Schemes ; together with a Treatise annexed of the Uses of the said Hemispheres , touching the Longitude and Latitude of the Stars ; and a Table of their right Ascensions , Declinations , Culminations , coming to the Meridian , Horary Distance , &c. He writ likewise of the Cross Staff. GUILLAUME DE NAUTONIER , a French-man , wrote a Treatise entituled La Mecometrie de l' Aimant , ou la Maniere de mesurer les Longitudes par le Moyen de l' Aimant , Printed at Vence . 1603. ANTHONY LINTON , sometime Parson of Worth in Sussex , set forth a small Treatise , by him entituled , News of the Complement of the Art of Navigation , &c. In which among other things ; he offers in 26 Propositions , by means of the Magnet to discover the secret of perfecting the said Art of Navigation ; and particularly for finding out of Longitudes , which according to his Project depends upon the Poles of the Magnetical Globe , for the finding out the Places of which Poles he pretends to have devised a Way , how any Man having some Knowledge and Practice in the Mathematicks , may by his own Observations exactly find-out the true Longitude and Latitude of the said Poles , and may also fit the same most Commodiously unto the Art of Navigation , and it unto them ; as likewise ( besides the Magnetical Globe and Chard by him proposed ) how all other the Instruments commonly used in the Art of Navigation , as the Compass , the Astrolabe , the Quadrant , the Cross Staff , and the Traverse Board may be excellently well amended and perfected . But these his Commendable Designs dying with him left Posterity deprived of the Benefit intended by them , which yet in these Dayes seems to be revived , and is promised with advantage to be made good , by HENRY BOND Senior , an Ancient and Industrious Professor of the Mathematicks in this City , who undertakes to shew the Cause of the Varietating of the Variation of the Magnetical Needle or Compass by the Motion of two Magnetical Poles , how these Poles are found , and what their distance is from the Poles of the Earth . What their Annual Motion is , and from whence it proceeds . By Calculation he finds all the Variations that have been observed at or near London for above Ninety years past , and so by Consequence it may be found at London to the End of the World. He hath calculated a Table to every five Minutes of the Inclination of the Inclinatory Needle ; so that by the Needles Inclination , that Table , and the Latitude of the Place he can find the Longitude of any Place in the World. Also by that Table he finds Mr. Robert Normans Inclination that he found in the year 1576. And can shew what will be the greatest and least Inclination of the Inclinatory Needle in any Latitude in the World. He hath four Examples of finding the Longitude by the help of the Inclinatory Needle ; One at Balsore , in East-India in the year 1657. Another at Cape Charles , on the Coast of Virginia , before that Time ; another at the Cape of Good Hope ; another at the Straits of Magellan . This is the Conclusion of thirty eight years Magnetick Study spent with much Pains in Supputations grounded on the Observations of himself , and of others ( not easily procured ) and the Author is willing and ready ( as we are credibly informed ) to impart the Result of these his many years Thoughts on this Subject , upon moderate and reasonable Encouragement for the same . SETHUS CALVISIUS published Elenchus Calendarii Gregoriani in quo Errores qui passim in Anni Quantitate & Epactis committuntur , manifestè demonstrantur , Printed Francofurti Marchionum 1612. JOANNES TERRENTIUS a Iesuit , wrote from the City of Changtscheu in China in the year 1623. an Epistle to the Mathematicians of Ingolstadt in Germany , wherein he gives an Accompt of some Astronomical Designs of the Chineses , more particularly touching the Emendation of their Calendar , Praediction of Eclipses , and Procession of the Equinoxes , desiring the Assistance of the European Astronomers in promoting the Progress of that Science among those People . Which Epistle Kepler published in Print in the year 1630. with his own brief , but learned Comment thereupon , Printed at Sagan in Silesia in 4 o. SAMUEL PETIT a learned French-man , among other Works by him published , set forth Eclogae Chronologicae , in quibus de variis Annorum Iudaeorum , Samaritanorum , Graecorum , Macedonum , Romanorum Typis , Cyclisque Veterum Christianorum Paschalibus , disputatur , Printed at Paris 1632. OCTAVIANUS MARINIUS put forth a Treatise entituled Statera Temporum , sive de Praestantia Kalendarii Gregoriani , & ejus facili Usu , Printed at Bologna , 1633. DAVID GOUBARD put forth Perpetual Tables of the Celestial Motions , in French , Printed at Middleburgh , 1634. NATALIS DURET a French-man , published New Ephemerides of the Celestial Motions , to which he gave the Title of Tabulae Richelianae , Printed at Paris , 1637. ERICUS OLAUS TORMIUS Publick Professor of Mathematicks at Copenhagen , published a small Treatise with this Specious Title , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Sive Disquisitio Mechanica , wherein he Disputes of , and asserts the Necessity , and Possibility of Instruments , their Number , and Amplitude , requisite in Astronomical Observations , Printed Hafniae , 1643. in 4 o. JACOB RAVENSPERG Professor of Mathematicks in the University of Utretch , published about the years 1640. and 1643. divers small Latin Astronomical and Meteorological Disputations of the Spots of the Sun , Moon , and Planets , as likewise several Theses about Light , Lightning , Thunder , and some concerning Optical Problems , and Telescopes . BENEDICTUS HEDRAEUS a Swede , put forth Nova & accurata Astrolabii Geometrici Structura , ubi Gradus horumque singula Minuta prima , nec non Quadrantis Astronomici Azimuthalis , quo non solum prima , sed & singula minuta secunda distinctè observari possunt ; together with a Treatise of the Use of the same illustrated with clear and perspicuous Examples , Printed at Leyden , 1643. in 8 o. GEORGIUS FROMMIUS set forth a Dissertation Astronomical De mediis quibusdam ad Astronomiam restituendam necessariis , Printed at Copenhagen , 1642. in 4 o. He published likewise an Answer to Io. Baptista Morinus his Defence of his Astronomia restituta , Printed at the same Place 1645. in 4 o. JOANNES BECHETT Professor of Mathematicks in the University of Paris , to his Theory of the Planets before mentioned , hath added Tables of the mean Motions , and a Parecbasis explaining the Doctrine of Directions according to the Rational Way ; as also an Appendix for finding out and computing the Lunary Periods . JOHANNES JACOBUS HAINLINIUS Superintendant General of the Diocess of Aldeberg in Saxony ; put forth a Mathematical Synopsis , wherein the chief Parts of the whole Mathematicks , both abstract and Concrete , that is to say , Arithmetick , Geometry , Astronomy , Geography , Opticks , &c. are methodically proposed by Definitions , Axioms , Postulates , Theorems , Problems , &c. very useful not only for young beginners , but for those also who have already made some Progress in those Sciences . In the Astronomical Part he treats particularly and distinctly De Astronomia Sphaerica , Theorica , & Chronologica , adding withall the Praxis and Use of those Parts Problematically laid down , and briefly and clearly explained , Printed at Tubinge 1653. in 8 o. JACOBUS DU BOIS , published by Way of Dialogue , a Theological-Astronomical Treatise , Printed at Leiden , 1653. in 4 o. wherein he opposes Copernicus his Hypothesis , and Des Cartes his Philosophy . Against which AN ANONYMUS Author put forth a Reply under this following Tide , Demonstratio Mathematica Ineptiarum & Ignorantiae Iacobi du Bois Ecclesiastae , Leidensis , in Oppugnanda Hypothesi Copernicana , & Philosophia Cartesiana , Printed at Roterdam 1656. in 4 o. JOANNES HERBINIUS a Silesian , Master of Arts , and Professor of Philosophy at Utrecht , undertook the like Controversie as Du Bois , and published a Treatise thereupon entituled , Famosae de Solis vel Telluris Motu Controversiae Examen , Theologico-Philosophicum , ad S. Sanctam Normam institutum , to which he hath annexed the Grounds of his said undertaking , in an Epistle addressed to the Excellently learned Maria Cunitia . GEORGIUS HILARIUS , besides what we have already mentioned , put forth Enchiridion Progymnasmatum Mathematicorum , containing , first , Apospasmation Primi Elementi Euclidaei Gr. Lat. Secondly , Praecepta Sphaerica . Thirdly , Globi Coelestis & Terrestris Explicatio & Usus . Fourthly , Geographiae Rudimonta . Fifthly , Computi Ecclesiastici Epitome , Printed at Copenhagen 1656. in 12 o. PETRUS BORELLUS , Councellour and Physician to the King of France , put forth a Treatise De vero Telescopii Inventore , wherein he treats of the History of Telescopes , and other Optick Glasses , their Matter , Fashion , Working , several Kinds or Species , and Uses ; as also of several Discoveries made by the said Author , as well with Telescopes as Microscopes ; ( of the later of which , he gives a Century of Observations ) and treats of what may yet be further found out by the means of Telescopes , where occasionally he speaks of the finding out of Longitudes , Printed at the Hague 1655. and 1656. in 4 o. EUSTACHIO DIVINI , an Excellent Worker of Telescopical Glasses at Rome , put forth something against Monsieur Hugens his Systema Saturnium , Printed at the Hague in Holland in 4 o. The Reverend and Learned Mr. WILLIAM BEVEREGE , late of St. Iohn's Colledge in Cambridge , is to be added to the number of those whose mention gives Honour to this Catalogue , for his excellent Piece of Chronological Institutions in two Books . In the first whereof he treats of the Nature of Chronology , and its Parts , of Time , and its various Distributions into Scruples , Hours , Dayes , Weeks , Moneths , Years ; in the second , of the Syzygies , and Eclipses of the Luminaries , of the Equinoxes and Solstices , Cycles of the Sun and Moon , Indictions , Epacts , and of the several Periods , Aera's and Epocha's of the Ancients , to which he hath likewise added two Books of Chronological Arithmetick ; all which are of great Use and Advantage to the Students in Astronomy , Printed at London 1669. in 4 o. AN ANONIMOUS French-man about this Time published in his own Language a Treatise entituled Discours sur les Influences des Astres selon les Principes de Monsieur des Cartes , Printed at Paris in 12 o. GUARINUS GUARINUS , of the Order of Clerks regular ( commonly called Theatins ) of Mutina ; Professor of Philosophy and Divinity , and Mathematician to the Duke of Savoy , published and Dedicated to the said Prince a large Mathematical Treatise in folio , entituled Euclides adauctus , & Methodicus , Mathematicaque Universalis : In which with great Perspicuity , and exactness of Method , he treats of all things falling under the Notion of Quantity , as well Discrete , continuous , as abstracted ; divided into 35. Tractates . In the 23 th whereof he handles the Doctrine of the Sphere , in two Parts ; the first , treating De Sphaerae Contactibus & Sectionibus in Genere ; the second , De Sectionibus Maximorum Circulorum Invicem , which being of great Use in Astronomical Operations , we have for that Reason in this Place made mention thereof . Mr. PATRICK MATHEWS Arch-Beadle to the Universiry of St. Andrews , published a small Treatise in 12 o. ( lately come up from Scotland ) under the Title of the Great and New Art of weighing Vanity , written against a Book intituled , Ars Magna & Nova Gravitatis & Levitatis . To which are annexed some Tentamina de Motu Penduli & Projectorum ; In which there being some Ingenious Debates about Astronomical Affairs , and the Theory of Pendulums for the exact measuring of Time , and Analytical Series's or Equations of great Ingenuity suited to the Motion thereof , and of Projects ; We thought the same worthy to be mentioned in this Catalogue , the said Treatise was Printed at Glasco 1670. JOHN GADBURY of London , Student in Physick and Astronomy , put forth Ephemerides of the Celestial Motions for ten years , beginning Anno 1672. and ending Anno 1681. compared with the most correct Observations of Tycho , Kepler , Mr. Wright , and other approved Astronomers , with an Introduction to the Use thereof , Printed 1673. in 4 o. By late Letters from Paris Information is given that the SIEURS AVOCATE and DE ROYER intend to write fully of Astronomy , and of the Theories of the Planets . And here , for a Close , we cannot but acquaint the learned World with the most praise-worthy Design of the BISHOPS , NOBLEMEN , and GENTRY of Scotland , who have nobly and liberally contributed toward the erecting an Astronomical Observatory in the University of St. Andrews , and furnishing the same with Books and Instruments for Observation to the value of above 500 l. Sterling , which Heroick Example we hope may animate those of like Condition and Abilities in this Nation to incourage the promoting of the same Laudable Design amongst us . And thus much of the Original and Progress of Astronomy , and of Astronomers . OF THE COSMICAL SYSTEM . THe next thing , according to the Method of our Author , to be considered , is the Cosmical or Mundane System , which is nothing else but the Coordination of the Parts of the World ; whose Matter is the Number of the Elements and Heavenly Orbs ; its Form , the Order and Disposition of them among themselves , and relatively , as to the Centre of the Universe . Of this Manilius gives but a short hint . For having told , how humane Reason had scaled Heaven , and contemplated the various Phoenomena within the Elementary Region , and Those to their proper Causes having brought , He adds next , That on the whole Worlds Mass she cast her thought , Of which the System in her self she fram'd . But not giving any particular Description thereof , either as to its Matter or Form , we conceive it requisite , for the Reader 's greater satisfaction , to explain and illustrate this Subject , by representing the several Opinions , as well of the Ancients as Moderns , touching the same . And seeing the Matter of this System , which is the Number of the Heavens , is variously and with much confusion discoursed of by the Learned ; some diminishing , others increasing them ; it will not be amiss , in the first place , to exhibit this short following Synopsis of the Number and Distribution of the Heavens , with the several Authors or Assertors thereof ; as the same is represented by Ricciolus , Almagest , Nov. Lib. 9. Sect. 3. A SYNOPSIS of the Number of the HEAVENS , according to several AUTHORS . I. One Heaven , that is , one World , according to Aristotle . One Heaven , and that Sydereal and Fluid , according to S. Chrysostom , Tertullian , S. Bonaventure , Tycho Brahe , Longomontanus , Kepler , Bulialdus , and Tellez . One Heaven , and that Sydereal , but Solid , according to Aegidius , Hurtadus , Cisalpinus , and Aversa . II. Two Heavens , that is , the Empyraeum created the first Day , and the Firmament created the second Day ; according to Clemens , Acacius , Theodoret , Anastasius Synaita , Procopius , Suidas , S. Bruno , and Claudianus Mamertus . Two Heavens , that is the Sydereal and Aereal , according to Iustin Martyr . Two Heavens , that is , one of the Fixed Stars , the other of the Planets , according to S. Gregory Nyssene . Two Heavens , that is , the Primum Mobile , and the Sydereal , according to Mastrius , and Bellutus . III. Three Heavens , to wit , the Empyraeum , Sydereal , and Aereal , according to S. Basil , S. Ambrose , Damascene , Cassiodorus , Genebrardus , Suarez , Tannerus , Hurtadus , Oviedus , Tellez , Borrus . Three Heavens , that is , one of the Fixed Stars , one of the Planets , and the other Aereal , according to S. Gregory Nyssene . Three Heavens , the Empyraeum , Watery , and Sydereal according to Thomas Aquinas . Three Heavens , that is , the Watery , Sydereal and Aereal , according to Cajetan . IV. Four Heavens , that is , the Empyraeum ; that of the Fixed Stars ; that of the Planets ; and the Aereal , according to S. Athanasis . V. Five Heavens , and all Sydereal and Solid , viz. of the Fixed Stars , of Saturn , Iupiter , and the Sun ( with Mars , Venus , and Mercury included ) and of the Moon , according to Oviedus . Five Heavens , that is , the Empyraeum , the Watery , that of the Fixed Stars , that of the Planets , and the Aereal ; according to Ricciolus . VII . Seven Heavens , but confusedly reckoned by Philastrius . Seven Heavens , that is , the Aer , the Aether , Olympus , the fiery Heaven , the Firmament , the Angelical Heaven , and the Heaven of the Trinity , are reckoned by Beda . Seven Heavens , that is , the lower Region of the Air ; the upper Region thereof ; the lower Region of the Fire ; the upper Region thereof ; the Sydereal Heaven ; the Chrystalline ; and Empyraeum ; according to Rabanus . VIII . Eight Heavens , and all Sydereal , that is , the Heaven , or Sphere of the Fixed Stars , and the several Spheres of the Seven Planets , according to the Babylonians , Egyptians , Eudoxus , Plato , Calippus , Aristotle , Cicero , Philo , S. Basil , S. Ambrose , Damascene , Bonaventure , Remigius , Thomas Aquinas , Aben-Ezra , Carthusianus , Lyranus , Tostatus , Brugensis , Riccius , Crontius , Cremoninus , Philalthaeus , Amicus , Ruvius . IX . Nine Heavens , that is , the Empyraeum , and eight Sydereal solid Heavens , according to Arriaga . Nine Heavens , that is , the Primum Mobile , the eight Sydereal Heavens , according to Macrobius , Haly , Alpetragius , Rabbi Iosue , Rabbi Moyses , Scotus , Abraham Zagutus , Sacroboscus , Claromontius , and , as some ( but falsely ) conjecture Hipparchus , and Ptolemy . X. Ten Heavens , that is , the Primum Mobile ; the Sphere for the Motion of the Fixed Stars ; the Eighth Sphere , for the Motion of Trepidation in Longitude ; and that of the Seven Planets ; according to Alphonsus and his followers , Fernelius , Purbachius Regiomontanus , Amicus , Appianus , Maurolycus , and Langius . Ten Heavens , that is , the Primum Mobile ; the Sphere of the Motion of Trepidation in Longitude ; that of the Fixed Stars ; and the Spheres of the Seven Planets ; according to Arzahel , Thebit , and Isaac Israelita . Ten Heavens , that is , the Empyraeum ; the Primum Mobile ; and Eight Sydereal Heavens ; according to Gulielmus Parisiensis , and Iohannes Antonius Delphiuus . XI . Eleven Heavens , that is , the Empyraeum , and the ten moveable Spheres of Alphonsus and his Followers , before mentioned , according to Petrus Alliacensis , the Colledge of Conimbra ▪ Martinengus , and ( sometime ) Clavius . Eleven Heavens , to wit , the Primum Mobile ; the Sphere of the first Libration in Latitude ; the Sphere of the second Libration in Longitude ; the Sphere of the Fixed Stars ; and those of the Seven Planets ; according to Iohannes Vernerus , Leopoldus de Austria ▪ Iohannes Antonius Maginus , and ( in his latter dayes ) Clavius . XII . To these foregoing , if you add the Empyraeum , there will be XII . Heavens . XIV . Iohannes Baptista Turrianus , and Fracastorius make XIV Heavens , that is Seven Spheres , or Orbs , counting from the Primum Mobile , to the Aplané , or Sphere of the Fixed Stars ; and Seven of the Planets . Having , by the foregoing Synopsis , sufficiently explained the Number of the Heavens , which is the Matter of the Mundane System ; we are in the next place to give an account of their Order and Disposition , which is the Form thereof . According to it's Form , the Mundane System is considered under a double Hypothesis ; either as having the Earth seated in the Centre of the Universe , immoveable , and the Sun and Heavens moving about it ; or having the Sun in the Centre , exempt from any Motion of Lation , and the Earth moving about it in the Solar Orb. And it is worthy Observation ( as Ricciolus notes ) that the Two Sects of Philosophers and Mathematicians , the one maintaining the Earth's Mobility , the other , its Immobility , have had in the Schools , through several Ages , like Castor and Pollux , alternately their Rise and their Fall. For first , Pythagoras , with some others of his Sect , placing the Earth in the Centre of the World , makeing use of Excentricks and Epicycles , seated the Sun in the midst of the Planets . But others of the Pythagoreans , retaining Epicycles and Excentricks , placed the Sun in the Centre of the World , and the Earth in the midst of the Seven Planets . Afterwards Plato , placing the Earth in the Centre of the World , seated the Sun in the midst of the Planets , yet so as for the most part he supposed Venus and Mercury to be carried above him ; whom Eudoxus , Calippus , and Aristotle followed , endeavouring to explain the Motion of the Planets , by Concentrick Circles . So that they conceived neither Venus nor Mercury moved in Epicycles , above and beneath the Sun ; but either alwayes above , or alwayes beneath the Sun. After this , Others again , reducing Excentricks and Epicycles , placed the Earth in the midst of the World , as Archimedes , Hipparchus , Sosigenes , Cicero , Vitruvius , Pliny , Macrobius , and Capella ; but differed among themselves , as to the various Order and Disposition of the Planets . Others again , as Aristarchus , Philolaus , and some Pythagoreans , removed the Earth out of its Central Position , and made it move about the Sun , by them placed in the midst of the World : But what their Opinion was touching Excentricks and Epicycles , they have not explained or delivered to Posterity . In process of time , Ptolemy , reviving the first and ancient Pythagorean System , re-established Excentricks and Epicycles , placing the Earth in the midst of the World , and the Sun in the midst of the Planets . Which Opinion continued , and was embraced by the greatest part of Astronomers , until the XIV . Century after Christ ; though the Order of the Planets were changed by Alpetragius and Geber . On the other side , Turrianus and Fracastorius , retaining the Ptolemaick Order , brought in again Concentrick Circles , and those more in number by many , than either Aristotle or Eudoxus had introduced . About which time , Copernicus , raising , as it were from the Grave , the Hypothesis of Philolaus and Aristarchus , touching the Earth's annual Motion about the Sun , in the Centre of the Universe , set forth and illustrated the same with such fair and probable Arguments , that it hath prevailed with most Astronomers at this Day . He made Venus and Mercury , with Plato , Vitruvius , Macrobius , Capella , and Bede , to move , now above , now beneath the Sun ▪ Hence Tycho Brahe ; and with him Longomontanus , took occasion of introducing another System ; wherein not only Venus and Mercury , but also Mars , Iupiter and Saturn are supposed to move about the Sun ; and the Sun and Moon , with the Fixed Stars about the Earth , immoveable in the Centre of the Universe , retaining the Excentricks , but rejecting the Epicycles of Ptolemy . At length Argolus , altering the Tychonick System , makes the three Superiour Planets to move about the Earth ; Venus and Mercury about the Sun ; seating the Earth in the midst of the World. From whom yet Ricciolus dissents , making Saturn , Iupiter , the Sun , Moon , and Fixed Stars , to move about the Earth , and Venus , Mercury , and Mars about the Sun. These various Sentiments of the Learned , touching the Order and Disposition of the several Parts of the Mundane System , ( as they have been in Divers Ages successively asserted ) being thus briefly enumerated , we shall next give somewhat a more ample Description and Illustration of the several Hypotheses , and exhibit withall to the Reader 's view the Schemes of each particular System ; beginning with the most Ancient , that of Pythagoras , which is this . SYSTEMA ANTIQVISSIMVM COMMVNE PYTHAGORAE PTOLEMAEI ET PLVRIMORVM . 1 In this System the Terraqueous Globe is seated in the midst or Centre ; about it , the Elementary Region ; next above that , the Moon ; then Mercury ; next above him , Venus ; the Sun , as Moderator of all , being placed , as in a Throne in the midst of the Planets , environed not only by the three foregoing , called the Inferiour , but by Mars likewise , Iupiter , and Saturn , called the Superiour Planets . Above Saturn is the Sphere of the Fixed Stars , called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Aplane , or Unerring ; by some , the Firmament . The reason of this System is thus explained by Pliny , Lib. 2. c. 22. Pythagoras ex Musicâ ratione appellat Tonum quantum absit à Terra Luna , &c. i. e. Pythagoras from Musical Reason , calls the space between the Earth and the Moon , a Tone ; the space from the Moon to Mercury , he will have to be half a Tone ; as much in a manner from him , to Venus ; from Venus to the Sun , as much and half again ; but from the Sun to Mars , as much as from the Earth to the Moon , that is a Tone ; from him to Jupiter , half a Tone ; from Jupiter to Saturn , another half Tone ; and from thence to the fixed Stars , as much and a half again . Thus are composed Seven Tones , which Harmony they call Diapason , that is , the generality or whole state of Consent or Concord . Now a Tone is by some interpreted the same as an Unite or Integer , and contains in Measure according to the Opinion of Pythagoras 125000 Stadia ; according to which Measure ; not only the foregoing space , but extent of the whole System , may be computed . And this was the first Pythagorean System , embraced by Archimedes , the Chaldeans , Aristotle , Cicero , Livy , Ptolemy , Alphonsus , Purbachius , and the greatest part of Astronomers , until the time of Maginus and Clavius . The next System is that which is called the Platonick . Touching which , thus Ricciolus , Lib. 9. c. 3. As Discord oftentimes produces Concord ; so on the other side Concord often begets Discord . For between Pythagoras and Plato , there was thus far a wonderful Concordancy , that they both conceived the Intervals and Order of the Planets ought to be constituted according to the Laws of Musick . But from their agreement sprung their dissent ; by reason the Platonists and Pythagoreans differed in their Opinions about the Harmonical Diastem . And as Plato differed from Pythagoras , so some of his own followers differed from him , as ( among others ) Porphyrius , Apuleius , and Mareilius Ficinus . Whosē difference will appear in the following Scheme . SYSTEMA PLATONICVM . 2 In which , in the first place , according to Plato , the Earth with the Elementary Region is placed ; above that , the Moon , and immediately above that , the Sun ; above him Mercury , then , Venus ; above Her , Mars ; then Iupiter ; lastly Saturn . In the second place is that of Porphyrius , and some other Platonists before mentioned , agreeing in all but this , That whereas Plato immediately above the Sun , placed Mercury , and then Venus , they immediately , above the Sun , placed Venus , and then Mercury above her . Of which last , Macrobius lib. 1. in Somn. Scip. c. 3. gives this accompt . The late Platonists ( sayes he ) repudiated the Dintensions of Archimedes , as not observing double and triple Intervals . For , they held , that what was the Distance , or Interval , from the Earth to the Moon , the same was double from the Earth to the Sun ; and the Distance from the Earth to Venus , was triple . to that from the Earth to the Sun ; and from the Earth to Mercury four times that from the Earth to Venus ; and how far the Distance was from the Earth to Mercury , nine times that was the Distance from the Earth to Mars ; and the Distance from the Earth to Jupiter , eight times that from the Earth to Mars ; and the Distance from the Earth to Saturn , seven and twenty times that from the Earth to Jupiter . The same Order is likewise asserted by the Author of the Book De Mundo . These three foregoing Systems are composed all of Concentrick Orbs. The next , which is the Egyptian , followed by Vitruvius , Martianus Capella , Macrobius , Beda , and Argol , is composed partly of Concentrick Orbs , partly of Excentrick , as may appear by the subsequent Scheme . SYSTEMA AEGPTIVM . 3 Wherein we may perceive the Earth seated in the midst of the World , with the Elements , and immediately above them the Moon , then the Sun , about whom , as their Centre , first Mercury , then Venus are supposed to move in Epicycles ; above these Mars , next Iupiter , and then Saturn . Of this System , thus Macrobius , in Somn. Scipion. l. 1. c. 19. The Egyptian subtlety is not without reason , which is this ; the Circle wherein the Sun runs his course is surrounded with the Circle of Mercury , as Interior , and by that of Venus as Exteriour . And hence it is that these two Stars , when they are in the upper part of their Circles , are understood to be above the Sun ; but when they are in the inferiour part of their Orbs , or Circles , the Sun is held to be above them . Those therefore who affirm the Spheres of these Planets to be under the Sun , are perswaded to believe it , from this Appearance of their Course , when they run in the Inferiour part of their Orbits , which is more remarkable and more clearly discernible , for when they are in the upper part of their Circles , they are more concealed . And therefore this perswasion of theirs hath prevailed , and accordingly the Order of those Planets hath been received almost by all Persons ; but more perspicacious Observation discovered this better Order . And justly does he stile it a perspicacious Observation , which so many Ages since by the only Sagacity of Wit so clearly discovered , what we find now really detected by the help of the Telescope . And therefore Ricciolus sayes of this System , that it is Pulcherrimum , ac pro hac quidem parte , Verissimum Systema . We come now to the most celebrious , and at this day most generally received Mundane System , from it's Reviver , called the Copernican , but owing it's original to the Samian and Italick School , as being proposed and asserted , in the one , by Philolaus , of Crotona , in the other , by Aristarchus Samius , both Pythagoreans , whence it is called the second Pythagorick System , as differing from the former before described ; That , fixing the Earth immoveable in the midst of the World ; This , on the contrary giving to the Earth , not only a Diurnal Motion about its Axis , but also an Annual , about the Sun , as the Centre of the Universe . An Hypothesis not unknown to the Romans ; and therefore Seneca , in his Natural Questions ( Lib. 7. ) proposes it as a thing necessary to be discussed ; To know whether the Earth standing still , the Heavens be moved about it ; or the Heavens standing still , the Earth be carried round . And again , It is a thing worthy contemplation to be assured , sayes he , in what condition We are ; whether in a Seat of all others most slow , or the most swift ? Whether God turns all things about us , or we our selves are turned about ? This System , about two Ages since , was resuscitated from Oblivion and the Grave , by Cardinal Cusanus , but imperfectly , until Copernicus came and gave it a perfect consummation , followed by the greatest Wits of this and the foregoing Age , to wit , Georgius Ioachimus Rheticus , Moestlinus , Rothmannus , Stevinus , Kepler , Galilaeo , Schickardus , Iordanus Brunus , Coelius Calcagninus , Didacus Astunica , Foscarinus , Herigonus , Renatus Des Cartes , Lansbergius , Bullialdus , Antonius Laurentius Politianus , Wendelinus and Gassendus ; Lansbergius and Bullialdus , only differing in this from Copernicus , that they allow to the Fixed Stars a proper Motion , which Copernicus denies . Take the same represented in the following Scheme . SYSTEMA PHILOLAI ET COPERNICI . 4 In this System , we may perceive the Sun placed in the Centre of the World ; next above him , Mercury , finishing his Course in the space of eighty dayes , or thereabouts ; then Venus , making her Revolution in nine Moneths time ; above her , the Earth , with the Elementary Sphere , in the Annual Orb , which it runs through in 365. dayes and half , by a Motion from West to East ; that is in the same Circle , wherein the Egyptian and Ptolemaick System place the Sun. Besides which Annual Motion , Copernicus assigns to the Earth a Diurnal Revolution , in which it turns about its own Centre and Axis , inclined in the Plane of the Ecliptick , in the space of 24. hours , from West to East : The Moon by a Menstrual Revolution being carryed about the Earth , as in an Epicicle ; Mars running about the Sun , as the Centre of the Universe in two years ; Iupiter above him in twelve ; and Saturn in thirty . The Sphere of the Fixed Stars being distant by so vast an Interval from the Sphere of Saturn , that the Annual Orb , in which the Earth moves , appears , in respect to it , no other than a Point . This System , though , in appearance , of all others , the most rationally grounded , could not yet give so general a satisfaction to the Curious , but that some of them conceived it might admit of Alteration , or Emendation . And thence the illustrious Tycho took occasion to introduce the following System of his , which is no other than a certain Transfiguration of the Copernican , after this manner . SYSTEMA TYCHONICVM . 5 First , the Earth is supposed fix'd without Motion in the Centre of the Universe , Concentrick to which is , first the Sphere or Circle of the Moon 's Motion ; next , that of the Sun 's Annual Course ; then the Sphere of the Fixed Stars . The Sun being placed as the Centre of the other Planets , in whose Orb ( as it were two Epycicles ) are drawn the Circles of Mercury and Venus . At a greater Distance is that of Mars , intersecting , when in Opposition to the Sun , part of the Solar Sphere , and therefore being Achronical is nearer to the Earth than the Sun. Above Mars is the Sphere of Iupiter ; above Iupiter , that of Saturn ; above that , the Fixed Stars . So that , in this System , the Sun is the Centre of five Planets ; that is , not only of Mercury and Venus , according to the Egyptian System , but also of Mars , Iupiter , and Saturn , according to the Copernican ; which likewise it resembles , as supposing fewer Conversions , and rejecting the Solidity of the Ptolemaick or Purbachian Orbs. But the Copernican , even in the Opinion of Ricciolus , seems to carry with it a greater simplicity and concinnity . Nicholaus Raimarus Ursus seemed to challenge this System , as first introduced by him , ascribing the Original of the Hypothesis , to Apollonius Pergaeus . But Tycho , in his Epistles , hath vindicated and asserted his own Right , and hath gained for his Followers Longomontanus ( who yet gives to the Earth a Motion about its Axis ) Scheinerus , Blancanus , and generally the Astronomers of the Iesuitical School . And the Reason of their adherence to this System , rather than to the Ptolemaick or Copernican , is given by Caramuel , in his Interim-Astronomicum ; which is , that Demonstration condemns the Ptolemaick , shewing it to be impossible and inconsistent with Modern Observations ; and as for the Copernican , that it stands condemned by a congregation of Cardinals , who have ( if you will believe them ) defined the same to be repugnant to the Sacred Scriptures . Among the several Systems either of the Ancients or Moderns which are grounded upon the Earth's Immobility , there are two ( besides the Tychonick ) which seem to Ricciolus the most probable ; the One is Semi-Ptolemaick , the other Semi-Tychonick . The Form of the first , admits the Centre of the Earth as the Term from whence the Excentricity of the several Orbs are measured , supposing Venus and Mercury to be carried about the Sun in Epicycles and the Excentricities of the other five Planets , as also their Epicycles , not to be alwayes of the same Quantity , which may be apprehended by the Figure of the Egyptian System already described , supposing only that Mars in Opposition to the Sun , be made to approach nearer to the Earth , than the Sun does . The Form of the second is represented in the following Scheme , and ows its Invention to Ricciolus , wherein the Sun is supposed to be the Centre of the Sphere of Mercury , Venus and Mars ; And the Earth , the Centre of the Circle of the Moon 's Motion , and of the Fixed Stars , as also of those of Saturn and Iupiter . The Reasons impelling him to embrace this Hypothesis , being these . First , he observed that Saturn and Iupiter had Secundary Planets moving about them , but Mars , Venus , and Mercury none ; whence he conceived it probable that Saturn and Iupiter exercised as it were their proper Monarchies in the Heavens ; and were no Attendants or Satellites of the Sun ; but moving about the Earth as their Centre . That Mars was one of the Sun 's greatest or utmost Satellites , including within his Sphere that of the Earth ; but Venus and Mercury his nearer and more interiour Gaurds . Secondly , Because in the Variation of the Excentricities of the Planets , he observed a greater Connexion of Mars , Venus , and Mercury with the Sun , then of Saturn and Iupiter . Thirdly , Because he conceived Saturn and Iupiter , being more slow and ponderous Planets , to have a greater Affinity to the slow Sphere of the Fixed Stars ; and to respect ( as do the Fixed Stars ) the Earth rather than the Sun as the Centre of their Motions . Fourthly , Seeing that Mars , Venus , and Mercury in their Courses or Circumgyrations enter into the Solar Heaven , he conceived it more probable that those Planets should have the Sun for the Centre of their Motions , and not to have any Distinct Aethereal Regions assigned them , but to move All in one common Region . But Saturn and Iupiter to have their Distinct Dominions and Regions allotted them . Fifthly , Because it seems very probable that among the Planets there should be one as it were a Mean or Middle , between the Superiour and the Inferiour , and which in his Motions should have some things common with Saturn and Iupiter , and some with Venus and Mercury ; to wit Mars . But see the Scheme it self . SYSTEMA SEMITYCHONICV̄ RICCIOLI . 6 In which is to be noted that the Intervals of the several Orbs are so ordered , that the lowest of the Concave Heaven of Saturn , does not touch the upper part of the Convex of Iupiter , or the lowest of Iupiters , the uppermost of Mars , as in the P●…olemaick , but there is a voyd Interval between the Fixed Stars , and the uppermost Convex of Saturn's Orb , of 9824 Semidiameters of the Earth , and between the Concave of Saturn and the Convex of Iupiter , an Interval of 10045 of the like Semidiameters , and between the Concave of Iupiter and Convex of Mars , an Interval of 5310 such Semidiameters , and between the Concave of Venus and Convex of the Moon 's Orb 1850 Semidiameters . Besides , the Thickness of the whole Heaven of Saturn computed together with his Satellites is supposed 32454 Semidiameters , and that of Iupiter with his Satellites 21361 Semidiameters ; That of the Sun , Mars , Venus and Mercury ; being but as one Heaven , is supposed to contain 19091 of the Earth's Semidiameters . These three last Systems suppose the Heavens , or the Aetherial Region to be pervious , fluid , and of a thin , liquid , and transparent Substance like the Air , but more pure , and not consisting of Solid Orbs , as the Peripateticks , and those of the Ptolemaick School affirm . This Fluidity of the Heavens being manifested , by the Maculae Solares , whether they be considered as Planets moving tumultuously about the Sun , or as Clouds , Vapours , and Fumosities issuing from the Solar Body ; Likewise by the Librating Motion of the Firmament it self , in which the Sun moves , as also by the Libration of the Moon ; and by the Satellites of Iupiter , not long since discovered to move about that Planet , as also those about Saturn , and the Extravagant Motion of Mars , as also that of Venus and Mercury running now above , now beneath the Sun. No less evidenced by the Production of Comets , and their divers Motions , which beginning in One , make their Progress through several Aetherial Regions ; which they could not do if the Celestial Orbs through which they pass were solid ; from which supposition several other Inconveniencies would likewise ensue by reason their Convexities and Concavities , as also those of so many Epi●…ycles and Excentricks would necessarily produce a Multiplicity of various Refractions of the several Rayes of the Sun , of the other Planets , and of the Fixed Stars . Lastly , it seems as incongruous that the Stars and Planets should be carried about in such vast solid Orbs , ( to which they bear no other proportion than a drop of Water to the Ocean ) as it is for the Earth to be imagined to move only to carry about a Fly or a Pissmire . Neither do those Celestial Bodies gravitate or need any Support , but move regularly within their several Sphericities , as having no Appetency of Motion beyond those Bounds . See Tycho Brahe , Progymnasm . Tom. 1. and Ricciolus repeating the several Arguments to this Purpose ( of Kepler , Lansbergius , Maginus , Galilaeo , Gassendus and Bulialdus ) Almag . Nov. Tom. 2. p. 24●… . and 243. Of the Constellations , We have in our Notes treated so particularly and so fully , that We shall not need to add any thing ( by way of further Illustration ) thereunto . Only whereas Manilius hath omitted among the Northern Constellations Coma Berenices , Ganymed or Antinous , and Equuleus or the lesser Horse , and in the Southern Hemisphere , Eridanus or Fluvius Orionis , and Corona Australis , besides those , which having been but lately detected by Modern Discoveries , could not therefore be known to the Ancients . We are obliged , according to the References given in our Notes , to satisfie the Readers Curiosity , by making a Particular Description of them in the same manner as we have done of the others . COMA BERENICES ; is by Bayerus called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Coma , Spicarum Manipulus , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 seu Crines , called likewise by the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Colus ; as being fashioned like to a Distaff of Flax ; by the Arab's it is called Alhaud , i. e. Lacus seu Cisterna , sayes Doctor Hyde in his Notes upon Ulugh Beigh's Table . It consists according to Proclus and Stoester of seven Stars , according to Kepler of fifteen . The Original of this Constellation was from Berenice the Wife of Ptolemaeus Euergetes , who vowed if her Husband returned Victorious from his Asian Expedition , she would shave her Head and offer her Hair ( one of her most beauteous Ornaments ) to Venus to be hung up in her Temple ; which having accordingly performed , it was the next Day after the offering thereof found missing , whereupon Conon to flatter King Ptolemy , discovered to him that the Head of Hair was translated to Heaven , and made a Celestial Constellation , celebrated by Callimachus in a particular Greek Poem ; turned into Latine Verse by Catullus . Pliny l. 2. c. 27. seems to make this a Southern Constellation , but Ptolemy places it to the North of the Sign Leo , not far from the Tayl thereof , whose Situation likewise is thus represented by Catullus in the forementioned Poem . Saevi contingens namque Leonis Lumina , Callisto juxta Lycaonida , Vertor in Occasum tardum dux ante Booten , Qui vix serò alto mergitur Oceano . ANTINOUS and GANYMED are one and the same Constellation for the Asterism which by the Greeks is feigned to represent Ganymed rap'd by the Eagle and carried up to Heaven to serve Iupiter as a Cup-bearer ; the Romans in Honour of Antinous ( the beloved Favourite of Hadrian the Emperour ) will have to be the Representation of that beautiful Bithynian , who dying a voluntary Death for the Welfare of the Emperor , was by him honoured with Statues , Temples , Priests , and a Place among the Celestial Constellations ; between the Eagle and Sagittary . It consists according to Kepler of seven Stars , according to Baierus of eleven , and comes to the Meridian at Midnight about the Middle of Iuly . EQUULEUS , or the Lesser Horse is by Ptolemy called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , by others 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Sectio Equi , in Chrysococca's Tables 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Caput Equi . By Ulugh Beigh Kit'a Al Pháras , i. e. Sectio , Praecisio , vel Segmentum Equi , by others of the Arabs called Al Pharas al Auwal , i. e. Equus Primus , consisting of four Stars in Form of a Horses Head and Neck ; it comes to the Meridian at Midnight about the Beginning of August . To these Northern Constellations some late Astronomers have added several other Asterisms composed out of the Inform Stars or Sporades . As of those between the greater Bear and the Sign Leo , they have formed the River Iordan . Of those between the North Pole , Perseus and Auriga an Asterism called Camelo Pardalis and Gyraffa . Of the four Stars interposed between the Triangle and the Tail of the Ram , another called Vespa , by some Apes , i. e. the Wasp or the Bees . Of the Tract of Stars running between the Swan and the Eagle , as far as Serpentarius , they have formed the River Tigris or Euphrates , and to a single Star of the second Magnitude , placed in the midst between Charles his Wain , and Coma Berenices ( from which if a right Line be drawn through the first Star in the Tayl of Ursa Major , towards the Pole , it will point directly to the Pole Star ) they have given , in Memory of the most Glorious Prince and Martyr , Charles the First , King of England , the Name of Cor Caroli . The Primary Invention and Denomination thereof being owing to the most Loyal and truly Learned , Sir Charles Scarborough Knight , Physician to His Majesty , and my Honoured Friend . ERIDANUS or PADUS is a Southern Asterism , which some will have to be made a Constellation in Memory of Phaeton , who was drowned therein ; the Egyptians challenge it for their Nilus . It is called by the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Fluvius , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Fluvius Orionis , because it springs from the left foot of Orion , and runs from thence in a flexuous Course Southward : Lycophron calls it Aetuse . It is called likewise Gyhon , and by those of Fetz ( sayes Ricciolus ) Vardi , i. e. Fluvius , by the Moores Guad , and by the Arabs Nah'r in the same sence . The Thuscans call it Botignon , the Ligurians Botigum , seu Bodintum , as Bayerus in Uranometr . Schilleriana affirms . It consists according to Ptolemy of 34 Stars , according to Baierus of 43. Kepler reckons therein 39. In which the 34 th Star ( of the first Magnitude ) is by the Arabs called Al Dalim , i. e. Agger , or as Doctor Hyde from the Authority of Golius Interprets it . Terra fossi primitus Putei , or Agger in Aquae Extremitate ; Hence in Chrysococca's Persian Tables ; it is called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Sulcus . Porca . It is likewise called in Arabick Acher Nah'r , i. e. Ultima Fluminis , whence the common Name Acarnar . It passes by the Meridian at Midnight in November . CORONA AUSTRALIS sive Notia , called by the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Coronae Australis Asterismus ; and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Corona Secunda , likewise 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Parvum Coelum , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Caduceum . It is called by the Greek Poets , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Rota Ixionis . The Arabs give it different Denominations , as Al Kubba , i. e. Testitudo vel Tabernaculum , propter circularem formam , and Az'ha Al Naâm , i. e. Nidus Struthionis , as being near two Stars in the Leg of Sagittarius called Al Naâim , whereof one is called Al Naâm al Sadir , i. e. Struthio adiens aquam , the other Al Naâm Al Wârid , i. e. Struthio rediens ab Aqua . Ulugh Beigh calls them in the Plural Number Al Naâim , which Doctor Hyde translates Pecora , because in Tizinus his Tables he finds them pourtrayed with a Shepheard near them , as reposing under the Al Kubba or Testudo . The Constellation confists , according to the joynt Computation of Ptolemy , Bayerus and Kepler , of thirteen Stars . It is fabled to have been made a Constellation by Bacchus in Honour and Remembrance of his Mother Semele . It comes to the Meridian at Mid-Night , ( but not visible in our Hemisphere ) in the beginning of Iuly . Besides these Southern Constellations omitted by our Poet , but known to the Ancients ; there are several other Southern Asterisms lately invented by Modern Astronomers ; whereof some were composed out of divers inform Stars heretofore known : Others out of such as have been newly discovered , and were never known in any former Ages : Of the first kind are the three following . First , Monoceros or Unicornus , placed between Orion the greater Dog and Hydra . Secondly , Alect●…r , i. e. Gallus , or the Cock , between the greater Dog and the Ship Argo ; which Stars yet Bayerus , and others reckon as belonging ad Scutulum Navis . Thirdly , Columba , or the Dove of Noah , with an Olive Branch in her Beak , not far from the greater Dog , which appears not above though it run near our Horizon . Of the other kind are these twelve Constellations following , first found out and denominated by some eminent Navigators sayling beyond the Line , as particularly by Americus Vespucius , Andreas Corsalius , Petrus Medina , but principally by Fredericus Houthman , who during his Abode in the Island Sumatra , made exact Observation of them , being by Petrus Theodorus , and Iacobus Bartschius reduced into Order , and by Iansonius , Hondius , and Iacobus Florentinus inserted in the Celestial Globes by them made and published . 1. GRUS or the Crane consisting of thirtteen Stars according to Kepler and Bayerus , whereof three of the second Magnitude , one in the Head , one in the Tail or Train , and another in the Southern Wing . It is called likewise Phaenicopterus and Geranos , but ( as Schillerus observes ) noviter , & affectatè cum notum sit Graecos , animalia haec circa Polum Meridionalem nunquam somniasse ; it is seated under the Southern Fish. 2. PHOENIX . on her Spicy Pyre , consisting of fifteen Stars , among which one of the Second Magnitude in the Neck thereof , and two Nebulous . It is placed between the Southern Fish , and Eridanus , sub Cauda Ceti . 3. TOUCAN or the American Goose called likewise , Pica Brasilica seu Indica , and Ramphestes , consisting of eight Stars , whereof four of the Second Magnitude ; according to Bayerus , though Kepler allow them to be but of the third . It is placed in the midst between the Phoenix and Indus . 4. INDUS , or the Indian , in the Figure of an Indian , holding in either Hand a Dart , and therefore likewise called Sagittifer , consisting of twelve Stars , seated between Toucan , and the Constellation called Pavo . 5. PAVO , or the Peacock , to which some have given the Greek Name 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , consisting according to Bayerus of sixteen Stars , as Kepler reckons of 23. Whereof one in the Head thereof is of the Second Magnitude , and two Nebulous . It is placed near to Indus , under Sagittarius . 6. APOUS , or Apis 〈◊〉 Avis Indica , Avis Paradisi , & Manu codiata , consisting of twelve Stars according to Bayerus , according to Kepler but of eleven , following after the Peacock with its Tail toward the Antartick Pole. 7. APIS , Musca , or Muia , called likewise Crabro Indicus , consisting of four Stars placed under the Feet of the Centaur . 8. TRIANGULUM AUSTRALE , Trigonum Notius sive Deltoton , to whom some likewise have given the affected Arabick Name of Almutabet Algenubi , consisting of five Stars , in each Angle one of the Second Magnitude , and two others . It is seated sub fera Centauri & Ara , called by Schillerus Signum Tau , sive Imago crucis , by the Spaniards el Cruziero . 9. CHAMAELEON placed directly in Opposition to the Lesser Bear , and whose Form , ( according to the Disposition of the Stars that compose it ) it represents ; consisting according to Kepler's Accompt of ten Stars , according to Bayerus but of nine . It is placed directly under the Constellation Musca or the Fly , in quam ( as Bartschius describs it ) Linguam vibrat . 10. PISCIS VOLANS , Volucris , & Volatilis , called likewise Passer Marinus , and Hirundo Marina , in which last sence it is noted by a new Greek Name , Chelidon Thalassia , consisting of seven Stars , seated under the Ship Argo , next to Dorado , or the Sword Fish. 11. DORADO , ( as the Spaniards call it ) Piscis auratus , Chrysophris , or the Golden Fish , called likewise Xiphias seu Gladius , or the Sword Fish , consisting of six Stars , or as Bartschius reckons of five , with which it describes and circumscribes the Pole of the Ecliptick . 12. HYDRUS , by the Dutch called the Wasser Schlange , consisting of fifteen Stars according to Bayerus , Kepler yet reckoning twenty , the Last Star in the Tayl whereof , was in the year 1600 distant two Degrees 30′ . from the Southern Pole , but at present as Ricciolus notes at a nearer Distance . To these are to be added the two NUBECULAE ; the Greater and the Lesser , and between them both , RHOMBUS , which Habrechtus hath formed in his Globe out of four Stars constituting each Angle thereof . And thus much touching the several Constellations Ancient and Modern . But since some have endeavoured to abrogate , the Ancient Ethnick Names and Figures of the several Asterisms , and to introduce a new Uranography , by representing the Celestial Constellations under Sacred and Christian Figures and Denominations , as Schillerus in his Coelum Stellatum Christianum , and Bartschius in his Celestial Globe ; We shall here for the Satisfaction of such as have not yet seen the same , add the following Synopsis of that Christian Astronomical Design , shewing first the new Morphoses of the Zodiacal Signs , next Those of the Northern Constellations , then of the Southern ; Lastly of the Planets . Zodiacal Signs . Old Names . New Names . Aries , Saint Petre , according to Schillerus ; according 〈◊〉 Schickardus , Abraham's Ram offered in the Room of Isaac . Taurus , Saint Andrew , or according to Harsdorfius , the offering or Burnt-Sacrifice commanded , Leviticus 1. 3. Gemini , Saint Iames the Elder , as Schillerus ; as Schickardus , Iacob and Esau. Cancer , Saint Iohn the Evangelist . Leo , Saint Thomas , or according to Schickardus , the Lion of the Tribe of Iuda . Virgo , Saint Iames the Younger , according to Schillerus ; or as Schickardus will have it the Virgin Mary . Libra , Saint Philip , or according to Hartsdorfius , the Tekel or Ballance of Belshasar , Daniel 5. 27. Scorpius , Saint Bartholomew . Sagittarius , Saint Matthew ; or as some will , Ismael , Genes . 21. 20. Capricornus , Saint Simon . Aquarius , Saint Iude , or Naaman , 1 Kings 25. 14. Pisces . Saint Mathias , or according to Schikardus the two Fishes in the Gospel , Iohn 6. 9. Northern Constellations . Old Names . New Names . Ursa Minor , Saint Michael , or according to Hartsdorfius , one of Elisa's Bears , 2 Kings 2. 24. or the Wagon of Iacob , or Chariot of Ioseph , Gen. 45. 27. and 46. 29. Ursa Major , Saint Petres Fisher Boat , or according to Hartsdorfius , the other of Elisa's Bears , or the Chariot of Elias , 2 Kings 2. 11. Draco , The Innocents , according to Schillerus , according to Schickardus Draco Infernus . Bootes , Saint Sylvester as Schillerus ; as Schickardus Nimrod . Coma Berenices . The Scourge wherewith our Saviour was whipp'd , or according to Harsdorfius , Absolon's Head of Hair ; or Samson's according to Schichardus . Corona Septentrionalis sive Ariadne , Our Saviour's Crown of Thorns ; or according to Harsdorfius , Queen Hester's Crown , Hester 2. 17. Hercules seu Engonast , The three Kings or Wise men that came to worship , at our Saviour's Birth according to Schillerus , or according to Schickardus , Samson . Lyra , The Manger wherein our Saviour was laid according to Schillerus ; or as Harsdorfius hath fancied it , David's Harp , 1 Sam. 16. 23. Cygnus , The Cross of Christ according to Schickardus , to which Schillerus adds Saint Helena its ▪ Repertrix . Cassiopea , Saint Mary Magdalen , as Schillerus , as Harsdorfius Bathsheba . Cepheus , Saint Stephen , as fancied by Schillerus , or Solomon according to Harsdorfius ▪ Perseus cum Capite Medusae . David with the head of Goliah , according to Schickardus , according to Schillerus Saint Paul. Andromeda , The Sepulchre of Christ according to Schillerus ; Harsdorfius will have it to be Abigal , 1 Sam. 30. 5. Auriga sive Heniochus . Iacob the Patriark according to Harsdorfius , Schillerus transforms it into Saint Ierome . Ophiuchus sive Serpentarius . Sanctus Benedictus inter spinas , according to Schillerus , or Saint Paul and the Viper , Acts 28. 7. Sagitta , The Nails , and Lance that wounded our Saviour , according to Schillerus , Schickardus makes it the Arrow of Ionathan . Aquila , Saint Katherine Martyr , or according to Schickardus , the Ensign or Standard of the Roman Empire . Ganimides seu Antinous , Part of Saint Katherine . Delphinus , The Pitcher of the Canaanitish Woman according to Schillerius ; Harsdorfius makes it the Leviathan mentioned , Psalm 104. 26. Equuleus , Mystica Rosa ; Schiller . Pegasus , Saint Gabriel according to Schillerus ; Harsdorfius makes of it the King of Babylon mentioned , Ierem. 4. 13. Triangulum seu Delta , The Mitre of Saint Peter ( Schiller . ) or Emblem of the blessed Trinity ( Schickard . ) Southern Constellations Ancient . Old Names . New Names . Cetus , Saint Ioachim and Anna ( Schiller . ) or Ionas his Whale according to Schickardus . Eridanus , The Passage of the Israelites through the Red Sea ( Schiller . ) or the Brook Cedron ( Schickard . ) Orion , Saint Ioseph ( Schiller . ) or Ioshua , ( Schickard . ) Lepus , Gideon's Fleece , Schillerus . Canis Major , Tobias his Dog ( Schikard . ) or Saint David ( Schiller . ) Canicula seu Canis Minor , The Paschal Lamb. ( Schiller . ) Argo Navis , Noah's Ark ( Schiller . ) Hydra , The River Iordan ( Schiller . ) Crater , The Ark of the Covenant according to Schillerus ; or Ioseph's Cup , or that of Saul according to Schickardus . Corvus , Part of the Ark of the Covenant ( Schillerus ) or the Crow sent out by Noah , or that of Elias ( Schickard . ) Centaurus , Abraham and Isaac ( Schiller . ) Lupus sive fera Centauri , Iacob the Patriark ( Schiller . ) Ara , The Altar of Incense . Corona Australis , David's Crown according to Harsdorfius , 2 Sam. 11. 30. or Solomon's Crown according to Schillerus . Piscis Notius . The Barrel of Meal of the Widdow of Sarephtha , or according to Schikardus the Fish taken by St. Peter with a Piece of Mony in its Mouth , Matth. 17. 27. Southern Constellations lately discovered . The Names first given them . The New Names . Grus , Aaron the High Priest.   Phoenix ,     Indus , Iob.   Pavo ,     Apus ,     Camaeleon , & . Eve. Schillerus . Piscis volans ,     Triangulum , Christ's Cross.   Dorado cum Nube ; Toucan & Hydrus cum Nube . Saint Raphael .   The Planets . Old Names . New Names . Saturnus , Adam ,   Iupiter , Moses ,   Mars , Iosua ,   Sol , Christ the Sun of Righteousness , according to Schillerus . Venus , Saint Iohn Baptist ,   Mercurius , Elias ,   Luna , The Virgin Mary ,   We shall only add the Number of the Stars in the several Signs and Constellations observed by the bare Eye without the help of a Telescope , according to   Order of the Signs and Constellations . Ptolemy , Alphonsus , Copernicus , and Clavius . Griembergerus from Clavius , Tycho and Pifferus . Bayerus from divers others . Keplerus and Bulialdus . The Northern Signs of the Zodiack . Aries 18 22 29 23   Taurus 44 52 48 52   Gemini 25 30 31 30   Cancer 13 16 35 17   Leo 35 40 43 40   Virgo . 32 41 42 43 The Southern Signs of the Zodiack . Libra 17 20 15 20   Scorpius 24 24 29 27   Sagittarius 31 31 31 31   Capricornus 28 28 29 28   Aquarius 45 45 41 45   Pisces 34 40 37 42 The Northern Constellations . Ursa Minor 7 21 8 20   Ursa Major 35 57 32 56   Draco 31 30 33 32   Cepheus 13 13 17 12   Bootes 23 29 34 29   Corona 8 8 20 8   Hercules 28 31 48 31   Lyra 10 11 13 11   Cygnus 19 20 35 28   Cassiopea 13 26 25 45   Perseus 29 35 38 34   Auriga 14 27 32 27   Ophiuchus 29 24 30 56   Serpens 18 13 37 26   Sagitta 5 8 8 8   Aquila 15 12 32 12   Antinous 0 7 0 7   Delphin 10 10 10 10   Equiculus 4 4 4 4   Pegasus 20 23 20 24   Andromeda 23 26 26 26   Triangulum 4 4 5 4   Coma Berenices 0 14 0 15 The Southern Constellations . Cetus 22 25 27 25   Orion 38 62 49 62   Eridanus 34 39 42 39   Lepus 12 13 13 13   Canis Major 29 29 19 29   Canis Minor 2 5 8 5   Argo Navis 45 50 63 53   Centaurus 37 37 40 37   Lupus 19 19 20 19   Hydra 27 34 29 33   Crater 7 8 11 8   Corvus 7 7 7 7   Ara 7 7 8 7   Corona Austr . 13 13 13 13   Pisis Notius 18 17 12 17 Grus — — 13 13   Phoenix — — 14 15   Indus — — 12 12   Pavo — — 16 23   Apus — — 12 11   Apis — — 4 4   Camaeleon — — 8 10   Triangulum Austr . — — 5 5   Piscis volans — — 7 7   Dorado — — 7 7   Toucan — — 8 8   Hydrus — — 15 21 Sum Total of the Number of the Fixed Stars of   Magnitude Ptol. Griemb . Bayer . Kepler .   1 15 15 17 15   2 45 55 63 58   3 208 201 196 218   4 474 456 415 494   5 217 304 348 354   6 49 186 341 240   Obscure and Nebulous 14 08 03 13   Inform or Sporades In the Zodiack   45       Northern   200       Southern   81     In All 1022 1225 1709 1392 See more of the Number of the Fixed Stars hereafter under that particular Head. The Celestial Circles come next to be treated of ; for the fuller Understanding whereof , besides what is already delivered in the Annotations , take the following Cosmographical-Astronomical Synopsis , for the most Part according to Mersennus . A Cosmographical-Astronomical SYNOPSIS . PROP. I. THe Equinoctial Circle , parting both the Celestial and Terrestrial Globes , into two equal Portions is , divided into 360 Degrees , as every other Circle greater or lesser , by reason of the facile Division of this Number into a Moyety , a third , fourth , fifth , sixth , or eighth ; its sixth part being sixty , which admits of many more Divisions , without any Fractions . II. The Equinoctial , when the Sun is therein posited , makes the Dayes and Nights eaven , and divides the Sphere into the Northern and Southern Hemispheres , whose Poles are the Poles of the World ; fifteen Degrees of this Circle hourly rise on one part , and as many on the other hourly set ; so that one Degree thereof rises every four minutes of an Hour . Wherefore the Equinoctial is said to be the measure of the Primum Mobile . III. This Circle shows the Equinoctial Points , which happen twice in a year , at the Sun's entrance into Aries and Libra . It divides the Zodiack into two Moyeties , the Southern and the Northern ; and thence the Signs are distinguished into Southern and Northern . It is the Measure of Time , and shows what Declination the Stars , or the Parts of the Ecliptick have , either Northern , or Southern . Moreover in this Circle are observed the Ascensions and Descensions of the Zodiacal Signs . IV. A Line perpendicular to the Meridian Line represents the Equator , and so on the contrary : Which yet may be described without the Meridian Line , if a Right Line be drawn from a Stile or Gnomon by the Points of the Shadows Extremity , on the Day of the Vernal or Autumnal Equinox . For the Altitude of the Pole being given , the Altitude of the Equinox is likewise given , as being the Complement of the Quadrant of a Circle . As for example ; The Altitude of the Pole at London , is 51° . 32′ . Therefore the Altitude of the Equinoctial , and consequently of the Sun in the first degree of Aries or Libra , is , 38° . 28′ . And contrary wise , the Altitude of the Equinoctial being given , the Elevation of the Pole is likewise given . Moreover , the State of the whole Heaven and Earth , from the given Elevation of any one of these Circles may be known , provided the Longitude of the Place be known . V. The Equator in a right Sphere passes by the Zenith or Pole of the Horizon ; in a Parallel Sphere it is coincident with the Horizon , and is the Horizon it self . In an oblique Sphere it makes acute Angles with the Horizon , and in a right Sphere it makes Rectangles ; in which Position of the Sphere , all the Points of the Heaven dayly rise and set , excepting the Poles of the World. Wherefore to the Inhabitants in a right Sphere , there is perpetual Equinox , a double Summer and double Winter , and different Meridian Shadows , to wit , sometimes Northern , sometimes Southern . Hence they are called Amphiscii , or Amphiumbrae ; which happens likewise to those in an oblique Sphere , whose Vertex is between the Equator , and one of the Tropicks . VI. In an oblique Sphere , whose Vertex is in one of the Tropicks , the Equator is raised 66° . and ●… . and consequently the Pole 23° . and ½ . and the Polar Circles constitutes the greatest Circle of the alwayes-apparent , and the alwayes-latent . The Inhabitants of this Sphere have one Summer and one Winter , and one and the same Meridian Shadow , that is to say , alwayes to the North under the Northern , alwayes to the South under the Southern Tropick ; thence called Heteroscii , or Alteriumbrae . These three Spheres , that is to say , the Right , and the two last Oblique , are in the torrid Zone , which is terminated by either Tropick , and which the Equator cuts in the middle , as the Ecliptick does the Zodiack . VII . In an Oblique Sphere , whose Vertex is in the midst , between the Tropick and the Polar Circle , the Equator and the Pole have both equal Elevations of 45° . Hence the heat of the Summer is as great as is the cold of the Winter ; the higher the Equator is , the greater being the heat , and the cold more intense , by how much the Pole is more elevated . But in an Oblique Sphere , whose Vertex is in the Polar Circle , the Equator is elevated 23° . and ½ . and the Pole 66° . and ½ . and the length of the greatest Day there is 24 hours , by which the temperate Zone is terminated towards the Pole , as it is towards the Equator by the Tropick . VIII . The frigid Zone begins from the Polar Circle , in which the greatest Nights and Dayes are made so much greater , by how much the Vertex of the several Habitations therein approaches nearer to the Pole , until such time as it becomes a Parallel-Sphere . In which they in the Northern Parts have this privilege , that their longest day is seven dayes , and more , longer than the greatest day , which they in the South enjoy , by reason of the Sun 's longer stay in the Septentrional Signs , wherein he moves more slowly to the place of his Apogaeum in Cancer . To which if we add the Twilight ( which is made by the Sun eighteen Degrees depressed beneath the Horizon ) as also the Refractions , the Artificial Day with the Inhabitants of such a Parallel-Sphere will be nine Months and twelve Dayes . But on the contrary , they in the South have their Night seven dayes longer than they in the North. These are called Periscii , or Circumumbrae . IX . The Zodiack cuts the Equator in two opposite Points at 〈◊〉 Angles , whose Latitude extends to near 20° . through the midst whereof runs the Ecliptick ; so called because the two great Luminaries , the Sun and Moon , when in Conjunction , diametrically opposed to one another , directly under the said Line , are then eclipsed . X. The Ecliptick indivisible as to Latitude , obliquely intersects the Aequator in two Points ; which two Points of Intersection are called the Equinoctial Points . Of which that ( in the first Degree of Aries ) which gives beginning to the Northern Semi-Circle of the Ecliptick , is called the Vernal ; The other ( in the first Degree of Libra ) whence the Southern Semi-Circle of the Ecliptick begins , is called the Autumnal . Equinoctial Point ; The two Points of its greatest Declination from the Equator are called the Solstitial Points , whereof the Northern ( in the first Degree of Cancer ) is called the Summer Solstice ; the Southern ( in the first Degree of Capricorn ) is called the Winter Solstice . In regard of which the Signs in the Zodiack are said to be Descendant from Cancer to Capricorn , and Ascendant from Capricorn to Cancer , because the Sun ascends in these , and descends in those Signs . XI . The twelve Natural Signs , into which the Zodiack is divided , begin from the common Section of the Equator , the Equinoctial Colure , and the Ecliptick , proceeding Eastward ; the first of which is Aries , the second Taurus , &c. which order they call the Succession or Sequence of the Signs ; as the contrary Order the Precedence of the Signs : The Zodiack and the Ecliptick measure the Secondary Motions of the Planets , as the Equator does the First . The Longitude of the Stars is numbred in the Ecliptick , from the beginning of Aries , according to the sequence of the Signs , unto a greater Circle , passing by the Poles of the Ecliptick , and place of the Star ; as the Longitude of a Place on the Earth is reckoned in the Equator , from the first Western Meridian unto the Meridian passing by the Place proposed . XII . From the Ecliptick to the Poles are reckoned the Latitudes of the Stars . Which Latitude is an Arch of a great Circle passing by the Poles of the Ecliptick and Center of the Star , intercepted between the Ecliptick and the Star. Those Arches are called the Circles of Latitude . The Points between the Equator and the Ecliptick , in respect of the Equator , are Northern ; in respect of the Ecliptick , Southern , or contrariwise . XIII . The Ecliptick contains the Place of all the Stars . For a Star is said to be in that Degree of the Ecliptick , through which the Circle of Latitude of the said Star passes : So the Star●… being in the Solstitial Colures are said to be in the first Degree of Cancer or Capricorn . By which reason , all the Stars in the Firmament are referred to some one of the twelve Signs . XIV . The Colures , passing by the Poles of the World , and the four Cardinal Points of the Zodiack , intersect each other at Spherical right Angles in the Poles of the World. They are so called , because in an oblique Sphere they seem mutilate and defective , since one part of them is alwayes depressed beneath , whilst the other is elevated above the Horizon . One of th●…se is called the Equinoctial Colure , which passing by the Points of the Intersection of the Equator and Ecliptick , constitutes the Equinoctial Points of Aries and Libra . The other being the Colur●… of the Solstices , dividing the Equator at right Angles in the Points wherein the Sun commences Winter and Summer , that is to say , in the first Degrees of Cancer and Capricorn , measures the Sun 's greatest Declinations , hath in it the Poles of the Zodiack , and shows the Distance of th●…se Poles from the Poles of the World. There may be likewise infinite Colures supposed , for the better demonstrating the particular Declinations of the Stars from the Equator . XV. The Meridian , in any Position of Sphere whatsoever , makes Mid-day and Mid-night , and hath in it the Zenith and Nadir Points , directly opposite to one another . The first Meridian is vulgarly placed in the Fortunate Islands , or the Canaries , by others in the Islands called the Azores . There are reckoned 36. Meridians , or rather 18. since the same Meridians of one Hemisphere , may serve the other Hemisphere likewise , each being distant ten Degrees from one another . But Geometrically speaking , there are as many Meridians as there are Vertical Points ; as there are on Earth so many Horizons , as there are divers Points upon the Terrestrial Globe . They who assign a Meridian to every Degree , make of them 180. XVI . The Meridian to those that travel directly North and South is still the same , as to Latitude . It shews likewise the greatest Altitude of the Sun and Stars , their distance from the Equator , the Elevation of the Pole , and measures the Latitude of all Places upon Earth . Of which in the two following Propositions . XVII . The Latitude of a Place is numbred in the Meridian from the Equator towards either of the Poles , and shews how much every Point is distant from the Equator , one Pole being elevated the other depressed . The Latitude of any Place being the Arch of a Meridian , intercepted between the Zenith of the said Place and the Equator , equal to the Elevation of the Pole above the Horizon . Which Elevation is an Arch of a Meridian , drawn from the Horizon to the Pole of the World , XVIII . As the Latitude of the Earth is numbred in the prime Meridian , or any other more oriental ; so the Declination of the Stars may be numbred in those Meridians , which are therefore called the Circles of Declination , because they shew how far the Fixed Stars , or Planets are distant from the Equator , or decline from it to either of the Poles . They are likewise called Vertical , inasmuch as passing by the Vertex of any Place , and descending perpendicularly by each Point of the Horizon , they measure the Altitude of the Stars above , or their Depression beneath the same ; and in Arabick they are called Azimuths , because they shew in what part of the World any Star rises or sets . The beginning likewise of the Astronomical Day is computed from the Meridian Circle . XIX . The Astronomical , or true Horizon divides the Sphere of the World into two equal Parts , that is to say , the upper , or the visible , and the lower or invisible Hemisphere , whose Centre is the same with the Centre of the World , and its Poles , the Zenith and Nadir Points . The Physical or sensible and visible Horizon , equidistant from the Astronomical , is that Part of the Earth as far as can be discerned by Sight , whose Semidiameter in an even Plane ( the Eye being placed at six foot height above the Level ) is about a League ; but if the Eye be elevated a League high , then the Semidiameter of the sensible Horizon will be 51. Leagues . XX. The Horizon concurs to the stating of all the forenamed Spheres , that is to say , either Right , Oblique , or Parallel ; whence it is denominated and distinguished into Right , Oblique and Parallel . It determines the rising and setting of the Stars , the Ortive and Occasive Amplitudes , beginning from the Eastern and Western Equinoctial Points , shews the Quantity of Day and Night , and the four Cardinal Points , East , West , North and South ; as likewise the Quantity of the two Circles parallel to the Equator and Tropicks , described from the Poles of the World , touching the Horizon in a Point ; of which that drawn from the Pole , to us conspicuous , is termed the greatest of the all-wayes-apparent , the other , opposite to it , the greatest of the not-apparent , that is to say , the Artick and Antartick Circles . XXI . The Circles parallel to the Horizon , which shew the Altitudes and Depressions of the Stars , are in the Astrolabe called Almicantarah , or Circles of Progression ; among which is numbred the Crepuscular Circle , or Circle of Twilight , which is Parallel to the Horizon , and depressed beneath it eighteen Degrees . Thus much of the Great Circles ; the Lesser follow . XXII . The Tropicks are lesser Circles Parallel to the Equator ; from whence they are in this present Age distant 23. Degrees and ½ , which Distance , according to the diversity of Times is diversly computed ; the variation hitherto being reckoned 24′ . These two Tropicks shew the Sun 's or the Ecliptick's greatest Declination from the Equator ; the Tropick of Cancer it 's Northern , the Tropick of Capricorn its Southern ; the former shewing the Sun's greatest , the latter its least Meridional Altitude ; this , the longest Day and shortest Night in the Summer Solstice ; the other , the longest Night and shortest Day in the Winter Solstice . Which said Quantities of Day and Night are not shewn by the Tropicks in a Right , or an Oblique Sphere beyond 66° . and ½ , of the Pole's Elevation . For in the first the Diurnal and Nocturnal Arches are alwayes equal ; in the latter , the said Quantities are shown by the Ecliptick , and in the Altitude of 66° . and ½ . One of the Tropicks is raised wholly above the Horizon ; the other is wholly depressed beneath it . XXIII . The Polar Circles are made by the Diurnal Conversion of the Poles of the Ecliptick about those of the Equator , from which they are distant 23° . and ½ , being the same with the distance of the Solsticial Points , or the Tropicks from the Equator . From which the five Zones may easily be apprehended , as being contained within four Circles , Parallel to the Equator . That which is called the Torrid Zone is between the two Tropicks ; the two Temperate Zones are between the Tropicks and the Polar Circles ; the two Frigid are comprehended within the two Polar Circles . XXIV . The Parallels are Circles on either side the Equator , Parallel thereto ; being seated at such a Distance from One Another , that the greatest Day of one differs from the greatest Day of another Parallel by the Quantity of one Quarter of an Hour , they are reckoned on either side of the Equator to the Polar Circles , or the 66 th Degree of the Poles Elevation 24. In All 48. XXV . The Climates are Spaces Parallel to the Equator , containing three Parallels , the Middlemost dividing the same into two Parts : The Latitude of each Climate from its Southern to its Northern Limit , is of that Extent , that the longest Day encreases half an Hour . The Climates are denominated from the chief Cities and Places by or through which they pass , as the first by Meroe , the second by Alexandria , the third by Rhodus and Babylon , the fourth by Rome , Corsica and the Hellespont , the fifth by Venice , the sixth by Podel●…a , the seventh by W●…teberg , the eighth by Rostoch , the ninth by Ireland , the tenth by Bohuse in Norway , the eleventh by Gothland , the twelfth by Wyburgh in Finland , the thirteenth by Arotia in Sweden , the fou●…eenth by the Mouth or Outlet of the River Darecally in Sweden , and the rest by other places of Norway , Sweden , Alba Russia , and the Adjacent Islands . And these are the Northern Climates ; the Southern are distinguished by the Title of Anti , as Anti-Meroes , Anti-Alexandrias , &c. in regard of their Opposite Position to the Northern Climates . But for the better understanding of the Climates , and what appertains to them see the following Tables divided into five Columns , the first shewing the Number of the Parallels , the second of the Climates , the third the longest Day in every Parallel , the fourth the Elevations of the Pole , or Latitudes of the respective Regions , the fifth the Amplitude of the Climates . Parall . Climates Longest Day in each Par. Altitude of the Pole Amplitude of each Cli. Hor. Min. Degr. Min. Degr. Min. 1 I 12 15 4 18 0 0 2   12 30 8 34     3 II 12 45 12 43 7 50 4   13 00 16 43     5 III 13 15 20 33 7 3 6   13 30 23 11     7 IV 13 45 27 36 6 9 8   14 0 30 47     9 V 14 15 33 45 5 17 10   14 30 36 30     11 VI 14 45 39 20 4 30 12   15 00 41 12     13 VII 15 15 43 32 3 48 14   15 30 44 29     15 VIII 15 45 47 20 3 13 16   16 0 49 1     17 IX 16 15 50 53 2 44 18   16 30 51 58     19 X 16 45 53 17 2 17 20   17 0 54 29     21 XI 17 15 55 34 2 0 22   17 30 56 37     23 XII 17 45 57 34 1 40 24   18 00 58 26     25 XIII 18 15 59 14 1 16 26   18 30 59 59     27 XIV 18 45 60 40 1 13 28   19 0 61 18     29 XV 19 15 61 53 1 1 30   19 30 62 25     31 XVI 19 45 62 54 0 52 32   20 0 63 22     33 XVII 20 15 63 46 0 44 34   20 30 64 6     35 XVIII 20 45 64 30 0 36 36   21 0 64 49     37 XIX 21 15 65 9 0 29 38   21 30 65 21     39 XX 21 45 65 35 0 22 40   22 0 65 47     41 XXI 22 15 65 57 0 16 42   22 30 66 6     43 XXII 22 45 66 14 0 11 44   23 0 66 20     45   23 15 66 25 0 6 46   23 30 66 28     47 XXIII 23 45 66 30 0 0 48   24 0 66 31     And here it is to be noted , that the Parallel Circles grow lesser and lesser , and the Climates narrower and more Contracted , by how much they recede from the Equator toward the Poles ; for one Degree , which in the Equator contains 51 German miles , contains but 14 of those Miles in the Latitude of 21 Degrees , and but 13 in the Latitude of 30. 12. in 37. 11 in 48 and ½ , and 6 in 66 Degrees of Latitude . Whence it is easie to compute how many German Miles is contained in every Parallel Circle ; For the Number of Degrees in any Parallel , viz. 360. being multiplied by the Miles comprized in every Degree , will give the number of Miles sought . It rests that something be said of the several Terrestrial Inhabitants , as they are differenced and distinguished by reason of their Situation and their Shadows . As to their Situation they are distinguished into Perioeci , Antoeci and Antipodes . The Perioeci are those which inhabit under one and the same Parallel and Meridian , but in Points directly opposite . These have the same Elevation of the Pole ; Equal Arches both Diurnal and Nocturnal ; the same Appearance of the Stars and Constellations , the same Occultations rising , and setting , Night and Day , but at contrary times , have Winter and Summer alike ; the same Meridian Shadows ▪ The Antoeci are those who inhabit under equal and opposite Parallels ; that is equally distant from the Equator Southward and Northward under a Portion of the same Meridian , to these the Elevation of the different Poles is equal , as the opposite Diurnal and Nocturnal Arches ; the same Appearance of the Stars and Signs , but opposite ; the same Occultation , rising , and setting : When it is Summer to These , it is Winter to Those , and Spring to the one , when it is Autumn to the others ; they have likewise equal Meridian Shadows , but diversly and oppositely projected . The Antipodes are those who dwell not only under equal but opposite Parallels , and in places diametrically opposed the one to the other ; the Feet of the one being directly against the Feet of the other . Insomuch that a right Line drawn from the one to the other must necessarily pass through the Centre of the Earth . therefore the same Accidents which happen to the Antoeci , happen likewise to the Antipodes . Only this is proper to the Antipodes , that they have one Common Horizon , and different Hemispheres ; have likewise different and opposite Zeniths : What rises to the one sets to the other ; what is apparent to these is hidden to those . The Noon of one is Midnight to the other . As to their Shadows they are distinguished into Amphiscii , Periscii , and Heteroscii . The Amphiscii are those who inhabit the Torrid Zone within the Tropicks , especially near or under the Equator . These have their Meridian shadows at different times of the year diversly projected ; now to the North , now to the South , according to the Course of the Sun on this , or that side of the Equator : when the Sun is in their Zenith they have no Noon Shadow at All. They have two Summers and two Winters . The Periscii are they which inhabit the Frigid Zones , especially near the Poles of the World , whose Shadows are carried round about them upon the Plain of their Horizon . The Heteroscii are they which inhabit the Temperate Zones ; they in the Northern temperate Zone having their Meridian Shadows alwayes projected toward the North Pole , those in the Southern , alwayes to the South . And this may suffice to compleat this Cosmographical-Astronomical Synopsis ; to which yet for the further Satisfaction of the more Curious Reader , we have thought fit to add the Twelve Propositions of Theodosius , de Habitationibus , in English. THEODOSIUS De Habitationibus . PROPOS . I. TO those that inhabit under the North Pole , one and the same Hemisphere of the World is alwayes apparent , but the other Hemisphere is alwayes hidden : Nor do any Stars either rise or set to them ; but those which are in the apparent Hemisphere are alwayes conspicuous , and contrarily those in that , which is hidden , never appear . Prop. II. To those that inhabit under the Equinoctial Circle , all the Stars both arise and set : And are moved in equal time [ of twelve hours ] above the Horizon , and beneath it . Prop. III. In every place within the middle Zone , the Zodiack Circle is at some certain time of the Day at right Angles to the Horizon of the place . For the Circle parallel to the Equator , drawn through the Vertex or Zenith of the Place , cuts the Zodiack Circle in two Points . When therefore the Point of either Intersection is co-united with the Zenith , then the Zodiack Circle passes through the Poles of the Horizon , and therefore , by the XV of the first of Theodosius Sphaerics , cuts the Horizon at right Angles , and this is done twice in one Diurnal Revolution . But to those inhabiting under either Tropick , only once in a day , that is , when the Solstitial Points in which the Zodiack Circle touches both the Tropicks come to the Zenith of that Place . Prop. IV. To those whose Zenith is as far distant from the Pole , as the Tropick from the Equator , six Signs shall at once happen to rise and six to set , in one Diurnal Revolution . That is , to those whose Zenith is in the Arctick or Antartick Circle . For whereas the Poles of the Zodiack are carried in the Peripheries of those Circles , therefore in one Diurnal Revolution the Pole is once co-united with the Zenith , that is , the Pole of the Zodiack with the Pole of the Horizon : And therefore the Zodiack also is co-united with the Horizon . Which Co-union is made in an instant , and after that instant the Zodiack is forthwith divided into two parts by the Horizon ; so that in an instant one Semicircle of the Zodiack rises , and the other Semicircle sets . Prop. V. To those Inhabiting under the Equinoctial Circle , the Meridian shall cut above the Horizon the Semicircle of the Zodiack into two equal Parts , when the Points of Contact of the Tropicks and Zodiack come to be in the Horizon , and then also the Zodiack shall be at right Angles to the Horizon . For , the Horizon passing then through the Poles of the Tropicks , and the Points of the Contact of the Tropicks and Zodiack shall ( by the VI. of the Second of Theodosius his Sphericks ) pass likewise through the Poles of the Zodiack , and therefore ( by tbe XV. of the First ) ●…all cut the same at right Angles . And so likewise the Zodiack shall passby the Poles of the Horizon , by which the Meridian also passes . From whence the Arches as well of the Meridian as of the Zodiack , Intercepted between the Pole of the Horizon , and the Horizon , are Quadrants . Prop. VI. To those inhabiting under the Equinoctial , all Semicircles of the Zodiack arise in equal time , as likewise do their opposite Peripheries . For there , every Semicircle of the Zodiack arises with the Diurnal Arch of its beginning ; ( but by the second of this Present ) all the Diurnal Arches are Semicircles , by which is manifest the first part of this Proposition : the other part is clear , seeing not only the opposite Peripheries of the Zodiack , but those likewise equally distant from the Equinoctial Point ascend , with equal Arches of the Equinoctial . Prop. VII . To those whose Horizons differ by a more Easterly Position ; the Stars neither arise together , nor set together , but by how much sooner they arise to those who live more Easterly , by so much sooner do they set . For the Horizons of such Places , by reason of the equal Altitudes of the Pole , touch the same Parallels of the Equator , wherefore ( by the XIII . of the Second of Theodosius's Sphericks ) the Arch from any Parallel of the Semicircle of the Horizons interjected , as well between the Places Eastward , as those Westward , are the same . Therefore every Star in a place Eastward by the same Arch , anticipates its rising , and thence its setting , and consequently in the same interval of time . Prop. VIII . To those inhabiting under the same Meridian , whatever Stars are between the greatest of the alwayes apparent Parallels and the Equinoctial , appear longer above the Horizon to those inhabiting Northward , then they do to those inhabiting Southward . And how much sooner they arise to those inhabiting Northward , so much later they set . But those Stars which are between the greatest of the Parallels alwayes latent , and the Equinoctial , appear longer above the Horizon , to those inhabiting Southward , then they do to those inhabiting Northward ; And how much sooner they rise to those inhabiting Southward , so much later they set . For to one travelling toward the apparent Pole , the Diurnal Arch of a Star declining that way from the Equator , increases ; and to one going toward the Pole that is depressed and unapparent , the Diurnal Arch of a Star , declining thitherward increases likewise : But by collating the Arches increasing on either side , that is to say , towards the East , or towards the West , the rest of the Proposition is manifest . Prop. IX . But if the Horizon's be neither under one Parallel , nor under the same Meridian , there will follow only an Inequallity of the Arches raised above the Horizon , after the manner as before expressed , but no Anticipation of risings or settings . This , as the premised , is manifest , by reason of the greater or lesser inclination of the Horizon . Prop. X. To those inhabiting under either Pole , the Sun is carried constantly for six Moneths above the Horizon , and as long underneath it . This appears by the first Propos. of this present Treatise . Since one half of the Zodiack is alwayes apparent , and the other alwayes latent , either of which by the Sun in near about six Months time is run through ; neither does the difference of the Sun's Motion , occasioned by his Excentricity , here come to be considered , for the Motion of the Sun is alwayes supposed equal in reference to the Arks of his first Motion . Prop. XI . To those going from the Pole toward the Artick or Antartick Circles , this constant stay of the Sun either above or under the Horizon , for six Months , grows lesser and lesser , until it be reduced to the space of twenty four hours either under the Artick or Antartick Circles . For , the Horizon of those Habitations , touches two Parallels of the Equator greater than the Tropicks , which on either side cut from the Zodiack two equal Peripheries ; And that Periphery which the Parallel alwayes apparent cuts off , never sets , and that which the alwayes latent abscinds , never rises . Prop. XII . To those inhabiting under the Artick or Antartick Circles , the longest Day is 24 hours , and the Night but an instant ; and on the contrary , the longest Night 24 hours , and the Day but an instant . The other Arks increase and decrease until they come to the equality of the Equinox . The Order of the Poem , leads us in the next place , after having treated of the several Mundane Systems , the Additional Constellations , the Celestial Circles , and the Appendages thereunto ( delivered , and explained in the former Discourses , and the foregoing Synopsis ) to consider with our Manilius , what yet remaens to compleat the Universe , and with Him , — To shew what does dispense Throughout the Whole , or Light , or Influence . And these by our Poet are reckoned to be , besides the fixed Stars ; the Luminaries , and the other Planets , fiery Meteors and Comets . OF THE Fixed STARS . HAving already treated sufficiently both in our Notes , and in this Appendix of the Fixed Stars , as reduced into Signs and Constellations ; We shall now consider them distinctly , and apart , as they are several Mundane Bodies disseminated and dispersed through the Immense Space of the Etherial Region , which We call Heaven . They are said to be fixed , because they alwayes keep ( at least seemingly ) the same invariable Distance from one another , and from the Ecliptick , as if they were so many Studs of Gold fixed in the Chrystal Firmament , as Empedocles and Anaximenes ( according to the Testimony of Plutarch De Placit . Philosoph . l. ●… . c. 13. ) held . Hence the Sphere wherein they are conceived to be ranged , is called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. inerrans in regard of the unalterable Order observed in their Intervals or Interstitia . And for this Reason chiefly , Ricciolus conceives the Multitude of the Fixed Stars ( as it were an Army drawn up in Battle Array ) might be called the Militia of Heaven . The Particulars to which We shall confine our Enquiries , touching these Glorious and splendid Bodies , shall be These following : First , Their Substance . Secondly , Their Light , Colour , and Scintillation . Thirdly , Their Number . Fourthly , Their Figure . Fifthly , Their Magnitude . Sixthly , Their Place and Distance from the Earth , or rather the Sun. As to their Substance , the Opinions of the Ancients are various , Zoroaster maintained the Stars to be of a fiery Nature ; Thales held them to be Earthly , yet withall fiery : Empedocles maintained them to be siery , and to consist of that Fire which the Aether containing in it self , struck forth in its first Secretion . Anaxagoras affirmed ( but very extravagantly ) that the Ambient Aether being of a fiery Nature , by the Swiftness of its Motion snatcheth up Stones from the Earth , which being set on Fire become Stars , and are carried from East to West . Diogenes conceived them to be of the Substance of Pumice Stones set on Fire , and to be the Spiracula or breathing Holes of the World. Plato with more Reason held them to be for the most Part of a fiery Nature , yet to admit of the mixture of other Elements , as it were Cement , to knit and consolidate them . Xenophanes supposed them to be Clouds , set on Fire in the manner of Coals , quenched in the Day Time , and in the Night rekindled . Heraclides and the Pythagoreans held every Star , to be a World by it self , existing in the Infinite Etherial Space , and containing an Earth , an Air and a Sky ; which Opinion is found in the Works of Orpheus , for his Followers affirmed the Stars to be so many Worlds . Aristotle and his Followers maintain them to be of the same Substance as the Heavens , but only more condensed ; and to be simple Bodies without the Mixture of any Elements . The Stoicks , and with them our Manilius , make them to be of a fiery Substance . Others conceive them to be composed of the same Matter as Exhalations and Vapours , and consequently to consist of a Substance partly Aqueous , partly Aerial , of which see Pliny l. 2. c. 9. Petrus Comestor , Hugo Victorinus , and Eugubinus . Of all These the most celebrated , and most probable Opinion , is , that the Stars are fiery Bodies . An Opinion which wants not the Authority of the Ancient Christian Church to back it , which ( in Hymn , seria secunda ad Vesper . of which Saint Ambrose is held to be the Composer ) sings after this Manner . Immense Caeli Conditor Qui mixta ne confunderent Aquae fluenta dividens Coelum dedisti Limitem Firmans Locum Coelestibus Simulque Terrae Rivulis Ut unda flammas temperet . Terrae solum nec dissipent , &c. Where we find the Reason why the Waters are placed above the Heavens , viz. to restrain and temper the excessive fervor of the Sun and Stars . Again in Hymn . fer . quarta ad Vesper . the same Church thus sings . Coeli Deus sanctissime Qui Lucidum Centrum Poli Candore pingis igneo . Of the same Sentiment are most of the Fathers , not only of the Latin , but the Greek Church , as Cyrillus Hierosolimitanus and Caesarius , who speaking of the Firmament , sayes , recepturum erat Subjectorum Luminarium Splendorem , Solem inquam , ( & Lunam ) & reliquum Astrorum Caetum , ex Igne Naturam habentem . Theodoretus likewise to the same Purpose ; Bifariam Deus Omnium divisit Aquarum Naturam , & quasdam sursum collocavit , quae suo liquore ▪ ac frigiditate non sinerent corrumpi Firmamentum ab Igne Luminarium . St. Chrysostom is positive for the fiery Nature of the Stars , with whom concurr Gregory Nissen . Procopius , and Anastasius Sinaita ; Conform to whose Opinions is that of Tertullian , St. Ambrose , St. Augustin , Arnobius , Lactantius , Anselmus , Alcuinus , Beda . Conclude we therefore , induced as well by the Authority of these Ancient Fathers , as perswaded by the concordant Sentiments of divers eminent Modern Philosophers , and Astronomers , that the Stars are compound , and not simple Bodies , made up of Elementary Matter , formed into fiery Globes , and consisting ex Solido & liquido , as this Terraqueous Globe of ours , and consequently Subject to Corruption and Alteration . See Franciscus Patricius l. 15. Pancosmias ; Ricciolus Almagest Nov. l. 9. Sect. 1. Scheinerus in Rosa Ursina l. 4. Part. 2. c. 22 , 23 , & 24. Kircherus in Itinerar . Extatic . & Schottus upon Him. From whom the more Curious Reader may receive further Satisfaction in his Enquiry touching the Igneous Nature and Substance of Those tremulous Tapers of the Skies Which burn at the Dayes Obsequies . Resplendent Sparks of the first Fire ! In which the Beauty We admire And Light of those eternal Rayes , The uncreated Mind displayes . Visible Prints by which We trace Time in it's Invisible Race ! Pure bright Idaea's that direct To the first Cause our Intellect . Iewels that deck with their rich Light The Sable Garment of the Night , Mirrors ▪ in whose clear polish●…d Faces , Nature sees hers : Th' World's Looking-Glasses . To express them in some of those Poetical Characters , which the Ingenious Marino hath given of them . The next thing We are to take Notice of is Their Light. As to their Light , that which is chiefly to be considered , is , whether it be innate , given them by God at their Creation , or Mutuatitious , borrowed from the Sun ? The latter is maintained by Metrodorus in Plutarch de Placit . Philosoph . l. 2. c. 17. with whom concurr Albategnius and Vitellio , and divers others both Philosophers and Astronomers at this Day . But the first Opinion seems to carry more of Truth in it , and is by Macrobius asserted in Somn. Scip. l. 1. c. 17. where he affirms Omnes Stellas ( i. e. fixas ) Lumine lucere suo , quod illae supra Solem locatae in ipso purissimo Aethere sunt ; in quo Omne quicquid est , Lux Naturalis & sua est . And this seems consequent to what hath already been declared touching their Igneous Nature ; for Fire cannot be without Light ; and indeed it appears altogether improbable that the Sun should illuminate the Fixed Stars , seeing as Bulialdus ( in Astronom . Philolaic . l. 1. c. 11. ) observes , the Sun's Diameter if beheld from Saturn would not appear greater than 3′ . 24″ . and therefore must needs afford too weak and extenuated a Light sufficiently to illustrate even that Planet , much less is it able to give Light to the Fixed Stars removed to so great a Distance beyond Saturn . Wherefore with Aristarchus Samius de Systemate Mundi ( if at least that Piece revived by Roberval , and published by Mersennus in Observat. Physico-Mathemat . be genuine ) We may reasonably imagine each of the Fixed Stars to be the Head and chief Part of a distinct Mundane System ; as the Sun is the Head and chief Part of our Visible System , and as the Sun hath several Planets constituted and carried about him ; so likewise every one of the Fixed Stars hath other Mundane Bodies like Planets disposed and moving about them , though not to be discerned by us by reason of their great Distance from our Earthly Habitation . And accordingly Galilaeo ( Dialog . 3. System . Cosmic . ) doubts not to assert that the fixed Stars are so many Suns , conform and like unto this Sun of ours ; serving to illuminate the innumerable other Planetary and Lunary Bodies within their respective Systems ; and there fore indued with innate and Original Light. Of the same Opinion is Antonius Maria de Reitha ( in suo Radio Sydereomystico p. 177. ) with whom Ricciolus ( Almagest Nov. l. 6. c. 2. ) concurrs , where he sayes , Mihi longe Probabilior horum Opinio videtur ( Bruni Galilaei Renati Des Cartes & Reithaei ) quia magis congruit Opisicis Numinis Majestati , ut non unicam Stellarum à se ipsa Lucentem , sed plures instar Solis accenderit ; Nec alium sui Luminis fontem agnoscerent quam omnium Luminum Patrem , Deum . See to this Effect more fully , Gassendus Syntagmat . Physic. part . 2. l. 4. c. 4. Kircherus Itinerar . Extatica Dialog . 1. c. 9. Hevelius in Cometograph . l. 7. and Otto de Gueriek l. 7. De vacuo spatio , where he treats , De Stellis Fixis . As to Their Colour . It is visibly various according to the Difference of their Light , attempered by the divers Constitution of their Matter or Substance ; some appearing of a ruddy , others of a gold colour ; some of a silver white , some pallid , others of a leaden hue ; whence some have made an Estimate of their Natures , and ranged them under the several Planets , of whose qualities they conceived them to be participant , according to the proportion they carry of Resemblance in their Colours , as for Example ; of the Nature of ♄ , they reckon Propus , and that in the Belly of the Southern Fish , and in the Belly and Tail of Cetus ; of the Nature partly of ♄ , partly of ♃ , they reckon that in the right shoulder of Cepheus , and in his left Foot , and those in the Girdle of Orion , Of the Nature of ♄ and ♂ , the first Star in Anes , that in the Beak of the Crow , and in the Head of Ophiu●…hus . Of ♄ and ♀ the Pole Star , those in the Head of the Dragon and Medusa , those in the Breast of Cassiopaea and Hydra , in the Side of Perseus , that in the Wing of Virgo , called Praevindemiarix , and in the Back and Tail of Leo. of ♄ and ☿ , those in the left shoulder of Bootes , in the Belly of the Hare , and in the Northern Scale of Libra . Of the Nature of ♄ , they count those in the Nodus or Commissura Piscium , of the Nature partly of ♃ , partly of ♂ . Arcturus , the Eagle and the Thigh of Pegasus , Regulus or Cor Leonis , Syrius and Cor Scorpii . Of the Nature of ♃ and ♀ , that in the Head of Andromeda , in the Thigh of Aquarius , and Achar Nahr sive ultima fluminis Orionis . Of the Nature of ♄ and ☿ , that in the Mouth and Shoulder of Pegasus , and the Southern Scale of Libra . Of the Nature of ♂ , the three in the Tail , and the four in the side of the greater Bear , Aldebaran , the Hyades , and Pollux ( one of the Twins . ) Of the Nature of ♂ and ☉ , the Aselli , and Oculus Sagittarii . Of the Nature of ♂ and ♀ , Spica Virginis . Of the Nature of ♂ and ☿ , the Head of Hercules , the Goat with the Kid , and those in either Shoulder of Orion . Of ♂ and ☽ , the Pleiades , and those in the Praesepe or Manger . Of ♀ , that in the Navel of Andromeda . Of ♀ and ☿ ; that in the shoulder Blade of Andromeda , those in the Lyra , in Corona Guossia in the Beak and Tail of the Swan , the Cup , and Fomalhaut . Of the Nature of ☿ , Procyon or the lesser Dog , as by Schikardus ( in Astroscopio ) we find them ranged and distinguished . Their Scintillation . Is that Pathos by which they are particularly distiguished from the Planets , for the Planets have no such Vibration , twinckling or glimering of Light ; but generally all the Fixed Stars , more or less ; and at sometimes more than at others , especially ( flante Euro ) while the wind blows ●…asterly , as Schickardus ( in Astroscop ) observes . The Cause of this their Scintillation is variously discoursed of , both by Philosophers and Astronomers . Aristotle among the Ancients ( l. 1. poster . c. 13. ) assigns the cause thereof to their Remoteness from our sight , by which they are weakly , and as it were by a trembling weariness reached , which Opinion Pontanus following , thus asserts the same in his Urania l. 2. Scilicet alta illis Regio , sedesque repostae , Quo postquam advenit de fesso Lumine Visus , Defessus tremit ipse , tamen tremere ipsa videntur . But this Reason is not at all convincing , for then Iupiter and Saturn , by reason of their great Distance should in some Proportion affect our Sight with such a kind of Tremor or Scintillation ; which yet we find they do not in their greatest Altitude . Blancanus ( in Sphaera Mundi ) ascribes the Cause thereof only to Refraction ; and therefore ( sayes he ) Syrius and Procyon twinckle or glimmer more than any of the rest , because they never ascend beyond 45° . above the Horizon : But then why does not Iupiter which is nearer to us , ( especially when within the Limits of Refraction ) do the like ? Schikardus is much of the same Opinion , and conceives this Phaenomenon to arise from the unequal Superficies of the fluctuating Air or Medium , as Stones in the Bottom of a River by the rapid Course of the Water , seem to have a kind of tremulous Motion , which is only in the crisped and uneven Undulation of the Stream . But if this Reason were true , not only the Fixed Stars , but the Planets , nay the Moon it self would be liable to the like Scintillation . Gassendus more probably conceives this Scintillation of the Fixed Stars to proceed from that Native and Primigenial Light they are indued with , like that of the Sun , sparkling , and casting forth ●…uch quick darted Rayes , as our Weaker Sight cannot behold without that trembling 〈◊〉 . To which likewise may be added the most swift and quick Motion of theirs about their own Axes , by that means making a more suddain and nimble variation in those radiant Objects than the Eye can pursue . From which Opinion yet the learned Scheinerus in his Mathematical Disquisitions clearly dissents . The Scintillation of the Stars ( sayes he ) is not their proper Revolution or C●…nvolution not any intern exestuating Commotion : No tremulous revibrating of the Sun beams proceeding 〈◊〉 their first or second Motions ; no unquiet or unequal Ejaculation of their Proper Rad●…i ; no ●…remor of the wearied Sight ; not any of These , nor all of These ; but the only and sole Intercision of their several Species falling upon the Eye , occasioned by the unquiet Intercursation of Vapours variously affected . But this Reason of his will not satisfie the more Curious Hevelius , who yet allows that of their Circumgyration about their proper Axes , instanced by Gassendus , yet only as an adjuvant not the sole Cause of their Scintillation , he imputing it rather to a constant Evibration of Lucid Matter , or a continual Exspiration of fiery Vapours and Effluvia from those Celestial bodies , in the same manner as we perceive those fulgurations and Ebullitions in the Body of the Sun , which by how much the grosser , and in greater plenty they are ejaculated , by so much the greater and more signal Scintillation is caused by them . And with this Reason , and that of Gassendus we may reasonably rest satisfied , until further Observation and Inquisition shall produce one more convincing . As to Their Number . If we look to those only which are most notable and visible , as being reduced to the six Vulgar Degrees of Magnitude , we shall find them according to Ptolemic's Computation to amount to but 1022. Pliny yet ( l. 2. c. 4. ) reckons them to be 1600. But if we reflect upon the absolute Number of all the Stars in the Firmament , we may conclude them ( though not with Iordanus Brunus to be infinite yet ) to be innumerable , at least by humane Calculation , either as looked upon by the bare Eye only , or by the Help of a Telescope ; by the means of which last Galilaeo ( in Nuncio Sidereo ) reports , that he discovered in the Cloudy Star in Orion , no less than 21. others ; in the Nebulous Star in the Praesepe , or Manger 36. In the Asterism of the Pleiades above 40. In the space between the Girdle and Sword of Orion , no fewer than 80 , and within little more than one Degrees Space in the Constellation of Orion above 500 Stars , by which numerous Discovery he was deterred from making out and describing that Constellation , which he had particularly intended to have done . Reitha likewise ( in suo Radio Sydereomystic . p. 197. ) affirms that he observed in the same Constellation above 2000. Stars . Whereupon Ricciolus thus argues , that if the Constellation of Orion take up in the Heavens the space of 500 square Degrees , as it is found to do , and that every square space whose side is but two Degrees , shall contain no less than 500 Stars , according to the observation of Galilaeo before mentioned , there will be found in the whole Constellation of Orion , at least 62500 Stars , whereas look'd upon by the Bare Eye only there appear not therein above 63 Stars . According to which Proportion if the rest of the Constellations were examined and the Difference computed of the number of the Stars appearing by the Telescope over and above those discerned by the bare Eye ; there might be reckoned above Ten hundred thousand Stars , besides those in the Via Lactea . Nay , if one should reckon them above twenty hundred thousand , Mihi quidem nihil inopinabile finxerit ( sayes Ricciol . Almagest . Nov. Tom. 1. l. 6. p. 413. ) Some of the Iewish Doctors reckon not above 12000 Stars in all , but those of the Cabala , no less than 29000 Myriads , which Number Schickardus conceives to be too transcendent ; and believes that the whole Area of the Heavens would not receiue above 26712 Myriads , though they were placed contiguous to one another , & but 1‴ . of a minute allowed for the space that every one should take up . But as to this Particular conclude we rather with Schottus in Praelus . in Firmament . Itiner . Exstatic . Kircheri . in Schol. 1. Punctum est Terra quam incolimus , &c. This Globe of the Earth which We inhabit , which We harrass with so many Armies , so many Warlike Fleets , and which We divide with such Insatiable Avarice , is but a Point , and yet We have not overrun every Kingdom , nor penetrated every Region thereof , although enriched with the Accession of America . There are greater Tracts from the Straits of Magellan to the Southern Pole which be yet undiscovered . What think We then remains undetected in the Vast Immensity of the Heavens , in that great Kingdom of the Almighty Creatour hardly to be approached by our Weak Eyes . It is intolerable Arrogance therefore to Imagine that our Sight though never so strengthened by the help of Tellescopes can discover all the Stars in the Celestial Expansum , and extream folly to go about to range them within the Limits of any definit Number ; That being the Work of God alone , who Numbers the Multitude of the Stars , and calls them by their Names . Their Figures . As to their Figure , it is apparently Spherical or round ; maintained to be such by the Stoicks , and with them by our Manilius , Plutarch yet ( De Placit . Plilisoph . l. 2. c. 14. ) gives us the different opinions of some of the Ancients , for Cleanthes held them to be Pyramidal or pointed ; Anaximenes conceived them to be like Studs or Nails fixed in the Chrystalline Firmament ; others imagined them to be fiery or lucid Plates or Laminae , like so many flat Pictures , not of any thickness or Profundity ; Scheinerus , and Antonius Maria de Reitha , will have them to be of divers Figures or Faces , of a Poly-angular shape , and such the larger sort of Telescopes represent them , or as Kepler in Epitom . Astron. ( p. 498. ) describes them , like so many Lucid Points or Sparks casting forth every way their Rayes , of Light ; so that we are to apprehend their Figure to be only Physically Spherical , not Mathematically such ; for in the first Acceptation they may be said to be round Bodies , however according to the later , their superficies may be found to be uneven , and to consist of many Angles and Sides . Their Magnitudes Before We undertake to say any thing as to the Magnitudes of the Stars , it will not be amiss in the first place , which Schickardus ingeniously to acknowledge , that Veras illorum Magnitudines verè ignoramus . But that we may in some measure satisfie the Readers Expectation . We shall in the following Tables , give some Accompt thereof , according to the divers Calculations made by several Eminent Astronomers ; the first of which Tables shews how many Minutes or Seconds their Apparent Diameters contain ; the second how many Diameters of the Earth their true Diameters contain ; the third , what is the Solidity of their Bodies to that of the Earth . In which Tables may be observed a great Diversity ; arising partly , from the various Distances assigned to them by several Authors from the Earth , the supposed Mundane Center ; partly , from the divers Estimate of their Apparent Diameters , made by the bare Eye , by Tycho and others more Ancient , and by Telescopes by Modern Astronomers . I. Table of the Apparent Diameters of the Fixed Stars . Their several Magnitudes . 1 2 3 4 5 6 According to Maginus 10′ 0″ 5′ 30″ 4′ 0″ 3′ 0″ 2′ 0″ 1′ 0″ Tycho , Longom . Blanc . 2 0 1 30 1 5 0 45 0 30 0 20 Lansbergius 1 0 0 40 0 30 0 20 0 10 0 5 Hortensius 0 8 0 6 0 5 0 4 0 3 0 2 Kepler 3 0 2 0 II. Table of the true Diameters of the Fixed Stars , and how many Diameters of the Earth each contains . Their several Magnitudes . 1 2 3 4 5 6 According to Maurolicus and Clavi●…s 4 ¾ 4 20 / 90 4 1 / ●… .3 ⅘ 3 11 / 3●… 2 5 / 8 Fernelius 4 3 / 6 4 ½ 4 7 / 60 3 ¾ 3 ¼ 2 7 / ●…2 Tycho 4 1⅓ 3 1 / 1●… 2 ⅕ 1 19 / 30 1 1 / 49 0 ⅖ Lansbergius 40712 27132 20356 13580 6776 3388 III. Table of the Solidity of the Fixed Stars to that of the Earth . Their several Magnitudes 1 2 3 4 5 6 According to As to As to As to As to As to As to Alfraganus 100 1 90 1 72 1 54 1 36 1 18 1 Fernel . Maurolyc . Clav. 107 1 90 1 72 1 55 1 36 1 18 1 Tycho , Boyer . Blancan . 68 1 28½ 1 11 1 4½ 1 1 1 / 1●… 1 0 1 / ●… 1 To these we shall add . IV. Table from the Observations of Ricciolus shewing as well their Apparent Magnitudes , as their true Magnitudes , deduced from their undermentioned supposed Distances from the Earth . Degrees of Magnitude Names of the Stars of the several Degrees of Magnitude Apparent Diameter The greatest Distance according to Ricciolus of 210000 Semidiameters of the Earth The least Distance according to Ricciolus of 100000 Semidiameters of the Earth The greatest Distance according to the Ptolemaick 40000 Semidiameters of the Earth The greatest Distance according to Tycho 14000 Semi-Diameters       The true Diameter contains the Earths Diameter The Body contains the Earths Body The true Diameter contains the Earths Diameter The Body contains the Earths Body The true Diameter contains the Earths Diameter The Body contains the Earths Body The true Diameter contains the Earths Diameter The Body contains the Earths Body 1 Sirius 18″ 0‴ 17 45 / 100 5355 8 7 / 10 815 3 ½ 42   0 61 / 100 0 1 / 7 1 Arcturus 16 42 16 ⅔ 3932 8 0 512 3 ⅕ 32   0 46 / 100 0 1 / 9 1 Aldebaran 15 24 14 ⅕ 2810 7 ⅗ 402 3 0 27   0 57 / 100 0 ⅛ 1 Spica 15 5 13 9 / 10 2660 7 ⅓ 374 2 7 / 10 18   0 47 / 100 0 1 / 10 1 Regulus 14 5 13 3 / 5 2202 6 ⅘ 249 2 6 / 10 16   0 43 / 100 0 1 / 1●… 1 Rigil 13 40 13 0 2197 6 ⅖ 220 2 ½ 15 ½ 0 1 / 2 0 41 / 100 2 Procyon 12 20 12 0 1728 6 0 216 2 3 / 10 12   0 39 / 100 0 1 / 1●… 2 Aquila 11 0 10 ⅗ 1120 5 7 / 25 137 2 1 / 10 8 ⅖ 0 37 / 100 0 1 / 20 2 Polaris 7 53 7 ⅗ 402 3 9 / 10 62 1 55 / 100 3 ¼ 0 27 / 100 0 1 / 50 3 Algol 7 3 6 ⅗ 260 3 2 / 5 34 1 35 / 100 2 ⅕ 0 24 / 100 0 7 / 500 4 Propus 6 10 6 0 216 2 9 / 10 26 1 15 / 100 1 ½ 0 20 / 100 0 4 / 500 5 Pleias 4 ⅘ 4 ⅘ 92 2 7 / 10 18 1 8 / 100 1 ¼ 0 18 / 100 0 3 / 500 6 Alcor 4 0 4 0 64 2 15 / 100 9 0 86 / 100 0 7 / 10 0 15 / 100 0 3 / 1000 But seeing the Astronomers of the Copernican Opinion , maintain the Magnitudes of the Fixed Stars to be far greater than the former Tables show them to be : It will not be amiss to annex the following One. V. Table shewing the true Magnitude of the Fixed Stars , that is of One of the Greatest , and One of the Least , viz. Sirius and Alcor ; supposing the Apparent Diameter of Sirius to be 18″ . of Alcor , 4″ . according to the Distance in the Copernican Hypothesis , maintaining the Parallax of the Fixed Stars made by the Earths Motion , not to exceed 10″ . and imagining the Diameter of the Annual Orb , to be such as upon those Principles it is stated to be . According to The Distances to be asserted in The true Magnitude of Sirius The true Magnitude of Alcor   Semidiameters of the Earth The Diameters of Sirius contains Diameters of the Earth The Body of Sirius contains the Earths Body The Diameter of Alcor contains Diameters of the Earth Its Body contains the Earths Body Copernicus 47 , 439 , 800 4170 71 , 6771 , 713 , 000 1992 4 , 378 , 454 , 048 Herigonius 49 , 502 , 400 4350 82 , 312 , 875 , 000 2068 8 , 844 , 058 , 432 Galilaeus 49 , 832 , 416 4380 8 , 427 , 672 , 000 2092 9 , 155 , 362 , 688 Bulialdus 60 , 227 , 920 5300 148 , 877 , 000 , 000 2530 15 , 941 , 277 , 000 Lansbergius 61 , 616 , 122 5424 159 , 371 , 956 , 024 2588 17 , 333 , 761 , 472 Keplerus 142 , 746 , 428 12550 1 , 967 , 656 , 371 , 000 6000 216 , 000 , 000 , 000 Vendelinus 604 , 589 , 312 53200 15 , 056 , 882 , 800 , 000 25380 1 , 767 , 384 , 872 , 000 These Magnitudes may to some ( happily ) seem Exorbitant ; but in the Judgment of the Intelligent Schikardus , Eorum Speculationes qui Coelum Stellatum longissimè à Nobis removent , & consequenter Astra plurimum amplificant , Veritati sunt propiores quoniam Minora neutiquam admittit concessa Orbis Annui Parallaxis . ( Astrocop . p. 14 ▪ ) Of their Place and Distance from the Earth ( or rather the Sun. ) This seems a Question of that Difficulty , that Pliny pronounced the Investigation thereof to be no less than a Piece of Madness . And therefore Ricciolus ( Almagest . Nov. l. 6. c. 7. ) treating upon this Subject , thought fit in the Front of his Discourse to prefix this Theorem , as a most certain Truth , that , Parallaxis & Distantia fixarum non potest certâ & evidenti Observatione humanitùs comprehendi . For we know not whether the Stars are all in the same Spherical Superficies equally distant from the Centre of the World , or whether they be placed at unequal Distances , some higher , some lower . This latter yet was the Sentiment of the Ancient Stoical Philosophers , who conceived the difference of their Lustre and Apparent Magnitudes , to proceed from their diversity of Situation , as more or less removed from our Sight . And this Opinion our Manilius long since declared , where speaking of some Stars in Orion , appearing more obscure than the rest , he gives the reason of that Phoenomenon to be Non quod clara minus , sed quod magis alta recedunt . An Hypothesis so seemingly rational , that the Famous Tycho , Galileo , and Kepler have readily imbraced the same ; and therefore we may reasonably suppose , that their Distances are as divers as those of the Planets , how ever our weak sight unable to distinguish their divers Intervals , judges them to be all inherent in the same Concave Spherical Superficies . Ricciolus in Almagest . Nov. l. 6. c. 7. reckons up five manner of wayes of attaining in some Probability to the Knowledge of their Immense and hitherto incomprehensible Distances , which I shall only reckon up ; referring the Reader to be further satisfied from the more Ample Discourse of that Author : The first is from the Supposition of their least sensible Parallax : The second is from the Proportion of the Periodical Motion , and Distance of some of the more certainly known Celestial Lights . The third , from the difference of Refractions of the Sun , Moon , or other of the Planets , and that of the Fixed Stars . The fourth , from the Computation of the bare Distance of Saturn from the Earth , without any regard to his shaddow : The fifth , from the Distance of Saturn joyned with the length of its shaddow , which Method Ricciolus supposes the most probable . As for example ; The shadow of Saturn is supposed ( according to Ricciolus ) to extend to 118680 Semidiameters of the Earth , which joyned with the greatest Distance of Saturn , being according to the said Author 90155 Semidiameters of the Earth . The Distance of the Fixed Stars can be computed no less than 200000. of those Semidiameters , or rather 208835. that they may be clearly exempt from the Reach of Saturns shadow , and although there is no fear of their being obscured by the same , in regard they are not illuminated by the Sun , but shine by their own innate Light ; yet it is supposed they are seated beyond it , by the wise and great Architect of Nature ; and ( if you will take the Opinion of Des Cartes ) for this Reason ; that there might be a convenient space between the Planetary Heaven , and that of the Fixed Stars , for the Production and Ascent of Comets and New Stars . Wherefore ( according to the computation of Ricciolus ) the least Distance that may be assigned to the Fixed Stars , to raise them beyond the shadow of Saturn and its Satellites , will be found to amount to 210000. Semidiameters of the Earth . The greatest being altogether uncertain , by reason the Crassitude or Profundity of their Heaven is not to be determined ; and that they are as well by their Extreme Parts , as by their Centers , unequally removed from us . But let the Reader for his more particular Satisfaction , look upon the following Tables . Table of the Distance of the Fixed Stars from the Earth ( or rather the Sun. ) According to the several Authors following . Semidiameters of the Earth . Horizontal Parallax of the Fixed Stars .   Least Distance Greatest Distance ″ ‴ Albategnius , Iunctinus 19000 Uncertain 10 58 Alfraganus , Barocius 20220 40440 10 14 Maurolycus 20077 20086 10 16 Fernelius , Clavius 22612 45225 9 08 Maginus 20110 40220 10 15 Tycho 13000 14000 15 6 Marius Bettinus 2290   90 0 Ant. Mar. Rheita . 20000000   00 1 Ricciolus according to the fourth Method 100000 Uncertain 2 0 To the fifth Method 210000   1 ferè The Parallaxes placed in the last Column answer to their least Distances , for according to their greatest Distances assigned by Alfraganus , Maginus , Fernelius , and Clavius , 5″ . or 6″ . would be sufficient . DISTANCE of the Fixed Stars asserted by the followers of Copernicus in   Semidiameters of the Earth The greatest Parallax of the Fixed Stars made from the Annual Motion of the Earth Authours   The Half from the Semidiameter The whole from the Diameter of the Annual Orb     ′ ″ ′ ″ Copernicus Indefinite * * * * Galilaeus 13,046,400 0 20 0 40 Kepler formerly 34,077,067 0 9 0 17 Kepler afterward 60,000,000 0 12 0 24 Lansbergius formerly 10,312,227 0 30 1 00 Lansbergius later dayes 41,958,000 0 07 0 15 Hortensius 10,312,227 0 30 1 00 Herigon 144,0000 3 0 6 00 Distance of the Fixed Stars , supposing the Earth's Annual Motion about the Sun , and the Copernican Distance of the Earth from the Sun. According to the Calculation of Semidiameters of the Earth Total Parallax of the Fixed Stars       ′ ″   Tycho and Maginus 7850,000 1 00   Longomontanus 7906,818 1 00   Scheinerus 13,133,376 0 40     10,320,000 0 48   Distance of the Fixed Stars from the Earth , supposing the Earths Motion , and the greatest Parallax of the Fixed Stars to be 10″ . and the Distances of the Sun and Earth , as underwritten . According to the several Authors following . Distance of * and Earth in Semidiameters of the Earth Distance of the Fixed Stars in Semidiameters of the Earth   Copernicus 1150 47,439,800   Maestlinus , Galilaeus 1208 49,832,416   Keplerus 3469 142,746,428   Lansbergius 1498½ 61,616,122   Bullialdus 1460 60,227,920   Herigonius 1200 49,502,400   Vendelinus 14656 604,589,312   It rests that something be said of the Proper Motion of the Fixed Stars , which is double . The first is their Circumrotation about their own Centers , termed Motus Vertiginis ; in which they are carried about with extraordinary Celerity ; whence the Reason in part ( as already hinted ) of their Scintillation . The second is their Motion of Revolution from West to East , Secundum Ductum Eclipticae , in which they are observed to move , but very slowly . Touching this , it will not be amiss to insert the three following Conclusions of Ricciolus in his Astronom . Reformat . p. 259. The first is , that the Motion of the Fixed Stars is equal and uniform . Secondly , That their Annual Motion is not less than 49″ . nor greater than 51″ . Third , That it seems most Probable that their Annual Motion is 50″ . 40‴ . though the Opinion of those who compute it to be within 50″ . or 51″ . wants not fair Probability . From the Supposition of their Annual Motion of 50″ . 40‴ . It follows that they complete not one Degree in the Ecliptick sooner than in 71 years and 16 / 304 , or 19 dayes and 12 Houres in a manner ; but the whole Circle of 360 Degrees they run not through save in 25579 years , which is the Annus Magnus Platonicus ( though by the Ancients computed to extend to no less than 36000 years ) which 25579 Sidereal years , are equal to 25580 Equinoctial years . But this will be clearlier manifested by the following Table . Table of the Motion of the Fixed Stars in Longitude . Years ′ ″ ‴   Years ′ ″ ‴   Years Gr. ′ ″ ‴ 1 0 50 40   43 36 18 40   83 1 10 5 20 2 1 41 20   44 37 9 20   84 1 10 56 0 3 2 22 00   45 38 0 0   85 1 11 46 40 4 3 22 40   46 38 50 40   86 1 12 37 20 5 4 13 20   47 39 41 20   87 1 13 28 0 6 5 4 0   48 40 32 0   88 1 14 18 40 7 5 54 40   49 41 22 40   89 1 15 09 20 8 6 45 20   50 42 13 20   90 1 16 0 0 9 7 36 00   51 43 04 0   91 1 16 50 40 10 8 26 40   52 43 54 40   92 1 17 41 20 11 9 17 20   53 44 45 20   93 1 18 32 0 12 10 8 0   54 45 36 0   94 1 19 22 40 13 10 58 40   55 46 26 40   95 1 20 13 20 14 11 49 20   56 47 17 20   96 1 21 4 0 15 12 40 0   57 48 8 0   97 1 21 54 40 16 13 30 40   58 48 58 40   98 1 22 45 20 17 14 21 20   59 49 49 20   99 1 23 36 0 18 15 12 0   60 50 40 0   100 1 24 26 40 19 16 2 40             200 2 48 53 20 20 16 53 20     Gr. ′ ″ ‴   300 4 13 20 0 21 17 44 0   61 0 51 30 40   400 5 37 46 40 22 18 34 40   62 0 52 21 20   500 7 2 13 20 23 19 25 20   63 0 53 12 0   600 8 26 40 0 24 20 16 0   64 0 54 2 40   700 9 51 6 40 25 21 6 40   65 0 54 53 20   800 11 15 33 20 26 21 57 20   66 0 55 44 0   900 12 40 0 0 27 22 48 0   67 0 56 34 40   1000 14 4 26 40 28 23 38 40   68 0 57 25 20   2000 28 8 53 20 29 24 29 20   69 0 58 16 0   3000 42 13 20 0 30 25 20 0   70 0 59 6 40   4000 56 17 46 40 31 26 10 40   71 0 59 57 20   5000 70 22 13 20 32 27 1 20   72 1 0 48 0   6000 84 26 40 0 33 27 52 0   73 1 1 38 40   7000 98 31 6 40 34 28 42 40   74 1 2 29 20   8000 112 35 33 20 35 29 33 20   75 1 3 20 0   9000 126 46 0 0 36 30 24 00   76 1 4 10 40   10000 140 44 26 40 37 31 14 40   77 1 5 01 20   20000 281 28 13 20 38 32 5 20   78 1 5 52 0   25579 360 0 0 0 39 32 56 0   79 1 6 42 40             40 33 46 40   80 1 7 33 20             41 34 37 20   81 1 8 24 0             42 35 28 0   82 1 9 14 40             Table of the Right Ascension and Declination of 100 of the Fixed Stars for the year of Christ 1700 completed : according to Ricciolus in Astronom . Reformat . Names of the fixed Stars . Right Ascention for the year 1700. Declination for the year 1700. Difference of Ascention in 100 years Declination in 100 years   Gr. ′ ″ Gr. ′ ″ Gr. ′ ′   Head of Andromeda 358 14 8 27 27 26 B 1 17 34 A Girdle of Andromeda 13 11 20 34 2 40 1 23 33 A Southern Foot of Andromeda 26 21 51 40 52 30 1 29 30 A Fomalhaut of ♒ 340 11 0 31 8 10 A 1 25 31 S Right Shoulder of ♒ 327 36 55 1 43 44 1 20 29 S Left Shoulder of ♒ 318 55 54 6 48 46 1 21 26 S Left Hand of ♒ 307 45 54 10 33 44 1 26 19 S Bright one in the Eagle 294 2 47 8 6 32 B 1 27 13 A First in ♈ Horn 24 17 2 17 48 24 B 1 23 31 A Second in ♈ Horn 24 30 3 19 19 24 1 22 31 A Bright one in Aries 27 35 58 22 1 30 1 25 30 A Goat of Auriga 73 35 56 45 40 0 1 49 10 A Right Shoulder of Auriga 84 29 42 44 51 30 1 58 4 ⅙ A Arcturus in Bootes 210 33 2 20 48 2 B 1 11 29 ½ S Left Shoulder of Bootes 215 2 33 39 35 12 1 2 27 S Praesepe in S 125 46 2 20 43 4 B 1 28 19 S Northern Asinego in S 126 26 0 22 3 0 1 30 20 S Southern Asinego in S 126 54 3 19 15 0 1 27 20 S Great Dog , Sirius 97 57 6 16 18 6 A 1 7 4 A Little Dog , Procyon 110 54 33 5 59 12 B 1 20 12 S Upper Horn of ♑ 300 24 34 13 22 6 A 1 25 16 S Lower Horn of ♑ 301 7 29 15 38 2 1 27 17 S First in the Tayl of ♑ 320 56 29 17 54 21 1 26 26 S Second in the Tayl of ♑ 322 43 30 17 22 22 1 25 27 S Bright one in Cassiopea's Chair 358 14 33 57 32 16 B 1 15 34 A Scheder or the Breast of Cassiopea 5 56 0 54 55 16 1 22 34 A In the flexure of Cassiopea 9 45 58 59 7 36 1 27 34 A In Cassiopea's Knee 16 36 0 58 40 22 1 35 33 A Cepheus his Girdle 321 6 20 69 17 10 0 22 26 A Bright one in the Whales Jaw 41 38 7 2 53 50 B 1 15 25 A Northern Whales Belly 24 12 0 11 44 50 A 1 15 31 S Southern in the Whales Tayl 7 5 8 19 35 40 1 18 34 S Northern in Whales Tayl 1 4 12 10 24 54 1 17 34 S Bright one in the Northern Crown 230 39 0 27 45 20 B 1 5 21 S In the Beak of the Swan 289 39 48 27 22 40 1 1 11 A In the Swans Breast 302 55 52 39 20 5 0 53 ½ 18 A In the Swans Tayl 307 47 17 44 14 51 0 51 ½ 20 ½ A Upper Wing of the Swan 293 56 2 44 26 21 0 48 14 A Lower Wing of the Swan 308 29 10 32 51 24 0 0 21 A Bright one of the Dragon 267 25 20 51 35 2 0 35 2 S In the Head of Castor 108 50 46 32 30 26 B 1 44 11 S In the Head of Pollux 111 43 36 28 43 2 1 34 12 S Bright one Foot of the Twins 95 3 32 16 37 32 1 28 2 S Head of Hercules 255 21 37 14 46 48 B 1 8 8 S Right Shoulder Hercules 244 19 35 22 11 40 1 5 15 S Left Shoulder Hercules 255 31 33 25 15 48 0 52 8 S Heart of Hydra 138 12 22 7 21 30 A 1 15 25 A Lions Heart Regulus 148 4 15 13 25 16 B 1 22 ½ 28 ½ S Lions Tayl 175 25 34 16 14 4 1 19 34 S Bright one in Iuba Leonis 150 48 47 21 21 0 1 25 ½ 29 S Bright one in Lumbis Leonis 164 32 20 22 7 44 1 27 34 S Uppermost in the Neck 149 58 52 24 53 54 1 28 29 S Lowest in the Neck 147 47 52 18 13 33 1 28 28 S Thigh of the Hare 78 51 30 20 59 0 A 1 5 7 S Northern Scale of Libra 225 15 26 8 14 46 1 21 ½ 24 A The rest of the Table of the Right Ascension , &c. Names of the fixed Stars . Right Ascension for the year 1700. Declination for the year 1700. Difference of Ascension in 100 years Declination in 100 years   Gr. ′ ″ Gr. ′ ″ Gr. ′ ′   Southern Scale of Libra 218 38 12 14 45 18 1 25 27 A Bright one in Lyra 276 39 32 38 32 16 B 0 50 4 A Head of Ophiuchus 260 15 38 12 49 22 B 1 11 7 S Left Hand of Ophiuchus 239 47 37 2 52 2 A 1 23 18 A Right Knee of Ophiuchus 252 39 40 9 53 30 0 50 10 A Left Knee of Ophiuchus 245 11 37 15 16 30 1 23 15 A Right Shoulder of Ophiuchus 162 8 38 4 44 40 B 1 13 5 S Uppermost in the Head of Orion 79 41 10 9 34 38 B 1 22 7 A Right Shoulder of Orion 84 43 4 7 18 20 1 22 4 A Left Shoulder of Orion 97 16 40 6 3 2 1 19 8 A Foot of Orion Rigel ▪ 75 2 50 8 33 42 A 1 15½ 9½ S 1. in the Belt of Orion 79 9 48 0 32 50 1 17 7 S 2. in the Belt of Orion 80 12 54 1 25 46 1 17 6 S 3. in the Belt of Orion 81 18 25 2 8 20 1 16 5 S Mouth of Pegasus 322 27 36 8 32 14 B 1 18 26 A Sa'd Alpharas in the Leg 342 20 36 26 28 38 1 12 32 A Markab in the joyning of the Wing 342 28 10 13 35 58 1 15 32 A End of Pegasus Wing 359 27 25 13 32 56 1 16 34 A Bright one in the side of Perseus 45 32 18 48 44 54 1 28 12 A Ras Al Gol of Perseus 42 12 42 39 46 30 1 37 25 A The Hindermost in the Head of the Southern Fish 345 24 5 1 40 2 1 17 33 A In the Knot in the Line of ♓ 26 38 5 1 19 0 1 18 30 A Bright one in the Head of ♐ 283 1 5 21 22 48 A 1 31 8 S Antares , Heart of Scorpius 242 47 28 25 39 54 1 32 16 A Northern Front of Scorpius 236 58 15 18 53 36 1 28 19 A Middlemost 236 14 34 21 41 40 1 30 20 A Southern Front of Scorpius 235 18 0 25 9 54 1 37½ 21 A Bright one in the Neck of the Serp. 232 24 0 7 24 36 B 1 15 21 S Aldebaran , or Southern Eye ♉ 64 41 35 15 52 10 B 1 26½ 15 A In the Northern Horn of ♉ 76 51 18 28 19 2 1 37 8 A Southern Horn of ♉ 79 55 20 20 55 58 1 31 7 A Northern Eye of ♉ 62 43 36 18 30 28 1 24 17 A Lowest of the Hyades ♉ 60 39 35 14 55 38 1 25 17 A Bright one of Pleiades ♉ 52 27 35 23 9 24 1 29 21 A Spica Virginis 197 22 55 9 33 30 1 19½ 32½ A Girdle of Virgo 190 10 22 5 2 54 B 1 18 34 S Vindemiatrix in Virgo 191 52 20 12 34 58 1 17 33 S The bright one in the Shoulder of the greater Bear 161 17 5 63 22 2 B 1 41 32 S The bright one in its Side 160 52 20 57 59 2 1 37 32 S The bright one in the hindermost Thigh 174 23 34 55 23 42 1 23 34 S On the Back near the Tayl 180 8 2 58 41 42 1 20 34 S 1. in the Tayl 190 7 56 57 36 58 1 9 33 S The 2. in the Tayl 197 55 2 56 30 52 1 3 32 S Last in the Tayl 203 53 50 50 50 56 1 2 31 S The last in the Tayl of the lesser Bear now the Pole-Star 9 52 10 87 42 51 3 10 34⅙ A The bright one in the Shoulder heretofore called Cynosura 222 39 20 75 37 30 1 15 2½ A The right Ascension of this still decreases .                     To what we have already said of the Fixed Stars , it will not be amiss to add something touching those , which in regard they are now and then visible at other times disappear , are called New Stars , as that in Cassiopea observed by Tycho ; and three others in the same Constellation lately discovered by Signeur Cassini , that in Serpentarius by Kepler and others ; two more in the beginning of the Constellation Eridanus detected by Cassini . That in the Whale's Neck , and in the Northern Part of Andromeda's Girdle , by Bullialdus ; that in the Swan's Breast , and another near its Beak , by Hevelius and Don Anthelm a Carthusian of Dijon ; and four others near the Artick Pole lately taken Notice of by Cassini . The Nature , Substance and Generation of which Stars are diversly discoursed of both by Philosophers and Astronomers ▪ Some conceiving them to be generated of Sublunary Matter , and to be Comets wanting their Bush or Train ; others conceive them to be generated of Celestial Matter by Condensation , as the other of the Fixed Stars at the first Creation ; but not so compact and solid as those other Fixed Stars are , and therefore by degrees come to lose their Consistence , and with the Dissipation of their Substance , their Light. Some imagine them to be of the same Nature , Substance , and of equal continuance with other of the Fixed Stars , but assign to them a different Motion ; by which Motion of theirs they sometime approach nearer to , sometimes recede further from the Earth ; by means of their first Motion becoming visible and solving the different Appearances of their Light and Magnitude ; by the latter , shewing the Reason of their Disappearance . But this Motion is by others denied ; but because they find even in the Fixed Stars themselves , the like Alteration of their Lights and Magnitudes , which sometimes appear so small , as if they were Stars of the last , at other Times so bright , as if they were of the first Degree ; they allow of some Alteration to be made in the very Bodies of these Stars ; and as the Sun appears sometimes over-cast with Spots ; so they conceive these Stars to be sometimes ore-clouded with such kind of Spots at what time they disappear ; at other times to recover their Light , and become visible ; others are of Opinion , that the Globes of these kind of Stars are so made , that but one side of them , shines , the other being altogether obscure ( the first Authour of which Opinion seems to be Ricciolus , as he affirms of himself , Almagest . Nov. Tom. 2. l. 8. c. 17. ) and that they move and have a Circumrotation about their own proper Axes , now turning their bright sides to us , at another time their dark ; And for this Reason they are by Le Pere Cherubin termed Stellae Versatiles . The Periods of their several Motions not being yet clearly determined ; but by the Observations hitherto made , it appears , that , that in the Whales Neck makes its Revolution in Eleven Moneths ; that in the Swans Breast is supposed not to finish the Period of its Revolution sooner then in fourteen Years , that near the Beak of the Swan compleating hers in about ten Months Time ; the Periods of the others Revolutions not being yet certainly known . Of the SUN . What seemed requisite to be added touching the Fixed Stars being dispatched ; Something is to be said concerning those which are commonly termed Erratick or Planets ; and among them in the first Place of the most glorious Luminary the Sun. Whose Nature or Substance , with Anaxagoras , Democritus , Metrodorus , Epicurus , Pythagoras and Plato of old , and with Kepler , Scheinerus , Rheita , Bullialdus , Kircher , Ricciolus , and others of late , We cannot with fairer probability conjecture to be other than a formal fiery Body , consisting of true proper Elementary Fire , partly liquid , partly solid . The liquid , being an Ocean of Light , and moving with fiery Billows , and flaming Ebullitions , as is manifest to those that look upon it through a Telescope . The solid Parts , being like the Land in our Terraqueous Globe , divided into Continents , Islands , Mountains , Rocks , that thereby the Vehement Motion of the exestuating Solar Ocean , might be restrained , and by frequent Allisions , repulsed , dissipated , and broken , to the end it might more efficaciously communicate its Panspermatick Virtue to all those Bodies , to which it is to afford Light and Influence . We may likewise probably conceive , that the Solar Globe , is , as this Earth of ours , hollowed with vast Subterraneous Caverns and Receptacles of Fire , which break forth out of the Solar Ignivomous Mountains , in the same manner as we find our Subterranean Fires to break out of Etna , Hecla , and Vesuvius . And it is in all Appearance as probable , that the solid Parts of the Sun within which the fluid and liquid Fire is contained , as Mettal in a Furnace , are thoroughly ignified in the same manner as we find the Bricks in the Roofs and sides of Furnaces , are made red hot , and look of the same colour as the fiery Mass of melted matter within them . We may further probably infer , that the earthly or solid Parts of the Sun are of an Asbestinous and incombustible Nature , and far better able to resist the Voracity of the Fire then this Earth of ours ; And though it should be supposed that some Parts here and there should be consumed , and perhaps whole Mountains be levelled and wasted ; yet it follows not that the Globe of the Sun should therefore be totally destroyed , more than this Earth of ours is , by the frequent Accidents of such kind of partial Ruines and Decayes . It is also evident that the Splendor as well of the fluid , as the solid Fire of the Solar Globe , is far more bright than our Earthly Fire or Flame . The End for which it was made necessarily requiring the same , as being intended for the Fountain of Light , and Lamp , if not of the whole World , at least , of the Planetary System . This fire , as well the Liquid , or Solar Sea , as that which breaks out of the Caverns and Mountains , exhales constantly fuliginous Vapours , not black and sooty , like the Smoak of our Fire ; but bright and pure , which collected together and condensed in the Circumambient Aether , do in a manner overcast the Sun , as Clouds overshadow the Earth . But all this will be clearlier represented in the annexed Scheme , taken from the joynt Observations of Scheinerus and Kircherus . From what hath been said , and the Evidence of frequent Observations lately made by help of the Telescope , it is manifest , that the Sun is not ( as Aristotle and his Followers fancy it to be ) of an unalterable Substance , but Subject to divers Changes and Alterations , as not only the Generation and Production , but the Dissolution and Corruption of several strange Phaenomena , in the Body thereof ( altogether unknown to the Ancients ) clearly demonstrate . Among which the most Eminent are those by later Astronomers termed the Maculae , & Faculae Solares . The Maculae or Spots , are certain Cloudy Obscurities appearing upon the Disque of the Sun ; supposed by some Astronomers , to be a fuliginous obscure Matter or Vapour , sometime closely compacted into one ; sometimes dispersed and dissipated into several Parcels issuing from its fervent fiery Body , by force of its extream Heat . And though it cannot be certainly determined ( by reason of the Want of Parallax ) whether they be in the Sun it self , or distant from it some space ; yet if one consider , their first Appearance or Birth , their Decay or Disappearance , their Shape or Figure , Increase , Diminution , Separation , Conjunction , Motion , and other like Accidents ; It is credible , and ( by what Observation makes out ) most probable , that they are in the very Body of the Sun , at least not far from the Superficies thereof ; in regard that when they are observed near the Border or Edge of the Sun 's Disque going off from its visible Hemisphere , and turning about to the other ( at what time they begin to disappear ) they cannot be perceived to be raised above the Superficies of the Sun , or to shew any apparent Space or Distance between them and the Edge of the Sun's Globe , as in reason they would , and indeed ( if it were so ) they ought to do . Their Shapes and Figures , are of unequal Form and Grandeur , and most irregular , which argues them not to be Stars or Planets moving about the Body of the Sun , as Tarde and Malapertius have supposed ; the one entituling them Sidera Borbonia , the other Sidera Austriaca . Some of these are more durable and lasting than others , and those are conceived to be the solid Parts of the Sun , shewing themselves variously figured , and of different Magnitudes , by reason of the vertiginous Motion of the Sun about its own Axis representing them to our Sight diversly situated , which diversity of their Appearance arises likewise from the Manner of the Sun's Circumgyration , which is such , that its Axis does not alwayes keep the same Inclination to the Plane of the Ecliptick . They have a Motion from the Oriental Part of the Sun 's Disque , to the Occidental , which Course they ordinarily finish within the space of thirteen Dayes more or less , according to their greater or lesser Latitude , for they make by their Motion as it it were a Zodiack of about sixty Degrees broad , that is , about thirty Degrees on each side of the Sun 's Ecliptick . The Faculae Solares Are conceived to be partly Massie fiery Globes bursting forth out of the Ignivomous Solar Mountains ; and by reason of their Brightness shining amidst the Fuliginous Cloudy Vapours , or Maculae , at sometimes suddenly disappearing , at others , making a long continuance or Duration . Partly Effervencies of the exestuating Solar Ocean : Which by reason of the excessive innate Fervour of the Sun's Globe , boyls up into mighty Waves like Mountains of Light , scattering and dispersing the darker Maculae , and discovering as it were a fiery Ocean fluctuating and agitated with Flaming Billows and unusual Splendour ; or as Scheinerus ( in Disquisit . Mathem . ) defines them . Faculae , sunt Areolae in Sole Lucidiores reliquo ejusdem Corpore , i. e. they are certain small Plats or Spaces in the Sun , brighter than the rest of its Body , thus described by Galilaeo ( in Letter . 3. Delle Macchie Solar . ) In the face of the Sun their appear certain Marks , brighter than the rest , in which is observed the same Motion as in the Maculae , which that they are inherent in the very Body of the Sun , cannot be doubted , in regard it is not credible there can be any other Substance beside brighter than that of the Sun ; In which few Words he hath comprized much . Of the Sun's Vertiginous Motion . The Observation of the Motion of the Sun's Spots and Lights , hath given Occasion to Astronomers to remark that the Sun hath a Motion about its own Axis , from East to West , which Conversion is finished in the space of twenty seven Dayes , or thereabouts , though there be some who will have it to move much faster , * making its Period of Circumrotation to be compleated in twenty four Hours . Others assigning to it a much more wonderful Celerity , and affirming its Vertiginous Schema corporis SOLARIS ▪ prout a P. P. Kirchero et Scheinero . Romae Anno 1635 observatum fuit . Course to be finished in a * Moments space . Of its Motion of Revolution Diurnal and Annual according to the Hypothesis of the Earth's Immobility , We shall here say nothing . Leaving likewise the Reader to be further satisfied as to what We have already briefly indicated touching this glorious Luminary from the larger Arguments of Galilaeo , Scheinerus in Rosa. Ursina . Kepler , Gassendus , Hevelius , Bullialdus . Kircherus in his Iter. Extatic . and Schottus upon him Ricciol . Almagest . Nov. l. 3. Hodierna in Ponderation . De Admirandis Phasibus in Sole & Luna Visis , &c. Otto de Guerick in Experiment . Magdeburg . and Le Pere Cherubin in his Dioptricks . Only adding something touching The Sun's Magnitude , and Distance from the Earth . The true Magnitude of the Sun ( sayes Ricciolus Almagest . l. 3. c. 11. ) is to be had from its true Semidiameter ; for that being doubled gives its true Diameter , whence it s other Species of Magnitudes are derived , according to the Rule of Proportion . Of which take the following Table . The true Magnitude of the Sun compared with the Earth . The Suns True Diameter contains Its Circumference contains The Area of its greatest Circle contains Its convex superficies contains Its solidity contains According to the following Authors Simple Diameters of the Earth Simple Diameters of the Earth Square Diameters of the Earth Square Diameters of the Earth The Solidity of the Earth Ptolemy , Maurolycus Clavius and Barocius 5 ½ 17 2 / 7 24 0 134 0 166 3 / 2 Aristarchus more than 6 1 / 3 20 1 / 7 30 ⅔ 127 0 254 1 / 17 Aristarchus less than 7 ⅙ 22 3 / 7 38 0 155 0 368 1 / 11 Albategnius 5 7 / 10 18 5 / 7 26 0 108 0 186 0 Copernicus 5 27 / 60 16 ½ 22 0 91 0 161 ●… Tycho and Blancanus 5 ●… 16 2 / 7 22 0 85 0 140 0 Longomontanus 5 807 / 1000 18 1 / 15 26 0 95 0 196 0 Keplerus 15 0 47 1 / 10 176 0 706 0 3375 0 Lansbergius 7 17 / 30 24 0 46 0 176 0 434 0 Bullialdus 7 0 22 2 / 7 39 0 156 0 343 0 Wendelinus 64 0 200 96 / 100 3216 0 12864 0 262144 0 Kircherus 5 ⅕ 16 0 21 0 83 0 140 0 Rheita 10 0 31 4 / 10 78 0 314 0 1000 0 Ricciolus 33 5 / 6 106 15 / 100 885 0 30056 0 38600 0 Times The Distance of the Sun from the Earth is such , that , if you will believe Pliny , to search after it , penè dementis otii est . Ricciolus likewise acknowledging its Sublimity to exceed the Subtlety of all Astronomers hitherto . Who yet proposes three several Methods or Wayes of finding it out . The first by means of the Horizontal or any other Parallax of the Sun ; the second by the Eclipses of the Sun and Moon ; the third by the Moon 's Dichotomy , and its Distance from the Earth . But however the Investigation thereof be made , this is to be considered , that the Sun is sometimes in Apogaeo , or its furthest Distance from the Earth , sometimes in Perigaeo , or its nearest Proximity to the Earth ; by the half of the Difference of which two Distances , the mean Distance of the Sun is determined . But it will be worth the while to represent to the Readers view in the following Table , the several Opinions as well of the Ancient as Modern Astronomers touching this matter . Table of the Sun's Distance from the Center of the Earth in Semidiameters of the same . AUTHORS Greatest Distance of the Sun in Apogaeo Mean Distance Least Distance in Perigaeo According to Hipparchus his Data 1586 1472 1357 Or 1429 1379 1231 Posidonius 13141 † † Ptolemaeus and Maurolycus 1210 1168 1126 Clavius and Barocius 1216 1168 1126 Albategnius and Alphonsus 1146 1107 1068 From the Data of Albategnius as Lansberg . 7936 † † Alfraganus 1220 1215 1210 Fernelius 1309 1256 1204 Copernicus and Maginus 1179 1142 1105 From the Data of Copernicus Lansberg . 0942 † † Michael Neander 1197 1160 1122 Maestlinus in Max. Excentr . 1208 ½ 1160 1111 ¾ Maestlinus in Min. Excentr . 1197 ½ 1160 1122 ¾ Io. Offusius † 1152 † Tycho and Blancanus 1182 1150 1117 Longomontanus 1334 1288 1242 Kepler in Ephemer . 1800 1768 1736 Kepler in Coment . Martis — — — Kepler in Stella Nova — 1432 — Kepler in Epitome Astronom . 3469 — — Kepler ex Parallax . in Tabul . Rudolphin . 3438 3381 3327 Lansberg . in Min. Excentr . 1550 52 / 60 1498 3●… / 60 1446 1●… / 60 Ismael Bullialdus 1485 56 / 60 1460 1433 ●… / 60 Athanas. Kircherus 1940 ¾ 1906 ¼ 1872 〈◊〉 Anton. Maria de Rheita 2073 2000 1927 Godefridus Vendelinus 14905 14656 14407 Galilaeus † 1208 † Marius Bettinus † 1145 † Langrenus † 3420 † Ricciolus 7580 7327 7074 Or 7600 7300 7000 Of the MOON . THE MOON the nearest Neighbour of all the Planets to this our Elementary Sphere comes next to be considered ; whose Nature , Composition , and Constitution , may best be judged of by its Opacity , Asperity , and Heterogeneity of Parts . The first shews it to be altogether deprived of any innate or proper Light , evidenced in its Total Eclipses , wherein She altogether looses her Lustre , which contrarily ( if She had any of her own ) would rather in the greatest darkness become more conspicuous . Hence it may be inferred the Light She hath is from the Sun , and that the Moon as She is an opacous , so She is a dense Body , apt to receive and reflect the Sun's Light. The second argues the Globe of the Moon to be full of Eminencies , and Depressions , like our Hills and Valleys , estimated to be such by the Conjectures of the Ancients , ( mentioned by Plutarch l. de facie in Orbe Lunae ) but at present manifest to sight by help of the Telescope , and ascertained to reason by those lesser Spots , which are called New ones , varying their Scituation and Magnitude , according to the divers Access and Recess of the Sun , to which their Site is alwayes opposite , thence evidencing them to be the Shadows of the more eminent Parts of the Moons Globe , emulating our Alps , Hills , and Mountains , and here and there surpassing them for Height . The third , viz. The Heterogeneity of its Parts was long since believed by the Ancients , as may appear by Plutarch ( l. 2. De Placit . Philosoph . c. 25. ) but at this day certainly demonstrated by the various Reflections of its Light ; whence We may conclude the brighter and more splendid Parts of the Moon , to be those which are more dense , solid , and opacous , like our Earth , in regard they reflect a greater Portion of Light ; but the obscurer Parts commonly called the Ancient Spots , for as much as they reflect a less , and absorbe a greater Quantity of Light , to be therefore Pellucid and Diaphanous , and Analogous to our Ocean , Seas , Lakes , and Rivers . From what hath been already said , We may probably inferr that the Moon is composed of Solid and Liquid Parts , as this our Terraqueous Globe which we inhabit ; above which it is placed in such a ●…itting Degree of Neighbourhood , that thereby the Light and Influence of the Celestial Bodies , especially of the Sun 's fervent Rayes , might by the Celerity of its Motion be so tempered , and by the Asperity and Inequality of its Superficies so received , and thence reflected , that they might be transmitted to us with less Incommodity than otherwise they would , if they were directly projected without that temperating Medium . We are not yet to imagine , though most Astronomers as well Ancient as Modern conceive the Moon to be as it were another Earth , that it is composed of the same Sand , Clay , Stones , as this Terrestrial Globe , or that the Lunary Seas , Lakes , Pools , &c. are of the same Water with our Seas , Lakes , or Pools ; but happily of a quite different Matter , and to us incomprehensible . And therefore as to its Nature and Substance , We shall forbear with Anaximander to determine that its Concave Orb is full of Fire , breathing out at one Part as out of a Tunnel ; or with Xenophanes , that it is a Constipated Cloud , or with Pythagoras , that it is a stony Body , or with the Stoicks , that it is composed of Fire and Air , or as Plato will of a terrene Composition , or as Anaxagoras pretends of a mixture cold and earthly , darkness being mixed with her fiery Nature , whence She is called a Star of false Light ; or with Heraclitus that it is another Earth inveloped within a misty dim Cloud ; or with Pliny and some of the Moderns , that it is of a Watery Substance , or as * Otto de Guerrick conjectures , that it is a Globe of Ice . But shall leave these Opinions as being dubious and uncertain to the further Disquisition of the learned , and give the Reader a view of its Figure and several Phases in the Annexed Scheme , according to the Observations of Ricciolus and Grimaldus . And seeing mention hath been made of the Maculae , or Spots appearing in the Face or Body of the Moon ; as well those obvious to the Bare Eye , as the others discernable by help of the Telescope ; We hold it necessary to make a more particular Description of them . They are distinguished into the ANCIENT and the NEW . The Ancient Spots , are those greater and larger Spots at all Times discernable without the Help of a Telescope , resembling , large Seas , Lakes and Bayes ; Heretofore known and taken Notice of by the Ancients , of which Plutarch hath written a Particular Treatise under the Title , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , &c. i. e. De facie in Orbe Lunae , translated and commented upon by Kepler , and annexed to his Somnium Lunare . The New Ones , are those Lesser Spots , which are not discernable but by the help of a Telescope , which are various ; differing in Magnitude , Figure , Scituation , Colour , &c. observed and with exactness described by sundry eminent Modern Astronomers : Some of whom have imposed , as well upon the Old as New , distinct Names and Appellations for the better Knowledge of them . Among whom Langrenus in his Selenographia , hath noted them by the Names of several Persons eminent either for their Skill in the Mathematicks , or their Dignity and Honours , or their Particular Friendship and Favour to him and his Studies . Hevelius , as if the Moon were another Earth , hath described and distinguished them by Geographical Marks and Denominations , transferring to them the Names proper to our Terrestrial Continents , Promontories , Mountains , Islands , Seas , Lakes , &c. Grimaldus hath signalized them by the Names ( for the most Part ) of Persons peculiarly addicted to , and eminent in the Study of Astronomy . The Scheme and Tables of the two last ( that of Langrenus not yet come to my hand ) the Reader may here take notice of , as being of great Use and Advantage to all Students in Astronomy , and very Necessary not only for making their own , but better Understanding others Observations . The first Scheme is that of Hevelius , whereof the Alphabetical Table follows . The Names of HEVELIUS his Selenographical TABLE . A. ABarim , a Mountain , called likewise Nebo and Phasga where Moses died . Acabe , a Mountain of Egypt , near the Arabian Gulf. Aconitus , a Hill , where likewise is the Acherusian Cave . Adriaticum Mare , at this day called Golfo di Venetia , by Vitruvius Gallicae Paludes ; the Inmost Recess of the Adriatick Sea , where Venice is seated , at this Day called Lagume di Venetia . Aea , an Island , at this day called Satabella . Aegyptus a famous Region of Africa , heretofore known by the Names of Aeria , Aetia , Ogygia , Hephaestia and Chemia , according to Herodotus , by the Iews called Chus , by the Turks Elchebitz , in the Egyptian Tongue Cam. Aegyptiacum Mare , the Egyptian Sea. Africae Pars , Part of Africa . Aemus or Haemus , a Mountain of Thrace called by some Catena Mundi , by the Italians Monte Argentario , by the Turks Balkan . Aerii Montes , Mountains of Sicily anciently so called . Aetna , a Mountain of Sicily , called by Pindar the Celestial Pillar , by Silius Italicus the Tiphaean Mountain ; at present Mongibello , anciently called Inesia . Aethusa , an Island not far from Sicily otherwise called Aegusa , Limoza , Aegates . Ajax , a Mountain of Egypt . Agarum , a Promontory of Sarmatia Europaea . Alabastrinus Mons , a Mountain of Africa . Alani Montes , sive Roxolani , Mountains near the River Tanais , and the Lake Maeotis . Alopecia , an Island in the Lake Maeotis ; called likewise Tanais , and Calarus , at present L'Isle des Renards . A●…aunus , a Mountain of Sarmatia . Alpes , a long Tract of Mountains dividing Italy from Germany and France . Amarae Paludes , about Arsinoe not far from the the Arabian Gulf. Amari Fontes , in Egypt . Amadoca , Palus , in Sarmatia Europaea . Amanus Mons , a Mountain of Syria , which it divides from Cilicia , called likewise Cedrenus and Monte Nero●… , and Monte di Scanderona , from the City Scanderoon seated at the Foot of the said Mountain . Ambenus Mons , a Mountain near the Outlet of Ister in Sarmatia Europaea , otherwise called Ambolus and Embolus . Animusa , an Island lying between Leopadusa and Aethusa , which in the African Tables are called the Pelagian and Taricinian Islands . Anna , a Mountain in Arabia Deserta . Antilibanus , a Mountain in Syria , or Phaenicia , between which and Libanus stretches along and fertile Valley well peopled and called by the Inhabitants Abellinas . Antitaurus , a Mountain in the Lesser Armenia , called according to Thevet , Roham Thoura . Apenninus Mons , a Ridge of mighty Hills , running through the middest of Italy from the Maritime Alps as far as the Brutii . Apollinis Promontorium , a Promontory of Mauritania Caesariensis , called at this Day Cabo de Tenes , or Cabo de tres Forcas . Apollonia , an Island called likewise Thynias . Apollonia Minor , an Island in the Euxine Sea. Arabia , at this Day called Aden , by some Aiman , by the Saracens Mamotta . Arabiae Paludes , the Moors or Fens of Arabia . Archerusia Palus , or Anthemois is not far from the Euxine Sea. Archerusia Promontorium , a Promontory not far from Apollo's Island in the Euxine Sea. Areesa Palus , or Arsina , or Arethusa in Armenia Major . Argentarius Mons , a Peninsula or Promontory of Thuscany ; at this day called Monte Argentaro , where once was the Town or Harbour , called Portus Herculis . Arietis frons seu Promontorium , a Promontory in the Taurick Chersonesus , of old called Brixaba , or Acroma , now Fanar , or Famar . Armeniae Montes , the Armenian , or Gordiaean Mountains . Arrhentias , an Island about the Cappadocian Sea. Asiae Pars , Part of Asia , by Sacred Writers called Semia , by the Asiaticks Siana . Atheniensis Sinus , the Bay of Athens in Cappadocia , not that of Greece ; called otherwise Themis , and Syrium , at this Day Cacari . Athos Mons , a Mountain of Greece ; now called Monte Santo ; by the Turks Monastir . Atlas Minor , a Mountain of Africa , Part of Atlas Major . Atlas Major , one of the greatest Mountains of Africa . Audus Mons , a Mountain of Africa , upon the Confines of Mauritania Caesariensis , by the Moores called Aurais . Aureus Mons , a Mountain in Maesia ; of which Name are several others in divers Regions . B. BAronisus , a Mountain within the Kingdom of Fesse and Marocco in Africa . Besbicus , an Island in the Propontick Sea , at this Day called Calomio , or Calolino , and Izola del Principe . Berosus , a Mountain of Scythia , where Pliny writes there were three Fountains , which if drunk of , killed without Pain or Remedy . Bontas Mons , or Tabas , seated about the Serrian Mountains . Borysthenes , a Lake near the Euxine Sea , into which the River Borysthenes discharges it self . Byces Palus , a Lake and River flowing into the Lake Maeotis , which is Part of the Euxine Sea , otherwise called Buges , and Suza Morsi . Byzantium , or Constantinople . TABVLA SELENOGRAPHICA Seu Vera adminiculo tubi Orthographica delineato Marium Sinuum Insularū Continent Promont . Lacuū Paludū Montium Planit Vallium in visibilis Lunae hemispherio existent 〈…〉 Autore Iohanno Helvelio . A o. 1645. C. CAdmus , a Mountain of Lydia , not far from Laodicea , whence the River Lycus springs . Calabraria , or rather Colubraria , at this day called Mont Colibre , and as some will , Dragonera , an Island in the Mediterranean Sea , under the Spanish Dominion , not far from Majorca . Calathe , an Island in the African Sea ; by some conceived to be the same with Goletta not far from Tunis . Calchistan , anciently Paropamissus , a Mountain of Persia. Capraria , an Island in the Tyrrhen Sea , now called Cabraia . Carpates , a mighty Mountain , or Ridge of Hills , dividing Moravia , Polonia , and Russia from Hungary and Transylvania , at this day called Crapack . Carpathus , an Island between Creet and Rhodes , one of the Sporades , known likewise by the Names of Porphyris and Tetrapolis , at present by that of Scarpanto . Caput de Tornese , a Promontory of Peloponesus , happily Promontorium Taenaria , or Taenarus , at present called Capo Matapan , and Capo Maina . Carcinites Sinus , a Bay between the Outlet of Borysthenes , and the Bosphorus Cymmerius ; known likewise by the Name of Tamyraces , at this day called Golfo di Nigropoli . Cassiotis , a Region in Egypt or Syria . Casius Mons , a Mountain on the Coast of Egypt , at this day Larissa ; where was the Sepulchre or Monument of Pompey the Great . Caspium Mare ; the Caspian Sea ; called likewise the Hyrcanian , Albanian , and Tartarian Sea , at present Abachu , Sala , Cunsar . Cataractes , a Mountain of Egypt ; not far from Nilus . Caucasius Sinus , a Bay of the Euxine Sea. Caucasus , or Caucasii Montes , Part of Mount Taurus , between the Euxine and the Caspian Sea , otherwise called Marpesia Cautes , at this day Cochias . Celenorum Tumulus , Mountains of Pamphilia , not far from Apamia . Cercinna , an Island in the African Sea , at this Day called Gamelaria , and Querquenes , by the Italians Chercara . Chadisia Promontorium , a Promontory otherwise called Phadisana on the Coast of the Euxine Sea. Cha●…idici Montes , Mountains of Sicily , at this day vulgarly called S. Riti , or S. Rici , Part of the N●…ptunian Mountain or Pelorus . Cilicum , an Island in the Euxine Sea. Cimmerius Mons , a Mountain or Promontory of the Taurick Chersonesus . Cimmeriae Paludes , the Moors or Fens of the Cimmerii . Cimaeus , a Mountain of Asia , near Troas . Circaeum Promontorium , a Promontory of Campania in Italy , now called Monte Circello . Cirna , a Mountain of Africa , Climax , a Mountain on the South of the Lower Egypt , as also of Phaenicia , not far from the City Biblus , called Passo di Cane ; there is another of the same Name in Arabia Felix . Coibacarani Montes , Mountains of Persia ; known likewise by the name of Bagous Mons , seated in the Region Aria , now Chorazan . Colchis , a Region of Asia , bordering on the Euxine Sea , now called Mengrelia , and by the Turks Caracomulu . Corax , a Mountain of Sarmatia Asiatica . Corocondametis Lacus , a Lake so called from the City Corocondame , scituate near the Euxine Sea , into which the said Lake falls . Corsica , an Island in the Tyrrhene Sea , anciently called Cyrnus , Corsis and Cerneatis , lying against Italy , not far from Sardinia ; at present by the Italians called Corsica , by the French La Corse . Cossyra , or Cossura , an Island in the Mediterranean , reckoned among the African Islands , called likewise Pantalerea . Cratas Mons , or Craton , a Mountain of Sicily , called likewise Nebrodes , at present Madonia . Crathis , or Chelidoreus Mons , a Mountain of Peloponesus , whence springs a River of the same Name . Cragus , a Mountain of Cilicia , or as others will of Lycia , now called Monte di Gorante , and Li Sette Cavi . Creta Insula , the Island of Creet or Candy , heretofore Aeria , Curetis , Macaros , and Macaronesus . Creticum Mare , the Cretan Sea ; that Part of the Aegean and Ionian Seas which surrounds Creet . Cydises , a Mountain about Armenia . Cyprus , an Island in the Mediterranean Sea ; heretofore known by the divers Names of Acamantis , Cerastis , Aspelia , Macaria , Cryptus , Colinia , Spechia , Mejonis , Erosa , Paphus , Chetima , Citica , &c. Cyanea Europaea , an Island near the Thracian Bosphorus . D. DElanguer , a Mountain of Scythia , rising from the Foot of Taurus , by Ptolomy called Chemantini Montes , anciently Imaus , running as far as India , which it divides from Scythia , called by several Names ; In Tartary , Moreghar , Belgyan and Althai ; by the Indians Dalanguer , and Naugracut . Didymae , small Islands in the Mediterranean Sea so called . Didymus , or Dindimus , a Mountain of the lesser Asia , of which Name likewise there are several others . E. EBissus , an Island in the Balearick Sea , now Yvica . Echinades , Islands in the Ionian Sea , at present called Cozzulari . Eos , a Mountain of Egypt . Eoum Mare , the Eastern or Indian Sea. Ericht ini Scopuli , Rocks in the Euxine Sea. Erroris Insula , an Island in the Mediterranean Sea , called likewise Albusama , and at this Day Alboran . Eryx Mons , a Mountain in Sicily , at this Day Monte S. Iuliano . Evila , a Desert in Palaestina . F. FIcaria , an Island not far from Sardinia , at this Day Serpentaria . Fontes Amari , Fountains so called near Nilus in Egypt , already mentioned . Fretum Ponticum , the Pontick Straits , the same with the Bosphorus Cimmerius . Fortis Mons. G. GAllicus Sinus , the Gallick Bay ; that Part of the Mediterranean Sea into which Rhodanus or the Rhosne discharges it self ; called likewise Angulus Gallicus & Salsus . Germanicianus , a Mountain of Africa , otherwise called Mons Iovis : H. HAjalon , a Vally in Palaestine , otherwise called Vallis Lunae , at present Val di Luna . Herculeus Lacus , a Lake in Sicily not far from Aetna , in the Leontine Region , at this Day Lago di Leontini . Herculis Mons , a Mountain near the Heraclean Promontory . Hereus Mons , a Mountain of Sicily , otherwise called Artisino and Tavis . Herculeum Promontorium , stretching into the Palus Maeotis . Heracleum Promontorium , a Promontory of the Euxine Sea. Hermo Mons , the Hill Hermon in Palaestina , called likewise Gal●…ad . Hier●… , an Island near Sicily , called likewise Maritima , at this Day Maretamo , not far from the Lylibaean Promontory . Hippici Montes , Mountains of Asia , near Tartary , at this Day Mazarisci . Hippolai Promontorium , in Europaean S●…ythia , near Borysthenes . Hipponiates Sinus , a Bay on the Calabrian Coast , at this Day Golfo di Taranto . Hor , a Mountain in Palaestine on the Borders of Edom , where Aaron dyed and was buried . Horminius Mons , or Ormenius , a Mountain in Asia near Pontus . Horeb , a Mountain in the Desert of Madian , and contiguous to Mount Sinai . Hiblaei Montes , Mountains of Sicily , of which Name Stephanus reckons three . Hyperboreum Mare , the Northern Frozen Sea. Hyperborei Montes , the Riphaean Mountains to the North of Russia Alba , or Muscovia , called at this Day Camenopoias , whose Summit or Top is called Stolp , they are known likewise by the Names of Doffrini , and Doffrafiel . Hyperboreus Lacus Superior , the upper Hyperborean Fenns . Hyperboreus Lacus Inferior , the lower Hyperborean Fenns . Hyperborei Scopuli , the Hyperborean Rocks . Hyperborea Regio , the Hyperborean Region . I. IDa Mons , a Mountain of Phrygia in the lesser Asia . Insula Orientalior , the Eastern Island in the Carpathian Sea. Insula Occidentalior , the Western Island in the same Sea. Insula , an Island near the Promontory of Aries in the Pontick Sea. Insula Major , the greater Island in the Caspian Sea. Insula Minor , the lesser Island in the Caspian Sea. Italia , heretofore called Ausonia , Hesperia , O●…notria , Saturnia , &c. L. LAcus Major Occidentalis , the greater Western Lake near the Palus Maeotis ; known more particularly by the Name of Odojum , and Iwanow . Lacus Minor Occidentalis , the lesser Western Lake ; more particularly called Ploto . Lacus Meridionalis , the Southern Lake . Lacus Niger Major , the greater black Lake . Lacus Niger Minor , the lesser black Lake . Lathmus Mons , a Mountain of Caria , famous for the Loves of Luna and Endymion , at this Day called Monte di Palatia . Lea , an Island on the Coast of Barbary . Lemnos , an Island in the Aegaean Sea , at this Day Stalimene . Lesbos , an Island in the Aegaean Sea , at this Day Metellino . Letoa , an Island in the Mediterranean not far from Creet , otherwise called Christiana . Leucopetra Promontorium , a Promontory of Italy on the Southern Coast of Calabria , called Capo Dell ' Armi , which yet Brietius conceives to be that called Punta Della Saetta . Libanus Mons , a Mountain of Syria , at this Day Libano . Ligustinus Mons , a Mountain of Italy , perhaps the Ligustick Alps called Montagna di Tenda . Lion sive Leonum Mons , a Mountain of Africa so called , near the Sea Coast of Guinne , heretofore by the Greeks called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. the Chariot of the Gods , by the Portugals Sierra Liona , from the continual Noise of Thunder there heard , resembling the roaring of Lions ; by the Natives it is called Boulombel . Lipulus Mons. Loca Paludosa , the Moores or Fenns in the Island Cercinna , in whose midst in an eminent Hill. Lunae Promontorium , a Promontory on the Coast of Thuscany so called . Lybicum Mare , the Libian or Aegyptian Sea. Lychnitis , a Moore or Fenn in A●…menia Major , called Exsechia . Lybiae Pars , Part of Africa heretofore known by the Names of Olympia , Oceania , Hesperia , and Cepheni●… . M. MAcra Insula , called likewise Achillis , and Leuce , seated in the Bay of Carcinites . Macrocemnii Montes , Mountains so called , in Sarmatia Europaea , not far from the Rivers Ister and Tyras . Malta , or Melita , an Island in the African Sea between Sicily and Africa , famous for the Order of Knights of St. Iohns of Ierusalem there residing . Majorca , an Island in the Balearick Sea. Mampsarus , a Mountain of Africa so called . Mantiana Palus , a large Meere or Pool , in Media on the Confines of Armenia , called by some Actamar , Van , and Vastan , by others Abaunias , and as Paulus Venetus affirms , Geluchalat . Marinus Lacus , a Lake in Thuscany , not far from Porto Ercole , at this Day called Lago d' Orbitello . Masicytus , a Mountain of the lesser Asia , by Strabo called Clymax . Mauritania , a Region of Africa , in Hebrew Phut ; at this Day called Regno d' Algier , and Regno di Tremessin , and by a more peculiar Name Barbary . Mediterraneum Mare , the Mediterranean Sea ; by the Italians and Spaniards called Mare di Levanto , by the Turks Actenitz , i. e. the White Sea , by the Arabs , Bohar Rumi , i. e. the Grecian Sea. Melos Insula , an Island in the Aegaean Sea , now Milo. Menyx Insula , an Island in the African Sea , known likewise heretofore by the Names of Lotophagitis , and Cyra . Mercurii Promontorium , a Promontory on the African Coast , over against Sicily , now called Capo Bon. Mesogys , a Mountain of Lydia . Mycale , a Mountain of Ionia . Mimas , a Mountain and Promontory of Ionia ; now Capo Stillari . Mingui , the same with Carmania Deserta , a Region of Asia . Minorca , an Island in the Balearick Sea. Miris , vel Maeris , a great Lake in Egypt , famous for King Maeris his Sepulcher . Mons Meridionalis . Montana Pharan , in Palaestina . Montana Seir , in Palaestina , or Idumaea , now Sardinay . Montuniates , a Mountain of Thuscany . Mortuum Mare , the dead Sea in Palaestina , called by the Greek and Latine Writers Asphaltites Lacus . Myconius Mons , a Mountain of Sicily , not far from Messana . Moesia , a Region of Europe , otherwise called , Servia , Bosnia , and Moldavia . Mysius Mons , a Mountain of Asia , heretofore called Collis Saturni ; by the Turks at this Day Geschisdage . N. NEptunius Mons , a Mountain of Sicily not far from Messana ; now Monte di Namari , heretofore Pelorus . Nerossus , a Mountain of Tartary . Nilus , or the River Triton . Nitria , a Mountain of Egypt . O. OLympus , here taken for a Mountain of Asia in the Province of Mysia ; known to the Turks at present by the several Names of Anatolaidag , Emerdag , or Emiodag , and Keschisdag . Ophiusa , an Island in the Balearick Sea , under the Dominion of Spain , now Formentera . P. PPaludes circa Mare Mortuum , the Moors or Fenns about the Dead Sea. Paludes Palaestinae , the Moors or Fenns of Palaestina . Paludes Superiores Ponti Euxini , the upper Moors or Fenns of the Euxine Sea. Paludes Inferiores Ponti Euxini , the lower Moors or Fenns of the Euxine Sea. Palus Maraeotis , the Lake , Moor , or Fenn Maraeotis in Egypt , now Lago di Buchiara . Palus Maeotis , the Lake , Moor , or Fenn Maeotis , at this Day called Mar Della Sabacche , Mar Della Tana , and Mar Bianco . Pamphylium Mare seu Phaselicum , the Pamphylian Sea , at this Day Mar di Carmania . Pangaeus Mons , a Mountain of Thrace , now called Malacca , and Castagna . Paestanus Sinus , sive Posidoniates , a Bay of the Mediterranean , at this Day Golfo Agropolitano , and Golfo di Salerno . Paropamisus Mons , Part of Mount Taurus , where it rises to the greatest Height ; by Aristotle called Parnassus , at present Pamer , by some Calchistan . Parthenius Mons , a Mountain of Peloponesus in Arcadia . Poloponesus , a Grecian Peninsula , at this Day Morea . Pentadactylus , a Mountain of Egypt , near the Red Sea. Peronticus Sinus , a Bay of the Euxine Sea , now Cabo de Manco . Persia a Region of Asia , at this Day Farsi , Azamia , and Curazan . S. Petro , an Island near Sardinia , heretofore called Herculis Insula . Petra Pyramidalis , seu Pyramis , sive Mons Faronianus , perhaps the same with Petra Santa in Tuscany , heretofore Fanum Feroniae . Petra Sogdiana , near the Hyrcanian Sea. Peuce , a Mountain in Sarmatia Europaea . Phasianus Sinus , a Bay ▪ so called in the Euxine Sea. Pherme , a Mountain of Egypt . Philyra , an Island of the Euxine Sea. Phaenix , a Mountain of Caria on the Coast over against Rhodes . Pontia , an Island of the Mediterranean Sea ; under the Dominion of Naples , at this Day Ponza . Pontus Euxinus , the Euxine Sea ; at this Day Mar de Marmora , Mar Majore , Caradenis , and Mauro-thalassa . Porphyrites Mons , a Mountain so called from its Colour , which tincture according to Agatharchides it receives from the Minium with which it abounds , of which Colour likewise is this of the Moon . Promontorium freti Pontici , a Promontory of the Pontick Straits . Propontis Sinus , a Bay between the Hellespont and the Euxine Sea ; heretofore known by the Names of Mare Bebricium , and Mare Thracium . Prophetarum Mons , a Mountain so called in Palaestine . R. RAphidim , a Desert in Palestine , not far from Mount Horeb. Rhodus , an Island in the Carpathian Sea , famous heretofore for the Colossus of the Sun. Riphaei Montes . Rupes in Sinu Atheniensi . S. SAcer Mons , a Mountain of Egypt so called . Sagaricus Sinus , a Bay of Scythia Europaea , into which the Rivers Sagaris and Tyras discharge themselves . Salmidessus Sinus , a Bay of the Euxine Sea , so called from the Town Salmidessus , at this Day Stagnara ; others make it Philia , a Promontory of Thrace , at the Mouth of the Pontick Sea. Sanctus Mon ▪ s , a Mountain near the Palus Maeotis . Sardinia Insula , an Island in the Tyrrhene Sea , under the Dominion of Spain , by the Italians called Sardegna , by the Spaniards Zerdegna . Sarmatiae Europaeae Pars , Part of Sarmatia Europaea . Sarmatici Montes , Mountains of Sarmatia Europaea , at this Day called Montes Scepusienses . Sarmatiae Asiaticae Pars , Part of Sarmatia Asiatica . Scithiae Pars , Part of Scythia at this Day Tartary . Sepher Mons , a Mountain of Palaestine ; but there is another so called in India , of an exceeding Height , as this likewise of the Moon is . S●…rrorum Mons , a Mountain of Sarmatia Europaea . Sicilia , the greatest Island in all the Mediterranean , heretofore called Sicania , Trinacria , Triquetra . Sinai Mons , Mount Sinai in Arabia Petraea , at this Day called S. Catharina , by the Turks Turla , and Gibel Thor , and Gibel Mousa ; that is , the Mountain of Moses . Sinopium Mons , a Mountain of Egypt , otherwise called Memphidis Mons , or the Mountain of Memphis . Sinus Orientalis Maris Hyperborei , the Eastern Bay of the Hyperborean Sea. Sinus Inferior Maris Caspii , the Inferior Bay of the Caspian Sea , in which there is seen a signal Rock . Sinus extremus Ponti Euxini , the utmost Bay of the Euxine Sea. Sinus ad Bosphorum Thracium Propontidis , the Bay of Propontis at the Thracian Bosphorus . Sinus ad Hellespontum Propontidis , the Bay of Propontis at the Hellespont . Sipylus , a Mountain of the lesser Asia ; of which Name likewise there are divers others . Sirbonidis Eruptio , the Sirbonick Straits . Sirbonis Sinus , a great Lake in Palaestina , upon the Confines of Egypt ; called at this Day by the several Names of Stagnone , Golfo di Tenesse , Golfo di Damiata , Camet Esturnel , and Baranguerlis . Sogdiani Montes , the Sogdian Mountains , the Boundaries of Media , and Assyria , at this Day Cabusco . Strobilus Mons , a Mountain so called , Part of Caucasus . Strophades , two small Islands in the Ionian Sea , at this Day Strivali . Strimonicus Sinus , the Bay of Strymon in the Aegaean Sea , or Archipelago , now Golfo di Contessa , from an adjacent Town of that Name . Syrticus Sinus Minor , the Bay of the lesser Syrtis in the Mediterranean , upon the Coast of Africa , at this Day Golfo de Capes . Syrticum Mare , the Bay of the great Syrtis in the Mediterranean extended between the Regions of Cyrene and Tripolis , now by the French called Les Seiches de Barbarie ▪ by the Spaniards Baxos de Barbaria , by the Italians , Golfo di Sidra . T. TAbor Mons , Mount Tabor in Iudaea , famous for the Transfiguration of our Saviour , at this day retaining its old Name . Taygetus , a Mountain of Laconia near Sparta ; now Portes . Tancon Mons , a Mountain so called near the Caspian Sea. Tarantinus Sinus , a Bay in the Mediterranean Sea , at this day Golfo di Taranto . Taurus Mons ; Mount Taurus the greatest of the whole Earth , as this of the Moon . Taurica Chersonesus , the Taurick Chersonesus ; at this Day Chrimski , Precopska , and Gazaria . Taraciniae Insulae . Techisandum Mons , a Mountain of Persia. Thambes Mons , a Mountain of Africa . FIGURA PRO NOMENCLATURA , ET LIBRATIONE LUNARI Tenarium Promontorium , the. Promontory of Taenarus in Peloponesus , now Capo Matapan . Thospitis Lacus , a great Lake or Meer in Armenia on the Borders of Mesopotamia , now Gabacu . Tmolus Mons , or Timolus , a Mountain of Phrygia , at this Day Tomalitze . Trapezus Mons , a Mountain in the Taurick Chersonesus , at this Day called Lustra , and Trebizonde , by the Turks Tarabossan . Trasimenus Lacus , a famous Lake of Italy , at this Day Lago di Perugia . Troicus Mons , a Mountain whence the Aegyptian Pyramids were hewen . U. VUlcania Insula , an Island in the Mediterranean Sea , near Lipara , on the right hand of Sicily not far from Italy , now Vulcano . Uxii Montes , Mountains so called in Armenia Major , whence Tygris hath its Source . Z. ZAcynthus , an Island near Peloponesus , at this Day Zante . And thus much as to the Explanation of the several Names of the Lunary Spots , according to the Design of HEVELIUS in his Selenographick Scheme or Mapp . To the Scheme of Hevelius , We shall add that of Grimaldi , as the same is represented by Ricciolus in his Almagest . l. 4. p. 204. divided into Eight Parts or Octants , and describing the several Parts , or Spots of the Moon , not according to the Geographical Design of Hevelius ; but by the Names of the most Eminent Philosophers , and Astronomers , as well Ancient as Modern , as may appear by the following Nomenclature , wherein the Synonyma of such Spots , or Parts as are added from the Selenography of Langrenus , and Hevelius , are respectively marked with the first Letters of their Names , L. and H. Nomenclature of the Parts of the Moon for the Selenography of P. Maria Grimaldi . 1. OCTANS . Anaximander Aristarchus L. Balthassar Cleostratus Ecphantus Eratosthenes L. Gassendus L. Haro Harpalus Helicon Cyzicenus Heraclides Ponticus Oenopides Pitheas Massil . L. Pythagoras Timocharis Xenophanes . 2. OCTANS . Anaxagoras Aratus Archimedes L. Roma H. Corsica Archytas Aristillus Aristoteles L. Brahe Autolycus Calippus Conon Democritus Epigenes Euctemon Eudoxus L. Pozzo Meton L. Amalsi Philolaus Plato L. Panciroli Lacus H. Lacus Niger Thales L. Xenophanes Theaetetus Timaeus . 3. OCTANS . Atlas Berosus Cepheus Endymion Geminus Hercules Hermes Hyginus Manilius L. Isabella R. Hisp : H. Insula Besbicus Menelaus L. Maria Imperatrix Mercurius Messala Arabs Osymandiez Posidonius L. Lafailli Sulpicius Gallus Zoroaster 4. OCTANS . Agrippa Alcuinus Ariadaeus Beda Cleomedes Dionysius Exiguus Firmicus Goclenius Iul. Caesar Langrenus Macrobius Plinius Plutarchus Proclus L. Puteanus Seneca Sosigenes Taruntius Vitruvius . 5. OCTANS . Aben Ezra Abulfeda Alfraganus Almaeon Azophi S. Catharina L. Picolomini S. Cyrillus Alex. S. Dionysius Areop . Fabricius Fracastorius Fournerius S. I. Geber Hypparchus Hypatia S. Isidorus Hisp. Rab. Levi Mart. Capella Metius Mulerius Neander Petavius S. I. Pontanus Picolomineus Reitha Riccius Sacroboscus Santbechius Snellius Stevinus Stiborius Tatius Achill . Theon Sen. Theon . Iun. S. Theophilus Alex. Vendelinus Zagutus 6. OCTANS . Albategnius L. Ferdinandus Imp. Aliacensis Alpetragius Alfonsus Rex L. Ludovicus 14. Apianus Arzachel Arzet S. I. Barocius Bettin●…s S. I. Blancanus S. I. Blanchinus Cabaeus S. I. Clavius S. I. L. Maximilianus Curtius S. I. Cysatus S. I. Daniel Bartolus S. I. Fernelius Gauricus Gemma Frisius Griembergerus S. I. Gulielm . Hassiae Princ. Hagecius Homelius Kircherus S. I. Licetus Lilii Fratres Longomontanus Maginus L. Visilii Manzinus Malapertius S. I. Maurolycus H. Estensis Dux Moretus S. I. Mutus Nonius Orontius Pitatus Pitiscus Ptolemaeus L. Innocentius X. H. Mons Sypilus Purbachius Regiomontanus Sasserides Scheinerus S. I. Schomberger S. I. Simpelius S. I. Stoeflerus Tannerus Waltherus Vernerus Zucchius S. I. 7. OCTANS . Bayerus Bullialdus L. Medicaei Byrgius Campanus Capuanus Cichus Asculanus Crugerus Dersennis S. I. Eichstadius Fontana Gassendus L. Annullus Neptuni Hainzelius Herigonus Iunctinus Kristmannus Mersennus Morinus Munosius Origanus Phocylides Profacius Rothmannus Schikardus Schillerus Vieta Zupus S. I. 8. OCTANS . Anton. Rocca Bessarion Billy S. I. Cardanus Cavallerius Copernicus L. Philippus 4. H. Mons Aetna Cusanus Dominicus Maria Egnatius Dante 's Eustachius Galilaeus Grimaldus S. I. L. Lacus Posidonii H. Lacus Maeotis Hortensius Hevelius Keplerus Lansbergius Linemannus Milichius Moletius Reinerus Reinholdus Rheticus Ricciolus S. I. Seleucus Simon Marius Sirsalis S. I. Stadius . Nomenclature of the Lunary Regions , whereto is added the Number of the respective Octants to which they appertain . Insula Ventorum , 8. Lacus Mortis , 3. Lacus Somniorum , 3. L. Lacus Scientiae H. Palus Hyperborea Littus Eclipticum , 1 , & 8. L. Littus Philippicum Mare Crisium , 4. L. Mare Caspium H. Palus Maeotis Mare faeeunditatis , 4 , 5. L. Mare Langreni Mare Frigoris , 2. L. Mare Astronomicum Mare Humorum , 7. L. Mare Venetum Mare Imbrium , 1 , 2. L. Mare Austriacum Mare Nubium , 7. L. Mare Borbonicum Mare Nectaris , 5. L. Sinus Batavicus Mare Serenitatis , 3 ▪ L. Mare Eugenianum H. Mare Euxinum Mare Tranquillitatis , 4. L. Mare Belgicum H. Euxinus Mare Vaporum , 3. Oceanus Procellarum , 1 , 8. L. Oceanus Philippicus H. Mare Eoum Palus Nebularum , 2. L. Terra Virtutis Palus Nimborum , 7. Palus Putredinis , 2. Palus Somni , 4. L. Aestuaria Bamelr . Peninsula Deliriorum , 7. Peninsula Fulgurum , 7. Peninsula fulminum , 7. Sinus Aestuum , 7. L. Sinus Medius H. Mare Hadriaticum Sinus Epidemiarum ▪ 7 L. Mare Populorum Sinus Iridum , 1. L. Sinus Geometricus H. Sinus Apollinis Sinus Roris , 1. L. Sinus Principis Stagnum Glaciei , 2. Terra Caloris , 7. Terra Iustitiae Terra Fertilitatis , 5 , 6. L. Terra Dignitatis H. Asia Terra Grandinis , 2. Terra Mannae , 4 , 5. L. Terra Temperantiae . H. Cholchis Terra Nivium , 2. L. Montes Austriaci H. Ital. Apenninus Terra P●…uinae , 1. L. Terra Laboris H. Mauritania Terrra Sanitatis , 5. L. Terra Dignitatis H. Asiae Pars Terra Siccitatis , 1 , 2. L. Terra Honoris Terra Sterilitatis , 7. Terra Vitae , 3 , 4. L. Terra Sapientiae H. Sarmatia Terra Vigoris , 4 , 5. L. Terra Pacis . Of its motion either of Revolution or Libration , We shall not here say any thing , it being beside our present Design . But as to its Distance , Apparent Diameter and Magnitude , We have thought fit to add the following Tables . Table of the Moons Distance from the Center of the Earth in Semidiameters of the same , and its Horizontal Parallax . In Opposition , or Conjunction Distance from the Center of the Earth Horizontal Parallax According to the following Authors Apog . Med. Perig.   Apog . Med. Perig.   Semid . ′ Semid . ′ Semid . ′   ′ ″ ′ ″ ′ ″ Ptolemaeus 64 10 59 0 53 50   53 34 58 16 63 51 Copernicus 65 30 60 19 55 8   52 56 57 0 62 54 Tycho 58 8 56 30 54 52   59 9 60 51 62 39 Longomontanus 57 38 56 0 54 23   59 37 61 26 63 14 Lansbergius 64 10 59 5 54 0   53 34 58 8 63 39 Bulialdus 61 40 59 5 56 30   55 56 58 16 60 52 Ricciolus 64 15 59 0 53 45   53 30 58 16 63 55 Kepler . in Ephemerid . 62 52 59 0 55 8   54 41 58 16 62 20 Kepler . in Epit. Astr. & Tab. Rudolph . 59 0 56 28 54 0   58 22 60 53 63 41 Hipparchus for sometime 83 0 77 0 71 0   41 30 45 0 48 30 Afterwards 72 30 67 30 62 30   47 30 51 30 55 30 Alphonsus 61 8 57 45 54 23   53 19 59 21 63 17 Argolus 60 4 56 0 51 57   56 45 61 17 65 36 Vendelinus 63 56 60 0 56 4   53 46 57 18 61 18 Kircherus . 67 50 62 37 57 24   — — — — — — In its Quadratures . Distance from the Center of the Earth Horizontal Parallax Authors Apog . Med. Perig.   Apog . Med. Perig.   Semid . ′ Semid . ′ Semid . ′   ′ ″ ′ ″ ′ ″ Ptolemaeus 43 53 38 43 33 33   60 19 89 0 103 0 Copernicus 68 21 60 19 52 17   50 19 57 0 65 48 Tycho 60 36 56 30 52 24   56 44 60 51 65 36 Longomontanus 60 4 56 0 51 57   57 15 61 26 66 9 Lansbergius 66 58 56 5 51 12   51 20 58 8 67 6 Bulialdus 64 15 59 5 53 55   53 30 58 8 63 43 Ricciolus 66 42 59 0 51 20   51 32 58 16 66 56 Kepler . in Ephemerid . 61 36 59 0 56 24   55 26 58 16 60 58 Kepler . in Epit. Astr. & Tab. Rudolph . 59 0 56 28 54 0   58 22 60 53 63 41 As to the Apparent Diameter of the Moon ( not saying any thing of the several Methods of attaining the same from the Observation of Eclipses , of which Ricciolus l. 4. Almagest . N. c. 16. ) the following Table ( taken from the said Ricciolus ) will shew the several Opinions of the Ancient and Modern Astronomers . Synopsis of the Apparent Diameters of the Moon In Opposition , Conjunction , and square Aspects Apparent Diameter of the Moon Apog . Perig. Authours   ′ ″ ′ ″ Ptolemaeus in ☌ and ☍ 31 20 35 20 in □ 42 8 55 0 Albategnius in ☌ and ☍ 29 30 35 20 Alphonsus and Purbacchius in ☌ and ☍ 29 0 36 8 Copernicus , Reinholdus , and sometime Maginus in ☌ and ☍ 30 0 35 38 in □ 28 45 36 44 Maginus in Suppl . Ephemer . in conjunction ; and ☍ 30 30 34 40 Clavius and Herigonius in ☌ and ☍ 30 0 36 8 Tycho , Origanus , and Mulerius in ☌ 25 36 28 48 in ☍ 32 0 36 0 in □ 32 32 36 0 Longomontanus Physice in ☌ and ☍ 32 0 34 0 Keplerus in Ephemer . in ☌ and ☍ 30 0 34 10 In Epit. and Tab. Rudolph in ☌ and ☍ 30 0 32 44 Lansbergius in ☌ and ☍ 30 0 35 38 Petr. Gassendus in ☌ and ☍ 26 36 31 06 Ism. Bulialdus in ☌ and ☍ 31 10 34 0 in □ 29 56 36 4 Got. Vendelinus in ☌ and ☍ 28 40 32 42 Sed in Vertice in ☌ and ☍ 29 10 33 18 Kircherus in ☌ and ☍ 29 22 34 40 Ricciolus in ☌ and ☍ 28 0 33 30 in □ 27 0 35 6 From the Distances of the Moon , and apparent Diameters already given , the true Magnitude thereof may methodically be deduced ; which ( without the trouble of calculating ) the Reader may see plainly exhibited , in the following Table , according to the Opinions of the several Authours therein mentioned . The true Magnitude of the Moon compared with that of the Earth and Sun. According to The true Diameters of the Moon and Sun unto that of the Earth supposed to be 100. The Solidity of the Moon to the Earth Sun Moon Earth Sun as to as to Aristarchus more than 31 2 / 4 100 633 1 16 1 5832 Aristarchus less than 39 4 / 5 100 716 1 32 1 8000 Ptolemaeus 29 2 / 6 100 550 1 40 1 6648 Copernicus 28 4 / 7 100 545 1 42 ●… 1 6999 1 / 60 Moestlinus 28 ●… 100 546 1 44 1 7300 Tycho 29 1 / 6 100 520 1 41 11 / 12 1 5848 Longomontanus 26 5 / 6 100 580 1 51 1 / 49 1 10000 Keplerus 25 7 / 10 100 1500 1 59 1 204671 Lansbergius 28   100 757 1 45 11 / 20 1 19770 Bullinldus 27 11 / 12 100 700 1 45 29 / 30 1 15765 1 / 3 Vendelinus 26 5 / 8 100 6400 1 53 1 13833632 Kircherus 29 7 / 17 100 520 1 40 1 5600 Schyrlaeus 28 3 / 7 100 1000 1 42 19 / 20 1 42875 Ricciolus in Alm. 26 1 / 5 100 3383 1 55 1 2123000 Ricciolus Astr. Ref. 27 1 / 2             Whether the MOON be Habitable . That the Moon is inhabited , is by divers as well Philosophers as Astronomers at this Day maintained and asserted ; from the Appearance of Mountains , Vallies , Woods , Lakes , Seas and Rivers discovered therein by help of the Telescope , which Opinion was long since embraced by the Ancients , as Cicero testifies , ( Academ . Quaest. l. 4. ) where he cites the Authority of Xenophanes . Habitari ait Xenophanes in Luna , Eamque esse Terram multarum Urbium & Montium . Plutarch likewise De Placit . Philosophicis l. 2. c. 30. reports that the Pythagoreans affirm , the Moon to be an other Earth , and that she is inhabited round about like this Earth of ours , and peopled with Living Creatures fifteen times larger than those with us . These Inhabitants were by the Ancients called Antichtones , in regard they dwelt in an Earth opposite to ours . And in that noted Piece of his , De faciè in Orbe Lunae . He sayes that there are Caverns in the Moon which are called Penetralia Hecates , and that the Upper Parts of the Moon which alwayes respect the Heavens are the Elysian Fields ; that it is likewise inhabited by Genii , which dwell not alwayes there , but sometime descend to the Earth to the Assistance or Punishment of Mankind , &c. Macrobius likewise in Somn. Scipionis l. 1. and Achilles Tatius in Isagog . report the like of the Moon 's being habitable . The Words of Macrobius are these , Lunam , Aetheream Terram Physici vocaverunt , & Habitatores Ejus Lunares populos nuncuparunt ; quod ita esse plurimis Argumentis , quae nunc longum est enumerare , docuerunt . See to this Purpose more in Kepler in his Astronomia Optica , and particularly in that marvellously ingenious Posthume Piece of his called Somnium , sive de Lunari Astronomia ; and in his Learned Annotations thereupon , and on Plutarch his Book , De facie in Orbe Lunae , thereto annexed : Nor will this seem an extravagant Opinion to those who shall upon due consideration , be perswaded to admit that the Moon enjoys as favourable an Aspect from the Sun as this Earth of ours ; though their Dayes and Nights be answerable to our half Months , in regard it is skreened with Hills and Mountains , under which lie deep and shady Vallies , with Hollow Caves and Recesses , equally advantagious against the Extremities of Heat and Cold , watered likewise with great Lakes and Rivers , and consequently by Nature furnished with all things requisite for sustentation of life , and therefore it cannot reasonably be thought , that these Advantages and Benefits should be conferred by Nature for no Use or End ; or that the Moon should only be made to reflect the Sun's Light to us . See the Learned Dr. Isaac Vossius in his Treatise De Natura & Propriet . Lucis . c. 19. But what kind of Creatures these Lunary Inhabitants are , is not agreed upon , though Kepler be something Positive , Concludendum videtur ( sayes he , in Not. ad Appendic . Selenograph . ) in Luna Creaturas esse Viventes , Rationis , ad Ordinata facienda , Capaces . The like is affirmed by him as to the other Planets , nay the Sun it self , touching which last , in the Epilogue to his Fifth Book , ▪ De Mundi Harmonia , he breaks out into this Expression , Vel Sensus ipsi exclamant , ignea hic habitare corpora , Mentium Simplic●…um Capacia , Veréque Solem esse 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Si non Regem , at saltem Regiam . This cannot perhaps seem more strange to some , than the following Assertion to Others , which maintains the Moon to be the Paradise wherein Our first Parents were created , and from whence for their Transgression they were thrust down to this Earth of ours ; and yet this from Reason and the Authority of Fathers and Schoolmen , is endeavoured to be proved by Hieronymus Vitalis in Lexic . Mathemat . in Voce Paradisus ; where he sayes , fateor id novum , Singulare & hactenus inauditum ; at non per hoc temerarium , atque intolerabile dixeris ; for , as he urges , modò partâ tantâ rerum Notitiâ , Lunae facie Telescopio penitissimè observatâ , Veterum dictis Expensis , Locis ( super hanc Terram ) investigatis , Paradisum in Lunae superficie collocare , Ratio ipsa compellit . To whose large Discourse upon that Subject we refer the Reader . MERCURY . The next Planet in order is Mercury ; of whose Place , Figure , Nature , and Substance something , according to our Method is briefly to be added . It is carried in an Epicycle about the Sun , as the Center of its Motion and Orb : Now running above , now beneath the Sun ; Sometimes higher than Venus , sometimes lower : For when these two Planets ( Venus and Mercury ) are in their Apogaea , and above the Sun , then Mercury is beneath Venus ; when in their Perigaea and beneath the Sun , then Mercury is above Venus : So when Venus is in her Apogaeum , and Mercury in his Perigaeum , then is he beneath Venus ; when Venus is in her Perigaeum , and Mercury in his Apogaeum , then is he above Venus , as may appear by the Egyptian and Tychonick Systems . It s Figure is orbicular or round , not Mathematically but Physically such , rising here and there with extuberating Hills and Mountains , in the same manner as this Earthly Globe of ours ; being , like that , an opacous Body , and receiving its Illumination from the Sun ; whence at several times it is seen under several Phases or Appearances ; for in it's greatest Digression from the Sun , ( which is never above 28° . ) it appears Dichotomous ; but when he is retrograde , and approaching to an Opposition with the Sun , he appears in a Figure like that of the New Moon , when distant about 60° . Degrees from the Sun ; though this Phasis be very rarely discerned by reason of his small Digression from the Sun , and the quick Vibration of his Rayes , ( whence by the Greeks he is called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , ) the Vivacity of his Light exceeding that of Venus and Iupiter , and thence impeding the Sight from rightly beholding that Phaenomenon , unless fortified by an excellent Telescope , as likewise in regard of the great Refractions made by Vapours near the Horizon , especially in Climates more obliquely posited , as is noted by Regiomontanus and Copernicus , who for that Reason could never be so happy as duly to observe these Mercurial Phases . Riccciolus ( in Astr. Reform . l. 10. ) reports that he , together with Franciscus Maria Grimaldi in the year 1643. the fifth of March , when Mercury was in the Upper Part of his Epicycle , and Vespertine at 15° . of Elongation from the Sun , beheld him in a Gibbous Figure , like the Moon when more than half full ; the like in the year 1656. December 16 th . In the year 1643. August 25 th . the same Persons , beheld him being Matutine , and 19° . distant from the Sun , in a Figure like that of a Sickle or Sy●…he ; so likewise in the year 1644. August the 6 th . being distant from the Sun 20° . But in the year 1647. April 30 th . being Vespertine , and distant from the Sun 20° . they beheld him in a like Sythe-like Figure , but more approaching toward a Dichotomy , in the same Figure likewise they beheld him in the year 1650. when Vespertine and distant 18° . from the Sun. There are observed in him likewise several Spots successively following one another , some light , some duskish ; which light Spots are by Kircherus ( in Itiner . Exstatic . Dial. 1. c. 4. ) conceived to be the said Terrestrial and Mountanous Parts of the Mercurial Globe illuminated by the Sun , the dusky ones to be the liquid or watery Parts thereof , which by their Successive Motion likewise evince that he hath a Vertiginous Rotation about its own Axis , determined within the space of six Hours , or thereabouts , as Rheita affirms . As to its Distance from the Earth , the same is by Tycho computed to be in its greatest Distance 1660. Semidiameters of the Earth , in its mean Distance 1150. in its least 630. but according to the Calculation of Ricciolus , in its greatest Distance 10868. Semidiameters , in its mean 8057. in its least 5246. It s Apparent Diameter in its mean Distance is by Tycho computed to be 2′ . 10″ . by Ricciolus in its greatest Distance to be only 9″ in its least Distance 25″ . It s true Magnitude , according to Ricciolus ( supposing its mean Distance to be as before exprest , and its Diameter to contain ¼ part of the Earth's Diameter ) is concluded to be less than the Earth's Body by 1 / 256 part . Which being reduced to the Measures of Kepler , its Diameter may be reckoned to contain 377 Italian Miles , the Solidity of its Body 21253933 Cubical Italian Miles , or thereabout . VENUS . The most illustrious of all the lesser Planets , hath been observed by the curious from all Antiquity : The chief Remarks made by the Ancients are these : First , they observed her sometime to precede the Sun , rising in the Morning before him , sometime to follow the Sun , setting in the Evening after him , now to be in Conjunction with the Sun , that is in the same right Line drawn from the Observers Eye to the Center of the Sun , at other times receeding from him , to the Distance of 48 Degrees , and this was the first and most obvious Phaenomenon . They observed her likewise to differ in Magnitude , appearing sometimes greater , sometimes less , sometime of a mean or middle Size , whence they concluded her to approach sometime nearer to the Earth , and to be in Perigaeo , at other times to recede further from it , and to be in Apogaeo , and this was the second Phaenomenon ; but not commonly observed or obvious to All. As to her rising and setting they observed that she was never so remote from the Sun , as that she ever set Cosmically , or rose Acronychally ; that is , that she ( the Sun rising in the Eastern Horizon ) never set at the same time in the West , or ( the Sun setting in the West ) never rose at the same time in the East ; for Venus cannot be opposed Diametrically to the Sun , in regard she never digresses from him above 48° . or thereabout : Whence , Venus rising in the Morning Heliacally , that is emerging out of the Sun's Beams , under which she lay hid , digresses more and more from him , and ( he rising ) appears higher and higher above the Horizon , until she comes to the Terms of her greatest Digression aforesaid ; thence reapproaching the Sun , is hidden in the Morning Heliacally , that is , is obscured under the Sun's Beams , until such time as emerging Heliacally in the Evening , she rises ( the Sun setting ) higher and higher above the Horizon , until she comes to the aforesaid Terms of her greatest Elongation ; which past , she again approaches toward the Sun until such time as in the Evening she sets Heliacally . And this is the third Phoenomenon , observable by All , but noted only by the curious , sayes Schottus ( in Praelus . in Vener . in Itiner . Exstat . Kircheri . ) Besides these Observations of the Ancients , Modern Astronomers by the help of the Telescope have noted several other signal Phaenomena , as that she is lyable to the same variety of Changes as the Moon , sometimes almost full , at other Times gibbous , and now and then horned , as well when she is Vespertine as Matutine , manifested by the various Observations of Galilaeo , Scheinerus , Fontana , Hortensius , Keplerus , Rheita , Gassendus , and Hevelius . She is sometime likewise seen by Day , at which time according to Galilaeus and Hevelius , her true Figure is best to be discerned in regard she is despoyled of those Adventitious Rayes , with which in the Night time she is invested . Ricciolus and Grimaldus in the year 1649. on the first of April beheld her of a Gibbous Figure ; and on the twentieth of the same Moneth bisected or dichotomised ; and on the first of May , and first of September the same year , horned , and so continued until the fourth Day , two Hours after Noon , and so to the eighth Day of the same Moneth from the Sun 's rising 'till Noon . On the eighteenth she was exactly Bisected or Dichotomised ; on the twenty sixth growing toward a Gibbous Figure . But the rarest and most Signal Phaenomenon of Venus ( sayes Ricciolus ) is when she hath greatest Latitude , near her Lowest Conjunction with the Sun : For being then seen by a good Telescope she appears horned , as big as the New Moon to the bare Eye . Of the Structure , Nature and Substance of this Planet from the Phaenomena already recited , it may be concluded that it is an opacous Body , and hath its Light from the Sun ; that it is spherical , because it is spherically illuminated ; that it is of a solid and consistent Substance in regard , though carried in a rapid Course through the liquid Aether it is not dissolved or dissipated : It is of a rough and uneven Superficies , in regard it is represented to be such by the Telescope , and otherwise , could not in such abundance reflect the Sun's Light upon the Earth , which it is observed sometimes to do to such an eminent Degree , that Bodies objected to its Rayes are seen to cast a shadow , it is made up of solid and liquid Matter , as our Terraqueous Globe , and is found to have a Vertiginous Motion about its own Axis and Center , which it compleats within the space of fourteen Hours , according to Rheita . As to its Apparent and true Diameter , its Solidity and Proportion to the Body of the Earth , as likewise its Distance from thence , Authours extreamly vary . Ricciolus in the Seventh Book of his Almagest , Sect. Sixth , hath collected their several Opinions into one Table , to which for Brevities sake We refer the Reader ; contenting our selves only to note that according to the said Ricciolus . The Apparent Diameter of Venus in its greatest Distance from the Earth , is , 0′ . 33″ . 30‴ . in its mean Distance 1′ . 44″ . 12‴ . in its least 4′ . 8″ . 0‴ . It s true Diameter contains of the Earth's Diameters 1. 15 / 1000. It s Circumference three Diameters of the Earth and ⅗ . the Area of its greatest Circle , square Diameters of the Earth 1. 4 / 1000. It s convex Superficies square Diameters 4. 15 / 1000. The Body of Venus that of the Earth 1. ½ . It s Distance from the Earth he makes to be when greatest 12919 Semidiameters of the Earth ; It s mean Distance 7580 , it s least 2241 of the same Semidiameters . MARS . Though of all the rest the most inobservable Planet ( as both Pliny and Kepler affirm ) hath not yet been able to lie hid from the subtle Discoveries of Astronomical Spies ; who have observed that he moves in a large Orbit about the Sun , as the Center of its Motion , in which Circle or Orbit he includes the Earth with the Moon , Mercury and Venus , and takes up a great Part of the Solar Region , and when in his Perigaeum , becomes nearer to the Earth than the Sun , as may appear by his Parallax , at that time greater than the Suns ; and the notable increase of his Light , by reason of which he is sometimes taken for a Comet or New Star. As to his Figure , it is without doubt ( as the other Planets ) Spherical ; and is observed by Kepler ( l. 6. Epit. Astr. ) when in □ with the Sun , to be almost bisected or Dichotomous , at other times between □ and ☍ to the Sun to be gibbous , and rarely perfectly round as Rheita affirms . Hevelius denies that it can ever be seen horned . Fontana in his Observations represents it , as by him viewed in the year 1636. in a round Figure with a black Spot in the Middle , which he conceives to be a Cavity , and not a rising or swelling . Nicholaus Zucchius , as Ricciolus ( in Astronom . Reform . ) reports , beheld him in the year 1640. between △ and □ with the Sun to be gibbous or bossed without any such Spot , perhaps by reason of his vertiginous Motion or Libration about his own Center changing its Position . Daniel Bartolus in the year 1644. ( as he writes to Ricciolus ) affirms , that Father Sirsalis the Jesuite at Naples beheld him with an excellent Telescope to be almost round with two Spots a little beneath the Middle of his Globe . Ricciolus likewise together which Grimaldus in the year 1651. on the fourth , fifth , and sixth of April beheld that black spot in him ; which appeared to them as if composed of divers smaller ones ; the same Phoenomenon being by them afterwards often observed in the years 1653 , 1655 , and 1657. which black or ruddy Macula or Spot Kircherus ( in Itiner . Exstat . ) conceives to be a great Vorago or Gulf , of no less Extent than all Africa ; the ingenuous Mounsieur Hugens in the year 1656. observed a broad obscure Zone or Belt , to shadow or obfuscate half the Disque of the said Planet . From the several Phases before mentioned of his Dichotomy and Gibbosity , Astronomers argue his light to be derived from the Sun , as that of the Moon ; and Ricciolus is of opinion that if he could be seen in ♂ with the Sun , We might discern him to be horned . As to the Structure and Nature of his Globe , it is as the rest of the Planets , composed ex Solido & Liquido . The Solid Parts by Kircherus ( in Itiner . Exstatic . ) supposed to consist of a fuliginous Substance like that of Sulphur , Arsenick or Orpiment , hard , and incombustible , evapourating malignant and destructive Qualities , and sweating out in great plenty a kind of bituminous Matter , not unlike to Naphtha . It s liquid Parts he imagines to consist of a soft and clammy Substance , like to our melted Pitch mixt with Sulphur . He hath a Vertiginous Motion about its own Center , which is compleated according to Rheita in the space of forty five Hours , six Minutes . It s apparent Diameter according to Ricciolus , being in its greatest Distance from the Earth 10″ . 6‴ . in its mean Distance 22″ . in its least 1′ . 32″ . It s true Diameter contains of the Earth's Diameter 0. 12 / 1000. Parts , the solidity of his Body , the Earth's Body 0. 14 / 1000. It s greatest Distance from the Center of the Earth , being by the said Ricciolus computed to be 21005 Semidiameters of the Earth , its Mean Distance 11000 , and its least 2373 of the said Semidiameters . JUPITER . One of the most noted and Beneficent Planets , is carried in an Orbit above Mars , as is manifest in the mutual Conjunctions of those Planets , at which time he is obscured and hidden from our Sight by the Interposition of Mars , as the Sun is by that of the Moon 's Body . Rheita affirms that he observed Iupiter to be invested round with a vapid Atmosphere . And Leander Bandtius Abbot of Duisburgh ( as Ricciolus in Astron. Reform . ) reports in the year 1643. observed the Edges or Margins of his Globe to be very rough and uneven , rising with Tumours like Hills and Mountains , and discovered in his Body by the help of an excellent Telescope , two small Maculae or Spots , and two great Ones , like hollow Caverns , one Round , the other Oval , equalling in Longitude the seaventh Part of his Diameter , as the Scheme thereof transmitted by the said Bandtius from Flanders to Ricciolus is said to have represented the same . Hevelius likewise in his Selenography ( p. 44 ) affirms , that the Face of Iupiter is variegated with Spots in a manner like that of the Moon , and rugged with uneven Swellings and Asperities as that is . But leaving these to further Discovery ; We shall only take Notice of the more Ordinary Phaenomena , manifested by frequent Observations . And those are : First , Certain Fasciae , or Belts , girdling as it were the Disque of Iupiter , whether eminent Parts of his Body like Ridges , or rather hollow Furrows or Trenches , is uncertain . But they are said first to have been discovered at Naples by Io. Baptista Zuppus , and Daniel Bartolus Jesuits ; since by Fontana , Grimaldi , Ricciolus , and others frequently discerned and distinguished . They appear sometimes three , sometimes two , at other times single , and bordered with two other smaller Welts like a Bend Cottize ( as the Heralds term it ) sometimes only with one of those small Welts . They are now and then beheld in the Middle of its Disque , now above it , at other Times below it , not alwayes strait , but sometimes crooked and bending ; their Convexities appearing turned sometimes upward , sometimes downward ; Evident Marks of the Vertiginous Motion or Rotation of that Planet about its Center . These sometimes cease to appear , and therefore being at such times observed by Gassendus , no marvail if in his Astronomical Institutions ( l. 3. ) he seems to suspect those Phaenomena , as denying that they ever could be discerned by him , though he made use of a very good Telescope , and one of Galilaeo's making . Secondly , His Satellites , being four Stars so called moving about the Body of Iupiter , as his Guards ; discovered first in Italy by Galilaeo in the year 1610. In Germany by Simon Marius by means of the Telescope ; without which by Reason of Iupiter's Splendor , and their small Distance from him ( None of them receding above twelve Degrees from the Body of Iupiter ) they are not to be discerned ; and therefore altogether unknown to the Ancients . The Number of these have by some Astronomers been questioned , Rheita maintaining them to be no less than nine . Io. Baptista Zuppus affirming he observed in the year 1644. no less than twelve smaller Stars moving about Iupiter , whereof he verily believed eight to be Jovial Guards . But the Number of four only is by Gassendus , Hevelius , and Vincentius Reinerus , who for ten years together most diligently observed them , as also by Vendelinus , Io. Phocylides Olwarda , Ricciolus , and Grimaldus upon surer Grounds defended and asserted . These by Galilaeus their first discoverer were called Sidera Medicaea . The first or inmost next to Iupiter he called Cosmus Minor ; the next or Penintimous Cosmus Major ; the third or Penextimus Maria Medicaea ; the fourth or outermost Katherina Medicaea ; Simon Marius giving yet to the Inmost the Name of Iovial Mercury , to the next Venus ; to the Third Iupiter ; to the Fourth Saturn : But Io. Baptista Hodierna , who lately first of all published Ephemerides of the Motions of the said Stars , names the first or inmost ( from the Young Prince of Tuscany ) Principharus ; the Second ( from Victoria Dutchess to the Grand Duke ) Victripharus ; the Third ( from Cosmus the first Duke of Florence ) Cosmipharus ; the Last ( from Ferdinand the late Duke ) Fernandipharus . Of these the greatest Digressions from the Body of Jupiter computed in Semidiameters of the same , are as followeth . Satellties 1 2 3 4 Authours Sem. ′ Sem. ′ Sem. ′ Sem. ′ Galilaeus 3 0 5 0 8 0 12 0 Sim. Marius 3 0 5 0 8 0 13 0 Rheita 3 0 4 0 6 0 10 0 Vendelinus 3 0 5 0 8 0 14 0 Hodierna 3 30 5 30 9 0 14 30 Their Periodical Revolutions in their several Orbits . Of the According to Dayes Hours ′ ″ 1 Galilaeus 1 18 30 fere Marius 1 18 28 30 Rheita 1 18 30 0 Hevelius 1 18 28 0 Hodierna 1 18 28 44 Vendelinus 1 769 / 1000   — 2 Galilaeus 3 13 20 circiter Marius 3 13 18 0 Rheita 3 13 20 0 Hevelius 3 13 18 0 Hodierna 3 13 18 15 Vendelinus 3 554 / 1000   — 3 Galilaeus 7 4 0 fere Marius 7 3 56 34 Rheita 7 4 0 0 Hevelius 7 3 57 0 Hodierna 7 4 1 26 Vendelinus 7 164 / 1000   — 4 Galilaeus 16 18 0 fere Marius 16 18 9 15 Rheita 16 18 0 0 Hevelius 16 18 9 0 Hodierna 16 18 14 33 Vendelinus 16 756 / 1000   — Their Diurnal and Horary Motion in their respective Orbits each divided into 360° . Of the According to Diurnal Horary 1   Gr. ′ ″ Gr. ′ ″ Galilaeus — — — 8 29 circiter Marius 203 25 0 8 28 30 Hodierna 203 23 44 8 28 29½ 2 Galilaeus — — — 4 13 fere Marius 101 17 22 4 13 0 Hodierna 101 17 21 4 13 13 3 Galilaeus — — — 2 6 circiter Marius 50 14 57 2 6 30 Hodierna 50 13 32 2 5 34 4 Galilaeus — — — 0 54 30 Marius 21 29 3½ 0 53 30 Hodierna 21 28 48 0 53 42 As to Iupiter's Distance from the Center of the Earth , the same is computed by Ricciolus , in its greatest Distance to be removed from thence 47552 Terrestrial Semidiameters ; in its Mean Distance 36500 , and in its least 26441 of the said Semidiameters . It s Apparent Diameter according to the said Ricciolus , being when least , in Apogaeo , 0′ . 38″ . ●…8‴ . when mean , in its mean Distance from the Earth , 0′ . 49″ . 46‴ . when greatest , in his Perigaeum , 1′ . 08″ . 46‴ . It s true Diameter contains of the Earth's Diameters Eight and 4 / 5. It s Circumference 27 , 63 / 100 of the said Diameters . The Area of his greatest Circle 64 square Diameters of the Earth : It s Convex Superficies 242 of the said square Diameters . The Solidity of its Body , contains that of the Earths 685 Times . As to the structure of its Globe , We may conclude it with the rest of the Planets , to be composed of Solid and Liquid Parts , and by what hath been already said , that it is of a Body though Physically Round , full of uneven Asperities , invested with a vapid Atmosphere , carried about its own Center by a Vertiginous Motion , finished according to Rheita in 11 Dayes , 20 Hours , 1 Minute 15″ . and that its Zones or Belts are solid Parts less capable of Light than the rest of its solid or liquid Parts are . SATURN . The Highest , and of all the Primary Planets ( hitherto known ) the most remote from the Earth , runs his Course above all the rest , and beneath the Fixed Stars ; as is collected from his Parallax , ( of all the Planets ) the least , and in a manner none at all . Nor are there any either of the Fixed or Erratick Stars that afford to the observing Eye , by means of the Telescope such strange and admirable Phaenomena : The chiefest and most worthy of Note are Three . First , That he appears girdled about , with a certain Fascia or Zone , or rather encompassed about with an Armilla or Ring of Light. Second , That he hath several Lunulae , or lesser Planets , like the Jovial Satellites moving about his Body . Third , That his Figure appears variously and incredibly diversified , being sometimes beheld solitary in a round Form , at other Times represented with two Rundles adhering to each side , which again alter their Figure , and appear like certain Ansae or Handles . As to the first Phaenomenon , the ingenious Mounsieur Hugens ( in his System . Saturn . p. 46. ) hath noted that the said Ring about the Body of Saturn is every way alike distant from it , the Plane whereof alwayes keeps in a certain and constant Inclination to the Ecliptick , appearing ( according to its diversity of Aspect ) now like a large Ellipsis , now like a more contracted one ; at other times like a strait Line , and now and then like two Brachia or Ansae , as it were on each side the Body of the said Planet . This Hypothesis of his he laid down in the following Proposition by him published in the year 1656. Annulo cingitur , tenui , plano , nusquam cohaerente , ad Eclipticam inclinato . But Ricciolus conceives the said Saturnian Phaenomena may be as well salved , if instead of Monsieur Hugens his Annulus or Ring distant from the Body of Saturn , there were an Elliptical Armilla supposed coherent to it at the Extremities of the Lesser Diameter of the Ellipsis , which his Hypothesis he delivers in this Proposition . Armilla cingitur tenui , plana , Elliptica , duobus locis cohaerente ; sive Parallela Aequatori ; sive in se circumvolubili , aut Libratili , Versus Mundi Polos . But of this let the learned Judge . As to the second Phaenomenon ; the forementioned Monsieur Hugens in the year 1655. on the 25 th of March , discovered a small Star or Planet moving about the Body of Saturn ; which Star Hevelius likewise observed at Danzick , and Sir Paul Neal , together with Sir Christopher Wrenn here in England , much about the same time ; but took it not to be a Planet , 'till ascertained of its being such by the Information of the said Monsieur Hugens . This Saturnian Companion , after several Moneths Observation , he found to finish his Periodical Revolution it its Orbit about the Body of Saturn , in the space of sixteen dayes . Since which the excellent Signiour Cassini hath lately made in the Royal Parisian Observatory , a Discovery of two other Planets moving about Saturn , the one nearer to the Body thereof than the Hugenian , the other farther removed from him than that . The Revolution of which interiour Planet he found to be compleated in four Dayes and an half , or rather four Dayes thirteen Hours . The Exteriour in something more than eighty Dayes . Touching the last and various Phaenomenon ; Hevelius in a Particular Treatise , De Nativâ Saturni facie , hath endeavoured to give the Reason . He conceiving that diversity of Appearance to proceed from the Diversity of Aspect , as he is more directly or more obliquely b●…ld by Us : For seeing according to the Rules of Opticks , a Cylinder and an Ellipsis being beheld at a Distance or obliquely , seem to be circular ; Hence he inferrs , that Saturn as well when in the Apogaeum as Perigaeum of his Excentrick appears , as he terms it , Elliptico Ansatus , but in his mean Distance either from the Earth or Sun , he appears Monosphaericus , solitary and round , in other positions he appears Sphaerico-Ansatus , but diversly figured according to his divers Latitude and Situation in his Epicycle . And seeing at this Time Saturn's Apogaeum is in the 27 th Degree of ♐ his Perigaeum in the 27 th of ♊ , and his Mean Distance in 27 th Degrees of ♍ and ♓ , he hath accordingly distributed the various Phases , and different Appearances of that Planet quite through his Excentrick . Of which see the following Table taken from Ricciolus in Paralip ▪ Astronom ▪ Reformat ▪ something differing from that of Hevelius inserted in his forementioned Treatise . Table of the divers Phases of Saturn according to the Opinion of HEVELIUS .   Sign . Gr. Denominations of the Figures Apog . ♐ 27 Elliptico-ansatus plenus Decreasing . ♑ 12     ♑ 27     ♒ 12 Sphaerico-cuspidatus Major   ♒ 27 Sphaerico-cuspidatus Minor   ♓ 12 Trisphaericus Mean Distance ♓ 27 Mono-sphaericus Increasing . ♈ 12 Trisphaericus   ♈ 27 Sphaerico-cuspidatus Minor   ♉ 12 Sphaerico-cuspidatus Major   ♉ 27 Sphaerico-ansatus   ♊ 12 Elliptico-ansatus Diminutus Perig. ♊ 27 Elliptico-ansatus Plenus Decreasing . ♋ 12 Elliptico-ansatus Diminutus   ♋ 27 Sphaerico-ansatus   ♌ 12 Sphaerico-cuspidatus Major   ♌ 27 Sphaerico-cuspidatus Minor   ♍ 12 Trisphaericus Mean Distance ♍ 27 Mono-sphaericus Phases increasing . ♎ 12 Trisphaericus   ♎ 27 Sphaerico-cuspidatus Minor   ♒ 12 Sphaerico-cuspidatus Major   ♒ 27 Sphaerico-ansatus   ♐ 12 Elliptico-ansatus Diminutus By the help of the foregoing Table and Ephemerides , the true Place of Saturn being given , it may be known ( sayes Hevelius ) what the Phases of Saturn will be for any Year to come , of which , for the greater Ease of such as would avoyd the trouble of Calculation , he hath composed the following Ephemerid ending in the Year 1701. EPHEMERIS PHASIUM SATURNI . Year Moneth Phases of Saturn 1674   Tricorpor 1677   Ansatus 1678     1679     1680     1682 From November to Iuly Tricorpor 1683     1684     1685 From September To October Rotundus perfecte 1686     1687   Tricorpor 1688     1690   Ansatus 1691     1692     1693     1694     1695     1696     1699   Tricorpor 1700     1701   Rotundus . But whether these Phases may exactly answer the Hypothesis , We leave to the Discovery of the Curious , and shall only add what we find reported by Ricciolus ( in Paralipom . ad Astronom . R●…mat . ) touching some Mechanical Trials , made by Signior Campani for the better discovering the various Face of this Celestial Proteus , being as follows . He caused a round white Ball or Globe to be inserted within an Armilla of the same colour , a Wire being made to pass through the Armilla , and the said Globe as a Diameter , so that the Armilla could be raised or deprest at Pleasure . This being placed in a convenient Light , and at a fitting Distance looked upon through a small Telescope , gave to him according to the divers Elevation or Depression of the said Armilla , all the Phases that were not only then ( viz. 1664. ) by him really observed in Saturn , but what likewise for the future might hereafter be observable . The same Tryal is also affirmed to have been made by Ricciolus by inserting a Globe as aforesaid , within an Armilla of an Elliptical Form. Touching the Structure , Nature , and Substance of this Planet , it may be probably concluded : First , That it is composed ex solido & liquido , of a plumbeous or leaden temper and colour ; that it is Spherical , but withall full of uneven Asperities . Secondly , That it is an Opacous Body , and illuminated ab extra , and although the Sun's Light may approach it , yet it is not sufficient to give a requisite Lustre to so great and so distant a Body , and therefore must needs receive its Light from some other Fountain . Thirdly , That his Companions or Satellites , have their proper light , and thereby administer Supplies to that of their Prince : Fourthly , that he hath a gyration about its own Center and Axis , compleated according to Rheita in 29 Dayes , 10 Hours , 1′ . 16″ . His Distance from the Earth is by divers Astronomers diversly computed , but according to Ricciolus , in his greatest Distance he is found to be distant from the Center of the Earth 90155 Semidiameters thereof , in his Mean Distance 73000 , in his least 57743 of the said Semidiameters . His apparent Diameter , according to Ricciolus , when least in his Apogaeo cum Comitib ▪ is reckoned to be 46″ . when in his Mean Distance from the Earth 57″ . when greatest in his Perigaeo 1′ . 12″ . His true Diameter cum Comitibus , contains of the Earth's Diameters 20. 1 / 6. His Body that of the Earth 891 Times . We are now come to the Conclusion of the Poem , wherein Manilius for the more perfect Consummation of this Work , by way of Corollary , hath inserted a brief but not unelegant Description Of Fiery Meteors and Comets . Touching the first of These , it will be needless to say much ; We shall only reckon them up . Those whose Place and Generation is in the Lower Region of the Aire , are Draco volans , Ignis Fatuus , Ignis Lambens , Sidus Helenae , Castor & Pollux : Those whose Birth is in the middle Region , are , Stella cadens , Lancea ardens , Fulmen , &c. In the Upper Region of the Air are reckoned , Fax , Ignis Perpendicularis , Bolis , Capra Saltans , Scintillae Volantes , Trabs &c. All which arise from Vapours and Exhalations which the Earth continually exspires , and diffuses round about through its ambient Atmosphere . Of the second Sort something more is to be said ; but with that Brevity as may suit with our Method ; it being not our Design to amass together what ever might be collected upon this Subject , but only to hint so much as may serve either to explain what our Author hath written thereon , or to supply in some measure what he hath omitted , referring the more Inquisitive Reader to what among the Ancients , Aristotle , Seneca , Pliny , Plutarch and Ptolemy have written ; among the Modern , to what Tycho , Blancanus , Cabaeus , Fortunius Licetus , Camillus Gloriosus , Longomontanus , Keplerus , Galilaeo , Fromondus , and divers others have largely and learnedly discoursed of ; more especially to what the Learned and Reverend Prelate , Seth Lord Bishop of Sarum , hath published in his Dissertation De Cometis , to what Monsieur Petit hath discoursed in his Piece of the Nature of Comets , as likewise Lubieniecius in his Theatrum Cometicum ; Hevelius in his accurate Cometographia , and Ricciolus in Almagest ▪ Nov. Tom. 2. de Cometis . Touching the Matter , Place , and efficient Cause of Comets , both the Ancient and Modern Philosophers and Astronomers differ much ; We shall here give the Reader their several Opinions , collected from divers of the forementioned Authours , which may be reduced to Twelve distinct Heads . The first will have Comets not to be any thing real , or distinct from other pre-existent Celestial Bodies , but rather a meer Emphasis or Appearance made by the Reflexion or Refraction of the Sun's Beams , or those of the Moon , in the same manner almost as is the Halo , Parelii , Paraselene and Rainbow . Of this Opinion was Panaetius , and some others mentioned by Seneca ( Natural . Quaest. ) and Plutarch ( De Pl●…it . Philosoph . ) The second likewise denies Comets to be any thing De Novo , existing in the Heavens ; but to be a 〈◊〉 Sympha●…s or Coappearance of divers Stars already known , joyned together in corporal Conjunction ▪ as Astrologers use to speak , and so making a kind of a long Star , as if it were ( as Sen●… expresses it ) duaru●… ( vel plurium ) Stellarum Ignis extensus , which Opinion is by some ascribed to Democritus , Anaxago●…as and Z●…no ; this is touched at by Manilius , where he sayes , Nature did those fading Lights design As subunited Stars in Heaven to shine . Which see already explained in our Notes . The third Opinion makes Comets to be some New and extraordinary Planets differing from the seven commonly known , being seldom seen , by reason either of their nearness to the Sun , or their too great Distance from the Earth , which after some space of time , emerging out of the Sun's Beams under which they lay hid , or approaching nearer to the Earth , become visible . This was the Opinion of the Pythagorean Italick Philosophers , Hippocrates , Diogenes , and generally of the Chaldaean Astronomers , and is likewise taken notice of by our Manilius . The fourth Opinion maintains Comets to be an Aggregate of many small but ancient Stars composed into one Body , which afterwards parting asunder vanish and disappear ; which Opinion Ricciolus conceives ought more properly to be ascribed to Democritus , Anaxagoras and Zeno , than that already under the second Head attributed to them . The fifth Opinion is that of Aristotle , and divers of his Interpreters , asserting Com●…ts to be Fiery Meteors , generated anew of copious Exhalations from the Earth and Sea , and elevated to the supream Region of the Aire ; which being closely compacted together , and hurried abou●… by the swift Motion of the primum Mobile , take fire , and last as long , as the Sulphur●… , Unc●…uous , Fat , Oleaginous , or Nitrous Matter of which they consist , affords them Fuel to burn and shine ; nor is this omitted by our Authour . The sixth Opinion allows Comets to be formed of Sublunary Vapours and Exhalations , but not to be set on fire ; only to be illustrated by the Sun , by reason of the Diaphaneity of their Matter , like Phials of Glass full of Water of a red or yellow Colour ; or as Scaliger ( Exercit. 79. ) Opines : That Comets are composed of a subtle Vapour raised by its own Levity , or attracted by the Stars , into the Upper Region of the Aire , and so attenuated , that it not only receives but transmits the Sun Beams , like those thin Clouds which in the time of twilight are discerned not far above the Horizon ; which Opinion seems to be derived from Heraclides Ponticus and Metrodorus . The seventh maintains Comets to be formed of Elementary Matter , that is to say of thin and subtle Exhalations , mounting by their Levity above the Orb of the Moon , and by reason of their Diaphaneity drinking up the Rayes of the Planets , chiefly of the Sun ; and afterwards transmitting them into a long Train , Bush , or Beard . Authours of this Opinion among the Moderns , are Guiduccius , Galilaeus , and Rothmannus . The eighth Opinion , affirms Comets to be made anew of Celestial Matter ; not by Generation of a new substantial Form , but by Condensation , with a Mixture of Darkness and Diaphaneity , aptly receiving the Light of the Sun , and transmitting it again , of which Opinion are Libavius , Licetus , Camillus gloriosus , Tannerus and Resta . The ninth Opinion conceives Comets to be generated a new of Celestial Matter , which after a Time corrupts and is dissolved . Of this Opinion are most of the Eminent Astronomers from Tycho to this present : Differing yet among themselves as to the Manner of this Generation ; Some conceiving the Generation of Comets to be made of that Celestial Matter , which is in the Via Lactea ; as being of all the other Parts of the Heavens more nearly prepared and disposed for such Productions . And that Comets are not Flagrant , but rather pespicuous , and tralucent Bodies . Kepler yet and with him Hevelius , and some others will have the Aetherial Region to be full of gross Fumes or Fuliginous Effluvia from the Bodies of the Stars , and Planets ( and more particularly of the Sun congregated as it were into one Aposthem ) and that their Origine and Matter is in a manner the same with that of the Solar Maculae and Faculae . The tenth Opinion is ( as Ricciolus notes ) peculiar only to Kepler ; which asserts Comets to be formed anew of Celestial Matter , but that some of them are abased and thrust down below the Orb of the Moon ; as on the contrary , the seventh Opinion ( before mentioned ) maintained them to be formed of Elementary Matter , yet notwithstanding to be carried up above the Orb of the Moon ; and certainly ( sayes the same Ricciolus ) I see no reason why Comets , being composed of the Effluvia of the Planets in their Perigaea's , may not sometimes be carried beneath the Moon . The eleventh Opinion supposes that Comets , if not All , yet the most Part , are created by God of Nothing , or at least formed of such Matter as best pleases him , whether Celestial or Elementary , and of such Shape and Figure , as may serve to terrifie , or admonish mankind and presignifie Calamities to ensue , which Opinion is likewise delivered by Manilius in these Verses Or God in pitty to our humane state , Sends these as Nuncio's of ensuing Fate . Touching which enough is already said in our Notes . The twelfth Opinion is not distinct from all the former , but rather distinctive of the Matter and Place of Comets . Of which it admits some to be composed of Terrestrial Exhalations beneath the Orb of the Moon , whether inflamed or set on fire , or only enlightned . Others to be generated of Celestial Matter after the manner already delivered in the tenth Opinion . And seeing mention hath been made in the ninth Head or Opinion , that the Origine and Matter of Comets is in a manner the same with the Solar Maculae . It will not be amiss here to add the Particulars in which they agree ; as by Hevelius in the seventh Book of his Cometographia , they are compendiously exhibited in the following Aphorisms . 1. Comets ( as the Maculae ) have both a Physical and Astronomical Rising ; but few of them have both Astronomical rising and setting , in regard they last not long , but are dissolved before they attain the Western Horizon . Others have neither Astronomical rising nor setting , but Physical only , as being produced and dissipated above the Horizon . 2. As the Maculae are composed , of the grosser Solar Matter , or more dense Effluvia , so Comets are formed of the Evaporations of divers Planetary Bodies . 3. Comets have a threefold Age ; their green and growing Age , their full grown or ripe Age , and their declining or decaying Age ; that is to say their time of Augmentation , Duration , and Decay . 4. Comets have their Augmentation and Decrement , as well Physical as Optical , not in a certain Part of the Heavens , but in any Part thereof ; and that without Intermission , successively , sensibly , and unequally . Hence it happens sometimes , that a Comet increasing slowly and more durably , is on a suddain extinguished , and on the contrary , another that suddainly shews it self , lasts a long time , and is slowly dissolved . 5. Comets ( as the Maculae ) are generated , and increase by the Accession of similar Matter , through Condensation , Adgeneration , substantial Generation , and Aggregation of Minute Bodies , and by contrary Means are dissipated , aud decay . 6. Comets ( as the Maculae ) are by no means spherical Bodies , but Plane , and of different thickness ; sometimes represented to our view like round or regular Figures , at other times appearing in irregular Forms , and differ in Magnitude , Crassitude , Colour , Obscurity , Density , and Rarity , and have their Nuclei ( Kernels or Knots of Light ) of divers Magnitudes , Crassitudes , Density and Colour . 7. The Nuclei , Kernels , or Knots of Comets sensibly increase and decrease . And those which suddainly increase are of shortest Duration , and are soonest dissolved ; Those which by Degrees augment , are of longest Continuance . 8. These Nuclei are composed of Dense and rare Parts ; That is , are generated of the most dilute Planetary Vapours and Exhalations , and of certain smallest Particles ; and sometimes grow together from many into one ; and not seldome from one are divided into two or three , or more . 9. Comets as they seldom and very rarely consist of one single Nucleus ; so the greater of these Nuclei is seldom seen , precisely placed in the middle of the Cometical Body , but declines toward the sides , drawing along with it the thinner Mass. 10. The Nuclei , as their rarer Parts by a Flux of Matter and Condensation , increase and become more splendid ; so by difflux of Matter and rarefaction they become more pale , wan , and dull . 11. Every Comet , as each Solar Macula , is circumvested with an other kind of Body , less obscure and more rare , as it were a peculiar Atmosphere , in which the Sun's Rayes are lodged , whence its Tayl or Bush is produced . 12. It seems likewise consonant to Reason , that the rarer Parts are procreated before the Nuclei or Kernels , and that in the Dissolution of a Comet , the Nuclei sensibly first decay ; so that the solid and more Dense Parts are sooner dissolved than the more rare . 13. The Nuclei of Comets ( as of the Solar Maculae ) have not their Generation or Corruption in one Part of the Heavens only , but every where indifferently . And of these some are more lasting than others , by reason of their more Unctuous and Dense Matter ; some of them likewise are formed about the beginning or Birth of the Comet ; others about the middle , and some toward the End. Yet sometime the same Nucleus lasts from the beginning to the End of the Comet now increasing , at other times decreasing . But in this , both Comets and their Nuclei altogether differ from the Solar Maculae , for that Comets , by reason of their Proper Motion in their Orbits never return again , and a second time ascend above our Horizon , that is to say rise again Astronomically ( except in their Diurnal Motion , which is not here considered ) insomuch as a Comet being once extinguished , cannot be again produced or continued . 14. Oftentimes divers Comets which seem at the same time to begin , and to be almost equal as to their Density and Magnitude ; have not yet the same Dissolution , but differ both as to the Time and Place ; the same is to be understood of their Nuclei . 15. Every Comet , as each Solar Macula , consists of an opacous , dense , and ( of it self ) obscure Matter , drawing all its Light wholly from the Sun. 16. Comets are alwayes greater than they seem to be ; be their Apparent Diameter greater or less than the Apparent Diameter of the Sun , which is the Body that illuminates them . 17. No Comet whatsoever either as to its Whole or Parts , or Nuclei , hath a Gyration about its Axis ; but alwayes turns the same face to the Earth and Sun , unless happily it may be carried in an equal librating or reciprocal Motion , according as it is more or less distant from the Earth . 18. The Nuclei of Comets ( as of the Solar Maculae ) have a peculiar Motion , but alwayes Irregular or Anomalous . Hence those Corpuscula or Nuclei , of which the Comet is composed , have Motions among themselves , as to their Accession , Conjunction , or separation , quite different from that proper Motion of the Comet in its Orbit , and thence proceed the suddain Coalitions , Digressions , and inordinate Deviations , as also the various Transformations of the Figures of the said Nuclei . 19. Comets : although sometime , as to their Diameter or Disque , or the Area of their greater Circle , they exceed in Magnitude the Moon and Earth ; yet do they not for all that exhaust the Planets , nor do those Bodies suffer any Detriment or Diminution , no more than the Sun does by Generation of his Maculae : for every Celestial Body calls back unto it self that Matter which by Dissolution or Attenuation issues from it . 20. Comets are never at one and the same equal Distance removed from the Earth or Sun ; but are sometimes higher , sometimes lower , as is evident ; in regard they are sometimes found to have a sensible Parallax , at other times to have none at All. 21. As the Sun does not constantly , but at certain times produce his Maculae ; So neither does the Aether at all times by reason of the defect of Matter , produce Comets . Since that tenuous Matter of which they are composed , being diffused beyond the Atmosphere of the several Planetary Bodies , whence it flows through the vast Aether , and most distant Parts of the Heavens ; it is not likely that those thin Exspirations can find so easie a Congress ; but that they concurr and are aggregated as it were by chance ; whence it comes to pass that Comets are so seldom seen . Of the Tayl , Train , or Bush of Comets , and the Causes thereof something is likewise to be said , touching which there are as many different Opinions produced by Ricciolus and Hevelius , as those already mentioned touching Comets . The first is that of Aristotle and his followers , asserting the Bush or Train of a Comet to be an Exhalation set on fire , in a more rare and less constipated Matter than that of its Head , and diversified , according to the divers Disposition of the Matter that feeds its Flame . The second is that of Seneca ; who conceives the Cauda or Bush to be no part of the Comet , nor a Flame , but the Rayes or Light which the Comet by its Native Vigour sends forth . The third is that of Gemma Frisius , who will have it to be a Fire of a simple Celestial Body , kindled by the Sun in the Head of the Comet , and by the Violent Action thereof thrust forth and expelled into the Opposite Part. The fourth is that of Petrus Apianus , who makes the Bush of a Comet to be nothing else , but the Rayes of the Sun , transmitted through the Semidiaphanous Head thereof , as it were through a Globe of Glass . The fifth is Tycho Brahe's , who conceives it to be nothing else but the Beams of the Sun penetrating the Head of the Comet , and terminated in some Matter not altogether Perspicuous , and reflected towards us ; for he supposes the Substance of the Aether not to be thoroughly Diaphanous . The sixth is that of Kepler ; who endeavours to give a double reason of this Phaenomenon ; for he supposes , First , that the Tayl or Bush may be enlightned by the Sun-Beams passing through the Body of the Comet , which he imagines to be purely pellucid , yet withall Dense , in such manner as the Sun's Beams are thereby conduplicated and coloured . In the second he makes the Comet to expire a certain Lucid Matter from its Head , toward that Part where the Sun's Beams break forth . With him in a manner Gassendus consents , who conceives the Tayl or Bush to be of the same Matter with the Head , only to differ in rarity , which rare and tenuous matter is by the force of the Sun's Beams expelled into the Part directly turned from the Sun ; and this Opinion is likewise embraced by Camillus Gloriosus , and Franciscus Reita . The seventh is that of Galilaeo ; viz. that the Tayl of a Comet is of its own Nature straight ; as being produced by the Sun-Beams , but appears to us to be crooked when near the Horizon , and inclined thereunto by reason of the Refraction of the Species , or of the Visual Rayes , made in the Spherical Superficies of the Aire , which near the Earth is filled with gross Vapours . This he illustrates by the Example of an Oar , which though straight , seems in the Water by the force of Refraction to be crooked . The eighth is that of Io. Baptista Cysatus , who conceives the Tayl of a Comet not to be a Flame , but a radious Cone or Pyramid , made by the Sun's Beams , transmitted through the Head of the Comet , in the same manner as the Sun 's Light passing through a Hole , or Convex Glass , illustrates a Room or Chamber , which he sayes is done partly by Refraction , partly by Reflexion from the Poly-angular Sides of the Corpuscula , that forme the Head of the Comet . The ninth is of Nichol. Cabaeus , who makes the Tayl of the Comet to be the Sun-Beams shineing through the Head of the Comet and refracted ; but since all Beams however refracted are propagated by right Lines , he affirms the Tayl of a Comet cannot possibly be really crooked , but only apparently such ; and the Cause of this apparent Crookedness he refers to the divers Site or Plane of the Eye , and of the Tayl or Bush of the Comet . The tenth is that of Fromondus Meteor . l. 3. c. 4. where he affirms the Tayl of a Comet to be the Sun-Beams transverberated per Cerebrum Capitis Cometae , as he terms it ; and at the beginning not to be of any Length , nor directly to tend toward the Part turned from the Sun , in regard of the various Diversion it meets with , by reason of the Profundity and Opacity of the Head of the Comet ; but after that Opacity is a little cleared , and the Matter better digested , then the Sun-Beams issue forth directly , and stream into a long Bush or Train . The eleventh is that of Fortunius Licetus , who conceives that to the Body of the Comet there is a certain Matter that adheres , by some Extrinsecal Appulse , and hath its coagmentation and generation near the Body of the Comet , from the same Cause that formed the Comet ; and either by the innate or proper Light of its Head , or by the Sun Beams is illuminated , and becomes visible in the shadow of the Comet , that is in that part of it which is directly turned from the Sun. The twelfth is that of Ricciolus , who first conceives it not improbable , that the Tayl or Train of a Comet is of the same Substance with the Comet , and to shine by its own Light propagated from its Head. The Face of which is alwayes converted to the Sun like a Heliotrope , or as a Magnet to the Pole ; and by a slow Vertiginous Motion about the Center of its Head to be so moved , that the more perfect part of the Comet alwayes respects the Sun , the other part to be turned from the Sun ; and to have divers Shapes and Figures , according to the several Species of Comets , and the diversity of its Matter and Configuration . Secondly , he holds it very probable , that the Train or Bush of a Comet , is a Multitude of most subtle Corpuscula in the Air or Aether , flying about the Head of the Comet , not such as We see through a Chink dancing in the Sun-Beams , nor like those Exhalations which make the Crepusculum or Twilight , but much more subtle and higher , nor apt by reason of their smallness , their little opacity and great distance from the Sun , to be discerned by us through the Reflexion of the Sun's Beams , unless very strongly illuminated ; that , that strong Illumination is made by the Collection of the Sun's Beams by the Power of Refraction into one , though not precisely after the same Manner as they unite after their trajection through a Sphere of Glass . He likewise conceives the Head of the Comet to consist of divers minute Bodies Homogenial , partly Polyangular , partly Spherical , partly Spheroeidal . Hence by the Benefit of these various Superficies , the Sun Beams passing after a divers Manner through the Head of the Comet , according to the Rules as well of Refraction as Reflexion , come forth much more multiplyed and collected together than otherwise they would do , if they passed not through the Head of the Comet , or were not refracted . To these We might add the different Opinions of the Excellent Des Cartes , and the much knowing Doctor Isaac Vossius , but that We are obliged to keep within the Bounds of our prescribed Brevity , and therefore shall referr the curious Reader to receive further satisfaction in this particular from their own better Pens ; as delivered by the first in Princip . Philosoph . Part. 3. by the other in his Learned Treatise De Natura & Propriet . Lucis . c. 32. and in his Appendix thereunto , c. 8. From the divers Figures and Appearances of these Trains or Bushes , Comets are distinguished into several Kinds or Species ; reducible to two chief Heads , that is to say , Criniti seu Comati , and Barbati ; to the first Head or Classis , relate these following , viz. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , seu Hircus ; to the latter 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Veru , seu Pertica , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . 1. Disceus , sive Disci-formis Cometa , is a Comet resembling in Shape or Form a round Dish or Platter , among these kind the chief is that which is called Rosa , sive Chryseus ; bright shining , and of a Silver Colour , mixed with Gold or Amber Colour . Those of this sort which are not absolutely round , resemble the Figure of a Shield , and are accordingly called Clypei-Formes . 2. Pitheus sive Doli-formis , resembles the Form or Shape of a Tun , of which there are divers Kinds ; some of an Oval Figure ; some like a Tun or Barrel erect or set on End ; some like one inclining , and cut short off ; others have a Bush or Train annexed . 3. Hippeus seu Equinus , resembles a Horses Main , not alwayes of the same Shape or Figure ; for now it spreads its Syrma or Train from the Fore-part or Front ; now from the hinder Part ; now of an Oval Figure ; now like a Rhomboides , and therefore it is distinguished into Equinus Barbatus , Equinus Angularis , sive Quadrangularis , and Equinus Ellipticus . Of this Pliny sayes , it is very swift in Motion , and turneth round about it self . 4. Argyrocomus , sive Argenticomus , is not much different from that which is called Solaris sive Rosa , but that it is of a whiter Colour , and shines with such a dazling silver haired Light , as it can scarce be looked upon . 5. Hircus , or the Goat is environed with a kind of Main , seemingly rough and hairy by the slender Fibrae of its Beams or Rayes ; it is sometimes of a round Figure without any Train or Bush. 6. Lampadias , sive Lampadi-formis , is a Comet resembling burning Lamps or Torches , and is of several Shapes , for sometimes it hath its Flame or Blaze carried upward like a Sword , sometimes double and treble pointed ; which Phaenomenon is yet very rare . 7. Ceratia , or the horned Comet , sometimes appears Bearded , sometimes with a Tayl or Train . Some have the Figure of a New Moon ; those that are tayled have sometimes a crooked Tayl bending upward , sometimes downward ; others have the Tayl of an unequal Breadth and thickness every Way ; some have their Hare or Bush pointed , others like a Horn or Trumpet . 8. Acontiae , are Comets formed like a Dart , or Javelin , with an oblong and close compressed Head , and prolix extenuated Tayl or Train . 9. Xiphias , sive Ensi-formis , is a Comet resembling a Sword ; the Head being fashioned like to a Hilt , the Tayl being long , straight , and pointed ; yet sometimes bending like a Cimitar ; when it is of a lesser and more contracted Form , it resembles a Dagger or Knife . 10. Lonchites seu hasti-formis , is a Comet resembling a Lance , its Head being of an Elliptical Figure , its stream of Light , or Tayl , being very long , thin and pointed . 11. Veru seu Pertica , is almost of the same Species with the Former , save that its Head is rounder , and its Train of Light longer and sharper pointed . 12. Tetragonias , seu Quadratus , is a Comet whose Head is for the most Part Quadrangular . It hath a long Train very thick and uniform , and is not unlike that Meteor called Trabs , or a fiery Beam. But all these will better appear by the several Schemes hereunto annexed , to which We referr the Reader , and shall forbear to add those Distinctions which some have given them in reference to the Planets ; making some Solar , others Lunar , Mercurial , Venerial , Martial , Iovial , and Saturnine , or of their Magnitudes , Duration , Motion , Prognosticks , or final Causes , of which Authours are full ; but give the Reader an Historical Abstract of the Times of the several Appearances of THESE SPLENDID AENIGMA'S , PROPOSED BY GOD , BUT NEVER TO BE RESOLVED BY HUMANE WIT ; as Ricciolus ingeniously sayes of them . Table exhibiting ( according to the Series of Time ) the several Comets that have appeared , together with their Principal Phaenomena ; Collected for the most from Hevelius and Lubieniecius ▪ Anni ante Christ. The time of first Appearing The time of Duration and Disappearance The time of Day or Night The Place or Region of the World The Motion , Direct or Retrograde , swift or slow The Nature , Magnitude , Figure & colour of the Head The length , shape , and scituation of the Bush or Tayl 2292 About three dayes before the Death of Methusaiem a Comet appeared Visible by the space of one Month , and disappearing the sixteenth of April Rochen●…ch   In Pisces under Iupiter . Passed through the twelve Signs of the Zodiack Iovial   2191 A little before the Confusion of Tongues at Balel La●…ed sixty five Dayes   In Capricorn visible in Egypt Passed three Signs in the Zodiack Saturnine   1920 in the 80 ▪ year of Abraham's life 5 years after his Departure from Ha●…an Shined for the space of twenty two days   In Aries visible in Chaldaea   Martial   182●… In the fifth year after Abraham's Death Lasted nine dayes   Under Leo in Egypt   The Head like an Imperfect Circle or Globe very fiery   1718 According to 〈◊〉 ( though 〈◊〉 will have ●…t to be in the year 1●…32 . ) not long before the seven years scarcity in the time of Ioseph     In Sagittary under Iupiter visible all over Arabia   Of a dreadful Aspect , called Typhon , by an Egyptian King then reigning , and resembling a Wheel .   1495 A little before the Children of Israel departed out of E●…ypt for the Land of Promise     Under Capricorn seen in Syria , Babyloniae ; and India   Like a Wheel   1200 In the Moneth of August , not long after which followed the Death of the impious Amenem●… King of Egypt , the Trojan War , and a great Sedition among the Israelites wherein 42000 of the Tribe of Ephraim were destroyed     In Cemint visible in Assyria   Of a dreadful Aspect   1100 In the Reign of ●…eutamus King of Assyria , contemporary with Samps●…n Lasted forty three Nights   Under Aries visible all over Greece       479 At which time according to Calvisius there hapned an extraordinary Eclipse of the Sun , and Nerues marched from Sardis against the Greeks , or rather ( according to Pliny ) incountred them in the Sea-fight at Salamis Lasted twenty two dayes         Like that called Ceratias , being crooked like a Horn 〈◊〉   Seventy five dayes After San-set     Fiery , and Martial , of a great and unusual Splendor , like a huge Beam   411 In the Month of Ianuary     Towards the North       371 In the Winter about the Time of the great Earthquake , and Inundation in Achaia , Aristaus being Archon at Athens   In the Evening after Sun-set   It ascended as high as the Girdle of Orion , and there vanished , and consequently its Motion was direct At the beginning it was like a Beam , and extended its Rayes to the third Part of the Heavens , and was therefore , as Aristotle ( l. 1. Met. c. 6. ) affirms , called the Way ▪ in the End it parted into two Stars At the first Day of its Appearance , it ▪ Tayl was seen and not the Head 354 About the time of Alexander the Great his Birth , and the burning of the Temple of Diana at Ephesus     In Leo     At first Bushy , or as some affirm , representing a kind of Beard , afterwards turned into the Figure of a Spear 339 About the beginning of Alexander's Reign , Nich●…machus being Archon at Athens Lasted 19 dayes Never rose in the Evening Appeared near the Equinoctial Circle about the 19° of Sagittary       220   Lasted twenty two dayes   In Aries       196 Two Comets ; first The second Lasted but few days nineteen dayes   In Capricorn In Cancer   Of a stupendious Magnitude   194 About the Birth of Mithridates King of Pontus Lasted eighty dayes       Of an extraordinary Bigness   183 A little before the Death of Scipio , Africanus Lasted eighty eight dayes   In Pisces   Exceeding the Sun in Brightness Taking up near the fourth part of the Heavens 174   Lasted thirty two Nights   In Aries       172   Lasted fifty five Weeks           166 September fourth     In Taurus   Of the Nature of that called Hircus   154   Lasted nine dayes           144   Lasted twenty two dayes   In Capricorn   Not less in appearance than the Sun , fiery red , bright shining , and dispelling the darkness of the Night ; but by degrees diminishing   134   Lasted eighty three dayes   In Gemini seen at Praneste in Italy   At first small , but in few dayes spread so , as to reach the Equinoctial Circle , and to be equal to that Part of the Heavens called the Via Lactea ▪   122   Lasted eighty dayes       It was so bright , that the Heavens seemed to be on Fire , and of that Magnitude as to take up the fourth Part of the Heavens , was more conspicuous than the Sun , and four Hours in rising and setting   111   Lasted fifteen dayes Appeared in the Evening In Cancer     Shedding a very conspicuous Train of Light. 65   Lasted ninety five dayes   In Virgo   A terrible and mighty Comet   60   Lasted nine dayes   The Sun totally losing its Light , it was seen ; whereas before it lay hid under its Beams       41   Lasted seven dayes Rising before Sun-set In Scorpio toward the North   Of a dreadful Magnitude Xiphias , with a long and sharp pointed Blade 29   Lasted ninety five dayes   In Libra       27   Lasted seven dayes Appeared about 11 of the Clock In the North   Clear and most Conspicuous   23   Lasted a few dayes   In Taurus       Anni post N. Christ.               1   Lasted three Nights   In Leo     Like to a flaming Torch or Firebrand 10   Lasted 32 Nights   In Aries       14   Lasted twenty days   In Aries       40       In Gemini       54   Lasted four Months   In Cancer Rose from the North towards the Heaven Eastward Every Day obscurer and obscurer   60   Lasted six Moneths   In the North Tending from the North , Westward , inclining toward the South ; and run through half the Heavens Growing every day more obscure   64           A hairy Comet   66       In Gemini       71 On Easter Day the eighth of April Lasted a whole year   In Virgo over the City of Ierusalem     Xiphias , or Ensiformis 76       in Taurus toward the East Rockenbach     Acontias , sive Iaculi-formis , of which the Emperour Titus wrote an excellent Poem , it is mentioned by Sextus Aurelius Victor in Vespas . 79   Lasted 180 dayes   In Scorpio       128   Lasted 39 Nights   In Aquarius and Capricorn       145   Lasted six Nights   In Aquarius       188             Of the Nature of that which from its Figure is termed Pogonias , or a B●…ard 204   Lasted many dayes   Seen at Rome       218   Lasted 18 dayes   In Pisces Moving from West to East , as Lycosthenes and Eichstormius out of Xiphilinus affirm     323       In Virgo       335   Lasted six Moneths three dayes   In Aries     Of an Immense and terrible Grandeur 367   Of many dayes continuance seen in the day time           370   Lasted 11 Weeks   In Aries       380 Appeared in the beginning of May Lasted four Months   In Libra   Of a round Figure bigger than the Planet Venus , and illuminating the whole Horizon   384           Like that which appeared over Hierusalem   389   Lasted twenty days Rose about Cock-crowing In Gemini toward the North   Shining like Lucifer , or the Morning-Star   390   Lasted thirty dayes       Hanging like a Pigeon or Dove of Light hovering in the Sky   392   Lasted forty dayes Rose about Midnight Near Venus , about the Zodiack Ascending sensibly from the Place of Venus towards Ursa Major , in the midst of which it disappeared Large and shining as bright as Venus , unto which divers other Stars assembling , compposed the Form or Figure of a Sword , whose Hilt was made of the former bright Star   396           The Figure not described by Aretius who affirms its Appearance   409 or 402             A Sword Comet , of extraordinary brightness , and of that Grandeur that it reached from Heaven down to the Earth 408 A little before the Death of Arcadius , Lubieneci . Lasted from Midsummer to the end of Autumn .   In Capricorn , Rockenboch       409 or 413 About the time when the Sun was totally Eclipsed Lasted four Months and more   In Virgo Moved from the Eastern Equinoctial Point by the Tayl of Ursa Major toward the West Its Light seemed to present the Figure of a Cone , not like a Star , but rather like a great Lanthorn , or Lamp , the Top of its Flame running into a great length , and pointed ; so that sometimes it varied from the proportion of a Cone , at other times again contracted it self into a Conick Figure   418 August the fourteenth Lasted till Septemtember   In Libra       423           A horrible Comet Of the Nature of those called Criniti 442   Lasted many dayes At Night the Moon being eclipsed         448   Lasted many dayes   In the East in Leo       454 or 457           Of a wonderful Magnitude , to whose Beám or Train of Light , adhered a Fiery Dragon , from whose Mouth issued two Rayes , the one extending beyond France , the other stretch'd toward Ireland , ending in seven other lesser Rayes   459 or 488           Of an unusual Figure and Magnitude surrounded with a dark cloud , but casting forth a bright Ray   504   Lasted many Nights         The Tayl very long crowned with the Figure of a fiery Dragon 519   Lasted twenty nine dayes   In the East     Of the Figure of a Beard , or Pogonias , the Rayes streaming Westward 531   Lasted twenty days         Its Beams ascending upward like that called Lampadias 539 In December     In Sagittary Running against the Course of the Moon     541 Upon Easter Day         A dreadful Comet   555 or 556       Seen at Constantinople Moving from North to South   In Form of a Lance 570           The Figure is not described by Ricciolus , who makes mention of it   589   Lasted a Moneth   Seen at Constantinople   Surrounded with a Duskish Cloud , and casting forth a single Ray   594 or 597 In Ianuary Lasted a Moneth Seen Morning and Evening     Of a Terrible Aspect   599           Its Figure not described either by Aimonius or Calvi●…s who mention its Appearance   601 In September Lasted many dayes       Of an extraordinary Magnitude Like a bright Sword without any Rayes 604 April and May , November and December Lasted many dayes       Very bright , its Figure not described   613   Lasted a Moneth       Martial   633   Lasted thirty dayes   Toward the South     Xiphias , or Ens●…formis 676 In August Lasted 3 Moneths Seen from Cock-crowing to Sun-rising In the East     Casting forth a great Flame like a fiery Trabs or Pillar 684 Between Christmas ▪ Day and Twelftide Lasted 3 Moneths Seen as well by Day as Night In the East near the Pleiades Moved from South to North Of a Duskish Colour like the Moon appearing through a Cloud   729 In Ianuary Lasted 14 dayes ▪ Seen in the Mornning before Sun-rising , and in the Evening after Sun-set       Like to a flaming Torch , or Firebrand streaming Northward 745 About the End of the Year     Seen in Syria       761   Appeared 10 dayes And 21 dayes   In the East In the West       763       In the East   Terrible to behold Like to a Beam 800 A little before the the time , the Empire of Rome was transferred to Charlemain         The Figure not described   814 In November immediately before the Death of Charlemain         A singular and terrible Comet , of a wonderful Figure , resembling two half Moons , now sensibly joyning together , anon parting asunder , and between them both exhibiting the Figure of a Man without a Head   830       In Aries       837 At Easter Lasted twenty five dayes   In Virgo , in that Part where her feet touch the Tayl of the Serpent and the Crow Ran through Leo , Cancer , and Gemini in a Retrograde Motion , and in the Head of Taurus vanished     838 In Autumne   Seen in the Morning before Sun-rising In Libra   Dreadful to behold   839 In the Spring Lasted but a few dayes In the Evening after Sun-setting In Aries       842       In Aquarius       844       Above Venus , as observed by Albumazar       868           Its Figure not described by Lavaterus and Rockinbach   874 In the beginning of April Lasted a Moneth     Preceding the Moon Dreadfully red and fiery , and projecting a long Train of Light   875 On the sixth of Iune Lasted a few nights Shining by Day as well as Night Preceding the Moon   Extraordinary sparkling , and more than usually red ▪ and flaring with long hairy . Beams   882 In the eighteenth of Ianuary           Its Bush or Tayl of a great length 902   Lasted forty dayes         Its Tayl projected toward the East 904 In the Moneth of May Its Duration not mentioned       Nor its Figure described by any   908           More than ordinary bright and glistring   930       In Cancer       942 On the seventeenth of November Lasted 14 Nights   Seen about Constance a City in upper Germany       945           Of a wonderful Magnitude and Procerity , scattering about fiery Rayes or Beams   962       In Italy   Of an unusual Grandeur   975 In August Lasted 8 Moneths           979       In Virgo       983   Its Duration not mentioned       Nor Figure described   999 or 1000 In the beginning of December   Seen about nine of the Clock in the Evening     Of a most stupendious Magnitude   1005 or 1009 About the end of May     In the South   Of a terrible Aspect   1017   Lasted four Months   In Leo   More strange than usual Like a mighty Beam 1027   Their Duration not mentioned       Nor Figures described   1031               1038               1042 On the sixth of October Lasted a Moneth Seen in the Mornning   Moving retrograde from East to West   With long flaming Hairs 1058 In Easter Week Lasted the whole Week   Seen in Polonia     Casting forth a long Train of Fire 1066 In Easter Week Lasted forty dayes   Following the setting Sun   At first equal in appearance to the Moon , afterward as its Tayl or Bush increased it diminished   1067 or 1068           Extreamly fiery   1071   Lasted twenty five dayes Seen in the Morning In the East     Its hair long and flaming 1096 or 1097 About the beginning of October Lasted a Week   In the West in Capricorn   Duskish Casting forth a single Ray or Beam 1098 or 1099 About the Nones of October Lasted 15 Dayes   In the Southern Part of the Heavens .     Like a Sword , but obliquely waved , casting forth long Haires toward the East , and shorter toward the South 1101     Soon after Sun-setting In the West   Of a wonderful greatness   1102 or 1103 February the twenty second     In the East Changing its Place by Leaps , and long Interstitia's   Broad spread and bright flaming 1104             Like burning Torches or fiery Darts 1106 In the first Week of Lent Lasted until Good-Fryday after , being twenty five dayes Seen in the Evening first Afterward in the Morning South west Eastward   Great and horrible to sight A Splendor issuing from it very clear , like a great Beam 1109   Lasted some few dayes           1110 On the sixth of Iune , as Calvisius , or of Iuly , as Myzaldus Lasted six Moneths     Its Motion Retrograde   Its Rayes directed to the South 1113 In the Moneth of May         A huge Comet   1132 or 1133 On the eighth of the Ides of October         Of a stupendious Greatness   1141               1145 In the Moneth of May             1146   Lasted a whole Moneth   In the West     Illuminating with its bright Rayes the circumambient Air 1165 Two Cem●…ts at the same time     Seen before Sun-rising In Libra , One in the South , the other in the North   Two together , or one with two long projected Rayes   1168 Two Comets together On the twenty fourth of December Disappeared after being seperated at a great Distance .   Seen in the West   One great , the other small , of a fiery colour   1180   Lasted only the remainder of the day of its first Appearance , and the Night following           1200       In the fifteenth of Scorpio Moving contrary to the Course of the Celestial Signs Appearing thrice bigger than Venus , of a round Figure , Casting as great a Light , as the Moon in her Quarter   1211 In the Moneth of May Lasted eighteen dayes   Near the North Pole     Its Tayl or Train directed in the Evening to the East , in the Morning to the West 1214 Two Comets In March   One appearing before Sun-rising ; the other after Sun-setting     Of a terrible Aspect   1217 In Autunme     In the South a little declining toward the West over against Ariadne's Crown     A Ray issuing from it like a Beam which seemed to ascend up to the Mid-heaven 1219       Seen in England   Of a vast Grandeur   1223       Conspicuous all over France   Of a dreadful Appearance , and of a bloody Colour   1238   Lasted some dayes Seen before Sun-rising     Of a vast Magnitude Sending forth Fire before it , and smoke behind it 1240 In February observed by Albertu ▪ Magnus Lasted six Moneths the last of any Conet , as noted by Lubieniecius , which ●…ad so long a dura ion Seen in the Evening Westward near the North Pole   Duskish A long Train casting its Rayes between East and South 1241 In Ianuary Lasted thirty dayes       Terrible to behold   1245 About the Feast of the Ascension , whic●… according to Calvisius was the twenty fifth of May     In Capricorn toward the South   Of a great Magnitude , clear but reddish like Mars , without a Tayl , perhaps mistaken ( as Hevelius supposes ) for that Planet   1254 or 1255   Lasted for some Moneths   Seen in Germany and in England   Of an Immense Grandeur   1264 In Iuly , much about the time of Pope Urban the fourth , his Decumbiture : observed by Palaeologus Lasted 3 Moneths and disappeared the very Night that Pope Urban the fourth dyed Rose in the Morning In Taurus behind Venus , or the Morning-Star Moving from East to West , and at length preceding the Morning Star Of a most signal Magnitude Its Tayl long and broad appeared before the Head , and extended its Rayes from the East unto the Mid-heaven 1267 On the eighteenth of Iuly Lasted not long A little before Sun-rising Near the Moon Running from the Moon by a swift Course Eastward to the Mid-heavens Of great brightness Leaving a white and fiery hairiness behind it 1268   Lasted many dayes Seen about Noon     Of a wonderful greatness   1284           Of a signal Magnitude Projecting its hairy Blaze to the West 1298 In Summer             1300           A dreadful Comet   1301 In the Kalends of December , or as some will at Michaelmas Lasted 15 Nights ▪ Rose after Sun-set , and set after Midnight In Aquarius and Pisces Moved from the East Northward   Its Blaze directed toward the East 1304   Lasted 3 Moneths   Toward the North       1305 About the Holy Week as some , as others about Easter             1307 Its Appearance Duration       Or Figure not described   1312   Lasted 14 dayes     Running its Course from North to South Of a stupendious greatness   1313         Moving from North to South , according to the Motion of Mars     1314 In Autumne in the Moneth of October Lasted as some will three Moneths , as others but six Weeks   Toward the North , in the last degrees of Virgo   Of a terrible As pect Its Flaming Train directed to the North 1315 In December Lasted 'till February   In Cancer Taking its Course the Pole Terrible to Sight Casting forth Rayes resembling a Broom one while Eastward , another Westward , and sometime Northward 1318       In Cancer , as Lubieniecius from the Authority of Herlicius       1337 Two Comets The first in April , The second in May Together with the first continuing , May , Iune , and Iuly   The first seen in Taurus       1338 In Iune   In the Evening About the Feet of Pegasus Moving toward the North , and ascending every day three degrees , by the lesser Bear , right Foot of Hercules , and left Hand of Ophiuchus Barbed After the Figure of a Sword , extended Eastward 1339 or 1340 or 1341 In March     Near Spica Virg. Moving every Day a degree , and coming to the Sign Leo disappeared   Xiphias or Ensiformis 1347 In August Lasted 2 Moneths   In Taurus toward the North       1351 or 1352 In December say some In September others     Far North     Like a fiery Beam 1353           Mentioned , but not described by Praetorius , and out of him by Alstedius and Ricciolus   1362 On the eleventh of March Lasted five Weeks Seen all Night In the End of Aquarius , with signal North Latitude     Its Tayl spread in the Evening toward the East 1375       In Aquarius   Of the Nature of those Comets called Criniti   1380   Lasted 3 Moneths           1382 In August Lasted 14 dayes           1394     Seen in the Evening In the West Passing toward the North   Having the Resemblance of that called Veru or Pertica , very remarkable with its Rayes standing upwards , and the Head hanging down below them 1399 Three Comets at once           The Heads not visible But three great fiery Tayls appearing 1400 In the time of Lent     Seen toward the North in the Oriental Angle Moving with great swiftness toward the East A most fiery and dreadful Comet Its Tayl long and projected toward the West 1401 In the End of February     In the West   A great , terrible , and most splendid Comet . It s Tayl expanded and stretched out like that of a Peacock , casting its Rayes like a Dart or Jayelin from West to East , and after Sun-set shining so bright , that hardly any Part of the World was not enlightned by its Beams ; which were of that brightness as hindred the Stars from shining , and quite expelled the darkness of the Night 1402 A little before Car nival Time Lasted many dayes Seen after Sun-set Towards the Northwest     Its Tayl erected like a Lance , about the thickness of three feet , sometimes more , sometimes less 1403 About the latter end of March , o●… beginning of April     Seen North-east     Its Tayl pointing toward the North 1407 or 1408 In Iune         Several Comets , of which we have no particular description   1426 On the ninth of Iune Continued near a Week   Seen directly over the City of Leige     Its Tayl pointing toward the Market-Place , as if it threatned that City 1432 In February , abou●… the beginning of the Moneth         A very small one Its Tayl or Train projected to the North 1433   Lasted 3 Moneths Seen from Evening till Morning     glistering bright and very great   1435 In Autumne             1439 or 1444 In the Summer Sel stice     In the West in Leo     Its Tayl extended toward the South 1450 In the Summer time   Seen immediately after Sun-setting   Moved from West to East , and passing under the Moon eclipsed the same   Like a two-handed Sword 1456 Two Comets In Iune Lasted a Moneth   In Cancer and Leo , one toward the West , the other toward the East     Their Tayls extending beyond sixty degrees 1457 In Iune ▪ Lasted 30 dayes   In the twentieth degree of Pisces   Black and dusky   1458 In Iuly     In Tauru●…       1460           A most bright , shinning and dreadful Comet   1463 The day before the Death of Iames the Second King of Scotland         Very clear and bright   1467 After Michaelmas   Seldom seen by reason of rainy Weather In Pisces oc Cancer perhaps , instead of Cancer should be put Capricorn     It cast its Rayes toward the East , the Sun being in the midst of Libra 1468 Two Comets   Lasted fifteen dayes each       The latter brighter than the first   1472 About the End of December , or beginning of Ianuary , observed by Regiomontanus Lasted eighty dayes At the beginning it appeared in the Morning , about the End in the Evening , at the middle shining all Night It past from Virgo , by Bootes , the Dragon , Ursa Major , feet of Cepheus , Breast of Cassiopaea , Belly of Andromeda , the Northern Fish , and came to the Whale ; where setting hellacally it disappeared : At first , and at its End moving slowly , in the middle extremely swift , in so much as it ran through in one day forty Degrees of the Circle it moved in   At the beginning its Head was small and thin , afterwards grew to a wonderful greatness , and then less and less ; sometime pale and white , sometime of a flame colour Its Tayl at the beginning short , about the middle stretching about fifty degrees in length resembling a Pertica , or Javelin , and directed at divers times to divers Quarters of the World 1473 Ianuary the seventeenth Lasted till the eighteenth of February following   Toward the South in Cancer       1475       In Libra , as Herlicicius , Rockenbach and Alstedius     Its Tayl alwayes directed towards Gemini , as Lubieniecius , citing Gassendus 1476 In Iune , as Lubieniecius from Schulerus in Disquis . Phi●…soph , De Comet .             1477           Of a pale Caerulean Colour inclining to Black.   1479       Seen in Arabia     In Form of a sharp Beam or Pillar ▪ wherein divers Points might be observed 1491 About the Feast of the Epiphany   Seen in the Evening . In the third Face or Decanate of Pisce ▪ or beginning of Aries with South Latitude   Its Head not great Its Tayl long but thin , casting but a small Light directed to the East 1492 In December Lasted two Months Seen after Sun-set         1500 Two Comets One in April The other in Ianuary Lasted four Months Lasted ten Dayes Seen as well by Day as Night In the North in Pisces , as also in Sagittarius & Aquarius       1505 About the Feast of St. Michael Lasted until Shrovetide following Seen from four in the Morning until eight before Sun-rising , or from four before Sun-rising until eight after Sun-set   Moving from the South toward the West Very large and shining , almost as bright as the Moon   1506 Two Comets One on the twelfth of April The other in the beginning of August The first lasted twenty five dayes . Continued 'till ▪ the fifteenth of August The latter seen at first near the Pole above Ursa Major , the next day among the Stars of the Wain , till at length it came to touch the Horizon and disappeared   The first passed from West to East . The other ran through the Signs Cancer , Leo and Virgo Of a hideous dark colour Its Tayl bright and splendid , and spread like that of a Peacock , whence it was so called 1510           From it fell certain small Sulphurious Stones of an ill Scent , as Cardan relates , sayes Lubieniecius citing Kecherman . System . Phys. l. 6. c. 5.   1511 or 1512 May the eleventh March and April Lasted till the third of Iuly   In Leo   Of a sanguine Colour   1513 In December Lasted from the End of December , to the nineteenth of 〈◊〉 ▪ following Shined all Night   Moved from the End of Cancer to the End of Virgo Variously coloured Its Tayl long 1515 or 1516       Seen in Italy , Roch. and Myzald . Ran in a short space through the twelve Signs Of the Nature of the Moon   1521 In April     In the End of Cancer   Cleer , and like the Moon in its Dichotomy Having short Rayes or Hair 1522       Toward the West   Of the Nature of Saturn .   1523 In November     Seen in the Kingdom of Naples       1526 August the twenty third Lasted until the twenty third of September         Like to a flaming Sword 1528 Ianuary the eighteenth     In Pisces in Opposition with Saturn       1529 Four Comets at ou●…       Mutually opposed to each other   Hevelius doubts whether they were genuine Comets Their Tayls pointed directly toward the four Quarters of the World 1530 In Iune             1531 August the sixth observed by P. Apianus Lasted till the third of September At first seen in the Morning before Sun-rising , at last in the Evening after Sun-set Seen all over Germany , Italy , and France Ran from the beginning of Leo , to the beginning of Libra in North Latitude Of a ruddy or rather yellow Colour   1532 September the twenty fifth observed by P. Apianus Lasted 'till the twentieth of November Seen in the Morning before Sun-rising   Ran from the beginning of Virgo to the beginning of Scorpio , at first in South , at last in North Latitude Thrice bigger than Iupiter , but of a pale obscure colour Its Tayl very long and radiant , stretching Southwest 1533 In the beginning of Iune observed by P. Apianus     It appeared first in Gemini near Perseus Thence moved retrograde unto Taurus encreasing dayly Bigger than Iupiter Its Tayl extending fifteen Degrees in length , like to a Military Spear ; by others resembled to a two-handed Sword 1538 In Ianuary observed by P. Apianus Lasted three Weeks Seene in the Evening In the West in the beginning of Pisces in seventeen Degrees of Northern Latitude   Of a fiery Colour , some yet make it obscure and pale Its Tayl extending thirty Degrees in length toward the East 1539 On May the sixth Lasted till May the seventeenth   In Leo in North Latitude at first , at last in South Latitude Moved according to the Course of the Signs direct ; but from North to South Its Head small and obscure Its Tayl short 1541 August the twenty first         Resembling the shape of a Dragon With a fiery Tayl 1542   Lasted forty dayes   Seen over Constantinople   Dreadful to behold   1545   Lasted a few dayes   In the West   Of a sanguine Colour   1554   Lasted some few dayes       Of the colour of Fire Its Tayl pointing to the West 1556 The fifth of March     From the left Wing of Virgo it passed by Bootes , and ascended to the Northern Pole of the Eclip tick , thence by Andromeda it came to the Northern Fish , where it was extinguished . In its middle Course most swift , running through fifteen Degrees dayly ; at first its Motion was retrograde , at last direct .   Its Rayes and Colour changed It seemed like a bright Globe of Flame , equal to the Half Moon Its Tayl rare and thin , casting forth rather a pale than ruddy Light , straiter near the Head , and extending Westward 1557 In the Moneth of October     Seen in the West in Sagittarie     In the Form of a Dagger , of a pale Colour , and its light thin and weak 1558 In August Lasted till the Nones of September Seen in the Evening Under Coma Berenices , above Leo in the East Moved Eastward Of a pallid Colour   1559 About the End of May Lasted to the second of Iune           1560 December the twenty eight Lasted twenty eight dayes   Seen over most Parts of France       1564 On the twenty fifth of Iuly Its. Duration not mentioned       Its Figure not described   1569 About the beginning of November Lasted to the End of the Moneth Seen in the Evening In 5° . of Capricorn near the bright Star of Sagittary ; but Ricciolus affirms it appeared in Serpentar●…s , and in the Signs Sagittarie and Capricorn It passed from Cancer , and declining from its right Course , went aside to the 4° . of Virgo , where it became Stationary Of a very bright Colour Streaming with fiery Rayes , directed to the East 1577 On the ninth of November sayes Hevelius , on the twelfth Rockenbach , on the tenth Ecstorm . Lasted 3 Moneths Appearing about five of the Clock in the Evening About the beginning of Capricorn , in the highest Heavens ; for its Parallax at the beginning was 19′ . 12″ . at the End 2′ . So that its Distance from the Earth at first was 173. at last 1733. Seinidiameters of the Earth It moved from the beginning of Capricorn by the Contact of the Equator , and the Meridian Line , passing the Pole of the Zodiack between Equiculus and the Dolphin , unto the Breast of Pegasus , its Motion continually decreasing . It ran through Capricorn and Aquarius to the middle of Pisces Its Colour was like the purest Silver , a little glittering , its apparent Magnitude exceeding that of Venus or Iupiter Its Tayl was of the colour of Blood , projected to a great length toward that part of the Heavens opposite to the Sun , in the mid●… crooked , the convexity thereof respecting the Zenith . It s concavity the Horizon , Its length extended to thirty Degrees , its Breadth to five 1578 On the sixteenth of May   Appeared about nine houres after Sun-set , at which time Iupiter and the Moon were in Conjunction in Libra Toward Southwest     Its Tayl long and directed to the North 1580 October the second sayes He●…l . eighth at Nortmberg . tenth at Gorlic . sayes Bucol●…rus I asted above three Moneths In the Evening about seven of the Clock , until the fourteenth of November , and then matutine till the sixth of December , whence only seen in the Morning Between the Zodiack and the Aequator , about the fifth degree of Pisces , distant from the Earth 157 S. D. thereof : So that ( as Hevelius notes , ) it was in the Orbe of Mercury or Confines of that of Venus At first moving in a slow and retrograde Motion , afterwards in a swifter Course it ran through Aquarius , Capricorn , and Sagittary . At the End its Motion was more remiss , and almost Stationary , at length direct , creeping forward from Aries , by the Aequator behind the Stars in the left hand of Aquarius to the Head of Pegasus , by Equiculus and the Dolphin , 'till in the Constellation of Serpentarius it disappeared Its looks sad , mournful , obscure , wan , and dull , exceeding in Magnitude ( as to appearance ) the Stars of the first Magnitude for its apparent Diameter on the fifteenth of October was found to be 16′ . 30″ . At first it wanted a Tayl , but afterward about the ninth of October it acquired a Tayl , but rare and thin , and alwayes extending precisely against that part of the Heaven opposed to the Sun 1582 On May the fourteenth Lasted to May the eighteenth In the Evening after Sun-set Between West and North Its Motion retrograde and swift , ascending toward the North Of a vast Magnitude , and dreadful to behold Its Tayl extended between the right and left shoulder of Auriga , ascending toward the Sun 1585 October the eighth Lasted 'till the fifth of November In the Evening about nine of the Clock In the 23° . 9′ . of Pisces , and in 13° . 52′ of Southern Latitude It moved continually in direct Motion , but something slow from Pisces to Aries , 'till toward the middle of Taurus , where about the eighteenth degree of that Sign it disappeared Its light obscure , rare , and cloudy , formed like a Crab ; It s apparent Magnitude , equalling that of Iupiter's . In the middle part of its Body shone a more compact Light , about the extremities thereof thin , and less appearing It had no Tayl or Beard , unless about the twentieth and twenty second of October , at which time there appeared some slight Marks thereof 1590 February the twenty third Lasted 'till the sixth of March Seen in the Evening Between the Constellations of Andromeda , and the Ram , near the Northern Fish. Its Place being in the highest Heavens , and not nearer to the Earth than the Sun It described by its Motion an Arch of a greater Circle , and measured in its Course a fourth part of the Hemisphere Its head small , shining with a pale and obscure light ; at the first biggest , but then not exceeding 3′ . in Diameter , and successively diminishing both in Magnitude and Light It cast forth some small Rayes , but thin and rare , and extended toward that part of the Heavens , opposite to the Sun 1593 Iuly the tenth Lasted 'till the twenty first of August Conspicuous before Sun-rising In the Cardinal Solstitial Signs By its Motion , it went from the Tropick of Cancer , to the Artick Circle , contrary to the Series of the Signs , that is from Cancer through Gemini and Taurus , and in Cepheus disappeared     1596 On the ninth of Iuly   In the Evening about the Prime of Night In the North among the Stars of Ursa Major By its Motion going forward a little toward the hinder Parts of the greater Bear , so that it ran through Cancer , Leo and Virgo , and at last became Stationary as to longitude , declining its course to the fourth Degree of Virgo Of the Colour of Saturn Its Tayl stretching to the Part opposed to the Sun toward the Pole of the Ecliptick , yet with some little deviatiation 1597 About the sixteenth of Iuly Lasted 'till the ninth of August           1607 On the twenty fifth on twenty sixth of September Lasted 'till the fifth of November Seen in the Evening about seven of the Clock , and from thence all Night Under the greater Bear a little higher than that Star which is toward the Square , in the 30° . of Leo , and 36° . of Northern Latitude ; its Parallax being found , not to exceed 3′ . and consequently its Place in the Highest Heaven or Aether It moved in direct Motion from the formost foot of the greater Bear under its Belly , passing by the midst of Bootes , and strook through the Serpent , coming under the Hand of Ophiuchus arrived at his formost foot and stayed in his Leg. The Orbit in which it was carried seemed to be a greater Circle ; at last extreamly bent or bowed toward the Ecliptick . On the thirtieth of September , its Diurnal Motion was thirteen Degrees ; but both before anc after , its Motion was slower ; at length Retrograd ▪ and Stationary , a to longitude Its Head was not of ●…n even or equal roundness , but here and there extuberating . It s apparent Magnitude greater than any of the Fixed Stars ; o●… than that of Iupiter . It s Light weak , p●…le and waterish , like that of the Moon when near the shadow of the Earth , towards its End diminishing more and more Its Tayl was something long and thick , projected with some little Deviation against that part of the Heavens opposite to the Sun. Vend●…nus saw it like a flameing Lance o●… Sword , seven Degrees in length 1618 The first Comet August the twenty fifth Lasted 'till the twenty fifth of September Appearing about three of the Clock before Sun-rising A little beneath the left fore-foot of Ursa Major inclining toward the Head of Leo , in the tenth Degree of the said Sign , and in the twenty second Degree of Northern Latitude The second of September it proceeded in Motion retrograde in Antecedence of the Signs ▪ one Degree afterwards in its Course more remi●…s It ●…ppeared ( as observed by a Telescope ) to be hairy ; Its Light not clear , shining , but cloudy and duskish Its Tayl short and broad , spreading toward the West 1618 The second Comet On the tenth of November Lasted to the eighteenth or twenty third of the same Moneth Appearing two hours before Sun-rising Between the Autumnal Section , and the eighteenth Degree of Libra Declining from the Ecliptick Southward 15° . It s Motion retrograde Its Head was not distinctly observed by the Europaeans , by reason of its vicinity to the Sun. But in Persia its colour was found to be like the Vapour of Flower of Brimstone set on fire Its Tayl was like that of an Estrid●…bowed ; In length forty five Degree●… In Persia it was observed to be like : Cymit●…r , or rathe●… like a young Palm-tree who●…e top Bowes bend but little 1618 The third Comet November the twenty second or twenty third Lasted to the thirteenth of December Seen in the Morning It took its Rise from the Equinoctial Eastern Point Its Motion wa●… Northward Its Colour was like that of Ve●…us , whose Magnitude it equalled if not exceeded It had a long Mai●… or Tresses 1618 The 4th ▪ and last Comet On the twenty fourth of November Lasted sixty dayes , viz. until the twenty fourth of Ianury next following Seen in the Morning before Sun-rising On the twenty ninth of November it was seen between the Scales of Libra , more Eastward than a Line drawn directly between the said Scales , and more approaching to the Northern Scale . It s true place being in the Aether , for at first it was distant from the Earth , seventy one of its Semidiameters . At last it was higher than the Sun it self , for its Parallax was found to be less than that of the Sun Its Motion was to the North , with some Inclination Westward ; for it passed by the middle of Libra and by Bootes , and when it had advanced as far as his Head , it shined all Night , thence proceeded above his Wrist , and over Ursa Major . It s Motion becoming every day flower and flower . As to its progress in the Ecliptick , it ran from the End of Scorpio to the middle of Cae●…er above one third part of the Heavens . At first Southern , at last Northern Its colour was palish , the lower part of its Head was perfectly round ; ●…e upper part whence the Tayl issued was uneven , and as it were indented ; It s light languid , whitish and cloudy , yet sometimes a little twinkling . In the midst of the Head at first was one single Kernel or Nucleus , afterwards separated into three or more , and at length parting into more lesser and lesser , was dissolved . It s apparent as well as true Magnitude being various , and unconstant Its Tayl toward the Head was very narrow , about the Middle , and its Extremity , prett●… large ; it was extended with some Incurvation , now to the 〈◊〉 , now to the 〈◊〉 , but not precisely in oppo●…ion to the Sun , through its middle , according to Longitude ran a clear Line like the Pith of a Tree , not seldom the whole Bush or Train ▪ seemed to have a kind of Scintillation an●… Fluctuation ; its Head likewise darting forth Ra●…es , and suddainly withdrawing them . It length was sometimes extended to 45 , 60 , 75 ▪ n●…y to 104 Degrees its Breadth to 〈◊〉 Degrees . It s C●…lour near the Head 〈◊〉 and fiery , toward the End pale and whitith 1647 On the twenty ninth of November Lasted but two dayes Seen in the Evening at half an hour past Eight In the Constellation of Berenice's hair , not so far as five Degrees from the left Leg of Bootes , about 10° ▪ from Arcturus , in the eighth degree of Libra , and in the twenty sixth Degree of Northern Latitude Its Motion was contrary to the Series of the Signs , viz. from the Head of Bootes towards the Ecliptick , and Spica Virginis It was something less in Appearance than Arcturus , but sufficiently bright and splendid Its Tayl was erected upwards toward the Zenith ; in length twelve Degrees , like to a Broom , conspicuous and splendid enough where it issued from the Head , towards its Extremity , more thin and dilute 1652 On the twentieth of December Lasted 'till Ianuary the tenth Appearing about six of the Clock in the Evening In 9° of Gemini , and 31° of Southern Latitude , not far from Rigel , in the left foot of Orion . So that by its Situation with the said Star , and another above the foot of Orion in Eridanus , it made in a manner an equilateral Triangle . It s true place was in the Aether or highest Heaven : for when it was nearest the Earth , its Distance thence was 110 Semidiameters thereof . It s Parallax at first being found to be 31′ . 15″ . but about the twelfth of Ianuary , it was distant from the Earth 22509 of the Earths Semidiameters ; its Parallax not above 9″ . and consequently it was as high as the Orb of Iupiter . It s Motion was constantly retrograde , from South to North , by the Hare , Foot of Orion , Taurus , to the Pleiades , and from thence as far as Perseus ; not directly but obliquely from East South East to North Northwest , in a great Circle inclined to the Ecliptick , and Aequator : At first by its Diurnal Motion compleating 11° . 16′ . at last 30′ . it ran through in the Time of its Duration 65° . 51′ . passing beyond and beside the Course of the Annual Orb. At first , distant from the Earth , ninety four S. D. thereof , at last seventy two of the said Semidiameters Its Head was round , and little less than the Moon at full . It s Light pale and dull , like that of the Moon , o'recast by a thin cloud In it were observed by the Telescope several Nuclei or Kernels every day varying their Situation . It s apparent Magnitude was not alwayes the same , being found at first to be 30′ . afterwards but 3′ . 30″ . It s Tayl at the beginning extended Eastward toward the Part of Heaven opposed to the Sun , ( yet with some small Deviation ) as far as to the handle of Orion's Sword , like to a sharp pointed Cone , in length 7° . of a whitish , but something obscure Colour , casting forth thin small Hairs or Rayes , which about the seventh of Ianuary it quite lost . It s Tayl still increast in Length , being at first only 3440. at last 163000 German Miles ▪ 1661 On the third of February Lasted fifty three dayes Seen in the Morning 47′ . after five of the Clock Eastward , beneath the Dolphin , between the Eagles Head , and that of the lesser Horse in 10° ▪ of Aquarius , and 22° . of Northern Latitude . In the very Aether or highest Heaven ; at first two thousand , at last nine thousand Semidiameters of the Earth distant from it , and consequently ( according to the Opinion of Hevelius ) higher than the Sun it self Its Course was from the East , Westward , by the Head , Neck , and neather Wing of Aquila , in a line almost parallel to the Ecliptick and Aequator but retrograde , and not in a greater Circle Its Head was round , and of a yellowish Colour , clear and conspicuous , in the middle whereof at first was a ruddy Nucleus or Kernel , equal almost to Iupiter , encompassed with a certain thin , and more dilute Matter Its Tayl extended above six Degrees in Length toward the Dolphin , narrower where it joyned to the Head , than in its Extremity , and pointing to that part of the Heaven , opposite to the Sun , but with some kind of Deflection . 1664 On the fourteenth of December Lasted almost three Moneths Seen at first in the Morning about five of the Clock afterwards in the Evening Near the Beak of the Crow , in 8° . of Libra and 22° . of Southern Latitude , in the highest Aether . It s Parallax at the beginning 59″ . in the Middle 4′ . and in the End 16″ . So that at first it was three thousand five hundred , then a thousand , and lastly one hundred twenty thousand Semidiameters of the Earth distant from the terrestial Globe , and higher than Mars Its Motion was Retrograde from Corvus by Hydra , Argus , the great Dog , the Hare , Eridanus , and Whales Head , unto Aries ▪ yet was not the Line of its Course carried altogether under that of a great Circle , it deflecting notably Northward . It ran through more than five Signs of the Zodiack , viz. Libra , Virgo , Leo , Cancer , Gemini , Taurus even unto Aries ; and in respect of its Orbit made a Progress of one hundred fifty four Degrees Its Head was very conspicuous : It●… Colour somewhat yellow : In the midst whereof was discerned a clea●… Light , surrounded with another more obscure , composed of sundry corpuscu la interspersed with other more subtle Matter of a divers Density , mixing at first with the Nuclei , after separating and dividing As to its apparent Magnitude , it exceeded six times the Diameter of the Earth Its Tayl extended fourteen Degrees in length Southwest ; sometimes ▪ longer , sometimes shorter ▪ On the eighth of December , it spread its Rayes upward in manner of a Peacocks Tayl ; from which time after it was directed toward the East All the time of its Duration extending it as far as the Sign Gemini , toward that Part of the Heavens opposed to the Sun , yet with some Deviation ▪ now Northward , now Southward ; towards its End it was sometimes quite lost , and then again recovered 1665 April the sixth Lasted fourteen Dayes Seen in the Morning half an hour after one In the Breast of Pegasus , in fifteen Degrees of Pisces , and 27° . of Northern Latitude . It s Parallax at the beginning having been found to be 69″ ▪ which decreased successively to 41″ . whence its Distance from the Earth at first could not be less than three thousand Semidiameters of the Earth , toward the End five thousand of the said S , D. distant from it and consequently sixty times higher than the Moon at first , and at last equal in height with the Sun it self Its Progress was by Pegasus under the Head of Andromeda , by the Northern Fish , as far as unto Aries ; in a Motion continually direct , at the beginning it ran through in one Day four Degrees and six Minutes , at last two Degrees twenthree Minutes Its Head was round of a yellowish Colour . It s Light quick and bright . In the very middle whereof was a single ▪ Nucleus of a conspicuous Magnitude , of a Gold Colour encompassed equally about with another thinner kind of Matter . the apparent Diameter of the Head was six Minutes Its Tayl at the beginning extended almost 17° . in length projected between the Mouth and the foremost Foot of Pegasus Westward ; where it issued from the Head , it was thick and lucid , and of the same dense Matter with that of the Head ; but toward the End or Cuspi●… , it was more thin and dilute . It stretched sometimes in length to 25° . streaming toward the Part opposed to the Sun , yet with some little Deviation Southward 1668 Fifth and tenth of March observed by Signior Cassini at Bologna   About the first hour of the Night after the Italian way of counting     The Head or Body was not seen , being hid under the Horizon The Tayl was of a stupendious length , being extended ( as it appeared at Lisbon in Portugal ) over almost the fourth Part of the Visible Heaven , from West to East , from the Whale through Eridanus to the Star which precedes the Eare of Lepus , as observed at Bologna in Italy by Signior Cassini 1672 Second of March Lasted till about the End of April , as Signior Cassini hath computed Seen both Mornings and Evenings At first between the Head of Medusa and the Pleiades , afterwards having continued his Course towards the Root of the Southern Horn of Taurus , and having passed the Ecliptick , went on above the Top of Orion's Head , to the Milky Way Its Motion falling into a Line little differing from an Arch of a great Circle , cutting the Ecliptick in the tenth Degree 45′ . of Gemini , its greatest Latitude in the tenth Degree 45′ . of Pisces , that is between 39° . and 40° . Northward , the same Circle cut the Aequator at 101° . of the Vernal Section Eastward , and its greatest Declination from the Aequator Northward was 38° . ½ . He made about 2° . 32′ , a day in the great Circle of his apparent Motion His Head seen with a Telescope of seventeen , foot appeared almost round , but well distinguished from the Mistiness which formed a kind of Chevelure wherewith it was encompassed ; and even the Middle was a little confused , and seemed to have inequalities , as are seen in Clouds The Tayl was almost imperceptible ; yet by the Telescope it was seen turned opposite to the Sun , and appeared of the length of two Diameters of the Head , or thereabout ; for it was not easie to measure it precisely , because being thinner according as it was farther from the Head , its Extremity was insensibly lost , and so the whole Comet Tayl , and Chevelure taken altogether , took up no more than three or four Minutes of a Degree fig : G. Cometae Discei seu Chrisei . 1. Solaris sive Rosa. 2. Disciformis . 3. Clypeiformis . 4. Clypeus ardens . Cometae Pithei 5. Doliiformis erectus . 6. Doliiformis truncatus . 7. Doliiformis caudatus . Hippei sive Equini 8. Equinus barbatus . 9. Equinus quadrangularis . 10. Equinus Ellipticus . Lampadiae 11. Lampadiformis . 12. Lampadiformis . 13. Lampadiformis . 14. Hircus . 15. Fusca nube circumdatus 16. Barbatus . fig. H. Ceratiae seu Cometae Cornuti . 17 Corniformis Lunatus 18. Corniformis . 19. Cornutus biscuspidatus . 20. Curvatus Divaricatus . 21. Tubiformis . Acontiae . 22. Jaculiformis Lunatus . 23. Jaculi-formis Ellipticus . 24. Iaculi-formis rotundus . fig. I. Xiphiae . 25. Ensiformis 1. 26. Ensiformis . 2. 27. Ensiformis . 3. 28. Ensiformis incurvatus . Longites . 30. Hastiformis . 1. 29. Ensiformis . 4. 31. Hastiformis . 2. fig K. Acontiae 32. Veru . 33. Pertica bifurcata 34. Cometa quadratus . 35. Coniformis . 36. Cometa Pyramidatus . 37. Cometa Monstriferus . 1. 38. Cometa Monstriferus . 2. 39. Cometa Monstriferus . 3. fig. L. 40. Cometa 1577. Die 17 Nov. à Tychone observ . 41. Cometa 1577. Die 28 nov . et 3 dec . à Cornel. Gemma . observ . 42. Cometa 1590. 43. Cometa 1607. 46. Cometa 1647. 44. Cometa 1618 Die 1. Dec. à Cysato observ . 45. Cometa 1618. Die 17. 18. et 20 Dec. observatus . 47. Cometa 1652. ab Autore observ . ADDITIONS and AMENDMENTS to be inserted , as followeth , VIZ. PAge 11. In the Annotat. Line 36. after Capricorn , add . But as to the Aspects as well the Antient , as those added by later Astronomers . See Bartschius his Usus Astronomicus Indicis Aspectuum , &c. Printed at Norimberg , 1661. Ibidem Line 43. after now lost ; add . except what is preserved in the Excerpta mentioned in Labbés Bibliotheca ; and what Ioannes Camaterus hath left on the same Subject , collected out of the Babylonian Writers . Page 12. Line 4. Annot. after Mochus the Sidonian , add . as Iamblicus in the Life of Pythagoras , and Damascius out of Eudemus call him . Ibidem Line 39. after resolve , add . Damascius allotted three Principles , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Ignis , Aer , & Aqua . Page 15. Annot. Line 13. after idem nasceris , add . And for this Reason the Sun is called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , quia Sol quotidie renovat sese . Hence that of Virgil ( Georg. l. 3. ) Manè Novum , vide Macrobium Saturnal . l. 1. & Festum in Voce Manare . Page 17. Annot. Line 41. add , the Chineses hold it Piacular not to relieve the Sun and Moon when eclipsed , ( at which time they believe them to be ready to be devoured by some Dog or Dragon ) by offering Solemn Sacrifices , and making a great Noise . See Martinius Histor. Sinic . p. 58. Page 18. Line ultim . add , The Chineses divide the Zodiack into 28 Constellations , according to the Arabs , who call them the Mansions of the Moon ; which Number Kepler ( in Comment atiuncula in P. Terrentii S. I. Epistolium ) conceives to arise from the Periodical Motion of the Moon , which is compleated in so many Dayes . Page 24. Line 36. Annot. after North Star , add . By the Chineses it is called REX , or the Kingly Star , quia olim ( according to their Imagination and Belief ) erat prope polum immobilis , quam Reliquae Omnes Stellae venerabantur , as Terrentius the Jesuit in his Epistle from China , anno 1623. affirms . Ibidem Line ultim . add . See likewise Io. Francisc. Grandis , in Dissertat . Philosoph . & Critic . p. 112. where he cites this Maxim from the Authority of Rambam , in More Nevochim . Page 31. Line 42. Annot , after Oculus Tauri , add , by Theon in his Treatise De Geodaesia , called Lambauras , i. e. fax ardens , as Barocius renders it in the Translation of that Piece . Page 33. Line 39. Annot. after Ulugh Beighs Table , add , and in Doctor Pocock's Notes in Specim . Histor. Arab. p. 132. Page 39. post Line 32. Annot. after derived , add . But it will be requisite further to explain this Place . The Antient Philosophers , especially those of Democritus his School , and most of the Mathematicians of those Times , asserted the Universe to be Infinite , and to be divided into two chief Portions ; whereof the One they held to be the World , or rather Worlds , finite as to Bulk and Dimension , but infinite as to Number . The other Part or Portion , they extended beyond the Worlds , which they fancied to be a Congeries of infinite Atoms . Out of which not only the Worlds already made received their Sustenance , but new Ones also were produced . And therefore the Cosmical System according to them was , or may be imagined to be as followeth . First , the Place of the Planets and the Earth ; then the Starry Firmament marked A. B. C. D. embracing within its Circumference the Planetary and Elementary System ; beyond which , a certain infinite Chaos of Atoms , in which this World of ours is supposed to float , and of which it was composed , and into which in time it is to be resolved . But see the Scheme as taken from Scheinerus his Disquisit . Mathemat . p. 17. SYSTEMA ANTIQVORVM . Planetarium Terraeque locus Coellum Stellatum . CHAOS INFINITVM EX ATOMIS . Page 43. Line 29. Annot. after Antients , add . See Hypsicles his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . seu De Ascension . who lived in the Time of Ptolemaeus Physcon . Propos. 4. where he divides the Zodiack into 360 Parts . Page 50. Line 17. Annot. after Iuno . add . But see this in Eratosthenes at the End of Aratus , lately Printed at Oxford . Page 54. Line 68. Annot. after Sword of Rome , add . The Honour of which Title is still preserved in an Antient Marble erected to his Memory at Nola , at this Day affixed to the Outer Wall of the House of Signior Marco Mastrilli , having therein this following Inscription transcribed by Gualterus in his Tabul . Antiqu. M. CL. MARCELLO ROMANORUM ENSI FUGATO HANNIBALE V. CONS . S. P. Q. NOLANUS . Page 55. Line 35. Annot. After the Chair , add , AS OFTEN QUESTOR . Page 59. Line 15. Annot. after Quies , add , by Proclus ( in his Paraphrase on Ptolemies Tetrabibl . ) said to be called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Ibidem Line 30. Annot. after powerful , add . See the Notes upon Cornutus , lately Printed at Cambridge p. 59. Ibidem Line 44. Annot. after Names ; add . See Doctor Pocock's Notes in Specim . Histor. Arab. p. 103. Ibidem Line 48. after Negotiator , add . In which Sence by the Arabs he is called Otared ( monente Almakrizio sayes Doctor Pocock . ) Ibidem Line 55. after cited , add . He is also called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 from the bright and quick Vibration of his Rayes . Ibidem Line 58. after videt , add ; for which Reason by the Arabian Astrologers he is called Menapheck , i. e. Hypocrita , vel Simulator ; teste Alkaswini . vid. D. Pocock : ut supra . Page 62. Line 40. Annot. after Motion , add ; the Learned Doctor Isaac Vossius in his Book De Natura Lucis , reduces them to the only means of Constipation and Attrition of solid Matter , for that of Propagation or kindling Fire by Fire , or by contraction of Radii in Burning-Glasses , is not properly generating of Fire , but multiplying and propagating it already actually existing . In the APPENDIX . Page 10. Line 3. after Astronomy , add . In which he was more particularly instructed by Sonches , chief Prophet of the Egyptians , as Clem. Alex. ( Stromat . l. 1. ) testifies . Page 11. Line 7. after Priests , add , especially Senchnouphis the Heliopolitan . Ibidem Line 38 ▪ after there ; add ; particularly of Konouphis , as Clem. Alexandr . ( Stromat . l. 1. ) attests . Page 12. Line 42. after Aratus , add , and found that Spica Virginis then preceded the Autumnal Equinoctial Point eight Degrees . Page 23. Line 8. after Explications , add . In Theodosii Sphaerica , &c. Page 29. Line 4. after Avicenna , add : whom some will have to be a Spaniard , descended of the Race of the Moores ; but others make him to be a Native of Bucara , a Town in Persia , upon the Confines of Tartary , and Son of a Chinese , as his Name imports . vide Perronian . p. 23. Page 29. Line 20. after into , add , very good Latine , as appears from the Astronomical Pieces extant in the Bodleian Library under his Name . Page 30. Line 15. after in France ; add , and at Oxford . Erasmius Bartholinus in his Learned Animadversions upon Heliodorus Larissaeus his Opticks , reports that he saw in Bulialdus his Library a MS. of Alkindus De Aspectibus ; which I conceive to be the same with that De Radiis Stellarum . Ibidem Line 17. after Alfraganum ; add ; and of the Disposition of the Celestial Orbs , and Motion of the Stars , conceived to be the same with Aben Ezra , of whom hereafter Page 31. Line 11. after Astronomia , add ; which is likewise to be found in Latine in the Bodleian Library . Page 33. Line 7. after that Age , add , many of his Works are preserved in the Bodleian and other the Oxonian Libraries , and also ( as I am informed ) in that of Mr. Theyer of Gloucestershire . Page 34. Line 4. after Manuscripts , add . As also an Institution of Astronomy extant in the Oxonian Libraries both in Persian and Arabick . Page 35. Line 1. after De Astronomia , add , and Canones de Conjunctionibus , Oppositionibus & Eclipsibus Solis & Lunae , as they are cited by Pitsaeus . Ibidem Line 10. after Geographer , add , a Specimen of &c. Ibidem Line 11. after Latine , add . The whole Work hath been essayed , or promised by many Learned Men , as , Schikardus , Erpinnius , Hornius , the learned Mr. Clerk of Oxford , and the ingenious Monsieur Thevenote . Ibidem Line 29. after Astronomicis , add . His Tables and Astronomical Pieces are yet preserved in the Libraries of Oxford . Ibidem Line 35. after Defensionem Dei , add . In the fifth Tractate of which Book , he affirms the Stars Spica Virginis and Regulus , to have been in the same Places in the Heavens in his Time , as they ought to have been in , according to Albategnius , as Riccius reports in his Treatise De Octava Sphaera . Page 36. Line 28. after Diligentia , add . His Observations of the change of the Weather at Oxford for several years together , are in MS. in the Bodleian Library . Page 37. Line 40. after Iudiciaria , add . Part whereof are in Print , and &c. Page 39. Line 29. and 33. for Arabick , read Persian . Page 46. after Line 42. add . 1520. NICHOLAUS KRATZERUS Native of Munichen in Bavaria , and Fellow of Corpus Christi Colledge in Oxford , read there by Command of Henry the Eighth , Lectures upon the Sphere of Io. Sacroboscus ; and wrote De Compositione Astrolabii , & in Geograph . Ptolemaei , likewise Canones horopti . Page 48. Line 29. after Robinus , add , sometime Fellow of All-Souls Colledge in Oxford , add likewise ibidem , Line 32. he wrote likewise De Culminatione fixarum Stellarum , and De Ortu & Occasu fixarum Stellarum , as also Annotationes Astrologicae in three Books ; All which are yet extant in MS. in the Bodleian Library , as I find in the Oxford Antiquities , l. 2. p. 178. Page 50. Line 38. after 1568. add ; He writ also a Treatise , De Anno & Die Passionis Christi , as Onuphrius Panvinius l. 6. Antiqu ▪ Veronens . affirms . Page 51. Line 32. after observes , add ; He put forth likewise Theodosius his Sphaerica in Greek and Latine , with Explanations and Notes , Printed at Paris 1558. 4 o. Page 56. Line 34. after Wales , add , and sometimes Fellow of All-Souls Colledge in Oxford . Ibidem Line 39. after Portuguez , add , an Eminent Professor , and Line 40. after Conimbra , add , who besides his Algebra . Page 57. post Line ult . add . 1556. JOANNES MARTINUS POBLACION , put forth a small Treatise entituled Compendium de Usu Astrolabii Schematibus commodissimis illustratum , Printed at Paris in the year 1556. 8 o. Page 60. Line 27. after Astronomical , add ; perpetual ; and after Printed , add , afterwards corrected and augmented , with an accurate Description of the Copernican System , and reprinted in the Year , 1592. Page 66. Line 28. after Authors , add ; he wrote a very large Comment upon Ptolemie's Quadripartite in Latine , which remains in a fair MS. in St. Iohn's Library Oxford ; together with the Scheme of his Nativity , and a remarkable Narration concerning his Death . Page 74. Line 23. after Cambridge ; add : and published at Paris in Greek and Latine by Erasmius Bartholinus , with his Learned Animadversions thereon , 1657. 4 o. Page 76. Line 18. after Work ; add , and also Commandinus in his Excellent Edition of the Ptolemaick Planisphere . Page 77. Line 4. after Oxford , add : He died in the year 1385 ▪ as I since find in the Author of the Oxford Antiquities , l. 2. p. 87. Page 78. add . 1600. THOMAS ALLEN sometime of Trinity Colledge in Oxford , afterward of Glocester-Hall in the same University , a Learned Antiquary , Philosopher , Mythologist and Mathematician ; In which last Concern he was by some conceived to be Equal to the Famous Roger Bacon , being stiled not only Princops & Coryphaeus , sed ipsa Anima , & Sol , omnium sui Aevi Mathematicorum , as Burton , sometimes his Fellow-Collegiate , in his Funeral Sermon sayes of him . Whose Learned Collections , and Observations Astronomical ( besides his other Mathematical and Philosophical Labours ) at this Day enrich the private Libraries of several Curious Persons ; The greatest Part falling to the share of the Noble Sir Kenelm Digby : His Exposition on the second and third Book of Ptolemy , De Astrorum Iudiciis , being at this Day preserved in MS. in the Hands of my worthy Friend , Elias Ashmole Esquire : See more in the Author of the Oxford Antiquities , l. 2. p. 382. Page 78. Line 19. after Hours ; add ; he wrote likewise , De Anni Crrrectione , ejusque Necessitate , de Kalendario Gregoriano , which is commonly Printed at the End of the Breviary set forth by the Authority of Urban the Eighth : Also ' De Novo ' Quadrante , ejusque Usu , nec non de Horologiis Solaribus peregrinis in Cylindro stabili concavo , & in Globo Descripto cum stilo fixo ad Solis Motum mobili . Horologii etiam Hydraulici Fabricam , in quo per Tabulam Refractionis Universalem ab ipso nunc primùm laboriose supputatam , Horariae Lineae , artificio in Depressiori parte Hemispherii concavi Descriptae Aquae Beneficio elevatae , à Solis Radio refracto per Gnomonem indicantur , as Leo Allatius describes the same in his Apes Urban . p. 240. Ibid em Line 30. after Oxford , add , many of which are yet preserved in MS. Page 79. Line 24. after 1621. add , and a Treatise published at Geneva , 1613. De Annis Nativitatis , Baptismi , & Passionis Christi , contra Scaligerum , Baronium , Deckerum , Susligam , & Keplerum . He wrote also divers other Pieces Astronomical and Chronological , which ( as I am informed by my Learned Friend Mr. Bernard Savilian , Professor of Astronomy in Oxford ) are yet preserved in several Volumes in the Hands of Doctor Camphire , History Professor in the said University ; and do well merit the Publick view . He was a Person that deserved the Esteem which the Famous Peirese bare him , and the Character which his good Colleagues of New Colledge have bestowed on Him in a fair Monument . Page 81. After Line 21. add . FRANCISCUS SITIUS a Florentine , published a Tractate entituled Dianoia Astronomica , Optica , Physica ; wherein he endeavours to refute the Nuncius Sidereus of Galilaeo ; touching the four Satellites of Iupiter , Printed at Venice , 4 o. 1611. Page 82. Line 35. after Scholar , add the Excellent . Ibidem Line 44. after mentioned , add , and taxed . Page 83. Line 26. after Padua , add , besides his Geometrical , and Algebraical Exercitations . Page 85. Line 38. after Celestial Bodies , add ; His Works are divided by some into ten Tomes : In the seventh whereof he treats De Astronomia , cum Examine Tychonis , Copernici , & Ptolemaei ; there is likewise attributed to Him among other his Opuscula , a small Treatise entituled Apologia pro Galilaeo de Motu Terrae , Printed at Franck fort apud Tambachium in 4 o. the year I find not . Vide Leon , Allatii Apes Urban . p. 242. Page 90. Line 19. after Holwarda , add , a very acute and Learned Person . Ibidem Line 37. after Aphoristica , add : besides these he put forth Astronomicorum Libri Tres , Printed at Rome 1629. and before that Problemata Astronomica ; likewise Catholicae & Probatae Astronomiae Epitome , treating of the Sphere , and Theory of the Planets , according to the Observations and Hypotheses of Tycho Brahé and Ephemerides Coperniceae & Tychonicae from the year 1640. to 1660. also Commentaries in Tetrabibl . Ptolemaei , with the Greek Text , and Latine Version , a Treatise De Novis Stellis nostro Aevo genitis , aliisque Phaenomen : Of which , with others , particular mention is made by Leo Allatius in his Apes Urban . Page 89. after Line 34. add . OSWALDUS KRUGER , by Birth a Prusian , by Profession a Jesuit , Doctor of Theology , and Reader of the Hebrew Tongue and Mathematicks at Vilna , put forth Theoremata & Problemata Mathematica ex Opticis , Geometria , Astromomia , Sphaera Elementari , Computo Ecclesiastico , Printed 1633. likewise Calendarium Romanum , published 1637. also Centuria Astronomica , and Horographia Practica ; with some other Mathematical Pieces mentioned by Alegambe in his Catalogue . Page 91. Line 35. after Tubinge , add : a most learned and ingenious Person , as by his Epistles to Gassendus , and his Celestial Observations , Printed by Curtius to supply Tycho's in the late Volume published in Germany , sufficiently appears : not to mention his Version of Abulfeda , and other Pieces yet preserved at Tubinge , nor his excellent Oriental Tractates . Page 92. Line 28. after made , add : He was a Person very expert and accurate at Calculations . Ibidem Line 37. after Meniscus , add : He made several good Observations to be found in his Letters now in the Hands of Richard Townley of Townley in Lancashire Esquire , or in their extracts by Mr. Io. Flamsteed ; and was questionless the first that ever exactly observed the Moon 's Diameter in a Telescope by the help of Skrews , which were not before thought of . Page 93. Line 30. after omit , add , only I think fit to add , that among the Letters of the Lancashire Correspondents , there are found some of one Tillitson to this Mr. Pighels , and mention of some others , who seeme to have been very able Astronomers by their Papers . Page 96. Line 45. after Ptolemy , add : his Hypothesis of the Planets . And after Canon , add : in Greek and Latine . Page 99. Line 17. after Studies , add : His Pyramidography and Roman Foot , will shortly be Printed at Oxford in Latine , together with his Life . Page 100. Line 41. after 175. add : and Printed in a large 4 o. at Bologna , ex Typograph . Hered . Victor . Benatii . Page 106. Line 16. after Astronomers , add . He published likewise in the Year 1672. Admonitio ad Astronomos , Geographos , rerumque caelestium curiosos , de Incursu Mercurii in Discum solis observando , Anno Christi , 1674. sexto Maii Stil . Nov. Ibidem Line 34. after Annua , add ; In which the Cycles of the Sun and Moon from the hitherto best known Principles of Astronomy are most accurately demonstrated . Page 115. Line 22. after Mars , add , by Observations of the Distances of Mars from three contiguous fixed Stars in the Water of Aquarius taken within his Tube September 1672. he discovered the Parallax of Mars at that Time , and thence the Sun's Parallax 9●…″ . which gives his Distance 22 thousand S. D. T. Page 123. Line 9. after Cross-Staff , add : and the making and Use of the Geometrical Instrument called a S●…ctor , Printed in the year 1598. in 4 o. London . Page 124. Line 18. after Marinius , add : Native of Terni in Italy ; and after Line 20. add ; penes se habet Globum sine Globo , in quo fere omnes Operationes Mathematicae facillimè perficiuntur , tam Geometrice auxilio Circini , quam per Supputationem Linearum medio Sinuum Tangentium ac Secantium . Sphaericorum Triangulorum Dimensionem ex paucis Regulis facillimè Memoria retinendis ita ut Operationibus non sint requirendae tot Formae . De Ephemeridum facili usu absque Auxilio aliarum Tabularum . Vide Leonem Allatium in Apibus Urban . p. 206. CHRISTOPHORUS BORRUS of Millan at first a Jesuit , after a Monk of the Cistertian Order ; Published a Piece entituled , Doctrina de tribus Coelis , Aereo , Sydereo , Empyraeo ; which Leo Allatius in Apes Urban . describes to be Opus Astronomis , Philosophis & Theologis favens , Printed at Lisbon by Alvarus Ferrera his Scholar in 4 o. 1632. DID A CUS PERESIUS MENSA , a Spaniard , published among divers other Works a Book De Cosmographia , seu Sphaera Mundi cum Omnibus suis Conclusionibus , & Demonstrationibus ex primis veris & immediatis . Also Ars Navigandi cum omnibus Demonstrationibus Geometricis : Likewise a Tractate De Incertitudine Iudiciorum Astrolog . See Leo Allatius his Apes Urban . FEDERICUS CAESIUS Duke of Aqua Sparta , and the Noble Founder of the Lyncean Academy ; wrote among other Curious and Learned Pieces , a Treatise De Coelo ; wherein he proves the Heavens to be fluid and not solid , published at the End of Scheinerus his Rosa Ursina . He likewise writ another Piece entituled Coelestis Natura exposita , in several Books ; whereof Leo Allatius in Ap. Urban . FLAMINIUS FIGLIUCCIUS the Familiar Friend of Cardinal Pietro Aldobrandini , published in Italian Stanze sopra le Stelle , & Macchie Solari scoverte co'l Nuovo Occhiale , Printed at Rome in 4 o. 1615. D r. WASMUTH Professor of the Oriental Languages at Kiel in Holsace ; promises ( as Mr. Hevelius intimates in his Letter to the Ingenious Author of the Philosophical Transactions published N o. 104. p. 74. ) to give the Learned World a new Astronomico-Chronological Work now by him preparing for the Press under the following Title , viz. Annales Coeli & Temporum Perpetui , sive Mysteria Astronomo-Chronologica , à Seculo abscondita , nunc per Dei Gratiam detecta , & evidenter Asserta , libris tribus . Of which the Learned Hevelius gives this Censure . Num res ipsa Promissis responsura sit , est quod valdè dubitem . Profectò si praestare ea posset , Omnes Astronomos maximâ curâ & Molestiâ , multoque labore qui nos diu Noctuque torquet liberaret ; nec foret opus imposterum Coelos tanto studio contemplari . But see the whole Design particularized in the Accompt before mentioned . Page 139. Line 27. after Signum Crucis , add ; not that by the Spaniards called Elcruziero ; for that is placed near the hinder Feet of Centaurus , the Stars that compose it being not unknown to Ptolemy , as our Countryman Mr. Hues ( who had seen and observed them ) in his Book De Globis affirms : However Corsalius make of it a wonderful and late discovered Phaenomenon . The Fable of ANDROMEDA and PERSEUS , Paraphrased ; to be referred to the Annotations , Page 28. after Line 45. MANILIUS L. 5. WHen the swoln Sea did with a Deluge Sack Phoenicia's Coast , and the Land fear'd a Wrack : Andromeda t' appease th' incensed Flood To a Sea Monster destin'd was for Food . These were her Nuptials ; and for Children , She Is only grac'd by Punishment to be A Weeping Victime for the publick Woes ; Deck'd in a Vest , prepar'd for other Vows . Hal'd to her Death 's sad Pomp , e're her Lifes Fall , A Funeral without a * Funeral . Soon as the angry Seas rough Shore they reach , Against the Rocks , her tender Arms they stretch , And her soft Feet with galling Fetters tie ; So leave the crucifixed Maid to die . Amid'st her Pains yet , her sweet Looks still shin'd , Her Sufferings more became her ; She inclin'd Gently her Snowy Neck , as if 't had been To keep a Guard on what she could not skreen . Her Mantle from her Sides and Shoulders fled , And 'gainst the Rocks were her loose Tresses spred . The pitying Halcyons hovering near the Shore , Did in sad Notes thy wretched Fate deplore , And with joyn'd Wings a plum'd Umbrella made : At Sight of Thee , his Waves the Ocean stay'd , And ceas'd his wonted Banks to overflow . The Sea Nymphs rising from their Beds below , Their Faces and the Waves with Tears bedew . The Wind which to refresh thee gently blew , In mournful murmurs made the Rocks complain . But loe ! from Conquest of the Gorgon slain That Day returning Perseus brought to Land. Seeing the Virgin fetter'd on the Strand , Pale grew He , whom no Foe could e're affright , His Hand scarce held his Spoyl ; and at first Sight , Medusa's Victor by Andromeda Is vanquish'd ; now the Rocks he envies ; They , They and her Fetters , happy are , he cries , That hold such Limbs ; then of her Miseries Hearing from her the Cause ; he vows to gain Her Bed by Combat , nor to quit the Main , Though thence another Gorgon should arise . Gliding through Air to her sad Friends he flies , And chears them with the Promise of her Life , On terms , when sav'd , to have her for his Wife . Then to the Shore returns ; where now he spies The Sea , by the huge Monster prest , to rise . The frighted Waves in heaps before him run , And strive , the Weight of what they bear , to shun . Above the Waters his fear'd Head appears , As he to Shore through foming Billows steers . Dash'd 'gainst his rocky Teeth , the Waves resound , And in his Gulphy Jaws the Sea is drown'd . In mighty Rolles he coyls his Lengthful Train , Whilst his Back swells above the scanty Main . The Sea turns Whirle-pool , roars on every side , The Mountains dread his coming to abide , Rocks as he rushes by , shrink as afraid . Ah then what Heart hadst Thou distressed Maid ! Though such a Champion by thee ; how then fled Thy frighted Blood , and left thy Limbs half dead ? When from the hollow Cliffs , thy Destiny , And floating Death , thou saw'st through Seas draw nigh , For the vast Ocean ( ' las ! ) how small a Prey ? But Nimble Perseus without longer stay Mounts up into the Skies on soaring Wings , Whence , dipt in Gorgon's blood , his Darts he flings . The Monster struck , raises his Head , and raves , And lifting his vast Body 'bove the Waves , Rests on his Sterns wreath'd Folds ; but the more still He rises up , the more with Nimble Skill Perseus gives back , and round about him plays , Whilst cleaving Blows on his hard Skull he lays . Yet yields he not , but the Air , raging , snapps , And makes vain wounds with his deluded chapps . Seas high as Heaven he spouts , which falling poure Upon his winged Foe a blood-stain'd shower : The Fight , the Cause of it , the Virgin views , And now her self forgetting , only rues Her Champions Fate , for him alone now fears ; And more in Mind than Body rack'd appears . Transfix'd with Shafts , at length , the Monster slain , Sinks down , and through his Wounds drinks in the Main ; Then rising up , floats on the Waves quite dead , Whose stretch'd-out Bulk does the wide Seas o'respread ; Ev'n then t' Andromeda too fear'd a Sight . His Limbs the conquering Hero soyl'd in Fight , In the Seas liquid Chrystal plunging , Laves ; Straight re-ascending greater from the VVaves , Flies to his Mistress ; looses her rude Bands , And then , in those of Hymen , links her Hands . FINIS . THE TABLE Of AUTHORS mentioned in the CATALOGUE . A. Names Page ABbasides Ibn ' Jahia 73 Abdalla Ebn ' Sahel , &c. 75 Abdorrachman 73 Abdorrachman Al-Suphi 27 Abenham 75 Abi L Assaker Abdoll , &c. 73 Abiosus Johannes 44 Abraham 7 Abraham Aben-Ezra , or Aven-Hesre 31 Abu-Sheliel 73 Abu-Shuker Affricanus 73 Abu-alli Ibn ' Sina 29 Abydas Astronomus 22 Achilles Tatius 27 Achillinus Alexander 42 Acosta Josephus 70 Adam 6 Adamus Johannes 85 Adda Rabbi 21 Addin Sjaheb 73 Aetius Amidenus 23 Agesianax , Alexander Aetolus 13 Agrippa 20 Aguilonius Franciscus 83 Alacenus 76 Albu-batur 16 Albategnius , or Albattanius Aracensis 27 Albumazar 31 Albertus Magnus 32 Albuassen , or Alboazen Haly 33 Albochary Omad Eedin 73 Alcmaeon 10 Alchabitius 43 Aldilazith Astrologus 76 Alexander Ephesius 16 Alexandrinus Jardagrid 74 Alexander 75 Alfraganus Mahumides 28 Alfarabius 28 Alfarr●…skonzi Ommaz 73 Alfaki Chalin 73 Algazel Abuhamad 72 Algimde Ibrahaim Ibn ' Ali-Alabashi 73 Alhazen Arabs 29 Ali Ibno'l Hozein 28 Aliacensis Petrus 39 Ali Cushgi 39 Ali Ibn ' Alhazen , &c. 73 Ali Alhazen Ib'n Ali , &c. 73 Alkindus 30 Alkasranus 73 Allatius Leo 99 Almaeon , or Almamon 26 Almeon Almansorius 30 Almugjareiti Harim 73 Almaraskolii 73 Al●…ajim 73 Alpetragius 30 Alphonsus 33 Amicus Cozentinus Johannes Baptista 50 Anaximander 9 Anaximenes 9 Anaxagoras Claromenius 10 Anatolius Alexandrinus 21 Andromachus Cretensis 19 Andruzagar 21 Andalo 42 Andubarius 119 Angelus Johannes 43 De Angelis Alexander 83 Anianus 23 Anonymus 125 ; 126 Antiochus 17 Antonius Delphinus Johannes 52 Apollonius Tyanaeus 19 Appianus Petrus 47 Apomasaris 17 De Apono Petrus 34 Apuleius 21 Aquila Ponticus 20 Aratus Solensis 13 Arcandam , or Arcandum , and Alcandrinus 75 Architas Tarentinus 11 Archimedes 14 Argyrus Isaacius Monachus 29 Argolus Andreas 90 Ariel Richardus 55 Aristotle 12 Aristyllus 12 Aristarchus Samius 13 Artemidorus Cosmographus 16 Arza●…l Ala Ben 28 Arzachel Hispanus 29 Arzet Andreas 89 Ascletarion 20 Asculanus Cichus 35 Ass●…itari Mahmond Ib'n Mesand 73 Athelardus 30 Athelstan R. Angl. 121 Atlas 7 Atreus 8 Aubderkem Rabbi David 36 Averroes 31 , 121 Avienus 75 Sieur . Avocate 26 Auria Josephus 68 , 122 Auzout Adrian 114 Azalus Pompilius 54 B. Names Page BAccarius Macceus 23 Bacon Rogerus 32 Baconthorp Johannes : 35 Bachmannus Georgius 69 Baersius alias Vekenstyl Henricus 47 Bainbridge Johannes 96 Baldus Bernardinus 70 Barwick Johannes 35 Barbarus Hermolaus 44 Barbarus Daniel 58 Baroccius Franciscus 61 Baranzanus Redemptus 83 Bartschius Jacobus 87 Bartholinus Erasmius 108 Barrow Isaac Doctor 112 Bassantinus Johannes 80 Baten Henricus 34 Batecumb alias Badecon 39 Battingius Rodolphus 58 Bavarus Angelus Joannes 44 Bavarus Johannes 55 Bayerus Johannes Rheinanus 79 Beausardus Petrus 63 Bechet Johannes 99 , 125 Beda 26 Belus 7 Bellerophon 8 Belinus 17 Bellantius Lucius 44 Ben-Maimon Rabbi Moses 31 Beneventanus Marcus 45 Bentherus Michael 59 Benedictus Johannes Baptista 67 , 122 Berosus 14 Bernard Edward 115 Bessarion 41 Bettinus Marius 98 Beverege William 125 Blanchinus Johannes 41 Blancanus Josephus 81 Blaeu vide Gul ▪ Jan Caesius 8●… Blebelius Thomas 65 Blondus Michael Angelus 53 Boccasius Johannes 37 Bodeinstein Adamus 64 Bolus Mendesius 16 Bonatus Guido Foro Juliensis 34 Bonincontrius Laurentius Hellbronensis 44 Bonettus 51 Bonaventura Fredricus . 70 Bond Henry 123 Bordinus Franciscus 64 Borellius Johannes 108 Borellus Petrus 125 Bornerus Gasper 51 Botener Gulielmus 40 Boulenger 88 Du Boys Jacobus 125 Brahe Tycho 63 Bredon , or Bridon Simon 37 Bressius Mauritius 66 Briggius Henricus 86 Brithus Gualterus 121 Brotheiel Hieremias 56 Brundzevius Albertus 47 Brunfelsius Otho 47 Brucaeus Henricus 61 Buchananus Georgius 59 Bulialdus Ismael 96 Buschius Georgius 64 Busaeus Johannes 69 Buzur Giumhur 25 C. Names Page CAbasilas Nicolaus 36 Cabaeus Nicolaus 91 Caerlion Ludovicus 37 Calippus Cyzicenus 12 Calvisius Sethus 124 Camaterus Johannes 26 Campanus Novariensis 28 Campegius Symphorianus 51 Camerarius Joachimus 53 Camerarius Elias 61 Camerarius Johannes Rudolphus 79 Campanella Thomas 85 Capuanus Johannes Baptista Sipontinus 42 Capra Balthazar 79 Carpus Antiochenus 24 Cario Johannes 48 Cardanus Hieronymus 56 Carellius Johannes Baptista 66 Carpenter Nathanael 90 Des Cartes Renatus 95 Cassiodorus 24 Cassini Giovan Dominico 114 Catton Gualterus 35 Catena Petrus 51 Caudas Astrologus 18 Caussinus Nicolaus 91 Cavallerius Bonaventura 89 Cavina Pietro M. 109 Caelus 7 Caelius Calcagninus 53 Caesius Georgius 66 Caesius Gulielmus Jansonius vide Blaen 87 Cellarius Andreas 106 Censorinus 21 Cepheus 8 Ceporinus Jacobus 49 Cham 6 Charlemaigne 26 Chaucer Galfridus 38 Charikaeus Mahumides 73 Chamber John 78 Chaeremon 19 Cherubin 111 Cheucungus 120 Chilvenuz vide Jardagird Alexandrinus 74 Ben Chora Thebit 34 Christmannus Jacobus 68 Chrysococca Georgius 121 Chuenhious 119 Chumcang 119 Chylmark Johannes 38 Cirvellus Petrus 47 Claramontius Scipio 98 Clavius Christopherus 78 Claudius Ptolomaeus 20 Claudius Galenus 21 Clemens Lanthoniensis 31 Cleomedes 22 Cleostratus 9 Clitchthoveus Jodocus Neoporticensis 49 Collins John 116 Columbus Christophorus 44 Colinitius Tannesletterus Georgius 47 Comnenus Manuel 31 Comes de Comitibus Nicolaus 43 Commandinus Fredericus 59 Conon 14 Conradus Cocus Wimpinae de Buchonia 45 Conradus Balthazar 91 Copernicus Nicolaus 49 Courcier Petrus 100 Crabtree William 92 Cremonensis Gerardus 38 Criton Naxius 17 Crusius Paulus 51 , 66 Crugerus Petrus 89 Cunitia Maria 99 Curiacus Alkas 66 Curtius Albertus 87 Cusanus Nicolaus 40 S. Cyrillus 23 Cysatus Johannes Baptista 84 D. Names Page DAcius Petrus 34 Damascenus Ib'n Shater 37 Daniel Surnamed Sapiens 72 Dank Johannes 35 Dante 's Egnasius 65 Dantforth Samuel 107 Dasypodius Conradus 58 Dee Johannes 62 Decimator Henricus 68 Dekerius Johannes 83 Democritus 10 , 120 Demophilus 12 Demetrius Triclinius 18 Deusingius Antonius 94 Diaz Emanuel 83 Digges Leonardus 60 Digges Thomas 69 Dion Nicaenus 18 Diodorus Monachus 25 Divini Eustachio 125 Dodonaeus Rembertus 67 Dopelstein Henricus 75 Dorotheus Sidonius 17 Dositheus Astrologus 17 Douza Janus 69 Driander Johannes 59 Drienes Johannes 99 Duditius Andreas 66 Dudley Robertus 97 Dullendius Gabriel 103 Duretellus Adelmus 26 Duret Natalis 124 Dyonisius Afer 15 Dyonisius Corinthius 17 Dyonisius Areopagita 19 Dyonisius Exiguus 25 E. Names Page EBerus Paulus Kytzingensis 56 Eberbachius Godescalcus 65 De Egmunda Johannes 38 Egmundus Astrologus 27 Egydius Johannes 32 Eichstadius Laurentius 95 Eligerus Johannes 36 Empedocles 10 Endymion 7 Enoch 6 De Epieres Johannes 97 Epigenes Byzantinus 14 Eracus Astronomus 13 Erastus Thomas 67 Eratosthenes 13 Ergom Johannes 43 Ethelwoldus Wentanus 28 Euctemon 10 Eudemus 12 Eudoxus Cnidius 11 Euthymius . 18 Ezler Johannes 45 F. Names Page FAber Jacobus 44 Fabritius Paulus 62 Fabricius Johannes 80 Fabricius David 82 Fantonius Philippus 58 Femillus Christophorus 71 Fernelius Johannes 48 Ferrerius Augerius 54 Ficinus Marsillius 43 Fineus Orontius 48 Finella Philippus 98 Fiornovellus Johannes Maria 65 Flaccus Albinus , or Alcuinus 26 Flavius Manlius , vide Manlius Theodorus 22 Flamsted John 115 Florentinus Maurus 51 Floriacensis Abbo 28 Foius Imp. Chin 119 Fortius Joachimus Ringelbergius 48 Fortius Angelus 52 Foster Samuel 97 Fournerius Georgius 94 Fracastorius Hieronymus 48 Frangipanus Cornelius 61 Frischlinus Nicodemus 67 Fritschius Marcus 57 Froidmont Libertus 83 Frommius Georgius 124 Fusor , or Fusorius Johannes 40 G. Names Page GAdbury John 126 Gadytanus Raymyrus 76 Galilaeus Galilaei 82 Galtruchius Petrus 108 Gallucius Johannes Paulus 70 Ganivetus Johannes 45 Garcaeus Johannes 57 Garibus Johannes 99 P , Gassarus Achilles 49 Gascoygn William 92 Gassendus Petrus 95 Gauricus Lucas 55 Gaza Theodorus 42 Gazulus Johannes 40 Geber Hispalensis Arabs 30 Geminus 15 Gemma Rainerus Frisius 53 Gemma Cornelius 61 Generini Francisco 96 Georgianus 73 Gerardus Rupelmundanus 70 Germanicus Caesar 19 Gerson Joannes 39 Gergiro 73 Geryon 120 Gez , or Gessius 17 Ghaminaeus 75 Giaphar Astrologus 18 Gigas Johannes Stainfortensis 51 Glareanus Henricus 48 Gloriosus Camillus 83 Goad John 113 Goclenius Rudolphus 82 Gontranus Carolus 90 De Gottignies Aegydius 111 Goubard David 124 Gramineus Theodorus 62 Grassus Horatius 83 Grandamicus Jacobus 94 Graves Johannes 99 Grevenstein Antonius 79 Gregory Johannes 94 Gregory Jaeobus 106 Griembergerus Cristopho●…us 81 Grimaldi Franciscus Maria 100 Grizaunt Gulielmus 36 Grotius Hugo 78 Grynaeus Simon 48 Guarinus , Guarinus 126 Guido Johannes 53 Guldinus Paulus 89 Gulielmus , Abbas Caenobii Hirsaugiensis 29 Gulielmus de Sancto Godialdo 34 Gulielmus Landtgrave of Hassia 70 H. Names Page HAbash Mcrwazensis 75 Hadrianus 20 Haggesius Thaddaeus 64 Hainlinius Jo. Jacobus 125 Hainzelius Paulus 62 Haly Ben Ragel 28 Halpericus 77 Haly Aben Rodoham 32 Harpalus 9 Hasfurt Johannes Virgundus 46 Haveman Michael . 75 Hazan Rabbi Isaac 32 Heckerus Johannes 106 Heckius Johannes 63 Hedraeus Benedictus 124 Helicon Cyzicenus 11 Heliconius 18 Hellerus Joachimus 54 Helvino 73 Henricus de Hassia 38 Henischius Georgius 80 Henrion Doctor 87 Hephaestion Thebanus 21 Heraclides 74 Haraclides Ponticus 10 Herbinius Johannes 125 Hercules 8 Heremita Johannes 46 Herigonius Petrus 94 Herlicius David 84 Hermes 7 Hermes Aegyptius 11 Hermanus Contractus 29 Hervartus Johannes Georgius 93 Hesiod 120 Hevelius Johannes 110 Heydon Sir Christopher 79 De Hexam Johannes 31 Hilarius Georgius 102 , 125 Hildericus Edo 60 Hipparchus 14 Hippocrates 10 Hodierna Johannes Baptista 102 Holcoth Robertus 35 Holwarda Johannes Phocylides 90 Homelius Jacobus 56 Honterus Johannes 59 H●…d Doctor Thomas 123 Hook Robert 112 Horma●…us Hadrianus 57 Horrox Hieremias 92 Hortensius Martinus 86 Hugenius Christianus 103 Hughes Robertus 86 Hugo sive Huo Heltilius 61 Humenius Aegyptius 31 Humius Jacobus 90 Humphrey Duke of Glocester 40 Hypatia 23 Hyperion 7 Hyperius Andreas Gerardus 54 Hypsicles 121 Hystaspes 9 I. Names Page JAquinot Dominique 82 Jarchas 19 Jaus 119 De Ineriis Johannes 75 Ib'n Junes , or Jounis 28 Ib'n Haitem 29 Ib'n Sina 73 Ib'n Sarcali 73 Inchofer Melchior 89 Joachimicus Johannes praetorius 66 Johannes Hispalensis 30 Joestelius Melchior 71 Josephus Chaldaeus 72 Isaac Israelita 34 Isidorus 25 Julius Caesar 15 Julianus Laodicensis Philosophus 17 Julius Hyginus 19 Julius Maternus Firmicus 21 Julius Caesar La Galla 81 Junctinus Franciscus 65 K. Names Page KAdi Zada 39 Kaebelius Jacobus 49 Keckermannus Bartholomaeus 80 Kent alias Kayleg Johannes 43 Keplerus Johannes 84 Killingworth Johannes 37 Kircherus Athanasius 96 Knitl . Balthazar   Kratzerus Nicolaus   Kusianus , or Keuxian Gilaeus 73 L. Names Page LAbbee Philippus 97 Lacher Ambrosius 75 Lalamantius Johannes 61 Langius Josephus 80 Langrenus Michael Florentius 94 Lansbergius Philippus 89 Lansbergius Jacobus 89 Larissaeus Heliodorus 74 Lasbas Babilonius 16 Lasus Magnes 17 Lavingham Richardus 37 Laurentius Joannes Philadelphensis Lydus 25 Laurenbergius Petrus 81 Lebdebenhazer Johannes 74 Legley Gilbertus 32 Lemoniensis Petrus 74 Leo 38 Leo Philosophus 27 Leoninus sive Leuwius Albertus 67 Leontius Mechanicus 17 Leopoldus de Austria 32 Leovitius Cyprianus 58 Levinus Lemnius 57 Leuterchomius Johannes 83 Levy Rabbi 35 Levera Franciscus 106 Licetus Fortunius 90 De Ligneriis Joannes 36 Lilius Aloysius 67 Lindought Henricus 79 De Lineriis Joannes 38 Linemanus Albertus 94 Linton ▪ Anthony 123 Lipstorpius Daniel 101 Du Liris Leonardus 101 Lobkowitz Johannes Caramuel 102 Locher Jacobus Philo-Musus Germ. 45 Longomontanus Chistopherus 84 Lonicerus Marcus Albertus 66 Lucian 21 Lucilius Santritter Heilbronensis 44 Lucidus Johannes Samosatheus 50 Ludovicus Lavaterus 64 Lupicinus Antonius 69 Lydiat Thomas 79 De Lynn Nicolaus 37 M. Names Page MAcrobius Ambrosius Aurelius Theodosius 22 Maginus Johannes Antonius 80 Mahommed Al-buziani 75 Mahumed Ben Malud 76 Maignanus Emanuel 95 Malapertus Carolus 88 Malvasia Cornelius 106 Manetho 12 Manilius Marcus 16 Manlius Theodorus vide Flav. Manlius 22 Mandovich Johannes 36 Mantz Johannes 45 Manzinus Carolus Antonius 87 Marius Victorinus Afer 22 Marianus 24 Marinus Neapolitanus 25 Martianus Foelix Minaeus Capella 25 Marius Aretius 53 Marmorarius Tobias 55 Marius Simon 84 Marinus Mersennus 95 Marcus Marci Johannes 98 Martinengus Ascanius 122 Marin●…ius Octavianus 124 Maslem 76 Massius Johannes 52 Mathers Patrick 126 Matroptus Aegidius 98 Maugantius 24 Maurolycus Franciscus 52 Medicus Georgius Chrysococca 32 Medmaeus Philippus 25 Meliteniotas Theodorus 26 De Meldis Gaufridus 36 Melancthon Philippus 52 Menelaus 20 Mengoli Pietro 111 Mena Joannes 122 Mercurius Trismegistus vid. Hermes 7 Merlinus Ambrosius 24 Mercurius Morsheimerus Johannes 54 Mercator Gerardus 61 Mergiouz Aben 74 Mercator Nicolaus 106 Messhala Arabs , or Messahulach 27 Mestlinus Goepingensis Michael 62 Mesud 73 Meton 10 Metius Hadrianus 91 De Meynier Honoratus 100 Milbourn William 91 Milichius Jacobus 48 Mercaellius Johannes 82 Mithobius Buchardus 53. Moderatus Columella 18 Mohammed Ibno'l Attar 47 Mohammed Ib'n Zachariae Alkazzi 27 Moletius Josephus 60 Molitor Christianus 42 Montanari Geminiano 115 Montebrunus Franciscus 93 De Montulmo Antonius 52 Moore Sir Jonas 93 Morientes 76 Morinus Johannes Baptista 88 Morley Daniel 32 Moses 7 Moses Eb'n Maimon 75 Moutonus Gabriel 110 Muhammed Ib'n Ahmed Aliberouni 28 Muhammed Ib'n Ali Chaz , &c. 74 Mulana Gijath Eddin Giemshed 39 Mullerus Johannes 41 Mullerus Nicolaus 80 Munsterus Sebastianus 48 Munosius Hieronymus 61 Mutolo Pietro Maria 107 Mutus Vincentius 99 Mutus Savinius 107 Myndius Apollonius 14 Myzaldus Antonius 55 N. Names Pages NAiboda Valentinus 66 Nasir Eddin Tusaeus 34 De Nautonier Guillaume 123 Neander Michael 60 Nebroch , or Nembroth , or Nimrod 7 Necepso 8 Nectarius 76 Nedaminen 74 Neil Sir Paul 101 Neperus Johannes 81 Newton Johannes 103 Newton Isaac 116 Nigidius Figulus 15 De Nigris Andalius 75 Niphus Augustinus Philotheus Suessanus 52 Nolthius Andreas 61 Nonius Petrus 56 Nostradamus Michael 57 Novaras Ferrariensis 43 Numa Pompilius 8 O. Names Pages OCkham Nicolaus 35 Oddi Johannes . 42 Odinton 33 Oenopides 9 Offusius Johannes Franciscus 64 Oliverius Malmsburiensis 29 Omar Astrologus , or Hoamar 32 Oresmius Nicolaus 42 Ori Rabbi 59 Origanus David 80 Oronius 120 Ortelius Abrahamus 61 Osiander Andreas 50 Oswaldus Shr●…kenfufius Erasmus 53 Ott Johannes 109 Otto de Guerrick 111 Oughtred William 98 P. Ovidius Nafo 16 P. Names Pages PAduanus Johannes 67 Paganus Comes 103 Palamedes 8 Palatius Petrus Brixiensis 107 Panodorus 23 Pantaleo Vincislaus 84 Pappus Alexandrinus 23 Papyrius Fabianus 16 Paracelsus Theophrastus 37 Partlicius Simeon 85 Paulus Alexandrinus 22 Paulus Middleburgensis 46 Payen Antonius Franciscus 107 Peckham Johannes 33 Pelacanis Blasius 38 Peletarius Jacobus 52 Doctor Pell 102 Pena Johannes 51 , 122 Perdix 120 Perlachius Andreas 56 Perso-Medus vide Zoroaster 7 Petavius Dionysius 88 P. Petit 101 Petit Samuel 124 Petosyris 8 Peucerus Gasper 56 Philalthaeus Lucillus 60 Philippi Henricus 88 Philolaus 10 Philomantio 97 Philoponus 25 Philosophus 11 Phlegon Trallianus 20 Phocus Samius 9 Picolomineus Alexander 60 Picus Johannes 43 Pierius Valerianus Johannes 51 Pierre Jean de Mesmes 58 Pighels Nathan 93 Pighius Albertus 46 Pilander Georgius 54 Pilatus Petrus 50 Pisanus Octavius 81 Piso Carolus 83 Plato 11 Pleppius Salomon 67 Pliny 19 Plutarchus Chaeronensis 19 Polaccus Georgius 94 Polemon Atheniensis 18 Pontanus Joannes Jovianus 40 Pope Walter Doctor 113 A Popma Titus 60 Porphyrius 22 Porta Johannes Baptista 68 Portus Emanuel 94 Possidonius Apamensis Syrus 15 Postellus Gulielmus 62 Proclus Lycius 24 Profatius 33 Prometheus 7 Prosdocimus De Beldemando 39 Protagoras 121 Providus Hemoaldus 26 Prucner Georgius 49 De Prusa Albertus 122 Prytaneus Autolychus 12 Psellus Michael 121 Purbacchius Georgius 40 Pythagoras 10 R. Names Pages RAbbi Jacob Ben-Machir 72 Rabbi Jehuda Bar Barzilei 72 Rabbi Isaac Ben Lataph 72 Rabbi Abrazarth 72 Rabbi ab Rusack 72 Rabbi Abraham 72 Rabbi Isaachar Ben Susan 72 Rabbi Isaac Alchadeb 72 Rabbi Solomon 72 Rabbi Simcha 72 Raimarus Nicolaus 70 , 122 Ramus Petrus 60 Rantzovius Henricus 69 Rapaldus Franciscus 56 Raphelengius Justus 74 Rasacherus Bartholomaeus 61 Raseh Johannes 64 Ravenspurg Jacob 124 Read Gulielmus 77 Record Robertus 56 Rembrantz Dirk 97 Resenius Johannes Paulus 81 Reynoldus Erasmus 54 Rhetius Georgius Joachimus 55 Richardus Monachus Eboracensis 30 Richard the Second King of England 38 Ricciolus 100 Riccius Augustinus 45 Riccius Matthaeus 66 De Rigiis Ludovicus 49 Ristorius Julianus de Prato 51 Robertus Lorrain 29 Robertus Lincolniensis 32 Robinus Johannes 48 Rochenbackius Abrahamus 78 Rodulphus Brugensis 30 Roeslinus Helizaeus 66 Roffenus Johannes . Antonius 91 Rogerus Herefordiensis 31 Roias Johannes 55 Rolianus Christianus 74 Romanus Adrianus 79 Romanus Aegidius 74 Rook Laurence 105 Rosa Andreas 64 Rosinus Stephanus 45 Rosius Jacobus Biberacensis 87 Rothmannus Christopherus 68 De Royer 126 Rubeus Theodosius 78 Ryff Petrus 69 , 122 S. Names Pages SAcroboscus Johannes 33 De Sacro Fonte Johannes 122 Salinus Bernardinus 80 Salmatius Claudius 98 Saminiatus Federicus 71 Samerius Henricus 78 Sanctius Brocensis Franciscus 122 Sandelinus Cherubinus 78 Sandwich Earle 108 Santbeck Daniel 60 Santutius Antonius 64 Sarzosus Franciscus 47 Sassarides Gellius 62 De Saxonia Johannes 36 Scala Josephus 68 Scaliger Josephus 71 Scheinerus Christophorus 88 Schickardus Gulielmus 91 Schillerius Julius 87 Schonheintz Jacobus 43 Schonerus Johannes 50 Schonerus Andreas 57 Schol Jacobus 64 Schombergerus Georgius 85 Schottus Regis Curianus Gaspar 104 Schraeterus Johannes Vinariensis 56 Schlusingerus Everhardus 41 Schulerus Wolfangus 64 Schyrlaeus De Reitha 96 Scribonius Gulielmus Adolphus 69 Scotus Michael 34 , 41 Scultetus Bartholomaeus . 65 Seldenus Johannes 94 Sempilius Hugo ●…9 Seneca 19 Seth 6 Sextus Empiricus 21 Sextus Avienus Rufus 22 Shackerley Jeremiah 93 Shirazita Kotboddinus 34 Sibrandus a Siccama 71 Sidin Sheriffus 74 Simeon 31 Simlerus Josias 65 Simplicius 24 Simus Nicolaus 57 Sixtus Senensis 65 Sixtus ab Heminga 67 Snellius Willebrodus 83 Solomon 8 Somer Johannes 38 Sophianus Nicolaus 54 Sosigenes 15 Stabius Johannes 56 Stadius Johannes 54 S●…antonius 76 Stevinus Simon 68 Stiborius Andreas 45 Stigellius Johannes 49 Stoeflerus Johannes Justingensis 46 S●…rabo 16 Strauch Aegidius 109 Street Thomas 104 Strigellius Victorinus 54 Sturmius Johannes Christopherus 110 Sulpitius Gallus 14 Swinsett , or Suissett George 121 Syderocrates Samuel 60 Synesius 23 T. Names Page TAlentonius Johannes 79 Tanaus 117 Tannerus Adamus 88 Tarde Johannes 84 Tacquet Andreas 108 Taruntius Firmanus 15 Teilesanus 74 Temporarius Johannes 58 Teucer Babilonius vide Zeucrus 16 Thales 9 Theaetetus Atheniensis 11 Themistus Pletho Constantinopolitanus 40 Theodoret 23 Theodosius Tripolita 15 Th●…on Alexandrinus Senior 20 Theon Alexandrinus Iunior 22 Theophrastus 12 Theut , or Thoth , vide Hermes 7 Thius Atheniensis 24 Thomas 74 Thrasyllus 18 Tiberius Caesar 18 Timeus 10 Timochares 12 De Titis Placidus 105 Tolosas Johannes Maria 55 Tormius Ericus Olaus 124 Torperley Nathanael 78 Townley Christopher Esquire 93 Townley Richard Esquire 114 Trapezuntius Georgius 39 Travagini Franciscus 109 Trechindus 76 Trew Abdias 9●… Tribonianus Sidetes 25 Trivett Nicolaus 34 , 121 De Tryllia Bernardus 77 Tullius Cicero 15 V. Names Page VAlerius Cornelius Veteraquinas 58 Valla Georgius 49 Varro Marcus 15 Ubaldus Guid ' , or Guidus 65 Vernerus Johannes 46 Verro Sebastianus 122 Vesputius Bartholomaeus 45 Vettius Valens 21 Victorinus Acquitanus 23 Vieta Franciscus 68 De Villa Nova Arnoldus 7●… De Villa Dei Alexander 32 Vinetus Elias 59 Virmius alias Virunnius Ponticus 43 Vitalis Ludovicus 46 Vitalis Hieronymus 108 Vitellio Thuringo-Polonus 33 Ulack Adrianus 87 Ulugh Beig 39 Vogellinus Johannes 47 Volaterranus Raphael 44 Uisinus Adamus 61 Ursinus Benjamin 83 Usserus Jacobus 97 Vuestisius Christianus 60 W. Names Page WAllingford Richard 35 Wallis Doctor John 111 Walterus Johannes 38 Waltherus Barnardus 43 Ward Seth L. Bishop Sarum 101 Weigellius Erhardus 103 Welperus Everardus 89 Wendelinus Gothofredus 97 Wendelinus Johannes 100 Wharton George Esquire 93 Wilkins John late Lord Bishop of Chester 91 Wing Vincent 104 Winkerus Nicolaus 65 Wittekindus Hermannus 64 Wolkenstein David 68 Wrenn Sir Christopher 112 Wright Edward 86 X. Names Page XEnocrates Calcedonius 12 Xunus 119 Xylander Gulielmus 58 Y. Names Page YUmchinius 119 Z. Names Page ZAgut , or Zacuti Abraham 41 Zahel sive Zael , or Zeel Bebis 76 Zalese Jacobus 74 Zanardus Michael 84 Zarlinus Josephus 58 Zeltus Danita 73 Zergol Andreas 86 Zeuchrus , or Teuchrus 16 Ziglerus Jacobus 49 Zineris Johannes 75 Zoroafter vide Perso-Medus 7 Zucchius Nicolaus 100 INDEX or TABLE of the Principal Matters contained in the ANNOTATIONS and APPENDIX . A.   Annot. Page Append. Page ABraham the Patriarch erected Astronomical Pillars , as Seth ●…ad done : Said to have taught Astronomy to the Egyptians , &c.   7 Acontiae , Comtes so called 61 193 Actian , Fight described 67   Adonysia , whence their Original 5   Aegyptian Priests , great Promoters of Astronomy 4   Their Hierogliphical Statue of the Sun 44   Aequinoctial Circle , its description 44 145 Aemilia Familia 57   Agriculture , by whom invented 7   Agrippa , his Character 57   Altar , the Asterism so called 35   One dedicated to Penury and Art in the Temple of Hercules at Gades 6   Amalthaean Goat , the Constellation 30   Andromeda , Constellation 28 , 36   The Fable of her Exposure and Rescue     Antarctick Circle 44   Aquarius , the Constellation 22   Aquila , or the Eagle Constellation 27   Artick Circle 43   Arcturus 25   Argo Constellatio 33   Ariadnes Crown 25   Aries , the Constellation 19   Arrow , Constellation 27   Arts , their Kinds 5   Astrology , its Authors 4 , 5   Astronomy , its first Authors 3 2 , 3 , 4 , 5 Studied by Princes 3   Authors that have written therein , vide Catalog .     Asterismes , by ●…hom first found out 10   Those of the Chaldeans , Persians , Egyptians , Arabians , Indians , Chinese and Tartars , differing from the Greek , which are conceived the newest and latest Ibidem   Christian Asterismes   140 Atomes 12 , 39   Athenae Antiquae & Novae 64   Augury 8   Auriga Constellatio 29   Axis of the World 22 , 23   B.   Annot. Page Append. Page BIrds and Beasts reputed to have Language 8   Believed by credulous Antiquity to have been understood by Magicians Ibidem   Bird , called a Hoop , said to be sent by Salomon with a Message to the Queen of Ethiopia Ibidem   Birds , whether Terrestrial , or Aereal Creatures 17   Bootes Constellation 25   Britain , known to the Ancients long before the Romans 5   Burning the dead 12 , 63 , 65   When given over Ibidem   C.   Annot. Page Append. Page Cabiri Dii , by way of Distinction from the Dii Casmilli , Camilli , or Camiri ; who they were 35   Camillus , his Elogium 53   Cancer , the Constellation 20   Supposed by the Chaldaick and Platonick Philosophers to have been the Gate . by which Souls descended into humane Bodies Ibidem   Canis Sirius , or the Dog-star 32 , 33   Canopus , a noted Star in the Rudder of the Ship Argo 16   Not seen to rise in Italy , the reason Ibidem   Capricornus 22   Ascendant in the Horoscope of Augustus , reputed , by the Pythagoreans and Platonists , the Gate by which Souls entered into Heaven , and therefore stil'd Porta Deorum Ibidem   Cassiopea , Constellation 29   Cato Uticensis , his Character 57   Cepheus Constellation 34   La Creda his Mistake in interpreting the greater Bend of Helice and lesser of Cynosura 23   Cete Constellation 36   Chaos , the Place , Region , or Receptacle of Universal Matter : The Fable thereof whence derived 11   Chariots drawn by four Horses , by whom first invented ; the manner of joyning the Horses , &c. 29 , 30   Chariot of the Moon how drawn 14   Cicero his Encomium 56   Cincinnulus Cometa 61   Cleopatra 67   Claudia Familia 57   Cloelia 53   Climates 45 149 Coluri Aequinoctialis 45 147 Coluri Solstitiorum 46   Comets , their Original 60 189 Duration 60   Presignification 63   Names 60   Kinds 60 192 , 193 History   194 Constellations 10 137 Northern omitted 31   Described   137 , 138 Southern how imagined by the Ancients 37   Those near the Southern Pole lately discovered   138 Christian , v. Asterisms     Corvus , or the Crow Constellation 34   Cossus 55   Crater , or the Cup , Constellation 34   Curius Dentatus ●…4   Cy●…nus , or the Swan Constellation 27   Cyllenius , vide Mercury     Cynosura , or the lesser Bear 24   D.   Annot. Page Append. Page DEcii , not two only but three are said to have devoted themselves for the good of their Country 55   Deifying of Julius Caesar 2   Of Augustus 2,58   Delphinus Constellation 27   Deltoton , or the Triangle Constellation 28   Dials , their Invention 40   Dii Majores 35   Divination , from the Inspection of the Entrails of sacrificed Beasts 8   The Parts inspected Ibidem   Despised by the Romans in time of their Greatness Ibidem   Draco , Constellation 24,34   E.   Annot. Page Append. Page EArth , Element 13   Its Place 14   Suspended in the Air 15   Earthquakes , the several kinds 9   Engonasi sive Ingeniculus Constell . 25   Erectheus King of Athens 63   Eventus , the proper Term among the Romans , by which they expressed the Product of Fruit , for which they sacrificed to the Deity called Bonus Eventus 32   Euphrates , its Description 3   Exotica Sidera , why so called 37   Exstispicium , vide Divination , &c.     F.   Annot. Page Append. Page FAbius Maximus , his Elogy 55   Fabricius , Exemplary for his Iustice , Valour , and Conduct 54   Fire , Element , not confined within the Convex of the Lunary Sphere according to Aristotle and his Followers , but with the Stoicks transmitted to the Etherial Region 13   Culinary , its Original 62   Several wayes of generating fire Ibidem   Subterranean 9   Fish , the Southern , a Constellation 37   Funera Pacis , interpreted contrary to the conjecture of Tanaquil Faber 64   Fusio Aquae , a Starry Stream running from the Urn of Aquarius , and Mouth of the Southern Fish 37   G.   Annot. Page Append. Page GAlaxie 48   Supposed by the Ancients to afford to all Plants their Milkie Iuice and Nourishment Ibidem   The Storehouse of most of the New Phaenomena's in these later Ages Ibidem   Gemini , Constellation 20   Goat , the Amalthaean , a bright Star in the Shoulder of Heniochus 30   Gods ; those called the great Gods , or Dii Majores 35   Gold , by whom invented 5   Gyants , the Fable 36   H.   Annot. Page Append. Page HAil 9   Hare , the Constellation 33   Heavens , their Name 41   Their Substance 15   Number   157 , 158 , 159 Fluid , and not solid   136 , 137 Helice Constellation 23   Helicon 1   Hesper 14   Hoedi Constellatio 30   Horatii & Curiatii 52   Horatius Cocles 53   Horizon 47 148 Horologes , Clocks , and Watches , how ancient 40   Hostifer , how interpreted 36   Hours , whether taken for the twelve Parts of the Day among the Ancients 40   Not used so among the Romans 'till 300 years post R. C. Ibidem   Derived from the Babylonians , and Egyptians Ibidem   Names of the Egyptian hours Ibidem   Chinese and Turkish Astronomers , their Division of the Natural Day Ibidem   Hyades Constellation 31   I.   Annot. Page Append. Page INvictus , a Title given to the Roman Emperour , and to Rome 68   Jupiter Tonans 10   The Planet 59 182 His Satellites   183 Julia Familia 38   Junius Brutus 54   K ,   Annot. Page Append. Page KIngdoms , their Vicissitudes 40 , 41   L.   Annot. Page Append. Page LAmpadias , a fiery Meteor so called 61   Laws of Augustus 2   Leo , Constellation 20   Lepus Constellation , vide Hare     Letters , by whom invented 6   Libra Constellation 21   Livius Salinator 56   Lucifer , or the Morning Star 14   Lycurgus 52   Lyra Constellation 26   M.   Annot. Page Append. Page MAgick 8   Marcellus 54   The Sword of Rome   214 Mars , the Planet 59 182 Medusae Caput , Constellation 29   Memnon 51   Mercury 3   Planet 59 , 62 180 Meridian 46   Metelli 57   Moon , her Chariot 14   When Eclipsed , believed by the Ancients to be drawn from her Sphere by Charms ; by the Indians supposed to be whipped till she bleed ; by the Chinese to be in danger of being devoured by a Dragon or great Dog. Brazen Vessels beaten in her Relief , practised by the Turks and Chinese Ibidem   Her Spots Old   169 Her Spots New   Selenography , according to Hevelius   170 according to Grimaldi , and Ricciolus   175 Whether inhabited   179 Conceived by some the Paradise of our first Parents   180 Mota Astra , misinterpreted by Salmasius 47   Mutius Scaevola 52   N.   Annot. Page Append. Page NAvigation , by whom invented 7,33   Nestor 51   Nilus , its several Denominations 4   O.   Annot. Page Append. Page OPhiuchus Constellation 26   Orion Constellation 31   Orpheus his Lyra , Constellation 26   P.   Annot. Page Append. Page PApyrii 54   Parallel Circles 45 148 , 149 Pegasus Constellation 28   Penthesilea 51   Perseus Constellation 28   Persidis Victor ; of whom meant 52   Phases , of the Moon 41   Phaenicians , their Voyages into the Atlantick Ocean 24   Their Discovery of the Western Coasts of Africa , and a large Island supposed some Part of America Ibidem   Piscis Notius 37   Pisces Constellation 22   Pithetes , a kind of Comet so named 61 193 Philippick Plains confounded with Pharsalian 66   The Battle of Philippi Ibidem   Planets 47   Their Particular Descriptions   165 & deinceps ▪ Plato 52   Pleiades Constellation 31   Pogonias , a kind of Comet 60 193 Pompeius Magnus 56   His Triumphs Ibidem   Princeps Aries , the reason of that Title 19   Principles Natural , first Chaos 11   Atomes 12 , 39   Fire 12   Water Ibidem   Elements Ibidem   Their Discordant Concord Ibidem   Procyon Constellation 33   Q.   Annot. Page Append. Page QUadriga , by whom invented 29   Quintilius Varus , his Defeat 65 , 66   R.   Annot. Page Append. Page RAin 10   Ram , the Constellation , vide Aries     S.   Annot. Page Append. Page SAgitta Constellation 27   Sagittarius , Zodiacal Sign 21   Sarpedon 51   Saturn 59 185 His various Phaenomena   186 His Satellites   Ibidem Scipio ' s , Fatal to Africa 56   Scorpius , Zodiacal Sign 21   Sea , held by Anaximander to be the Remainder of Primitive Moisture , after its Exclusion from the Earth 13   Supposed to round the Earth like a Girdle 17   Called by the Phaenicians Ogg Ibidem   Serpents , said to be burst by the Power of Incantations 8   Their faculty to dissolve the Charm , if aware of the Charmer Ibidem   Servile Bellum ; why so called ? 68   Sexta Hora , how called the first and last 46   Shadows , their Increase and Decrease whence ? 5 , 7   Sirius , or the Dog-star 32   Held to be another Sun 33   Sistra Isiaca , their Description 67   Sphere , how divided by the Ancients 43 , 44   Socrates 52   Solon Ibidem   Solstices 43   Sow , honoured by the Cretans as sacred 30   Snow , its Original Cause 9   Why compared to Wool Ibidem   By Anaxagoras maintained to be black . In Armenia of a ruddy colour Ibidem   Contexture and Figure of its Parts Sexangular Ibidem   Spirits evocated 8   Spiritus Diei , what ? 47   Spolia Opima 54   By whom won Ibidem   Stars , whence named 41   Their Prescience 1   Influence 24   Names 10   Aspects 11   Rising and setting 14   Motion 15   Nourishment 38   Fixed Stars , their Substance , Light , Colour , Scintillation , Number , Figure , Magnitude , Place , and Distance from the Earth , or rather the Sun   155 Stars falling 61   Stipulae Ardentes , fiery Meteors so called Ibidem   Sun , by Xenophanes supposed to be extinguished every Night , and rekindled every Morning 14   His several Denominations 59   His Maculae & Faculae   166 Substance   165 Magnitude and Distance   166 T.   Annot. Page Append. Page TAu Signum , sive Triangulum Australe   139 Taurus , Zodiacal Sign 19   Trabs , a Meteor and Comet so called 61   Traffick , its Original 7   Themistocles 52   Thunder 9   Triangulum , seu Deltoton 28   Tropicks of Cancer 43   Tropicks of Capricorn 44   Hieroglyphically deciphered by the Ancient Aegyptians under the Figure of two Dogs Ibidem   V.   Annot. Page Append. Page VAlerius Corvinus 53   His Story Ibidem   Venus 59 , 62 181 Vigiliae Constellation 39   Virgo , Zodiacal Sign 21   Ulisses 51   Universe , according to the Pythagoreans subsists by the Conjunction of two Natures , the one alwayes Active , the other alwayes Passive 18   W.   Annot. Page Append. Page WAter , the first Principle of all Natural Bodies according to Thales and Pherecydes 12   Weeping in Exequies 64   The dead supposed by the Ancients to be delighted with the Tears of their living Friends Ibidem   Whale , the Constellation 36   Wind , its Original reckoned among the Abscondita of Nature 10   Its Causes reduced to several Heads Ibidem   World , a Rational Creature according to the Stoicks 1   Eternal 11   Disproved to be such 41   Its Soul 1 , 18   Its Eyes 12   A Secondary God 38   The Fusion or Extent of the Divine Mind Ibidem   Above it nothing either of Body , Place , Vacuum or Time according to Aristotle 42   The Stoicks yet allowing a certain Vacuity or Imaginary Space , in which it is by them said to suspend Ibidem   Called Nature's Publick House Ibidem   Z.   Annot. Page Append. Page ZOdiack 18 , 47 , 48 147 Zones 45   ERRATA . PReface . Page 2. line 17. for have read hath . Annotations . Page 3. line ult . for Ptolomy r. Ptolemy ▪ and so else where . p. 4. l. 64. for X●…ophantus r. X●…ophantes . p. 5. l. 〈◊〉 for saying that this r. saying this . p. 10. l. 22. for 〈◊〉 r. 〈◊〉 . p. 12. l. 33. for Scyrus r. Syr●… . p. 21. l. 39. for Ta●…uncius r. Taruntiu●… . p. 28. l. 48. for was the Grandchild ●… . the Grandchild . p. 29. l. 61. for Mir●…ilus r. Myrtilus . ibidem l. 73. for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ibid. for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . p. 30. l. 60. for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ibid. l. 61. for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . ibid. l. 63. for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ibid. for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . p. 31. l. 34. for Co●…ymo r. Co●…ymo . ibid. l. 52. for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . p. 34. l. 53. for Chyron r. Chiron . ibid. for Phellyra r. Ph●…lyra . p. 35. l. 4. for Ba●…hilus r. Batilus . p. 39. for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . ibid. l. 54. for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . p. 41. l. 23. for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . p. 51. l. 3. for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Appendix . Page 9. lin●… 28. for Ars●…s r. Ars●… . p. 23. l. 2. for Oblectata r. Obluctata . p. 38. l. 10. L●…o Emperour of Constantinople is misplaced ▪ to be inserted before in p. 27. at No. 879. ( which ought rather to be 886. ) under the Title of L●…o Philosophus . p. 39. l. 29 , 33. for Arabick r. P●…rsian . p. 5●… . l. 26. for Civit●… 〈◊〉 r. Civita Castellana . p 56. l. 35. del●…atur in . p. 77. l. 7. del●…atur Iacobus Zales , &c. p , 93. l. 10. for White Be●… r. White Le●… . p. 104. l. 3. for Planet r. Plane . p. 116. l. 6. for already r. ready . p. 126. l. 12. for Mathews r. Mathers p. 139. l. 27. for by the Spaniards r. not that by the Spaniards , &c. p. 146. l. 28. for right Angles ●… . Oblique Angles . p. 158. l. 16. for which r. with . p. 193. l. 38. for no●… r. or . FINIS . Notes, typically marginal, from the original text Notes for div A51768-e640 * Cassiodor . Variar . l. 3. Epistol . 51. Sic factum est ut Naturae Mysteria Spectaculorum compositâ Imaginatione ●…uderentur . * Imp. Iustinianus Institut . l. ●… . Titul . 1. Notes for div A51768-e7130 a S●…lmasius ( in Diatrib . de Annis Climact . & de Antiqu. Astrolog . ) expounds divinas Artes according to the opinion of the Stoicks ; who held the Stars to be Deities , and thinks that Manilius gave to Astrology that Epithete in regard of the Divinity of its subject : We rather take it in the same sence as Divinatrices . So Horace uses the Word Imbrium Avis Divina Imminentûm : so Iuvenal . Satyr . 10. Exta & candiduli Divina Tomacula Porci . See Scaliger , and Barthius Adversar . lib. 25. c. 2. b So we have chosen ( for the better cadence of the Verse ) to render — conscia fati sydera — not assuming a greater liberty than the sence of the words will bear , in making conscia fati in this place ( according to the Tenet of Manilius ) to express as much as praesciae venturi . How far yet this foreknowledge of the Stars extends , is not agreed upon by the Antients . Some ( with Plotinus , in libro si faciunt Astra , as cited by Macrob. in somn . Scip. ) believe , that the Stars of themselves know nothing of Fate , but that men skill'd in the Art of Divination read it in the Book of the Stars , as in the Tables of the Gods ; as Birds are not conceived to be skill'd in Augury , though from their voice or flight , men knowing therein foretel future events : Others , that the Stars know all things , but not that they effect what they know or signifie . Some that the Stars carry about ( as included within them ) the Fate of all things , and what they know requisite to be done , produce into act . Which last Opinion , though by Seueca ( Epistol . 80. ) proposed as doubtful , is by Manilius ( in the heighth of Stoicism ) positively asserted : See Lips. Philosoph . Stoic . l. 2. c. 14. And Vossius l. 2. Idololatr . c. 49. The Proem . c So Ausonius , Omnia quae varìo rerum metimur in Actu Astrorum Dominatus agit ; terrenaque tantum Membra homini ; è superis Fortuna & Spiritus Auris . And ( before him ) Seneca : Ex syderum quinque levissimis motibus Fortunae Populorum dependent : & Maxima ac Minima proinde formantur , prout aequum iniquumve sydus incessit . Some went yet further , and assign'd peculiar Stars to the particular condition of Persons , as the large and bright to the Rich , the lesser to the Poor , the obscure to the feeble and decrepid : But this opinion is by Pliny exploded as a vulgar error , Sydera quae affixa dicimus mundo , non illa , ut existimat vulgus , singulis tributa sunt nobis : Clara divitibus , minora pauperibus , obscura defectis , & pro sorte eujusque lucentia ad munera mortalibus . Non tanta coelo Societas nobiscum est . Vid. Plin. l. 2. d The Stoicks held the World to be a rational Creature , and to consist of Heaven and Earth , as Soul and Body : The Heavens ( according to them ) being the same to the whole , as reason to man. Hence Arnobius ( l. 3. advers . Gent. ) In Philosophiae Memorabiles studio , atque ad istius nominis columen ( vobis laudatoribus ) elevati , universam ìstam molem Mundi , eujus omnibus amplexibus ambimur , regimur , ac sustinemur , Animans esse unum , Sapiens , Rationale , Consultum , probabili Asseveratione definiunt ; with whom consents Hilarius in Genes . Haec tamen Aethereoquae machina volvitur Axe , Non tantum pictura poli est , sed celsa voluntas , Mens Ratioque subest . — Upon which Verses Barthius ( l. 31. Adversar . c. 12. ) notes , that Mens & Ratio Coeli est Astrorum , ut vocant , Influentia , quae Genus gubernat humanum . Expressing the sence and meaning of our Author ; but how truly , the thing I leave to be considered . e Helicon●… Aoniae Baeotiaeque Mons Musis Sacer ( Vib. Sequester ) so call'd , according to Plutarch ( l. de Nominibus fluviorum & Montium ) from Helicon , the Brother of Cithaeron , of which see there the Fable . Or , as Casaubon ( in Pers. ) conjectures from the Hebrew word , Halike , i. e. Ambulatio , in regard the Antients used to have there their Walks , and to confer and discourse of natural and divine Matters : Where also as Athenaeus ( l. 14. Deipnosoph . ) from the Authority of Amphion Thespiensis reports , there was a Colledge instituted for all Musical Exercises , in which the Youth of those Times were accurately instructed . But Bochartus conceives the name derived from the Arabick , Halic , or Halica , which signifies a high Mountain , for such is it describ'd to be by Strabo l. 8. & l. 9. f Augustus Caesar : of whom Horace , Ames dici Pater atque Princeps . A Title first given to Iulius Caesar ( as his Coins attest ) for his singular Clemency . Yet Cicero enjoy'd it before either of them , though not in the same Extent and Latitude , yet as the Encomium of a good Patriot : hence Iuvenal Satyr . 8. — Roma Parentem Roma Patrem Patriae Ciceronem Libera dixit . The reason of this Imperial Title Seneca gives ( in de Clementia I o ) Patrem quidem appellavimus , ut sci ret sibi datam esse Potestatem , quae est Temperatissima subditis tanquam Liberis consulent , suaque post illas reponens . The Ceremony of Augustus his Instalment in this Titular Dignity , is thus describ'd by Suet mius . Valerius Messala was deputed by the Senate to present him with the Votes of the House , which he deliver'd in these Words , Quod foelix faustumque sit tibi domuique tuae , Auguste ! ( sic enim nos perpetuam Reipublicae foelicitatem , & laeta huic precari existimamus ) Senatus Te ( consentiens cum Populo Romano ) consalutat Patriae Patrem . To whom Augustus with tears in his eyes thus answer'd : Compos factus votorum meorum ( Patres Conscripti ) quid habeo aliud Deos immortales precari quàm ut hunc consensum v●…strum , ad ultimum vitae finem mihi perferre liceat ? g The Original hath Augustas Leges , which Epithete our Author doubtless made use of in Allusion to the Title of Augustus given by the Senate at the instance of Munacius Plancus to Octavianus Caesar : who after his settlement in the Empire according to Eusebius in Chronie . ( as rendred by Saint Ierom ) Romanis plurimas leges statuit . To which Ovid likewise alludes ( Metam . 15 ) Pace datâ terris , Animum ad Civilia vertet Iura suum ; Legesque feret Iustissimus Auctor . These Laws in honour of Iulius Caesar , were by Augustus call'd Iuliae , either as being first enacted by Iulius Caesar , or as reviv'd and put into execution by Augustus , according to the Advice and direction of his Uncle , left in his Memorials , or Commentaries behind him , as he perswaded the People to believe ; which see enumerated by Donatus in Tacitum . p. 144. and Polletus de foro Romano . l. 4. and more particularly by R●…smus in Antiqu. Rom. l. 8. h Our Author here seems to make a difference between the Divinity of Augustus , and that of Iulius Caesar , attributing to the Nephew Heaven as his due and Merit ; to the Uncle , as the Grace and Concession only of the Gods. Plin. l. 7. c. 45. speaking of Augustus , says ; Ille Deus , Coelumque nescio adeptus magis an meritus . Of the other , Vitruvius in Praefat. Iulius Caesar Consilio Coelestium in Sedibus Immortalitatis dedicatus est . i Propter numen Caesaris jam receptum ; vel Augusti jam recipiendum , says Barthius Adversar . l. 1. c. 8. Or rather in regard of the great Discoveries made by the Extent and Progress of the Roman Conquests in Climates and Regions formerly unknown , by which means ( to use Valerius Flaccus his Expression , Argon . 1. ) — Tantum terrae , tantum cognoscere coeli Permissum est . — k That is from West to East , contrary to the Motion of the Primum Mobile ; which Motion of the Planets in the time of Democritus was not known among the Greeks ; Eudoxus being the first that discovered it to his Countrymen , as Seneca observes Natural . Quaest. l. 7. c. 3. ) having deriv'd that knowledge from the Aegyptians , to whom he travel'd in the Company of Chrysippus the Physician and others , supported by the Bounty of his Friends , and recommended by Agesilaus his Letters to Nectabis the King , and by him to the Priests , as Diogenes Laertius in his life , l. 8. Yet Lucian ( de Astrolog . ) assigns the first Observation thereof to Atreus , King of the Argives , confirm'd by Achilles Tatius ( in Arati Phaenomen . ) who saies , that Atreus ( 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ) found out the opposite motion of the Planets . So that Gassendus ( Tom. 1. l. 3. p. 591. ) conceives the more universal and exact Theory of that Motion , rather than the Original or Primary Invention thereof , is to be ascribed to Eudoxus . l Not unlike to that of Virgil ( in Culicis Prooemio : ) Phoebus erit nostri Princeps & Carminis Author , Et recinente Lyra fautor — The Poets usually applying that Musical Instrument to their Songs ; quod dum mens foeta parturit , ipsa ferat opem . And therefore a late triple Crowned Poet ( Urban 8. in his Ode upon St. Lewis ) calls the Lyra , Sonoram Cantûs Obstetricem , as is noted by Paganinus Gaudentius in Additament . Crit. c. 9. And for this reason Manilius here brings in Phaebus with his Lyra to bear a part with him in confort . m Justly does Scaliger condemn Lilius Giraldus for supposing our Author in this place to profess himself to have been twice Lawreat : who means no more by these double Sacrifices than the Invocation of double Assistance , being to treat of the gravest subject in the most pleasing style ; and therefore he erects two Altars to the two Patrons of Astronomy and Poetry . The Original and Progress of Astronomy . n Mercury ; so called ( according to Festus ) Quòd omnem rem sermone sine manibus conficiat , quibus Partibus Corporis qui car●…nt 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 vocantur . And therefore the Hermetical Statues were made of a square Trunk , or Stone only . Others ( saith Festus ) will have him so called ( not à Cyllenia via , as it is commonly read ; but as Mr. V●…ssius in Melam . corrects the Text ) à Cyllene Avia , from his Grand-Mother Cyllene , by whom he was educated . Others will have him to be so called from the Mountain Cyllenius in Arcadia , where he was bred . That he first taught the Aegyptians Astrónomy , and indeed all other Arts and Sciences , is the generally received Opinion ; which ( besides Iámblichus ) is asserted by Plato in Phaedro , ( where he is styled 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ) and by Cicero , Lib. 3. Divinat . Vide etiam Lactantium lib. 1. c. 6. But as to the first Authors of Astronomy , see more in the History of its Original and Progress in the Appendix . o Lucian ( de Astrolog . ) makes Astrology to be 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , The study of Antient Kings belov'd of the Gods : The Poet here particularly respects the Babylonian and Aegyptian Princes . p One of the most celebrated Rivers of the East , arising in Armenia Major , and watering on the left hand Mesopot●…mia , on the right hand Syria , Arabia , and Babylonia ( now Caldar . ) It was heretofore according to Plutarch ( de Nominfluv . & montium ) call'd Medus , and before that Zarandus , of which see there the Reasons . It s Modern Name answering to its Antient Apherat , or Phraat , which owes its Original ( as some conceive ) to the Arabick , in which Language Pharatta signifies inundare , whence Iphraton Inundatio ( this River overflowing in the same manner as Nilus ) or rather from the Hebrew Huperath , signifying frugifer , crescens , or fructificans : It was antiently divided into five Principal streams . The first whereof passing by Seleucia falls into Tygris . The other four loosing themselves in so many great Lak●…s . The first of these four Branches , and most Easterly , was call'd Tsartsar : The second , Naar-Malcha , ( by Pliny corruptly Armalchar ) i. e. Regium flumen ; by the Arabs in the same sence Al Melic , in memory of some of the Babylonian Princes , who caused that Cut to be made ; and Chobar from the Name of the Praefect or Overseer of the Work , as observed by Scaliger , l. 5. de Emendatione Temporum . The third passing by Babylon , was that , which was properly called Euphrates ; as believed to be the Native Channel of the River , and not made by Art as the others ; call'd likewise Sur , from the City Sura , or Sora , seated upon its Banks . The fourth and most Westerly was ( according to Pliny ) called Narragam , by Ptolomy Baarsarem , or Maarsarem , and by some others 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which Bochartus ( in Phaleg . lib. 1 c. 8. ) rather reads 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which nearlier answers to Plinie's Narragam , or Naar-Agam , i. e. fluvius stagni . By the Greeks antiently this great River was otherwise nam'd , being call'd from its Source to the Mountain Taurus , Pixyrates ; where it breaks into the Mountain Taurus , Omyra ; after its emersion from thence , Euphrates , as Pliny lib. 5. c. 24. See likewise Ptolomy lib. 5. Strabo lib. 11. & alibi . And Salmasius at large in Plin. Exercitat . Tom. 1. pag. 625. & sequent . q The Learned Mr. Vossius ( de aetate mundi & in Melam ) conceives our Poet in this place to follow the Opinion of the Antients , who before the discovery of the Indian Ocean , were so ignorant as to believe , that Nilus derived its source from the utmost East , even from India it self . With which Error ( besides divers others of the Antients ) Virgil seems to comply ( Georg. 3. ) Quaque Pharetratae Vicinia Persidis u●…get , Et ●…iridem Aegyptum nigra foecundat Arena ; Et diversa Ruens septem discurrit in Ora Usque coloratis Annis devexus ab Indis . On Quiver-bearing Persia's Hem he strains , With black Sands marling Aegypts verdant Plains : In seven Streams forcing his divided Course , And from the Sun-tann'd Indians draws his Source . But our Poet does no more than concisely mark and point out the Babylonian and Aegyptian Territories , Per flumina Urbes eorum alluentia ac foecund●…tia , as Barthius notes , l. 1. Adversar . c. 9. The several Names given by the Antients to this River are collected by the Learned Maussacus ( in Plutarch . de Fluv . & Mont. nominibus . ) It was first of all called Oceanus , or ( but as he saies barbarè ) Oceames : Then Ae●…os seu Aquila , and Melas from its Profundity or depth , because all deep Waters seem black , or from Melas , the Son of Neptune : Afterwards Aegyptus , either from Aegyptus , the Son of Belus , or of Vulcan and Leucippes , who threw himself into it ; or 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , à Capras pinguefaciendo . From whence likewise the whole Country of Aegypt seems to be so nam'd . The Hebrews call it Gebon , and Schior , the latter signifying nigrum seu turbidum ; whence happily is derived the Aethiopian Name , Siris : It was called also 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , sive Nùs & Trito ; and lastly Nilus , from the Husband of Garmathones , an Aegyptian Queen so named ; or from Nilus the Son of Cyclops , or Nileus , or Nilasius , Aegyptian Princes ; or rather 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. à novum limum aut foecem ferendo . By the Latines it was peculiarly call'd Melo , as is evident from the Testimonies of Ennius , Festus , Servius and Ausonius . Of the Original of Nilus , and Cause of its Inundation , in former Ages so unknown ; See Kircherus in Mund. Subterran . and Mr. Vossius in his particular Tract of that subject . r Taken from Hesiod 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . — 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 — — Super Nigrorum Hominum Populum , Urbemque Vertitur — Meaning the Aethiopians ; particularly those seated beyond the Eastern Bank of Nilus . s Aegyptian Priests , from whom Astronomy received its first Rise and Increase in that Nation : Instructed therein by Hermes Trismegistus , whom the Arabs called Adris ; the Aegyptians , Theut , or Thoth . These Priests in their Supplications and Vows , as Kircher ( in his Oedip. Aegypt . Tom 3. ) tells us , Primo ante omnia Sapientiam & Mentis petebant illuminationem : Quam adepti , ab omni fatorum Necessitate se absolvi & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 effici putabant , perpetuo Numinum Consortio beatos . Which gives some light to the following Verses . t Not unlike to this , Statius de Vindic. Hercul . Sylv. 4. — Deus ille Deus , seseque videndum Indu'sit Lysippe Tibi — And Quintilian Declamat . 10. Quales Humanis se offerunt Oculis Propitii Dii , quale laetissimum numen est , cum se patitur videri . u Cicero Lib. 1. de Divinat : ascribes this to the Assyriant . The Assyrians ( Ut ab ultimis Auctoritatem repetam , says he ) by reason of the plainness and large Extent of their Country , affording on all sides a clear and open view of Heaven , observed the Course and Motion of the Stars . Which having duly calculated , they from thence made Predictions of future Events . Amongst whom the Chaldeans ( Non ex Artis sed ex Gentis vocabulo Nominati ) arriv'd to that perfection of skill , as to be able to foretel what should happen to any one , and under what Fate they were born . Which Art the Aegyptians acquired from them many Ages since . Thus Cicero . Vitruvius ( Lib. 9. c. 7. ) more particularly ; Among the Chaldeans ( says he ) Berosus was the first , who taught the Greeks judiciary Astrology : After him Antipater and Achinapolus were reputed famous Gencthliologists . Of Natural Causes and Effects , Thales Milesius , Anaxagoras Clazomenius , Pythagoras Samius , Xenophantus Colophonius , and Democritus are reckoned the most eminent Observers : following whose Inventions , and observing the Rise and setting of the Stars , and the Seasons of the Year , Eudoxus , Eudaemon , Callisthus , Melo , Philippus , ( and not as Salmasius will have the Text to be read , Phainus ) Hipparchus , Aratus , and others left to Posterity their Astrological Prognosticks , in their Tables or Parapegmata . Of which see Geminus , and Theon in Arati Phaenomena . x Omnis enim nostrae paulatim industria vitae Fluxit ab exemplis — Claudian de Hystrice . But by Example here our Authour means the Observations and Prognosticks , which Posterity received from the Tables or Parapegmata of the Antients . y Ingeniously imitated by Statius ( Theb. 4. speaking of the Primitive Arcadians . ) Hi Lucis stupuisse vices , Noctisque feruntur Nubila , & occiduum , longe Titana secuti Desperasse Diem — And by D●…acontius ( in Hexaemer . ) Nec Lucem remeareputat terrena Propago . Ast ubi purpureum surgentem ex aequore cernunt Luciferum , vibrare Iubar , flammasque ciere Et reducem super Astra Diem de sole rubentem . Mox revocata fovent hesterna in gaudia Mentes , Temporis & requiem noscentes Luce diurna Coeperunt sperare Diem , ridere Tenebras . The learned Mr. Selden de Diis Syris , Syntagm . 2. ( citing for Testimony this Place of Manilius ) conceives the Original of Adonis Festivals with the Antients to have sprung from no other ground . Non aliud cogitarunt , ( says he ) qui primum bas Naenias instituerunt , quam Solis Accessum & Recessum . Quem ut amissum nunc Lugebant , & renatum Laetis excipiebant Austiciis . Ita Rudiores olim , & qui simpliciorem vitam degebant , priusquam ab Astronomis Leges siderum didicerant . z The Demonstration of this depends upon Gnomonick Principles : One is , That the lower the Sun is , the longer shadow it makes upon an Horizontal Plain ; the higher and more elevated , the shorter . Hence when the Sun approaches near the Horizon , the shadows of things become greater , according to that of Virgil ( Eclog. 1. ) Majoresque cadunt altis de Montibus umbrae . But the farther he is mounted above the Horizon till he comes to his Meridian Altitude , the shadows are less . Ovid. Metamorph . 3. Iamque Dies Medius rerum contraxerat umbras . So likewise when the Sun is in the Tropick of Cancer , and in its greatest Northern Elevation ; we are then ( to use the expression of Achilles Tatius in Arat. ) Brachyscii , and cast the shortest shadows . But when it is in the opposite Tropick , and consequently in its greatest Depression as to us , we are Macroscii , and cast the longest shadows . See , as to this subject , more particularly Iunctinus in Sacrobosc . c. 3. and Aldus Manutius in Praefat , ad scriptores Rei Rusticae . To which may be added Beda his Poemation de Compositione Horologii . a Arts are distinguished into Illiberal or Manual , and Liberal or Ingenuous . And though of the first , the number be almost numberless , yet both kinds vulgarly ( though very imperfectly ) are reduc'd to a Septenary Division , and exprest in this Distich : Lingua , Tropus , Ratio , Numerus , Tonus , Angulus , Astra . Rus , Nemus , Arma , Faber , Vulnera , Lana , Rates . The first Verse expressing Grammar , Rhetorick , Logick , Arithmetick , Musick , Geometry and Astronomy . The second Agriculture , Hunting , Arts Military and Fabrile , Chirurgery , Spinning and Weaving , and Arts Nautical . Of whose first Inventors see Pliny , l. 7. c. 56. Polydor Virgil , Garzoni his Piazza universale , and Vessius de Sect. Philosoph . As to the different esteem and practice of these Arts among the Greeks and Romans , see Aldus Manutius in Quaesit . per Epistol . lib. 2. c. 9. b The first that found out Gold is said to be Cadmus the Phoenician ; or , as others , Thoas , in the Mountain Pangaeus ; or according to the Chronicon Alexandrinum , Mercury the Son of Iupiter or Picus King of Italy , who quitting his own Countrey , travell'd into Aegypt , and was there elected King after Misraim the Grand-child of Cham , for this Invention called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Deus Aureus . Aeschylus attributes the Invention both of that and all other Metals to Prometheus . There are others who write that Aeaclis ( Hyginus calls him Caeacus the Son of Iupiter ) or Sol the Son of Oceanus was the first Inventor of Gold in Panchaia , see Pliny , l. 7. c. 56. and Polydor Virgil. l. 2. de rer . Inventor . c. 9. c Our Poet here alludes to the Detection and Conquest of Great-Britain by Iulius Caesar , which the Romans then called a New World , from their recent discovery thereof . However it was long before known to others of the Antients , as is manifest by the Testimony of Pytheas , mentioned by Strabo , who in the time of Ptolom . Philadelph . wrote 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Touching which see Casaubon ( in Strabon . l. 1. & 2. ) Vossius de Histor. Graec. l. 4. c. 11. and Paganinus Gaudentius delli Peregrinatione Philosophica . And that it was some Ages before Caesar's time known to the Phoe●…icians , the learned Bochartus in his Geogr. Sacr. Tom. 2. l. 1. c. 29. evinces , who blames our Camden for saying , that this Island of Ours non nisi serò fuisse cognitam , was not known till of late . d To this purpose appositely Seneca in Medea . Audex nimi●…m qui freta primus , Rate tam f●…gili perfida rupit : Terrasque suas post Terga videns , Animam levibus eredidit Austris , &c. Candida nostri saecula patres Videre , procul fra●…de rem●…á , Sua quisque piger Litora tange●…s , Patrioque Senex factus in A●…vo , Parvo dives ; nisi quas ●…ulerat Natale solum , non nôrat Opes . Rash man was he with Ships frail Beak Did first the treacherous Billows break : And leaving the safe Shoar behind , Durst trust his life to trustless wind , &c. The candid Age of Innocence Our Fathers saw ; free from all sense Of fraud : then in secured rest Each man on his own ground liv'd blest With length of days , with little rich ; Nor of more wealth , than that with which His Native Soyl was stor'd , could tell . With which last likewise Ovid concludes , lib. Metamorph. 1. Nullaque mortales praeter sua litora nôrant . To Mortals in those days were known No other Shoares , besides their own . e Theocritus , Idyll . 21. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Want , Diophantus , is Arts only Spur , The Rise and Rule of labour is from her , For Care keeps watch in every poor mans eyes ▪ Hence Arnobius lib. 2. Supellectiles necessariae quas familiaris usus exposcit , non sunt ista scientiae munera , sed pauperrimae necessitatis Inventa . And hitherto not impertinently may be applyed , what I find recorded of the Temple of Hercules at Gades by Philostratus in vita Apollonii , ( as cited by Photius ; ) wherein among other Altars there was one Dedicated to Penury and Art ; Intimating , that as Penury stirr'd up A●…t , so A●…t drove away Penury ; as Hercules put to flight and subdued Monsters , the Incitements of his Val ur . Vide Riccard . Brixian . See likewise Casaubon explicating this Verse of Perseus in Prologo : Magister Artis Ingeniique largitor Venter . f Consonant to this place is that of Columella , l. 10. Ipsa novas Artes varia Experientia rerum Et labor ostendit Miseris , usus que Magister Tradidit . — g As all our Actions , saies Scaliger ( l. 1. Poetices , c. 1. ) so Speech is to be considered under three kinds . First , that of Necessary ; Secondly , of Useful ; Thirdly , of Delightful . The first kind was that which serv'd as a means of necessary Intercourse between Man and Man , to make themselves barely understood . Such may be imagined that manner of Speech , which we find in Lactant. ( de vero cultu ) that Mankind according to the Opinion of some of the Antients us'd ; for they believed at first that men exprest their meanings by signs and nods . Afterwards ( as he saies , and before him Diodor. Sicul. Bib●… . l. 1. and Horace l. 1. Satyr . 3. ) They made Essays of Language by imposing distinct nominal Notes upon several things , and so by degrees perfected a kind of Speech . The second sort ( saies Scaliger ) was something more refin'd by apting it for use and commodiousness , and applying as it were certain Dimensions , Prescriptions and Lineaments to the rude and inchoated Body , whence proceeded a certain Law and Rule of Speaking . The third sort was yet more polite ; and had added to it the Ornament of Elegancy , as it were its Dress and Apparrel . Now among these Laws of Language , not in the last place is to be reckon'd the Invention of Letters , which , as Cicero ( in 1. Tuscul. ) Sonos vocis , qui infiniti videbantur , p●…cis literarum notis terminavit . This Suidas calls 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and attributes the Invention thereof to Prometheus . But as to the first Characterizers of Speech ( besides the learned Digression of Ioseph Scaliger de liter . antiqu . in Euseb. and Petit. in observ ●… . l. 2. c. 1. ) take these antient Anonymous Verses , as they are recorded by Crinitus and Giraldu●… , and ●…rom them transcrib'd by Gerard. Ioh. Vossius , l. 1. de Arte Grammat . Primus Moyses Hebraieas exaravit literas . Mente Phoenices sagaci condiderunt A●…ticas . Qu●…s Latini scriptitamus , edidit Nicostrat●… . Abraham Syras & idem reperit Chaldai●…as . Isis Arte non minore protulit Aegyptias . Gulfilas prompsit Getarum quas videmus Literas . But with more likelihood is their Original by others referr'd to Adam himself ; It being conceiv'd very Improbable that he , who was to convey all Learning and knowledge to his Posterity , should want those necessary Organs for such a Work : for which Opinion makes the early mention of Letters , even in Seth's time , who was his Son , and doubtless receiv'd them from him . To which purpose there is extant in the Vatican Library at Rome , an Antient Picture of Adam with an Hebrew Inscription over his Head , and under his Feet , this Latine one ; ADAM DIVINITUS EDOCTUS , PRIMUS SCIENTIARUM ET LITERARUM INVENTOR . Vide Lomeier . de Biblioth . p. 10. h Of all Arts , Agriculture , by the Confession and Testimony of Varro ( l. 3. de R. R. ) is the most antient . This among the Ae●…yptians was first said to be found out by Osyris or Maneros . In Greece by Ceres , so called , quasi geres , à gerendis frugibús , ( as Cicero , ) or rather ( as Vossius conceives ) from the Hebrew word Geres , which signifies a Green Spike of Corn. In Italy by Saturn , the Son of Coelus and Iellus . By whom the said Vossius ( l. de Philosoph . c. 6. ) not improbably supposes Adam to be meant : for who besides him was the Son of Heaven and Earth ? The name Saturn seeming likewise to be deriv'd from the Hebrew word Satar , which signifies to lie hid , and is applicable to Adam for his flight and absconding himself after his Fall. Iosephus yet attributes it to Cain , ( l. 1. Antiqu. c. 3. ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , &c. Pastorit●…am vitam Abel , Agricul●…sram verò primus excogitavit Cain . Manuring of Ground by Stercoration is by Pliny , l. 17. c. 9. ascribed to King 〈◊〉 , who is said first to have instructed the Greeks therein , as Hercules the Italians , who for that reason likewise immortal●…z'd their King Stercutius , the Son of Faunus , but rather the same with Evander , the Arcadian , who first brought the Worship of Faunus , ( which is Pan , or universal Nature ) into Italy , and taught the Latines the Art of Manuring Ground , for which he was honoured as a God by the name of Stercutius ; by Tertullian . in Apologet. call'd Sterculus or Sterculius ; by Servi●…s in 8 Ae●…eid . Sterquilinius , whom he will have to be Pitumnus , Brother of Pilumnus ; by Macrobius called Sterculus ; 〈◊〉 he makes to be one of the Attributes of Saturn : Saturnum Romanietiam Stercutum vocant , quòd primus Stercore foecundit●… Agris c●…mparaverit . Vide Macrob. Saturnal . l. 1. c. 7. i The Original hath — in caecum penetravit Navita Pontum . By caecum understanding obscurum quid , incertum , vel 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , the Sea being yet undiscover'd , impervious and unknown ; Lucretius , Improba Navigii ratio tum caeca manebat , ( i. e. ) Ignota , as Lambin upon the Place . So likewise Virgil , Georg. 2. more expresly to the sence of our Authour . Sollicitant alii remis freta caeca — And Propert. l. 2. Eleg. 27. Et Maris & terrae caeca perîcla viae . Upon which words caeca Pericla , Passeratius notes , caecum non tantùm quod non vide●… , sed etiam quicquid non videtur ; in which respect the Ocean may be term'd caecus , its Bounds being stretch'd beyond Ken , and its many dangers undiscoverable . Of the Original of Navigation , and the first Essaies thereof , Claudian elegantly in Praefat. Rapt . Proserp . Inventá secuit primus qui Nave profundum Et rudibus remis sollicitavit Aquas , Tranquillis primùm trepidus se credidit undis ; Litora securo tramite summa legens . Mox longos tentare Sinus , & linquere Terras ; Et le●…i coepit pandere vela Noto . Ast ubi paulatim praeceps Audacia cre●…it , Cordaque languentem dedidicêre metum , Iam vagus erupit Palago , Coelumque secutus ; Aegeas Hyemes Ioniumque domat . He who in new built Ship first Plow'd the Main , And with rude Oars furrow'd the Watry Plain , Fearful at first the Seas calm Billows try'd , Securely steering by the Shoares known side . Straight leaving Land , through wide stretch'd Bays , he sails , Spreading his Canvas unto Gentle Gales . At length by often daring , bolder grown , His heart by past Fears taught Fear to disown , He takes the deep ; Heaven his sole Guide ; and braves Aegean storms , and the Ionian Waves . The Nations who are fam'd for this Invention , are , first , the Phoenicians , from whence it came to the Aegyptians , from them to the Greeks , and among them in the first place to the Cretans or Candiotts . But more particularly as to the first building and use of Ships ( not to instance in that of Noah's Ark ) Clemens Alexandrinus ascribes it to Atlas the Lybian ; Aeschylus to Prometheus ; Diodorus Siculus to Neptune . The Invention likewise of Sails Aeschylus ascribes to Prometheus ; Diodorus to Aeoius ; Pliny and Pausanias to Daedalus and his Son Icarus ; Cassiodorus ( l. 5. Variar . ) and Hyginus to Isis ; who for that reason on the Reverse of some of the Roman Coins , is figured holding in her hands a Sail swelling with the Wind , and by the Latines she was term'd Isis Pelagia , as President of Navigation , as may appear by this Inscription in Gruterus , pag. 312. DIIS MANIBUS SAC . SER. SULPICIO AUG . L : ALCIMO AEDITUO AD ISIDEM PELAGIAM . k To this effect our Country-man Ioseph of Excester ( not unpoetically , ) — Sine remigis usu , Non nôsset Memphis Romam ; non Indus Iberum , Non Scytha Cecropidem , non nostra Britannia Gallum . — Without the Seaman's pain , Memphis had ne'r known Rome ; nor ▪ India Sp●…in ; Greece Scythia , nor our Britain France . The Original of Traffick is generally ascribed to the Phoenicians ; some particularly attribute it to Mercury , as Ph●…rnutus , ( o●… Cornutus ) de naturâ deorum , and Caesar , l. 6. de Bello Gallico ; for which reason by Arnobius ( l. 3. ) he is stil'd Nundinarum , Mercium , Commerciorumque Mutator . To whom Merchants us'd to sacrifice , as to the God of Gain , and President of Negotiation and Commerce : confirm'd by Ovid , l. 5. Fast. Te quicunque suas profitent●…r vendere Mer●…es , Thure dato , tribuas ut sibi l●…cra , rogant . To this purpose likewise makes that antient Inscription , found at Metz , Anno 1589. Recorded by Philip. Thomasinus 〈◊〉 Donariis , p. 17●… ▪ MERCURIO NEGOTIATORI SACRUM NUMISIUS ALBINUS EX VOTO . l That Birds and brute Beasts have a Language , seems to be maintain'd by Sextus Empiricus ( l. 1. Pyrh●…n . 〈◊〉 . ) with whom complies Lactan. de I●…a Dei , ●… . 7. ) where he saies , No●…is quidem v●…ces eorum videntur ●…conditae , sicut i●…is f●…rtasse nostrae , s●…d ipsis , qui se in●…elligunt , verba sunt . That Magicians understood them , was believ'd by credulous Antiquity : Hence that Fable of Apollonius Ty●…naeus expounding the Notes of Swallows ( as Porphyr . ) or the Chirpings of Sparrows ▪ ( as Philostratus ▪ ) for which s●…ill likewise Tyr●…s is fam'd . And Mopsus in Apollon . Rhod. l. 3. is said to expound the Language of Crows and D●…ws . And that Me●…mpus was taught the Interpretation of the Tongues of Birds , by a Serpent licking his ears , we find ( yet as fabulous ) related by Pliny , l. 10. c. 49. And for such reports he , what Democritus delivers ; That out of the Blood of certain Birds mixing together and corrupting , a Serpent is produc'd , which whoever ●…ates , Intellec●…us sit Alitum Colloquia . Not to instance that Salomon ( according to some Rabinical Tales ) was skill'd therein , and by a certain Bird is said to have sent a Message to the Queen of Aethiopia ( who must therefore be believ'd to be as knowing in this Birdish Language : ) Or that in the Alcoran he is made to say , O Homines intelligite Avium 〈◊〉 ! And that a Lapwing , or a Bird called a Houp , brought to him the first News of the Queen of Sheb●… . Of which in Prolegom . in Bibl. Polygl●…t . But Delrius denies that Birds or Beasts can use Discourse , as wanting Reason ; yet confesses they have certain Indications of their affections and appetites , which men by long Observation may come to be acquainted with ; and that they are perfectly known to the Devil , and that he may instruct Magicians therein . Which whether he ever did ( saies he ) I know not , Non est incredibile fecisse . Vid. illum disquis . Mag. l. 2. c. 19. m Divination from the Inspection of the Entrails of sacrificed Beasts , Pliny ascribes to the Delphians , Cicero ( de divin . ) to one Tage●… , who appearing suddainly out of the Ground to the H●…trurians as they were plowing , is said to have instructed them therein . 〈◊〉 yet re●…ers the Invention thereof to Prometheus . The Divination was made from the Site , Colour , and Marks of the Entrails . The Parts inspected were the Heart , Lungs , Liver and Gall. That of the Heart , not practic'd by the Romans , until the 123 Olympiad . That of the Liver , most antient and usual . The Parts of this Inspected , were the Fi●…rae , Fissum , and Caput . Of which see particularly Brissonius de formulis , l. 1. Yet this kind of Divination seems by the Romans themselves in the time of their Greatness to have been despis'd , as may appear by Tacitus , and Quintus Curtius ; The later of whom condemns Alexander the Great , for being addicted to those Superstitions , which he terms , Humanarum Mentium Ludibri●… , &c. n The Charming of Serpents even from the Testimony of Scripture it self ( Psalm 58. ver . 5. Ierem. 8. ver . 17. Eccles. 10. ●…er . 11. ) appears to have been frequent with the Antients : To which we may add the farther Testimony of Virgil. ( Eclog. 8. ) Frigidus in Pratis cantando rumpitur Anguis . And Ovid , ( l. Metam . 7. ) in whom Mede●… boasts of her self , Vipereas rumpo & verbis & carmine fauce●… . As likewise Nemesianus , ( Eclog. 4. ) Cantavit quod Luna timet , quo rumpitur anguis . See Pliny , ( l. 8. c. 16. and l. 28. c. 2. ) where treating of the power of Enchantments , he writes , Figlinarum opera multi credunt rumpi tali m●…do . N●…n pauci etiam Serpentes . Upon which place Turnebus notes , That Serpents , if aware of the Charmer , have the faculty recanere , i. e. retorquere & dissolvere Incantationem , to dissolve the Charme . Pliny ( loco citato ) asserting hunc unum esse illis intellectum . The people most notorious for these kind of Incantations , were the Psylli , a people of Africa , and the Marsi , a People of Italy , of which later thus Lucilius in Satyr . Iam disrumpetur medius , jam ut Marsus Colubras Disrumpit cantu , venas cum extenderit omnes . Horace likewise in Ca●…id . Caputque Marsae dissilire Naenia . And Ovid de Medicamine faci●…i . Et mediae Marsis findantur cantibus Angues . The Aegyptians were likewise of old famous for the charming of Serpents , as at this Day the Indians , Negros , and those of Peru ; Vide B●…art . in Praefat. ad Hieroz . o In this many of the Antients vainly gloried . So Empedocles in Laertius ( l. 8. ) boasts he could teach the Art by which , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Extinctumque Hominem nigra revocabis ab Orco . So Canidia in Horace , ( Epod. ult . ) Possum crematos excitare mortuos . And Tibullus of a certain Witch , Haec cantu finditque solum , Manesque Sepulchri●… Elicit . — So the Nurse in Seneca his Hercul . Oct. — Mea jussi prece M●…nes loquuntur . And Alecto in Claudian . in Ruffin . — Condita funera traxi . Carminibus victura meir . See Delrius Disquis . Magic . l. 8. quaest . 26. and particularly Leo Allatius refuting this Diabolical Vanity in his Learned Syntagma de Engastrimytho . p So , in Seneca , Medea boasts she had Heavens Laws invert●…d , shown the World the Light Of Sun and Stars , at once . — Mundus Lege confusa Aetheris Et Solem & Astra vidit . — But this is more than M●…gick can perform ; Divine Providence not permitting the Divel or his Agents to interrupt or disturb the Course and Motion of the Heavens or Stars , or confound the Order of the Universe , however by Poetical Licence 't is allowed . Hence the Tragoedian Seneca in Hercule furente , Nox media Solem vidit & Noctem Dies . And Petronius — Trepidusque furentes Fl●…ctere Phoe●…us Equos revoluto cogitur Orbe : Tantum dicta valent . — So likewise A●…eius ( l. 2. de Au●… . Asin. ) speaking of a certain Witch , Omnem istam Lucem Mundi siderali●… imis Tartari & in V●…tustum Cha●…s submergere no●…it . q Anaximander and Metrodorus supposed Thunder to be a Wind conceiv'd and inclos'd within a thick Cloud , which breaking forth with violence makes a crack : the Lightning being caused by the breaking of the Cloud ; as is illustrated by Anaximenes his Comparison of the Sea , which being broken with Oares , sparkles and shines . Anaxagoras held it to be a portion of ardent matter quencht in a moist Cloud , which makes a noise , as red hot Iron dipt in water . The Stoicks believ'd it to be a Noise occasioned by the Collision of two hollow Clouds , Lightning proceeding from their attrition . Descartes ( not much differing from them ) conceives Thunder to be occasioned when divers ●…at Clouds ( Tabulatorum instar ) like so many Floores or Scaffolds ) are driven with violence the higher upon the lower , and clatter one upon another ; the Lightning proceeding from the Nature of the Exhalations included in the Interstiti●… or spaces between the Clouds , which by them falling one upon another , is violently crusht out . Our Countrey-man Mr. Hobbs will have it to be the breaking of a Cloud congeal'd to Ice , by the strugling of inclosed Air , which he borrowed from Lucretius , l. 6. Denique saepe geli multus fragor , atque Ruina Grandinis , in magnis sonitum dat nubibus ●…lte . But much more consonant to Truth is the Opinion of those , who hold Thunder to be an Exhalation hot and dry , of a Sulph●…reous and Nitrous matter contracted within a cold and moist Cloud , from which striving to get out , it kindles by Agitation , and violently breaks through its Prison . r Pliny , l. 17. c. 2. calls Snow the Foam of Coelestial Waters . Aristotle , and from him most Modern Philosophers , describe it to be begotten of a moist but rare and thin Cloud , which being condensed by a sharp cold falling down , parts ( that it may the easilier divide the Air ) into Flakes like Fleeces of Wool , to which the Psalmist alludes , Qui dat Nivem sicut Lanam ; Though Bodin ( in Theatro Naturae ) conceives the Psalmist resembles Snow to Wool , for the warmth it affords to Plants and Vegetables in the cold time of Winter , ( as Woollen Vestments do to men ) rather than for its Fleece-like Similitude . It s whiteness ( though Anaxagoras maintain'd it to be black , and in Armenia it is found of a ruddy colour , by reason the Terrestrial Particles or Atoms of that soil , which abounds in Minium , mixing with those of the Air , tinge it , and give it that hue , as Eustath . in Iliad . 2. ) is derived from its Efficient cause , Cold ; and the copious mixture of Aerial Spirits : Of the Admirable Contexture and Figure of its Parts , which are said to be always Sexangular ; See Kepler in his particular Tract upon that Subject . s Hail is nothing else but Rain congeal'd in its fall ; and this Concretion or Congelation happens not far from the Earth , as is Manifest by high Mountains ; on which Snow is often found , but never Hail . The nearer to the Earth it hath its fall , the more Triangular or Pyramidal is its Figure , the higher its fall , the rounder . Those Angles or Inequalities being worn away and rounded by the length of its passage through the Air. The cause of its congeal'd hardnes , is the Ant peristasis of the lower Region of the Air , which is the Reason likewise why it falls more frequently in Summer , than in Winter , and seldom in the Night , unless the Night be warm . Vide Fromond . Meteorolog . l. 5. c. 9. t Thales & Democritus ascribe the Cause of Earth-quakes , to Subterranean Waters breaking out and undermining the Bowels of the Earth . The Stoicks , to Moisture rarified into Air ; which seeking for room to break ●…orth , when it meets ( as Anaxagoras likewise held ) with the thick and tough Body of the Earth , by its strugling for vent it shakes it . Others conceive it proceeds from inclosed Air , or Spirits arising from combustible matter ( such as Sulphur , Nitre , Allom , Sal Armoniack , or Bitumen ) set on fire , and consequently rarified , causing the like effect , as Gunpowder in Mines . See Fromond . Meteorolog . l. 4. c. 1 , 2 , 3. and Kircher in his Mund. Subterran . l. 4. c. 2. The several kinds of Earth-quakes are thus reckon'd up by Apuleius , l. de Mundo ; The first is term'd Epiclintes seu Inclinator , that is , when it strikes at oblique Angles , turning things sideward . The second is called Brastes , or ●…ffervescens , from the similitude of boiling Water , bearing up all above it in a direct Line . The third is termed Chasmatias , whose Violence makes a Breach or Hiatus , in which the place forced , is swallowed up . The fourth is called Rhectes , from forcing its way by a Rupture , but not making such a Chasma , as the former . The fifth Ostes , which at once shakes and overturns . The sixth , Palmatias , which shakes but overturns not . The last , Mycematias , from the bellowing Noise it makes . Ammianus Marcellinus , l. 16. and Coelius Rhodiginus from him reckon but four kinds . u That there are Subterranean Fires , and those great and many , appears by the Vulcanian Islands ; by the Mountains Aetna , Vesuvius , Hecla , and others , ejecting Flames , and by hot Baths and Fountains breaking out of the Earth , which as Vitru●…īus ; l. 2. instances could not be , Si non in imo haberent aut de Sulphure , aut de Alumine , aut Bitumine ardentes Maximos Ignes . In which words he briefly declares their Causes . To which , as a further Proof , ( to omit divers others ) may be added Earth-quakes , deriving ( as but now alledged ) their Original from these Subterranean Fires , and therefore by our Authour not unproperly joyn'd together in this Verse . Who would be further satisfied touching this matter , may consult Pliny , l. 2. c. 106. Gassendus his Epicurean Animadversions ▪ and particularly Kircher in his Mund. Subterran . l. 4. where the Natures of these Fires , their Necessity , Diffusiveness , Fo●…d and Prodigious Effects are exactly described . See likewise I●…tigius expresly upon this Subject in his Tract de Montium Incend . and the Curious Disquisition of Alphonsus Borellus in Historia & Meteorologia Incendi●… 〈◊〉 , Anno 1669. x Rain is defin'd by Aristotle a Cloud converted into Water , and distilling in drops . Epicurus makes two ways or means of generating Rain ; One by Transmutation , when the parts of a Cloud , either by absence of Heat , or accession of Cold , are so transpos'd and varied , as render them more apt to flow and fall , as is exemplified by Vapo●… in a Limbeck , gathering together , and then falling in drops . The other by Compression ; when by wind or cold the Cloud is comprest , and the vaporous Corpuscula within the hollows thereof are crowded together , and by accession get weight and fall . Whence it appears that the drops of Rain are form'd by Coalition , rather than Division ; And that Rain is not ( as vulgarly conceiv'd ) a watry Mass effus'd from a Cloud , like water from a watring-Pot , ( or as ●…repsiades jestingly in Aristophanes , declar'd it to be caus'd when Iupiter , urin'd through a sive ) For if there were any such stagnation of Water in a Cloud , it would fall from thence like a Torrent or Spout , rather than in Drops . Of Rain there are reckon'd three kinds , S●…illicidium , Imber , and Nimbus . The first is a small Misty Rain . The second is more intense , and composed of greater Drops . The last is yet more violent , and falls more thick , and as Fromondus says , Decumanis Gu●…tis . Apuleius de Mundo sums up the Matter when he sa●…es , Tot Diversitatibus pluviae cadunt , quot modis Aer Nubium conditionibus cogitur . y The Original of Wind is reckoned among the Abscondita of Nature ; But I find it reduc'd chiefly to three Heads or Causes , Viz. the Earth , the Water , the Air. The first is maintain'd by Aristotle , who makes it a dry Earthy Exhalation . The second is maintain'd by Metrodorus , and partly by Anaximander , chiefly by Vitruvius , l. 1. c. 6. Where he says , Ventus est Aeris fluens unda , cum incerta motus redundantia : Nasciturque cum fervor offendit Humorem , & Impe●…us fervoris exprimit vim Spiritûs flantis . Which he illustrates by your Aeolipilae , or Wind-balls , so demonstrated likewise by Descartes , l. 4 Metear . c. 4. and asserted by Salmasius ( l. de Ann. Climacter . p. 811. ) in Vitruvius his own words . The third seems to be most antient , which makes Wind to be nothing else but Air moved . Apuleius de Mundo is of the same Opinion ; Nec enim aliud est ventus , nisi multum & vehemens in unum coacti Aeris flumen . But this not assigning the first Cause of that Motion , leaves the matter undetermin'd . The most probable Opinion is , that Wind is an Earthy or Watry Exhalation mixed with saline Spirits , and other Vapours , drawn or forc'd out of the Earth or Sea , by the power of the Sun or Subterranean Fires ; which being rarified by Heat , or condensed by Cold , and impelled for the most part by a transverse , sometimes by a direct Motion , ex●…gitates the Earth , Air , and Sea. But of this Subject , see particularly the Lord Verulam , in his Book de ventis , Descartes ( loc . cit . ) Gassend . Animadvers . in Epicur . Fromond ▪ Meteor . Kircherus in Mund. Subterran . and Mr. Isaac Vossius de Motu Marium & ventorum . z See Lucretius , l. 6. arguing to this effect , against the pretended and fabulous Power of Thundring Iupiter . But far better and with more Analogy to Truth , Seneca in Natural . Quaest. l. 2. Interim hoc dico , Fulmina non mi●…i à Iove ; sed sic omnia disposita , ut etiam ea , quae ab illo non ●…ant , sine ratione non fiunt , quae illius est . Vis eorum illius permissio est . Nam etsi Iupiter illa nunc non facit , fecit ut fierent : singulis non adest , sed signum & Vim & Causam dedit omnibus ; Thus far Seneca . In which there only wants the true Name of the first Divine Cause . Why Iupiter is said to be the Author of Thunder and Lightning , Pliny ( l. 2. c. 20. ) gives this Physical reason . That the Fires of the three uppermost Planets falling to the Earth , carry the name of Lightning , but that especially which is seated in the midst , that is to say , Jupiter ; because participating of the excessive Cold and Moisture from the upper Circle of Saturn , and the immoderate Heat of Mars that is next under , be by this means discharges the superfluity of either ; whereupon it is commonly said , that Jupiter darts Lightning , &c. Of the Superstitious Opinions of the Antients touching Thunder and Lightning , see Nardius in his 27. accurate Animadversion on the 6. Book of Lucretius de rerum Naturâ . a Of the several Mundane Systems , Antient and Modern , see the Appendix . b Who first reduced the Stars into Asterisms , or Constellations , is not easily to be found out : As hard a Task it is to reconcile the different Morphoses or Figures in the several Spheres of the Chaldaeans , Persians , Aegyptians , Greeks , Arabibians , Indians , Chineses and Tartars , whose various differences may appear partly by the Description of Abu Masher , commonly called , Albumazar , partly by Aben Ezra de Decanis Signorum , published by Scaliger in his Notes upon our Authour : Of all which Salmatius ( in Praefat. ad Diatrib . de Antiqu. Astrolog . ) conceives those of the Greeks ( most vulgarly used amongst us ) to be the newest and latest . As to the Names of the Stars , it is not to be doubted , but that they were first imposed by Adam , Though those ( except some few preserv'd in Scripture ) be long since utterly lost . Yet the Names we now use are most of them above two thousand years standing , as is manifest by Hesiod and Homer . It is not yet to be imagined , that they were all impos'd about one and the same time ; some being of much later Denomination , as particularly Coma Berenices ( so called by Conon ) Antinous , and others . Some report Astraeus to be the first , who gave Names to the Stars ; whom for that reason — Fama Parentem Tradidit Astrorum — As Germanicus makes Aratus speak , concerning which see Theon . Others ascribe this to Mercury . But as to the several Denominations of the Signs and Constellations , see after in the following Notes . c The Aspects or mutual Radiations of the Signs and Stars , are the Habitudes of one unto another in a determinate distance , in which they are apt to Cooperate ; and these commonly are reckoned five in number , and are attributed peculiarly to the Stars and Signs within the Zodiack , but extended likewise to the rest . These Censorinus de die Natal . c. 8. calls Conspectus , the Antient Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , the later 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . The Arabs , Almantar . Their Characteristick Notes , Names , and Distances , thus exprest : ☌ Conjunctio , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 — Gr. 0 ⚹ Sextilis , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 — Gr. 60 □ Quadratus 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 — Gr. 90 △ Trinus , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 — Gr. 120 ☍ Oppositio , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 — Gr. 180 To which Kepler and Mestlinus add several others : But the most eminent Aspects are the great Conjunctions of the three Superior Planets , and their distances in Trine Aspects of the Zodiacal Signs , called therefore Triplicities . The first fiery , whose Angles answer to the fiery Signs , Aries , Leo , and Sagittary . The second aery , answering to the aery Signs , Gemini , Libra , Aquarius . The third watry , pointing to the watry Signs , Cancer ; Scorpio , and Pisces . The last Earthy , whose Angles are terminated in the Earthy Signs , Taurus , Virgo , and Capricorn . d Others of the Romans , says Scaliger , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 tentarunt , essay'd to write of this Subject in Prose , as Varro and Nigidius , who both wrote of the Sphere , ( as well the Barbarick as the Greek ) Cassiodorus ( in Astronom . ) mentioning the first , Servius ( in Georg. ) the other . And among the Greeks , Eratosthenes , Aratus , Heg●…syanax , and Hermippus wrote of the Coelestial Phaenomena ; and Ovid , after Marcus Tullius , and Germanicus after him , translated Aratus into Latine Verse ; But not any amongst the Romans before our Authour ( for ought appears ) ever wrote an Astronomical or Astrological Poem of their own Invention . Nor of the later sort any among the Greeks , save only Dorotheus Sidonius , who wrote an Apotelesmatick Poem , though now lost . And therefore not unjustly does our Authour assume the Glory of this to himself from all the Latines . The Original of the World according to the various Opinions of the Antients . e The Opinion of Xenophanes , who held the World to be eternal , ungenerated , uncreated and incorruptible ; with whom agree Parmenides , Melissus and Aristotle , to whose Opinion likewise Xenocrates subscribes , and with them Pliny ( l. 2. c. 1. ) thus concludes . Numen esse Mundum credi par est , aeternum immensum , neque genitum neque interiturum unquam . Vide etiam Censorin . de die Natal . c. 4. And as to this and the several other Opinions of the Antients touching the Efficient Cause , Matter and Principles of the Universe , ( besides Plutareb de Placit . Philosoph . and Stobaeus in Eclog. Physic. ) see Paul. Merula his Learned Dissertation in Q. Ennii Annal. p. 119. upon these Verses . Corpore Tartarino prognata Paluda Virago , Quoi par Imber & Ignis , Spiritus & Gravi ' Terra . f Our Authour here makes Chaos to disclose and separate the mixed Principles of things , and to bring forth the World. Claudian more conform and agreable to the Antient Theologie of the Ethnicks , makes Clemency or Love to effect this Work , l. 2. de La●…d . Stilicon . — Prima Chaos Clementia solvit , Congeriem miserata rudem , vultuque sereno Discussis Tenebris in Lucem Saecula fudit . Hesiod ( as Plutarch delivers his Opinion l. de Iside & Osyride ) makes the Principles of all things to be Chaos , Earth , Tartarus , and Love ; By Earth understanding Isis ; by Love Osyris ; by Tartarus Typho ; by Chaos 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . The Place ▪ Region or receptacle of universal matter ; to which its name answers : Chaos signifying no other than Hiatus seu vistitas quaedam . Philo Biblius from the Writings of Sancuniathou , as cited by Eusebius in prima Praeparat . writes thus : 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , &c. ( i. e. ) The Theology of the Phoenicians makes the Principles of the Universe●… dark Spiritual Air , or a Spirit of dark Air , and confus'd Chaos involv'd in Obscurity ; These were infinite , and for some time without Bound or Term : But when the Spirit was touch'd with the love of his own Principles , and a Mixtion was made , there was given to that Ne●…re the name of Love. This was the beginning of the production of all things ; But the Spirit it self had no Generation : And from this Connexion of the Spirit was begotten M●…T ; which some call slime , &c. From which Theology of the Phoenicians , Hesiod , Ovid , and others deriy'd their Fables of Chaos , as the Phoenicians theirs from their Neighbours , the Iews , and the Writings of Moses not clearly understood . See Grotius in his Notes upon his Book deveritat . Relig. Christ. l. 1. Of the several acceptions of the word , Chaos , according to the different Notions of the Poets , Philosopher●… and Divines ; See Ri●…ciolus on that Subject in Almagest . Nov. Tom. 2. lib. 9. g The Opinion of Democritus , Leucippus , and Epicurus , and before them of M●…schus , or rather M●…chus , the Sidonian , who as Strabo ( l. 16. ) from the Authority of P●…sidonius , affirms , was the first Authour or Introducer of these Indivisible Principles , and liv'd before the time of the Trojan War. By Atoms is to be understood what the Latines call Insectile , that is , a Body incapable of Division both by reason of its solidity , ob vacui care●…iam , and the Minuteness of its Body , whence it is properly said to be quid minimum , or as our Authour terms it penè Nihilum . But see these explain'd in Lucretius de Rerum Naturâ , and the Ingenious Interpreter of his first Book Mr. Evelyn ; more especially Gassendus in his incomparable Epicurean Animadversions . h This was asserted by Hyppasus the Metapontine , and from him by Heraclitus the Ephesian ; The Opinion thus delivered by Laertius ; All things consist of Fire , and into that are resolv'd : for since all things are made by Condensation and Rar●…faction , and flow for the most part in manner of a River ; Fire when it is condens'd , bumectates and becomes Air ; Air when comprest , becomes Water ; Water contracting and growing concrete becomes Earth : this is the way down . On the contrary , the Earth being diffus'd , thereof Water is made , of Water the rest after like manner : this is the way up . To this effect likewise Plutarch de Placit . Philosoph . l. 1. & Stobaeus Eclog. Physic. l. 1. i Meaning the Stars , according to the Stoicks ; who make the World to be a Corporeal Deity , and the Stars its Eys . See Plutarch de facie in Orbe Lunae , and Lips. Physiol . Stoic . l. 2. Dissert . 10. k Of this Opinion was Thales the Milesian , and Pherecydes of Scyrus ; who held Water to be the first principle of all natural Bodies , whereof they consist , and into which they resolve . The Reasons or Grounds for which Opinion are these . First , because the Seminal and generating principle of all living Creatures is humid . Secondly , because all kinds of Plants are nourished by moisture , wanting which they wither and decay . Thirdly , because Fire , even the Sun it self and the Stars are maintained by Vapours proceeding from Water , and consequently the whole World consists thereof . See Plutarch de Placit . Philosoph . and particularly ( to omit divers others ) my learned Dear Friend Mr. Stanley in his History of Philosophy , Part. I. l Not improperly is that Epithet given to Fire ; it being by some of the Antients believed to be a devouring Animal : And for that reason the Aegyptians refused to burn their dead , imagining fire to be 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Animata Bellua , as Herodot . l. 3. informs us . m Asserted by Empedocles , who held the Principles of all things to be the four Elements ; to which he added two Powers , Amity and Discord , the one Unitive , the other Discretive : See Plutarch de Placit . Philosoph . Laertius in Vit. Empedocl . Achilles Tatius in Arat. Phaen●…men ▪ and Lactantius lib. 2. Which last conceives he deriv'd this Opinion from Hermes Trismegistus . These Elements he called after this manner . Fire he termed Iupiter : the Air Iuno , or ( as Laertius saies , but not with so good reason ) Pluto . The Water Nestis 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. fluere . The Earth Pluto , or ( according to Laertius ) Iuno , i. e. Vesta . Consonant to this Opinion of Empedocles , thus Ovid Metam . l. 1. Quatuor aeternus genitalia Corpora Mundus Continet . — and again , l. 15. — Omnia fiunt Ex ipsis , & in ipsa Cadunt — Lipsius Philosoph . Stoic . lib. 1. conceives our Authour in these Verses to touch at the Opinion of Strato the Peripatetick , who h●…ld this Mundane Deity to be formed of these four Elemental Limbs , Sine Mente gubernante . Of which thus S●…neca ( in a fragment of his , cited by St. Augustine , l. 6. de Civitat . dei ) Egone feram Platonem , aut Peripateticum Stratonem , quorum alter ( scil . Plato ) Deum sine Corpore fecit , alter sine Anima ? n To this purpose Lactantius ; l. 2. Philosophi quidam & P●…e taedis●…ordi Concordia Mundum constare dixerunt , i. e. some Philosophers and l●…oets report the World to consist ●…f discording Concord : So likew●…se Cassiodorus ( lib. 2. Variarum ) Merito dicunt Philosophi Elementa sibi Mutuis complexi●…us illigari & mirabili conjungi foederatione , quae inter se contrariâ intelliguntur varietate pugnare . This dis●…onant Harmony of Nature being represented by Orpheus in his Tetrachord ; In which , as there were four strings ; from the mixture of whose different Tones resulted a sweet Harmony ; so by concourse and mixture of the four Elements , all things are generated . And as in the Tetrachord the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 rendred the gravest sound , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the most acute , and the nearest in gravity of sound to the first came the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , to the second in acuteness the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 So among the Elements , there is one the heaviest , Earth , and one the lightest , Fire , answering to the two first Notes ; Water and Air answering to the two intermediate Tones . This admirable Consent of the contrary Elements is here not unaptly called The Matrimonial Band of Nature . And for this reason , saies Lactantius ( loco citato ) The Marriages of the Antients were confirmed and plighted by the Sacrament of two contrary Elements , Fire and Water . In regard that Heat and Moisture are the Parents of all Generation , as Ovid ( l. 1. Metam . ) hath likewise exprest it . Quippe ubi Temperiem sumpsere Humorque Calorque , Concipiunt , & ab his oriuntur ●…unctá duobus , Cumque sit Ignis Aquae Pugnax , vapor humidus omnes Res Creat ; & Discors Concordia foetibus apta est . Disposition and Order of its Parts . o Our Authour here Confines not the Element of Fire within the Convex of the Lunary Sphere , as Aristotle , and his followers ; but with the Stoicks transmits it to the Aethereal Region , which they will have so called , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. ab Ardore , as consisting of Fire , and to be Heaven it self , imbracing all things , as Cleanthes in Cicero , ( i. e. de Natura Deorum ) describes it . Ultimum , & altissimum , atque undique circumfusum , & extremum omnia cingentem atque complexum Ardorem , qui Aeaher nominatur . To this purpose likewise Macrobius ( in Somnio Scipionis ) Quicquid ex omni Materiâ , de quâ facta sunt omnia ; purissimum ac liquidissimum fuit , id tenuit summitatem ; & Aether vocatus est . Fire . Air. Water . p So Ovid , — Tellus Elementaque grandia traxit , Et pressa est gravitate suâ — Upon which Words Iacobus Cruceus ; Per Elementa grandia nos materialem intelligimus All●…vionem , &c. By the heavy Elements we understand that Material Conflux , which the Greeks call 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , being the settling and Dregs of all the Elements ; To the same sence likewise Lucretius , — Terrae concreto corpore pondus Constitit , atque omnis Mundi quasi Limus in Imum Confluxit , gravis & subsedit funditus ut ▪ faex . So the Scholiast of Apollonius Rhodius , in l. 1. — 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , &c. Zeno affirm'd The Chaos , whereof all things , according to Hesiod , were made , was water ; which settling became slime ; the slime condens'd into solid Earth ▪ Earth . q Virgil , Eclog. 6. Tum durare solum , atque excludere Nerea Ponto Coeperit — Our Authour perhaps in this place hints at Anaximander , who said of the Sea , that it was 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 The remainder of Primitive Moisture , after this Exclusion and Separation . Plutarch . l. 1. c. 4. de placit . Philosoph . thus expresses the sence of our Authour : Of those Bodies which settled below , was made the Earth ; and that part thereof which was m●…re subtile and of a thinner form and consistence , gathered round together , and engendred the Element of Water , which being of a liquid and fl●…wing nature , ran downward to hollow place●… lying low , which were able to receive and hold it . The Earth in the midst of the World. r To this purpose Cicero , l. 2. de Naturá Deorum . Si Mundus Glob●…sus est , Omnesque ejus partes undique aequabiles , &c. If the World be round and of a Globose Figure , and all its Parts contained in like proportion , by and among themselves ; It must happen to the Earth by necessary Conse●…uence , seeing all its parts press and tend to the middle , ( now the middle in a Sphere is that which is lowest ) that nothing can p●…ssibly interpose , which may be able to weaken or hinder so great a Convention of Gravity . s Homer and O●…id make the Moon to be drawn in a Chariot by two Horses ; whereof the one is said to be white , the other black , in regard ( as Bassus in Germanicum gives the reason ) she is sometimes apparent by Day , as well as by Night . Others will have her to be drawn by Oxen , and therefore by N●…nus in Dionys. l. 12. she is called — 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . — Boum Agitatrix Luna . Of both which we have express representations in the Roman Coyns , and particularly in those of the Empress Iulia Domna , touching which , see Tristan in his Historic . Commentar . Tom. 2. p. 129 , 130. She is said likewise to be drawn by Mules , in regard , ( as Festus in v●…ce Mulus observes ) that as Mules are not generated ex suo genere , sed Equi ; So the Moon is said to shine not by her own , but as Catullus expresses it , — Notho Lumine , which she derives from the Sun. Claudian l. 3. de laudibus Stiliconis , makes her to be drawn by Stags , in regard of the swiftness of her Motion , & c. and so we have her likewise represented in divers Consular and Imperial Coyns , in Ursinus , Golzius and Gorlaeus . t The Star or Planet Venus , called likewise Lucifer , ( as Cicero in 2. de Naturâ Deorum , and Pliny , l. 2. c. 8. ) when it precedes the rising Sun , as being the Harbinger of Light , ( and not as Iulius Scaliger Exercit. 75. conceives , for being the brightest of all the Stars , and from its splendour so nam'd . ) It is likewise call'd Hesperus , Vesper , & Vesperugo , when it rises in the Evening and ushers the Night . Of this , thus Seneca in Hypolit . Qualis est Primas r●…ferens Tenebras Nuncius noctis , modo lotus undis Hesperus , pulsis Iterum Tenebris Lucifer idem . Such the bright Usher of dark Night Rises from Seas with new-bath'd Light , Hesper : The same , Night chac'd away , Phosphor , the Herald of the Day . We shall only add as a further Illustration to this , and the foregoing Note , what Cassiodorus hath ( l. Variarum 3. ) in Explanation of the Circensian Games . Big a quas●… Lunae , quadriga Solis Imitatione reper●…a est . Equi Desultorii , per quos Circensium Ministri miss●…s denuntian●… Exitu●…os , Luciferi Praecursori●…s velocit●…tes imitantur . u He points at the ridiculous Opinion of Xenophanes the Colop●…onian , who held that the Moon and Stars were certain Clouds set on Fire , extinguish'd every Day , and re-kindled at Night ; as on the contrary , the Sun extinguish'd every Night , and re-kindled every Morning ; or , to express it in Minucius Foelix his Words , Congregatis ignium Seminibus Soles alios atque alios semper splendere . For the Rising and Setting of the Sun , Moon , and Stars , according to this Tenet , is nothing else but their kindling and extinguishing . Of the same Opinion like wise was Heraclitus , whence the Proverb in Plato , Heracliteo Sole ci ius extingui . From them Epicurus receiv'd by Succession , Haereditatem ●…tultitiae ( as Lactantius terms it ) This Inheritance of Folly , which he left improv'd by himself , and Lucretius , who thus asserts it , l. 5. — conveniu●… Ignes , & semina multa C●…fluere Ardoris consuerunt tempore certo , Quae faciunt Solis n●… semper Lumina gigni , Quod genus Idaeis fam●… est è montibus al●…is Dispersos ignes ori●…i Lumine cerni , Inde c●…ire Globum quasi in u●…um , & conficere Orbem . By which instance of Lucretius i●… may appear , that Epicurus did not hold so much the Quotidian Creation of a new Sun , as the dayly Renovation of the Old ; To which Horace in Carmine Saecular . seems to allude , Alme Sol Curr●… nitid●… di●…m Qui promis & celas , aliusque Et idem nasceris — And to this purpose I find his Opinion expressed by Gassendus . Seeing the Ocean compasses the Earth , the Sun may be extinguished by it in the West , and return all along it by the North into the East , and thence rise re-kindled , which yet little mends the matter . x To this may be applied that of Plato ( in Timaeo ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , &c. Thus interpreted by Cicero in his Fragment of Timaeus , seu de universe . Nec Maenus ei Deus affixit , quia nec capiendum quicquam erat , nec repellendum , necpedes , nec alia membra quibus Ingressu corpus sustineret , &c. i. e. God affixed to the World no hands , because it was neither to take nor repel any thing ; nor Feet , nor other Members , whereby it might sustain its body by walking or going ▪ But gave it a Motion , which is most sutable to its Figure ; wherefore by one and the same Conversion , it is whirl'd and turn'd about it self . y Aristotle , Anaximander , and their followers at this day , hold the Heavens to be solid , and the Stars fixed therein , as Nails in a Wheel , or Jewels in a Ring ; the contrary to which Opinion is here asserted by our Authour , with whom concur among the Antients , Homer , Virgil , Cicero , Lucretius , Seneca , Ptolemy , Pliny , Metrodorus , and others : And of the Moderns , the most Eminent Astronomers from Tycho , to this present , who all maintain the Heavens to be fluid , and the Stars to move therein , as Fishes in the Water , or Birds in the Air. Between these there is a middle Opinion , which maintains the Heaven of the fixed Stars to be solid , but that of the Planets to be fluid . The first Authour of which distinction , is conceiv'd to be Empedocles ; Of which see Plutarch , l. 2. de Placit . Philosoph . c. 13. and upon the whole subject matter , Ricciolus in Almagest . Nov. l. 9. c. 7. z This Libration , or Suspension of the Earth , Achilles Tatius in Arat. Phaenomen . thus illustrates , If any one should put a Millet-Seed , or other small Grain into a Bladder , and by blowing into it fill it with Air , the Seed or Grain will be carried up , and remain in the middle of the Bladder . After the same manner , the Earth being on all sides forced by the Air , suspends poiz'd in she midst thereof . To which Aristophanes in Nubibus , alludes ; 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ▪ Great Lord and King , Thou Immense Air ! Which dost the Earth suspended bear . See Turnebus , l. Adversar ▪ 4. c. 17 ▪ explaining these Verses of Ovid , ( l. 1. Metam . ) Et circumfuso pendebat in Aere Tellus Ponderibus Librata suis — The Earth of a Spherical Form. a He alludes perhaps to the Opinion of Leucippus 〈◊〉 , which see more particularly exprest in Hesych . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 in voce 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . b This is a Noted Star of the first Magnitude , in the Southern Rudder of the Ship , Argo ; so called , from Canopus , Pilot to Osyris , ( according to the Aegyptians ) or to Menelaus , ( according to the Greeks ) who landing in Aegypt , was by the biting of a Serpent slain , and buried near one of the Out-lets of Nilus , from him called Ostium Canopicum ; the place of his burial receiving likewise his Name , and growing to a City , in which he had his Temple , being honoured with Divine Rites , and worshipped in the form of a Pitcher or Watring-Pot , with a large round Belly , as the Deity presiding over Nilus , and the watry Element : Of whose Contest with the God of the Chaldeans ( Fire , ) and Victory thereupon ; see the Story in Suidas in verb. Canop . and from him in Kircher . in Oedip. Aegypt . Tom. 1. p. 209. c To this purpose Vitruvius , l. 9. c 7. U●…i Septentriones circum Axis Cardinem versantes non occidunt , neque sub Terrâ subeunt : Sic & circa Meridianum Cardinem , qui est propter inclinationem Mundi subjectus terrae , Sydera versabunda la●…entiaque non habent egressus orientes , &c. i. e. As the seven Stars , or the Bears turning about the Northern Axis of the World never set ; so the Stars near the Southern Pole , which ( by reason of the Worlds Inclination , being deprest under the Earth , ) make occult and hidden Revolutions , never rise , nor can be observed or known by us in regard of the Earths Interposition . Of which the Star Canopus is proof , which in these Regions is unknown , as those Merchants which travail to the uttermost Parts of Aegypt inform us . d To the same effect Pliny . Septentriones non cernit Trogloditice , & Confinis Aegyptus ; nec Canopum Italia . i. e. The Land of the Troglodites , and its Neighbouring Aegypt sees not Helice , nor Italy Canopus . Scaliger yet condemns both Pliny and our Authour , as mistaken in the first particular ; for at Alexandria the Sun being about five Degrees of Pisces under the Horizon , both Helice and Canopus are in the Evening seen to rise in the East ; and were so to be seen in the time of Manilius , the Sun setting in the twenty third Degree of Aquarius . What is said of Canopus , as not appearing in Italy , is true . e Gassendus in Append. Animadvers . in Epicur . noting upon this place , thus advises . Cautè esse interpretandum quod ad ha●…c rem Manilius habet . For those Words , Pariter , prius , & post , ( saies he ) are not to be taken as to divers Moments of time , for the Moon at one and the same instant is beheld to be Eclipsed by all those , to whom she appears above the Horizon ; but to be meant of the diversity of Hours by reason of the several Meridians ; by which means it happens that at the same instant of time that the Moon is seen to be Eclipsed , above our Horizon , They Eastward of us may reckon the Eclipse at one , two , or three in the Morning ; They Westward at nine , ten , or eleven at Night , after the preceding Noon . Vide etiam Baltoreum in l. 1. Cleomedis Meteor . f So Ovid , ( l. 4. Metamorph . ) — resonant aera auxiliaria Lunae . And Statius , l. 6. Theb. — Procul auxiliaria Gentes Aera crepant — That Custom springing from the foolish belief of the Antients , that the Moon at the time of her Eclipse , was endeavoured by the Charms of Witches to be drawn from her Sphere . And therefore they made that Noise that she might not hear their Incantations ; Practised by the Ignorant People , even in St. Ambrose his time , as we find by his reprehension of that Piece of Paganism , cited by Turnebus in Adversar . And what is more affirm'd by B●…nincontrius ( who first within less than two Centuries of Years , Commented upon our Authour ) to have by himself been seen acted upon the like Occasion , by his own Countrey-men , the Italians . The Turks continue it to this Day , as Scaliger affirms . Plutarch in Ae-milio reports that the Romans , besides their beating of Brazen Vessels , and sounding of Trumpets , us'd to reach up flaming Links and Torches towards Heaven , to re-supply the Light of the Moon , which they believed by Charms to be extinguish'd . Delrius in Senec . Tragoed . says , he hath read that the Indians us'd with Tears and Lamentations to prosecute this defect , or Deliquium of the Moon , as believing she was then by the Sun whip'd till she bled , to which they attributed her dark and sanguine colour . Vide Delrium in Commentar . ad Hippolyt . p. 195. See likewise Turnebus in Adversar . l. 22. c. 23 & 24. And Pincierus in Parerg. Otii Marpurg . l. 2. c. 37. g Whether Birds , which are generally call'd Genus Aereum ; and by the sacred Text it self , volatilia Coeli , may be properly reckoned among Terrestial Animals , is by some questioned . Ovid ( Metam . l. 1. ) seems not to allow thereof in his Distribution of Animals , Astra tenent Coeleste solum , Formaeque Deorum , Cesserunt nitidis habitandae Piscibus undae , Terra feras cepit , Vol●…cres agitabilis Aer . The like Division is made by Cicero , l. 2. de Nat. Deor. and in Timaeo , and by Aristotle , as he is cited by Plutarch . in 5. de Placit . Philos. To which may be added that belief of the Antient Greeks ( derived to them from the Aegyptians ) that Birds were produc'd before ever the Earth was form'd , whereunto Aristophanes in Avibus , alludes . But Apuleius sides with our Authour , and ends the Controversie in these words : Si sedulo animadvertas , ipsae quoque Aves , Terrestre Animal non Aereum rectiùs perhibeantur ; Semper enim illis victus omnis in Terra , ibidem Pabulum , ibidem Cubile , tantúmque Aera proximum Terrae volando verberant ; Iterum cum illis fessa sunt Remigia Alarum , Terra seu Portus est . i. e. If you seriously consider , Birds may be more truly reckon'd a Terrestrial Animal , than Aereal ; For all their living is upon the Earth , there is their Food , there their Nests . They only in their flight beat the Air ; But when their Oars and Sails , their Wings , begin to fail them , the Earth is their Harbour . But as to this Question , ( not much unlike that which troubled the heads of Aristotle , Theophrastus , and most of the Antient Peripateticks , as Censorinus de die Natal . c. 14. delivers it , which was , Avesne ante , an Ova generata sint , cum & Ovum sine Ave , & Avis sine Ovo gigni non possit ? ) See Hieron . Magius , l. 1. Miscellan . c. ult . Iacobus Cruceus Syllog . 3. and Kircher . in his Iter. Extatic . 2. Dialog . 2. c. 5. h Homer ( saies Geminus ) and almost all the Antient Poets , make the Sea to round the Earth , as an Horizon , dividing the upper from the lower Hemisphere ; whence the Horizon it self is by them call'd the Ocean , according to this Verse of Neoptolemus Parianus , and Euph●…rion cited by Achilles Tatius in A●…at . Ph●…nom . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . The Ocean girdling the surrounded Earth . To the same purpose Agatharchides , as cited by Ph●…ius ( in Bibli●…th . ) asserts , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , &c. Quod Orbem t●…tum O●…anus ct●…umluet & ambi●…t ; Custodiens eum fluxib●…s suis & continens . Hence H●…mer gives to Neptune the title of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Terram continens , sive ambitu su●… c●…mplectens ; and by Secundus ( 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ) the Sea is stil'd , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Mundi amplexus , Corona Maritima , salsu●… vinculum , Cingulum A●…lanticum , totius naturae Ambitus , Orbis fascia ; Being of old likewise among the Greeks called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , probably deriv'd from the Phoenician Ogg. i. e. Circulus , sive Ambitus ( for so they call'd the Ocean ) as first observed by Vossius Idol . l. 2. from H●…sychius ▪ And from him by Bochartus ( in Geograph . sacra , l. 1. c. 35. ) Vide etiam Casaubon . Animadvers . in Strabon . l. 1. p. 4. The Divine Spirit or Soul of the World. i Plato , Trismegistus , Pythagoras , and many other of the Antient Philosophers , conceive the World to be indued with a Rational Soul , perswaded thereunto by the admirable Order and Connexion of its Parts , which they conceiv'd , could not be sustain'd , but by a soul intrinsically informing , ordering , disposing and connecting them . Hence that of Virgil , imitated by our Authour , Spiritus intus alit , Totosque infusa per Artus Mens agitat Molem , & Magnose Corpore miscet . This Soul , Thales imagines to be God himself ; thus explained by the Hermetick Philosophers . The Divine Spirit which produc'd this World out of the first Water , being infus'd as it were by a continual Inspiration into the Works of Nature , and diffus'd largely through , by a certain secret and continual Act , moving the whole and every particular according to its kind , is the Soul of the World. See Mr. Stanley in the Life of Thales . Plato , and the old Academists , ( as Cicero in Acad. Quaest. l. 1. delivers their Opinion , ) say thus of it : The Parts of the World and all things therein , are kept together by a sensitive Nature , wherein is likewise perfect Reason ; It is also Sempiternal , for there is nothing more strong , whereby it may be dissolv'd . This Power is call'd the Soul of the World. Heraclitus asfirm'd the Soul of the World to be an Exhalation of the humid Parts thereof , as Plutarch in 4. de placit . Philos●…ph . c. 1. Varro , fire , of which Tertul ▪ ad Nat. l. 2. perhaps meaning the same with Chalcidius in Timaeum , who calls Vesta ▪ animum Corporis universi ●… or with Pliny , who asserts the Sun to be this Soul of the World. Hunc Mundi esse ●…otius Animum ●…c plane Mentem , Hunc principale Naturae Regimen ac Numen credere decet , says he , l. 2. c. 6. Of the same Opinion is Iulius Firmi●…us . But as to this , see more particularly Caelius Rhodigin . Antiqu. Lect. l. 1. c. 14. l. 6. c. 11. & alibi . As likewise K●…pler , in Harmon . Mundi , l. 4. Kircher . O●…dip . Aegypt . Tom. 2. Part. 2. p. 526. Gassendus . And Ieronymus Vitalis in Lex . Mathem●…t . p 305. &c. k To the same sence Crito Pythagoricus in Stob. Sermon . 2. — 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 &c. In the Universe the Conjunction of either Nature , viz. of that which is always Active , and the other which is always Passive , make this World , which otherwise could not subsist . Consonant to which a Modern Italian Poet , Ianus Pannonius ( in obitum Guarini Veronensis ) as cited by Barthius Adversar . l. 54. c. 25. Iunge etiam semper Patientis , semper Agentis Materiae Fluxus , & Fata regentia Mundum . The Twelve Signs of the Zodiack . l That is the Zodiack . The Aeeyptians held , that in every Asterism or Sign in the Zodiack , or rather in each Dodecatem●…rion thereof , a peculiar Deity resided ; and in every Star belonging to one of those Constellations a peculiar Genius , as the inferiour Ministers of each Deity ; whose vertue they believed to flow by an Influx in form of a Pyramide , whose Basis contain'd the whole Extent of the Asterism , or rather D●…decatemorion , and whose Vertex or Top was terminated in the Centre of the Earth ; and these they termed 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , seu Arces Deorum ; and from them the Arabians call'd the Signs Bu●…ugi , signifying Towers , Castles or Forts ; and in the singular Burgi , believing the Signs to reside in so many Castles or Palaces , by the Persian●… call'd K●…shk , or as we usually term them Houses . And therefore our Authour elsewhere calls the twelve Signs or Houses in the Zodiack , Castra ; and the Zodiack it self in this place , Arcem Mundi , or the Tower , or Citadel of Heaven ▪ consisting of so many Bulwarks . See Kircher . in Oedip. Aegypt . Tem. 2. and Mr. Hyde the Learned Commentator upon Ulugh B●…gh , his Tables , p. 30. m I have chosen so to English Princeps Aries , rather than the Leading Ram , perswaded thereunto by the Authority of our Poet , who , l. 2. gives him that Title , — Aries Caput est ante omnia Princeps Sortitus — And again , l. 4. Consilium ipse suum est Aries , ut Principe dignum est . And by that of Germanicus , in Aratum ; where he is stil'd Princeps Aries — And of Columella , ( l. 10. ) who gives him the Title of Signorum & Pecorum Princeps — So likewise Varro , l. 5. de Linguâ Latin. speaking of the Original and Etymology of the Agonalian Festivals , ( in which , antiently the Kings of the Romans us'd in their Palace to sacrifice a Ram ) tells us , they were so call'd from the Question of the Sacrificer , Ago ne ? Eo quod Interrogatur Princeps Civitatis , & Princeps Gregis immolatur . This Principality being given to this Sign above the rest , in regard that at the Worlds Nativity , according to the Astronomical Computation of the Antients , he was found seated as in a Throne , in Medio Coeli , i. e. the Tenth House ; of which Macrobius in Somnio Scip. and Salmasius Diatrib . de Antiq. Astrolog . p. 180. And for this reason ( perhaps ) it was , that the Ram among the Romans was taken for the Symbol of Principality : To which effect , we find among the Coyns of Domitian , some , on whose Reverse is stamp'd a Ram with this Motto , PRINCEPS JUVENTUTIS . And with the Greeks , the Word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which signifies a Ram , is taken for a Prince or Potentate . See Magius Miscellan . l. 2. and Tristan . in his Historical Commentar . Tom. 1. p. 323. n This Sign is by the Greeks called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Chrysomallus , Iupiter Ammon ; by the Aegyptians or Copties , Tametouro Amnou , i. e. Regnum Ammonis ; in Hebrew , Tele ; in the Syriack , Emro ; by the Arabians , Al Hámal ; by the Persians , Bérri , or Bére ; by the Turks , Kuzi . All signifying a Lamb full grown , as I find in the Learned Commentator upon Ulugh Beigh his Tables ; whom in the Nomenclature of these Signs , and th' other Constellations I most particularly follow , as being in that more exact and copious than either Scaliger , in Sphaer . Barbar . Schickardus , Bayerus , Hues de Globis , Grotius in Arat. Ricciol●…s , or ( whom he follows , ) Kircher , whose several assistances I yet make use of upon occasion ; and only premise this to avoid ( for brevity sake ) the trouble of future Citations . In this Constellation are reckoned according to Ptolomies Computation , seventeen Stars , whereof four inform ( which sort of Stars , reckoned either in this , or any other Constellation , are by the Greeks call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Informes ; and by the Arabs , particularly by Ulugh Beigh , Chârigi Sûrat . i. e. extra figuram positae . ) Bayerus reckons nineteen , whereof three are of the third Magnitude , two in the Western , and one in the Eastern Horn , called by the Arabs , Alsheratein , or Alsheratân ; in Hebrew , Sartai , and Mezarthim ; the third in his Head , in Arabick , Al Ashra ; all from the singular Sherat , i. e. Signum seu Indicium , a Sign or Mark ; the seventh , eighth , and eleventh Stars are call'd in Arabick , Min Botein , from their Situation near the Belly of the Ram. This according to the Tradition of the Aegyptians , was made a Constellation in Honour of Cham. But as Nigidius ( cited by the Scholiast of Germanicus ) reports , for discovering to Bacchus , and his thirsty Army in the Desarts of Africa , a Fountain of Water ; or , according to Pherecides , for transporting of Phryxus , and Helle over the Sea , flying from the fury of their Step-Mother Ino. It is under the Tutelage of Iupiter and Minerva , according to the Doctrine of the Pythagoreans , deriv'd from the Chaldaeans , who held the Principal Gods to be twelve ; To each of whom they attributed a Month in the Year ; and one of the twelve Signs in the Zodiack , as is observ'd by Diodorus Siculus , l. 1. Bibliothec. This Sign was first discover'd by Cleostratus the Tenedian , as Pliny witnesses , l. 2. c. 8. and comes to the Meridian at Midnight , about the end of October , and beginning of November . Aries . o This Sign is called Io , Isis , Apis , and Orias , i. e. Statio Hori , by the Aegyptians ; by the Greeks and Latines 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and Taurus ; in Hebrew , Shôr ; by the Arabs , Al Thaur ; by the Syrians , Thauro ; by the Persians , Ghau ; and by the Turks , Ughuz , i. e. Bos. It consists according to Ptolomy , of 44 Stars , whereof 11 shapeless ; or as Bayerus counts , of 48 , as Kepler , of 52 ; among which there is one of the first Magnitude , by the Greeks called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; by Ptolomy , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; by the Arabs Aldebaran , i. e. Stella Dominatrix , and Ain Al Thaur , i. e. Oculus Tauri ; by the Aegyptians , Piorion , i. e. Statio , seu Dominium Hori , in regard of the power of the Sun in Conjunction with that Star ; by the Romans , Palilicium , because heretofore it rose at Rome on the Feast-day of Pales , translated into Heaven in Memory of the Rape of Europa by Iupiter in that shape ; or in Honour of Io , or Isis , transform'd by Iuno into a Cow , and Constellated by Iupiter . Hence Ovid. Vacca sit an Taurus non est cognoscere promptum , Pars prior apparet , Posteriora latent . Seu tamen est Taurus , sive est haec foemina Signu●… Iunone invitâ Munus Amoris habet . If Bull or Heifer hard 't is to descry Seen are its fore ▪ parts , hid its hinder lie . But be 't a Masculine or Female Sign , It spite of Iuno , as Loves Mark does shine . Others will have it to be the Symbol of Osyris or Mesoris , or Mizraim , the Son of Cham , who first taught the Egyptians Tillage ; or rather of the Patriarch Ioseph , for his preserving Aegypt in the time of Famine ; to which the Learned Grotius , in his Tragedy of Sophomphania , alludes . To confirm which Opinion , Ger. Io. Vossius in his most accurate Work de Orig. & Progress . Idololatr . shews that Apis was the same with Joseph ( de quo etiam vide Tertull. l. 2. ad nationes ) and that under the Symbol of an Ox , he was honoured by the Aegyptians , as the most proper to express the Benefit conferr'd by him upon that People ; as among the Romans , we find L. Minucius , Praefect of the Corn-stores , Bove aurato extra Portam Trigeminam est donatus , because in a time of scarcity he supplied the Roman People with Corn at a Cheape Rate . Venus is Patroness of this Sign ; which about the end of November , and beginning of December , is at midnight seen in the Meridian . Taurus . p These are call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Tindaridae , and Dioscuri by the Greeks and Litine●… ; In the Coptick , Clusos , ( i. e. ) Claustrum Hori ; in the Hebrew , Te●…min ; in Syriack , Tóm●… ; in Arabick , Taw ' amân , i. e. Gemelli . They are likewise by the Arabs call'd Giauzâ , as it were by a Me●…athesis , or Transposition of the Word from Zaugi , i. e. Bini , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . Others derive it from Giauz , signifying a Nut ; and therefore the Turks call this Sign , Kùs Siphetlu Burgi , i. e. Nucem , vel Nuces referens Signum ; by the Persians , Ghi●…degán , to the same sence . But with more probability , ( says my Authour ) they are call'd Giauza , because plac'd i●… Giauz al Samà , i. e. in Medio Coeli . There are reckon'd in this Constellation , according to Ptolomy , twenty five Stars , whereof seven are inform ; Repler makes them thirty , Bayerus thirty three ; whereof that in the Head of the Western Twin , which first rises , is by the Arabs call'd Ras al Tawum A●…mukeddem , i. e. Caput p●…ioris geminorum ; the other , Ras al Tawum Muaccher , i. e. Caput posterioris Geminorum . The Star reckon'd the fourteenth in number in this Constellation , is by Higynus and Bassus , call'd Prop●…s , by Ptolomy 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , quia praecedit Pedes Geminorum ; and by the Persians , Pish-pai . The seventeenth and eighteenth opposite to one another in the feet of the said Gemini , are by the Arabs call'd al Hen'a , ( i. e. ) quaevis res quae aliam immediate sequitur . These Twins Varro and Servius ( in 11 Virgil. Aen. ) will have to be Apollo and Hercules , call'd by the Arabs , Ap●…ellan , and Hie●…aclus , and commonly , but most corruptly , Aphellar , Anhelar , and Abrachileus . Others will have them to be Triptolemus and Iason ; some Amphion , and Zethus ; or Dii Samothraces ; Plutarob , according to the Tradition of the Aegyptians , makes them to be Helitomenius and Harpocration , the Sons of Isis , and Osyris . But with more probability they are conceived to be Castor , and Pollux . For as the same Plutarch ( l. de Amore fraterno ) affirms , the Spartans of old us'd to call the Statues of Castor , and Pollux , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Trabalia , being no other than two Wooden Pests set parallel one to another , and joyn'd together at each end by two other traverse Beams . Hence ( saies the Learned Palmeriu●… upon that place of Plutarch ) Astrologers make use of the like Figure or Character to denote this Twin Sign , which they deriv'd from the Lacedemonians . It comes to the Mid-Heaven at Midnight , in the end of December , and beginning of Ianuary , and hath Phoebus for its Superintendent . Gemini . Cancer . q Cancer is in the Greek call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Octipes ; It is likewise called Nepa Astacus , Camarus ; In Arabick , Assert●…n ; in Hebrew , Sartan ; in Syriack , Sartóno ; in Persian , Chercjengh ; by the Turks , Lenkutch , or Lenki●…ch , and Yenkutch , or Yenkitch , and Yilenkutch , or Yilenkitch , i. e. Cancer ; In the Coptick it is called Klaria , i. e. Besti●… , seu stati●… Typhonis . The whole Constellation made up of thirteen Stars , whereof four shapeless , according to 〈◊〉 my ; Kepler reckons seventeen , and Bayerus thirty five . Among which , the first Star in this Constellation is call'd in A●…bick , Malaph , i. e. Praesepe , or the Manger ; in Greek , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 : It is likewise by the Arabs call'd Al Net●…ra ; in Chaldi●… , Pesebre ; and is a Cloudy Star , by Galilaeo discover'd to consist of thirty six smaller ones . The fourth and fifth Stars are by the Arabs call'd Al Himarein , or Al Him●…rân , i. e. du●… Asini ; Our Authour elsewhere calls them Iugulas . The Crab was made a Constellation at the Intreaty of Iuno , being kill'd by Hercules , for biting him by the Foot , when he encountred Hydra : The Asinegoes , with their Manger , were constellated , because in the Fight with the Gyants , Bacchus and Vulcan charged upon Asses , who with their Brayings , frighted , and so put to flight their Enemies ; see Higyn . and Bassus in Germani●… . ( or rather Eratosthenes , for that Comment is no other than Eratosthenes translated . ) This Sign is appropriate to Mercury , and is famous according to the Chaldaick and Platonick Philosophy , for being supposed the Gate by which Souls descended into Humane Bodies ; touching which , see Mecrobius in Somn. Sc●…p . Coel. Rhodig . antiq . Lect. l. 15. c. 23. and Kircher in Oedip. Aegypt . Tom. 2. p. 535. It illustrates the Mid-Heaven about Midnight , from a little after the beginning , until the end of Ianuary . r This Sign by the Greeks is called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; in Hebrew , Ar'ye ; by the Arabs , al Asad ▪ in Syriack , Ar'yo ; in the Persian , Shîr ; the Turk●… call it 〈◊〉 , or As●…in , i. e. Leo ; the Aegyptian Cop●…ies call it Pimentekeon , i. e. Cubitus Nili . It consists of thirty nine Stars , whereof eight inform , according to Ptolomy , of forty according to Kepler ; to which number Bayerus adds three more . The first Star in this Constellation , is by the Arabs called Minchir al Asad , i. e. Nares Leonis . The third , Ras al Asad , al Schemali , i. e. Caput Leonis Boreale . The fourth , Ras al Asad , al Gienubi , i. e. Capu●… Leonis Australe . The fifth sixth , and seventh Stars are called by them al Gieb'ha , i. e. Frons . The eighth they call Mesichi , to which the Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and the Latine , Regulus , answers ; they give it likewise the name of Kal●… al Asad , i. e. Cor Leonis , being a Star of the first Magnitude . The twentieth Star is in Arabick call'd Duhr al Asad , i. e. Dorsum Leonis , and is also with the twenty second call'd Min al Zub'ra , i. e. de Crine Dorsi . The twenty seventh Star they call S●…rpha , i. e. Mutatrix , from the Change it brings of Heat from Cold ; and Danab al Asad , i. e. Cauda Leonis ; and is likewise of the first Magnitude . The Lyon was made a Coelestial Sign by Iuno , to spite Her●…ules , by whom he was slain ; and is said to have been bred in the Moon , and from thence to have fallen near the Nemaeean Grove in Arcadia , from whence call'd Nemaeeu●… ; as likewise , Claeoneus , and Herculeus ; to which , besides Achilles Tatius in Arat. Seneca alludes in He●…cul . furente , in these Words , Sublimis alias Luna concipiat feras . And again — Leo Flammiferis aestihu●… ardens , Iterum è Coelo cadet Herculeus . The Poets , ( as is observ'd by Scaliger . not . in Ceirim ) feigning Animals , exceeding th' ordinary ●…ize , to be bred in , and to come from the Moon ; Hence Claudi●… , or some one more Antient than him , in the Poem of the Praises of Hercules , speaking of the Marathoni●…n Bull , subdu'd by that Hero , — Taurus med●… nam Sydere Lunae Progenitus , Dictaea Iovis possederat arv●… . This Sign , — Iupiter ( & cum Matre Deûm ) regit , — says our Authour , l. 2. It appears in the Meridian at Midnight , in the Moneth of February . Leo. s This Constellation in Greek bears the name of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; to which the Latine Virgo answers . In Hebrew it is call'd Bethula ; in Syriack , B●…thulto ; in Arabick ; Adra , and Adrenedepha ; and in the Persian , D●…shiza Pakiza , all to the same sence with the former ; in the Aegyptian or Coptick , it is called Aspholia , i. e. Statio Am●…ris ; It is likewise in respect of the chief Star by which it is signaliz'd , being one of the first Magnitude in her left hand ( though Vitruvius and Hyginus erroneously place it on her right , ) call'd by the Hebrews , Shibboleth ; by the Syrians , Shev●…lto ; by the Arabs , Súmbela ; by the Persians , Chûshe ; and by the Turks , Sálkim ; All signifying a Spike , or Ear of Corn. In this Sign ; Ptolomy reckons thirty two Stars , six whereof inform ; Kepler thirty nine , and Bayerus forty two , of which the sixth and seventh Stars are by the Arabs called Min al Auwa , i. e. de latratore ; and so likewise the tenth . The seventh is by them called Zawija al Auwa , i. e. Angulus Latratoris . The thirteenth , which is also one of the first Magnitude in her right wing , call'd by Proclus 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Praevindemiator , is by the Arabs in the same signification called Mûkdim al Kétaph . The fourteenth , which is the Spica , is by them likewise call'd Simak al A'zal , i. e. Efferens Inermem , scil . Virginem ; to distinguish it from another Star , in Bootes , call'd Simâk al Ramih , i. e. Efferens Hastiferum , vulgarly , but corruptly call'd Azimeth and Huzimeth , and by S●…aliger , ( but amiss ) Huzmet al Hisál , i. e. Fasciculus frumenti vel segetis . The twenty second , twenty third , twenty fourth and twenty fifth Stars are call'd Min al Gaph'r , i. e. Ex al Gaphr , which signifies Velamen , Ventrem & Tect●…ram , Quòd Stellae ejus obtectae sint . This Sign according to the Vulgar Opinion , is taken for Astraea , o●… Justice , by others , for Erigone , Daughter of Icarius , ( so Servius . ) Others suppose her to be Ceres , quòd s●…icas teneat , ( says Bassus . ) Others call her Atergatis , the Goddess of the Ass●…rians . Some will have her to be Fortune , pro eo quòd sine Capite Astris infer●…ur , says the same Bassus . Avienus makes her to be Isis ; and others again will have her to be Concord , or Peace ; for which Opinion ( says Vossius l. 2. Idol . ) makes the Figure in Commelins Antient Manuscript of Hyginus , and that of Grotius in Germanic . Arat. ubi manu dextrâ Olivam , sinistrâ Caduceum tenet , as commonly the Antients represent Peace . Ceres is Lady of this Sign , which visits the Meridian at Midnight about the end of March , and beginning of April . t This Asterisme by the Greeks is call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; to which the Latine Libra answers ; by Cicero it is called Iugum , particularly answering to the last of the Greek names . In Hebrew it is called Mozenâim ; in Syri●…ck , Masáth●… , in Arabick , al Mizan ; by the Persians , Terazu : All signifying Libram , Stateram , seu Bilancem . The Turks commonly use the Arabick name Mizan , which by them in their Language is explain'd Tartagick alati , i. e. Ponderandi Instrumentum . In the C●…ptick it is call'd Lamb●…dia , i. e. Statio Propitiationi●… . The Constellation is made up of seventeen Stars , according to Prolomy , whereof nine inform ; Bayerus reckons but fifteen , Kepler eighteen . Among which the first Star in Account , by the Greeks called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , is by the Arabs , in the same signification , call'd Zubâna Gjenubi , i. e. Chela australis , and Al Kiffa , Al Gienubija , i. e. Lanx australis ; the third , call'd by the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , is accordingly by the Arabs call'd Zubâna Shemâli , i. e. Chela Borealis , and al Kiffa al Shemâlija , i. e. Lanx Borealis . This Sign owns Vulcan for its Patron , and is famous for being ascendant in the Horoscope of Rome , at its Foundation , according to the Calculation of Lucius Tarruncius Firmanus , as Cicero witnesses ( l. 2. de Divin . ) There is no distinct Fable of this Sign , it being part of Scorpius , whose Chelae or Claws ( by the Arabs call'd Zubâna ) make ▪ the Scales ; Hence our Authour , lib. 2. Scorpius in Librâ Consumit Brac●…hia . — It mounts the Meridian at Midnight in the beginning of May. Virgo . Libra . u The Hebrews call this Sign Akrab , pro Akatzrab , à magno aculeo ( mediâ vocis literâ per compendium elisâ ) according to Bochart his Interpretation . The Syrians call it Akr●…vo ; the Arabs , Al Akrab ; the Persians , Ghezdum ; the Turks , K●…irughi , quasi 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Caudatus , or Uzûn Koirughi , i. e. longá Caudâ praeditus . By Cicero it is call'd Nepa ▪ which Festus says is an African Word , happily a Phoenician says Bochartus , Neb or Nebba ( b chang'd into p ) à Caudae Internodii's ; by the Greeks ; 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; and by the Aegyptian Copties , Isias , i. e. Statio Isidis . There are counted therein by Ptolomy twenty four Stars ; whereof three shapeless ; by Kepler ▪ twenty eight ; by Bayerus twenty nine ; of which the six first are by the Arabs call'd I●…lil al Gieb'ha , i. e. Corona Fro●…tis , and simply I●…lil ▪ Corona . The sixth is particularly called Gieb'ha al Akrab , i. e. Frons Scorpii . The eighth is by them called Kalb ' al Akrab , i. e. Cor Scorpii , &c. In Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Tyrannus . On each side of which Star there are two others , by the Arabs call'd al Niyât , i. e. Praecordia . The twentieth and twenty first they call al Shaula , which properly signifies the Tail of a Scorpion , and not of any other Creature . From which name al Shaula , not rightly read or written , have proceeded the corrupt names of Shomleck , Moshleck , and alasha , commonly found in most Authours . The Scorpion is fabled to have been made a Constellation , for having slain Orion , who boasted he would in Hunting destroy all the Wild Beasts in the Forrests ; or according to Nigidius , for that hunting with Diana in the Mountain Chelippius in the Island Chios , he contemn'd and derided her , as inferiour to him in Skill ; or according to Palaephatus and Ni●…ander in Theriac . for daring to have violated her Chastity ; for which in Revenge , she is said to have sent this Scorpion to sting him to death ( though Horace says he was — Virgineâ domitus sagittâ ) being for that , at her request , by Iupiter made an Asterism in Heaven ; owning Mars for his Deity ; and is seen to crawl toward the Meridian at Midnight , about the end of May and beginning of Iune . Scorpio . x This Constellation is in Hebrew call'd Kesheth ; in Syriack , Keshto ; in Arabick , Al Kaus ; in the Persian Tongue Kamân ; in the Turkish , Yai . All signifying an Arrow . In Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Sagittarius ; according to which signification it is likewise by the Arabs call'd al Rami ; by the Aegyptians , Pimaere , i. e. St●…tio Amoenitatis ▪ It consists of 31 Stars , as Ptolomy reckons ; of 32 , as Bayerus ; of 34 , as Kepler . Of which the first is by some among the Arabians call'd Zugi al Nushaba , i. e. Cuspis , vel Ferramentum Spiculi . But both that and the second in Ulugh Beighs Tables ; Min al Nâaim , al Wârida , i. e. E pecoribus ad●…untibus ( scil . ad aquam ▪ ) The 6th and 7th according to those Tables , Min al Nâim , al Sadira ; i. e. E pecoribus redcuntibus ( scil . ab aquatione . ) The 8th Star in this Constellation , is by the Arabs call'd Ain al Rami , i. e. Oculus Sagittarii . The 23d Urkûb al Rami , i. e. Suffrago ; the Hough or Pastern . The 24th Rukb●… al Rami , i. e. Genu , the Knee of Sagittarius . Hyginus , from the Authority of Sositheus , will have this to be Crotus , the Son of Euphemis , or Eu●…hemis , the Nurse of the Muses , at their instance by Iupiter plac'd in the Zodiack . Others will have him to be Chiron . This Sign is under the Tutelage of Diana , and of Apollo likewise , to whom it is sacred ; as Tristan , in his Com●…entar . Tom. 3. evinces , from the Coyns of Gallienus , on some of whose Reverses is stamp'd the Figure of Sagittarius , with this Inscription , APOLLINI CONSERV . AUG . This Sign at Midnight aims at the Meridian , about the end of Iune , and beginning of Iuly . Sagittar . y The Greeks give to this Sign the Name 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; The Latines , Hircus Aequ●…ris ( so Asclepiadius and Vomanus ) and Pelagi Procella ( so Vitalis ) by Horace being styl'd , — Tyrannus Hesperiae Capricornus undae . In Hebrew , it is call'd G●…di ; in Syria●… , G●…dio ; in Arabick , Al Gjedi ; in the Persian , Buzegh●…le ; in Turkish , Uglack ; all signifying a Kid or Goat . In the Coptick or Aegyptian Tongue it is call'd Hopeutus , i. e. Brachium Sacrificii . It is made up , by the joynt Account of Ptolomy , Kepler and Bayerus , of 29 Stars ; of which the first and third are by the Arabs call'd Min Sad Al D●…ih , i. e. Ex fortuna Mactantis ; and simply , D●…bigh , i. e. Mactans . The 23d and 24th Stars are call'd by them , Sad N●…shira , i. e. Fortuna averruncantis , vel divulgantis Nuncium . But the 24th by a particular Name , from its situation , is called Da●…ab Al Gjedi , i. e. Ca●…da Capricorni . This was made a Constellation in honour of Aegip in the Son of Iupiter , by the Olenian Goat , or rather his Foster Brother , Son of Aega the Wife of Pan , whence his Name ▪ who as Bassus in Germani●… . from the Authority of Epimenides , writes , assisted Iupiter in his Wars against the Titans , and armed the God ; and for that reason honoured with this Coelestial Dignity . The reason of his being figur'd half Goat half Fish , Theon the Scoliast of A●…atus reports , was , for that he finding on the Sea-shore an empty Murex or purple shell , is said to have wound it like a Horn , thereby striking a Panick ●…ear into the Titans , and therefore they represented him with a Tail like a Sea-Mons●…er . Celebrated it is according to the Doctrine of the Pythagoreans , and Platonists , for being the Gate , by which Souls ascend into Heaven ; and therefore stil'd Porta Deorum : Nor less Famous , to use our Authours Words , — In Augusti foelix quòd fulserit Ortum . Of which see Suetonius in August . Scaliger in Manil. ●…ct . Sam. Petit. in Observa●… . l. 1. c. 5. Vindelinus and Albertus Rubeniu●… upon that subject ; Ricciolus in Chronolog . reformo 〈◊〉 . T●…m . 1. l. 4. p. 104. and Spanhemius in Dissertat . de Numismat . Vesta is the Goddess appropriate to this Sign . It climbs the Mid-heaven at Midnight , about the end of Iuly , and beginning of August . Caprico : z This Sign is by the Greeks call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; by Appian , Hydridurus , and in the same signification by the Arabs , Sakib Al M●… , i. e. Effus●…r A●…uae . It is by them likewise called Al Delu , and in H●…brew , Deli ; in Syriac , Daulo ; in the Persian Tongue , D●…l ; in the Turkish , K●…gha ; all signifying a●… Urn , or Watring-pot . The Aegyptians or Copties , call it Hup●…utherian , i. e. Brachium Beneficii . There are reckon'd therein according to Ptolomy and Kepler , 45 Stars , whereof three inform . Bayerus yet reckons but 41. Of which the 2d and 3d are in Arabick call'd Sa'd Al Melick , or Sa'd Al Mùlck ; the first signifying fortuna Regis , the later , fortuna Opum & Substantiae . The 4th and 5th are call'd Sa'd Al Suûd , i. e. fortuna fortunarum ; under which are some other Stars of less note call'd Al An●… . The 6th and 7th are call'd Sa'd Bulâ & Al Bul●…an , i. e. fortuna Deglutientis , or D●…glutientium . The 9th , 10th and 11th Stars are call'd Sa'd Al Ahbija , i. e. fortuna Tentoriorum . The 14th Star in this Constellation , being one of the first Magnitude , is in Arabick call'd Diphd●… al Auwal , i. e. Rana Prima ; It is likewise call'd Phom al H●…ut al Gje●…bi , i. e. Os Piscis Australis , commonly , but corruptly , Phomahant . This Asterism is by some fabl'd to be Ganym●…de the Cup-bearer of Iupiter , by some Deucalion ; ( whence by Vomanus this Sign is entituled Deucalionis Aquae ; ) by others , Aristaeus ; of which , see the Scholiast of Germanicus . It is seen in the Meridian at Midnight , about the end of August , and beginning of September ▪ Iuno is its Lady Regent . Aquar . a This Sign in the Greek is call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and by the Iews accordingly Dagáim , i. e. Duo Pisces . But the Arabs call it Al H●…ut , & Al S●…maca ; the Syrians , Nâno ; the Persians , M●…hi ; the Turks , Balick , which signifies a Fish in the singular number ; so likewise in the C●…ptick , it is call'd Pikotorion , i. e. Piscis Hori . The Northern of these Fishes is in the Arabick call'd Haut Ash●…li , i. e. Piscis B●…realis , and is known by the peculiar Name of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , as being represented by the C●…ns with the Head of a Swallow ; the reason as Scaliger conceives , because when the Sun is in that Sign , the Swallow begins to appear in those Regions . The Southern is call'd Haut al Gjenubi , i. e. Piscis Australis . The whole Constellation consists , according to Ptolomy , of 38 Stars , ( whereof four inform , ) according to Bayerus of 39. But Kepler reckons therein 59. The Stream , or Tenuis fusio Stellarum utris●…ue Piscibus disposita , Vitruvius , l. 9. c. 7. calls 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Mercuri●… Donum s●…u Delici●…s , which Scaliger conceives ought to be read 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Laqueum ; or as Pliny terms it , Commissuram Piscium . The Compiler of the Vitruvi●…n Lexicon seems to come nearer to the truer Reading , and will have it to be 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Nodum , or to use the Words of the said Lexicon , Coaptatimem qua Piscis Pisci seu vinculo al●…gatur ; by Proclus call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , by Aratus , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which Cicero renders Coelestem Nodum . The Arabians call it Ch●…it , vel Ch●… Kettani , i. e. Filum Linteum . These are fabled to be the Syrian Deities according to Germanicus , Syriae du●… Numi●…a Pisces , by which are understood Venus and Cupid , as Hyginus ( from the Authority of Diognetus Erythraeus ) writes . For Venus and her Son Cupid coming to the River Euphrates , and frighted with the suddain appearance of the Gyant Typ●…n , cast themselves into the River , and assum'd the shapes of Fishes , by which means they scap'd from danger . For this reason the Syrians abstain from eating of Fish , lest they might happen to devour their Deities . But the Scholiast of Germanicus ( from Nigidius ) writes , that these were the Fishes , which turn'd or roll'd up upon the Bank of Euphrates a great Egg , upon which a Dove sitting , hatch'd Venus , the Syrian Goddess . The Exposition whereof , see in Beyerus in Additamen ▪ in Seldeni System ▪ de Diis Syriis , p. 290. This Sign is under the Patronage of Neptune , and is seen in the Meridian at Midnight , almost throughout the whole Moneths of September and October . Pis●…es . b The Axis of the World ( so called ab 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , v●…lvo ) is an Imaginary right Line , passing through the Center of the Mundane Sphere from North to South , whose extremities are terminated in the superficies thereof ; the two points term●…ating the said A●…is being called the Poles of the World : About which immoveable Line the Sphere it self is turned . By this Description it may appear that the Axi●… of the Sphere is likewise the Diameter thereof ; but on the contrary every Diameter thereof is not its Axis ; because the Sphere is not turned about every Diameter , but only about that , which is extended from North to South . Vid. Cl●…v . in Sacrobosc . The Axis of the World , and the Poles . c To this purpose Achilles Tatius in A●…at . Phaenom . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , &c. Of the M●…teriality of this Axis , ( though some Philos●…phers have conceiv'd i●… a Spirit passing through the interjected Mundane space ) Aratus ( saith he ) hath taught us n●…thing . For if any shall conceive it to consist of a fiery substance , when it passes through the Sphere ●…f the Water , it would be extinguish'd , or consum'd by the Sphere of the fiery Element ; or should it be supposed to consist of any other of the Elements , as of Air or Water , it would not mix with the others , but would be destroy'd by its contraries : Wherefore Mathematicians have defin'd it 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Li●…eam quandam subtilem , seu tenuem , and is here by our Authour excellently described . d Homer and most of the Antient Poets seem to attribute to the Sphere of the World a kind of Gravity or tendency downward , and for this Reason they describe it to be supported by A●…las . But this Fancy Aristotle eludes in his Book De Communi Animalium Mo●…u , by applying ( not unappositely ) the Fable of A●…las to the Axis of the World , upon which it is imagined to be supported and turned about . The Constellations of the Northern Hemisphere . e So named by the Greeks , quòd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. volvitur ( Circa Polum A●…ticum : ) It is likewise called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Ursa Major & Plaustrum Majus . In Arabick ( according to Ulugh Beigh ) Dub Ackber , i. e. Ursus Major in the Masculine Gender ; as likewise Agala , i. e. Plaustrum seu v●…hiculum ▪ from whence by the change of one only Letter , is that corrupt Name of Aganna , mentioned by Scaliger from Hesychius . It is likewise by the Arabs call'd Benât Al Nash Al Cubra , i. e. Filiae feretri Majoris , in regard the four Stars that make the Body of the Bear resemble a Bier , and the three in the Tayl , the Virgins or Maids that attend the Corps . And for this reason saies Kircher the Christian Arabs call the four Stars in this Constellation , Nash L●…ázar , i. e. Feretrum Lazari ; and the three in the Tayl , Mary Magdalen , Martha and their Maid . By the Persians it is call'd Haphtûrengh Mihîn , i. e. Septentrio Major ; and by the Turks , Yidigher Yilduz , i. e. Septenae stel●…ae ; and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Yidigher , i. e. Septenae ; as by the Latines , Septem Triones , quasi Teriones , à terendo semitam circa Polum . The whole Constellation consists according to Ptolomy of thirty five Stars , whereof eight inform ; according to Bayerus , of thirty two ; Kepler yet reckons fifty six ; among which the twelfth and thirteenth Stars are in Arabick call'd Al Nekra Al Th●…litha , i. e. Cotyle , Scrobs seu Cavitas ossis Tali . The sixteenth D●…br Al Dub Al Ackber , i. e. Dorsum ursi Majoris : The seventeenth Merák Al Dub Al Ackber , i. e. Epigastrium ursi Majoris . The eighteenth Meg'res Al Dub Al Ackber , i. e. Uropygium ursi Majoris . The nineteenth is call'd Phaid Al Dub Al Ackber , i. e. F●…mur ursi Majoris ; and these four last named , make up Al Na'sh Al Cubrá , Feretrum Majus . The twentieth and twenty first Stars are called Al Phikra , or rather Al Nekra , Al Thanija , i. e. Vertebra seu Cotyle secunda . The twenty third and twenty fourth Al Phikra , or rather Al Nekra , Al Ula , i. e. Vertebra seu Cotyle prima , as the Commentator upon Ulugh Beigh his Tables would rather have it read in both Places . The three Stars , that make the Tayl , are call'd Al Benát , i. e. Filiae : Whereof the first is called by some Al Haun , or Al Gjaun , signifying albam Nubeculam ; by others , Al H●…er or Al Haur ( commonly but corruptly , Alcor ) i. e. Albedo oculi , or Populu●… Alba. The second is called Al In●…k , or Al An●…k , i. e. Capella . The third Alkaid , i. e. Gubernator . This Constellation was first found out by N●…uplius , as Theon , the Scholiast of Aratus , affirms , and was antiently the Greek Sea-mans Guide , as the lesser , the Phoe●…icians : The Reason ; because to the Greeks , who sayl'd the Mediterranean , Pontick and Euxine Seas , this Constellation was still apparent , but to the Sidonians , Phoenicians and Carthaginians , who were more Southerly , part of the greater Bear was either by the Position of Sphere , or some other Accident , sometimes deprest and obscur'd ; but Cynosura always apparent to them ; whence that of Valerius Flaccus in Argonaut . — Certior in Tyrias Cynosura Carinas . And therefore these last chose the lesser , as the Greeks the Greater Bear for their Directress . Vide Ricciol . in Almagest . Nov. f La Cerda explicating this Verse of Virgil's ( in Georg. 1. ) [ Maximus hic flexu sinuoso elabitur Anguis ] Cites these Verses ; and conceives by the greater Bend and lesser Orb , our Poet means the greater and the lesser flexure of the Serpent ; that is to say , that of the Tayl ( being the larger ) about Helice , that of the head ( being the more contracted ) about Cynosure . But this is far from the meaning of Manilius , whose sence is this , that Helice being more removed from the Pole , makes by its Circumgyration a larger Circle than Cynosura , which being nearer to it , must consequently make breviorem 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , as Grotius ( in Arat. Phaenom . ) terms it : This Interpretation is confirm'd by these Verses of Aratus , to which doubtless ou●… Authour had respect . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Multa lucens Helice primâ à Nocte : Altera vero parva , s●…d N●…utis Melior ; Minori enim Tota convertitur Orb●… . To which purpose see likewise Theon , the Scholiast of Aratus . Helice . g So called by the Greeks , quasi Canis Cauda , or as V●…ssius ( l. de Scient . Mathemat . c. 32. ) derives it from the Hebrew ▪ , Ura , i. e. Lumen , flamma , Ignis ; and Nghus , i. e. coligere , ut sit Cynosura quasi Collectio luminis seu Ignis , or from the Chaldae●…n , Kinush , i. e. Umbilicus ; for by its Conversion is made a small Circle , as it were Umbilicus Igneus . The Hebrews call it Genash , i. e. Gallinam cum filiis suis , as Kircher expounds it . By the Arabs it is called Dub Asgher , i. e. U●…sus Minor , and Benat al Mash al Sughra , i. e. Filiae Feretri Minoris ; by some of them it is called Agiala , i. e. Plaustrum , and by Scaliger and Schickardus Al Rueba , vel Arrucba , which yet Mr. Hyde says is not to be sound in any Arabick writer , unless happily they derive it from the Chaldaick Recubà or Recuvà , which signifies Currum , vel V●…hiculum . By the Persians it is call'd Haphturengh 〈◊〉 i. e. S●…entrio Minor. The Star in the Extremity of the Tayl is by the 〈◊〉 call'd Caucab Shem●…i , i. e. Stella Borealis ; by the Turks , Yilduz Shemali , and absolutely Yilduz , i. e. Stella ; and by a peculiar Name in Arabick it is called Gjedi , i. e. Hoedus . The Italians call it Tramontana ; and we the Pole , or North Star. The two last and brightest in the Feretrum or square , are by the Arabs call'd Al Phercadân or Al Phercadein , i. e. Duo vituli . The whole Constellation consisting according to P●…olomy and Bayerus of eight Stars , whereof one inform ; as Kepler reckons , of twenty . Of the Fabulous Anastr●…sis of this and the former Constellation , Diodorus Siculus Biblio●…b . Histor. l. 4. reports , that these were the Nurses of Jupiter , and privately kept him from the search of Saturn ; for which they were by him in Gratitude plac'd in the Heavens , and call'd by the Name of the two Bears , being worshipped with Divine Rites , by the Cretans and Sicilians ; by whom they were styl'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Deae Matres . Others refer it to the Fable of Callisto and her Son Arcas , of which see Hesiod and Ovid. This Constellation was ( among the Greeks ) first discovered by Thales the Milesian , as ( besides Theon and Laertius from the Testimony of Callimachus ) Hyginus , l. 2. Astronom . Poet. affirms , for which reason it was call'd likewise Phoenice , from Thales its Inventor being by descent a Phoenician , who first gave it the Name of Arctos , or the Bear. But trulier so denominated , from the whole Nation of the Phoenicians , who in their Navigations ( and that long before the time of Thales ) observ'd her , as their Directress : See Palmerius his Learned Exercitations , p. 445 , and 446. 〈◊〉 h Of the frequent Voyages of the Phoenicians and Carthaginians into the Atlantick Ocean , and their Discoveries of the Western Coasts of Africk , and a large and wealthy Island in that vast Ocean ; See Diodorus Siculus Biblioth , l. 5. and Aristotle ( in Admirand . Audition . ) which forementioned Island Turnebus ( l. Adversar . 20. c. 11. ) conjectures to have been some part of America not fully discovered ; of which Opinion likewise is Cluverius ( in Sicilia Antiqu. l. 2. ) And for further proof of the Punick Navigations , we have the Periplus of Hanno yet extant ; though by many as well of the Antients , as Moderns , supposed a Fiction ( whence the Proverb , applicable to a credulous Person , Dignus est quem oblectent Lybici libri de Erroribus Hannonis , as Casaubon notes in his Animadversions on Athenaeus ) yet is the truth thereof asserted by the learned B●…chartus in Geograph . Sacra ; and by Mr. Vossius ( in Melam ) commended as a signal Monument not only of Historical Verity , but of Antiquity likewise , beyond any Extant Remains of Graecian Learning . i This Constellation the Poets feign to have been the Dragon that kept the Hesperides slain by Hercules , and made an Asterism by Iuno . Others ( says Stoefler ) will have the Dragon to be brought by the Gyants in their fight with the Gods to oppose Minerva , and by her to have been strangled and thrown up to Heaven , and there fixt as a Trophy of her Victory . This by the Greeks is call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; by the Latines , Draco ; in Hebrew , Tannin , i. e. Draco ; by the Arabs , Tinnin and Tannin , as the Hebrew : it is by them likewise call'd ( according to Kircher ) Taaban , or rather Thuban , and in the same sence by the Persians , Ashdeha , which is interpreted Serpens , qui Homines ac Bestias devorat . Some among the Arabians give it likewise the Name of Al Haija , which is also appropriate to the Southern Constellation of the same kind . It is made up ( as Ptolomy reckons ) of 31 Stars ; as Kepler , of 32 ; as Bayerus , of 33. Of which the first Star in the Tongue is by the Arabs call'd Al R●…kis , or Arrakis , i. e. Saltator , seu Tripudiator , the three next Al Awaîd , i. e. Pulsatores Testudinis . The fifth in the Head is call'd Ras Al Tinn●…n , i. e. Caput Draconis . The 14th , 15th and 16th Stars are call'd Al Thâphi , i. e. 〈◊〉 , from their Posture , representing a Skillet with Feet Tripod or Brandiron . The 20th and 21th are called Adphar Al Dib , i. e. Ungula Lupi . The 27th is called Aldibe●… , i. e. Victima , as being plac'd before that in the Horn of Capricorn , call'd Sa'd Al Da●… , i. e. F●…rtuna Mactantis . This is seen in the Meridian at Midnight about the end of Iune . k Macrobius ( in Somn. Scip. l. 1. c. 18. ) Septentrionum quoque Compago non solvitur ; Anguis qui inter eos labitur semel circumfusum non mutat amplexum . l From the Philosophy of the Egyptians , of which thus Diogenes Laertius in Prooem . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i e. That the Stars are of a fiery Nature , and that by their Contemperation all Things are produced on the Earth . To this Effect is that Caballistick Maxim , Non est Herba inferiùs , quae non habeat S●…ellam superiùs , qu●… dicat ei Cresce ; of which Kircher in Magnet . Natur. Regn. Sect. 2. c. 3. m This Asterism in Greek bears the Name 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Ingeniculus ; It is likewise call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Clavator s●… Claviger , and by some of the Latines , Nisus vel Nixus , quia Laboranti similis . By the Arabs Giathi ala Rucbatei●…i , i. e. Incumbens Genubus , ( from which corrupted may come those commonly mistaken Names of Elgiaziale and Rulxba●…ei ) by the Persians interpreted Bersanu Nisheste , i. e. genubus insidens , from whence the Commentator upon U●…ugh Beigh conceives the corrupt Persian Name , Ternevelles Sandes , may be deriv'd ; which he supposes ought to be read Zurnai , vel Zernai Zan ; implying as much as fistulator , sive vir aureo canens calamo . The number of Stars in this Constellation are by Ptolomy reckon'd to be 29 ; by Bayerus , 48 ; by Kepler but 28 ; of which the first is called Ras Al Gi●…hi , i. e. Caput Ingeniculi , and commonly , but falsly , Ras Al Aben. That in his Elbow from its situation is called Marphak ; that in his Wrist Mi ' sám , i. e. Carpus , and by mistake commonly Maasym . This Constellation some will have to represent Theseus , or Ixion ; others , Orpheus or Prometheus ; others , Thamyris or Thamyras a Thracian Poet , who contending with the Muses for Skill , and by them overcome , was punish'd with the loss of his Eyes , and in the Memorial of their Victory plac'd in the Heavens in a supplicating posture , as deprecating his punishment . But Panyases ( in Heraclid . ) will have this Asterism to represent Hercules ; so likewise Hyginus from the Authority of Aeschylus , with whom agrees the Scholiast of Germanicus . This comes to the Meridian at Midnight in the Moneth of Iune . Engonasi . n Arctophylax and Boötes are one and the same Constellation ; the first signifying Custos Ursarum ; the later so call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Bovis , & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. pellere , quasi Boum Agitator , to which Name our Authour alludes ; but in the Eastern Tongues the same seems to be deriv'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. à Clamando , whence by the Arabs call'd Al Auwa , i. e. V●…ferator , and Al Neckar , i. e. Fossor seu Pastinator . It consists according to Ptolomy of 23 Stars , Kepler counts 28 , and Bayerus 34. This some Fable to be Lycaon ; Others Arcas , the Son of Callisto his Daughter by Iupiter . The Scholiast of Germanicus makes it to be the Constellation of I●…arus , and accordingly Propertius stiles the Septentriones , I●…arus his Oxen , in this Verse ; Flectant Icarii Sidera tarda B●…ves . This is seen in the Meridian at Midnight about the beginning of May. Arctophylax or Bootes . o Some will have this Star so call'd , quasi ab 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. à Cauda Ursae , but trulier ab 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Custos Ursae , in the same sence as Arctophylax . This the Arabs call al Simak al Râmih , i. e. efferens H●…stiferum ; in the common Globes falsly Huzme : Tzetzes says it is likewise call'd by the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and in Chrysococea's Persian Tables ( published by E●…lialdus at the end of his Astronom . Philolaic . ) it is called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Hastili aut Conto armatus . It is a Star of the first Magnitude , by Vitruvius plac'd Media Genuorum Custodis Arcti , but according to others in the knot of Arctophylax his Girdle ; so Germanicus in Ara●…is ; Arcturum dicunt sidus quà vincula nodant : Arcturus . p This by the Greeks is call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Corona Borealis , & Prima ; And accordingly by the Arabs , Al I●…lil Shemali , i. e. Corona Borealis , and simply Al I●…lil , i. e. Corona ; it is by them likewise called Al Phecca , i. e. Apertio ; in Hebrew Kir Schetali , i. e. Corona Sinistra , and in Chaldee Malphelcarti , i. e. Sertum Pupillae . The Constellation is in form of a Circle , not compleated , and therefore by the Vulgar Arabs call'd Kâse Shekéste , i. e. Scutella fracta , and Kas●…hi Dervishan , i. e. Scutella pauperum , and in the same sence , by some of them Kasa Al Masakin , or Alsa●…lik . In 〈◊〉 's Tables 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Discus fractus . The brightest in this Circle being of the second Magnitude , is call'd Lucida Coronae , and by the Arabs , Nair Phecca , i. e. Lucida Pheccae , & Mumir , i. e. Pupillae . It consists according to Ptolomy and Kepler of eight Stars , yet Bayerus reckons twenty . This Crown some fable to have been of Gold : Athenaeus l. 15. from the Authority of Timachides , says it was made of a Flower or Herb , call'd Theseus ; others will have it to be of Lawrel or Myrtle : Bayerus from some Antient Greek Coyns describes it to have been composed of Elder Leaves , mix'd with Berries . Ph●…tius in Bibliotheca ( out of P●…olomaeus Ephaestionis his fifth Book Nov. Histor. ) gives this Fable thereof . They report ( saith he ) that a certain Nymph named Psalacantha in the Island Icaria being in love with Bacchus , endeavoured to procure Ariadne to his Bed , on condition , he would likewise be kind to her : Which Bacchus refusing , she plotted to do Ariadne a Mischief : This the God discovering , he in Passion transform'd her to an Herb bearing her Name : But afterwards repenting the Fact , by way of Recompence and Honour he caus'd the Flower to be entwin'd about Ariadnes Crown , which he had already fix'd in the 〈◊〉 . As to the Fable of Ariadne deserted by Theseus in the Island Naxos , and reliev'd by Bacchus , the same is sufficiently known . And though most make only her Crown to be constellated , yet others place Ariadne her self in Heaven ; as Sca●…iger hath observ'd in his Notes upon Catullus his Poem de Coma Berenices , of which Opinion likewise is Propertius in these Verses ; Te quoque enim non esse rudem testantur , in Astris Lyncibus in coelum vecta Ariadna tuis . To which as a further Proof we shall add the Testimony of one of Nero's and another of Trajan his silver Coyns , having on their Reverse , the Figure of Ariadne , carried up to Heaven in the same manner , as is represented by Propertius ; touching which see Monsieur du Choul , de la Religion des Anciens Romains ; and Occo in Nu●…ismat . p. 199. Videsis etian●… Tertullian . in Sc●…rpiace , & Pascalium de Coronis . Ariadnes Crown . y This Constellation is call'd Pegasus , by the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . It is called likewise Equus Major , Medusaeus , Gorg●…nius , Beller ph●…maeus and Me●…ppe , or rather Melanippe ; by the Arabs , Al Pharas Adam , i. e. E●…uus Major , and Alpharas Al Th●…ni , i. e. Equus Secundus , to distinguish it from the Equus Mi●…r , omitted by our Poet. In Hebrew it is call'd Ha Sus chail Kernim , i. e. Equus 〈◊〉 . It consists according to P●…olomy of twenty Stars ; according to B●…yerus and Kepler , of twenty three . Among which the Chief ( being in Umbilico Equi ) is promiscuously reckon'd as appertaining to the Head of Andromeda , as well as to Part of this Constellation , and therefore by the Arabs called as well Ras Al Mara Al M●…salsala , i. e. Caput Mulieris Catenatae , as Sirra Al Pharas , i. e. Umbilicus Equi . That in the joyning of the Wing is call'd 〈◊〉 , i. e. Equitandi vel vehendi locus , Sagma , Ephippium . The third Star is call'd by them Menkib Al Pharas , i. e. Hu●…erus Equi . The fourth they call Mat'n Al Pharas , i. e. Lumbus Equi , vel Dorsum . The fifth and sixth Stars are call'd Alkerb , vel Alkereb , i. e. Funis . The seventh and eighth Sa'd Mátar , i. e. Fortuna Pluviae . The ninth and tenth Sa'd Bari , i. e. Fortuna praecellentis . The eleventh and twelfth Sa'd Al Homam , i. e. Fortuna Herois , vel Sad Al Hamm●…m , i. e. Fortuna Obtrectatrieis . The fifteenth and sixteenth are call'd Sa'd Al Bahâim , i. e. Fortuna Besti●…rum . In the Common Globes for Sa'd is mistakenly put Sheat . The sevent●…enth Star is call'd Phom Al Pharas , i. e. Os Equi , and Gjahphela Al Pharas , i. e. Labrum Equi ; by others Enph or Emph Al Pharas , i. e. Nasus Equi ; this some will have to be Bellerophons ; others Perseus his Horse : Callimachus and Catullus call him Unigenam Memnonis , Brother of Memnon and Son of Aurora . The Greek Commentators make him to have been presented by Aurora to Iupiter ; but Lycophron describes him to be the winged Steed of the Morning , upon which she is said to ride . Palaephatus and Artemidorus yet make Pegosus to be a Ship and not a Horse ; so Sch●…ffer de Mi●…it . N●…vali , l. 1. c. 4. and according to Vossius , ( l. 3. de Idololatr . ) The Name Pegasus seems to be derived à 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , sive 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. compingo , quia Navis è multis componitur lignis . It is seen in the Meridian at Midnight about the middle of August , and beginning of September . Pegasus . z This Asterism is by the Arabs call'd Al Mara Al M●…salsala , i. e. Mulier Catenata . In Hebrew Isha Shalahajala B●…al , i. e. Foemina c●…rens viro. It consists of twenty three Stars according to Ptolomy and Kepler ; according to Bayerus , of twenty seven . Among which the twelfth is by the Arabs call'd Gjemb Al Mosalsala , i. e. Latus Catenatae , and Bet'n Al Hut , i. e. Venter Piscis . That in her Zone or Girdle is for that reason by them call'd Izar and Mizar , whence come the corrupt Names of Mirach , Mirar , Mirath , and Miraz . The twenty first Star being in the Hem or Border of her Vest is therefore by the Arabs call'd Al Deil , vel Addeil , i. e. Syrma seu Lacinia Vestis . The fifteenth is called Rigil Al Mosálsala , i. e. Pes Catenatae ; by Ulugh Beigh , Anâk Al Ard ; which Scaliger and others will have to be read Al Amach or Almâk , i. e. Cothurnus ; which Errour Mr. Hyde from good Authority consutes , and thews that Anâk is a little Beast , by the Persians call'd Siyâh Gush , i. e. Nigra Au●…icula , ( the Epithete of Al Ard , i. e. Terrestris being added ) from its Ears which are black ; It s whole Body besides being of a Brown or Ruddy Colour ; and is Usher to the Lion , when he hunts for his Prey . We call it a Jack-call , for by his barking he calls the Lion to the Place , where his Prey lies . It comes to the Meridian at Midnight about the middle of October . As to the Fable of Andromeda ; see after in the Notes upon the Whale , and in the Appendix or Comment . Andromeda . a Was the Grand-child of Acrisius , King of the Argives , begotten by Iupiter on his Daughter , Danae , plac'd in the Heavens by favour of Minerva for having slain Medusa or the Gorgon , and freed Andromeda from the devouring Sea Monster . This Constellation is by the Arabs call'd Cheleub or Chelùb , i. e. Deceptor ; or ( happily ) Kellùb , i. e. H●…rpago , seu aduncum quodvis , ( says Mr. Hyde ; ) and from the Greek Name Perseus , Bershâush and Bersheush . It is likewise call'd by them H●…mil Ras Al Ghùl , i. e. Portans caput Larvae . It consists of twenty nine Stars according to Ptolomy , whereof three inform ; Bayerus reckons thirty eight ; Kepler thirty three ; whereof the first is call'd Misam Al Thuraiyâ , i. e. Carpus Plei●…dum , and Al Gjemb Bershâush , i. e. Latus Persei . The twelfth is call'd Ras Al Ghùl , i. e. Caput Larvae . By the Iews , R●…sh ha Sathan , i. e. Caput Diaboli . The twenty fourth Star is in Arabick call'd Menkib Al Thuraiyâ , i. e. Interscapilium Pleiadum . This Constellation is seen in the Meridian at Midnight in the Moneth of November . Perseus . Deltoton or the Triang●… . b Call'd likewise Trigones , and Delta , by the Latines Triangulum , and Nili Donum ; by the Arabs , Mothallath , i. e. Triangulum ; In Hebrew , Hammosciush , i. e. Tripartitus . It consists of four Stars according to Ptolomy and Kepler ; Bayerus reckons five , whereof that in the top of the Triangle is call'd in Arabick , Ras Almothallath , i. e. Caput Trianguli . This is said to have been plac'd in Heaven by Mercury in Memorial of the first Letter of Iupiters Name 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , of which Grotius in N●…t . ad Arat. Bassus in Germanicum , and Hyginus write that Mercury at the Command of Iupiter plac'd it over the Head of Aries , as a Mark the better to discern that sign , of it self , — Obscuro lumine labens : As Ci●…ro in Arataeis . Others will have it to be the Figure of that part of Aegypt constellated , which Nilus after that manner encompasses . Vide Bassum in Germ●…nic . This at Midnight comes to the Meridian in the Moneth of 〈◊〉 . c The Name of this Ast●…rism by the Arabs ( to use Scaliger's Words ) ridiculè exearnificatum est : For sometimes they call it Kikaus or Kekeus ; sometimes Cancaus , and often Phicares . Which Erroneous Names proceed from the mistake of the Letter 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Kaph for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Phe. Whence instead of Keiphus , which is the true Arabick Name , deriv'd from the Greek ; it is commonly written Keikaus or Kekeus . In Hebrew it is call'd Baalath Halab , i. e. Domina Flammae , and in Arabick , Múltahab , i. e. Inflammatus . It consists of 13 Stars according to Ptolomy , whereof two inform . Bayerus reckons 17. Among which there is one in his Foot , call'd Al Rai , i. e. Pastor ; and between his Feet another , call'd AlKelb , i. e. Canis , and upon his Hands certain others called Al Agh'nâm , i. e. Pecudes . The 3d , 4th and 5th Stars in this Constellation are by Ulugh Beigh call'd Cawâkib Al Phirk , i. e. Stella Gregis . This Cepheus was Son of Belus by Anchinoe the Daughter of Nilus , from whom the Persians were heretofore call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , over whom he was King , as likewise of Phoenieia , and reign'd both in Babylon and Ioppa , reckon'd among the Royal Fautors of Astronomy . It is beheld in the Meridian at Midnight about the end of August and beginning of September . Cepheus . d It is likewise by the Greeks call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Mulier sedis , sive Throni . By the Arabs , Dât Al Cúrsa , i. e. Inthronata . It is also known by the Latine Names of Cathedra , Thronus & Sedes Regia . It consists of 13 Stars according to Ptolomy ; Bayerus counts therein 25. And Tycho Brahe hath observed therein no less than 45 ; besides the New Star which appear'd in the Year 1573. and vanished the Year following : It is resembled by Aratus to the form of a Laconian or a Carian Key , as his Paraphrast Avienus expresses it . — Sic qualem Caria quondam Noveratintrantem per Claustra Tena●…ia Clavens Formatur Stellis distantibus . — The first Star in this Constellation is by the Arabs call'd Caph Al Chadib , i. e. Manus tincta . Whence in Chrysoc●…cea's Tables 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Manus tincta , in the same sence with the Arabick . The 2d Star is 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 call'd by the Name of the whole Constellation Dât Al Cursa . The 5th is call'd Rueba Dât Al Cursa , i. e. Genu Inthronatae . The Bright one in its Breast is call'd Sad'r , i. e. Pectus . This Cassiopea was the Wife of Cepheus , and Mother of Andromeda , who contending for Beauty with the Neveides , was as a Punishment , and in Memorial of her Arrogance , plac'd in Heaven with her heels upward . But Tycho gives us a better ground of the Fable , who writes , That Cepheus was a great Astronomer , or at least a Favourer of the Professours of that Science , who in a grateful acknowledgment of his Encouragement of their Studies , gave to several Constellations the Name of himself , Wife , Daughter , and Son in Law ; which he received from Cicero , where he says , Nec Stellatus Cepheus cum uxore , genero , filiâ , traderetur , nisi Coelestium Divina cognitio Nomen eorum ad Errorem Fabulae traduxisset . He likewise reports that in the time of Cepheus those Starrs , which make the Constellation of Cassiopea , did rise with the first Degrees of Aries : And that under that Constellation the Aethiopians did solemnize the Inauguration of their succeeding Kings in Memorial of their first Mother , Cassiopea , whom he supposes more probably to have been called Cussiepea . Vide Tychon . Brahaeu●… in Progymnasm . l. 1. p. 233. This Asterism is discovered in the Meridian partly in the end of March and beginning of May ; partly at the end of September and beginning of October . Cassiopea . Caput Algol , or Medusa's head . e The Latine Text of Scaliger's Edition hath — Testemque videnti . Testem being interpreted by Scaliger , idem quod praesentem . We have rather chosen according to the conjecture of Lannoius , as noted by Iunius , and with Gevartius ( Elector . l. 2. e. 5. ) to read , Pestemque videnti , i. e. Exitium & mortem ; expressing the sence of the Fable , which makes all such as beheld the Gorgons Head to be thereby converted into Stone . Gevartius confirms this reading by that Exclamation of the Gyant Pallas , converted into Stone by Minerva , as Claudian in Gigantomachia expresses it , — Quis Torpor inertem Marmoreá me Peste ligat . Pestis being taken ( as Meursius in Auctar. Philolog . c. 28. observes ) for any kind of Death , as Febris for any kind of Disease . Auriga or the Charrioteer . f This by the Greeks is call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . By the Iews Ha Roah schobid Ha resan , i. e. Pastor tenens fraenum ; and in the same sence by the Arabs , Mâsik Al Inán , i. e. Tenens Habenam ; or Múmsik Al Ainna , i. e ; Tenens Habenas , to which the Greek Name Heniochus answers , i. e. Habenifer . It is by some of the Arabs likewise call'd Roha , i. e. Auriga , and Memesciath , i. e. Mulus Clitellatus . It consists according to Ptolomy of 14 Stars ; according to Bayerus of 32 , Kepler reckons 27. Among which the 4th 〈◊〉 call'd Menkib Dil Inan , i. e. Humerus Heniochi . The 11th , Ca'b Dil Inan , i. e. Talus Heni●…chi . This Constellation the Scholiast of Germanicus will have to be Mirti●…us ; The Trezenians are for Hippolytus , others for Ericthonius , whom Pliny makes the first that joyn'd four Horses in a Chariot , as before him Virgil in these Verses in 3 Georg. Primus Ericthonius Cu●…us , & quattuor ausus Iungere Equos , rapidisque Rotis insistere Victor . Eus●…bius in Chronic. makes Trochilus the Argive , who was Son of Callithea , the Priestess of Iuno , the first Inventor thereof ▪ of whom likewise Tertullian de Spectac . He is mistakenly by Hyginus call'd Orsilochus . In which Errour he is followed by Corippus in Panegyr . 1. in these Verses , as cited by Scaliger in Eusebium : Orsilochum referunt primas junxisse Quadrigas Et Currus armasse 〈◊〉 , Pelopemq●…e Secundum In Soceri venisse Necem — Dempster yet in his Edition of Corippus instead of Orsilochum reads Cecropidem , thereby meaning Ericthonius the 4th King of Athens , from Cecrops ; others will have him to be Oenomaus . But Theon the Scholiast of Aratus says plainly , That the Constellation of Heniochus is 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; The Representation either of Bellerophon or Trochilus , the first Inventor of the Quadrigae . This Sign attains the Meridian at Midnight about the middle of December . g In the manner of joyning these 4 Horses to a Chariot , the Antients as they differ'd from us , so they differ'd among themselves ; for some made 2 Poles to a Chariot , one between each two Horses , for they went aequatâ fronte , all a breast ; so that all the Horses were 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Iugales , yoak'd , or coller'd to the Poles , Afterwards Clisthenes the Sicyonian chang'd that manner and made only one Pole to a Chariot ; so that the two middle Horses were only Iugales ; the other two outmost on either hand , had only Reins and Harness , and therefore call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Funales , and were at more liberty than the Iugales : Of these We have in Suetonius in Tiberio an eminent Example , where he says , Tiberius pubescens Actiaco Triumpho currum Augusti comitatus est sinisteriore funali Equo , cum Marcellus Octaviae filius dexteriore veheretur ; which Place by Alexander ab Alex. ( who undertakes to explain it ) is not clearly understood ; he conceiving the Equi funales to be so called à funalibus , i. e. Facibus Triumphalibus , &c. from the Triumphal Lights , or Torches born by their Riders : But not having opportunity to say more hereof in this Place , I refer the Reader to Salmasius , who particularly and at large handles this subject in his Plinian Exercitations , Tom. 2. p. 899. to the Figures of the Currus Quadrijuges in the Consular and Imperial Coins in Ursinus , Goltzius , and Panvinius de ludis Circensibus ; more particularly to Scheffer , who hath expresly written upon this Subject in a late Treatise de Re vehiculari veterum . Romulus is said to have first shewed the Quadriga to the Romans , as Tertullian l. de spectaculis witnesses : Of the Currus Sejuges , Chariots drawn by six Horses , Pliny mentions the first among the Romans to have been in the time of Augustus , to whom the Senate decreed it as a Triumphal Honour , but by the modest Prince refused . h These are 2 Stars in the left Arm of Heniochus , call'd by the Arabs ( according to Scaliger in Sphaer . Barbar . ) Saclateni , or trulier Sadateni , i. e. Brac●…ium sequentes ; they are likewise call'd Giedyân , and in the Common Globes instead thereof Maazein , i. e. duo Capri. These Cleostratus the Tenedian ( according to Hyginus ) is said first to have discovered . They are observed both at their rising and setting to cause Storms and Tempests , and therefore by the Poets call'd horrida & insana Sydera ; and by Germanicus — Nautis inimicum sydus in undis . By our Poet they are said to close or bar up the Sea ; So Vegetius l. 5. c. 9. Circa Nonas Octobris , Hoedi Pluviales , &c. Ex die igitur tertio Novembris usque in Diem sext . Id. Mart. Maria Clauduntur ; and as the first of those days did shut up the Seas ; so the later ( to use Plinies Words ) did aperire Navigantibus Maria ; which not unaptly by Vegetius is stil'd Natalis Navigationis , and was celebrated among the Antients Solemni Certamine , publicóque Spectaculo , by the Greeks in their Panathenaean , by the Romans in their Quinquatrian Games : See Turneb . Adversar . l. 18. c. 24. and Steweeb . in Veget. l. 5. c. 9. Hoedi●…r ▪ the 〈◊〉 The A 〈…〉 an 〈◊〉 . i This is a bright Star in the shoulder of Heniochus of the first Magnitude , call'd by the Arabs Aiynk , and commonly instead thereof Atud . In Hebrew , Ash , or Aish ; in Syriack , Iyûtho . All signifying Capellam . This the Poets fable to have been Mother of the two Kids , and Nurse to Iupiter ; though others ( from the Authority of Agathocles Babylonius ) report him to have been suckled by a Sow ; the Cretans for that Cause honouring that Creature , as sacred : Of which see Casaubon in Animadvers . in Athenaeum , p. 649. But the more general Opinion is , that he was suckled by a Goat , and from thence he deriv'd the Title of Ae●…iochus , or the Goat-nurst . And to this effect in some Medails of the Emperour Valerianus he is represented in the Figure of a Child , mounted on the back of a Goat , with this Inscription , JOVI CRESCENTI : Touching which see Choulius de la Religion des Anciens Romains , &c. I shall hereto only apply an Ingenious Epigram of Crinagoras in the Greek Anthologie , l. 1. c. 33. upon a Goat , whose Milk Augustus Caesar us'd to drink . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 When Caesar did our full Bags Nectar taste , Whose Spring th' exhausting Pale could never waste : Me , that he might not want that Milky store , To Sea with him in his own Ship he bore . Straight 'mong the Stars shall I be made to shine , For he I serve , than Iove's no less divine . k Seven Stars on the Back of the Ball , by the Latines from the time of their rising call'd Vergiliae , by the Greeks ( 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , quòd ortu suo Tempus navigandi ostendant , or from their Plurality ) 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . By the Arabs for the last Reason Al Thuraiyá , from the singular Therwa , i. e. Multus seu Copi●…sus . They are likewise by them called ( 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ) Al Negim , i. e. Astrum . By the Aegyptian Coptic 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . By the Syrians they are called Chima ; by the Persians Peru , and 〈◊〉 ; by the Turks , Ulgher ; by the Iews they are distinguish'd by two several Names ; the first is Chima , answering to the Arabick Al Thuraiyá ▪ the other is Succoth Benoth , which is interpreted commonly Tabernacula filiarum , and represented after the similitude of a Hen , brooding over her Chickens . According to which Interpretation this Asterism is by the Italians call'd La Gallinella . These are said to have been the Daughters of Atlas and Pleione , whom Maero Poetria Bysantina ( as cited by Athenaeus l. 11. ) makes the Nurses of Iupiter , who sed him with Ambrosia ; But commonly they are reputed the Nurses of Bacchus , and for that constellated . Their Names Maia , Sterope , Taygeta , Celeno , Electra , Merope ; or according to the Scholiast of Theocr. ( in Idyll . 13. ) Coacymo , Glaucia , Protis , Parthenia , Maia , Stonychia , Lampado . Michael Florentius Langrenus ( who as Ricciolus writes was an exact observer of them ) adds to them two other Stars , which he calls Atlas and Pleione . Galilaeo hath observ'd in this Constellation above 40 Stars , and Ricciolus no less than 50. l Seven Stars in the Head of the Bull , called , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , by the Greeks , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 pluere , because when they arise Cosmically they cause Rain and Showers , or from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , for that they resemble the gaping Jaws of a Swine , whence by the Latines call'd Suculae , or ( according to Theon and Bassus in Germanic . ) from the Greek Letter Y. Upsilon , which they resemble , or from their Mother Hya , Daughter of Oceanus , and Wife of Atlas : by Ulugh Beigh they are call'd Al Debarân , from their Position , the word signifying quicquid ponè , vel posterius est . However that Name is peculiarly applyed to the brightest of them , commonly call'd Oculus Tauri . They are sometimes by the Arabs call'd Al Najmon , or Negim , i. e. Stella , and Althu●…aîya ; for the same reason as the Pleiades . In Hebrew they are likewise called Chima , from the Number of Stars of which they consist . These excessively lamenting the Death of their Brother Hyas , slain in hunting by a Lyon , were by the commiserating Gods converted into Stars : their Names , Ambrosia , Eudora ( or Eudoxa ) Ph●…sile ( or Pasithae ) Coronis , Prolixo ( or Plexauris ) Phileto ( or Pytho ) and Thyene ( or Tuke . ) The Pleiades and Hyades . m In the Catalogue of these Northern Stars our Poet hath omitted Coma Berenices , Ganymed or Antinous , and Equicul●…s or the lesser Horse ; touching which see the Appendix . The Southern Constellations . n This Constellation was first by the Boeotians call'd Candaon , as Lycophron testifies , afterwards 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , call'd by the Latines Hyriades and Hyrides , from his Father Hyreus , of which see the Fable in Ovid Fasto●…m l. 5. It is by Plautus , Festus , and Varro call'd Iugula , eò quòd armatus sit ut Gladius , says Bassus in Germanic . By the Iews it is called Gibbor , i. e. Gigas , and Kelb Ha Giebbor , i. e. Canis fortis , and Bellator fortis ; by the Arabs , Al Giauza , and that for the same reason as is before alledged in the Constellation of the Twins ; as likewise Al Giebbar , i. e. Gigas fortis . In which sence it is in the Syriack call'd Gavoro ; in Chaldee , Niphla , answering to the Hebrew Chesil , or Kesil . It consists according to Ptolomy of 38 Stars ; according to Bayerus of 49 ; as Repler reckons of 62. Among which the first Star is by Ulugh Beigh call'd H●●ka , which signifies a white Circle or Mark. By which Name likewise the three Stars in his Head are denominated . The second is call'd Menkib Al Giauza , i. e. Humerus Orionis , and Ied Al Giauza Al Iumma , i. e. Manus dextra Orionis , vulgarly , but erroneously being read Bet or Beit Al Giauz , i. e. Brachium Orionis . The third Star is call'd Mirzam Al Nagjid , i. e. Leo Strenuus . The 17th and 25th are in the Arabick call'd Al Tagis and Al Dawaib , the first signifying Tiara , the other Antiae seu Lemnisci . The 26th , 27th , and 28th are call'd Mintaka al Giauza , and Nitak Al Giauza , i. e. Cingulum seu Baltheus Orionis . By our English Mariners , the Golden Yard ; as likewise Al Nid●…m vel Al Nedin , i. e. Series , seu quicquid ordine disponitur ; also Phikár Al Giauza , i. e. Vertebra Dorsi Orionis . The 29th , 30th , 31th and 32th Stars are call'd Saiph Al Giebbar , i. e. Ensis Gigantis . The 35th is call'd Rigil Al Giauza Al Iusra , i. e. Pes Gigamis Sinister ; and Rai Al Giauza , i. e. Pastor Orionis . The 38th is call'd Rigil Al Iumma , i. e. Pes dexter . The Fable of this Constellation ( to omit others ) is by some thus related . Orim being a great Companion of Diana's in her hunting Diversions , Apollo grew jealous of his too much samiliarity with his Sister , and to be revenged , seeing Orion one day swimming in the Sea , his Head appearing above the Waters like a black Mark , he shew'd it to his Sister , and told her she could not hit it : Whereupon she presently drawing her Bow let fly , and kill'd him , not knowing who he was , till the Sea had cast him on the Shoar ; which perceiving and much troubled , to make amends she plac'd him in Heaven near the Dog and the Hare , where he seems still to hunt . The Persians will have this Asterism to represent Nimrod . It is seen in the Meridian at Midnight in the Moneth of December ▪ Orion . o The Southern Constellations are here said to follow Orion , as Souldiers , their General : and Scripture it self hath reduc'd the Stars into a Military Order , and call'd th●…m 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , Militiam Coeli , the Host of Heaven . Vide Petr. Fabri . Semestr . l 3. c. 1. p This is fabled to have been Orion's Dog , named Laelaps ; others make it Isis her Dog ; some again Caephalus his . By Ovid it is called Canis Icarius and Erigonius . By the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Canis Asterismus , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which Timosthenes cited by the Scholiast of Apollonius reports to have been 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ▪ the Dog 's name . By the Latines it is call'd Canicula . Why it is call'd the Dog Star , Artemidorus in On●…irocrit . l. 2. c. 2. gives this Reason : The Star Syrius ( saies he ) is the Cause of Feavers , and therefore by some called the Dog , which is a Creature fierce , and yet fawning , and for that reason 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , resembled to a ▪ Feaver . The antient Aegyptians ( as Plutarch testifies ) believ'd this Constellation to be the Soul of Isis ; but more properly ( according to the relation of Diodorus Siculus , l. 1. ) that Star in Ore Canis , call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . From which Greek name the Arabick Shiri or Shira seems to be deriv'd . As 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 from the Greek word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which signifies to gape , or a 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which is to make dry , because at its rising the Earth becomes dry , Agente Terrá per Caniculam Rimas , ( as Vi●…gil in Catalect . ) and Dogs gape with heat ; or ab 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. aestum , whence 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , or à 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. exi●…anio , quia sudore fluxo nos exinaniat , says the Scholiast of Apollonius , l. 2. Or from Siris , which Name ( as Dionysius in Perieges . witnesses ) the Aethiopians gave to Nilus , as if it were Sydus Niloticum , by reason of the great Affinity between Nilus and that Star , for in the Dog days that River hath its greatest Inundation . Germanicus and Hyginus give it the Name of Maera ; and by the Greeks it is call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . By the Arabs , Kelb Acbur , i. e. Canis Major . By the Syrians , Kelbo Gavoro , i. e. Canis Gigantis . By the Aegyptians it was call'd Sothis , perhaps in Memory of the King of that Name ( Father of Rhameses ) who was a great Erector of Obelisks , and Restorer of the Aegyptian Learning , de quo vide Kircherum in Obelisc . Pamphil. & alibi . The Constellation consists according to Ptolomy and Kepler of 29 Stars , whereof 11 inform . Bayerus reckons but 19. It is seen in the Meridian at Midnight about the end of December . Sirius or the Dog-Star . q Of the time of the Dog-Stars rising there is much difference among the Antients ; ( touching which see Ricciolus Almagest . Nov. Tom. 1. p. 471. Petavius Uranol●…g . l. 2. c. 10. and Kepler Epitom . Astronom . l. 3. ) That difference arising from the Antients confounding the true and Cosmical rising with the Heliacal , or from their different Computation of the Suns Ingress into the Cardinal Points , or their misapplying the Astronomical Fasti of one Climate to another ; but the greater part of the Antients assign it to the time of the Sun 's first entring into Leo , or as Pliny writes , 23 days after the Summer Solstice , as Varro 29 , as Columella 30. See besides the forecited Authours Salmas . in Plinian . Exercitat . Tom. 1. p. 430. At this day with us according to Vulgar computation , the rising and setting of the said Star is in a manner coincident with the Feasts of St. Margaret , ( which is about the 13th of our Iuly ) and St. Lawrence ( which falls upon the 10th of August ) as this common Verse expresses it , Margaris Os Canis est , Caudam Laurentius affert . Vide Bambrigium in Canicular . c. 3. & Weighel Sphaer . l. 1 §. 2. c. 2. r What our Authour here applies to the Observation of the Cilicians ( which Scaliger conceives is done in respect to the Memory of Aratus ) Cicero ( l. 1. de Divinat . ) attributes to the Ceans . Ceos accepimus Ortum Caniculae diligenter quotannis solere servare , Conjecturamque capere , ut scribit Ponticlus Heraclides , Salubrisne an Pestilens Annus futurus sit ; Nam si obscurior , quasi caliginosa , stella extiterit , Pingue atque Concretum esse Coelum , ut ejus Aspiratio gravis , ac Pestilens futura sit ; Sin illustris & perlucida Stella apparuit , significari Coelum esse Tenue purumqu●… , & propterea salubre . So likewise Horus Apollo , l. 1. c. 3. speaking of this Star , by the Aegyptians call'd Sothis , In exortu hujus Syderis , Ea signis quibusdam observamus , quae toto Anno peragenda sunt . For this reason was it honoured , as the chief of all the fixed Stars . Hence Pliny , l. 2. Non est Minor ei veneratio quam descriptis in Deos stellis : And Apollonius Rhod. l. 2. Argonaut . affirms — 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . — Hodie Saderdotes in Co Ante Caniculae Exortum operantur in Sacris . So among the Romans , as Ovid in quinto Fastorum testifies , Pro Cane Sidereo Canis hic imponitur Aris. And Festus . Rutilae Canes , ut ait Atteius Capito , canario sacrificio immolantur pro frugibus , deprecandae saevitiae causa Syderis Caniculae . s The Growth or product of Fruit the Romans exprest by the peculiar Term of Eventus . Among whom there was the Deity , call'd Bonus Eventus , principally worshipp'd by Husbandmen , as Varro de Re Rusticâ , l. 1. testifies . Uti fruges , frumenta virgultaque grandire & bene evenire sinat : ( to use Cato's words . ) Festus likewise writes that they sacrificed also to Pan , ob frugum Eventum ; which propriety of Term is here observed by Manilius , and is noted by the Learned Valesius ( in Annotat. in Ammian . Marcellin . l. 29 ) t Hence the Name 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 applicable as well to the Sun as to this Star , propter splendorem 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , signifying as much as lucere Solis & Siderum in morem . So Hyginus ( in fabul . speaking of this Star ) Syrion appellatur propter flammae Candorem ; quòd ejusmodi sit , ut praeter caeteras lucere videatur . 〈◊〉 being by some held to be another Sun , and to illuminate the more remote Stars , within the Aetherial ▪ Recess , as our Sun illuminates the Moon and the Planetary System . Vide Kircher . Itinerar . Exstat . Dialog . 1. c. 9. inque illum Schot●…um Schol. 3. nec non Gassend . Tom. 1. part . 2. p. 138. u This Constellation is by the Greeks call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; by the Latines , Lepus . The Arabs call it Arneb , and the Iews Arnebeth , i. e. Lepus . It consists of 12 Stars according to Ptolomy , as Bayerus and Kepler reckon of 13 ; whereof the 7th , 8th , 9th and 10th are call'd in Arabick ; Arsh Al Giauza , i. e. Solium Orionis . Some will have this to be plac'd in Heaven in Memorial of the Chace affected by Diana and Orion ; others make Mercury the Authour of this Constellation in Testimony of the fruitfulness and pregnancy of this Creature ; of which Aristotle speaks in Histor. Animal . Hyginus and Bassies write , that antiently in the Island Hiero there were no Hares , until one of the Islanders brought thither from beyond the Seas a female Hare big with young ; and that from thence in a short time ( every one being desirous by his example to breed up some ) they increast and grew so numerous , as wanting sufficient food , they destroy'd all the Crop of the Island , and brought a famine upon the Place . In Memorial of which this Asterism was figur'd in the Heavens , ut Homines Meminissent Nihil his exoptandum in vit●… , si insol●…ter utantur laetitiâ , quin dolorem capere posterius cogantur ; saies the same Mythologist . There is an Ingenious Epigram of Caesar Germanicus in the Greek Anthology , imitated by Ausonius , which may not improperly be hitherto applied . Trinacrii quo●…dam currentem in litoris Ora , Anticanis leporem Caeruleus rapuit . At lepus ; in me omnis Terrae Pelagique ruina est , Forsitan & Coeli , si Canis Astra tenet . A Hare by Hounds pursu'd , them having scap'd Met on the shoar a Dog-fish , and was snapt . Then cries ; us Earth and Seas are bent t' undo . Heaven's only left ; yet there is a Dog too . This is to be seen in her form near the Meridian at Midnight in the Moneth of December . x Call'd likewise Canis Minor , Procynis , and Praecanis ; by Cicero and Ausonius , Anticanis . Pliny saies , the Romans had no Name for it , unless ( saies he ) we should call it Caniculam . By the Arabs it is call'd Kelb Asgher , i. e. Canis Minor. It is likewise by them call'd Shira Al Shamiya , i. e. Syrius Shamensi●… ( eò quòd Occultatio ejus sit in plaga Al Shám , i. e. Syriae ) and Shira Al Ghomeisa , vel Al Ghomuz ; i. e. Syrius Oculi fluxu laborans , of which we find this Arabick Fable in the Commentator upon Ulugh Beigh his Tables . Shira Al Ghomoisa sic dicunt , quòd soror ejus Shira Al Abùr , i. e. Canis Major , ( for the Arabs make the greater and the lesser Dog to be the sisters of Canopus ) transierit Galaxiam ad assequendum Can●…pum ; Illa vero manens in tractu boreali , propter Canopum , ita plorat , ut oculi sui lippitudine capti sint . This Constellation according to Ptolomy consists only of two Stars : Bayerus reckons eight , Kepler five . Among which that in his shoulder is by the Arabs call'd Al Mirzam , and Al Dira Al Mesbûta , i. e. Brachium expansum . The other ( ad Radicem Caudae ) is call'd Al Shira Al Shamiya , i. e. Syrius Shamensis , and Al Ghomeisa , as before . This Dog the Poets Fable to have been Erigone's , which mourn'd to death for the loss of his Mistress , who hang'd her self for grief that her Father Icarus was slain by his drunken Paysants . It is seen at Midnight in the Meridian in the Moneth of Ianuary . Procyon and the Hare . Argo . y This Constellation is by Ptolomy call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and by some simply 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Navis . By the Arabs , Mercab , i. e. Currus , seu vehiculum ; for so by the Poets the Ship Argo , which this Asterism represents , is call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and Currus volitans . It is likewise in Arabick call'd Al Sephina , i. e. Navis . It consists as Ptolomy counts of 45 Stars ; according to the Computation of Bayerus , of 63 ; as Kepler reckons of 53. In which the 3d , 6th , 7th and 22th Stars are by some Arabs call'd Tur'yeish , and in the Plural Tur'yeishat , which Mr. Hyde conceives ought to be read Tur'eis , and in the Plural Tur'eisat , which answers to Ptolomies 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Scutulùs , a little shield . The 44th Star , which is in the extremity of the Southern Rudder of the ship ( for every ship antiently had two Rudders ) is by the Greeks call'd Canopus , and in honour of Ptolomaeus Lagus , one of the Aegyptian Princes , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; by the Aegyptians , Sampilos ; by the Persians in Chrysococca's Tables , Soail Iamane ; and by the Arabs , Soheil Al Iemin , i. e. Canopus Iemanensis ▪ ( Ieman signifying Arabia foelix . ) Some make Soheil or Suhel to signifie Ponderosum , in the same sence perhaps with Bassus , by whom it is call'd Stella Terrestris , because to us Europaeans it seems to sink low , and as it were stringere Horizontem , or as Salmasius ( in his Plin. Exercitat . & in Diatrib . de Antiqu. Astrolog . ) from the meaning of the name Canopus , which in the Coptick or Egyptian Language is 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Aurum , that being the heaviest Metal the Earth produces . There are several stars of the second Magnitude not far from it , viz. the 17th , 31th and 35th , which by the Arabs are call'd Soheil Telkin vel Belkin , or as Mr. Hide reads it Belkis ( that being the name of the Queen of Sheba that came to visit Salomon ) and Soheil Hadar , Soheil Rekas or Rekash ; Soheil Al Wez'n , and Soheil Al Muh●…iph . The Fable of Argo ( which Bochartus in Geograph . sacrâ will have so called , not from Argos its Builder , nor from the Son of Phryxus so nam'd , nor for that it was built near Argos , nor from the Argives which Mann'd her , but from the Figure of her Built , her length , and therefore in the Phoenician Tongue , call'd Arco , i. e. Navis l●…nga , or as Hoelelin notes in Appollon . Argon . l. 1. from the Hebrew , Areg , i. e. Textura , à Pineis Textis ) is sufficiently known . By the Poets generally reputed the first ship , that ever sayl'd the seas . But Diodorus Siculus l. 4. plainly affirms the contrary ; for speaking of Iason he says that he first under the Mountain Pelius , built a ship of far greater bulk than any that were then us'd , for at that time ( says he ) Men only sayl'd in small Barques or Skiffs . So that Argo seems not to have been the first ship , but rather the first of its kind . Touching which Argument see ( besides Fournier and Baiffius ) Scheffer . de Militiâ Navali . This sails by the Meridian at Midnight about the end of Ianuary . z This Serpent is by Ptolomy call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Hydri Asterismus ; ( of which see the Fable in the next Note ) by the Greeks likewise call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; and by the Arabs with little alteration from that , Alshugia , i. e. Serpens tenuis ; or as Scaliger reads it , Asvia f●…rtis seu Audax . Ricciolus says it is in Arabick call'd El Hawick and Kirker Aphaak ; in Hebrew , Hajah , i. e. Serpens . There is reckon'd in this Constellation by Ptolomy 32 Stars , whereof seven Sporades or inform ; by Bayerus . 29 ; by Kepler 33. Whereof the first star is call'd Minchir Al Shugjâ , and the others from that to the seventh inclusive Min Al A'zal , i. e. ex 〈◊〉 , as if appertaining to the sign Virgo . The twelfth star , which by the Latines is call'd Cor Hyd●…ae , is in the Persian Tables call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and accordingly in Ulugh Beigh , Unuk Al Shugjâ , Collum Serpentis ; and Pherd Al Shugjâ , i. e. Solitaria Hydri ; and simply Pherd , solitaria ; quianullae in Circuitu stellae adjacent . The head of this Constellation is seen in the Meridian at Midnight about the beginning of February ; its middle parts about mid March , and its tayl in the beginning of April . Drace . The Crow . The Cup. The Centaur . a This by the Greeks is call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. Corvus & Corvi Asterismus : in the same sence by the Iews it is call'd Orev ; and from thence by the Arabs , Al Gorab , Corvus . It is likewise by them call'd Al Chiba , i. e. Tentorium , and A●…sh Al Simâk , i. e. Solium efferentis ( scil . inermem vel Virginem ) and Agiar Al Asad , i. e. Clunes Lemis , and Al Ag●…mâl , i. e. Cameli . It is seated upon the Tayl of the Serpent , and consists of seven 〈◊〉 , according to the joynt Accompt of Ptolomy , Bayerus and Kepler ; whereof the first in Arabick call'd Minkar Al Gorab , i. e. Rostrum Corvi . The fourth Gienah Al Gorab Al Aiman , i. e. Ala dextra Corvi : The Fable of this Constellation is thus ; The Crow being by Apollo sent to fetch Water for a Libation , seeing a Fig-tree full of Fruit , but not ripe , made stay there until the Figs were come to Maturity ( which Fable , says the learned Bochart in Hierozoic . l. 2. c. 13. seems to be derived from N●…ab's sending the Crow out of the Ark ) and having satisfied his longing went to the Fountain to fetch Water ; but coming there , meets with the Serpent before mentioned , whereat 〈◊〉 , he returns back with the empty pitcher , telling Apollo there was no Water in the Fountain . This untruth being discover'd by Apollo , he prohibited the Crow from ever drinking at that time of the Year , and in Memorial of the Fact , plac'd the Crow , Snake , and Pitcher in the Heavens ; see Hyginus and Bassus in Germanicum . The Crow is sacred to Apollo , the President of Divination ; forasmuch as this Fowl by its different Notes is said to foretel fair and sowl weather ; or . for that Apollo , fearing the pursuit of Typhon , is said to have assum'd the Figure of that Fowl ; or in Allusion to the Suns departure , causing darkness and night , of the same colour with the Crow , as his Return does the Day or Light resembling the whiteness of the Swan , which is likewise sacred to that God. See Ricciard Brixian . Commentar . Symbolic . in voce Corvus . This Asterism at Midnight is seen in the Meridian about the middle of March. b Our Poet here appropriates this Cup to Bacchus ; Aratus , Hyginus and Bassus to Apollo , according to the Fable before mentioned : But Pontanus in Urania seems to give it , with our Poet , to the first , where he says , by that is denoted to such in whose Horoscope it is ascendant — Meri Genialis Amor studiumque bibendi . It is called by Ptolomy 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; by others , Hydria , Calpe , Cratera , Patera , Urna , & Vas. By the Arabs , Batiya ; from the Persian , Badiya , i. e. Poculum Magnum . By some it is call'd Alkis , instead of Alkas , i. e. Cyathus , from the Hebrew , Kus , or Kos , signifying the same . Kircher says it is by the Arabs likewise call'd Alphun . It consists as Ptolomy reckons of seven , as Bayerus , of eleven , as Kepler , of eight Stars , which by the Arabs are call'd Al Ma●…laph , i. e. Praesepe . It is apparent in the Meridian at Midnight about the middle of March. c Some will have this to be the Minotaur ; others , Ch●…ron the Son of Saturn and Phi●…yra , the Daughter of Oceanus , who taught Aesculapius Physick , Achilles Musick , and Hercules Astronomy ; with one of whose poysonous Arrows casually falling out of his Quiver he was wounded in the Foot , and of that wound died , and by commiserating Iupiter was made a sign in Heaven ; call'd by Ptolomy 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 : The Arabs making use of the Greek Name , by whom yet according to Ricciolus it is call'd Albeze and Asmeat ; by the Greeks , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , and in barbarous Greek , Taraopoz . It consists according to Ptolomy of 37 Stars , according to Bayerus of 40 , as Kepler reckons o●… 56. All which , together with those that make up the Fera Centauri , are by the Arabs call'd promiscuously 〈◊〉 , i. e. Spadices , bright dappled , propter multitudinem ac densitudinem collectionis earum . The 35th and 36th are by the Arabs call'd Al Hadur , i. e. solum , and Al Wez'n , i. e. Pondus , and Muhtalaphein , i. e. Iuratas , and 〈◊〉 , i. e. Pejuratas , as being by some Observer mistaken for Canopus , and averr'd upon Oath to be it , by at other sworn to the contrary , whence the Original of those Arabick Names . The 35th Star is yet by Ulugh Beigh call'd Rigil Kentaurus , i. e. Pes Centauri . Our Poet here omits his Hasta ; by Proclus and Bassus call'd Thyrsi●…s , and Thirsolochus ; as likewise the Bestia Centauri , by the Greeks call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. fera , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 à rapacitate , scil . Lupus . In Arabick it is call'd Sebu ' , i. e. Fera , and Pheh'd , i. e. Thos , Pardus . This Constellation gallops by the Meridian at Midnight in the end of April . d Call'd by the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . By the Latines , Thuribulum , 〈◊〉 , Bathilus , Sacrarium , 〈◊〉 , Templum , Lar , Ac●…rra , A●…a , & 〈◊〉 . By the Arabs ( according to Ricciolus ) Almegrameth or Al Mugamrah . It consists of 7 Stars according to Ptolomy and Kepler ; as Bayerus reckons of 8. This was the first Altar ( according to the Poets ) that ever was erected , In qua devoti quondam cecidere Gigan●…es ; Nec prius armavit violento sulmine dextram Iupiter , ante Deos quàm constitit ipse Sacerdos . ( As our Poet l. 5. ) It was fram'd by the Cyclops , and in memorial of the fact constellated . Lactantius yet , l. 1. de falsa Relig. reports that the first Altar that Iupiter erected was in honour to Caelus . Deinde ( says he ) Pan cum deducit in montem , 〈◊〉 catur Caeli Stela ; Postquam eò ascendit contemplatus est latè Terras , ibique in eo Monte Aram creat Caelo , primusque in ea Arâ Iupiter Sacrificavit . The Deities , to whom Iupiter sacrific'd upon this Expedition against the Gyants , we find from 〈◊〉 Sioulus Bibliothec. l. 5. to have been the Sun , Heaven and the Earth . This Constellation about the end of Iune passes the Meridian at Midnight under our Horizon . The Altar . e These were by the Greeks call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ; by the Latines , Dii Majores , Dii Valentes & Potentes . , and Dii Samothraces , of whom see Dionys. Halicarnass . Antiq. lib. 1. and Macrob. Sa●…urnal . l. 3. c. 4. They are likewise by the Greeks call'd 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , which Scaliger ( in Varron . de Linguâ Lat. ) conceives to be deriv'd from a Phaenician or Syrian Original , Cabir in that Language signifying Potens ; which Gods were so call'd in Opposition to and Distinction from the Dii Casmilli , Camilli , or Camiri , i. e. Dii Ministri sive Minores , as observ'd by Heinsius ( in Aristarcho sacro ▪ ) These some will have to be Castor and Pollux , confirm'd by this Antient Latine Inscription , CASTORI ET POLLUCI DIS MAGNIS SULPICIAE . Q. SULPIC ▪ F. VOTUM . &c. And this Greek one , cited by Argolus in l. 2. Panvinii de Lud. Circens . extant at Venice in Aed . Episc. Torcell . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 i. e. CAIUS CAII ACHARNENSIS SACERDOS FACTUS DEORUM MAGNORUM DIOSCURORUM CABEIRORUM . These yet the Scholiast of Apollonius ( l. 1. ) says were Iupiter and Bacchus ; or , according to Athenian , Iasion and 〈◊〉 Varro conceives them rather to be Ops and Saturn . Nigidius and Cornelius Labeo ( as cited by Macrobius ) will have them to be Neptune and Apollo . They are reputed likewise to be Cybele and Attys , as by two Antient Monuments erected to their Honour , with this Inscription DIS MAGNIS , in Gruterus may appear , of which more particularly Pign●…rius de Magna Deùm Matre & A●…tide . Others make them to be the Dii Penates : against which Opinion thus Turneb . Adversar . l. 15. c. 21. Magnos Deos à Penatibus diversos facit Maro ; Penates enim Dii Penetrales videntur fuisse , Diique familiae : Dii magni , illi qui maximum Imperium & Numen habent , publicéque coluntur , &c. or according to Antonius Goveanus ( in Terrent . ) Dii Magni quos majorum Gentium Cicero vocat , qui à Terris in Coelum non pervenêre . These by Diodorus Siculus , l. 1. c. 8. are said to be five in number , i. e. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 seu Spiritus , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 seu Ignis , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 seu Siccum , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 seu Humidum , and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 seu Aer . By the first , meaning Iupiter ; by the second , Vulcan ; by the third , Tellus seu Ceres ; by the fourth , Neptune , sive Oceanus ; by the last , Minerva . Theon Smyrnaeus ( in Mathemat . Plat. ) reckons them to be eight ; 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. aiunt octo esse Deos omnium Dominos : Thus enumerated in an Antient Inscription upon an Aegyptian Pillar , as cited by the said Theon from the Testimony of Evander . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , * 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 &c. i. e. ANTIQUISSIMUS OMNIUM REX OSIRIS DIS IMMORTALIBUS , SPIRITUI , ET COELO , SOLI , ET LUNAE , ET TERRAE , ET NOCTI , ET DIEI , ET PATRI EORUM QUAE SUNT , QUAEQUE FUTURA SUNT , AMORI . &c. And from hence the Proverb 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , i. e. omnia octo ; which see explain'd in the learn'd Notes of Bulial●…us upon that Authour . Others make them to be twelve in Number , reckoning them according to this Distich of Ennius . Iuno , Vesta , Ceres , Diana , Minerva , Venus , Mars , Mercurius , Iovi ' , Neptunus , Vulcanus , Apollo . Whose several Interests or Concerns are thus describ'd and distinguish'd by Sallustius ( 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ) mundum eff●…ciunt Iupiter , Neptunus , Vulcanus ; animant Ceres , Iuno , Diana ; adaptant Apollo , Venus , Mercurius ; 〈◊〉 Vesta , Palias , Mars . Yet these Great Gods , though in degree above the rest , were not invested with absolute Rule , that being only reserved for Iupiter , according to Aeschylus in Prometh . vinct . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Omnia sunt Diis concessa praeter imperare , Nam nullus est Liber nisi Iupiter . Who was ( as Apuleius Met. l. 1. says of Osyris ) Deus Deûm , Magnorum Potior , & Majorum Summus , & Summerus Maximus , & Maximorum Regnator . * For so we read that Inscription according to the ingenious Emendation of the Excellent Msr. de Fermat , in his Epistle ( to Msr. de Pellisson ) annexed to the last Edition of Diepha●…tus Alex. Notes for div A51768-e90320 a a Salmas . in Pli●… . Ex●…rcitat . Tom. 1. p ; 6 ; * 〈◊〉 . Astron. * ●…rasat . in Tom. ●… . ●…lmagest . ●…ov . * L. 11. Autiq. Iud. c. 3 & 8. * M●… . Is. Voss. l. de ●…tate Mundi , p. 271. * R●…bbi Isa●… . 〈◊〉 , 〈◊〉 . de lon ●…vitate prim . Patr. * L. 9. Pr●…par , Evan●… ▪ c. 16 , 17 , 18 , &c. * Vid. 〈◊〉 , in Praefa●… . ad Vit. T●…ch . Brahae●…non Dom. Io. 〈◊〉 〈◊〉 , p. ●…1 . * 〈◊〉 l. ●… a Fabul . 271. * Orat. ●…9 . 〈◊〉 . Notes for div A51768-e92650 ANNI ANTE CHRISTUM juxta LXX . 5600. 5200. 4400. 3400. ANNI ANTE CHRISTUM . 2847. 2346. 2069. 1990. 1800. 1750. 1593. 1590. 1590. 1480. 1445. ANNI ANTE CHRIST●… . 1360. 1345. 1238. 1205. 1200. 1012. 716. 660. 660. ANNI ANTE CHRISTV●… 600. 590. 560. 544. 540. 540. 530. 520. 〈…〉 . 5●…9 . 490. 480. 470. 470. 450. 432. 432. 432. 430. 430. ANNI ANTE CHRISTUM . 420. 410. 410. 405. 404. 390. 368. ●…NI ANTE CHRISTUM . 366. 360. 350. 340. 322. 322. 300. 300. 294. 282. ANNI ANTE CHRISTUM . 280. 280. 280. 270. 〈…〉 270. 270. 270. 270. 26●… . 168. 140. ANNI ANTE CHRISTUM . 86. 86. 86. 83. 60. 80. 52. 45. 45. 30. 〈◊〉 〈◊〉 〈◊〉 . 30. 20. 20. 20. 15. ANNI ANTE CHRISTUM . 〈◊〉 〈◊〉 〈◊〉 ANNI POST CHRISTUM . 10. 14. 14. ANNI POST CHRISTUM . 15. 25. 34. 34. 50. 60. 80. 90. 90. 90. ANNI POST CHRISTUM . 91. 92. 95. 120. 130. 132. 134. 135. ANNI POST CHRISTUM . 135. 140. 140. 160. 171. 230. 238. 283. 298. 314. 320. 〈◊〉 〈◊〉 〈◊〉 325. 340. 36●… . 375. 378. 390. 390. 395. ●…99 . ANNI POST CHRISTUM . 400. 400. 400. 410. 434. 437. 460. 466. 467. ANNI POS●… CHRISTUM . 469. 470. 480. 490. 490. 500. 500. 500. 500. ANNI POST CHRISTUM . 500. 500. 520. 526. 550. 550. 574. 580. 600. 636. ANNI POST CHRISTUM 640. 680. 700. 709. 770. 770. 790. 827. ANNI POST CHRISTUM . 446. 860. 879. 880. 890. 930. 936. ANNI POST CHRISTUM . 950. 956. 970. 980. 980. 984. 995. 996. 1004. 1030. ANNI POST CHRISTUM . 1032. 1035. 1050. 1050. 1060. 1070. 1070. 1071. 1072. A●…I 〈◊〉 CHRISTUM . 1090. 1100. 1115. 1130. 1132. 1140. 1142. 1144. 1149. ANNI POST CHRISTUM . 1150. 1150. 1160. 1160. 1160. 1164. 1166. 1170. 1170. 1170. ANNI POST CH●…ISTUM . 1190. 1199. 1200. 1200. 1210. 1224. 1240. 1240. 1252. 1252. 1253. 1255. ANNI POST CHRISTUM . 1255. 1256. 1256. 1260. 1260. 1269. 1270. ANNI POST CHRISTUM . 1272. 1272. 1275. 1282. 1290. 1290. 1293. 1300. 1310. 1320. 1320. ANNI POST CHRISTUM . 1320. 1320. 1322. 1322. 1326. 1330. 1330. 1335. 1340. 1340. 〈◊〉 POST CH●…ISTUM . 1340. 1341. 1342. 1347. 1350. 1350. 1350. 1350. ANNI POST CHRISTUM . 1360. 1360. 1360. 1363. 1370. 1370. 1370. 1370. 1370. ANNI POST CHRISTUM . 1378. 1385. 1390. 1390. 1390. 1390. 1396. 1400. 1400. 1402. 1410. ANNI POST CHRISTUM . 1410. 1410. 1419. 1434. 1436. 1437. 1437. 1437. 1437. ANNI POST CHRISTUM . 1438. 1440. 1440. 1440. 1450. 1450. 1460. 1460. ANNI POST CHRISTUM . 1460. 1460. 1462. 1470. 1473. 1474. 〈…〉 1475. 1475. 1475. 1478. 1480. 1480. 1480. ANNI POST CHRISTUM . 1480. 1480. 1482. 1488. 1490. 1490. 1490. 1490. 1490. 1490. 1491. ANNI POST . CHRISTUM 1492. 1493. 1494. 1494. 1494. 1494. 1495. 1495. 1495. ANNI POST CHRISTUM . 1497. 1500. 1500. 1500. 1507. 1507. 1508. 1509. 1510. 1513. ANNI POST CHRISTUM . 1514. 1514. 1515. 1515. 1516. 1518. 1521. ANNI POST CHRISTUM . 1522. 1523. 1524. 1524. 1525. 1527. 1528. 1528. 1528. ANNI POST , CHRISTUM 1528. 1530. 1530. 1530. 1530. 1530. 1530. 1530. 1530. 1531. ANNI POST CHRISTUM . 1532. 1533. 1533. 1534. 1535. 1535. 1536. 1536. 1536. ANNI POST CHRISTUM . 1536. 1536. 1536. 1537. 1537. 1537. ANNI POST CHRISTUM . 1537. 1537. 1538. 1538. 1539. 1540. 1540. 1540. 1540. 1540. 〈…〉 1540. 1540. 1540. 1540. 1540. 1540. 1540. 1540. ANXI POST CHRISTUM ▪ 1541. 1541. . 1542. 1543. 1544. 1544. 1544. 1544. ANNI POST 〈◊〉 1544. 1544. 1545. 1548. 1548. 1548. 1548. 1548. 1548. 1549. 〈…〉 1549. 1550. 1550. 1550. 1550. 1550. 1550. 1550. 〈◊〉 POST CHRISTUM 1550. 1550. 1550. 1551. 1551. 1551. 1551. 1552. 1552. 1552. 1553. ANNI POST CHRISTUM 1554. 1555. 1555. 1555. 1556. 1556. 1556. ANNI POST CHRISTUM . 1557. 1557. 1557. 1557. 1557. 1558. 1559. 1560. 1560. 1●…60 . ANNI POST CHRISTUM . 1560. 1560. 1560. 1560. 1560. 1560. 1560. ANNI POST . CHRISTUM 1560. 1561. 1561. 1562. 1563. 1564. 1565. 1567. 1568. 1568. 1568. ANNI POST CHRISTUM . 1570. 1570. 1570. 1570. 1570. 1571. 1572. 1572. 1572. 1572. 1572. 1572. 1572. ANNI POST CHRISTUM ▪ 1572. 1572. 1572. 1572. 1572. 1572. 1572. ANNI POST CHRISTUM . 1572. 1572. 1573. ANNI POST CHRISTUM . 1573. 1573. 1573. 1573. 1573. 1573. 1573. 1574. 1574. 1574. 1574. 1574. ANNI POST CHRISTUM . 1574. 1574. 1576. 1576. 1576. 1576. 1577. 1577. 1577. 1577. ANNI POST CHRISTUM . 1577. 1578. 1578. 1579. 1579. 1580. 1580. 1580. 1580. 1581. 1532. ANNI POST CHRISTUM . 1582. 1583. 1583. 1583. 1583. 1584. 1585. 1586. 1587. ANNI POST CHRISTUM . 1587. 1589. 1590. 1590. 1590. 1590. 1590. 1590. 1590. ANNI POST CHRISTUM . 1590. 1590. 1591. 1591. 1591. 1591. 1592. 1593. ANNI POST . CHRISTUM . 1593. 1594. 1594. 1595. 1595. 1597. 1597. 1597. ANNI POST CHRISTUM . 1598. 1599. 1599. 1599. 1599. ANNI POST CHRISTUM . 1600. 1600. 1600. 1600. 1600. 1601. 1602. 1602. ANNI POST CHRISTUM . 1603. 1603. 1603. 1605. 1606. 1606. 1607. 1608. 1608. ANNI POST CHRISTUM . 1608. 1609. 1609. 1609. 1610. 1610. 1611. 1611. 1612. ANNI POST CHRISTUM . 1612. 1612. 1612. 1613. 1614. 1615. 1615. ANNI POST CHRISTUM . 1615. 1615. 1616. 1617. 1617. ANNI POST CHRISTUM . 1617. 1617. 1618. 1618. 1618. 1618. 1619. 1619. 1619. 1619. 1619. 1619. ANNI POST CHRI●…TUM 1619. 1619. 1620. 1620. 1620. 1620. 1620. 〈◊〉 . ANNI POST CHRISTUM . 1620. 1622. 1623. 1624. ●…NNI ●…OST CHRISTUM . 1624. 1624. 1624. 1624. 1625. ●…NNI POST CHRISTUM . 1626. 1626. 1627. 1627. 1628. 1628. 1628. 1629. ANNI POST CHRISTUM . 1630. 1630. 1630. 1630. 1630. 1630. 1632. ANNI POST CHRISTUM . 1632. 1633. 1633. 1634. 1634. 1634. 1635. 1635. 1635. ANNI POST CHRISTUM . 1635. 1635. 1637. 1637. 1638. 1640. 1640. ANNI POST CHRISTUM . 1640. 1640. 1640. 1640. 1640. 1640. 1640. 1640. ANNI POST CHRISTUM 1640. 1640. 1640. ANNI POST CHRISTUM . 1640. 1640. 1640. 1640. 1641. 1642. ANNI POST CHRISTUM . 1643. 1643. 1643. 1644. 1644. 1644. 1644. 1644. 1644. 1645. ANNI POST CHRISTUM . 1645. 1645. 1645. 1645. 1645. ANNI POST CHRISTUM . 1645. 1645. 1645. 1645. 1645. ANNI POST CHRISTUM . 1645. 1646. 1646. 1646. 1646. 1647. 1648. 1648. ANNI POST CHRISTUM . 1648. 1648. 1648. 1649. 1650. 1650. 1650. ANNI POST CHRISTUM . 1650. 1650. 1650. 1650. 1650. 1651. 1651. ANNI POST CHRISTUM 1651. 1651. 1651. 1651. 1652. 1653. ANNI POST CHRISTUM . 1653. 1654. 1654. 1654. 1655. ANNI ●…OST CHRISTUM . 1655. 1655. 1656. 1656. ANNI POST CHRISTUM . 1657. 1657. 1657. 1658. 1659. ANNI POST CHRISTUM 1660. 1661. 1661. ANNI POST CHRISTUM . 1661. 1661. ANNI POST CHRISTUM . 1661. 1662. 1662. 1663. 1663. 1663. ANNI POST CHRISTUM . 1664. 1664. 1657. 1665. 1666. ANNI POST 〈◊〉 . 1666. 1666. 1666. 1668. 1668. 1669. ANNI POST CHRISTUM . 1669. 1669. 1669. 1670. ANNI POST CHRISTUM . 1670. 1670. 1670. ANNI POST CHRISTUM . 1670. 1671. 1672. 1672. 1672. ANNI POST CHRISTUM . 1673. 1673. 1673. ANNI POST CHRISTUM . 1673. 1673. ANNI POST CHRISTUM . 1673. 1673. 1673. ANNI POST CHRISTUM . 1673. 1673. 1673. ANNI POST CHRISTUM . 1673. 1673. ANNI POST CHRISTUM . ANNI POST CHRISTUM . Anni Ante Christum secundum vulgatam Epocham . 2952. 2697. 2513. 2513. 2400. 2357. 2258. 2158. ANNI ANTE CHRISTUM . 1120. 1100. 960. 760. 470. ANNI ANTE CHRISTUM . 224. ANNI POST CHRISTUM . 140. 930. 1100. 1160. 1320. 1346. 1350. 1390. ANNI POST CHRISTUM . 14●… . 1494. 1558. 1583. 1585. 1590. 1590. 1598. 1600. ANNI POST CHRISTUM . 1603. 1609. ANNI POST CHRISTUM . 1612. 1623. 1632. 1633. 1634. 1637. 1648. 1643. 1643. 1645. ANNI POST CHRISTUM . 1650. 1653. 1653. 1655. 1656. 1656. 1660. 1669. ANNI POST CHRISTUM . 1671. 1671. 1672. 1673. Notes for div A51768-e180470 NUMBER OF THE HEAVENS . NUMBER OF THE HEAVENS . NUMBER OF THE HEAVENS . Notes for div A51768-e199270 The Equinoctial Circle . The Equator considered as to the several Positions of the Sphere . The Zodiack . The Ecliptick . The Colures ▪ The Meridian . The Horizon . The Tropicks . The P●…lar Circles . Zones . Parallels . Climates . Notes for div A51768-e207110 It s Nature and Substance . Maculae , or Spots . Their Shapes and Figures . Their Motion . * Kepler . * Otto de Guerick . * Experiment . Magdeburg l. ●… ▪ c. 1. & 6. The several sorts of fiery Meteors . Of the Matter , Place , and eff●…cient Cause of Comets . Cometical Aphorisms ▪ Of the Tayl , Train , or Bush of Comets . Of the several Kinds of Comets . Notes for div A51768-e323370 * Optimis linguae Latiae Conditoribus , funus non saepius ipsam Sepulturam aut ejus Pompam significat , quam Cadaver , sic accipitur à Virgilio , & enarratur à Servio , in 3. Aeneid . Funus propriè est incensum Cadaver . vide . Barthii Adversar . l. 6. ●… . 9. 
A52255	----	Astronomia Britannica exhibiting the doctrine of the sphere, and theory of the planets decimally by trigonometry, and by tables : fitted for the meridian of London ... / by John Newton ... Newton, John, 1622-1678. 1657 Approx. 1286 KB of XML-encoded text transcribed from 176 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2004-08 (EEBO-TCP Phase 1). A52255 Wing N1053 ESTC R20418 12354962 ocm 12354962 60115 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A52255) Transcribed from: (Early English Books Online ; image set 60115) Images scanned from microfilm: (Early English books, 1641-1700 ; 217:13) Astronomia Britannica exhibiting the doctrine of the sphere, and theory of the planets decimally by trigonometry, and by tables : fitted for the meridian of London ... / by John Newton ... Newton, John, 1622-1678. [13], 168, 156 p., [1] folded leaf of plates : ill. Printed for the author by R. and W. Leybourn, and are to be sold by Thomas Piercepoint ..., London : 1657. Pts. 2 and 3 each have special t.p.'s and are dated 1656; pt. 3 is separately paged. Reproduction of original in British Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. 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Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Astronomy -- Early works to 1800. Planetary theory -- Early works to 1800. Astronomy -- Mathematics -- Early works to 1800. 2004-04 TCP Assigned for keying and markup 2004-04 Apex CoVantage Keyed and coded from ProQuest page images 2004-05 Mona Logarbo Sampled and proofread 2004-05 Mona Logarbo Text and markup reviewed and edited 2004-07 pfs Batch review (QC) and XML conversion Astronomia BRITANNICA , Exhibiting The Doctrine of the Sphere , and Theory of the Planets Decimally by Trigonometry , and by Tables . Fitted for the Meridian of LONDON , according to the Copernican Systeme As it is illustrated by Bullialdus , and the easie way of Calculation , lately published by Doctor WARD . By JOHN NEWTON , M : A : bookseller's logo LONDON , Printed for the Author , by R. and W. Leybourn , and are to be sold by Thomas Pierrepoint , at the Sun in St. Pauls Church-yard , 1657. To the Right Honourable ROBERT Earl of WARWICK , Baron of LEES , &c. RIGHT HONOURABLE , AS it were presumption in me , to think , that I have any thing in my selfe , that is worthy the presenting to your Honour : so it were injustice to keep from you , that which is your own ; He that is once an Admiral , hath so great an interest in the Sea , that of necessity he must have some ●n the Stars also , because Navigation without Astronomy is very lame and defective . The compass I know is the Sea-mans best direction when the weather is foul , but the Sun is found a better when it is faire , yea , serveth to correct the errors committed by the other ; unlesse his place therefore be rightly known , our Sea-men , how otherwise skilfull soever , will be many times troubled to steer their course aright : This then ( without prejudice to other mens endeavors ) is that which I aim at , and do believe I have effected , as with more ease , so also with more exactness , then those who have written before me , and that not only in relation to the Sun , but also to the Moon and other Planets , the truth of which Time only can discover , & must be therefore waited for . And now that these endeavors of mine may in the mean while receive some shelter from the envious , through your Honors protection , is the humble suit of him that is Your Honours to dispose of IOHN NEWTON . To the Courteous READER . Courteous Reader , AS there is no part of Mathematicall learning more excellent , so is there none more difficult then this of Astronomy , it hath for some thousands of yeares been much studied , and not without great expence of treasure , brought to that perfection , in which we now enjoy it ; nor can we expect , that those mistakes , to which this noble Science is yet too often lyable , should ever be redressed , without the expence of more , and hard it is to perswade the men of this earthly-minded age , to look higher then the earth they tread upon , and wallow in ; they will not look so high as Heaven themselves , nor give encouragement unto those that would ; but that our Students should neglect the benefit of that knowledg they might enjoy ; that they should be in love with those difficulties they might avoid , in a study that is too intricate and difficult at the best , can never be sufficiently admired . It is therefore our chief and principal aime to shew how much of trouble may be avoyded in computing the motions of the heavenly bodies ; if only the form of our Tables were changed from Sexagenary into Decimall , the excellency of Decimal Arithmeticke will in part appeare , if wee but consider the manner of working , in our Sexagenary Canons of naturall Sines and Tangents , in which ( to avoid the vast trouble , if not almost the impossibity of working with a Canon that should consist of vulgar Fractions ) the Sine and Tangent of every minute is nothing else but the Decimall of a Unite ; and this that famous Mathematician of our age Mr. Henry Brigges did well perceive , when ( having perfected that noble invention of Logarithms , first found out by the Right Honourable , John , Lord Neiper , Baron of Merchiston in Scotland ) he tooke the paines to make a new Canon of Sines and Tangents , dividing the degrees into Decimals , as well as the parts of the Radius answering unto those degrees ; and according to which Canon , Mr. Henry Gillebrand did since prepare a Treatise of Astronomy for the Presse , but his death prevented the publication : To these I may adde Mr. William Oughtred , who is the present wonder of our age , for his extraordinary knowledge in this kind of learning , who in his Clavis Mathematica , doth not only wish that this Decimall form were observed in all Astronomical Canons , but hath also lately professed , that he ever found so much trouble in the Sexagenary way , that he took the pains to turn the Equations in the Rudolphin Tables into Decimals before he used them ; besides the trouble of Reduction this advantage our Decimal Tables have above the Sexagenary , that in finding the part proportional , the half of your work is done before you begin , there being a necessity both of Multiplication and Division , in Sexagenary numbers , but here of Multiplication onely , or onely of Division . And now that this wonderful ease in calculation , commended to us by these famous men , might not still lie buried in oblivion , & that our Artists might be no longer enforced to use those labyrinthical Tables in the Sexagenary form , we have adventured to publish these , which never should have seene the light , if there had been any hope of those which Mr. Gillebrand did long since compose , or that Mr. Moore could have found encouragement to have published his ; or that any other could have been perswaded to this Decimal form . The ease then that is in the form of our Tables , is in truth the reason for which we have undergone this labour , and yet the method of Calculation , which Dr. Ward professor of Astronomy in Oxford hath lately published ( in his Book entituled Inquisitio in Bullialdi Astronomiae Philolaicae fundamenta ) and which we have used in the composure of our Tables , is so brief , so easie , and so exact , as that a better is not to be expected . I am not ignorant , that some ( which have a desire to make others and themselves work ) are not therewith satisfied , they will rather take the pains of seven or eight operations , and yet the aequation at last found , is not so legitimate as that which here we find at one ; of which there needs no other proof then the Geometry of our Method , our very Enemies being Judges ; yet all that we shall promise is the places of the Planets prope rerum , at a cheaper rate ; if we do fail of their true Phenomenon , it shall be with less trouble and expence of time . Our Middle-motions , Aphelions , Excentricities , and Dimensions of the several Orbs mentioned in the ensuing Treatise , we have borrowed from Bullialdus , the method by which they are computed is the same in all , and therefore as to the Excentricities & Aphelions , we thought it sufficient to instance in the Sun or Earth : and for the proportions between the Earths Orb , and the Orbs of the other Planets with their angles of Inclination , we have given an Example in Saturn only , and refer you to Bullialdus for the rest . And although this method of his be not Geometrically true , yet knowing no better ; we have contented our selves with his , untill there be a better found ; and to make his Middle-motions to us more useful , we have reduced their Epoches to the Meridian of London , the most famous City of this our Island of Great Britain : For which reason , and for the easiness of the calculation which our own Country-man hath invented , and we here used , the Treatise it selfe doth carry the style of Astronomia Britannica . And whether this method of finding the first inequality will agree with observation , cannot be known ; until a Geometrical way of finding the Excentricities & Aphelions of the Planets in an Ellipsis be also propounded to us ; and if at last , when all things in this Elliptical Astronomy shall geometrically be demonstrated , the places of the Planets thus found shall not agree with observation , it will be hard to say in what particular the fault doth lie , and therefore we must not then impute it to the first inequality , much lesse now , when the Geometry of that is demonstrated , & other parts are defective , but a new Hypothesis must be thought of ; and until this shall be effected , as there are no Tables extant , by which the places of the Planets can be computed with so much ease , so none can be expected , by which their places may be computed with more probability of truth , then by these which wee must now submit to thy censure , and do commend to thy perusal . IOHN NEWTON . The Contents of the severall Books or parts of Astronomia Britannica . The first Book . The Preface . Page 1. THe Suns greatest declination being given , to find his declination in any point of the Eclipticke 9 How to finde the declination of a Planet or fixed Star , with latitude 10 How to finde the Right Ascension of any point of the Eclipticke 13 How to finde the Right Ascension of a Planet or other Star with latitude 15 The elevat . of the Pole , & declin . of the Sun given , to find his amplit . 16 The Meridian altitude , and declination of the Sun , with the Poles elevation given to find his true place in the Zodiacke 17 Having the Meridian altitude of an unknown Star , and the distance thereof from a known Starre , to find the Right Ascension of the unknown Star Ibid. Having the declin . and Right Ascension of a Star given , to finde the longitude and latitude thereof 19 How to finde the Ascensionall difference 20 How to finde the Oblique Ascension or Descention of any point of the Eclipticke 21 The Poles elevation and the Suns declination being given , to finde his altitude at any time assigned 22 Having the Suns greatest declination , with his distance from the next Equinoctional point , to finde the Meridian angle , or intersection of the Meridian with the Eclipticke 26 To finde the angle of the Meridian , with the Horizon Ibid. The Poles elevation , with the Suns altitude and declination given , to finde his Azimuth Ibid. How to erect a Figure of Heaven 27 To find the angle of the Ecliptick with the horizon , or the altitude of the Nonagesime deg . together with its distance from the mid-heaven 36 To finde the Parallactical angle , or angle of the Ecliptick , with the verticall circle ●7 The elevation of the Pole , and declination of the Sun given , to finde the time when he will be due East and West 39 The elevation of the Pole , with the Suns declination and altitude given , to finde his distance from the Meridian 40 To finde the time of the Suns rising and setting , with the length of the Day and Night Ibid. To finde the distance of a Star from the Meridian 41 To finde the elevation of the Pole above any circle of Position Ibid. Of the Arke of Direction what it is , and how to finde it 45 How to direct the Mid-heaven , and the Imum Coeli 46 How to direct the Ascendent , or Significator posited in the Signes ascending Ibid. How to direct a Significator , posited in the Signes descending 47 How to find the Arch of the Equator , whereby is made the generall Table of Positions 48 How by the generall Table of Positions to make a particular Table for any latitude there exprest 49 Of the doctrine of the Sphere in Tables 51 The second Book . OF the yeare Civill and Astronomical 57 Of the Figure which the Planets describe in their Motion 66 Of the lines and method to be used for the finding of a Planets true longitude from the Aphelion in this Figure 72 Of the proportion by which the motion of the Planets do increase from the Aphelion to the Perihelion 74 Of the inequality of the Earths annuall motion , and of the Diameter in which the Aphelion and Perihelion are placed 81 Of stating the Earths middle motions by sundry observations 90 To calculate the Suns true place and distance from the Earth 94 Of the Aequation of Civill Dayes 97 Of the Theory and motion of the Moon 98 To calculate the true motion of the Moon by Tables 109 To find the Moons true latitude and place in the Ecliptick 113 Of the motion of the fixed Starres 115 Of the motion of Saturn 116 Of the motion of Jupiter 121 Of the motion of Mars 124 Of the motion of Venus 128 Of the motion of Mercury 133 Of the Semidiameters of the Sun , Moon , and shadow of the Earth 136 Of the proportion and magnitude of the three great bodies , the Sunne , Moon , and the Earth 142 Of the proportion between the Orbs of the superiour and inferiour Planets , and the Orbe of the Earth 144 To finde the mean Conjunction and Opposition of the Sun & Moon 151 To finde the true Opposition and Conjunction of the Sun and Moon 152 To finde whether there will be an Eclipse or not 154 To finde the quantity of a Lunar Eclipse Ibid. To finde the duration of a Lunar Eclipse , or the continuance of the totall darknesse , where the Eclipse is totall 155 To finde the Moons latitude at the beginning & end of the Eclipse 156 To finde the middle of the Eclipse or greatest darknesse 157 Of the calculation of the Suns Eclipse 159 To finde the Parallaxes of longitude and latitude 160 To finde the visible motion of the Moon from the Sun for any time assigned 162 To find the time of the visible Conjunction of the Sun and Moon Ibid. To finde the visible latitude of the Moon , at the time of the visible Conjunction 163 To finde the quantity of a Solar Eclipse 164 To finde the beginning and ending of the Suns Eclipse Ibid. To finde the visible latitude of the Moon at the beginning and end of the Suns Eclipse 165 To delineat the Eclipses of the Sun and Moon 166 The use of the Table of Refractions 168 The Index of the Tables . A View of the more notable Epochae 2 A Table shewing the Dominical Letter in both accompts 4 A Table shewing the Golden number & Epact in both accompts Ibid. The Anticipation of the Gregorian Kallender Ibid. A Table of moveable Feasts in both accompts 5 A Table of fixed Feasts 6 A Catalogue of Places , their latitudes and distance in longitude from the Meridian of London 8 A Table to convert Sexagenary minutes , seconds , thirds , fourths and fifths into Decimalls , and the contrary 10 A Table to convert the hours , minutes , seconds , thirds , fourths and fifths of a day into Decimalls , and the contrary 14 A Table to convert hours & parts into deg . & parts of the Aequator 20 A perpetual Table for the Equation of Time 21 The Suns mean motions 22 The Aequations of the Suns Excerntrick 26 The Moons mean motions 29 The Aequations of the Moons Excentrick 34 A Table for the finding of the secōd & third inequalities of the Moon 37 Bullialdus his Table of Evection 40 A compounded Table of the Moons Evection and Variation 43 A Table of the Aequations of Nodes and Moons latitude 53 A Table of the Reductions to the Ecliptick 56 The difference of the true ☌ or ☍ from the middle of the obscuration 57 A Table of the mean Lunations 58 The Horizontall Parallaxes , Semidiameters , and hourly motions of the Sun and Moon 59 The Declination and Meridian Angles 60 Tycho's Table of Refractions 61 Saturn's mean motions 62 Jupiter's mean motions 66 The mean motions of Mars 70 The mean motions of Venus 74 Mercuries mean motions 78 A Table of Declinations 82 A Table of Right Ascensions 89 A Table of Ascensional Differences 100 A Table of Oblique Ascensions 108 A Table of Positions for the latitude of 51 degrees 53 parts 138 A Table shewing the elevation of the Pole upon the severall circles of Position of the 11 , 12 , 2 and 3 houses for 60 degrees of latitude 151 A generall Table of Positions 152 A Catalogue of the more notable fixed Stars with their longitude , latitude , and magnitude for the yeare 1650 compleat . 154 The Preface . ALL Propositions Astronomical and Astrological , have some dependence on the Sphere or Globe , for the better understanding therefore of that which follows , it is fit that the Reader be somewhat acquainted with the doctrine thereof ; that he know at least what a Globe is , and what the lines , circles and arches usually drawn thereon do represent . Now a Globe or Sphere , is an Analogical representation either of the Heavens or the Earth . And in this Sphere or Globe there are ten imaginary circles whereof there are six great and foure small . A great circle is such a one as divideth the body of the Globe into two equal Hemispheres . And a small circle is that which divideth the same , into two unequal Hemispheres , wherof the one is more , the other less then half the body of the Globe or Sphere . The six great circles are these . 1 The Horizon . 2 The Meridian . 3 The Equinoctial . 4 The Zodiack . The fifft and sixt are the two colures . The four lesser circles are , 1 The Tropick of Cancer . 2 The Tropique of Capricorn . 3 The circle Artick . 4 The circle Antarctick . And are all exprest in this annexed Diagram . 1 The Horizon which is also called the Finitor , is a circle which divideth the visible part of the Heavens from the not visible , that is the lower Hemisphere from the higher , in the figure noted with A B. 2 The Meridian is a circle which passeth by the Poles of the World , and through the Zenith and Nadir , and is marked with A Z B N. 3 The Equinoctial is a Circle which divideth the whole Sphere into two equal parts , and is therefore equally distant from both the Poles , to which when the Sun cometh ( which is twice in the Year ) the Dayes and Nights are of equal length all the World over , this circle is noted with E F. 4 The Zodiack is a great circle which conteineth the 12 Signes , cutting in the very middle the Equinoctial in two points , which are the beginning of Aries and Libra , whereof the one half . viz. six Signes decline from the Aequator to the North Pole , and are therefore called the Northern Signes , as Aries ♈ , Taurus ♉ , Gemini ♊ , Cancer ♋ , Leo ♌ ; Virgo ♍ . The other six decline towards the South Pole and are therfore caled the Southern Signes , as Libra ♎ , Scorpio ♏ , Sagittarius ♐ , Capricornus ♑ , Aquarius ♒ , Pisces ♓ . 5 The one of the Colures which dividing the Sphere into two parts passeth by the Poles of the World and the two Equinoctial points , called the Equinoctial Colure , and marked with C D. 6 The other Colure which dividing the Sphere also into two equal parts , passeth by the beginning of Cancer and Capricorn , and the Poles of the World , called the Solstitial Colure , and is the same with the Meridian as the Sphere is here projected . 7 The Tropick of Cancer is one of the lesser circles distant from the Equinoctial towards the North Pole 23 deg . 31 min. 30 seconds , or in Decimal Numbers , 23 deg . 525 , to which when the Sun cometh he causeth the longest day , and shortest night to all Northern , the shortest day and longest night to all Southern inhabitants , and is noted with G ♋ . 8 The Tropick of Capricorn is a circle distant from the Equinoctial towards the South Pole : 23 deg . 31 min. 30 seconds , or in Decimal numbers , 23 deg . 525 parts , to which when the Sun cometh , he maketh the longest day and shortest night , to all Southern the shortest day & longest night to all Northern Inhabitants , and is noted , with H ♑ . These two circles are called of the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 à convertendo , because when the Sun toucheth any of these circles , he is at his greatest distance from the Aequator , and returneth thither again . 9 The Artick circle is distant from the North pole of the world as much as the Tropick of Cancer is distant from the Equinoctial , and is noted with K L. 10 The Antartick circle is distant from the South Pole as much as the Tropick of Capricorn is distant from the Aequator , and is noted with O M. Besides these circles exprest upon the Globe , there are other circles not exprest , that are also in familiar use ; but these being sufficient for our intended matter , omitting the rest , we will now speak of the several affections of the Sphere or Globe , and so proceed to practice . According to the diverse habitude of the Aequator to the Horizon ( which is either Paralel to it , or else cutteth it , and that either in right or oblique angles ) there is a threefold position or Situation of Spheres . The first is of those that have either Pole for there Zenith or vertical point , with these the Aequator and Horizon are Parallel to each other , or rather indeed do make but one circle between them ; and this is called a Parallel Sphere , and they which there inhabit ( if any such be ) see not the Sun or other Star either rising or setting , or higher or lower , in their diurnal revolution . The third position of the Sphere agreeth to all other places else , and is called an oblique Sphere , in which the dayes are sometimes longer then the nights , sometimes shorter , and sometimes of equal length : when the Sun is placed in the Equinoctial point , the dayes and nights are equal , but when he declineth from the Aequator , the dayes are observed to increase , and when he declineth towards the opposite Pole the dayes decrease , as it is manifest in the first figure . And thus having briefly shewed , what a Globe is , the lines thereon described , with the several affections belonging thereunto , what remayneth but that we now proceed to practice , & shew there use as to the matter in hand ; wch is to find the Declinations and Asceusions of the Sun and other Stars whether right or oblique , and divers other things depending on , or belonging to the Doctrine of the Spheare , the which we will shew first by Trigonometrical Calculation , and then by Tables . Astronomia BRITANNICA : The first Book . CHAP. 1. To find the Suns greatest Declination , and the Poles Elevation . THe Declination of a Planet , or other Star is his distance from the Aequator , and as he declines from thence either Northward or Southward , so is his declination nominated North or South . And because that all the Planets ( the Sun onely excepted ) do move sometimes in and sometimes out of the Ecliptick besides there declination North or South from the Aequator , they have also latitude North or South from the Ecliptique , while the Planets keep in the ecliptique , one rule will serve to find their Declination , as well as the Declination , of the Sun , but if they have either North or South latitude , there must another rule be given , in both which rules the greatest Declination of the Sun is supposed to be known ; and first therefore we will shew how , that may be found instrumentally , and then compute the Declination of a Planet or other Star , with latitude or without . For the finding the Suns greatest Declination , you must by a Quadrant or other Instrument , take his greatest and his least Meridian altitude ; the difference between which altitudes is the distance of the Tropiques , and half the distance of the Tropiques , is the quantity of the Suns great Declination , as by the following Figure it doth appear . In which A Z B N represents the Meridian , E F the Eq●inoctial , ♋ ♑ the Zodiack , the North pole D the South A B the Horizon Z the Zenith , N the Nadir , ♋ G a parallel of the Suns Diurnall motion at ♋ , or the Suns greatest Declination from the Equator towards the North Pole. From whence it is apparent that from A to ♋ is the Suns greatest Meridian altitude from A to H his least , if therefore you deduct A H the least Meridian altitude from A ♋ the greatest , the difference H ♋ is the distance of the Tropiques , and because the angles ♋ center F and ♑ center E are equal , therefore the Suns greatest Declination towards the South Pole is equal to his greatest Declination towards the North , and consequently halfe the distance of the Tropiques , or the arch that is the arch ♋ F is the quantity of the Suns greatest declination . And then if you deduct the Suns greatest declination or the arch A ♋ F from the Suns greatest Meridian altitude or the arch A ♋ the difference wil be A F or the height of the Aequator above the Horizon , the complement whereof to a quadrant is the arch A D equal to C B the height of the Pole. Example . The Suns greatest Meridian altitude taken , June 11 at London 61 , 99167 The Suns least Meridian altitude , December the 10th . 14 , 94167 Their difference is the distance of the Tropiques 47 , 05000 Half that difference is the Suns greatest Declination whose difference from the greatest altitude is 23 , 52500 The elevation of the Equator and the complement thereof to 90 is the Elevation of the Pole 38 , 46667   51 , 53333 CHAP. 2. The Suns greatest Declination being given , to find his Declination in any point of the Ecliptique . LEt DFHG represent the Solstitial Colure , D BAG the Equator , F A H the Ecliptique , I the Pole of the Ecliptick , E the pole of the Equator , E C B a meridian line passing from E , through the Sun at C , and falling upon the Equator D A G with right angles at the point B. Therefore in the Rectangle sphaericall Triangle A B C we have known . 1 The Hypothenuse A C the Suns distance from the next Aequinoctiall Point , whether Aries or Libra and may be supposed to be in 10 degrees of Cancer , and that being neerer unto Libra then Aries , I take his distance from Libra which is two signs and 20 degrees , or 80 degrees . 2. We have known the angle B A C the Suns greatest declination , which by the accurate Observation of Tycho is found to be 23 deg . 31 minutes and 30 seconds . And in Decimall numbers 23. 525. Hence to find the present declination the proportion is . As the Radius is to the sine of the Suns geatest declination . So is the sine of the planets distance from the next Aeqninoctiall point , To the sine of the declination required . And by this proportion , together with the help of the Canon of artificiall sines and tangents , I find the declination of the Sun at the time proposed thus . First , I seek for the sine of Radius or 90 degrees , the measure of the right angle at B , and I find the sine thereof 10 , 000000 , next I seeke the sine of 80 degrees , and likewise the sine of 23. 5250 , these two I adde together and from their aggregate , I substract the Radius and what remaineth is the sine of the declination sought , as in the following work you may perceive . As Radius     To the sine of B A C 23. 525 9 , 6011352 So sine of A C 70. 9 , 9729858 To the sine of B C 22. 02910 9 , 5741210 CHAP. 3. How to find the Declination of a planet or fixed Star with Latitude . What the Declination of a planet is , and how to find the same in any point of the Ecliptique hath been already shewed , we will now shew how to finde the same with latitude either north or south , and for demonstration sake . Let G F I H represent the Solstitial Colure , H A F the Aequator , I A E the Ecliptique , K M N a circle of latitude , G M C a circle of declination , A N the longitude of the star , M C the declination . Then in the Oblique angled spheical ▪ Triangle M G K we have limited . 1 The side K G the Suns greatest declination . 2 The side K M the complement of latitude . 3 The angle M K G the complement of longit . From hence the declination M C may be found at two operations , for first to find K O the proportion is , As the Radius to the Cosine of the complement of Longitude , so is the tangent of the Suns greatest declination , To the tangent of the first arch : K O , which being added to or substracted from the complement of Latitude K M , according to the direction ollowing their aggregate or difference will be the arch O M. If the Declination sought be in the Northerne Signes and North Latitude , substract the arch found from the complement of latitude and what remaineth is the second Arch O M. South Latitude add the arch found to the complement of latitude and their aggregate is the second arch if lesse then a quadrant , but if more the complement thereof to a semicircle . Southerne Signes and North Latitude , adde the arch found to the complement of Latitude , and their aggregate is the second arch . South latitude substract the arch found from the complement of latitude , and what remaineth is the second arch . And then the second proportion is , As the Consine of the first arch found , Is to the cosine of the Suns greatest declination , So is the Cosine of the second arch found , to the Cosine of an arch , whose complement is the declination sought : To make it plain we will in each case adde an example . In the first Quadrant . We will suppose a starre to be in 10 deg . of Gemini , with 4 deg . of north latitude . The longitude of a starre so posited is 70 deg . the complement thereof M K G is 20 deg . The latitude 4 deg . north , the complement thereof 86 M K. And the Suns greatest declination K G 23 deg . 5250. Then according to the former analogie , first I say , As the Radius 90. 10 , 000000 To the Cosine of M K G 20. 9 , 9729858 So is the tangent of K G 23. 5250 9 , 6388198 To the tangent of K O 22. 25 9 , 6118056 The complement of latitude 00 s. 86 d. 00 The arch K O 22 25 Their aggregate 108 25 Their difference 63 75 Because the latitude is North I take their difference and say , As the Cosine of K O : 22. ●5 9 , 9663954 To the Cosine of K G 23. 5250 9 , 9623154 So is the Cosine of O M : 6● . 75 9 , 6457058 To the Cosine of G M : 64. 01 9 , 6416258 The complement thereof 25. 99 is the declination sought . To find the declination of the same point with 4 degrees of South latitude : I take the complement of 108. 25. viz. 71. 75. And say as the Cosine of K O 22. 25. 9 , 9663954 To the Cosine of K G 23. 5250 9 , 9623154 So the Cosine of O M 71. 75 9 , 4957715 To the Cosine of G M 71. 93 9 , 4916915 whose complement is the declination sought , viz. 18. 7. The point of the Ecliptique answering hereunto in the 2 quadrant , is the 20 of Cancer , and hath the same declination North and South . In the third and fourth quadrant the 10 of Sagittary , and the 20 of Capricorn , have the same declination , but with contrary latitude . In the second Quadrant . We will suppose a starre in 10 deg . of Leo whose longitude is 130. The latitude 4 deg . north . The complement of longitude M K G is 50 , but because the longitude is more then a quadrant , I take the complement of 50 , viz. 40 deg . The complement of latitude M K is 86 as before . And the Suns declination fixed , first then I fay , As the Radius 90 10 , 0000000 To the Cosine of M K G 40 9 , 8842539 So the tangent of K G 23. 5250 9 , 6388198 To the tangent of K O. 18. 44 9 , 5230737 The complement of latitude   86. 00 The arch K O   18. 44 Their aggregate   104. 44 Their difference   67. 56 For the north latitude I take their difference and say ,     As the Cosine of K O 18. 44 9 , 9771084 To the Cosine of K G 23. 5250 9 , 9623154 So the Cosine of O M 67. 56 9 , 5817400 To the Cosine of G M 68. 35 9 , 5669470 whose complement 21. 65 is the declination sought . For the declination of the same point with South latitude , I take the complement of 104. 44 : viz. 75. 56. And say , As the Cosine of K O 18. 44 9 , 9771084 To the Cosine of K G 23. 52. 50 9 , 9623154 So the Cosine of O M 75. 56 9 , 3968372 To the Cosine of G M 76. 05 9 , 3820442 whose complement 13. 95 is the declination with South latitude The point of the Ecliptique answering hereunto in the first quadrant is the 20 of Taurus , and hath the same declination North latitude North and South . In the third and fourth Quadrants the points answering thereunto are the 20 of Scorpio and the 10 of Aquarius , and have the same declination but with contrary latitude . CHAP. 4. How to find the Right Ascension of any point of the Ecliptique . THe Ascension of the Sun or Starres is the degree of the Aequator that riseth with the same above the Horizno . And the Descension of it is the degree of the Aequator that goeth under the Horizon with the same , both these are either Right or Oblique . The Right Ascension or Descension is the degree of the Aequator that Ascendeth or Descendeth with the Sun or other starre in a Right Spheare , and the Oblique Ascension is the degree of the Aequator , that ascendeth or descendeth with the same in an oblique spheare . The former of these is simple , and of one kind onely ; because there can be but one position of a Right spheare , but the later is various and manifold according to the diverse inclination of the same . To find the Right Ascension of a planet in the Eclptique , There must be given as in the first Chapter , the planets longitude or distance from the next Equinoctiall point : and the Suns greatest declination . Then in the Rectangle sphericall Triangle of the first chapter A B C , we have limited . 1 The angle B A C , the Suns greatest declination 23. 31. 30. 2 The Hypothenuse A C , the Suns distance from the next Equinoctiall point , whose place we will suppose to be in 10 degrees of Gemini , and consequently his distance from Aries is 70 degrees . Hence to find the base A B , the right Right Ascension the point sought , the proportion is . As the Radius is to the tangent of the planets distance from the next Aequinoctial point : So is the Cosine of the Suns greatest declination ▪ to the tangent of the Right Ascension of the point sought , Example . As the Radius 90 10 , 0000000 To tangent of A C 70. 10 , 4389341 So is the Cosine of B A C 23. 5250 9 , 9623154 To the tangent of A B 68. 34874 10 , 4012495 which is the Right Ascension of the Sun or any other planet without latitude , when they be in the the 10 degree of Gemini . Note that if the Right Ascension of the point sought be in the second quadrant ( is in Cancer , Leo , Virgo . ) you must take the complement of the arch found to a semicircle : if in the third Quadrant ( as in Libra , Scorpio , Sagitarius ) you must add a semicircle to the arch found : if in the last quadrant ( as in Capricorn , Aquarius , Pisces ) you must substract the arch found from a whole circle or 360 , and so shall you have the Right Ascension of any point of the Ecliptique , to make it plaine we will in each case add an Example . In the second Quadrant . Let the Right Ascension of the point sought be 10 degrees of Virgo , the distance thereof from Libra , which is the next Aequinoctiall point is 20 degrees , according therefore to the former Analogie , I say . As the Radius 90. 10. 0000000 To the tangent of A C 20. 9. 5610658 So is the cosine of B A C 23. 5250 9. 9623154 To the tangent of A B 18. 45 9. 5233813 whose complement to a semicircle 161. 55 is the Right Ascension thereof . In the third Quadrant . Let the Right Ascension of the point sought be in 14 degrees of Scorpio , the distance thereof from Libra , the next Aequinoctiall point is 44 degrees . Therefore I say . As the Radius 90. 10. 0000000 To the tangent of A C 44. deg . 9. 9848371 So is the Cosine of 23. 5250 9. 9623154 To the tangent of A B 4152 9. 9471525 to which if you adde a semicircle or 180 degrees the Right Ascension of of the point sought will be 221. 52. In the last Quadrant . Let the Right Ascension of the point sought , be 22 degrees of Aquarius ; the distance thereof from Aries , which is the next Aequinoctiall point ●s 38 degrees . Therefore I say . As the Raduis 90. 10. 000000 To the Tangent of A C 38. 9. 8928098 So is the Cosine of 23. 5250 9. 9623154 To the tangent of A B 35. 62 9. 8551252 which being subtracted from 360 there rests ▪ 324. 38 for the Right Ascension of the point sought . CHAP. 5. How to finde the Right Ascension of a Planet or other Star with Latitude . THe Declination being found by the 3 Chapter , we have in the oblique angled Sphericall Triangle of that Diagram G K M all the sides given with the angle M K G , therefore to finde the angle K G M , say . As the Cosins of the declination , is to the Cosine of the Planets distance from the next Aequinoctiall point . So is the Cosine of its latitude to the Cosine of its Right Ascension . For Example . The Declination of 10 degrees of Gemini , was found to be 25. 99. with 4 degrees North Latitude . Whose complement is G M. 64. 01 the complement of Longitude is the angle M K G 20 , the complement of Latitude is M K 86 , hence to finde the Right Ascension , the Analogie is . As the Sine of G M 64. ●01 . co . arith . 0. 0463059 To the sine of M K G 20. 9. 5340516 So is the sine of K M 86. 9. 9984407 To the sine of K G M. 22. 28 9. 5787982 whose complement 67. 72 is the right Ascension of a Star in 10 degrees of Gemini , with 4 degrees of North Latitude . CHAP. 6. The Elevation of the Pole and Declination of the Sun given , to find his Amplitude . THe Amplitude of the Suns rising or setting is an arch of the Horizon intercepted betwixt the Aequator and the place of the rising and setting of the Sun. And it is either Northern or Southward , the Northern Amplitude is when he sets and riseth on this side of the Equator , toward he North Pole : and the Southern when he sets or riseth on the contrary side . Now when the Sun is in the Aequator , he hath no Amplitude at all : but when he is in the Solstitial points , he hath then the greatest Amplitude . That we may find then the Suns amplitude or distance from the East or West points at the time of his rising or setting ; let D P L G F represent the Meridian , F A I the Horizon , D A L the Equinoctial . P the Pole of the Aequator . Then in the Rectangle Spherical Triangle A B C , let there be given the angle B A C or complement of the Poles elevation , 38. 47 and B C the Suns Declination 23. 15. To find A B the Suns Amplitude , The Analogie is . As the sine of B A C. 38. 47. co . ar . 0. 2061365 To Radius . 90. 10. 0000000 So is the sine of B C. 23. 15. 9. 5945468 To the sine A B 39. 19. 9. 8006833 CHAP. 7. The Meridian Altitude and Declination of the Sun with the Poles Elevation given to finde his true place in the Zodiac . IF the Meridian Altitude of the Sun be lesse then the complement of the Poles elevation , subtract the meridian altitude from the height of the Aequator , and what remaineth is the Suns Declination towards the South Pole ; But if the Meridian altitude of the Sun be more then the height of the Aequator , subtract the height of the Aequator from the Meridian altitude and what remaineth is the Suns Declination towards the South Pole. Then in the Diagram of the second Chapter , in the right angle Sphaericall Triangle A B C , we have known , the angle B A C the Suns greatest Declination , and the perpendicular B C the present Declination to finde the Hypothenuse A C , the Suns distance from the next Equinoctiall point , or true place in the Zodiac , for which the Analogie is . As the sine of B A C. 23. 5250 co . ar . 0. 3988648 To the sine of B C. 23. 15 9. 5945468 So is the Radius or whole sine . 90. 10. 0000000 To the sine of A C 80. 04 9. 9934116 That is in 20 degrees of Gemini , and 4 Centesmes , if the Meridian altitude were taken in Summer : But in 20 degrees 04 Centesmes of Capricorn , if the Meridian altitude was taken in Winter . CHAP. 8. Having the Meridian Altitude of an unknown Star and the distance thereof from a known Star , to finde the Right Ascension of the unknown Star. ABout the end of the year 1577 Tycho observed the distance of the litle Star in the breast of Pegasus from the bright Star of the Vultur to be exactly 45 deg . 31 min. or in decimal numbers 45. 51667. And by the Meridian altitude thereof , he found the Declination to be 22 deg . 26 min. North that is 22. 43333. Which given the Right ascension of the said Starre is to be enquired . For the finding whereof in the oblique angled Sphaericall Triangle ( of the annexed Diagram ) F O L , there is knowne First , F L the complement of the Declinat . of the bright Star of the Vultur 82. 13333. Secondly F O the complement of the Declination of the Star in the brest of Pegasus , 67. 56667. Thirdly O L the distance of them , 45. 51667 , to finde the angle at F or difference of their Right ascension . The side L O. 45. 51667.   The side F L. 82. 13333.   The side F O. 67. 56667.   Sum of the sides . 195. 21667.   The halfe Sum. 97. 60833.   Sine of F L. 82. 13333. co . ar . 0. 0041064 Sine of F O. 67. 56667. co . ar . 0. 0341757 Dif . of F L ½ sum . 15. 47500. 9. 4262148 Dif . of F O ½ sum . 30. 04167. 9. 6995164 Quadrat of the sine of halfe the angle .   19. 1640133 Halfe is the sine of 22. 45453. 9. 5820066 Double is the angle L F O. 44. 90906. Equall to the arch D E the difference of their Right ascensions , which being added to the Right ascension of the bright Star of the Vulture . 292. 58333. The summe 337. 49239 is the Right ascension of the little Star in the breast of Pegasus . CHAP. 9. Having the Declination and Right ascension of a star given , to finde the longitude and latitude thereof . IN the Diagram of the 3 Chapter , having the Right ascension of the little Star in the breast of Pegasus A C. 337. 49239. And the declination C M. 22. 43333. with the greatest obliquity of the Ecliptique B A C. 23. 5250. we are to enquire its Longitude A N. and Latitude M N. wherefore in the Triangle A B C. we have the angle B A C. 23. 5250. and the side A C 22. 50761 the complement of the Right ascension : then I say . As Radius .     To Tangent of B A C 23. 5250 9 ▪ 63●●198 So sine of A C. 22. 50761 9. ●8●●787 To Tangent of B C. 6. 46125 9. 2217985 Adde C M. 22. 43333 The Declination   Sum is M B. 31. 89458   when the Declination is South the arch found must be subtracted from it , and their difference shall be M B. 2. To finde the angle A B C. As the sine of B C 9. 46125 co . ar . 0. 7841497 To the sine B A C 23. 5250 9. 6011352 So the sine of A C 22. 50761 9. 5829787 To the sine of A B C 68. 36843 9. 9682836 3. To finde the side A B. As the sine of B A C. 23. 52520. co . ar . 0. 3988648 To the sine of B C. 9. 46125. 9. 2158503 So is Radius .   10. 0000000 To the sine of A B. 24. 31967 9. 6147151 4. The angle A B C is equall to the angle M B N , therefore to finde the latitude M N. As the sine M N B 90.   To the sine of M B 31. 89458. 9. 722928● So the sine of M B N. 68. 36843. 9. 9682836 To the sine of M N. 29. 41602. 9. 6912118 Lastly , to finde the arch B N. As Radins .     To Cotangent of . M B N. 68. 36843. 9. 5983151 So Tangent of M N. 29. 41602. 9. 7511554 To the sine of B N. 12. 92052. 9. 3494705 Which is to be added to A B if the Right ascension be lesse then a semicircle , but if the Right ascension exceed 180 , as in our example , the Complement of B N. 357 ▪ 07948 , is the longitude desired . CHAP. 10. How to finde the Ascensionall Difference . Then in the Right angled sphaericall Triangle B M C we have limited . 1. The angle C M B the complement of the Pole 38. 46667. Secondly , the side B C 19 deg . the Suns Declination , hence to finde , the ascensional difference M C the Analogie is . As the Cotangent of the poles Elevation , is to Radius . So is the tangent of the planets Declination , to the sine of the ascensionall difference . As the tangent of C M B 38. 46667. co . ar . 0. 09991●6 Is to Radius   10. 000000 So is tangent of B C 22. 0291 9. 6070441 To the sine of M C 30. 61613 9. 7069577 which is the Ascensionall Difference sought . CHAP. 11. How to find the Oblique Ascension or Descension of any point in the Ecliptique . OBlique ascension is when a less arch or portion of the Aequator●iseth ●iseth , then doth of the Zodiack , or else of that Star may be said to rise obliquely with whom a less portion of the Aequator ascendeth above the Horizon , & so the oblike Descension or setting of a Star , is when a less proportion of the Aequator descendeth with it , then doth in a right Sphere . In the former Diagram , D C represents the right Ascension , M C the Ascensional Difference , D M the oblique Ascension , D B an arch of the Ecliptique above the Horizon , which being greater then D M , a Star in this position of the Sphere , is said to rise obliquely . The quantity whereof is found , by deducting the Ascensional difference C M from the right ascension D C , according to the direction following . If the Declination be North Subt. The Ascensional Difference from the right Ascension , and it giveth the oblique Ascension . Adde The Ascensional Difference to the Right Ascension , and it giveth the oblique Descension . South Adde The Ascensional Difference to the Right Ascension , and it giveth the oblique Ascension . Subt. The Ascensional Difference from the Right Ascension , it giveth the oblique Descension . Right Ascension of ten degrees of Gemini , 68. 348●● Ascensional Difference 30. 61613 Oblique Ascension of ten degrees of Gemini , 37. 73261 Oblique Descension of ten degrees of Gemini , 99. 08137 CHAP. 12. The Poles Elevation and the Suns Declination being given , to finde his Altitude at any time assigned . IN this proposition there are three varieties , first , when the Sun is in the Aequator , that is the begining of Aries and Libra , in which case supposing in this Diagram the Sun to be at H two houres or 30 degrees distant from the Meridian A , and the poles Elevation R F equall to A C 51. 53333 , the angle at A being right , I say . As the Radius .     To the Cosine of A H 30 9. 9375●06 So the Cosine of A C 51. 53333 9. 793831● To the Cosine of C H 57. 40351 9. 7313624 whose complement 32. 59649 is the side L H or altitude sought . The second varietie is when the Sun is in the Northerne signes Aries , Taurus , Gemini , Cancer , Leo , Virgo . For the solving of the Probleme in this varietie , let A E C represent the Aequinoctiall . F the pole thereof , L E R the Horizon , G the pole thereof . B D a parallel of the Suns declination . F O the Meridian of the Sun. B H the distance of the Sun from the Meridian . H O the Suns declination North , R F the poles elevation , F G the complement . First , the side F G 38. 46667. Secondly , the side F H. 67. 97090. and the included angle F G H. 45 degrees to find G H. As the Radius     To the Tangent of F G 38. 46667 9. 9000864 So the Cosine of F G H 45. 9. 8494850 To the Tangent of F K 29. 32669 9. 7495714 Then from F H 67. 97090   Deduct F K 29. 32669   There rests H K 38. 64421   2. As the Cosine of F K 29. 32669. co . ar . 0. 0595626 To the Cosine of F G 38. 46667 9. 8937451 So Cosine of K H 38. 64421 9. 8926710 To the Cosine of G H 44. 54111 9. 8459787 The complement whereof N H 45. 45889. is the altitude of the Sun above the Horizon . The third variety is when the Sun is in the southern signes Libra , Scorpio , Sagittarius , Capricorn , Aquarius , Pisces . And in this case supposing the Sun to be in 10 deg . of Sagittarius , and having South declination 22. 02910 , and also 45 deg . distant from the Meridian as before in the oblique angled triangle F G H of the annexed Diagram we have given 1. The side F G. 38. 46667. 2. The side F H 112. 02910 and the angle G F H 45 deg . Then as before , I say As Radius     To the tangent of G F 38. 46667 9 , 9000864 So Cosine of G F H 45. 9 , 8494850 To the tangent of F K 29. 32669 9 , 7495714 From F H 112. 02910   Deduct F K 29. 32669   Rest K H 82. 70241   As the Cosine of F K 29. 32669 co . ar . 0 , 05956●6 To the Cosine of F G 38. 46667 9 , 8937451 So the Cosine of K H 82. 70341 9 , 1038818 To the Cosine of G H 83. 43974 9 , 0571895 whose compl . H N. 6. 56026 is the Suns altitude required . The like is to be observed of the Moon with the other planets and fixed Starres . CHAP. 13. Having the Suns greatest Declination , with his distance from the next Equinoctiall point , to find the Meridian angle or intersection of the Meridian with the Ecliptique . IN the Diagram of the 10 chapter , we have in the triangle D C B. 1. The angle B D C 23. 5250 the Suns greatest Declination . 2 The Hypothenusal D B 70 the distance of the Sun from Aries . 3 The angle B C D 90 , to find the angle D B C. The Analogie is , As the Radius     To the tangent of B D C. 23. 525 9. 6388198 So the cosine of D B 70 9. 5340516 To the Cotang . of D B C 81. 53133 9. 1728714 or the angle of the Ecliptique with the Meridian . CHAP. 14. To find the angle of the Meridian with the Horizon . IN the Diagram of the 5 chapter , we have in the triangle B C M , first , the angle B M C 38. 46667 the elevation of the Equator . 2 B C 22. 02910 the Declination of the point given , to find M B C. As the Cosine of B C 22. 02910 co ar . 0. 0329234 Is to Radius   10. 000000 So is Cosine of B M C 38. 46667 9. 8937451 To the Sine of M B C 57. 63275 9. 9266685 CHAP. 15. The Poles elevation , with the Suns Altitude and Declination given , to find his Azimnth . IN the oblique angled sphaericall triangle G H F , in the second Diagram of the 12 Chapter , we have known H F the complement of the Suns Declination . 2 The side G F the complement of the poles elevation . 3 The side H G the complement of the Suns altitude , to find H G F. ● . The side F H 67. 97090 2. The side G F 38. 46667 3. The side H G 44. 54111 Summe 150. 97868 Halfe summe 75. 48934 Sine of G F 38. 46667 co . ar . 0. 2061682 Sine of H G 44. 54111 co . ar . 0. 1540214 Diff. G F ½ sum 37. 02267 9. 7796909 Diff. H G ½ sum 30. 94823 9. 7111855 Quadrat of the Sine of ½ the angle   19. 8510560 Half is the Sine of 57. 39644 9. 9255280 whose double 104. 79288 is the Suns Azimuth from the North , and the complement thereof 75. 20712 is the Suns Azimuth from the South . CHAP. 16. How to erect a Figure of Heaven . AMong the severall wayes for the erecting of a figure , used by the ancient Astronomers , that is held most rationall which divideth the Equinoctiall into twelve parts by circles meeting at the intersections of the Meridian and Horizon , which is according to the following Scheame , in which the line W Z E represents the East and West Azimuth W ♈ E is that halfe of the Equinoctiall above the eareh , and W ♎ E is that half of the Equator under the earth . The arch 7 ♈ 1 , doth represent that halfe of the ecliptick above the earth . And 7 ♎ 1 that part under the earth . The utmost circle N E S W represents the Horizon , N Z S the meridian , N the north , and S the South end thereof . The Eqninoctiall circle W ♈ E ♎ is divided in to 12 equall parts , by which divisions passe arches , from the North and South intersections of the meridian with the Horizon , which cut the Ecliptique at the cuspe of the houses , N 1 S is the cuspe of the Ascendant , N 7 S of the 7 house N 2. 12 S of the second and twelfth , N 3. 11 S of the third and eleventh , and so of the rest as you see in the Figure . To find the Mid-heaven or Tenth House . When you would erect a figure you must have the true place and Right Ascension of the Sun for the time proposed , let the given time in the meridian of London where the North pole is elevated above the Horizon 51. 53333 be July the 16. After noon 18 hours , 4564 in the yeare 1587. For which time according to our Tables the Suns place is in Virgo 4. 07368 which known the Midheaven or 10 house may thus be found . First , enquire the Right Ascension of the Sun at the time proposed by the 4 Chapter thus As the Radius     To the tangent of A C 25. 92632 9. 6867627 So consine of B A C 23. 52500 9. 9623154 To the tangent of B C 24. 02427 9. 6490781 whose complement 155. 97573 is the Right Ascension sought . To the Right Ascension of the Sun 155. 97573 Adde the Right Ascension of time 276. 84600 Right Ascension of the Mid-heaven 432. 82173 Deduct a whole circle 360. Then rests for the Right Ascension 072. 82173 Then in the Rectangle Sphericall Triangle ♈ 10 F we have given . 1 ♈ F the Right Ascension of the mid-heaven . 72. 82173 2 The Suns greatest Declination F ♈ 10. 23. 5250 to find ♈ 10 the point culminating . As the Radius .     To the Cotangent of F ♈ 72. 82173 9. 4901498 So cosine of 10 ♈ F 23. 5250 9. 9623154 To the cotangent of ♈ F O 74. 17501 9. 4524652 To find the Cuspe of the 11 house . Unto the Right Ascension of the 10 house 72. 82173 Adde 30 degrees 30. 00000 And then the oblique Ascension of the 11 house 102. 82173 To this adde 30. Oblique Ascension of the 12 house 132. 82173   30. Oblique Ascension of the Ascendant 162. 82173   30. Oblique Ascension of the 2 house 192. 82173   30. Oblique Ascension of the 3 house 222. 82173 The Oblique Ascension of the houses thus found by a continuall addition of 30 degrees , we must next find the poles elevation upon their severall circles of position thus , In the rectangle sphericall Triangles E A B and E C D we have limited . 1. Their common angle at E the latitude of the place . 2. E B and E D 38 and 60 with the right angles A and C to find the angles B and D , being the angles that the circles of position make with the Equator . First , then for the 11 and 3 houses . As the Radius     To the Cosine of E D 60. 9. 69470●0 So tangent of C E D 51. 53333 10. 0999136 To cotangent of C D E 57. 81626 9. 7988836 whose complement 32. 18374 is the height of the pole above those circles of position . For the 12 and 2 houses . As the Radius     To the Cosine of E B 30 9. 375306 So tangent of A E B 51. 53333 10. 0999236 To cotangent of A B E 42. 53308 10. 0374442 whose complement 47. 46692 is the height of the pole required .   Having thus found the severall oblique Ascensions of the severall houses together with the elevation of the pole , above their severall circles of position , in the oblique angled sphericall Triangle ♈ C D we have limited 1. The angle ♈ D C complement to C D E. 2. The angle C ♈ D the Suns greatest Declination . 3. Their included side ♈ D the oblique Ascension of each house to find ♈ C the point of the Ecliptique . The Analogies are . For the 1 Operation . As the Sine of the halfe summe of the angles . To the Sine of halfe their difference . So the tangent of halfe the side comprehended . To the tangent of halfe the difference of the sides For the 2 Operation . As the Cosine of the half summe of the angles To the Cosine of their halfe difference . So the Tangent of halfe the side comprehended . To the Tangent of half the Summe of the sides . The Summe of these two arches , shall give you the point of the Ecliptique desired . For the Cuspe of the 11 house . The oblique Ascension or arch ♈ D is 102. 82173 The halfe thereof is 51. 41086 The complement of C D E 57. 81626 is the angle ♈ D C. 122. 18374.       C ♈ D. 23. 52500. Or the Suns greatest Declination Summe 145. 70874 Half Summe 72. 85437   Differ . 98. 65874 ½ Differ . 49. 32937   Sine ½ Summe 72. 85437   co . ar . 0. 0197429 Sine ½ Differ . 49. 32937     9. 8799374 Tang. ½ ♈ D 51. 41086     10. 0980083 Tang ½ Differ . 44. 84740     9. 9976886 For the 2 Operation . Cosine ½ Summe 72. 85437 co . ar . 0 , 5304705 Cosine ½ Differ . 49. ●2937 9. 8140541 Tangent ½ ♈ D 51. 41086 10. 0980083 Tangent ½ Summe 70. 15211 10. 44●5329 1 Arch adde 44. 84740   Summe 114. 99951 or ♋ 24. 99951 is the point of the Ecliptique for the 11 house . For the 12 house . The Oblique Ascension or arch ♈ D is 132. 82173 The halfe thereof is 66. 41086 The complement of C D E 42. 53308 is the angle ♈ D C 137. 46692       C ♈ D 23. 52500       Summe 160. 99192 ½ Summe 80. 49596   Differ . 113. 94192 ½ Differ . 56. 97096   Sine ½ Summe 80. 49596 co . ar .   0. 0060025 Sine ½ Differ . 56. 97096     9. 9234483 Tang. ½ ♈ D 66. 41086     10. 3598529 Tang. ½ Differ . 62. 81111     10. 2893037 For the 2 Operation . Cosine ½ Summe 80. 49596 co . ar . 0. 7822080 Cosine ½ Differ . 56. 97096 9. 7364475 Tangent ½ ♈ D 66. 41086 10. 3598529 Tangent ½ Summe 82. 46470 10. 8785084 1 arch adde 62. 81111   Summe 145. 27581 or ♌ 25. 27581 is the point of the Ecliptique for the 12 house . For the Cuspe of the Ascendant . The Oblique Ascension or ♈ D is 162. 82173 The halfe thereof is 81. 41086 The angle C D E is the same with the height of the Equator 38. 46667 whose complement to a semicircle is the angle . ♈ D C 141. 53333     C ♈ D 23. 52500     Summe 165. 05833 ½ Summe 82. 51916 Differ . 118. 00833 ½ Differ . 59. 00416 Sine ½ Sum 82. 52916 co . ar . 0. 0037026 Sine ½ Differ . 59. 00416   9. 9330844 Tangent ½ ♈ D 81. 41086   10. 8209024 Tangent ½ Dif . 80. 09004   10. 7576894 For the 2 Operation . Cosine ½ Summe 82. 52916 co . ar . 0. 8859846 Cosine ½ Differ . 59. 00416 9. 7117867 Tang. ½ ♈ D 81. 41086 10. 8209024 Tang. ½ Summe 87. 81606 11. 4186737 1 Arch add 80. 09004 11. 4186737 Summe 167. 90610. Or ♍ 17. 90610 is the point of the Ecliptique for the Ascendant For the Cuspe of the 2 house . The Oblique Ascension is 192. 82173 whose complement is the Arch ♈ D 167. 17827. The half whereof is 83. 58913. The summe and Difference of the angles are the same with those for the 12 house . Therefore I say first , Sine ½ Summe 80. 49596 co . ar . 0. 0060025 Sine ½ Differ . 56. 97096 9. 9234483 Tangent ½ ♈ D 83. 58913 10. 9493879 Tangent ½ Diff. 82. 47036 10. 8788387 For the 2 Operation . Cosine ½ Summe 80. 49596 co . ar . 0. 7822080 Cosine ½ Differ . 56. 97096 0. 7364475 Tangent ½ ♈ D 83. 58913 10. 9493879 Tangent ½ Summe 88. 05055 11. 4680434 1 Arch adde 82. 47036   Summe 170. 52091 whose complement 189. 47909 or ♎ 9. 47909 , is the Cuspe of the 2 house . For the Cuspe of the 3 house . The Oblique Ascension is 222. 82173 , whose complement is the arch ♈ D 137. 17827. The half whereof is 68. 58913. The summe and difference of the angles are the same with these for the 11 house . Therefore I say first , Sine ½ Summe 72. 85437 co . ar . 0. 0297429 Sine ½ Differ . 49. 32937 9. 8799374 Tangent ½ ♈ D 68. 58913 10. 4065869 Tangent ½ Diff. 63. 71032 10. 3062672 For the 2 Operation . Cosine ½ Summe 72. 85437 co . ar . 0. 5304705 Cosine ½ Differ . 49. 32937 9. 8140541 Tangent ½ ♈ D 68. 58913 10. 4065869 Tangent ½ Sum 79. 94186 10. 7511115 1 Arch adde 63. 71032   Summe 143. 65218 whose complem . 216. 34782 or ♏ 6. 34782 is the point of the Ecliptique for the Cuspe of the third house . The six Orientall houses being thus found , the other 6 are also found , by consequence , being the same degrees and parts of the opposite signes . And thus we have not onely erected a figure for the time given , but composed a Table , for the generall erecting a figure in this latitude , for by adding together the first and second numbers , in every of these proportions , there is composed 2 numbers for every house , to each of which the Artificiall tangent of halfe the oblique Ascension being added , their aggregates are the tangents of two arches , which added together is the distance of the Cuspe of the house from the first point of Aries . Onely note that if the oblique Ascension be more then 180 deg . you must take the tangent of halfe the complement to a whole circle ; And to find the Cuspe of the house , you must also take the complement of the added arches , as shall be cleared by example . A New Table of Houses for the Latitude of London .   11 & 3 hous . Ascendent 12 & 2 hous . 1 Oper. 9. 8996803 9. 9367870 9. 9294508 2 Oper. 10. 3445246 10. 5977713 10. 5186555 Having found the oblique Ascensions of the houses as before was shewed , take out the tangent of half thereof from a Table of Tangents , whose Radius is 10. 0000000 , and set them down twice on your paper as you see in the following example , then seek in the top of the Table , the house whose cuspe you would find ; and under the same you have two numbers , the first of which being added to one of the tangents in the paper , and the second to the other , will give you the tangents of two arches , whose aggregate is the Cuspe desired . Example . The Oblique Ascension of the 11 house was before found to be 102. 82173. And the tangent of the halfe thereof 51. 41086 is 10. 0980083 the first number in the Table under the 11 house is 9. 8996803 their same rejecting Radius 9. 9976886 , is the tangent of 44. 84740. The second number in the Table . Tangent 51. 41086 10. 0980083 1 Number   9. 8996803 Tangent 44. 84740 9. 9976886 is ●0 . 3445246 , which being added to the same tangent , there summe 10. 4425329 is the tangent of 70. 25211 and the aggregate of these two arches . Tangent 51. 41086 10. 0980083 2 Number   10. 3445246 Tangent 70. 15211 10. 4425329 1 Arch 44. 84740   Summe 114. 99951   gives the point of the Ecliptique in Cancer 24. 999 2 Example . The Oblique Ascension of the 2 house was before found to be 192. 82173 The tangent of halfe the complement 83. 58913 is 10. 9493879 Tangent 83. 58913 10. 9493879 1 Number   9. 9294508 Tangent 82. 47036 10. 8788387 Tangent 83. 58913 10. 9493879 2 Number   10. 5186555 Tangent 88. 05055 11. 4680434 1 Arch. 82. 47036 Summe 170. 52091 whose complement ●●●●47909 ▪ is the Cuspe desired . The Cuspe of your houses being thus found , draw your figure after this manner , and then place the Signes and Degrees on the Cuspes of their proper houses , beginning with the 10 house . A Figure of the 12 Houses of Heaven . 10 house ♊ 14. 17. The opposite houses are in the opposite Signes . 4 house ♐ 14. 17. 11 house ♋ 24. 99. The opposite houses are in the opposite Signes . 5 house ♑ 24. 99. 12 house ♌ 25. 27. The opposite houses are in the opposite Signes . 6 house ♒ 25. 27. Ascendent ♍ 17. 90. The opposite houses are in the opposite Signes . 7 house ♓ 17 90. 2 house ♎ 09. 47. The opposite houses are in the opposite Signes . 8 house ♈ 9. 47. 3 house ♏ 06. 34. The opposite houses are in the opposite Signes . 9 house ♉ 6. 34. The 12 signes being placed in the figure we must next enquire for the true places of the Planets , with the Dragons head , the which according to the doctrine of the second Book at the time proposed are as followeth . Suns place ♍ 4. 07. ☊ ♏ 1. 40. ♃ ♌ 5. 19. ♀ ♏ 16. 58. Moons place ♊ 26. 24. ♄ ♌ ● 5. 19. ♂ ♑ 8. 87. ☿ ♎ 19. 81. The places of the Planets being thus found , consider under what signe any of them falleth , which being observed , note which of the houses contain the signe in which the planet is , observing the number of Degrees , and in due order place the planet in that house . Right Ascension of the Mid-heaven , 72. 82. A Scheme of Heaven for July 16 , Hour 18 , parts 4564 , AD. 1587. In the Meridian of London , whose Latitude is 51. 53. And when a Planet contains a lesser number of Degrees then the Cuspe of the house , he is to be placed before the house , in the house preceding , but if greater , he is be placed beyond the Cuspe , according to the sequel , and consequence of the signes . As in the figure , Sol is in 9 degrees and 7 parts of Virgo , and the signe is placed upon the Cuspe of the Ascendent , but because the Cu●pe thereof containeth more degrees of that signe then the Sun , I place the Sun in the preceding house , that is in the twelfth . CHAP. 17. To find the Angle of the Ecliptick with the Horizon , or the Altitude of the Nonagesime deg . together with its distance from the Mid-heaven . BY the rules delivered in the last Chapter , find the point culminating , whose declination being ended to the altitude of the Equator ●n the Northerne signes , or subtracted in the Southern , gives you the altitude of the Mid-heaven , suppose 10 degrees of Gemini were in the Mid-heaven , the declination thereof by the 2 Chapter is 22. 02910. which being added to the altitude of the Equator 38. 46667 , because the declination is North , their sum 60. 49577 is the Altitude of the Mid-heaven , and the meridian angle of the same point by the 13 Chapter is 81. 53133 , hence in the triangle 7. 10. S of the Diagram in the last Chapter , we have given 10. S. 60. 49577 the altitude of Mid-heaven . The angle 7. 10. S 81. 53133. the Meridian angle to find the angle 10. 7. S. As the Radius To the sine of 7. 10. S. 81. 53133 9. 9952385 So Cosine of 10. S 60. 49577 9 , 6923956 To Cosine of 10. 7. S 60. 84861 9. 6876341 And to find 7. 10 or the distance of Mid-heaven from the Nonagesime degree , the Analogie is As Radius To the Cosine of 7. 10. S 81. 53133 9. 6677126 So is the cotangent of 10. S 60. 49577 9. 7527167 To the tangent of 7. 10 14. 75047 9. 4204293 Mid-heaven add 70. 00000   Summe 84. 75047 is the Nonagesime degree . And note that arch found is to be added to the Mid-heaven from Capricorn to Cancer , to be subtracted from Cancer to Capricorn . CHAP. 18. To find the Parallactical angle , or angle of the Ecliptique with the Verticall circle . THe angle of the Ecliptique with the verticall circle , is an angle made by the oblique cutting of the circle of altitude , with the Ecliptique , which is a right angle , when the said circle passeth through the 90 degree of the Ecliptique , but falling without the same it is oblique ; as in the following figure , D denotes the Zenith , D C B the verticall circle , D E H V T the Meridian , T A B H the Horizon , V A E the Ecliptique , C the angle of the intersection of the Ecliptique with the Vertical . In the 16 Chapter is shewed how to find the point of the Ecliptique Ascending , and the Suns altitude at any time in the 12 Chapter , which being obtained we may speedily find the parallactical angle . As the tangent of A C 13 , 9061 co . ar . 0. 6062707 Is to Radius   10. 0000000 So tangent B C 12. 10189 9. 3312569 To Cosine of A C B 30. 00067 9. 9375276 CHAP. 19. The elevation of the Pole and Declination of the Sun given , to find the time when he will be due East and West . IN the second variety of the 12 Chapter , the complement of the Suns Declination F H i● 67. 97090 and the complement , of the poles elevation F G 38. 46667 , hence the angle G F H equal to the Arch of the Aequator A O is to be sought , therefore I say . As Radius To Cotangent F H 67. 97090 9. 6070621 So tangent F G 38. 46667 9. 9000864 To Cosine of G F H 71. 24779 9. 5071485 whose comple . O F E 18. 75221 being converted into time giveth 1 hour 25147 parts of an hour , and so long it is after 6 in the morning when the Sun will be due East , and before 6 at night when he will be due West . CHAP. 20 The Elevation of the Pole , with the Suns Declination and Altitude given , to find his distance from the Meridian . IN the Oblique angled Spherical triangle G H F in the 2 Diagram of the 12 Chapter , we have known H F the complement of the Suns Declination , G F the complement of the poles elevation , H G the complement of the Suns altitude , to find G F H the angle of the Suns distance from the Meridian . 1 The side H G 44. 54111   2 The side F H 67. 97090   3 The side G F 38. 46667   Summe 150. 97868   ●alf Summe 75. 48934   ●●ne of F H 67. 97090 co . ar . 0. 0329234 ●●ne of G F 38. 46667 co . ar . 0. 2061682 Differ . G F ½ Summe 37. 02267 9. 7796909 Differ . F H ½ Summe 07. 51844 9. 1167578 Quadrat of the sine of half the Angle   19. 1355403 Which bisected , is sine of 21. 69295 9. 5677701 And the double therof is 43. 38590. The Suns distance from the Meridian , And converted into time , gives two houres , 89259 parts . CHAP. 21. To find the time of the Suns rising and setting , with the length of the Day and Night . THe Ascensional difference of the Sun being added to the Semidiurnal arch in a Right Sphere , that is to 90 degrees in the Northern signes , or substracted from it in the Southern , there summe or difference will be the Semidiurnal arch , which doubled is the day Arch , and the Complement to 360 is the night Arch , which bisected is the time of the Suns rising , and the day Arch bisected is the time of his setting . As when the Sun is in ten degrees of Gemini , his Ascensional difference is found to be 30. 61613 The Quadrant Add 90. The Semidiurnal Arch 120. 61613 The diurnal arch 241. 23226 Whos 's Complement 118. 76774 Converted into time gives 7 houres 91078 parts , which bisected gives the time of the Suns rising . 3 hours 95539 , parts ; or a little before 4 of the clock . CHAP. 22. To find the distance of a star from the Meridian . IF a Starre be between the Mid-heaven and the Horoscope deduct the Right Ascension of the Mid-heaven from the Right Ascension of the Starre , what remaineth is the distance from the Meridian . If a starre be between the Mid-heaven and the 7 house , deduct the Right Ascension of the starre from the Right Ascension of the Mid-heaven , and what remaineth is the distance as before . IF a starre be between the 7 house and the Imum Coeli or fourth house , deduct the Right Ascension of the Imum Coeli from the Right Ascension of the starre , and what remaineth is the distance from the Meridan . If a star be between the Ascendant and the Imum Coeli deduct the Right Ascension of the star from the Right Ascension of the Imum Coeli , and what remaineth is the distance from the Meridian as before . For Example . In the preceding figure , the Right Ascension of the Mid-heaven is 072 deg . 82 parts . The Sun is in the 12 house and his Right Ascension 155. 97 From which deduct the Right Ascension of the M. C. 72. 82 The distance of the Sun from the Meridian is 83. 15 CHAP. 23. To find the Elevation of the Pole above any circle of position . A Circle of position , is as it were a certaine Horizon ( upon which the point or star proposed doth arise ) passing by the two intersections of the Horizon with the Meridian , and may be either above or under the Earth , in respect of the place for which the figure is erected . A star posited in the 1 , 2 , 3 , 4 , 5 , 6 , house is Under the earth 7 , 8 , 9 , 10 , 11 , 12 , house is Above the earth Thus in the annexed Diagram A H C is a circle of position passing by the Horizontal point of the Significator at H , and the two intersections of the Horizon of the place at A and C , and L M is the elevation of the pole above this Horizon of the star or circle of position . To find which there must be known . 1. The latitude of the place . 2. The Declination of the star or point proposed . 3. The distance thereof from the Meridian . Hence to find the angle of Inclination of the circle of position with the meridian , the proportions are as followeth . 1. As the Radius , To the tangent of the complement of the stars declination : so is the Cosine of the stars distance from the meridian , To the tangent of the first-arch . To which the pole of the place being added , or subtractod from it according to the following direction , their summe or difference is the second arch . If the distance of the star from the meridian , be more then 90 and the declination South under the earth or north above it , subtract the first arch from the poles elevation , and what remaineth is the second arch . If the distance of a star from the meridian be lesse then 90 , and the declination south under the earth , or north above it , adde the poles elevation , to the first arch , and their agg●gate if lesse then 90 is the second arch , if more then ●0 the complement thereof . If the distance of a star from the meridian , be either more or lesse then 90 , and the Declination North under the earth , or South above it . Substract the elevation of the Pole from the first arch , and what remaine●●●s the second arch . If the distance of a star from the Meridian be a just quadrant , the angle of inclination may be found at one operation , as in the fourth example . 2 As the sine of the first arch found : Is to the cotongent of the Stars distance from the Meridian : So is the sine of the second arch found ; To the cotangent of the angle of inclination . Then to find the elevation of the Pole above the circle of position , the analogie is . 3 As the Radius , To the sine of the Pole of the place : So is the sine of the angle of inclination ; to the sine of the Pole of the Circle . 1 Example . Let the distance of a Star from the Meridian , be more then 90 , viz. 97 deg . And the Declination of the Star 31 deg . North above the earth : the Pole of the place 45. Then in the oblique Spherical Triangle H M C we have limited . 1 The side M C the Poles elevation 45 degrees . 2 The side H M the complement of the Stars declination 59 degrees . 3 The angle H M C , the Stars distance from the Meridian 97 , or instead thereof the acue angle I M H 83 , the complement of the other to a Semicircle . Hence to find I M the proportion is . As the Radius 90 10. 000000● To the tangent of H M 59 10. 2212262 So is the Cosine of I M H 83 9. 085894● To the tangent of I M 11. 47 9. 3071206 which being substracted from 45 the Poles elevation , there resteth 33. 53 the second arch . 2 As the sine of I M 11. 47 9. 2985361 To the Cotangent of I M H 83 9. 089143● So is the sine of I C 33. 53 9. 742232● To the Cotangent of H C M 71. 17 9. 5328404 The angle of inclination . 3 As the Radius 90 10. 0000000 To the sine of C M 45 9. 8494850 So is the sine of H C M. 71. 17 9. 9761116 To the sine of L M. 42. 01 9. 8255966 The height of the Pole above that Circle of position . 2 Example . Let the distance of a Star from the meridian be less then a quadrant , viz. 44. 7. The Declination of the Star , 14. 51. North above the Earth , the Pole of the place 45. then as before . 1 I say , As the Radius 90 10. 0000000 To the tangent of H M. 75. 15. 10. 5765162 So the Cosine of I M H 44. 7. 9. 8574210 To the tangent of I M. 69. 74. 10. 4329372 To which add the Pole , 45. 00. There aggregate is 114. 74. whose Complement 65 ▪ 26. is the second Arch. 2 As the sine of I M. 69. 74. 9. 9722634 To the cotangent of I M H. 44. 7. 10. 0141010 So the sine of I C 65. 26. 9. 9581892 To the Cotangent of H C M 45 10. 0000267 The angle of Inclination . 3 As the Radius 90 10. 0000000 To the sine of C M 45 9. 8494850 So is the sine of H C M 45 19. 8494850 To the sine of L M 30 9. 6989700 The height of the Pole above that Circle of position . 3 Example . Let the distance of a Star from the Meridian be 22. 82. the declination 13. 53. South above the Earth : And the Pole 49. 1 Then as the Radius 90 10. 0000000 To the tangent of H M 76. 47 10. 6186455 So is the Cosine of I M H 22. 82 9. 9646026 To the tangent of I M 75. 37 10. 5832481 Subtract the Pole 49. 0● . There rests 26. 37. for the 2d arch 2 As the sine of IM 75. 37 9. 9856855 To the Cotangent of I M H 22. 82 10. 3759530 So is the sine of I C 26. 37 9. 6475454 To the Cotangent of H C M 42. 51 10. 0378229 The angle of Inclination . 3 As the Radius 90. 10. 0000000 To the sine of C M 49. 9. 8777798 So is the sine of H C M 42. 51 9. 8297661 To the sine of L M 30. 66 9. 7075459 The height of the Pole above that Circle of position . 4 Example . If the distance from the Meridian be a just Quadrant , or 90 degrees then omitting the two first proportions , the angle of Inclination may be found at one operation , by this analogie . As the tangent of the Complement of declination , is to Radius . So is the sine of the Pole , to the cotangent of the angle of inclination . Let then the declination be 23 , and the Pole 45. I say , As the tangent of H M 67 10. 372148● Is to Radius or the angle H M C 90 10. 0000000 So is the sine of M C 45. 9. 8494850 To the Cotangent of H C M 73. 30 9. 4773369 Then as Radius , to the sine of M C 45. 9. 8494850 So is the sine of H C M 73. 30 9. 9812850 To the sine of L M 42. 63 9. 8307700 The height of the Pole above that Circle of position . CHAP. 24. Of the Ark of Direction , what it is , and how to finde it . AStrologers use to fore-tel the general Fortune of any Native by the consideration of the 12 Houses , but the particular time , in which we may expect , what is promised by the position of the Heavens at the time of the Birth , they measure out by the arke of Direction . That is , by the distance of the Significators from there Promittors reckoned in the Aequator , by Significators usually meaning , the Ascendent , Mid-heaven , Sun , Moon , and part of Fortune : And by Promittors , the several Aspects of these Significators to the Planets , or the twelve Houses . For the clearer understanding of what the arke of Direction is , in the Diagram of the last Chapter , Let A D C represent the Meridian D V S E the Aequator , A C the Horizon , M the North-pole , A H C a Circle of position above the Earth , H B and N R two parallels of Declination . H the Significator , D O his right Ascension . H O his Declination . R the Promittor D S his right Ascension , R S his declination . Now when the Promittor at R comes to N , it is in the same Circle of position with the Significator at H , and the Circle of Declination M R S will be changed into the Circle of Declination M N V , and then the arch of the Aequator , D V is the Right Ascension of the Promittor at N , and therefore the arch of the Aequator V S is the arke of Direction sought . And the manner of finding thereof is as various , as the position of the Significator may be in the figure , which is threefold , viz. Either in the Meridian , in the Signes Ascending , or in the Signes Descending . CHAP. 25. How to direct the Mid-heaven , and the Imum Coeli . A Star posited in the meridian , that is , either in the mid-heaven or Imum Coeli , must be directed to his Promittors , by the right Ascensions of the Significator and Promittor . If a Significator posited in the mid-heaven be to be directed . Substact the Right Ascension of the mid-heaven , from the Right Ascension of the Star or Promittor , taken with its latitude if it have any , and what remaineth is the ark of Direction . For Example . Let the mid-heaven of the preceding figure in the 16 Chapter , be directed to the 12 degree of Capricorn . The Right Ascension of the 12 degree of Capricorn is 283. 03 From which substract the Right Ascension of the mid-heaven 072. 02 There rests for the Ark of Direction 211. 23 In like manner : If the Imum Coeli or fourth House , or a Star posited upon the Cuspe thereof be to be directed , you must substract the Right Ascension of the Imum Coeli , or fourth House , from the Right Ascension of the Promittor , and what remaineth is the ark of Direction . CHAP. 26. How to direct the Ascendent , or Significator posited in the Signes Ascending . THe Horoscope or Ascendent , or a Significator posited in the signes ascending , that is , in the 12 , 11 , 10 , 1 , 2 , or 3 houses , must be directed to Promittors , by the oblique Ascensions answering to the elevation of the Pole above the Circle of position of the Significator . The elevation of the Pole above the ascendent is the same with that of the place for which the figure is erected . The Poles elevation above the Circle of position of any other Significator must be found as hath been shewed in 22 Chapter . Then if you deduct the oblique Ascension of your Significator , from the oblique Ascension of your Promittor , what remaineth is the arke of direction . For example . Let the Ascendent of the preceding figure in the 16 Chapter be to be directed to the 26 deg of Taurus . The elevation of the Pole of the Circle is the same with that of the place . viz. 51. 5● . And therefore the oblique Ascension of 26 deg . of Taurus , 27. 50 To which add a Circle that substraction may be made 360 And then the Oblique Ascension is 387. 50 The Oblique Ascension of the Ascendent substract 162. 82 There rests for the ark of Direction 224. 68 Another Example . Let us suppose a Significator to be posited in the signes Ascending but not upon the Cuspe of the Ascendent , in this case though the Arke of Direction must be found out by the Oblique Ascensions as before ; yet the elevation of the Pole above the Circle of position must be first found , because it is not given , as in the last Example . In the Diagram of the 23 Chapter , let the distance of the Significator from the meridian be 44. 07. The declination thereof North above the Earth H O 14. 85. Hence the Pole L M is 30 degrees . Let this Significator be posited in 10 degrees of Taurus , the Right Ascension thereof D O 37. 58. His Ascensional difference under the elevation of 30 degrees F O 8. 80. Let the Promittor be in 25 of Gemini , the Right Ascension thereof D S. 84. 55. And the Ascensional difference when this Promittor comes to N. is represented by the letters F V. 14. 47. Now then if you substract the Ascensional Difference of the Significator F O , 8. 80. from the Ascensional Difference of the Promittor F V. 14. 47. There will remaine O V 5. 67. we call it the Aequation of the Arke of Direction , which being added to the Right Ascension of the Significator D O. 37. 58. There aggregate is the arch D V 43. 25. Then if you deduct the arch D V 43. 25 from the Right Ascension of the Promittor , D S. 84. 55. There difference is V S 41. 30. The Ark of Direction sought . Or thus , the Oblique Ascension of the Promittor is 70. 08. The Oblique Ascension of the Significator is 28. 78. There difference 41. 30 , is the Ark● of direction sought , as before . CHAP. 27. How to direct a Significator posited in the Signes Descending . THe Descendent or seventh House or Significator there posited , or in any signe descending , that is , in the 4 , 5 , 6 , 7 , 8 , or 9 Houses , must be directed to his Promittors , by the oblique Descensions answering to the Elevation of the Pole of the Circle of position of the Significator . As suppose the mid-heaven be in 22. 33 of Gemini . And the Right Ascension thereof , 81. 65. Let the Significator be in 10 degrees of Taur●s . The declination thereof 14. 85. North. His distance from the meridian 44. 07. Hence the Elevation of the Pole above that Circle of position is 30 , as before . Let the Promittor be in 25 degrees of Gemini , the declination 23. 40 North : Now the declination of the Significator and Prommittor being the same with the former , and the Pole of the Circle the same , the Ascensional Differences as well of the Significator as of the Promittor , must needs be the same with the former Example , and consequently the same Aequation of the ark of Direction : if then you would find this ark of Direction , by the Right Ascensions , Adde this Aequation of the ark of Direction , to the Right Ascension of the opposite point of the Promittor : and from their aggregate , subtract the Right Ascension of the opposite point of the Significator , and what remaineth is the ark of Direction . As the opposite point to this Promittor in the 25 of Gemini , is the 25 of Sagittarius , the Right Ascension whereof is 264. 55 The former Aequation of the ark of Direction 5. 67 Their Aggregate 270. 22 The opposite point to the Significator in the 10 of Taurus is the 10 of Scorpio , whose Right Ascension is 217. 56 Which subtracted from the former aggregate leaveth 52. 64 For the ark of Direction sought . Or if you will by the oblique Ascensions of these opposite points thus : The oblique Ascension of the 25 of Sagittarius is 279. 01 The oblique Ascension of the 10 of Scorpio , is 226. 38 There Difference is 52. 63 The ark of Direction as before . Or lastly , by the oblique Descensions , according to the intention of this Chapter , if you subtract the oblique Descension of the Significator , from the oblique Descension of the Promittor , what remaineth will be the ark of Direction . As in this Example the oblique Descension of the Promittor , under the elevation of 30 degrees is 99. 01 The oblique Descension of the Significator , 46. 38 Which being subtracted from the oblique Descension of the Promittor , there resteth 52. 63 The ark of Direction sought as before . CHAP. 28. How to find the Arch of the Aequator , whereby is made the general Table of Positions . FOr finding this arch of the Aequator , there must be given the angle of Inclination of the Circle of position with the Meridian , & the height of the Pole above that Circle , both which may be found by the 9 Chapter : but ●● to our present purpose , we are not tied unto such a ●●dious calculation , because the Pole of the Circle may be supposed , and then the angle of Inclination may be found at one Operation , and this arch of the Aequator at another . And first , the Elevation of the Pole above any Circle of position being given together with the latitude of the place or Countrey , the angle of Inclination may be found , by this analogy . As the sine of the Pole of the place , is in proportion to Radius : So is the sine of the Pole of the Circle , to the sine of the angle of Inclination . For Example . In the Rectangle Spherical Triangle of the 9th Chapter L M C right angled at L. Let M C the Elevation of the Pole of the place be 45. And the Pole of the circle LM 42 , hence to find the angle LCM . I say , As the sine of M C 45. 9. 8494850 Is to the Radius 90. 10. 0000000 So is the sine of L M 42. 9. 8255108 To the sine of L C M 71. 13 9. 9760258 Then to find the arch of the Aequator , the proportion is : As the Radius to the sine of the Complement of the Pole of the place : So is the tangent of the angle of Inclination , to the tangent of the arch of the Aequator . For Example , In the triangle A D F of the afore-said Diagram , Let there be given the side A D the Comple . of the Pole of the place 45. The angle of Inclinat . DAF 71. 9. Hence to find the arch of the Aequator . DF , I say , As the Radius 90 10. 0000000 To the sine of AD 45 9. 8494850 So is the tangent of D A F 71. 13 10. 4662●85 To the tangent of D F 64. 20 10. 3157275 Which is the arch of the Aequator sought . CHAP. 29. How by the general Table of Positions , to make a particular Table for any Latitude there exprest . IF thou wouldst make a particular table of positions , first , divide your paper or book into as many Columnes as the largness of the page will bear , then in the head of your table write the particular latitude , for which you would have the table , and under this title write in the third Column of your page . 1 In the fourth , 2 , and so forward till you have fild the Columnes of your first page , do so likewise in the 2d . page , and so forward till you have written twice over the several Elevations of the Pole above the circle of position from one unto that degree for which your table is intended ; then in the first Columne of your left hand page write , North Declination under the earth and South above it , in the second columne thereof write orderly the several degrees of declination , beginning with a cypher or nought , and then 1 , 2 , 3 , and so forwards till you have written 32 , and in the two first columnes of your right hand page write the contrary , that is , in the first thereof write South Declination under the earth and north above it ; and in the second the severall degrees of Declination beginning with 32 , and so downward 31. 30. 29. until you come to nought : having thus prepared your book according to that Table in this book , enter your general table of positions with one degree of Elevation , and in a straight line directy under the latitude of your place , you shall find the arch of the Aequator answering thereunto , then look for the Ascensional differences answering to every degree of Declination , under one degree of the Poles Elevation , the which being substracted from the arch of the Aequator , write the remainder in a direct line under one degree of Elevation , in that page which must serve for North Declination under the Earth : but for the South Declination under the Earth adde the Ascensional difference of every degree of Declination to the former arch of the Aequator , and write their aggregate under one degree of Elevation and right against that degree of Declination , whose Ascensional difference was added thereunto , and so shall you have one Column of your table finished , to make it plain we will add an Example . In the latitude of 51 degrees 33 hundred parts , the arch of the Aequator answering to one degree of the Circle is 0 deg . 79. and the Ascensional difference for one degree of Declination under one degree of Elevation is 0. 1. of which being subtracted from 79 , there remaineth 78 , which I write against one degree of Declination in that page of the Table serving for North Declination . Again , to the same arch of the Aequator , I add 0. 01. and their aggregate is 80 , and this I write against one degree of Declination , and under one degree of Elevation in that page of the Table which serveth for South Declination under the Earth , and thus must you also add or subtract the Ascensional differences of all the other degrees of Declination , according to this Example . And so shall you have a particular Table of positions for your particular latitude . The use of this Table is to finde the Elevation of the Pole above any Circle or position in that particular latitude , for which the Table is framed , as shall be shewed in his proper place . CHAP. 30. Of the Doctrine of the Sphere in Tables . ALthough in the former book there is plainly shewed you , how to find the Declination , Right Ascension , Ascensional Difference , Oblique Ascension , Cuspes of the 12 Houses , and the height of Pole above any Circle of position , by Trigonometrical calculation : yet considering that , that way is not altogether so expedite and ready for practice , as some may desire , wee will also shew you how to finde the same by those Tables , that are hereunto annexed . Precept 1. The Declination of the Sun or other Planet is found by the signe in the head or foot , and the degree on the right side , if the signe be in the foot , or on the left side if it be in the head : for the common angle gives the Declination sought , if you have respect , to your Planets proper latitude , and the proper part proportional . For Example : Suppose the Moon were in 19 degrees 56 parts of Leo , and her declination were required , having North latitude 3 degrees . Her Declination in that latitude , in 19 degrees of Leo will be found 18. 02 In 20 degrees it is   17. 70 There difference is   0. 32 Now then if one degree give 0. 32 1. 5051499 ▪ What shall 0. 56 1. 7481880 They give 18 ferè   1. 2533379 Which being subtracted from 18. 02 because the Declination doth decrease , the Moons Declination will be found to be 17. 84 Precept 2. The Right Ascension by the Table following is had by the signe in the head and degree in the left side , and in the common angle is the Right Ascension . Example . The Right Ascension of a Planet in Aries 1● 251 , and 2 degrees of South latitude be sought . The Right Ascension of 13 Degrees 12. 73 The Right Ascension of 12 Degrees 11. 82 Difference 91 If one Degree give 91 1. 9590413 What shall 25 1. 3979400 They give 22 1. 3569813 Which being added to 11. 82 , the R. ascension of the point sought will be 12. 04. But if the R. ascen . of the point sought be in Southern signes , you must add 180 to the arch found in the table , and you have your desire , thus the R. ascens . of 12 deg . 25 parts of Libra , with two degrees of North Latitude by adding 180 to the former arch will be 192. 04. Precept 3. The ascensional difference of any part of the Zodiack is found by the degree of declination in the left side , and the degree of the Poles elevation in the head , the common angle gives the ascensional difference ●ought . Example . Let a planets Declination be 4. 43. whos 's ascensional difference is sought under the elevation of 52 deg . The ascensional difference in that Elevation answering to 5 degrees of Declination is 6. 43. to 4 degrees is 5. 13. there difference is 1. 30. If one degree Give 1. 30 2. 1139433 What shall 4● 1. 6334684 They give 56 ferè 1. 7474117 Which being added to ● . 13 , the ascensional difference of the point sought will be 5. 69. Precept 4. The oblique ascension of any part of the Zodiack is found by the signe and degree in the first Column in the left hand , and the Poles Elevation on the head of the Table , the common angle will give you the oblique Ascension sought . Example . Let the Oblique Ascension of Virgo 09. 23. in the elevation of 42 degrees be sought . In that elevation . The Oblique Ascension of Virgo 10 degrees is 15● . 87 Virgo 6 degree is 155. 80 Their Difference 4. 07 If 4 degrees 4. 00 9. 3979400 Give 4. 07 0. 6095944 What shall 3. 23 0. 50920●5 They give 3. 28 0. 5167369 Which being added to 155. 80. the obli●● Ascension sought will be 159. 08 Precept 5. These things premised , the Right Ascension of M. C , and thereby the Mid-heaven it self will easily be found for the houres from Noon ( converted into Aequinoctial degrees , by the table for that purpose ) being added to the Suns Right Ascension , do make the Right Ascension of the Mid heaven , which sought in the Area of the Table of Right Ascensions gives the mid-heaven it self . Example . Let the Sun be in 4 deg . 07 parts of Virgo , as in the 16 Chapter , the time from Noon , Houres 18. 4564 The Suns Right Ascension in 4 degrees of Virgo 1●5 . 9● His Right Ascension in 5 deg . of Virgo , 156. 85 Difference ●0 . 95 If one degree give 95 0. 9777236 What shall 07 1. 8450980 They give 06 1. 8228216 Which being added to 155. 90. The Suns Right Ascension is 155. 96. The Aequinoctial degrees answering to 18 houres , viz. 270 degrees . And the degrees answering to 4564 parts of an houre are 06. 84 , and therefore the Right Ascension of time is 276. 84 , which being added to the Suns Right Ascension , their aggregate 432. 80. or rejecting 360 degrees , the remainer 72. 80 , is the Right Ascension of the Medium Coeli , whereto answers in the Table of R. Ascensions ; 74. 75. ●● , the point of the Ecliptick for the Mid-heaven it self . Precept 6. The Oblique Ascensions of the other Houses are found by a continual addition of 30 degrees to the Right Ascension of the Mid-heaven , as hath been also shewed in the 16 Chapter , and thus the Oblique Ascension of the 11 House is 102. 80. 12 House is 132. 80. Ascendent is 162. 80. 2 House is 192. 80. 3 House is 222. 80. The Poles of Elevation above the Circle of Position of the Ascendent is always the same with that of the place , for which the figure is erected , the Poles Elevation for the 11 , 12 , 2 and 3 Houses you may find in the Table for that purpose annexed to the Table of Oblique Ascensions . Example . By that Table under our Elevation of 51. 53. the Poles Elevation above the Circles of position of the 11 and 3 Houses , is 32. 18. And the Poles Elevation above the 12 and 2 Houses is 47. 46. Now then to find the Cuspe of the 11 House , look the Oblique Ascension thereof , 102. 80. in the Table of Oblique Ascensions answering to 32. 18 , of Elevation , and the point of the Ecliptick answering thereunto is Cancer 24. 98. In like manner , if you look the oblique Ascension of the 12 house , 132. 80 under the elevation of 47. 46. the Cuspe thereof will be Leo , 25 , 26. If you look the oblique Ascension of the Ascendent 162. 80. under the Elevation of 51. 43 the Cuspe thereof will be Virgo 17. 94. If you look the Oblique Ascension of the second House 192. 80. under the Elevation of 47. 46. the Cuspe will be Libra 9. 44. Lastly , if you look the Oblique Ascension of the third House , 222. 80 under the Elevation of 32. 18. the Cuspe thereof will be Scorpio , 6. 35. The other 6 Houses , are in the same Degrees and parts of the opposite signes . Precept 7. The Poles Elevation above the Horizon of a Star is found by the degree of his Declination , in the second Column of the right hand page of your Table , if the Declination thereof be North under the Earth , or South above it ; And in the second Column of the left hand page , if the declination be South under the Earth , or North above it , and his distance from the Meridian in a straight line , for in the head of your Table in a direct line ( using a double proportional part if need be ) you shall have the degree of the Poles Elevation above the Circle of position . Example . In the preceding figure of the 16 Chapter , the Sun is in Virgo , 4. 07 and therefore his Declination is 10. 05. North above the Earth ; his distance from the Meridian by the 22 Chapter , was found to be 83. 15. Now then to find the Poles Elevation , I look in that Table for the Suns declination in the second Column of the left hand page , and his distance from the Meridian in a straight line , and in the last folio of that Table , I finde against 10 degrees of Declination , the distance of a Star from the Meridian neerest to my number to be 83. 37. and over the head thereof 50 , which is the degree of the Poles Elevation above that Circle of Position . Astronomia BRITANNICA The second Book . OR , The Theory of Planets , according to the Copernican Systeme and Demonstration of the Learned BULLIALDUS . Exhibiting their first Inequalities at one Operation Trigonometrical . Their other Inequalities , and Eclipses of the SUN and MOON with much Ease . bookseller's logo LONDON , Printed 1656. Astronomia BRITANNICA : The second Book . CHAP. 1. Of the year Civil and Astronomical . THe Altitudes of the Planets being given to find their places in the Zodiack , hath been already shewed in the Doctrine of the Sphere , & thence their annual or periodical revolutions , together with their middle motiōs must be sought , but how to state them so exactly as that we may thereby find their true or apparent places for any time required , is that which many have endevoured , but none have as yet found out , at least not so , as that their places computed by their rules , shall exactly agree with observation , nor was Astronomy brought to that perfection in which it now stands but by degrees , and although there hath been very much done of late towards the perfecting thereof , yet shall it not perhaps come to its full Acme in this our age . That which we intend , is not to shew you from what small beginnings it hath been increased , or by whose labours , it hath from time to time been still corrected and amended , but to shew you how to compute the places of heavenly Bodies , by the plainest , speediest , and exactest ways that are as yet made publike . And in order hereunto we will shew you first the usual way of finding out the time in which the Planets make their Annual or Periodical revolutions , and how from thence to compute their middle Motions , that their annual revolutions may be known , the time of their entrance into one and the same point of the Zodiack , taken in divers years by observation must be given , with a considerable interval of time between these Observations . And because the Observations taken in any one Meridian ( that are as yet published ) are not sufficient for our present purpose we must of necessity , use the observations made in diverse places , but the intervall of time between those observations cannot be had , unlesse we can reduce the time of an observation made in one account to the like time in another ; Although the periodicall revolutions therefore of the planets are the onely proper yeares and first in nature ; yet since the civil yeare in every nation is somewhat different from them , we will first shew the quantity of that in most nations , and how to reduce the day of the moneth given in one accont , to the correspondent time in another . The Civil yeare then , though it doth not exactly agree , yet hath it some proportion with the motions of the Sunne or Moone in every nation ; Twelve Moones or Moneths is the common measure of the year in Turkey , in every moneth they have 29 or 30 dayes , in the whole yeare 354 , and in every third yeare 355 dayes . The Persians and Egyptians do also account 12 Months to their yeare , but their months are proportioned to the time of the Suns continuance in every of the 12 signes ; in their year therefore which is Solar , there are alwayes 365 dayes . And the Julian yeare , which is the account of all Christendome doth differ from the other onely in this , ( that by reason of the Suns excesse in motion above 365 dayes , which is about 5 hours 49 minutes ) it hath a day intercalated once in 4 yeares , and by reason of this intercalation it is more agreeable with the motion of the Sun then the former , and yet here is a considerable difference between them , which hath occasioned the Church of Rome to make some further amendment of the Solar year , but hath not brought it to that exactness which is desired , nor will ( as is to be feared ) be over-hastily brought to that exactnes which it might ; taking these accounts therefore as they now stand , if we will reconcile that discrepancy that is between them , there must be some beginning appointed to every of these accounts , and that beginning must be referred to some one , as to the common measure of the rest . The most natural beginning of all accounts , is the time of the Worlds Creation , but they who could not attain the Worlds beginning , have reckoned from their own , as the Romanes , ab urbe condita , or from some great name or notable event ; so the Greeks account from their Olympicks , and the Assyrians from Nabonasser , and all Christians from the birth of Christ , the beginning of which and all other the most notable Epochaes , as others formerly , so we now have also ascertained to their correspondent times in the Julian Period , which Scaliger contrived by the continual multiplication of three circles all in former times of good use , & two of them do yet remain ; the Circles yet in use are those of the Sun and Moon , the one to wit the Sun is a Circle of 28 years , in which time the Sunday Letter makes all the varieties that it can have by reason of the Bisextile or Leap-year , and the Circle of the Moon is the revolution of 19 years , in which time , though not precisely , the Lunations do recur ; it is called the Golden Number , and was made Christian by the Fathers of the Nicene Council , as being altogether necessaay to the finding out of the Neomenia Paschalis , upon which the Feast of Easter , and the rest of the moveable Feasts depend . The third Circle which now serves for no other use , then the constituting of the Julian Period , is the Roman Indiction , or a Circle of 15 years , for if you multiply 28 the Cycle of the Sun , by 19 the Cycle of the Moon , the product will be 532 , & this by 15 , the product will be 7980 the number of years in the Julian Period ; whose admirable condition is to distinguish every year within the whole Circle , by a several certain character , the year of the Sun , Moon , and Indiction , being never the same again until the revolution of 7980 years be gon about : this Period , the Authour fixed in the Tohu , or eternal Chaos of the World , 764 Julian years before the most reputed time of Creation ; which being , premised , we will now by example shew you how to reduce the years of Forreigners to our Julian years , and the contrary . 1 Example . I desire to know at what time in the Turkish account , the 5 of June 1649 , falls . The work is this The years compleat are 1648 , and are thus turned into Dayes , by the table of Dayes , and Decimals of Dayes in Julian Years . 1000 Julian yeares give dayes 365250 600 years give 219150 40 years give 14610 8 years give 292● May Compleat 151 Dayes 5 The Summe 602088 Now because the Turkish account began July the 16. Anno Christi 622 , convert these yeares into dayes also thus 600 Julian years give 219150 20 years give 7305 1 year gives 365 June Compleat 181 Dayes 15 The Summe subtract 227016 From 602088 There rests 375072 900 Turkish years gives 318930 There rests 56142 150 years gives 53155 There rests 2987 8 years give 2835 There rests 152 Giumadi I. gives 148 There rests 4 Therefore the 5th . of June 1649 , in our English accompt , falls in the Turkish accompt , in the year of Mahomet , or their Hegira , 1058 , the 4th . day of Giumadi II. 2 Example . I desire to know upon what day of our Julian year , the 23 day of the moneth Pharmuthi in the 1912 year currant of the Aegyptian accompt from the death of Alexanders fall . The beginning of this Epoch● is from the beginning of the Julian Period in compleat dayes .   1603397 1000 Egyptian years give 365000 900 yeares give 328500 10 years give 3650 1 yeare gives 365 Phamenoth compleat 2●0 Dayes 23 The summe 2301145 6000 Julian yeares 2191500 There rests 109645 300 yeares give 109575 There rests 70 April compleat 59 There rests 11 It therefore fell out in the yeare of the Iulian period 6300 the 11 of March , that is subtracting from that period , 4712 in the yeare of Christ 1588. He that understands this may by like method convert the yeare , of other Epochaes into our Julian yeares and the contrary . Next to the tables which concern the reduction of years in general , we annexed tables for the perpetual finding of the Sunday letter , Golden number and Epact in both the Old Julian , and New Gregorian accompt , with the fixed and moveable Feasts , and a Catalogue of some famous places with their latitude and distance in longitude from the meridian of London , whose use is so obvious that it needs but little explanation ; yet to take away all difficulty we have added these directions . The Cycle of Sun , Sunday Letter , Golden Number and the Epact in both accounts are set against the yeare of our Lord , and when those years are out , they may be renewed againe as oft as you please , thus for the yeare 1656 the Cycle of the Sun 1513 , the Sunday letters in the English account are F E , in the Gregorian B A the prime or Golden number in both is 4 , the Epact in the English accompt is 14 in the Gregorian 4. And now to find the movable Feast , seek the English Epact , in the first Columne of that Table towards the left hand , and the first F that follows ▪ will shew you that the 3d. of February is L X X Sunday , the 17 of February ▪ L Sunday , & the 20th of February Ashwednesday , & the first E that follows will shew that Easter day is the 6th . of April , Ascension day the 15th . day of May , Whitsunday the 25 of May , Corpus Christi the fifth of June , Advent Sunday , November the 30th . But in the Gregorian , the Epact and Sunday Letters must be sought in the first Columne towards the right hand , so shall the Sunday Letters B A shew the Feast of Easter to be on the 9th of their April , and the rest as in that line they are set down . The fixed Feasts , together with the Week-day Letters , are set against their proper dayes in every moneth of the Julian year , knowing therefore the Sunday Letter , you may easily know upon what day of the Week any Feast or day of the moneth shall be . The Catalogue of places doth serve to shew the height of the Pole in those places , and the Difference of the Meridians of any place in the Catalogue from that of London . The Letter S notes that the distance is Westward , A that it is Eastward , the figures under the title of Time are Hours and Decimal parts of an houre , the Earth or any Starre comes sooner or later to the Meridian of that place then that of London . If the time of a Lunar Eclipse then or other appearance be given at London , afternoon 8 hours , 23 parts , and the time when this happens at Uraniburge be inquired , there is found in the Catalogue for Uraniburge 0 hour 83 parts A , if therefore according to the letter A , 83 parts be added to the time given it makes 9 houres 06 parts for the time at Uraniburge . But if the time of another place be to be reduced to the time at London , the difference is to be applied with the contrary title . And that these Reductions whether in time or motion may be the better compared with those bookes that are written in the old Sexagenary forme , we have added tables for the ready converting of Sexagenary parts into Decimall and the contrary , the first of these tables is for the converting of the Minutes and Seconds , &c. of a Degree in motion ; and the other of the parts of a day in time , an example in each will be a sufficient explanation . Let it be required to find the Decimall answering to 37′ 25″ 16‴ 5 ' ' ' ' 29 ' ' ' ' ' in motion . In the first page of the table I find 37′ 12″ which is the nearest lesse , and 62 answering thereunto , and in the third columne of the second page in the top of the page I find 12″ , in which columne I find 25 seconds , and in the sixt and last columne of that page right against 25″ , I find this number 36111111 , which being annexed to 62. The Decimall of 37 minutes 25 seconds is 6236111111 And the Decimall of 16 thuds 0000740741 The Decimall of 5 fourths 0000003858 The Decimall of 29 fifths 0000000373 Their summe 6236856083 is the Decimall sought 2. Example Again , if it be required to find the Decimall of 8 hours , 17 minutes , 8 seconds , 5 thirds , 12 fourths , 9 fifts . In the first columne of the table entituled , A Table to convert the hours and minutes of a day into Decimalls , I find 7 hours 12 minutes , and in the second columne the figure 3 , then looking the 12 minutes in the top of the pages , I cast mine eye downward in that column till I come to 8 hours 17 minutes , and in the last columne of the page against 8 houres 17 minutes , I find this number 451388889 and therefore , The Decimall of 8 hours 17 minutes is 3451388889 The Decimall of 8 seconds 925926 The Decimall of 5 thirds 009645 The Decimall of 12 fourths 0387 The Decimal of 9 fifths 0005 Their aggregate 3452324852 Is the decimall sought . To find the parts of a degree in motion , or of a day in time answering to any Decimal given , is but the contrary worke to the former ; Example . As if it were required to find the parts of a degree answering to 6236856083 , the 2 first figures of this Decimall are 62 which being sought in the first page of the table give me 37′ . 12 and 62 being subtract ▪ from 6236856083 , the remainder will be 36856083 which being sought in the last columne , my nearest number is 36111111 , and right against that number under 12 in the top of the page I find 25 , therefore 37′ 25″ are the parts of a degree answering to the Decimall given , but if you would find the thirds , fourths and fifths , from 36856083 Subtract 36111111 The remainder is 749972 Which being sought amongst the Decimals of the thirds , gives me 16 thirds , and this number to be subtracted from it 740741 ; and the remainder 004231 being sought amongst the Decimals of the fourths gives me 5 fourths , and this number to be subtracted from it 3858 , and the remainder 373 sought amongst the Decimals of the fifths gives me 29 fifths , and so the parts of a degree answering to the Decimall given are 37 minutes , 25 seconds , 16 thirds , 11 fourths , and 29 fifths . Thus may you also find the parts of a day in time answering to any Decimall given . The next thing to be done towards the finding of the annuall revolutions of the planets is to find their entrance into any point of the Zodiack desired , and that may be done thus . Having the place of the planet taken by observation before and after its entrance into the point desired , subtract the observed place next before from the observed place next after , and the remainder shall shew you the apparent motion answerable to the time between those observation , subtract also the former place , from the place in the point desired , and note their difference : for as the former remainder , that is the apparent motion between the observations , is to the time between those observations : so is this difference , to the time between the first observation , and the planets entrance into the point desired : thus we are to deal with those observations that we our selves shall make , but one mans age not being distance enough between the observations from whence the middle motions may be rightly stated , we must take some observations upon trust ; and find the middle motions by comparing the observations made in former ages with those of our owne , of the Sun or Earth , take this Example following . The vernal Equinox observed by Hypparchus in the year from the death of Alexander 178 , was Mechir the 26 day , and 95833333 , that is at London 86746111. And the vernal Equinox observed at Uraniburge by Tycho 1588 was March the 9th . 86458333 , that is at London 82986111. And that the intervall of time between these two vernall Equinoctialls may be known , the 9 of March 1588 must be reduced to the correspondent time in Egyptian yeares from the death of Alexander , which according to the former directions is thus . The Christian Aera began in the 4713 complete yeare of Julian period , to which 1587 being added , it makes 6●00 from the beginning of the Julian period therefore to the 11 of March 1588 , there are dayes as followeth . 6000 Julia● yeares give 2191500 300 years give 109575 February 59 Dayes 08 The Summe 2301142 The Aera Alexandri began in the 12 of November in 4390 yeare of the Julian period in which there are dayes , 4000 1461000 300 109575 80 29226 9 3287 October 304 Dayes 11 Which being subtracted 1603397 From 2301142 There rests 697745 1000 Egyptian yeares give 365000 There rests 332745 900 yeares give 328500 There rests 4246 10 years give 3650 There rests 596 1 yeare gives 365 There rests 231 Phamenoth compleate 210 There rests 21 Therefore the 11 of March 2588 in our English account , falls in the 1912 yeare of the Aera Alexandri the ●1 day of Pharmuthi . In which space of time There are dayes 697746 And from the death of Alexander to the 26 of Mechir 178 , there are 64781 There rests 632965 From days 697746. 829●6111 Subtract 64781. 86746111 There rests 632964. 96240000 And in this time the Earth or Sun hath gone 1733 circles , 〈◊〉 623880 degrees . Hence to find the mean motion for a year or 365 days I say ▪ If 632964. 9624 d ▪ Give 623880 degrees ; How many degrees shall 365 dayes give ? And the answer is 359 deg . 7611456036. That is in Sexagenary numbers 359 deg . 45 minutes , 41 seconds , 1 third , 27 fourths . Again , to find the mean motion for a day I say , If 365 dayes gives 359 degrees , 7611456036 , what shall one day give ? And the answer is 0. 9856469743. That is in Sexagenary numbers 0 deg , 59 minutes , 8 seconds , 19 thirds , 44 fourths . And what is here done for the middle motion of the Earth or Sun , may be done for the other planets . CHAP. 2. Of the figure which the planets describe in their Motion . HAving shewed in the former Chapter , by what means the Annuall or Periodicall revolutions of the Planets may be knowne , with their mean or equal motion , for any part of those revolutions , we should now shew you , how by those equal motions to find their true or apparent places . But we can never hope to find the true and exact Phenomenon of the planets , unlesse we first know the figure in which they move ; And this must be collected from such affections , as are by the constant observations of all ages found to be proper and naturall to them , or may be rationally collected from them . 1 That the planets have one onely motion , in one onely line , and that those motions are equal , constant and perpetual , hath been confirmed by the observation of all ages , 2 And therefore they must needs be regular , their motions must be in a circle or some other line returning into it selfe , or else their motions could not be perpetuall . 3 Their equall motions must have some place assigned ( which the planets naturally behold ) to be the beginning of this equall motion . 4 And because the apparent place of a planet taken by observation , is generally different from the place reckoned in its middle motion , the inequality of this middle and apparent motion must be referred to the center of the Zodiacke , ●s to the point of that inequ●lity . 5 And because the center of the Zodiacke and of the world is to out appearance the same , the point of this inequality must be referred to the center of the world . 6 And because of this difference between the middle and apparent motion , the center of the world cannot be the true and exact center of the planets , but the center of that figure which the planets describe in their motion , must be some other point then the center of the Zodiacke . 7 And though the planets to our appearance are observed to be sometimes swifter in motion , then at other some , yet the cause of this inequality of motion must not be such as shall alter the natural and equal motion of the planet , it must be such as shall make the planet to be slower in its furthest distance from the center of the world , and swifter at his nearest , without transposing the equal motion into any other then the first place assigned , whether superficies or circle . 8 And further the apparent motions of the planets in their nearest and furthest distances from the center of the world being the same with their middle , the way of the planets must be such , that when they have gone 90 degrees from their farthest distance in their middle motions , their apparent motions must be lesse then 90 by the quantity of that whole inequality between the middle and apparent motion ; And when the planets have gone a quadrant in their apparent motions , their difference between their motions shall be that whole inequality also , and therefore the center of that figure which the planets describe in their motions must be in the middle between the points of their equal and apparent motions . 9 And because the mean motion from the point of a planets farthest distance from the center of the world , to the first quadrant is greater then the apparent , therefore the apparent motion must be greater then the mean , from the first quadrant to the point of the planets nearest distance , and consequently a greater portion of the line in which the planets move , must be allowed to the apparent from the first quadrant to the point of nearest distance , then from the point of farthest distance to the first quadrant . 10 And because the equal motion must not change and that the apparent motion doth increase from the point of the planets farthest distance from the center of the world , the angles of the middle motion must be reckoned , in the arches of many parallel circles , which shall also increase from the points of farthest to the point of their nearest distance to the center of the world , and the line of the apparent motion , must containe those circles in one and the same superficies , and therefore that line must be excentricall from those circles of apparent motion , and so placed that all the parts of apparent motion may proportionably answer to all the parts of equal , yet so as that the least circles of equal motion , shall agree with the point of the planets farthest distance , and the greatest circles with the point of the planets nearest distance from the center of the world . Seeing now that these circles of middle motion must be parallel , succeeding one another in a continued series , and are not one within another , and that the apparent motion must in the farthest distance answer to the least circles , & in the nearest distance from the center of the world to the greatest , there is none but a solid Superficies that can be capable of those greater and lesser circles : And that an unequal sided Cone may be so cut , as that the figure upon the plaine of that Section shall truly represent these affections of the planets , the learned Bullialldus doth Demonstrate , and for a preparation thereunto he sheweth first , How two equal right lines may be so drawn in an unequal sided Triangle , as that the one shall bisect the other . An unequal sided Cone being cut through the Axis by a plaine perpendicular to the plain of the base , shall make an unequal sided Triangle , and let A B C be such a Triangle , whose base B C let be bisected in I , and parallel therunto draw the line P S , which being within the triangle shall be also bisected in the point R , and from a point taken in this line at pleasure , suppose at H , to the Axis of the Cone A I , draw the line H M so , as that the angles H M R and M R H may be equal ; then shall H M and H R be equal also , and let the line H M being continued to the sides of the Triangle A B and A C be bisected in the point X , and by the point of bisection at X , draw the line V X T parallel to the base B C , then are the right lines E K and V T equal , and E K is bisected by V T in the point X. And now if this unequal sided Cone be cut through the bisected line E K , the figure made on that plane by such section shall be an Ellipsis one of whose umbilique points shall fall in the Axis of the Cone . For V T being equal to E K , and E K being bisected in X , the right line X O in the circle V O T shall be the conjugate diameter in the Ellipsis E K , because it is perpendicular to the line E K in the point X , and reacheth to the extremitie of the plain V O T , and it is also a mean proportionall between V X and X T , because it cuts the line V T at right angles in the point X. And therefore the square of X O is equal to the rectangle V X T more by the square of Z X but the rectangle V X T more by the square of Z X shall be equal to the square of Z V , and the square of Z V shall be equal to the square of E X , because Z V and E X are equal , and therefore the squares of X O and Z X , shall be equal to the square of E X , but E X is the greatest semidiameter , X O the lesser , and the square of Z X or M X the difference between the squares of E X and X O , and therefore M X shall be the distance of the umbilique point from the center X , and M the umbilique which by construction is placed in the Axis of the Cone A B C , as was to be proved . And because the center of the Ellipsis at X is distant from the Axis A I , by the quantity of X Z equal to M X , the plane which bisects the Ellipsis by the conjugate Diameter O X N shall not bisect the circles , but shall cut off V X a greater part towards E , and X T a lesser part towards K. Let the equal motion of the planet therefore be about the Axis of the Cone A I , and through all the circles which are intercepted between E D and P K , and let the centers of those circles be in the Axis of the Cone , and upon those centers let the planets be conceived to make equal angles in equal portions of time , but the terme of apparent motion to which it is referred , let be the other umbilique at H , the place of the Sun ( if we suppose him according to our new Astronomy to be the center of the World. ) . Then is the Aphelion or part remotest from the Sun at E , the Perihelion or nearest part at K. And now while the planets describing the Ellipsis shall be equally moved about the Axis of the Cone , in their equal or middle motions , they shall have gone a quadrant about the Cone , when yet they shall want of a quadrant in the Ellipsis by the quantity of the right line M X , and shall be in the point Y , which point is in the circle F M G , and in the Ellipsis , and the right line M Y which is drawn from the center of the circle F G , is set at right angles , upon the Diameters both of its owne circle F G and of the Ellipsis E K , and consequently the angle F M Y is a right angle , and therefore the planets shall move 90 deg . of middle motion about the axis of the Cone when they come to Y , but in the Ellipsis they shall not move so much by the arch Y O , or the right line M X. That this is the true and naturall Hypothesis may thus appeare , because 1 The planets thus describe one onely line about the axis of the Cone , in their equal constant and perpetual motions . 2 Their motions thus are regular , though not in a perfect circle , yet in a line returning into it selfe . 3 Their equal motions have their beginning alwayes in one place , ●●at is , in the Axis of the Cone . 4 , 5 The apparent motion of the planets is referred to the Sun at H , as to the center of the Zodiac . 6 And the whole inequality between the middle and apprent motion , is between the umbilique points M and H. 7 The motion of the Planets are thus made to be flower in the Aphelion , then in the Perihelion , and yet the equal motion is not reckoned any where but in the first place assigned the axis of the Cone . 8 The Planets in their middle motions will thus goe 90 degrees about the axis , being come to Y , when yet they want of a quadrant in the Ellipsis , the arch Y O , or M X , and so the center of the Ellipsis is in X , the middle of the whole Inequality . 9 There equal motions from the Aphelion at E to the first quadrant are greater then the apparent , but from the first quadrant to the Perihelion at K , the apparent motions are greater then the mean , and therefore a smaller portion of the line which the Planets describe is allowed to the apparent motion from the Aphelion to the first quadrant , to wit , F Y , and a greater part from the first quadrant to the Perihelion , to wit , Y O R. 10 And lastly , because the circles of middle motion , F G , V T , &c. do increase from the Aphelion to the Perihelion , & that the Planets notwithstanding make equal angles in equal portions of time about the axis of the cone , their motions in the Ellipsis do increase also from the Aphelion to the Periheliō , because these greater angles are subtēded by greater lines in greater circles , by lesser lines in lesser circles , & because the lesser circles are placed towards the top of the Cone at A , & Aphelion at E , the greater towards the base and Perihelion at K , the motion in the Ellipsis is slower about the Aphelion and swister towards the Perihelion ; And thus the middle motions are not reckoned in one onely circle , but in many parallel circles comprehended between E D and P K , these circles are contained in one plain Superficies , and by these circles the planets describing an Ellipsis doe continually passe , and yet they are all of them excentricall in respect of the figure which the planets describe , as was before required . Thus then there is an admirable Harmony between the motions of the planets in this figure , and their motions in the heavens found by observation ; probably therefore we may conclude that the figure which the planets describe in their motions is an Ellipsis . CHAP. 3. Of the Lines and Method to be used for the finding of a Planets true longitude from the Aphelion in this figure . HAving resolved upon the figure which the Planets describe in their motions , we come now to shew you what lines must be drawn , and method used for the finding a planets true longitude from the Aphelion in this figure ; and in order thereunto , we will shew you first the order of the spheares in which the planets move , and how mechanically to draw this Ellipticall figure of their motions upon a plane . As to the Spheares , 1 We suppose that the Sun is placed in the middle of the world in or about the center of the Spheare of the fixed Starres , and hath no circular motion but centrall onely . 2 That the Earth is one of the planets , and with her annual motion about the Sun describeth her Orbe between the Orbs of Mars and Venus . 3 That the Moon is moved about the Earth , as her center , and so in her annuall motion hath respect both to the Earth , and to the center of the Earths orbe the Sun. 4 That the Orbe of Venus is next under the Orbe of the earth , and the Orbe of Mercury between the Sun & the Orbe of Venus . Next above the Orbe of the earth we suppose the orbe of Mars , the Orbe of Jupiter next above Mars , and the Orbe of Saturn next to the Orbe of the fixed Stars . According to these supposed principles , we would have immediately shewed the method of calculation , but that the Mechanicall way of drawing an Ellpsis , doth if not demostrate , yet at least illustrate that method . An Ellipsis by the helpe of a thread may be mechanically made thus , first draw a right line to that length which you would have the greatest Diameter to be , which let be A P , and from the middle of this line at X , set off with your Compasses the equal distances X M and X H. Then take a piece of thrid of the same length with the diameter AP , & fasten one end of the thrid in the point M , and the other at H , & with your pen extending the thread thus fastened to A , & from thence towards P , keeping the thrid stiffe upon your pen , draw a line from P by B to A , the line so drawne shall be an Ellipsis , in which because the whole thread is equal to the Diameter A P therefore the two lines made by the thread in drawing of the Ellipsis must in every point of the Ellipsis be also equal to the fame diameter A P , they that desire a demonstration thereof Geometrically may consult with Apollonius Pergaeus , Claudius Mydorgius , o● others , in their treatises of Conicall sections ; for our present purpose this is sufficient , and from the equality of those two lines , with the Diameter , a brief Method of Calculation , is thus demonstrated by Dr. Warde . Let the line M E be equal to A P , and draw the lines H B and H E , then in the plaine triangle M H E , having the sides M E equal to the Diameter , and M H the distance of the umbilique points , with the angle H M E , the angles M E H and M H E shall be given also , but the angles B E H and B H E are equal , because the sides B H and B E are equal by construction , and therefore if you subtract the angle B E H from the angle M H E , there will remaine the angle at the Sun M H B , which is a planets true longitude from the Aphelion or the equated Anomaly . And of these three things propounded to be given , the side M E is by construction made equal to the Diameter A P , how the angle H M E and the side M H must be had shall plainely appeare by that which followes . CHAP. 4. Of the proportion by which the motion of the Planets doe increase from the Aphelion to the Perihelion . THough the equal motions of the planets are to be reckoned ( as hath been said ) in diverse parallel circles about the Axis of the Cone , whose diameters must still increase from the top of the Cone at A , to the base B C , that the motions of the planets in the Ellipsis may encrease also ; yet in the calculation we cannot conveniently reckon the middle motion in any more circles then one , and therefore it must be proved , that the angle comprehended between the lines drawn from E to that point in the diameter of the Ellipsis which is made the common Center of the Circles of middle motion , and fr●● that Center to the planet in the Ellipsis , is alwayes equal to the a●gle of middle motion , comprehended between the s●midiamet●● of the planets proper circle of middle motion and the line d●●wn from the center of that circle to the planet in the Ellipsis , this Bull●aldus takes for granted , and Dr. Ward doth thus demonstrate . F M G is a circle of middle motion whose center is in the Axis of the Cone , and in the umbilique point of the Ellipsis M , but a planet being in the Ellipsis at R the proper circle of its middle motion is L β Q and the angle comprehended by the Radius of that circle Lβ , and the line drawn from β the center thereof to R the place of the planet is equal to the angle comprehended between the line E M and the line drawn from M to R in the Ellipsis , for thus there are made two right angled triangles M H R and β H R , in which the side H R is common to both , for it is set at right angles in the Ellipsis and in the circle equant , and the sides M H and β H are equal by what hath beene already said in the 2 Chapter , therefore the angle R M H is equal to the angle R β H , and by consequence R β L and R M E are equal also , but the angle R β L is the angle of the middle motion of a planet from the Aphelion , or the angle of the simple excentricke anomaly , and therefore the angle R M E is the mean anomaly also , whose complement to a semicircle is the angle M E H in the Diagram of the preceding Chapter . When a Planet therefore descends from E to K , the angles at the axis of the Cone , or at M the umbilique point of the Ellipsis do alwayes increase , and therefore the meane anomalie is increased , for the angles of its circle Equant do answer to more degrees at the axis , and those angles also , are alwayes degrees or parts of greater circles , and therefore the planets increase in the swiftnesse of their motion in such proportion as the circles , Diameters , or Radii of those circles equant do increase . For Demonstration whereof let the line E ψ be made parallel to the axis of the Cone , then shall the parts of the semidiameters of the circles equant comprehended between those parallels E ψ and A I be equal to the semidiameter of the least circle E O , and the parts intercepted between that parallel E ψ and the side of the triangle A B , shall be the proportionall excesse above the least motion in E O. And the mean acceleration is in that circle equant whose plain parallel to the base of the cone doth pass by the center of the Ellipsis , that is in the circle V D T , for seeing that M X & Z X are equal , as also V D & Z X , V D must needs be the difference between the semidiameter of the least circle E L & the middle circle V T , & the excess of that semidiameter , above the semidiameter of the least circle , must be equal to M X or the excentricity , but the distance of this circle from the Aphelion is 90 degrees , and may be called the Diacentrick circle , and is the Radius of the circle of the equated anomalie E X And the difference between the semidiamater of V T , and the parallel circle ω K is also equal to M X , for as E V to E ω so is E X to E K , and again , as E V to E ω so is V D to ω ψ , and because E X is the halfe of E K , therefore V D shall be equal to ω Y or to the halfe of ω ψ , and therefore ω Y is also equal to M X , when a planet therefore is in the circle V T , it is swift in motion , and is in the middle between the swiftest and the slowest motion , and because that middle acceleration of the planets , is the acceleration in a quadrant , therefore as E X to V D , so is E M to G π. That is , as Radius to the excentricity , so is the versed sine of the distance from the Aphelion , to the part proportionall of the planets acceleration ; and therefore also ( faith Bullialdus ) it is as the whole sine , to the whole difference , so is the sine of the distance of the middle motion from the Aphelion , to the part of the difference answering to that distance . From hence and the two following problemes of Vieta , he propounds a method for the finding of the Aphelion and distance of the umbilique points . Probleme 1. Three points in the circumference of a circle being given , to find a diameter ▪ upon which there being perpendiculars let fall from the points given ; the segments of the diameter intercepted by these perpendiculars shall be proportional to another proportion given . Let the line C B be cut in E , so as C B may be to E B , as S to R , and let D E , cut the Diameter F G at right angles in H. Then is F G the Diameter sought , upon which seeing the lines B I , C K , D H doe fall perpendicularly , K I shall be to H I as S to R. For the right lines C B are parallel , or not parallel , if they be parallel , C B shall be equal to K I , and E B to H I , and then by construction K I shall be H I , that is C B to E B , in the given proportion as S to R. But if they can meet , let the point of their meeting be at L. Then it shall be as L C to L K , so L E to L H , and so is L B to L I. And then dividing and changing the termes , it shall be as K I to H I , so is C B to E B , or so is S to R as was required . And thus likewise K H and H I , with the arches B C , C D , and B D , being given , we may find the arch B G , and the Diameter F G in the same parts with K H and H I , for the arches C D and D B being given , the subtenses of those arches and angles opposite to them in the triangle B C D shall be given also in the parts of the Diameter F G , and therefore the sides E B and D B with the angle E B D being given , the angle E D B or D B M shall be given also , which being deducted from the arch B M D shall leave B M or the double of B G. Probleme 2. Two points in the circumference of a given circle being given , to find the Diameter , upon which perpendiculars being let fall from the points given , the segment of the Diameter intercepted by those perpendiculars shall be equal to a line given . In the circle B C whose center is A , let the given points be B C , let the given line be Z. Subttend the periphery B C , and let the right line B C be made the Diameter of a circle , in which draw the line C D equal to Z. But by the center let there be drawn E F the Diameter of the circle B L C parallel to D C , and then the perpendicular B D being let fall upon M C , the angle B D C shall be a right angle . And because E F and D C are parallel , B D shall cut E F at right angles in the point K , and B K shall be parallel to C I , and therefore D C and K I shall be equal , therefore in the circle B C , the points B and C being given , there is found the Diameter E F , upon which the perpendiculars B K and C I being let fall , the segment K I intercepted by those perpendiculars is equal to C D that is to Z the line given . Thus likewise the summe of the arches , and the summe of the Sines of these arches being given , we may distinguish the arches and the Sines if the center A be between K and I. Or the difference of the arches and the difference of their sines being given , we may distinguish the arches and the sines , if the point K be betweene the center A and the point I. When three places therefore in the apparent motion of the Sun orany other planet , with the intervall of time are given , the middle motion of the planet shall be given also , with the difference between the middle and apparent in those intervalls , and the rest from these . For if the points B C D in the Diagrams of the first probleme be given , to wit , three places in the apparent motion , & the middle motion in the intervalls of time B C , C D , the difference between the middle and apparent motion shall be given also ; let K I the part of the diameter F G , be the difference of the middle from the apparent in the intervall B C , and let H I be the difference in the intervall B D. Then in the triangle B C D , the arches B C and C D are known , and therefore the angles at D and B are known also , and by consequence the third angle at C , and from thence the subtense C B , now that we may find the angle E D B , the side C B must be cut in the same proportion as the line K I is cut in H. That so K I may be to H I as C B to E B. And so we shall have E B in the like parts with B D ; and the sides E B , B D , with the angle at B , in the triangle B E D being given , the rest shall be given also , and the angle at D being given , we shall have the arches M B and M D. And lastly , F G shall be given in the like parts in which K H , and H I are given . For as the summe of the Sines complement B I and C K , to K I , so is the Diameter F G , to the same diameter in the parts of K E and so the first inequality shall be given , and the diameter from whence it begins . CHAP. 5. Of the inequality of the Earths annual motion , and of the Diameter in which the Aphelion and Perihelion are placed . THe inequality of the Earths annual motion , if we suppose the motion to be exactly circular , may from the Observations of Copernicus made at Fruenburg in Prussia , 1525 , or rather as they were corrected by Tycho , 1584 be they found ; Between the Autumne and the Vernal Equinox , according to Tycho there were dayes 178. 43333. 33333. And between the Autumne Equinox , and the middle of Mars there were dayes 45. 15416. 66667. Upon the Center F describe the Suns Orbe A B C , let A be the Vernal Equinox the the Autumne , D the middle of Mars , and let D E intersect A C in the point G , and draw the line A D : Then is the ark of middle motion C D 44 degrees , 5061111111 , and therefore the angle C A D , 22. 25305. 55556. and the angle of apparent motion C G D 45 degrees , which being deducted from 180 degrees , give the obtuse angle A G D , 135 degrees . And therefore the angle C D G 22. 74694. 44444. And the arch A E 45. 49388. 88889. Again , the ark C D A , 175 deg . 87500. 00000. from which deducting C D 44. 50611. 11111. the remainder is D A , 1●1 . 36888. 88889. The subtense A D 18225828. to which A E being added , the whole is D E , 176. 86277. 77778. and the subtense of D E , 19992506. And because that neither of these Segments do make a Semicircle , we must find the Aphelion in the other part of the circle E B C. Let the line E B represent the Aphelion and Perihelion , G F the excentricity , F H then being drawne perpendicularly shall bisect D E and make right angles in the point H. And in the triangle A G D , the angles being given with the side A D , there is also given G D 9763585 , whch being deducted from the halfe of D E there shall remaine G H 232668 , and the perpendicular F H may be thus found , D A E wants deg . 3. 13722. 22222 of a semicircle , the halfe whereof is 1. 56861. 11111 , whose sine 273740 is the side F H , now then H G and F H being given , we may find the angle F G H 49. 63666. 66667 , which with the arch A E 45. 49388. 88889 makes 95. 13055. 55556 , therefore the Aphelion is ♋ 5. 13055. 55556 , or in sexagenary numbers , in 5 degrees of Cancer 7 min. 50 seconds . And the excentricity F G 359261. But the method for the finding of the Aphelion and excentricity which we propounded in the last chapter , is more sutable to the Elliptical motion of the planets , and according to that method the earths Aphelion and Excentricity , or semidifference of the umbilique points , from the accurate observations of Tycho in the year 1588 may be thus found . From the middle of Taurus to the middle of Leo there were dayes in the apparent motion , 94. 24662. 03703. From the middle of Leo to the Autumne Aequinox there were dayes 46. 40277. 77778. From the middle of Taurus to the Autumne Aequinox there were therefore dayes 140. 64939. 81481. In the annexed Diagram let C represent Taurus 15 deg . D 15 deg . of Leo. Then shall the arch of apparent motion C D be 90 deg . and D B 45 , but in the middle motion the arch C D shall be 92. 89277 , and D B 45. 73777 , and CB 138. 63055. First , we will worke with the arches of apparent motion . Arch. Deg. Angles Deg. Sides C D 90. 00000 C B D 45. 00 C D 70711 D B 45. D C B 22. 50 D B 38268 C B 135. C D B 67. 50 C B 92388 The halfe differences of the middle from the true . 1 Deg. 1. 44638 K H 2524   2 Deg. 0. 36888 H O 644   Deg. 1. 81526 K O 3168   As K O 3168 co . arith .     6. 4992149 To C B 92388     4. 9656155 So is H O 644     2. 8088858 To E B 18780     4. ●7●7152 And now in the triangle E D B we have the sides D B 38268 , ● B 18780 , and the angle E B D 45 deg . to find the angle E D B. As the summe of D B and E B 57048 co . ar . 5. 2437596 To their difference 19488 4. 2897673 So the tangent of ½ D and E 67. 50 10. 3827756 To the tang . ½ the difference 39. 51283 9. 9163025 The angle E D B 27. 98717 and the double thereof is the arch B M N 55. 97434 from whence taking M N ●q●al to D B 45 there rests B M 10. 97434 , and the halfe of that is B G 5. 48717 , and the summe of D B and B G 50. 48717 , now D represents the 15 deg . of Leo and the complement of D G to a quadrant is the arch D L 39. 51283 from the vernall Equinox to the 15 deg . of Leo is 135 deg . from which deducting D L 39. 51283 , there rests for the point of the Aphelion at L 95. 48717 , that is in Cancer deg . 5. 48717. And now to find the Semidistance of the umbiliques , As the summe of the Sin●s of the complements of B O and C K , is to K O , So is the Radius A G to the same Radius A G. Now if you deduct 15 deg of Taurus from Cancer 5. 48717 the arch C L will be 50. 48717 and B G 5. 48717 being d●ducted from L G 90 , there rests L B , 84. 51283 the sine of L C is K A 77●●8 and the sine of A O 99541 and the summe of K A and A O is 176●8● now then , As the summe of K A and A O 176689 co . ar . 4. 7527●94 Is to the ½ difference K O 3168 3. 5007851 So is the Radius A G 100000   To the same Radius A G in the parts of K O 1792 8. 2534945 or degrees 1. 02139 halfe the inequality desired . But if we take the arches of Middle motion the calculation will be as followeth , Arch. Deg. Add Ded. Sides . C D 92. 89277 C B D 46. 446 85 C D. 72473 D B 45. 73777 D C B 22. 868885 D B. 38862 C B 138. 63054 C D B   C B. 93554 Halfe the differences of the middle from the true ▪ as before . 1 Deg. 1. 44638 K H 2524. 14119 2 Deg. 0. 36888 H O 643. 81259 Deg. 1. 81526 K O 3167. 95378 As K O 3168 co . arith . 6. 4992149 Is to C B 93554 4. 9710623 So is H O 644 2. 8088858 To E B 19018 4. 2791630 And in the triangle E D B the angle at D may be thus found . The side D B is 38862   The sine E B is 19018   The summe is 57880 5. 2374765 The difference 19844 4. 2976292 Tangent ½ D & E 66. 77681 10. 3674618 To the tangent ½ 38. 62586 9. 9025625 28. 15095 the angle E D B and the double thereof is the arch B M N 56. 30190 & from thence taking M N equal to D B 45. 73777 There rests B M 10. 56413 and the half of that is B G 5. 282065. and the summe of D B and B G 51. 01997. Now D represents the 15 degrees of Leo , and the complement of D G to a quadrant is D L 38. 9800● . from the Vernal Equinox . to the 15 deg . of Leo , is 135 deg . from which deducting D L. 38. 98003 , there rests for the point of the Aphelion at L , 96. 01997. that is in Cancer , 6 deg . 01997 , from which the difference between the true and mean motion in that interval being deducted 73776 , the place of the Aphelion will be in Cancer , 5. 28221. And to find the Semidistance of the umbiliques deduct 15 deg . of Taurus from Cancer 5. 28221 , there will remaine for the arch C L 50. 28221 , and B G 5. 28206 being deducted from L G 90 there rests for the arch , L B 84. 71779 , the sine of C L is K A 76921 The sine of L B is A O 99575 As their summe 1764964 co . ar . 4. 7532652 Is to K O 3168 3. 5007851 So is the Radius A G   10. 0000000 To the same A G 1795   8. 2540503 This excentricity Bullialdus corrects by the apparent places of the planets in the center of the Ellipsis , and that angle according to the Method of our calculation may be thus found . From 15 degrees of Taurus , or from 225. deg . Deduct the Aphelion 095. 28221 There rests the angle M H E 129. 71779 whose complement to 180 deg . is 50. 28221 the summe of M E H and E M H and the halfe thereof 25. 14110 The side H E 200000   The side M H 3590   The summe 203590 4. 6912436 The Differ . 196410 5. 2931636 Tang. ½ summe 25. 14110 9. 6714590 Tang. ½ differ . 24. 35902 9. 6558662 The summe 49. 50012 E M H   Difference 00. 78208 M E H being doublled is the angle   M B H 1. 56416     From E M H 49. 50012   Deduct M E H or E M B 00. 78208   There rests B M H 48. 71804 As the sine of M B H 1. 56416 co . ar . 1. 5638976 Is to the side M H 3590 3. 5550944 So is the sine of B M H 48. 71804 9. 8759126 4. 9949046 To the side B H 98833   The side X H 1795   The Summe 100628 co . ar . 4. 9972811 The Differ . 97038 4. 9869418 Tang. ½ sum 25. 14110 9. 6714590 9. 6556819 Tang. ½ Dif . 24. 34989   Differ . 00. 79121 X B H. From the 15 deg . of Taurus or from 45 45. Deduct the angle X B H 00. 79121 There rests the place required 44. 20879 Again , from 0 deg . of Libra or from 180. Subtract the Aphelion 95. 28221 There rests the angle M H E 84. 71779 And therefore ½ of M E H and E M H 47. 64110 The side H E 200000   The side H M 3590   The Summe 203590 co . ar . 4. 6912436 The Differ . 196410 5. 2931636 Tang. ½ summe 47. 64110 10. 0400951 Tang. ½ Differ . 46. 61542 10. 0245023 Aggregate 94. 25652 E M H Difference 1. 02568 M E H which being doubled is the angle M B H 2. 05136 From E M H 94. 25652 Deduct M E H 1. 02568 There rests B M H 93. 23084 whose complement is A M B 86. 76916 The summe 101927 co . ar . 4. 9917108 The differ . 98337 4. 9927169 Tang. ½ summe 47. 64110 10. 0400951 Tang ½ differ . 46. 61677 10. 0245228 Differ . 1. 02433 The angle X B H.   And therefore the Earths place 181. 02433 Now then from the Aphelion 95. 28221 Subtract Taurus , that is 44. 20879 There rests the arch C L 51. 07342 And from L G 91. 02433 Deduct B G 5. 28206 There rests the arch L B 85. 74227 77795 is the sine of 51. 07342 99724 is the sine of 85. 74227 Summe 177519   As the summe 177519 com . ar . 4. 7505576 Is to K O 3168 3. 5007851 So is A G 100000 5. 0000000 To the same A G 1784 3. 2513427 But according to this method , the Aphelion may be somewhat more exactly found , if we take the Arithmetical mean , between the apparent and middle motion , and so ; Arch. Deg Angle Deg. Side C D 91. 44638 C B D 45. 723●9 C D 71597 D B 45. 36889 D C B 22. 68444 D B 38565 C B 136. 81527 C D B 68. 40763 C B 9●983 Now then to find E B I say , As K O 3160 co . ar . 6. 4992149 Is to C B 92983 4. 9684035 So is H O 644 2. 8088858 To E B 18902 4. 2765042 Then in the triangle E D B , we have known the side D B 38565 , the side E B 18902 , and their contained angle E B D 45. 72318 , whose complement to a semicircle is 134. 27681. The half summe 67. 13840. As the summe of D B and EB 57467 co . ar . 5. 2405815 Is to their differ . 19663 4. 2936497 So is Tang. ½ D and E 67. 13840 10. 3750715 To the Tang ½ differ . 39. 06019   Differ . 28. 07821 the angle E D B   The angle E D B 28. 07821 E D B doubled is the arch B M N 56. 17926 From which subtract M N or D B 45. 36889 There rests B M 10. 78753 The halfe of B M is the arch B G 5. 39376 And D B being added to B G , D G is 50. 76265 And the complement there of is D L 39. 23735 Which being deducted from ♌ or 435. 00000 There rests the Aphelion at L 95. 76265 And the halfe difference D B 0. 36889 Being deducted there rests 95. 39377 The Aphelion then is in Cancer 5 deg . 39377 And to correct the excentricity from the 15 degree of Taurus or adding a semicircle from 225. Deduct the Aphelion 95. 39●77 There rests in the Ellipsis M H E 129. 60623 whose complement to 180 is the summe of the opposite angles M E H and EMH 50. 39377 In the Triangle therefore of the last Diagram M E H , we have , 1. The side H E 200000 2. The side H M 3568 3. The angle M H E given As the summe 203568 co . ar . 4. 6912904 To the difference 196432 5. ●932122 So tang . halfe summe 25. 19688 9. 6724222 To tang . halfe differ . 24. 41154 9. 6569248 Aggregate 49. 60842 the angle E M H   Difference 00. 78534 the angle M E H   Differ . doubled is 1. 57068 the angle M B H   Differ . subtracted 48. 82308 is the angle B M H ▪   As the sine of M B H 1. 57068 co . ar . 1. 5620900 To the side M H 3568 3. 5524248 So is the sine of B M H 48. 82508 9. 8766104 To the side H B 97977 4. 9911252 The side X H 1784   The summe 099761 co . ar . 5. 0010393 The differ . 96193 4. 9831434 Tang ½ summe 25. 19688 9. 6724222 Tang. ½ differ . 24. 39566 9. 6566049 Differ . 00. 80122 the angle X B H which being subtracted from 15 degrees of Taurus , or from 45 deg . there rests 44. 19878 the Aphelion 95. 39377 Place of the earth subtract   44. 39878 There rests the arch C L   51. 19499 Againe from 0 degrees of Libra or from 180. Deduct the Aphelion   95. 39377 There rests in the Ellipsis M H E   84. 60623 And therefore the ½ summe of the angles E M H and M E H   47. 69688 As the summe 203568 co . ar . 4. 6912904 To the differ . 196432 5. 2932122 So tang . ½ summe 47. 69688 10. 0409444 To tang . ½ differ . 46. 67763 10. 0254470 Aggregate 94. 37451 angle E M H   Difference 01. 01925 angle M E H   Differ . doubled 2. 03850 angle M B H   Differ . subtract 93. 35526 angle B M H   As the sine of M ● H 2. 0385 co . ar . 1. 4489043 To the side M H 3568 3. 5524248 So is the sine of B M H 86. 64474 9. 9992548 To the side H B 100134 5. 0095839 The side X H 1784   The summe 101918 co . ar . 4. 9917492 The differ 98●50 4. 9927743 The tang . ½ summe 47. 69688 10. 0409444 Tang. ½ differ . 46. 67901 10. 0254679 Difference 01. 01787 , X B H which being added to ♎ the place will be 181. 01787 , from which subtract B G 5. ●9376 there rests 175 or L B 85. 62411.   The sine of C L 77927   The sine of L B 99707   As the summe 177634 co . ar . 4. 7504740 Is to K O 3168 3. 5007851 So is A G 10000 5. 0000000 To A G 1783 3. 2512591 which comes so neer to the Excentricity before found that we may without manifest error make use of either . CHAP. 6. Of Stating the Earths middle motions by sundry observations . TO find the Earths middle motion for any time under a yeare , the way already prescribed in the first Chapter ( as to the use for which it was intended ) is exact enough , but to state the true quantity of the Earths annual motion , the apparent Equinoctials must be reduced into the mean , which cannot be done unless the Aphelion be first found , having found that therefore by the observations of Tycho , we will now find it by the observations of Albategnius , in the year from the death of Alexander , 1206 , and the intervall of time then between the Autumne and the Vernal Equinox was dayes 178. 51250 , and the middle motion for that time , is deg . 175. 95083. The true motion is 180. From which subtract 175. 95083 Their difference is 4. 04917 The half difference is K L 2. 02458 Therefore as A E 3568 com . ar . 6. 4475752 To A E 100000 5. 0000000 So is K L 3533 3. 5481436 To K L 99019 4. 9957188 Half the arch H I L is 87. 97541 , whose sine 99938 is the side H L , and therefore , This Autumne Equinox was observed September the 19th , from the death of Alexander 1206 yeares , that is in the yeare of our Lord 882. In the beginning therefore of the yeare of Christ 883 , the Aphelion was in Gemini 24 d. 25176 And in June 1588 , the Aphelion was in Cancer 5. 39377 Their difference is 11. 14201 And betweene both observations there are 706 Egyptian years , now then to find the mean motion of the Aphelion for a yeare I say , If 706 years give 11. 14201 , what shall one yeare or 365 dayes give ? and the answer is Deg. 0. 0157818838 And againe , if 365 dayes give 0157818838 one day shall give o deg . 0000432380. In 882 Julian years there are 322150 dayes , by which if you multiply 0000432380 the product will be deg . 13. 9291217 , which being deducted from the aphelion before found , Gemini 24. 25176 , the aphelion in the beginning of the Christian Aera will be in Gemini 10. 3226383 , that is , 19 21 29. But from Hypparchus , that is from 177 yeare from the death of Alexander to the 1205 yeare compleate in the same account , there are 1028 Egyptian years , and the meane motion of the Aphelion in that time is , Deg. 16. 2237765464 Gemini 24. 2516600000 Gemini 08. 0278834536 which being deducted from there rests for the aphelion at that time . And therefore the vernall Equinox observed by Hypparchus in the yeare from the death of Alexander 178 Mechir 26. 95833333 , was distant from the Aphelion deg . 68. 027883 , which being deducted from a Semicircle the angle in the Ellipsis of the next Chapter A M E will be found to be 111. 972117 , and this angle is the summe of the angles M E H and M H E , and therefore the equation to be subtracted may be thus found . The side M E 200000   The side M H 3568 Logarithms The summe 203568 co . ar . 4. 6912905 The Differ . 196432 5. 2932122 The tang . ½ summe 55. 98606 10. 1707846 Tang. ½ differ 55. 03186 10. 1552873 Differ . 00. 95420 angle M E H   Differ . doubled . 01. 90840 angle M B H or the Equation sought : which may be converted into time thus , if the parts of a degree of equal motion , 98564 give one day ; 1. 90840 snall give 1. 93620 , and this being added to the true Equinoctial , Mechir 26. 95833 the middle will be Mechir 28. 8945● , or deducting 05625 ; for the difference of meridians between Uraniburge and Alexandria , it will be at Uraniburge ; Mechir 28. 83828. And the vernall Equinox observed by Tycho at Uraniburge 1588 , was March the 9. 86458 , and the Earths aphelion then was in Cancer 5. 39377 ; and therefore the arch answering to the excentricity 3568 , viz. deg . 2. 04529 being converted into time as before , will be days 2. 07508 , which being added to the former time the middle Equinoctial wil be March the 11. 93966. And in the Egyptian account from the death of Alexander it was 1912 Pharmuthi 23. 93966 , from which if you deduct in the same account 178 , Mechir 28. 83828 between both observations there will be found , 1734 Egyptian years , dayes 55. 10138 , which being converted into dayes give 632965. 10138. Hence to find the quantity of the Tropicall yeare , I say , if 1733 Zodiacks give dayes 632965. 10138 , that one Zodiack shall give dayes 365. 2418357126. And to find the earths middle motion for a yeare , I convert 1733 Zodiacks into degrees , and they amount to 623880 degrees ; then I say , if 632965. 10138 give 623880 , that 365 days shal give 359. 76106661098 that is in Sexagenary numbers 359 deg . 45 minutes , 39 seconds , 50 thirds , 24 fourths . And to find the meane motion for a day , I say , if 365 dayes give 359. 76106661098 , that one day shall give 9856467579 , that is in Sexagenary numbers 0 degrees , 59 minutes , 8 seconds , 19 thirds , 41 fourths , 57 fifths . And the daily motion of the Aphelion is 0000432380 , which being deducted from the diurnall longitude gives the daily motion of the Anomaly 985603599 , these things premised we will now determine the Epochaes of the middle motions . The middle Equinoctiall Anno Christi 1588 , March 11. 9●966 , is from the Aera Nabonassari 2336 Pharmuthi●3 ●3 . 93966. 2335 years being multiplyed by 359. 761067 the product will be 840042. 091445 , and the diurnal motion 985647 , being multiplied by 232 days , the product will be 228. 670104 and the middle motion answering to the parts of a day , 93966 , is 926173 , the which being added togethea do amount to 840●71 degrees 687722 parts of a degree , that is , rejecting the whole circles 31 d. 687722 , which being deducted from 360 , the remainder 328. 312278 or 10 Signes 28 degrees and 312278 parts , is the Radix of the earth or Suns mean longitude in the beginning of the Aera Nabonassari . To which if you add deg . 258. 692408 the middle motion for 424 years , the whole circles being rejected , the Radix of the earths middle motion to the beginning of the Aera Alexandri shall be 227. 004686 or 7 sines 17 deg . 004686 parts . And adding to this Epocha , deg . 51. 944398 , which is the middle motion for 323 years 131 dayes , the whole circles being rejected , the Radix of the earths middle motion in the beginning of the Christian Aera shall be deg . 278. 949084 or 9 signes , 8 deg . 949084 , to which if you add 034223 the equal motion belonging to 034722 the difference between the Meridians of Uraniburge and London , the Radix of middle motion at London will be 278. 983307 And the Aphelion 70. 322638 And the Mean Anomaly 208. 660669 CHAP. 7. To calculate the Suns true place and distance from the Earth . HAving composed tables of the Suns middle motions , according to the directions of the last Chapter , his true place in the Zodiack , and distance from the earth may thus be found . 1 Write out the Epocha next before the given time and severally under that , set the motions belonging to the years , moneths , and days compleat , and to the houres and scruples current , every one under his like ( onely remember that in the Bissextile year , after the end of February , the dayes must be increased by an Unite ) then adding them altogether , the summe shall be the Suns meane motion for the time given . Example . Let the time given be May the 12th . houre 11 parts 15 before noon at London in the Bissextile yeare 1656 , and the Suns place to be soughts The numbers are thus ,     Suns Longitude Suns Apogeon     Deg. parts Deg. parts The Epocha 1640 291. 24777 96. 22265 Years comp . 15 359. 37294   23686 April 118. 27760   519 Dayes 12 011. 82776   52 Houres 23   94458     Scruples 15   616     Suns Mean Longitude 421. 87681 96. 46522 2 Subtract the Apogaeum from the Mean Longitude , there rests the mean Anomaly . Example . The Suns mean longitude 421. 67681 Apogaeum substract 96. 46522 Rest mean Anomaly 325. 21459 Whos 's complement to a Circle 34. 78541 is the angle A M E in the Ellipsis . And the complement of A M E to a semicircle is the angle E M H 145. 21459. The side M E 200000   The side M H 3568   The summe 203568 co . ar . 4. 6912905 Differ . 196432 5. 2932122 Tang. ½ summe of the opposite angles 17. 39270 9. 4958787   17. 39270   Tang. ½ Differ 16. 81799 9. 4803814 Differ 57471 is the angle M E H.   Difference doubled 1. 14942 is the angle M B H   3 The mean Anomaly being above 180 deg . the Aequation found must be added to the sunsmeane longitude , so have you the Suns true place . Example . The Suns meane longitude 421. 67681 Aequation adde 1 14942 The Suns true place 422. 82623 or 2 Signes 2 degrees 82623 parts of a degree   Lastly , to find his distance from the earth , I say , As the sine of M B H 1. 14942 co ▪ ar . 1. 6977118 Is to the side M H 3568 3. 5524249 So is the sine of B M H 34. 78541 9. 7562590 To the side B H   5. 0063957 or distance required 101483   Thus we have found the Suns place by calculation , we will now shew how to reduce the Suns mean longitude to his true , by the Table of Aequations of the Suns excentrick . The Suns Anomaly in this example is 325. 21459 The Aequation of 325 is 1. 15566 326 1. 12648 Difference is 02918 Now then I say if one deg . co . ar . 5. Give 2918 3. 4650853 What shall 21459 4. 3316095 The answer is 6●6 2. 7966948 Aequation of 325 deg . 1. 15566 Part proportional subt . 626 Aequation equated 1. 14940 The Snns mean longitude 61. 67681 Aequation adde 1. 14940 Suns true place 62. 82621 And in like manner the Logarithme of the Suns distance from the Earth will be found to be 5. 0063633 , which being more necessary then the distance it self , in the calculation of the places of the other planets , we have as most convenient placed in the table . CHAP. 8. Of the Aequation of Civil Dayes . SOme there are of late , which allow not of any Aequation of Civil Dayes , others will have the inequality proceed from two causes . First , from the unequal motion of the Sun in the Zodiack , and the other from the Zodiacks obliquity ; Tycho ( whom we shall follow in this particular , ) doth make the difference between the Suns true longitude and his Right Ascension ; to be the absolute Aequation of naturall dayes , the which is also clearly demonstrated , according to the Copernican Systeme by Thomas Street in his Ephemeris for the yeare 1655 ; which being but short is here inserted . The Aequation of time demonstrated . Let A be the center of the Sun , and E of the Earth , ♎ E the earths longitude from the Equinoctiall point in the ecliptick , ♎ F the like arch projected in the Equator , ♎ B the Right Ascension of the Earths or Suns true place , G H is a diameter of the Equinoctiall and Meridian of the earths apparent diurnal revolution , A B the semidiameter of the true meridian , and equinoctial supposed in the heavens ; and G H parallel to A B ( though here they appeare as one right line . Then let C D parallel to A F be likewise a diameter of the Equinoctial and Meridian of the meane or equal diurnal revolution . Hence C E G the angle of the earths libration , equal to B A F the difference of longitude and Right Ascension is the true Equation of time or the difference between the equal and apparent time . And according to this Demonstration is our Table ( entituled , A perpetual Table for the Equation of time ) composed . In which you must enter with the signe and degree of the Suns place either in the uppermost and left hand columnes descending , or in the lowermost and right hand ascending , and in the common angle is the Equation ( according to the titles ) to be added or subtracted to or from the equal time , that it may be made apparent ; But to reduce the apparent to the equal , take the contrary title . CHAP. 9. Of the Theory and Motion of the Moon . THe Moon according to our Hypothesis is a secondary planet , moving about the earth , as the earth and other planets doe about the Sun , and so not onely the earth , but the whole Systeme of the Moone is also carryed about the Sun in a yeare , And hence according to Hypparchus there ariseth a twofold , but according to Tycho a threefold inequality in the Moons motion . The first is periodicall , and is to be obtained , after the same manner , as was the excentrique Equation of the Sun or Earth ; in order whereunto her middle motions should be first stated , the which Bullialdus by the rules delivered in the fourth and fifth Chapters preceding hath for the Meridian of Uraniburge determined to be as followeth . From the Equinoctiall to the beginning of the Christian Aera , the Moons middle motion was 135d . 16′ 27″ The Meane Anomalie 355 5 18 And the Radix of her latitude 366 29 56 These then we will take for granted , until there be a more exact , and true Geometrical way propounded to us , ; onely we will convert them into Decimall numbers , and reduce them to the Meridian of London . From the Equinoctial to the beginning of the Christian Aera , The Moons middle motion in decimal numbers at Uraniburge was 135. 27417 For the Difference of Merid. adde . 45750 The Moons mean longitude at London 135. 73167 The Meane Anomaly , At Uraniburge 355. 08833 Differ . Merid. adde . 45361 Mean Anomaly at London 355. 54194 The Radix of Latitude At Vraniburge 366. 49889 Differ . Merid. adde . 45944 Latitude at London 366. 95833 d. The Diurnal Motion of the Moons Mean longitude 13. 17639 Anomaly 13. 06500 Latitude 13. 22944 The Annual Motion . In longitude 129. 38389 Anomaly 88. 71889 Latitude 148. 71278 According to which limitations of the Moones middle motions , we have composed our Tables , by help whereof and the Semi-excentricity of the Moons Orbe , which according to Bullialdus is 4362 the Moons excentrique equation , or place first equated may be found , as before was shewed in the Sun. Save onely that here the Moons Anomaly is given without subtraction . Example . Anno 1587 , August 17 ho. 19. 41667 in the apparent time , or ho. 19. 28973 in the middle time , the Moon being in the meridian of Vraniburge noble Tycho observed her in 26 deg . 38333 of Gemini with latitude 5 deg . 23333 S. from which middle time if you subtract 83333 for the difference of the meridians of London and Vraniburge , the time in our meridian is , ho. 18. 45640. And the Suns true place 154. 07347. The Suns distance from the Earth 100895. The Log●rithme of that distance 5. 0038707 The Moons middle motions for the same time are as here you see them . Time given ☽ Longitud ☽ Anomaly ☽ Latitude Years 1500 072. 88194 313. 06916 017. 17805 80 174. 24805 158. 80139 281. 61167 6 069. 48028 18● . 37750 185. 50583 Iuly 27● . 39555 249. 77639 284. 62194 D●yes 16 ●10 . 82222 209. 0●972 211. 66944 H●●res 18 ●9 . 88222 9. 79861 9. 92222 Paris 4564 . 250●1 . 24848 . 25152 Mean Longitude 810. 96077 1126. 11125 990. 76067 Ded●ct 720. 1080. 720. There rests 90. 96077 46. 11125 270. 76067 The Moones meane Anomaly 46. 11125 is the angle A M E in the preceding Ellip●is , or the summe of the angles M E H and M H E. Therefore in the triangle M E H we have given , 1. The side M E 200000. 2. The side M H 8724. 3. The angle E M H the complements of the Moones Anomaly , to find M E H , whose double , is the excentrique Equation M B H. I say then , As the summe of M E and M H 208724 co . ar . 4. 6804276 Is to their difference 191276 5. 2816605 So is the tang . half summe of the opposite angles , 23. 05562 9. 6290228 To the tang halfe diff . 21. 30786 9. 5911109 Differ . 1. 74776 is the angle M E H   Differ ▪ doubled 3. 49552 is the angle M B H or the equation sought which being subtracted from the Moons mean longitude , because the Anomaly is lesse then a semicircle you shall have the Moones place first equated . Example . The Moones meane longitude 90. 96077 Equation subtract 3. 49552 The Moones place first equated 87. 46525 And to find her distance from the Umbilique point at H. As the sine of M B H 3. 49552 co . ar . 1. 2148808 Is to the side M H 8724 3. 9407156 So is the Sine of B M H 46. 11125 9. 8577468 To the side B H 103120 5. 0133432 But whilest the Moone is thus making her owne periodicall revolution , her whole Systeme is by the motion of the Earth removed from the proper seats thereof , whence there ariseth another revolution which is called Synodicall , the beginning whereof is the line which passeth through the center of the earth to the Sun , and therefore the Moone in that line is void of this second inequality , which is both at the Conjunction and opposition , but being in or about her quarters , where she is farthest removed from the said Zyzigiacal line the angle of her evection is 2 deg . 50′ as is cleerely proved by the observations of Tycho and Bullialdus , whose method we follow , in our calculation of this inequality of the Moon , making 4362 the sine of the greatest evection to be the Diameter K D in the little circle K C D H. The motion of this libration of the Moone must be measured by her double distance from the Sun , because she is void of this inequality at her conjunctions and oppositions as was said before . Now then let the angle M H B represent the Moones equated Anomaly , found by subtracting the former Equation from the simple Anomaly , which is 46. 11125 Aequation subtract 3. 49552 Aequated Anomaly 42. 61573 And if from the place of the moon first equated 87. 46525 You subtract the Suns true place 154. 07347 Their distance is 293. 39178 The double distance 226. 78356 is the arch K C D H and drawing the lines F H and H K there shall be made the equicrurall Triangle H F K , whose exteriour angle H F D is known , viz. the excesse of the Sun and Moons double distance above a se micircle 46. 78356. The halfe whereof is the angle D K H 23. ●9178 , equal to the angle A H G , which being subtracted from the Equated Anomaly A H B 42. 61573. The angle G H B or the Synodical Anomaly will be 19. 2239● , whose complement to a semicircle is the angle B H K 160. 77605. The side H B 103120 as before , and the side H K may be found in this manner . The arch H V K is the complement of the double distance of the Sun and Moon to a whole circle 13● . 21644 the subtense of this arch is H K , H V the halfe arch is 66. 60822 , and H X is the right sine thereof . Now then , As the Radius ,     Is to the Diameter K D 4●62 . 3. 6396857 So is the sine of H V or H X 66. 60822 9. 9627533 To the Subtense H K 4003 3. 6024390 Therefore in the Triangle B H K we have known , 1. The angle B H K 160. 77605.   2. The side H B 103120 To find the angle H B K.   3. The side H K 4003 To find the angle H B K.   As the summe 107123 co . ar . 4. 9701173 To the differ . 99117 4. 9961481 So tang . ½ the opposite ang . 9. 61197 9. 2287638 To the tang . ½ differ . 8. 90502 9. 1950292 Their difference 0. 70695 is the angle of the evection , H B K to be added if the Synodicall Anomaly be more then 180 , and to be subtracted from the place of the Moone first equated when lesse , as here it is in our example , and therefore to be subtracted from the Moons place 87 46525 , and then her place secondly equated will be 86. 7●830 . And according to this Analogie may be made a table of the Moons evection , when she is in quadrature or 90 degrees distant from the Sun ; for then the equated and Synodicall Anomalies are both the same , and therefore in the Triangle E M H we have give the angle E H M , or the equated Anomaly which suppose 25 degrees , the side M H 8724 and the side H E ●00000 , to find the angle at E. As the sum of H E and M H 208724 co . ar . 4. 6804276 Is to their difference 191276 5. 2816605 So is the tang . half summe   10. 6542447 To tang . half differ . 76. 40435 10. 6163328 Their differ . 1. 09565 is the angle M E H   Whose double is 2. 19130 is the angle M B H   Then as the sine of M B H 2. 1913 co . ar . 1. 4175273 To the sine of B M H 27. 1913 9. 6598808 So is the side M H . 8724 3. 9407156 To the side B H 10. 4161 5. 0181235 or the Moons distance from the umbilique .     Hence in the first Diagram of this Chapter , in the Triangle B H K we have given A H B the equated Anomaly , 25 degrees , the Moons distance H B 104161 , with the side H K , or rather D K , the Diameter of the little circle 4362 , to find the angle H B K. As the summe of H B and H K 108523 co . ar . 4. 9644782 To their difference 99799 4. 9991262 So is tang . halfe summe 12. 50 9. 3447552 To tang . halfe differ . 11. 52314 9. 3093596 whose difference . 97686 is the evection sought and by Bullialdus . 97805 which is so little differing from what we have found , that I have taken his Table and converted it into Decimall numbers . And for the finding the part proportial between the quadrature and the Zyzygia , Bullialdus whom we follow , hath annexed scruples of proportion in this manner . As Radius to 60 minutes or one degree ; so is the fine of halfe the degrees of the equated Anomaly to the scruples of proportion required . But this proportion in the Sexagenary Canon will not give the scruples either so easily or so exactly as the Decimal Canon will , because the seconds must still be found in that Canon by the part proportional , which in the beginning of the Canon cannot be true , but working by a Decimal Canon the natural sines of halfe the degrees , are the Decimall parts required , as the naturall sine of 4 degrees ; 069756 , are the Decimall parts for 8 degrees of equated anomaly , and so of the rest . Having done with the first and second inequalities of the Moon , we come to the third which Tycho calls the variation , Bullialdus the Reflection for as the Moons Systeme is carryed about by the earth , the place of her Apogaeon is changed , or doth reflect contrary to the succession of the Signes , by reason of which reflection the angle of her Evection is sometimes more sometimes lesse then it will be found by the former directions , but the quantity of this variation according to Tycho doth never exceed 40′ 30″ or in Decimal numbers 67500 , to be added to or subtracted from the place of the Moone secondly equated , and the proportion by which he finds it is thus , As the Radius To the sine of the complement of the double distance of the Sun and Moon if lesse then a Semicircle : To the excesse if more : So is the sine of the greatest variation , or Reflection . To the variation required , which is to be added to the Moons place , secondly , equated if the double distance be lesse then 180 deg . to be subtracted , when it is more . Therefore in our Example , As the Radius     To the sine of H F D 46. 78356 9. 8625917 So is the sine of 67500 8. 0711591 To the variation 49189 7. 9337508 The Moones place secondly equated 86. 75830 Variation subtract 49189 The Moones place in her Orbe 86. 26641 Lastly , to find the Moones latitude and place in the Ecliptique , take the middle motion of her latitude for the time propounded , the which rejecting the whole circles is 270. 76067 and in which according to Tycho there is a twofold variation , The first is occasioned by the various intersection of the Moones orbe with the Zodiack , and the other by the reciprocal progression and retrogradation of the Nodes . In the New and Full Moones the limits of her greatest latitude , are 4. 97500 , but in her quarters 5. 29167 , as Tycho hath experimented by many diligent and accurate observations , whose method of calculation is as followeth . From the meane motion of the Moones latitude 270. 76067 Subtract the Moones absolute Equation 4. 694 6 The Equated latitude of the Moon 266. 06631 Then to find the Equation of the Nodes , let the line A D or the angle A T D 5. 13333 represent the meane inclination of the Moones Orbe with the Ecliptique , let the least inclination be represented by A B 4. 97500 , and the greatest by A C 5. 29166. And from the distance of the Sun and Moon before found ,   293. 39178 Subtract the evection and variation ●●1 . ●9884 True distance of the Sun and Moon 292. 19●94 The double thereof is 224. 385●8 which being numbred from B by C to F in the Triangle F D A we have known A D 5. 13333 the meane inclination of the Moones Orbe . 2. D F 15833 the halfe difference of the least and greatest inclination . 3. With the angle F D A 135. 61412 , the complement of the double distance of the Sun and Moon to a whole circle : whence to find the angle F A D the Aequation of the Nodes , by the Doctrine of spherical Triangles say , First , As the Radius     To the cosine of F D C 44. 38588 9. 8540905 So is the tang . of D F 15833 7. 4413175 To the tang of D C 11321 7. 2954080 Adde the arch A D 5. 13333   Summe is A C 5. 24654   2 As sine D C 11321 c● . ar . 2. 7046002 To the sine A C 5. 24654 8. 9611430 So cotang . F D C 44. 38588 10. 0093107 To cotang . F A D 1. 21062 11. 6750539 From the Moones latitude equated   266. 06787 Equation Nodes subtract   1. 21062 True motion of the Moones latitude .   264. 85725 whose complement to a whole circle   95. 14275 And to find A F or the angle of 〈◊〉 A T ● , the 〈…〉 of the Sun and Moone being more than 180 degrees , and lesse th●●●●● ▪ I deduct the Moones double distance 224 d. 3858● being numbred ●● the little circle , from B by C to F , from the Arch B C F G 270 , there remaines F G 45. 61412 , and then the A●alogie is , As the Radius D C   10. 0000000 To the sine of F G or D F 45. 61412 9. 8540305 So is the sine of the arch , D C . 15833 7. 4413159 To the sine of the arch D E . 11319 7. 2953464 The aggregate is B E . 27152 which being added to the least angle of inclination A T B , or the arch A B 4. 97500 the present inclination is A F or the angle A T F 5. 24652. Hence to find the Moones true latitude , I say , As Radius   10. 0000000 To the sine of A T F 5. 24652 8. 9611413 So is the sine of A T 84. 85725 9. 9982481 To the sine of A F 5. 22533 8. 9593894 or the angle A S F.     And by these Analogies may be made the Table of the Moons latitude wc● we have borrowed of Tycho , converting it onely into Decimall numbers . ) For supposing the Moon to be in her Syzygial points , the angle of Inclination is alwayes A T B 4. 975 , and then her latitude for every degree of her true motion of latitude may be found by the last Analogie ; As Radius Example . To the sine of A T B 4. 975 8. 9381242 So is the sine of A T 45. 9. 8494850 To the sine of A B 3. 51564 8. 7876092 And her latitude when she is in Quadratu●e or 90 degrees distant from the Sun may be found by the same analogie , if you make the angle of Inclination A T C 5. 29166. Example . As Radius     To the sine of A T C 5. 29166 8. 9648517 So is the sine of A T 45. 9. 8494850 To the sine of A F 3. 73910 8. 8143367 Subtract A B 3. 51564 there rests the Excesse to be placed in the Table 0. 22346. The proportipnal part of which excesse to be added to the Moones laitude must be found by scruples of proportion , and the Scruples themselves for every degree of the Moones distance from the Sunne may thus be had . As Radius ▪     To the Co●ine of the Moones double distance D H 40 9. 8842539 So is the sine of D B 0. 15833 7. 4413575 To the sine of D H 0. 12142 7. 3256114 Their differ ▪ is B H 0. 03691   Then as the Diameter B C 31666 5. 4994068 Is to the Diameter B C 100. 000 5. 0000000 So is B H 0. 03691 3. 5671440 To B H 0 , 11656 4. 0665508 Or more readily thus D H 76604 is the sine of 50 or the Cosine of 40 the Moones double distance from the Sun , which being deducted from Radius , the remainder is the versed sine B H 23396 the halfe 11698 , are the scruples of proportion answering to 20 deg . of the Moones single distance from the Sun , From the Moones place in her Orbe 86. 26641 Subtract the Moones true latitude 264. 85725 The Moones Node ascending 181. 40916 Lastly , for her Reduction ▪ As Radius     To the Cosine of A T F 5. 24775 9. 9981757 So tang . of A T 84. 85725 11. 0458587 To tang . of T F 84. 83689 11. 0440344 Difference 02036 is the Reduction sought From the place in her Orbe 86. 26641 Subtract her Reduction . 02036 The Moones place in the Ecliptique 86. 24605 CHAP. 10. To calculate the true Motion of the Moon by Tables . HAving gathered the meane motions of the Moones Longitude , Anomaly , and argument of Latitude , as in the last Chapter , by the Anomaly find the Moones Eccentrick equation , and by that her Eccentrick place . 2 Apply her eccentrick Equation acoording to the title both to the meane Anomaly , and to the motion or argument of Latitude ; So have you the equated Anomaly and motion of Latitude , first equated . Example . Anno 1587 , August 17 ho. 18. 45640 the Moons meane Longitude was before found to be 90. 96077 Her meane Anomaly   46. 11125 Her motion of Latitude   270. 76067 Her Eccentrick equation to 47 deg . 3. 54892   46 deg . 3. 48880 Differ .   0. 06012 Now then as 1 deg .   5. 0000000 Is to 06012 3. 7790190 So is 11125 4. 0463000 To 00668 2. 8253190 To the Equation of 46 deg .   3. 48880 Adde the part proportionall   668 The Moones eccentrick Equation   3. 49548 which being subtracted from her meane Longitude , Anomaly and Latitude . Her place first equated is 87. 46529 Her equated Anomaly 42. 61577 Her Latitude first Equated 267. 26519 3. By her meane Anomaly you must also find the Logarithme o●he● distance from her umbilique . The Logarithme to 46 Deg. is 5. 0133649   47 Deg. is 5. 0131474   Differ . 2175 As if one Degree   5. 0000000 Is to 2175 3. 3374592 So is 11125 4. 0463000 To 241 2. 837592 Which being deducted from   5. 0133649 The Moones Logarithme is   5. 0133408 4 ▪ Subtract the true place of the Sun , from the Moones eccentrick place , so have you the distance of the luminaries , with the double whereof seeke in the Table the eccentricity of the Moones evection , and the quantity of her variation or reflection , using the part proportional if need require . 5 If the double distance of the luminaries with which you enter the Table be lesse then a semicircle , adde halfe the complement thereof unto the equated Anomaly , or if it be more than a semicircle , deduct halfe the excesse above a semicircle from the equated Anomaly , then the summe or difference if lesse then a Semicircle , is the summe of the opposite angles , or if it be more , take the complement , to a whole circle . Example .   ☉ Longitude ☉ Apogaon Years 1500 290. 20076 94. 01167 80 . 59826 1. 26342 6 359. 55205 . 09473 Iuly 208. 95710 917 Dayes 16 15. 77035 69 Houres 18 . 73923   Parts 4564 . 01874   Suns Longitude 875. 83649 95. 37968 Apogaeon subtract 095. 37968   Mean Anomaly 060. 45681   The Suns eccentrick to 61 deg . 1. 77254 The Suns eccentrick to 60 deg . 1. 75464 Difference   1790 As one degree   5. 0000000 Is to 1790 3. 2528530 So is 45681 4. 6597●56 To 817 2. 9125886 The equation to 60 deg .   1. 75464 Adde th● part proportional   817 The absolute Equation subtract   1. 76281 From the Suns meane Longitude   155. 83649 The Suns true place subtract   154. 07368 From the Moones eccentrick place   87. 46529 The distance of the Sun and Moon   293. 39161 The double distance   226. 78322 The Logarithme of the Eccentrick to 226 deg . 3. 6037118 The Logarithme of the Eccentrick to 227 deg . 3. 60208●4 Difference   16284 As one degree   5. Is to 16284 4. 2117610 So is 78322 4. 8938837 To 12753 4. 1056447 which being subtracted from   3. 6037118 The Logarithme of the Eccentricity is   3. 6024365 Thus we have found the Logarithms of the two lateral distances , namely of the distance of the Moon from her Umbilique ▪ 5. 0133408 and of the Eccentricity of her Evectioon 3. 6024365. And because the double distance of the Sun and Moone is more then a semicircle 226. 78322 Deduct 180 there rests 46. 78322 The halfe whereof 23 39161 Deduct from the equated Anomaly 42. 61577 There resteth the Synodical Anomaly ●9 . 22416 or summe of the opposite angles . Hence to find the Evection , Say , As the greater Logarithme co ▪ ar . 4. 9866502 Is to the lesser 3. 6024365 So is Radius ●0 . 000●●●0 To the tang . of 2 deg . 22494 8. ●890●●● Adde 45 2 Operation . As Radius   10. 0000000 To the Cotang . 47. 22494 9. 9662367 So tang . half sum 9. 61208 9. 2287955 To the tang . half dif . 8. 90555 9. 1950324 Evection 0. 70653. Subtract because the Synodical anomaly is lesse then 180. Then for the variation , I enter the Table with the Moones double distance 22678322 ; and using the part proportional I find it to be 0. 49186 subtract . The Evection to be subtracted is 0. 70653 The Variation to be subtracted is . 49186 Their summe 1. 19839 Subtract from the Moons Eccentrick place 87. 46529 There rests the Moones place in her Orbe 86. 26690 Otherwise thus . Enter the Table entit●led Bullialdus his Table of Evections , with the Synodical Anomaly 19. 224●6 , and using the part proportional you shall find it to be 75942 , subtract , then take from thence with the Moones double distance 226. 78322 the scruples of proportion also , the which observing the part proportional are ; 91781 , by which the Evection found is thus to be corrected . As 1 degree is to 75942 : so is 91781 to the Evection sought 69701 subtract , and this subtracted according to the title from the Moones Eccentrick place 87. 46529 There rests her place secondly equated 86. 75828 Then for the variation enter this or the former table with the Moons double distance 226. 78322 , and using the part proportional you shall find it to be 49186 as before , with the title Subtract ; and therefore the Moons place in her Orbe 86. 26742 , but little differing from the former . And from these two Tables of Evection & Variation , we have composed a third Table , entituled a compounded Table of the Moones second and third inequalities , for the yet more speedy finding of these equations , whose construction is thus . First , enter the Table of the Moones Evection with her Synodicall Anomaly to find the Evection , and with her double distance from the Sun to find the Scruples of proportion . The Moones double distance may be supposed , and the Synodicall anomaly easily made from it : as suppose the Moones distance from the Sun to be 3 degrees thereof to a quadrant 87 being added to the equated Anomaly which you may also suppose to be what you please , will give the synodical Anomaly , thus if the equated Anomaly be 25 , adde 87 thereto , and then the synodical Anomaly will be 112 and the angle of evection answering thereto 2. 38861 subtract : and the scruples of proportion answering to 6 degrees 52335. Hence to finde the true evection . I say , As 1 degree 1. 00000 0. 0000000 Is to the evection in the table 2. 38861 0. 3781452 So are the Scruples of prop. 0. 52335 1. 7187912 To the evection sought , Sub. 0. 12500 0. 0969374 The variation to 6 deg . adde 0. 07055   And because the evection and variation are of different titles therefore there difference 05445 is the compounded equation sought , which I place against 25 degrees of equated Anomaly in the columne of 3 deg . of the Moons distance from the Sun , with the title subtract , because the title of the biggest number was subtract . And therefore the second and the third inequalities of the Moone are to be found in this table by entering it with the Moones distance from the Sun in the head or foot of the table , and with the equated Anomaly in the sides , for so the common angle using the part proportional , if need require , will give the Equation sought to be applyed to the Moons place according to the title . Example . Suppose the distance of the Sun and Moone were 293. 39161 , that is , deducting a Semicircle 113. 39161 , and her equated Anomaly 42. 61577 because the Moones distance from the Sun is found in the bottome of the table , I number the equated Anomaly in the first columne towards the right hand ascending , and in the common angle ( by making proportion for the intercepted degrees ) I finde the Equation to be 1. 188 S. that is the title subtract , and therefore this Equation being subtracted from the Moones Eccentrick place , what remaineth shall be the Moones place in her orbe . CHAP. 11. To finde the Moones true Latitude and place in the Ecliptick . TO the motion of Latitude first Equated , according to the title apply the agregate of the Moones second and third Equations , so have you the motion of Latitude secondly equated . 2. To the distance of the Sun and Moon before found apply the agregate of the Moons 2 d. and ● d. Equations according to the title , so have you the true distance of the Sun and Moone . Example . Motion of Latitude first equated 267. 26519 Second and third equations sub . 1. 19839 Motion of Latitude secondly equated 266. 06680 Distance of the Sun and Moone as before 293. 39161 Second and third Equation sub . 1. 19839 True distance of the Sun and Moone 292. 19322 3. With the true distance of the Sun and Moon enter the table of the Equation of the Nodes , and take thence the Equation of the Nodes , which according to the title , apply to the motion of Latitude secondly Equated , and you have the true and absolute motion of Latitude . At the same entrance take out also the scruples of proportion and reserve them . Example . With the true distance of the Sun and Moone 292. 19322 I finde the Equation of the Nodes , subt . 1. 21103 From the Latitude secondly Equated 266. 06680 So the true motion of Latitude 264. 85577 And the scruples of proportion 85729 4. With the true motion of Latitude enter the table of Latitude , and thence take the Latitude and the excesse , then say , as one degree to the excesse in the table : so are the scruples of proportion before reserved , to the excess sought , which being added to the Latitude found by the table , the summe shall be the true Latitude of the Moone , which is North when the true motion of Latitude is lesse then 6 ●ignes , and South when it is more . Example . The true motion of Latitude   264. 85577 Gives The Latitude   4. 95490 Gives The Excess   31519 As one degree 1. 00000   To the excess in the table 31519 1. 4985724 So the scrupls of propor . 85729 1. 9331277 To the excess desired 27020 1. 4317001 Which being added to the Latitude   4. 95490 It gives the true Latitude ▪ South   5. 22510 5. If the true motion of Latitude be subtracted from the Moones true place in her orbe , there resteth the Node Ascendant . As The Moones true place 86. 26690 As The Motion of Latitude subt . 264. 85577 The Node ascendant 181. 41113 6. With the true motion of Latitude enter the table of Reduction , and take out the Reduction , which according to the title apply to the Moones place in her orbe , you have her true place in the Ecliptick . Example . The true motion of Latitude 264. 85577 Gives the reduction to be subt . 02067 From the Moones place in her Orbe 86. 26690 The Moons place in the Ecliptick 86. 24623 CHAP. 12. Of the motion of the fixed Starres . THe motions of the fixed Stars are by the observations of all ages found to be equall , and the quantity of that equal motion , Noble Tycho by comparing his owne observations with those of the ancients hath determined to be exact 51 seconds , Bullialdus 50″ 55‴ ferè , and the place of the first Star in Aries in the yeare of our Lord 1600 compleat to be 27 deg . 37 min. which being converted into Decimalls the Radix of the middle motions of the fixed Stars at that time will be 27. 61667 and the yearely motion . 01414 , that is the decimall of 50 seconds 55 thirds . Hence to finde their places at any time assigned , we have exhibited a table of the longitudes and latitudes of some of the most notable fixed Stars for the yeare 1650 compleat , which by the motions of the fixed stars in the tables of the Suns meane motions , may thus be done for any other time . Take the difference betweene the time given and 1650 compleat , and the motion agreeing to that difference , this motion subtract from the place in the table when the time given is before 1650 , or else adde it , and you have the place desired . The Latitudes and Magnitudes are still the same . Example . The time given 1683 September . Difference from 1650 compl . 33 yeare 8 Moneths Motion Correspondent . 476●8 Place of Oculus ♉ 1650 compl . ♊ 4. 91667 Place required ♊ 5. 39305 Latitude South 5. 51667 CHAP. 13. Of the Motion of Saturne . OUr Tables of Saturns meane motions as of the other Planets , are he same with those of Bullialdus , being onely reduced to the Meridian of London , and converted into Decimall numbers whose eccentrick being so easie to be found , and the investigation of his true place , with the places of Jupiter , Mars , Venus and Mercury , being out of curiosity , rather then use ▪ we shall content our selves with the Trigonometricall calculation onely , first , of Saturne for the time before given 1587. August 17 : h : 18 : 4564 : and then of the rest . An. Christ. Longit. ♄ Aphel . ♄ Node ♄ 1500 064. 98279 262. 82583 109. 79361 80 258. 76528 2. 5●694 0. 57611 6 73. 39056 . 19078 0. 04306 Iuly ▪ 7. 10111 . 01833 . 00444 D 16 . 53183 . 00139 . 00030 H 18 . 02500     P 4564 . 00063     Meane Mot. 404. 801 20265. 57327110. 41752 Aphel . Subt. 265. 57327 Rests Anomaly 139. 22793 The halfe of Saturns first inequality , or his eccentricity supposing the Semidiameter of Saturns orbe to be 100. 000. is 5774. and the Semidiameter of the Earths orbe 10480. As they are computed by Bullialdus , but the Semidiameter of the Earths orbe being before supposed to be 100. 000 the Semidiameter of Saturns orbe will be 954198 , for as 10480 is to 100. 000. So is 100. 000. to 954198. and Saturns eccentricity in the same parts will be 55145. for as 100. 000 is to 954198. So is 5774 to 55145. whose double 110200 is the side M H in the figure following ; in the triangle therefore M E H , we have knowne , 1. The Angle H M E 40. 77207 , the complement of Saturns Anomaly to a semicircle ●●9 . 22793 or the halfe sum of the angles M E H and M H E viz. halfe the anomaly 69. 61396. 2. The side M E 1908396 To finde the Angle M E H. 3. The side M H 110290 To finde the Angle M E H. As there sum 2●18686 co . ar . 3. 694931● Is to their differ . 1798106 6. 2548153 So is tang . halfe sum 69. 61396 10. 4299016 To tang . halfe diff . 67. ●5375 10. 3796482 Difference 2. 26021 is the angle M E H.   Difference doubled 4. 52042 is the angle M B H , or the Equation sought , to be subtracted from Saturns meane Longitude , the Anomaly being lesse then a semicircle . Saturns meane Longitude 44. 80120 Equation Subt. 4. 52042 Saturns eccentrick place 40. 28078 2. To finde his distance from the Sun. As the sine M B H 4. 52042 co . ar . 1. 1034042 Is to the side M H. 110290 5. 0425361 So sine E M H 40. 77207 9. 8149473 To the side B H 913876 5. 9608876 ● . From the eccentrick place of Saturne subduct the Node , there resteth the argument of Latitude : by help whereof and the angle of his greatest inclination , which according to Bullialdus is 2 d. 50 , or 4362 , we may easily finde his Reduction , but the side E B 4362 in the parts of 100. 000 , must be reduced into the parts of Saturns semidiameter 954198 , to finde the curtation . As 100. 000 is to 954198 , so is 4●62 to 41622. Saturns eccentrick place Example .   40. 28078 Node substract 110. 41752 Argument of Latitude 289. 86326 Whos 's complement is K L 70. 13674 As Radius     To cosine of XKL 2. 50 9. 999586 So is tang . of KL 70. 13674 10. 4421682 To tang . of 70. 12929 10. 4417546 Whos 's difference . 01745 is the Reduction sought :   And to be subtracted from the ecceutrick place , if he move from either Node towards the limits of his greatest latitude , but if he depart from the limits and approach towards the Nodes the reduction is to be added , for so the sum or difference will be the place in the Ecliptique . As in our example , Saturne is past the limits of his greatest latitude , and is approaching towards his Node , and therefore the reduction is to be added . Saturns eccentrick place 40. 28078 Reduction adde . 01745 The eccentrick reduced 40. 29823 The inclination of his orbite from the eccliptique represented in the second figure following by the line XL , may thus be found . As the Radius KE 90.     To the greatest in clination EB 41622 4. 6193229 So is the sine of KL 70. 13674 9. 9733616 To the side XL ●9145 4 ▪ 5926845 which is the inclination agreeing to the common Radius 954 198 , whereas the distance of Saturne from the sun is to be put for the Radius , and then XL will be but 37491. As DL 954198 co . ar . 4. 0203616 To AL 913876 5. 9608876 So is XL 39145 4. 5926845 To XL 37491 4. 5739336 The distance of Saturne in his orbite from the Sun being given with the inclination of his orbite from the eccliptique , the distance corrected by curtation may thus be found . To finde Saturns second inequality . Subtract the suns place from the Eccentrick reduced , or this from it , so that lesse then 180 degrees may remain , this remainer is the Anomaly of the orbe , the complement whereof is the angle NAS , or the halfe , is the halfe sum of the opposite angles . Example ▪ Saturns Eccentrick reduced   40. 29823 The Suns true place   154. 07347 The Anomaly of the orbe   113. 77524 The angle NAS   66. 22476 The halfe Anomaly   56. 88762 As the greater side AN 913107 co , ar . 4. 0394781 Is to the less AS 100895 5. 0038707 So Radius , to the tang . 6. 30541 9. 0433488 Adde 45.   As Radius     To cotang . of the summe 51. 30541 9. 9036304 So is tang . halfe summe 56. 88762 10. 1856192 To tang . halfe differ . 50. 84613 10. 0892496 Summe 107. 73375 Angle ASN .   Differ . 6. 04149 Angle ANS .   Because Saturne eccentrick reduced was subtracted from the Suns true place , therefore the angle of his Elongation ASN 107. 73375 must be subtracted also , and then Saturns place will be 125. 19972. To finde Saturns distance from the Earth . To find the latitude of ♄ from the earth .     As SX . 877291 Co. ar . 4. 0568610 Is to Radius   10. 0000000 So is XL , 37491 4. 5739336 To the tang . of XSL , 2. 44711. 8. 6307946 which is the quantity of ♄ Southern Latitude , because the argument of Latitude was more then 6 signes , when it is less then 6 signs , the Latitude is North. CHAP. 14. Of the Motion of Jupiter . THe investigation of the place of this and the other Planets , is well nigh the same with that of ♄ , they differ more in the Dimensions of their Orbs , then in the manner of their calculation . Yet that there may be no mistake , we will not onely give you the Dimensions of their several orbs , but makes examples of their calculation to the former time given . The meane motions of Jupiter . Anno Christi . Longitude ♃ Aphelion ♃ Node ♃ Years 1500 004. 50000 185. 54833 097. 93889 80 269. 04444 1. 98000 . 54722 6 182. 13667 . 14833 . 04111 Iuly 17. 62333 . 01444 . 00389 Dayes 16 1. 33000 . 00104 . 00030 Houres 18 . 06222     Parts 4564 . 00154     Mean motion . 474. 69820 187. 68414 98. 53141 Aphelion subt . 187. 68414 Rests Anomaly 287. 01406 The halfe of Jupiter first inequality , or his eccentricity , supposing his Semidiameter to be 100. 000 by the computation of Bullialdus is 4856 , and the Semidiameter of the Earths Orbe 19138 ▪ and therefore to find ♃ Semidiameter , when the Semidiameter of the Earths Orb is 100. 000 the proportion is , As 19138. Is to 100. 000 so is 100. 000 to 522520 , the Semidiameter required , which being doubled is the Diameter of the Ellipsis , or the side M E 1045040. And to find the eccentricity in the same parts , say , as 100. 000. is to 522520 , so is 4856 , to 2537● . the excentricity , and the double thereof . 50746 is M H the distance of the foces . The complement of the Anomaly 72. 98594 is the angle A M E , and the halfe compl : 36. 49297 , is the halfe sum of the opposite angles M E H and M H E. The side M E 1045040   The side M H 50746   Sum 1095786 co . ar . 3. 9602744 Differ 994294 5. 9975147 Tang. ½ sum 36. 49297 9. 8690974 Tang. ½ differ 33. 87162 9. 8268865 Differ . 2. 62135 Angle M E H   Double differ . 5. 24270 Angle M B H or the Equatiō sought , and to be added to Jupiters mean longitude , the Anomaly being above a Semi-circle . Jupiters mean longitude 114. 69820 Equation add 5. 24270 Jupiters eccentrick place 119. 94090 The Node subt . 98. 53141 Argument of Latitude . 21. 40949 By help whereof , and the angle of his greatest inclination 1. 36333 , or E B 2379 , we may find the reduction : but to find the parts of inclination in proportion to the given Radius 522520. say , As 100. 000. is to 2379 , so is 522520 to 13619. the parts required . To finde the Reduction . As Radius     So Cosine of X K L. 1. 36333 9. 9998770 To tang . of K L. 21. 40949 9. 5933823 To tang . of X K. 21. 40353 9. 5932593 Differ . . 00596 Reduction .   Because the argument of Latitude is lesse then 90. the Reduction must be subtracted from the eccentrick place . Jupiters eccentrick place 119. 94090 Reduction subt . . 00596 Eccentrick reduced 119. 93494 To find the Inclination . As Radius     To the greatest inclin : E B 13619 4. 1341452 So is the sine of K L 21. 40949 9. 5623296 To the side X L 4971 3. 6964748 which are the parts of inclination agreeing to the cōmon Radius 522520 , but the distance of ♃ from the ☉ is to be put for the Radius , the which distance may thus be found . As the sine of M B H 5. 24270. Co. ar . 1. 0391741 Is to the side M H 50746 4. 7054018 So is the fine of E M H 72. 98594 9. 9805636 To the side B H 531055 5. 7251395 As the common Rad : D L 522520 Co. ar . 4. 2818971 To Jupiter dist : B H or A L 531055 5. 7251●95 So is X L 4971 3. 69647●8 To X L 5052 3. 7035114 To finde ♃ distance corrected by Curtation . As A L 531055 Co. ar . 4. 2748605 Is to Radius   10. 0000000 So is L X 5052 3. 7035114 To the sine of L A X 54515 7. 9783719 As the Radius     To A L 531055 5. 7251395 So is the Cosine of L A X   9. 9999831 To A X 531034 5. 7251226 To finde the second inequality of Jupiter . We must have given , 1. The angle N A S , which is to be found by subducting the ☉ place from ♃ eccentrick or reduced , or this from it , so that lesse then 6 Signes may remain , this remainer is the Anomaly of the Orbe , and the Complement thereof is the Angle N A S , or the halfe is the halfe sum of the opposite angles . Example . Jupiters eccentrick reduced 119. 9●494 ☉ True place 154. 07347 The Anomaly of the Orbe 34. 13893 The angle N A S 14. 86107 The halfe Anomaly is 17. 0694● These given with the sides N A and A S , I say . As the greater side A N 531034 co . ar . 4. 2748774 Is to the Radius   10. 0000000 So is the lesser side A S 100895 5. 0038707 To the tang . of 10. 75783 9. 2787481 Adde 45   As Radius to Co-tang . 55. 75783 9. 8329403 So tang : of ½ summe 17. 06946 9. 4872186 To tang . of ½ differ . 11. 80522 9. 3201589 Summe 28. 87468 Angle A S N   Differ . 5. 26424 Angle A N S   Because ♃ eccentrick reduced was subtracted from the ☉ place , therefore the angle of his Elongation A S N 28. 87468 must be subtracted also , and so ♃ place 125. 19839. To finde the distance of Jupiter from the Earth . As the sine of A N S 5. 26424 co . ar . 1. 0373985 To the side A S 100895 5. 0038707 So the sine of N A S 34. 13893 9. 7491287 To the side S N 603111 5. 7803979 To finde the latitude of ♃ from the Earth . As the side S N 603111 co . ar . 4. 2196021 To the side X L 5052 3. 7035114 So is the Radius 90 10. 0000000 To tang . of X S L 0. 47998 7. 9231135 Which is the quantity of ♃ Northern latitude .     CHAP. 15. Of the Motion of Mars . THere being no other variety in calculating the place of this Planet , then what hath been already shewed , in the motions of Saturn and Jupiter , we will proceed in the same method , and gather first the middle motions for the former time given , and then shew the Dimensions of his several Orbs , as we shall have occasion for them . An. Christ. Longit. ♂ Aphel . ♂ Node ♂ Yeares 1500 245. 61611 146. 80916 45. 40250 80 193. 32778 1. 75139 1. 07194 6 68. 23750 . 13139 . 08028 Iuly 111. 10306 . 01250 . 00778 D 16 8. 38500 . 00096 . 00057 H 18 . 39306     P 4564 . 00996     Mean Mot. 627. 07247 148. 70540 046. 56307 Aphel . Subt. 14. 70540 Rest Anom . ●19 . 36707 Supposing the Semidiameter of ♂ his Orbe 100. 000 His eccentricity according to Bullialdus is 9239 Semidiameter of the Earths Orbe 656●8 The sine of his angle of Inclination 3230 And the Arch answering thereto 1. 85111 And therefore suppose the R. of the Earths Orbe 100. 000 The eccentricity of Mars will be 14075 The Semidiameter of his Orbe 152350 The parts of his greatest Inclination 4921 The Anomaly 119. 36707 is the angle A M E in the Ellipsis of the 13 Chapter , and therefore the halfe of it is the halfe sum of the angles M E H and M H E 59. 68353 2. The side M E 304700   3. The side M H 28150   Summe 332850 co . ar . 4. 4777515 Differ . 276550 5. 4417726 Tang : ½ sum 59. 68353 10. 2330382 Tang : ½ diff : 54. 86290 10. 1525633 Difference 4. 82063 Angle M E H   Difference doubled 9. 64126 Angle M B H or the Aequation sought , and to be subtracted from the planets mean Longitude , because the Anomaly is lesse then 180. viz. 119. 36707. Meane longitude of Mars 267. 07247 Aequation subtracted 9. 64126 Mars his Eccentrick place 257. 43121 To finde his distance from the Sun. As the sine of M B H 9. 64126 co . ar . 0. 7760404 To the side M H 28150 4. 4494783 So is the sine of M B H 60. 63293 9. 9402403 To the side B H 146473 5. 1657590 From the eccentrick place sub : Node .   119. 36707 Argument of Latitude   128. 06614 Whos 's complement is K L   51. 93586 To finde the Reduction . As the sine of 90     To Cosine the great inclin : X K L 1. 85111 9. 9997732 So tang : of K L 51. 93494 10. 1061739 To tang : of X K 51. 92039 10. 1059471 Differ . . 01455 Reduction .   Because the argument of Latitude is more then 90 , the Reduction must be added to the Eccentrick place . The eccentrick place of Mars 257. 43121 Reduction adde . 01455 Eccentrick reduced 257. 44576 To finde the present inclination . As Radius     To the greatest inclin : E B 9921 3. 6920533 So the sine of K L 51. 93494 9. 8960878 To the X L 3873 3. 5881411 Which are the parts of inclination agreeing to the common Radius , 152350. But the distance of Mars from the ☉ is to be put for the Radius , and then the parts of inclination will be 3724. For as common Radius D L 152350 co . ar . 4. 8171576 To ♂ distance B H or A L 146473 5. 1657590 So is X L 3873 3. 5881411 To X L 3724 3. 5710577 To finde the distance of ♂ corrected by Curtation . As A L 146473 co . ar . 4. 8342410 To Radius   10. 0000000 So is X L 3724 3. 5710577 To the sine of L A X 1. 45703 8. 4052987 As Radius     To A L 146473 5. 1657590 So Cosine of L A X 1. 45703 9. 9998596 To A X 146426 5. 1656186 To finde the second inequality of Mars . We must have given , 1 The angle N A S , which is to be found by subducting the ☉ place from the eccentrick of ♂ reduced , or this from it , so that lesse then 6 signes may remain , this remainer is the Anomaly of the Orbe , and the complement thereof is the angle N A S , or the halfe , is the halfe sum of the opposite angles . Example . The eccentrick of ♂ reduced 257. 44576 The ☉ true place 154. 07347 Anomaly of the Orbe 103. 37229 Complement is N A S 76. 62771 Halfe Anomaly 51. 68614 These given with the sides N A & S A , I say , As the greatest side N A 146426 co . ar . 4. 8343814 Is to Radius   10. 0000000 So is the lesser side S A 100895 5. 0038707 To the tang . of 34. 56887 9. 8382521 Adde 45   As Radius     To co-tang . 79. 56887 9. 2650444 So tang . ● / ● sum 51. 68614 10. 1022929 To tang . ½ diff . 13. 11536 9. 3673373 Summe 64. 80150 angle A S N   Differ . 38. 57078 angle A N S   Because the Suns place was subtracted from the eccentrick of ♂ reduced , therefore the angle of elongation A S N 64. 80150 must be added to the ☉ place 154. 07347 and then the place of ♂ will be 218. 87497. To finde the distance of ♂ from the Earth . As the sine of A N S 38. 57078 co . ar . 0. 2051769 To the side A S 100895 5. 0038707 So sine of N A S 76. 62771 9. 9880626 To the S N 157438 5. 1971102 To finde the latitude of Mars from the Earth . As the side S X 157438 co . ar . 4. 8028898 To the side X L 3724 3. 5710577 So is Radius   10. 0000000 To tangent of X S L 0. 13560 7. 3739475 Which is the quantity of ♂ his Northern latitude .     CHAP. 16. Of the Motion of Venus . HAving done with the three superiour Planets , Saturn , Iupiter and Mars , we come to the two inferiour , Venus and Mercury , the investigation of whose places is much after the same manner with the former , the difference is in the second inequality , occasioned by their motion under the earth , the Orbs of the other Planets being above it ; that this difference may be the better discerned , we have added an example in each for the time before given . The meane motions of Venus . An. Christ. Longit. ♀ Aphel . ♀ Node ♀ Yeares 1500 333. 11667 303. 97639 073. 28944 80 15. 48472 1. 12694 . 67028 6 270. 36028 . 08444 . 05028 Iuly 339. 65833 . 00806 . 00500 D 16 25. 63472 . 00062 . 00039 H 18 1. 20194     P 4564 . 03048     Meane Mot. 265. 48714 305. 19645 074. 01537 Aphel . Subt. 305. 19645 Rest Anom . 320. 29069 The Semidiameter of the orbe of Venus , in such parts of which the Earths orbe is 100. 000 , by the computation of Bullialdus is 72398 , her Eccentricity 575. The parts of her greatest inclination 4270. And the angle it selfe 3. 38111. In the triangle therefore of the following Diagram M E H , we have three things given . 1. The halfe sum of the angles M E H and M H E 19. 85465 , viz. the halfe complement of the meane Anomaly to a circle . 2. The side M E 144796   3. The side M H. 1150   Summe 145946 co . ar . 4. 8358079 Difference 143646 5. 1572934 Tang. halfe sum . 19. 85465 9. 5576273 Tangent halfe difference 19. 56560 9. 55072●6 Difference . 28905 Angle M E H.   Differ . doubled . 57810 Angle M B H.   or the Equation to be added to the mean longitude , because the Anomaly is more then a semicircle . The meane Longitude of Venus 265. 48714 Equation adde . 57810 The eccentrick place of Venus 266. 06524 Node subtract 74. 01537 Argument of latitude K L 192. 04987 To finde the distance of Venus from the Sun. As the sine of M B H 0. 57810 co . ar . 1. 9961373 To the side M H 1150 3. 0606978 So the sine of H M B 39. 70931 9. 8054279 To the side B H 72822 4. 8622630 To finde the Reduction . As the Radius     To the Cosine of the great inclina . X K L 3. 38111 9. 999●433 ▪ So tangent of K L 12. 04987 9. 329●295 To tangent of X K 12. 02950 9. 3285728 Difference . 02037 Reduction . Because the Argument of Latitude is more then 180 , the Reduction must be subtracted from the eccentrick place . The eccentrick place of Venus 266. 06524 Reduction subtract . 02037 Eccentrick reduced 266. 04487 To finde the present inclination . As Radius     To the greatest inclinat . E B. 4270 3. 6304●78 So sine of K L 12. 04987 9. 3196533 To the inclinat . X L 891 2. 9500811 Which are the parts of inclination agreeing to the common Radius 72398 , but the distance of Venus from the Sun , 72822 being put for Radius , the inclination will be 896. As the common Radius D L 72398 co . ar . 5. 1402735 To Venus distance B H or A L 72822 4. 8622630 So is X L 891 2. 9508115 To X L 896 2. 9526176 To finde the distance corrected by Curtation . As A L 7●822 co . ar . 5. 1377370 To Radius , so is X L 896 2. 9526176 To the sine of L A X 0. 70550 8. 0903546 As Radius     To A L 72822 4. 8622630 So Cosine of L A X 07055 9. 9999671 To A X 72816 4. 8622301 To finde the second inequality of Venus . We must have given , 1. The angle N A S which is to be found by subducting the Suns place from the eccentrick of Venus reduced , or this from it so that less then 6 signes may remain , this remainer is the Anomaly of the orbe and the complement is the angle N A S , or the halfe is the halfe sum of the opposite angle . Example . The eccentrick of Venus reduced 266. 04487 The Suns true place 154. 07347 Anomaly of the orbe 111. 97140 Complement is N A S 68. 02860 Halfe Anomaly 55. 98570 These given with the sides N A and S A the Analogies are . As the greater side S A 100895 co . ar . 4. 9961293 Is to Radius   10. 0000000 So is the lesser side N A 72816 4. 8622300 To the tangent of 35. 81815 9. 8583593 Adde 45.   As Radius     To cotangent 80. 81815 9. 2085475 So tang . halfe sum 55. 98570 10. 1707787 To tang . halfe diff . 13. 46926 9. 3793262 Summe 69. 45496 Angle A N S   Difference 42. 51644 Angle A S N   In the superiour Planets , Saturne , Iupiter , and Mars , the summe of these angles is the elongation , but in the inferiour Venus and Mercury there difference is the Elongation sought , and in our Example is to be added to the Suns place , because the Suns place was subtracted from the Eccentrick of Venus reduced . Suns true place 154. 07347 Elongation A S N add 42. 51644 True place of Venus 196. 58991 To finde the distance of Venus from the Earth . As the sine of A N S 69. 45496 co . ar . 0. 0285403 To the side A S 100895 5. 0038707 So sine of N A S 68. 02860 9. 9672296 To the side S N 99917 4. 9996406 To finde the latitude of Venus from the Earth . As the side S X 9991. 7 co . ar . 5. 0003594 Is to Radius   10. 0000000 So is X L 896 2. 9526176 To the tangent of X S L 0. 51417 7. 9529770 which is the South latitude of Venus .     CHAP. 17. Of the Motion of Mercury . THe forme of calculating the place of this Planet is the same with Venus , the Dimensions of whose orbs we shall give you , as the learned Bullialdus hath computed them , but first we will set down the middle motions thereof to the former time . The middle motions of Mercury . An. Christ. Longit. ☿ Aphel . ☿ Node ☿ 1500 352. 53750 248. 73556 039. 85639 80 59. 53472 2. 31611 2. 12417 6 326. 41889 . 17361 . 15917 Iuly 147. 58583 . 01694 . 01528 D 1● 65. 47806 . 00126 . 00117 H 18 3. 06917     P 4564 . 07781     Meane Mot. 234. 70198 251. 24348 42. 15618 Aphel . Snbt. 251. 24348 Rest Anom . 343. 45850 The proportion between the Earths orb , and the orbe of Mercury is as 100. 000 to 38585 Semicentricity in the same parts is , 8105. The parts or greatest inclination 4635. And the angle it selfe 6. 90. In the triangle therefore M E H , of the first Diagram of the former Chapter we have known . 1. The halfe sum of the opposite angles M E H and M H E , 8. 27075 the halfe of 16. 54150 which is the complement of the meane Anomaly , 343. 4585 to a circle . 2. The side M E 77170   3. The side M H 16210   Summe 93380 co . ar . 5. 0297462 Differ . 60960 4. 7850449 So tang . halfe sum . 8. 27075 9. 1628126 To tang . halfe differ . 5. 42532 8. 9776037 Difference 2. 84543 Angle M E H   Difference doubled 5. 69086 Angle M B H or the Equation to be added to the meane longitude , because the Anomaly is more then a semicircle .   Example . The meane Longitude of Mercury 234. 70198 Equation adde 5. 69086 Eccentrick place 240. 39284 Node subtract 42. 15618 Argument of Latitude K L 198. 23666 To finde the distance of Mercury from the Sun. As the sine of MBH 5. 69086 co . ar . 1. 0036592 To the side MH 16210 4. 20978●0 So sine of EMH 16. 54150 9. 4544022 To the side BH 46541 4. 6678444 To finde the Reduction . As Radius , to cosine of XKL 6. 90 9. 9968431 So tangent of KL 18. 23666 9. 5178453 To tangent of XK 11. 11322 9. 5146884 Reduction 12344   And because the argument of Latitude is more then 180 , it must be subtracted from the eccentrick place 240. 39284 And then the eccentrick reduced will be . 240. 26940 To finde the present inclination . As Radius     To the greatest inclination EB 4635 3. 6660497 So sine of KL . 18. 23666 9. 4954646 To the inclinat . XL 1450 3. 1615143 Which are the parts of inclination agreeing to the common Radius 38585. But the distance of Mercury from the Sun being put for Radius , the inclination will be . 1749 For as Radius DL 38585 co . ar . 5. 41358●5 To Mercury dist . BH or AL 46541 4. 6678444 So is XL 1450 3. 1615143 To XL 1749 3. 2429402 To finde the distance corrected by Curtation . As AL 46541 co . ar . 5. 3321556 To Radius   10. 0000000 So is XL 1749 3. 2429402 To the sine of LAX 2. 15437 8. 5750958 As Radius   10. 0000000 To AL 46541 4. 6678444 So cosine of LAX 2. 15437 9. 9996929 To AX 46509 4. 6675373 To finde the second inequality of Mercury . We must have given , 1. The Angle NAS which is to be found by subductiug the Suns place , from the eccentrick place of Mercury reduced , or this from it , so that less then 6 signes may remain , this remainer is the Anomaly of the orbe , and the complement thereof is the Angle NAS , or the halfe , is the halfe sum of the opposite angles . Example . The eccentrick of Mercury reduced 220. 26940 The Suns true place 154. 07347 Anomaly of the orbe 96. 19593 Complement is NAS 83. 80407 Halfe Anomaly 48. 09796 These given with the sides NA and SA . the Analogies are As the greater side SA 100895 co . ar . 4. 9961293 Is to Radius   10. 0000000 So is the lesser side NA 46509 4. 6675373 To the tangent of 24. 74799 9. 6636666 Adde 45.   As Radius     To the cotang . of 69. 74799 9. 5669785 So tang . halfe summe 48. 09796 10. 0470559 To tang . halfe difference 22. 35160 9. 6140344 Summe 70. 44956 Angle ANS   Difference 25. 74636 Angle ASN   Because the Suns place was subtracted from the eccentrick of Mercury reduced , therefore the angle of Elongation ASN must be added to the Suns place . 154. 07347 Elongation ASN adde 25. 74636 True place of Mercury 179. 81983 To finde the distance of Mercury from the Earth . As the sine of ANS 70. 44956 co . ar . 0. 0257891 To the side AS 100895 5. 0038707 So the sine of NAS 83. 80407 9. 9974556 To the side SN 106442 5. 0271154 To finde the Latitude of Mercury from the Earth . As the side SX 106442 co . ar . 4. 9728846 Is to Radius   10. 0000000 So is XL 1749 3. 2429402 To the tang . of XSL 0. 94169 8. 2158248 Which is the south Latitude of Mercury .     CHAP. 18. Of the Semidiameters of the Sun , Moon , and shadow of the Earth . THe angle of the Suns apparent Semidiameter , in his nearest distance to the Earth , Bullialdus hath by observation found to be 16′ 45″ , or in Decimall numbers 27917. And by an Eclipse of the Moon , December 1638 , he found her Semidiameter to be 16′ 54″ or 28167 , and the Semidiameter of the Earth ; shadow 44′ 9″ , or 7 583 , at which time ( being the time of incidence ) her distance from the Earth by his computation was 97908 parts of the Semiaxis of the Elipsis 100. 000. By this and another observation in the same Eclipse , he sheweth how to finde her apparent semidiameter , in all the other intervalls . The inferiour limbe of the Moon and the first Starre in the foot of the former Twin , ( whose place then according to Tycho was Gemini 28. 25′ 17″ , or Gemini 28. 42138 with South Latitude , 0 d. 58′ or 0. 96667. ) being in the same Azimuth , was 8′ or 13333 higher then the Star and the Altitude of the heart of Hydra then taken by him at Paris was 30 deg . 37′ , or 30 d. 61667. From whence the hour was found , 30 h. 40′ , or 13 h. 66667 and the houre being given the altitude of the Starre is also given , deg . 56. 42′ 15″ , or deg . 56. 70416. The apparent altitude of the center of the Moone was deg . 57 7′ 9″ , or deg . 57 11916 , but by her latitude and place it should have beene deg . 57 40′ 4″ , or deg . 57 66778 and therefore her parallax of altitude 32′ 55″ , or 54861. The situation of the Moone and Azimuth in which her interiour limbe and the Stars were , being given , her aparent Longitude was almost in Gemini , deg . 28 38′ 30″ , or Gemini deg . 28 64167 , her parallax of longitude 18 min. or 30000 and therefore the center of the Moon in her true motion in Gemini 28 d. 57 min. fere . or in Gemini 28 d. 95000 , her parallax of Latitude is 19 min. or 31667. to which 21′ or 35007 , the difference of the observed latitude of the Moon and Stars , being added the true difference is 50 min. or 83333 min. and thence the Moons Latitude 8 min. or 13333 S. Now then to finde the distance of the Moon from the Earth , in this Eclipse , the Earths semidiameter being one degree , Let FEC represent the true Horizon , BDE , the vertical at Paris E the center of the earth , D the City of Paris : the Moons true altitude , AEF , deg . 5766778 , the observed altitude ADG , deg . 5711916. The parallacticall angle DAE , deg . 0. 34861. Therefore in the Triangle ADE we have given all the angles , and the finde DE one Semidiameter of the Earth , to finde AE , for which the anolagy is . As the sine of DAE 0 d. 54861 co . ar . 2. 0188745 To the side DE 1   0. 0000000 So is the sine of ADB 32 d. 88084 9. 7347147 To the side AE 56. 70 1. 7535892 This foundation being laid , he proceedeth to the rest : and to shew how we may possibly fall into some absurditie , he supposeth the Moons distance from the Earth in this Ecclipse to be but 55 semidiameters , or the side BC in the following figure , the apparent angle of the semidiameter of the Earths shadow CHI , 0. 73583 AEF represents the Sun , his semidiameter AE , the angle of his apparent Semidiameter when he is Perig. AGE 16. 45 , or in decimalls 27916 BHG represents the Earth . BG the Semidiameter thereof , hence to finde HI in the triangle HIC the proportion is . As the sine of HIC 89. 26417 co . ar . 0. 0000358 To the side HC 54 1. 7323937 So is the Radius HCI 90 10. 0000000 To the Hypothenusal HI 54. 004 1. 7324295 2. In the triangle HBI we have given the sides BH . 1. and HI 54. 004 with the angle BHI 179. 26417 , hence to finde the Angle BHI , the Analogie is . As the greater side H I 54. 004 co . ar . 8. 2675705 Is to the less H B 1. 0. 0000000 So is Radius   10. 0000000 To the tangent of 1. 06082 8. 2675705 Adde 45.   As Radius   10. 0000000 To the Cotang . of 46. 06082 9. 9839145 So Tang. halfe summe 36791 7. 8075980 To tang . halfe differ . 35454 7. 7915125 Angle B I H 01337. And the angle C B I 72246 3. In the triangle C B I , we have given the angles and the side B C 55 to find C I. Therefore say , As Radius To the tangent of C B I 72246 8. 1007064 So is B C 55 1. 7403627 To C I 0. 6935 = to B K 1. 8410691 and therefore K G 3065 , and the angle K I G 0. 31857. For , ●● I K 55 co . ar . 8. 2596373 To Radius   10. 0000000 So is K G 0. 3065 1. 4864305 To the tangent of K I G 0. 31857 7. 7450678 and the angle B D G is equal thereunto , but so the angle of the Suns appar●n● Semidiameter A G E 27916 by observation , is lesse then the angle A D E , which is absurd , and therefore some part assumed is false . The Semidiameters of the Sun and Moon must not be changed , constant experience agreeing with these observations . In this Eclipse therefore Bullialdus doth take for the distance of the Moone from the earth , B C 57. 85 Semidiameters of the earth , and the Semidiameter of the earths shadow , C B I 75111. Hence to find C I , the analogie is . As Radius To the side B C 57. 85 1. 7623034 So the tang . of B C 0. 75111 8. 1176019 To C. I. 0. 75841 1. 8799053 Let B K be equal to C. I. So is K G 24159. The● As I K 57. 85 co . ar . 8. 2376066 To Radius   10. 0000000 So is K G 24159 1. 3830789 To the tang . of K I G. 23928 or B D G 7. 6207755 equal to E D A , and the Suns apparent Semidiameter being given A G E , 27916 , the angle G A B , or the difference between the angles A G E , and E D A shall be given also , viz. 03988. the Suns Horizontal parallax when he is Perigaeon . And the Moones Perigaeon distance from the earth , in Syzigiis , 56. 50 Semidiameters of the earth . For , as 97908 co . ar . 5. 0091819 To 57. 85 1. 7623034 So is 95638 4. 9806304 To B C 56. 50 1. 7521157 Hence to find the Moones Horizontal parallax when she is perigaeon , the analogie is , in the preceding Diagram . As E G or B C 56. 50 co , ar . 8. 2478843 Is to Radius : So is D E 1. 0. 0000000 To the sine of E G D 1. 01399 8. 2478843 The Horizontal parallax of the Sun when he is perigaeon or the angle B A G was found to be . 03988 The Moones Horizontal parallax is 1. 01399 Their aggregate 2. 05387 Semidiameter of the Sun subtract . 27916 There rests the angle C B I . 77471 or the apparent semidiameter of the earths shadow in loco transitus Lun● , Perig. In the triangle therefore B C I , we having the angles and the side B C given , C I shall be also given . For , As the sine of 90 deg .   Is the side B C 56. 50 1. 7521157 So tang . of C B I 77472 8. 1310339 To the side C I 7640 = B K 1. 8831496 And therefore K G ●360   And in the triangle A G B having the angles and B G given the side A B is also given , for As the tang . of B A G 03988 co . ar . 3. 1585620 Is to B G 1. So is Radius   10. 0000000 To A B 1440. 66 3. 1585520 which is the distance of the Earth from the Sun , when he is Perihelion . And because the Suns eccentricity is 1784 , his Apogaean distance is 101784 , hence to find his distance , in Semidiameters of the earth , say , As his Perigaean distance 98216 co . ar . 5. 0078178 Is to his distance 1440. 66 3. 1585620 So is his Apog . distance 101784 5. 0076794 To his Apog . dist . 1493. 03 3. 1740692 Then as B S 1493. 03. or E G 6. 8259308 To Radius , so is E D. 1 10. 0000000 To the sine of E G D 0. 3855 6. 8259308 The Suns Horizontal parallax when he is Apogaeon . As Radius , to A B : 1440. 66 3. 1585620 So is tang . of A B E 27916 7. 6877120 To A E 70189 0. 8462740 Then as B S 1493. 03 co . ar . 6. 8259308 To Radius , so is S T 70189 ▪ ☉ Semid . 0. 8462740 To the tang . of S B T 26936 7. 6722048 The apparent Semidiameter of the Sun when he is Apogaeon . The Sun being Perigaean , we have given B G 1. K B. 75841. KG . 24159 and B C. 56. 50 , the distance of the Moon from the Earth when she is Perigaean ; from whence the longitude of the earths shadow may thus be found . As K G 2360 co . ar . 10. 6270880 To K I 56. 50 1. 7521157 So is C I 7640 1. 8831496 To C D 182. 93 2. 2623533 Add B C 56. 50 then is B D 239. 43. the longitude of the earths shadow . Let B S be the Apogaean distance of the Sun , 1493. 03 The angle of the Suns apparent Semidiameter S G T 26936 The Perigaean Semidiameter or the angle A G E 27916 Their difference is the angle Z G E 00980 Let TG be produced to N , then shall the angle I G N be equal to the angle Z G E , but the Sun being Perigaean , the angle B D G was found to be o. degrees 239●8 . whose complement is the angle B G D 89. 76072 therefore when the Sun is Apogaean , it shall be 89 ▪ 77052 , therefore B X G 0. 22948 , equal to K N G. Hence to find K G the analogie is . As Radius 90 10. 0000000 To K I 56. 50 1. 7521157 So tang . of K I G 0. 22948 7. 6006035 To K G 22632 1. 3547192 And K B 77368. Then to find C B N. Say.   As B C 56. 50 co . ar . 8. 247●843 To Radius 90 10. 0000000 So C I or rather C N. 77368 1. 8885613 To the tang . of C B N 7844● 8. 1364456 The Sun being Apogaean ; and the angle C B I , the Sun being Paerigaean , was before found to be 77471 , and therefore the difference of the earths shadow between the Suns Apogaean and Perigaean is , 00971. Then , As K G 22632 co . ar . 10. 6452808 To K I 56. 50 1. 7521157 So is C N 77368 1. 8885613 To C X 19● . 18 2. 2859578 Add B C 56. 50. Then is B X 249. 68. The semidiameter of the Moon , when she is Perigaean , is greater then the semidiameter of the Sun , being Apogaean , and therefore Bullialdus doth make it 17. or 28333 , and because the eccentricity of the Moon is given 4362 , her Apogaean distance in Syzygiis 104362 , the Moon being Perigaean her distance from the earth is , 95638 , and in semidiameters of the earth 56. 50 and therefore her Apogaean distance in semidiameters of the earth , by the analogy following , As 95638 co . ar . 5. 0193696 To 56. 50 1. 7521157 So is 104362 5. 0185423 To 61. 66 1. 7900276 As her Apogaean dist . 61. 66 Co. ar . 8. 2099724 To the Moons Perig. semid . 28333 1. 4522925 So is the Moon Perig. dist . 56. 50 1. 7521157 To the Apog . semid . 25964 1. 4143806 We have the semidiameter of the Cone C I 76400 , and her Perigaean distance 56. 50 , and D C 182. 93 , but when the Moon is Apogaean , D C will be no more then 177. 77. found by abating K I or K N 61. 66. from B D 239. 43. Hence to find C I or C N in the same parts say . As D C 182. 93 co . ar . 7. 7376467 To C I 7640 1. 8831496 So is C D 177. 77 2. 2498584 To C I 7424 1. 8706547 Then as B C 61. 66 co . ar . 8. 2099724 Is to Radius 90 10. 0000000 So is C I 7424 1. 8706547 To the tang . of C B I . 68981 8. 0806271 Here then we have determined     Apogaeon 26936 The Suns Semidiameter       Perigaeon 27916   Apogaeon 1493. 03 His distance from the earth       Perigaeon 1440. 66   Apogaeon ☉ 249. 68 The Axis of the earths shadow       Perigaeon ☉ 239. 43 The Semidiameter of the shadow , when the Sun is Apogaeon . In loco ●ransitus Lunae , Apog 78442 Perig. 77471.   Apogaeon 25964 The Semidiater of the Moone in Syzygiis       Perigaeon 28333   Apog . 61. 66 The distance of the Moon from the earth in Syzygiis       Perig. 56. 50   Perig. 23928. Semiangle of the Cone       Apog . 22948. CHAP. 19. Of the Proportion and Magnitude of the three great b●dies , the Sun , Moon and the Earth . THat it is a hard matter exactly to determine the true Magnitude of the coelestial bodies , is not I beleeve denied by any , it will be therefore sufficient if we shall determine them so , as that there be no sensible errour in them ; and to such exactnesse , we may traine by the rules and proportions following . As the Semidiameter of the Earths shadow C B I. Is to the Semidiameter of the shadow in parts of the Earths Semidiameter C I = B K : So is the apparent Semidiameter of the Moon . To the Semidiameter of the Moone in parts of the Ear●hs Semidiameter , that is As C B I 77471 co . ar . 10. 1108609 To C I 7640 1. 8831496 So is the Moones semid . 28333 1. 4522925 To the Moones semid . 27945 1. 4463030 And Sphears being in triplicated proportion of their diameters , the proportion of the earth to the Moone will be as 1. 00000. 00000. 00000. the Cube of the earths Semidiameter to 02182. 28939. 33625. the Cube of the Moones semid . 27945. and therefore dividing the earths Semidiameter by the Moons , the quotient will be 45. 823 , and so many times is the body of the Moon contained in the Earth . The proportion between the Semidiameter of the Earth and the Semidiameter of the Sun , may be found by this analogy , As Radius 90   To A B 1440. 66 3. 1585614 So is tang . A B E 27916 7. 687706● To A E 7. 0189 0. 8462683 But if to A B 1440. 66   You adde B D 239. 43   Their summe is A D 1680. 09   And then , As Radius 90   To the side A D 1680. 09 3. 2255415 So is tang . of A D E or K I G 23928 7. 6207755 To A E 7. 0197 0. 8463170 And now if you take the lesser semidiameter of the Sun , the Cube thereof will be ●45 . 781 , but taking the Semidiameter of the Sun to be but 7 semidiameters of the earth , the Sun will be 343 times bigger then the Earth . The proportion of the Semidiameter of the earth and the Moone is as 1 to 27945 , of the Sun and the Earth as 7 to 1 , and therefore of the Sun and the Moon as 7 to 27945. The Cube of 7 is 343 , the Cube of 27945 is 02182 , &c , by which dividing the Cube of the Suns semidiameter the quotient will be 15717. 47 and so many times is the Moone contained in the Sun. CHAP. 20. Of the proportion between the Orbs of the superiour and inferiour Planets , and the Orb of the Earth . WHat proportion the Orbs of these Planets have to the earths Orb , we have set down in those Chapters , in which we have shewed the manner of computing their places , and by what meanes the truth of those proportions may appeare , we shall set downe in this , and because we have used those proportions which Bullialdus hath with great diligence computed ; we shall exhibit here an Example in Saturne according to which method the proportions between the orbe of the earth and the orbes of the other planets are also to be found . And Saturns proportion to the earths orbe , as Bullialdus hath determined it , and which we have used , Chap. 13. is as 100. 000 to 10480. The observation from whence this proportion is gathered was made Anno Christi 1587. January the 9th . Hour 9th . 75 parts , at which time Saturn was observed to be in Aries 26 , 13333. with South latitude , deg . 2. 46667. The Suns true place then was in ♉ deg . 29 , 41778. and his distance from the earth , 98374. Saturns true place from the Sun by calculation was in ♉ deg . 2 , 31416. whose difference from his observed place , deg . 6 , 18083. is the parallax of the orbe or the angle A N S , and the angle N A S , 87. ●0362 , is found by deducting Saturns place from the place of the Sun , which with his distance from the Sun or side A N 95596 being given , the side A S will be found to be 10310. Now as the Suns distance from the earth , 98374 Is to the distance , 10310 So is the Semidiameter of ♄ orbe , 100. 000 To the Semidiameter of the earths orbe , 10480 By a second Observation made Anno Christi 1590 , February 8 , about 8 of the clock in the evening ; Saturn was in Gemini , deg . 7. 53333. with South latitude , deg . 1. 50. The true place of the Sun at the same time was in Pisces , deg . 0. 02805. and his distance from the earth , 98953. And Saturns place from the Sun by calculation was in Gemini , deg . 13. 82167. from which deducting his place taken by observation , their difference , 6. 28834 is the parallax of his orbe , represented by the angle A I S. And subtracting Saturns place 73. 82167 from the Suns place 330. 02805 their differences 256. 20638 reject a semicircle is the angle , I A S 76. 20638 and Saturns distance from the Sun represented by A I 94338 and hence the side A S 10423. And now as the Suns distance from the earth 9893 Is to the distance A G 10423. So is the Semidiameter of Saturns orbe 100. 000 To the Semidiameter of the earths orbe 10533 By a third observation made in the same year of Christ 1590 Septemb. 7 at midnight , Saturns place was in Gemini deg . 28. 1 with South latitude deg . 1. 18333. The Suns true place at the same time was in Virgo deg 24. 49833. And his distance from the earth 100300. Saturnes place from the Suns by calculation , was in Gemini deg . 21. 76722 , which being deducted from his place taken by observation , their difference is the parallax of his o●●e , or the angle A K L 6. 33278 , and deducting Saturns place from the place of the Sun the angle A L K is 9● . 73111 , and therefore the side A L 10415. Now as the Suns distance from the earth 100300 Is to the distance A L 10415 So is the Semidiameter of Saturns Orbe 100000 To the Semidiameter of the earths orbe 10383 But Bullialdus whom we follow doth retaine the first of these 10480 as being the meane , and most agreeable to Tycho's observation ; And from these three observations the inclination of Saturns orbe may thus be found . The Triangles L D. N. I D O , and D G M of the following Diagram , have their sides and angles equal with the triangles , N A S. I A S and L A K in the Diagram preceding , being drawne from the same observations ; in every of which we are to compute ♄ distance from the earth ; for which in the triangle L D N by the first of these observations we have given the angle L N D 86. 71556. The angle L D N 87. 10362 and ♄ distance from the Sun L D 95596 to find L N. As the sine of L N D 86. 71556 co . ar . 0. 0007130 Is to the side D L 95596 4. 9804397 So the sine of L D N 87. 10362 9. 9994447 To the side L N 95630 4. 9805974 Then in the right angled triangle L K N right angled at K , we have given the angle of South latitude L N K 2. 46667 , and the side L N 95630 , to find L K. As Radius   10. 0000000 Is to L N 95630 4. 9805974 So is the sine of L N K 2. 46667 8. 6338534 To the side L K 4116 3. 6144508 Hence to find the angle of Latitude at the Sun say , As the side L D 95596 co . ar . 5. 0195603 Is to Radius   10. 0000000 So is the side L K ●116 3. 6144508 To the Sine of L D K 2. 46756 8. 6340111 By the second observation in the triangle I D O we have given the angle I O D 97. 50528 whose complement is 82. 49472 the angle I D O 76. 20638 , and ♄ distance from the Sun I D , to find his distance from the earth I O. As the sine of I O D 82. 49472 co . ar . ● . 00373●● Is to the side I D 94338 4. 974686● So is the sine of I D O 76. 20638 9. 9872910 To the side I O 92409 4. 9657145 Then in the right angled Triangle H I O right angled at H , we have given the angle of Saturns South latitude H O I 1. 50 , and the side I O to find H I. By the third observation in the triangle GMD we have given the angle M D G 87. 26889 the angle M G D 86. 39833 the side G D 94239 to find M G. As the sine of G M D 86. 39833 co . ar . 0. 0008588 To the sine of M D G 87. 26889 9. 9995064 So is the side G D 94239 4. 9742306 To the side M G 94318 4. 9745958 Then in the right angled triangle G M F right angled at F we have given the angle of Saturns South latitude G M F 1. 18333 , and the side G M to find G F. As Radius   10. 0000000 Is to the side M G 94318 4. 9745958 So is the sine of G M F 1. 18333 8. 3149535 To the side G F 1948 3. 2895493 Hence to find the angle of latitude at the Sun , As the side D G 94239 co . ar . 5. 0257694 Is to Radius   10. 0000000 So is the side G F 1948 3. 2895493 To the sine of G D F 1. 18434 8. 3153187 These things premised the places of the Nodes and the angle of inclination of the planes may thus be found . In the following Diagram let the place of the first observation be at A , and the angle of latitude at the Sun D G 2. 46756. The second at B , and the latitude G E 1. 4693● . The third at C , and the latitude G F 1. 18434. The Arches of apparent motion from the First observation to the second A B 41. 50751 Second to the the third B C 7. 94555 First to the third A C 49. 45306 The halfe of these arches are the measure of the angle B A C 3. 97277 whose sines are the sides A B 35435 of the angle B C A 20. 75375 whose sines are the sides B C 6929     whose sines are the sides A C 41828 The angles of Latitude at the Sun found are L D K 2. 46756 whose sines are the sides G D 4306 I D K 1. 46932 whose sines are the sides G E 2617 G D F 1. 18434 whose sines are the sides G F 2064 The difference between G E and G F is F E 553 The difference between G D and G F is F D 2242 The difference between G E and G D is E D 1689 Hence to find the side A L in the triangle A B L use this analogie As F D 2242 co ar . 6. 6493644 Is to C A 41828 4. 621467● So is E D 1689 3. 2276296 To A L 31511 4. 4984611 Then to find the angle A B L We have given the side A B 35435 and B A L 3. 97277 We have given the side A L 31511 and B A L 3. 97277 whose complement is 176. 02723 , and the halfe thereof 88. 01361 is the halfe summe of the opposite angles . As the summe of A B and A L 66946 co . ar . 5. 1742754 Is to their difference 3924 3. 3937289 So the tang . halfe summe 88. 01361 11. 4598852 To the tang . halfe differ . 59. 38668 10. 22889● The summe 147. 40029 is the angle A L B   The difference 28. 62693 is the angle A B L   whose double 57. 25386 is the arch A M , ●o which if you adde the arch A B 41. 50751 their summe is the Arch B A M 98. 76137 , whose complement to 180 gives the arch B H and M I 81. 23863 , and the halfe thereof is the arch B H 40. 61931. Now then the point B is in 73. 82167 To which if you adde B H 40. 61931 The Node ascending is 114. 44098 And deducting B C from B H 40. 61931 whos 's natural sines are G E 65098 Their difference is C H 32. 67376 whos 's natural sines are G F 53980 The summe of H B and B A is H A 82. 12682 whos 's natural sines are G D 99057 To find the angle of Inclination by the first observation , say As G D 99057 co . ar . 5. 0041149 To G D 4306 3. 6340740 So is G K Radius   10. 0000000 To G K the sine of deg . 2. 48908 8. 6381889 To find the angle of Inclination by the second observation , say As G E 65098 co . ar . 5. 1864324 To G E 2617 3. 4178037 So G K Radius   10. 0000000 To G K the sine of D. 2. 30397 8. 6042361 To find the angle of Inclination by the third observation , say As G F 53980 co . ar . 5. 2677672 To G F 2064 3. 3147096 So is G K 100. 000 or Radius 10. 0000000 To G K the sine of deg . 2. 19128 8. 5824768 But by reason of this varietie , we may well suspect the truth of one or other , of the observations given ; and therefore Bullialdus hath a●●igned another place for the point of the Node ascending ; viz. deg . 110. 42333 and the angle of Inclination somewhat more then that found by the first observation . viz. deg . 1. 50 that so he might make these observations to agree as neere as might be . And now if you suppose the Node ascending to be 110. 42333 And from thence deduct the place of the 2d . observation 73. 82167 Their difference shall be the arch H B 36. 60166 and the sine thereof is G E 59624. Againe deducting B C 7. 94555 from B H , their difference will give C H 28. 65611 , and the sine thereof G F 47954. And by adding A B 41. 50751 to H B their summe shall be H A 78. 10917 and the sine thereof G D 97854. For the latitude agreeing to the first observation As G K 100. 000 5. 0000000 Is to G K deg . 2. 50 8. 6396795 So is G D 9. 7854 4. 9905785 To G D or the latitude 2. 44632 8. 6302580 whereas it should have been 2. 46667. For the latitude agreeing to the second observation As G K 100. 000 5. 0000000 Is to K G deg . 2. 50 8. 6396795 So is G E 59624 4. 7754210 To G E or the latitude 1. 49029 8. 4151005 whereas it should have been 1. 56667. For the latitude agreeing to the third observation As G K 100. 000 5. 0000000 Is to G K or the angle of inclin . 2. 50 8. 6396795 So is G F 47954 4. 6808248 To G F or the sine of latit . 1. 19856 8. 3205043 whereas it should have been but 1. 19 CHAP. 21. To find the mean Conjunction and Opposition of the Sun and Moon . FOr this purpose the Table which Shakerley transcribed from Bullialdus , we have here exhibited in Decimall numbers , the use whereof , as he hath explaind the same is this : Set down first the Epoch● next preceding the yeare given , then the yeares and moneths compleate having a care of the yeare Bisse●tile , and to every one set downe the time answering in the Table ; then adde them altogether , and the summe subtract from the next greater in the Canonian , under the title● , if you ●ee● a Conjunction , or ☌ , if an opposition , the remainer sheweth the time required compleat from the beginning of the moneth current . Example . I would know the time of the meane opposition of the Sun and Moon in March , 1652. The worke is this .   Hou . Parts The Epocha 1640 701. 96639 Yeares compleat 11 20. 14722 February compleat Bissextile 022. 53539 The summe subtract 744. 64500 From the Opposition next greater 1063. 10139 Rests the meane opposition 318. 45639 that is 13 dayes 6 houres and 45639 parts . CHAP. 22. To find the true Opposition or Conjunction of the Sun and Moon . FOr the time of the meane Conjunction or Opposition given , find the true place of the Sun , and the eccentrick place of the Moon , and compare them ; if they either be precisely the same or precisely opposite , the time of the true Conjunction or Opposition agrees with the meane ; but if they differ take the difference , by subtracting the lesse from the greater , and that call the distance of the Sun and Moon . 2 Out of the Table of Semidiameters , and hourly motions ; with the meane Anomalies of the Sun and Moon , take out their hourly motions , and subtract the hourly motion of the Sun , from the hourly motion of the Moon , by the remainer ( which is the hourly motion of the Moon from the Sun ) divide the distance of the Sun and Moone before kept , the quotient gives the time , which must be added to the mean time of Conjunction or Opposition , if the excesse be in the Suns place , or subtracted , if in the Moones place . 3 At this time thus corrected , find againe the true place of the Sun and ●●centrick place of the Moon , together with their distance , and repeat your former work , till you find them absolutely to concurre , and the time thus found shall be the true time of Conjunction or Opposition . As in the Example ,   D. Hou . parts At the time of the meane ☍ March 13 6. 45639 The true place of the Sun is   4. 85039 The Eccentrick place of the Moone   180. 38631 The Distance of the Sun from ☍ Moon   4. 46408 Mean Anomaly of the Sun   266. 40860 His hourly motion   . 04112 Meane Anomaly of the Moone   30. 26681 Her hourly motion   . 51827 Hourly motion of the Moone from the Sun   . 47715 By which dividing the distance   4. 46408 The quotient gives Hours 9. 3558 to be added .     So the time first corrected March 13 15. 81279 The true place of the Sun is   5. 23520 The eccentrick place of the Moone   1●5 . 15798 The distance of the Sun from ☍ of the Moon   . 07722 Which divided by the hourly motion of the Moon from the Sun   . 48114 Gives in time to be added   . 16049 So the time secondly corrected 13 15. 97328 The true place of the Sun is   5. 24180 The eccentrick place of the Moon   185. ●4010 The distance of the Sun from ☍ the Moon   . 00170 Which divided by the hourly motion of the Moon from the Sun   . 48121 Gives in time to be added   . 00353 So the true time 13 15. 97681 The true place of the Sun is   5. 24194 The eccentrick place of the Moon   185. 24190 4 For this time find out the true motion of the Moons Latitude , and thereby the Reduction , which divide by the hourly motion of the Moon from the Sun , and the quotient contrary to the title of Reduction , apply to the last corrected ; so have you the true time . In our Example . The true motion of Latitude   174. 04881 The Reduction Adde   . 02398 The quotient Subt.   . 04983 So the true opposition 13 15. 92698 5 Lastly , apply the equation of time to this equal time to make it apparent . The true time of the ☍ 13 15. 92698 The equation of time Subt.   . 02884 The apparent time of the ☍ ▪ 13 15. 89814 CHAP. 23. To find whether there will be an Eclipse or not . THere are two wayes to know this , of which the one is more easie , the other more certain , The first is this ; At the true conjunction , if the true motion of latitude be within 17 degrees backward or forward of 6 or 12 signes , or at the opposition within 12 degrees , there is a possibility of an Ecclipse , otherwise not . In our Example the Moons true motion of latitude is 174 deg . 04881 , which being not fully 6 degrees distant from 6 signes , shewes the necessity of an Eclipse . The other way is this . If at the visible conjunction the visible latitude of the Moon be lesse then the aggregate of the Semidiameters of the Sun and Moon , there must be an eclipse or else not . 2. If at the true opposition the true latitude of the Moon , be lesse then the summe of the Semidiameters of the Moon and the earths shadow , there must be an Eclipse otherwise not . This latter way is most certain , onely subject to this inconvenience , that a great part of the calculation is performed before we come to the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , or power to judge of the possibility . CHAP. 24. To find the Quantity of a Lunar Ecclipse . BY the true motion of the Moons Latitude , find her true latitude , according to the former directions : this in our example is 0. 51496 North Descendant . 2 Find out the Semidiameter of the Moon by her meane anomaly out of the Table , as also h●● Horizontall parallax ; and with the meane anomaly of the Sun , take out the Semiangle of the Cone of the shadow ; and this subtract from the Moons Horizontall parallax , there rests the Semid . of shaddow . 3 Adde together the Semidiameter of the shadow , and Semidiameter of the Moon , and from the summe subtract the Latitude of the Moon , the remainder is the scruples of the Moons diameter ecclipsed . Example . Horizontall parallax of the Moon . 94409 Semiangle of the Cone Subt. . 23455 Semidiameter of the shaddow . 70954 Semidia meter of the Moon . 26431 Summe of the Semidiameters . 97385 Latitud● of the Moon , Subt. . 51496 Scruples deficient . 45889 4 Convert these Scruples into digits or parts , whereof the Moones body containes 12 , thus , As the Moones diameter 52862 co . ar . 5. 276857 Is to the Scruples deficient 45889 4. 661708 So is 12 digits 1. 079181 To the digits ecclipsed 10. 417 1. 017746 Yet note that Lunar Eclipses are of three sorts . 1 Partiall , when the Scruples deficient are lesse then the diameter . 2 Totall without continuance when they are equall . 3 Totall with continuance when the scruples deficient are greater then the diameter , and in these the digits eclipsed are more then 12 , which are so to be understood , as that they shew how far the ecclipse is over the body of the Moon . CHAP. 25. To find the duration of a Lunar Ecclipse , or the continuance of the totall darknesse , where the Ecclipse is totall . FInd the scruples of Incidence thus : Take the Logarithmes of the summe and difference , of the Moones latitude and the summ of the Semidiameters of the Moon , and the shadow , halfe the summe of the two Logarithmes shall be the Logarithme of the Scruples of incidence required . Example . Summe of the Semidiameters 97385   Latitude of the Moone 51496   Their summe 1. 48881 5. 172836 Their difference . 45889 4. 661308 Summe of the Logarithmes   9. 834544 Scruples of incidence 82656   4. 917272 2 Divide the Scruples of incidence by the hourly motion of the Moon from the Sun , the quotient gives the time of incidence or halfe duration of the Eclipse . This subtracted from the true time of the opposition ▪ gives the beginning of the Eclipse ; or added to it gives the ending . Example . The Scruples of incidence 82656 4. 917272 Divided by the hourly motion of the Moon from the Sun 48121 4. 682326 Time of incidence , hours 1. 7177 0. 234946 The true time of the opposition 13 d. 15. 89814 Time of incidence subt . 1. 71770 The beginning of the Eclipse 14. 18044 Time of incidence added , gives the end 17. 61584 The whole duration 3. 43540 3 If the Eclipse be total and you desire to know the continuance of total darkenesse , take the difference of the Semidiameters instead of the sum , and thereby worke as you are directed in the first example of this Chapter , and you have the halfe tarrience in the shadow , whose double is the thing sought . CHAP. 26. To find the Moons Latitude at the beginning and end of the Eclipse . MUltiply the Suns hourly motion , by the time of incidence , the product being added to the scruples of incidence , gives you the motion of the Moone agreeing to the time of incidence . 2 From the true motion of latitude at the true opposition subtract , this motion of the Moon ; there rests the true motion of latitude at the beginning of the Eclipse ; or if you adde it you have the motion of latitude at the ending , with which out of the Table of latitude you may find out the latitude , answering to the beginning and end , as in our Example . The time of incidence 1. 7177 The Suns hourly motion . 0411 Their product is . 07059 The scruples of incidence . 82656 The summe . 89715 Motion of Latitude at true ☍ 1●4 . 04882 Motion of Latitude at beginning 173. 15166 Latitude at beginning North Desc. . 59223 Motion of Latitude at ending 174. 94596 Latitude at ending North Desc. . 43746 CHAP 27. To find the middle of the Eclipse or greatest darkenesse . THe time of the true Conjunction or Opposition the most received , is when the Sun and Moon are in one line perpendicular to the Ecliptique , to find this with the Moons true Latitude at the true opposition , enter the little Table of the difference of the true Conjunction or opposition from the greatest obscuration , and you shall find the difference with the title , which divide by the hourly motion of the Moon from the Sun , and the quotient according to the title , apply to the time of the true opposition ; so have you the time of the greatest darkenesse , or middle obscuration . Example . The Moons Latitude , North Descend .   . 51496 The difference adde   . 04489 Which divide by the hourly motion of the Moon   . 48121 Gives the difference in time to be added   . 09328 To the true opposition March 13. 15   . 89814 So the middle of the Eclipse 13. 15h. 99142 The Calculation of the forementioned Ecclipse according to the preceding directions .   d. ho. Meane opposition March 13 6. 45639 Interval Adde   9. 35580 True opposition 13. 15. 97681 True place of Sun   5. 24194 Eccentrick place of the Moone   185. 24190 Meane Anomaly of the Sun   266. 79954 Meane Anomaly of the Moone   35. 44378 True motion of Latitude   174. 04881 True Latitude North descend .   . 51496 Reduction Adde   . 02398 Hourly motion of the Sun   . 04111 Hourly motion of the Moon   0. 52232 Hourly motion of the Moon from the Sun   . 48121 Reduction in time Subt.   . 04983 True opposition corrected 13 15. 92698 Equation of time Subt.   . 02884 T●uest opposition 13. 15. 89814 Horizontall Parallax of the Moone   . 94409 Semiangle of the Cone   . 23455 Semidiameter of the shadow   . 70954 Semidiameter of the Moone   . 26431 Sum of the Semidiameters   . 97385 Scruples deficient   . 45880 Digits eclipsed   10. 4197 Scruples of incidence   . 82656 Time of incidence   1. 71770 Beginning of the Eclipse 13 14. 18044 End of the Eclipse 13 17. 61584 The whole duration   3. 43540 Latitude of the Moone at the beginning North D.   . 59223 Latitude of the Moone at the ending North D.   . 43746 Difference from the middle , Added   . 09328 The middle of the Eclipse 13. 15 . 99142 CHAP. 28. Of the Calculation of the Suns Eclipse . THis Eclipse is not properly , the Eclipse of the Sun , but of the earth in regard it is not the Sun , but the earth which looseth light the Sun being only apparently darke , the earth in truth , we will how ever use the name , that others have given it , and shew you the manner of the Calculation . Find the meane conjnction , and from thence the true , which correct by the Reduction and Equation of time in all things as in the Moon . Example of a Solar Eclipse , which happened March 28. 1652.   D   Mean Conjunction March 28 0. 82333 Suns place   19. 36150 Eccentrick place of the Moon   20. 89832 Distance of the Moon from the Sun   1. 53682 Meane Anomaly of the Sun   280. 96132 His hourly motion   . 04090 Meane Anomaly of the Moon   223. 17513 Her hourly motion   . 60109 Hourly motion of the Moon from the Sun   . 56019 which dividing the distance   1. 53682 Gives in the quotient subt .   2. 74336 So the time first corrected ●7 22. 07997 True place of the Sun   19. 24962 The Eccentrick place of the Moon   19. 29533 The distance of the Sun from the Moon   . 04571 which divided by the hourly motion of the Moon from the Sun   . 56137 Gives in time subtract   . 08143 So the time secondly corrected 27 21. 99854 True place of the Sun   19. 24631 Eccentrick place of the Moon   19. 24766 Distance of the Sun from the Moone   . 00135 which divided by the hourly motion of the Moon from the Sun ▪   . 56140 Gives in time subtract   . 00240 So the true time of Conjunction 27 21. 99614 The true pl●ce of the Sun   19. 24621 Eccentrick place of the Moon   19. 24625 True motion of Latitude   8. 80745 The Reduction Subtract   0. 03536 The quotient   . 06298 So the true Conjunction . 27 22. 05912 Equation of time subtract   . 09970 The apparent time of the ☌ . 27 21. 95942 CHAP. 29. To find the Parallaxes of Longitude and Latitude . BY the rules delivered in the former part , find at the true Conjuction the Midheaven , with its altitude and the Meridian angle . Example . The Suns place ♈ 19. 246 The Suns Right Ascension 17. 749 Time in Degrees 329. 391 Right Ascension of Midheaven 347. 140 Midheaven ♓ 16. 022 Meridian angle 67 , 078 Declination of Midheaven 5. 533 Altitude of the Equator at London 38. 467 Altitude of Midheaven 32. 834 2 The angle of the Ecliptique and Horizon , or altitude of the Nonagesime degree , and his distance from the Midheaven is thus found , by the 17 Chapter of the first part . As the Radius To the sine of the Meridian angle 67. 07 9. 9642509 So is Cosine of the Altitude of M C 32. 83 9. 9244255 To the Cosine of the Angle , &c. 39. 30 9. 8886764 Then as Radius To the Cosine of the Meridian angle 67. 07 9. 5906259 So is cotang . of the altitude of the M. C. 32. 83 10. 1903074 To the tang . of the distance of the M. C. from the Nonagesime degree 16. 02 9. 7809333 This M C falling betweene Capricorn and Cancer this distance is to be added to the Midheaven   ♓ 16. 02 And the Nonagesime degree will be in   ♈ 17. 14 3 Find the Node Ascendent and Subtract it from the Nonagesime degree , with the remainder enter the Table of the Moones latitude , which if North adde to the angle of the Ecliptique and Horizon ; if South subtract it from it , so have you the altitude of the Nonagesime degree of the Moones orbe . Example . The Node Ascendent Subt. 10. 439 The Nonagesime degree 17. 140 There rests 6. 701 Which gives the Moones Latitude Adde . 570 The angle of the Ecliptick and Horizon 39. 300 Altitude of the Nonagesime degree of the Moones orbe 39. 870 4 Take the distance of the S●n from the Nonagesime degree , which in our Example of the true Conj●ction is ● d. 10. 5 Out of the table of Horizontall parallaxes , take the Horizontall Parallax of the Sun and Moon , the difference of them is the Horizantall parallax of the Moon from the Sun. Example . The Horizontall parallax of the Sun is . 03912 The Horizontall parallax of the Moon . 99396 Horizontall parallax of the Moon from the Sun . 95484 6 Adde the Logarithme of the Horizontall parallax of the Moon from the Sun , the sine of the Altitude of the Moones orbe , and the sine of the distance of the Sun from the Nonagesime , their summe subtracting twice Radius , is the Logarithme of the parallax of longitude . Example . Horizontall parallax of the Moon from the Sun 95484 1. 9799306 Altitude of Nonagesime in the Moones orbe , sine 39. 87 9. 8068904 Distance of the Sun from the Nonagesime , sine 2. 10 8. 5639994 Parallax of longitude 02243   2. 3508204 Here note that whensoever the Suns place is lesse then the Nonagesime degree , the Parallax of Longitude , makes the luminaries appeare more west than the truth , and in the occidentall Quadrant , when more then in the orientall . 7 Adde the Logarithme of the Horizontall parallax of the Moon from the Sun to the Cosine of the Nonagesime in the Moones orb ; the summe rejecting Radius is the Logarithme of the parallax of Latitude . Example . Horizontall parrallax of the Moon from the Sun 95484 1. 979930● Altitude of Nonag . in the Moones orb , Cos●ne 39. 87 9. 8850789 Parallax of latitude 0. 73284 1. 8650095 CHAP. 30. To find the visible motion of the Moon from the Sun for any time assigned . AT the beginning and end of the time proposed find the parallax of the Moone from the Sun in Longitude , and then observe these rules . 1 If during all the time proposed , the luminaries be in the orientall quadrant , and the parallax of longitude increase or be greater at the end of the time given then at the beginning , adde the differences of the two parallaxes of longitude unto the true motion of the Moone from the Sun agreeing to the time given , or if it decrease , subtract it and you have what you desire . 2 If during all the time the luminaries be in the occidentall quadrant , and the parallax of longitude increase , subtract the said difference from the true motion , if it decrease , adde it , and you have the visible motion . 3 If at the beginning of the time the luminaries be in the orientall quadrant , and at the ending in the occidentall , subtract the said difference from the true motion , and you have the visible motion during that time . Example . Let it be proposed to find the visi●le motion of the Moon from the Sun , for one halfe hour before the true Conjunction . In our Example , the true halfe hourly motion is . 28070 Parallax of Longitude at the beginning . 07628 Parallax of Longitude at the end . 02243 Their difference is Subtract . 05385 from the true halfe hourly motion Rests . 22658 the visible halfe hourly motion before the Conjunction . CHAP. 31. To finde the time of the visible Conjunction of the Sun and Moon . USe this Analogie , As the apparent motion in any time assigned ( found by the former Chapter ) is to the time assigned ; so is the parallax of longitude at the true Conjunction to the difference in time between the true and visible Conjunction . This difference in the orientall quadrant must be subtracted from the time of the true Conjunction , in the occidentall quadrant added thereto ; so have you the visible Conjunction . Example . As the visible halfe hourly motion 22685 co . ar . 0. 644262 Is to the time assigned 50′ 1. 698970 So parallax longitude 02243 2. 350829 To the difference betwixt the true and visible Conjunction 04943 2. 694061 The true Conjunction 27 21. 95942 Difference subtract . 04943 The visible Conjunction 27 21. 90999 At this time finde out the true distance of the Moon from the Sun , as also the parallax of longitude , if they agree it is a signe that the visible Conjunction is truly found , otherwise repeat the former worke till there be a concurrance . Example At the visible Conjunction , March 27 21. 90999 The true distance of the Moone from the Sun . 0●847 The Parallax of Longitude . 02775 Their difference . 00072 which being so small sheweth that the visible Conjunction is precisely enough found . CHAP. 32. To finde the visible Latitude of the Moon , at the time of the visible Conjunction . IN these Northerne regions which we inhabit , the parallax of latitude allwayes makes the Moon to appeare more South then indeed she is to find the visible latitude therefore observe these rules . 1 At the time of the visible conjunction find out the true latitude of the Moon thus . If the Eclipse happen in the orientall quadrant , adde the parallax of longitude to the motion of the Sun , agreeing to the difference between the true and visible Conjunction , and the summe subtract from the true motion of latitude at the time of the true Conjunction ; or if the Eclipse happen in the occidentall quadrant adde the said summ● thereto , and you have the true motion of latitude at the visible Conjunction , by which as formerly taught , finde out the true Latitude of the Moone . Example . Motion of the Sun agreeing to 04943 . 00202 Parallax of Longitude at visible ☌ . 02775 The Summ Sub● . . 02977 Motion of Latitude at true ☌ 8. 80745 Motion of Latitude at visible ☌ 8. 77768 True Latitude at visible ☌ North . 75808 At the same time find the parallax of latitude , and compare it with the true latitude . If the latitude be South , adde them together , the summe is the South visible latitude of the Moone , but if North , subtract the lesse from the greater ; there remaines the visible latitude of the Moon , which shall be North when the latitude is greater then the parallax , otherwise South . Example . The true latitude of the Moon , North 0. 75808 Parallax of Latitude 0. 73633 The visible latitude North . 02175 CHAP. 33. To find the quantity of a Solar Eclipse . THis differs very little from that in the 24 Chapter , for finding the quantity of a lunar Eclipse , for it with their meane Anomalie● you enter the Table , and thence take out the Semidiameter of the Sun and Moone , and adde them together ; and from the summe subduct the visible latitude of the Moone , at the visible Conjunction , there rests the Scruples of the Suns body deficient , which as in the Moon , so here in the Sun convert into digits . Example . Semidiameter of the Sun . 27386 Semidiameter of the Moon . 27815 Summe of the ●emidiameters . 55201 Visible latitude Subtracted . 02175 Scruples deficient . 53026 So the digits eclipsed 11. 61500 CHAP. 34. To find the beginning and ending of the Suns Eclipse . BY the visible latitude of the Moon , and the summe of the Semidiameters of the Sun and Moon , find the Scruples of incidence , as in the Moones Eclipse Chap. 25. 2 For one hour before the visible Conjunction , find by the 30 Chapter , the visible hourly motion of the Moon from the Sun , by which divide the Scruples of incidence , the quotient is the time of incidence , which subtracted from the time of the visible Conjunction , leaves the beginning of the Eclipse 3 For one hour after the visible Conjunction , finde the visible hourly motion of the Moon from the Sun , by which divide the Scruples of incidence , the quotient is the time of Repletion : which added to the time of the visible Conjunction , gives the end of the Eclipse . Example . Summe of the Semidiameters . 55201 Visible latitude . 02175 Scruples of Incidence . 55158 At 1 ho. before the visible ☌ March 27 20. 90999 Parallax of longitude Orient . . 13209 True hourly motion of the Moon from the Sun . 56140 Visible hourly motion . 45174 Time of incidence 1. 22150 Beginning of the Eclipse March 27 20. 68849 At 1 ho. after the visible ☌ 27 22. 90999 Parallax of longitude Occid . . 10119 Visible hourly motion of the Moone from the Sun 48796 Time of repletion 1 h. . 1303● End of the Eclipse 27 23. 04029 The whole duration 2. 35180 CHAP. 35. To find the Visible latitude of the , Moon at the beginning and end of the Suns Eclipse . FOr the beginning , adde to the minutes of Incidence the motion of the Sun agreeing to the time of Incidence , and the summe subtract from the true motion of latitude at the time of the visible Synod , so have you the true motion of latitude at the beginning , by which find the true latitude , and by these according to the second rule of the 32 Chapter , may be had the visible latitude . Example . The Scruples of incidence . 5515● Motion of the Sun answering to the time . 05016 The summe subt . . 60174 Motion of latitude at visible ☌ 8. 77768 Motion of latitude at beginning 8. 17594 True latitude North . 70648 Parallax of latitude . 82004 Visible latitude South . 11353 2 For the end , adde to the minutes of incidence the motion of the Sun agreeing to the time of repletion and the sum adde to the true motion of latitude at the time of the visible Conjunction ; so have you the true motion of latitude at the end ; by which proceed as before , to find the visible Latitude . Example . Scruples of Incidence . 55158 Motion of the Sun agreeing to the time of repl . . 04642 The Summe Adde . 59800 Motion of Latitude at the visible ☌ 8. 77768 Motion of Latitude at the ending 9. 37568 True Latitude North . 80925 Parallax of Latitude . 65218 Visible Latitude North . 15707 CHAP. 36. To Delineate the Eclipses ▪ of the Sun and Moon . FOr the Moon draw the lines AC and BD to intersect one another at right angles in E , which point of intersection is the place of the Ecliptique where the Eclipse happens : upon which as a Center draw the Peripherie ABCD , of the quantity of the summe of the Semidiameters of the Moon and the earths shadow ( which may be done by helpe of a Scale or Sector of equal divisions ) also to the quantity of the Semidiameter of the earths shadow , draw upon the same center another Peripherie . Then because the Moones Eclipse begins on the east part of her body , you must upon the west side of your plane , note downe the latitude of the Moon in the arch BCD , which here ▪ represents the west part ▪ and may be thus done , From E upon the line BD prick out the latitude at the beginning ; towards B , if the Latitude be North , towards D if South , and it terminat●s at G , from which draw a parallel to AC , and in the arch BC it marks out F. Also for the end of the Eclipse proceed in like manner on the other side , and you have the latitude terminated at I , and the parallel falling at H. Then draw a line between F and H and where it intersects BD marke it with K. Lastly , upon the centers F , K and H , draw three equal circles , having for Radius the Semidiameter of the Moone , and the worke is done . Typus Eclipseos Lunae praedictae . Example of the forementioned Eclipse of the Moon March 15. 1652 Summe of the Semidiameters EB . 97385 Semidiameter of shadow EM . 70954 Initial latitude of the Moon EG , North . 59223 Final latitude of the Moon EI North . 43746 Semidiameter of the Moon MB . 26431 2 For the Eclipse of the Sun , it differs nothing at all from this of the Moon , but onely that instead of the Semidiameter of the shadow of the earth you use the Semidiameter of the Sun ; and the visible latitude for the true . Example of the forementioned Sol●● Eclipse March 28. ●652 . Summe of the Semidiameters EB . 5520● Semidiameter of the Sun EM . 27386 Initiall visible latitude EG South . 11353 Finall visible latitude EI North . 15707 Semidiameter of the Moon MB . 27815 Typus Eclipseos Solis pr●dict● . CHAP. 37. The use of the Table of Refractions . ALthough the Table of Refractions , belongs not to the calaulation of these Tables , yet will it not be amisse to shew its use in comparing of observation with calculation . Know then that Refraction , causeth the stars to appeare higher then really they are . Therefore with an observed altitude enter this Table and take out the Refraction , which subtract from the observed altitude , and you have the true altitude , or having the true altitude , the apparent is found by adding the Refraction thereto . FINIS . This Scheame hath particular relation to page 103 , and is there printed in most Copies , but in some Copies there is another Scheame placed instead thereof , the Reader is therefore desired ( where it is wanting ) to insert it . Errata . Page 7. line the last , for the North read C the North. Page 8. line 10 read or the arch H ♋ . Page 21. line 20 for else of that , read else that . Page 29. line 39 for ED 38 read ED 30. Page 37. line 23 for paraallctical read parallactical . Page 76. line 14 for plane parallel read plane is parallel . In the Tables . Page 26 against degree 11 for 0 , 38836 read 0 , 38336. Page 27 against degree 90 for 5 , 0201387 read 5 , 0001387. Page 27 against degree 117 for 4 , 9961795 read 4 , 9965795. Page 34 against degree 56 for 3 , 04 &c. read 4 , 04 &c. Page 35 against degree 87 for 5 , 0010809 read 5 , 0018089. Page 35 against degree 119 for 4 , 163 &c. read 4 , 463 &c. Page 36 against degree 132 for 3 , 874 &c. read 824 &c. Page 36 against degree 139 for 3 , 38920 read 3 , 38902. Page 36 against degree 126 for 4 , 9895915 read 4 , 9895925. Page 36 against degree 179 for 0 , 69126 read 0 , 09126. Page 86 In the Title , for A Table of Declinations , read A Table of Right Ascensions . Let this leafe be folded in at page 168 , which is between the second and third Books . This Diagram having particular relation to the 18 Chapter of the second Book , will be in use for diverse leaves together , I thought it therefore convenient , to place it so that when the Book is opened in any part , the Dirgram might be in ▪ sight , and have therefore ordered it to be folded in . Astronomia BRITANNICA The third Part : Exhibiting Tables , for the converting of Sexagenary Numbers into Decimal and the contrary , for Astrononomical Chronologie with the Ecclesiastical Computation , and the Calculation of the places of the Planets , Eclipses of the Luminaries and Doctrine of the Sphere . bookseller's logo LONDON . Printed by R. and W. Leybourne Anno Domini 1656. A view of the more notable Epochae . Epochae Yeares of the Julian Period Moneths The Iulian Period 1 Ianuar. 1 Creation of the World 765 Ianuar. 1 Aera of the Olympiades 3938 Iuly 8 The building of Rome 3961 April 21 Epochae of Nabonassor 3667 Febru . 26 The beginning of Meton's Circle 4281 Iune 26 The beginning of the Periods of Calippus 4384 Iune 28 The Death of Alexander the great 4390 Nove. 12 Aera of the Chaldees 4403 Octob. 15 The Aera of Dyonisius 4429 Marc. 25 The beginning of the Christian Aera falls in the 4713 Yeare of the Julian period compleat . Yeares of Christ Moneth . The Diocletian Aera 284 Augu. 29 The Turkish Aera or Negyra 622 Iuly 16 The Persian Aera from Jesdagird 632 Iune 16 The Aera of the Persian Sultan 1079 Marc. 14 Dayes in yeares of the Julian accompt Egypt . and Persian accompt 1 0 0 0 365 2 5 0 1 0 0 0 365 0 0 0 2 0 0 0 730 5 0 0 2 0 0 0 730 0 0   3 0 0 0 1095 7 5 0 3 0 0 0 1095 0 0   4 0 0 0 1461 0 0 0 4 0 0 0 1460 0 0   5 0 0 0 1826 2 5 0 5 0 0 0 1825 0 0 0 6 0 0 0 2191 5 0 0 6 0 0 0 2190 0 0 0 7 0 0 0 2556 7 5 0 7 0 0 0 2555 0 0   8 0 0 0 2922 0 0 0 8 0 0 0 2920 0 0 0 9 0 0 0 3287 2 5 0 9 0 0 0 3285 0 0 0 10 0 0 0 3652 5 0 0 10 0 0 0 3650 0 0 0 Dayes in Moneths of the Julian Com. B ss Egyptian Persian accompt . Januar. 31 1 Th●th 30 Pharvadin 30 Februar . 5● 60 Paophi 60 Aripehest 60 March 90 91 Athyr 90 Chortat 90 April 120 121 Chaeac 120 Tyrma 120 May 151 152 Tybi 150 Mertat 150 June 181 182 Mechir 180 Sachriur 180 July 212 213 Phamenoth 210 Mecherma 210 August 243 244 Pharmuthi 240 Apanma 245 Septem . 273 274 Pachon 270 Wahak 245 Octob. 304 305 Payni 300 Ad●rma 275 Novem 334 335 Ephephi 330 Dima 305 Decem. 365 366 Mesori 360 Pechmam 335     Epagomena 365 Asphander 365 Dayes in Turkish or Arabical Years . 1   354   2   709   3   . 1063   4   . 1417   5   . 1772   6   . 2126   7   . 2480   8   . 2835   9   . 3189   10   . 3543   11   . 3898   12   . 4252   13   . 4607   14   . 4961   15   . 5315   16   . 5670   17   . 6024   18   . 6378   19   . 6733   20   . 7087   21   . 7442   22   . 7796   23   . 8150   24   . 8505   25   . 88●9   26   . 9213   27   9568   28   9922   29   10276   30 0 10631 0 60 0 21262 0 90 0 31893 0 120 0 42524 0 150 0 53155 0 180 0 63786 0 210 0 74417   240 0 85048 0 270 0 95679 0 300 0 106310 0 Dayes in Turkish Moneths . Muharram 30 Sahahen 236 Sephar 59 Ramadhan 266 Rabie I 89 Schevall 295 Rabie II 118 Dulkadati 325 Giumadi I 148 Dulhajati 354 Giumadi II 177 Dsilhit●sche , Tur● . 354 Regeb 207 In anno abundanti 355 A Table shewing the Dominical Letter in both accompts . Years of our Lord Cycle of the Sun Julian accom Greg. accom 1644 1 G F C B 1645 2 E A 1646 3 D G 1647 4 C F 1648 5 B A E D 1649 6 G C 1650 7 F B 1651 8 E A 1652 9 D C G F 1653 10 B E 1654 11 A D 1655 12 G C 1656 13 F E B A 1657 14 D G 1658 15 C F 1659 16 B E 1660 17 A G D C 1661 18 F B 1662 19 E A 1663 20 D G 1664 21 C B F ● 1665 22 A D 1666 23 G C 1667 24 F B 1668 25 E D A G 1669 26 C F 1670 27 B E 1671 28 A D A Table shewing the Epact in both accompts . Years of our Lord Gold Num. Epac . Juliā . Epact Greg. 1653 1 11 1 1654 2 22 12 1655 3 3 23 1656 4 14 4 1657 5 25 15 1658 6 6 26 1659 7 17 7 1660 8 28 18 1661 9 9 29 1662 10 20 10 1663 11 1 21 1664 12 12 2 1665 13 23 13 1666 14 4 24 1667 15 15 5 1668 16 26 16 1669 17 7 27 1670 18 18 8 1671 19 29 19 The Anticipation of the Gregorian Kalender . A5Oct . 10 1582   11 1700 A24Fe . 12 1800   13 1900   14 2100   15 2200   16 2●●0   d. A. D.   17 2500   18 2600   19 2700   20 2900   21 3000   22 3100 A Table of moveable Feasts in both accompts . Ep DL Lxx L Ash. East . Asce . Pen. Corp. Advent Sun.     25 D Jan 18 Feb. 1 Feb. 4 March Ap. 30 May 1● May 29 Nove. D ●2 24 E 19 2 5 23 May 1 11 22 30   E 21 23 F 20 3 6 24 2 12 23 1 Decem F 20 22 G 21 4 7 25 4 13 24 2   G 19 21 A 22 5 8 26 4 14 25 3   A 18 20 B 23 6 9 27 5 15 26 27 Nove. B 17 19 C 24 7 10 28 6 16 27 28   C 16 18 D 25 8 11 29 7 17 28 29   D 15 17 E 26 9 12 30 8 18 29 30   E 14 16 F 27 10 13 31 9 19 30 1 Decem F 13 15 G 28 11 14 Ap. 1 10 20 31 2   G 12 34 A 29 12 15 2 11 21 June 1 3   A 11 13 B 30 13 16 3 12 22 2 27 Nove. B 10 12 C 31 14 17 4 13 23 3 28   C 9 11 D Feb. 1 15 18 5 14 24 4 29   D 8 10 E 2 16 19 6 15 25 5 30   E 7 9 F 3 17 20 7 16 26 6 1 Decem F 6 8 G 4 18 21 8 17 27 7 2   G 5 7 A 5 19 22 9 18 28 8 3   A 4 6 B 6 20 23 10 19 29 9 27 Nove. B 3 5 C 7 21 24 11 20 30 10 28   C 2 4 D 8 22 25 12 21 31 11 29   D 1 3 E 9 23 26 13 22 June 1 12 30   E * 2 F 10 24 27 14 23 2 13 1 Decem F 29 1 G 11 25 28 15 24 3 14 2   G 28 * A 12 26 Mar. 1 16 25 4 15 3   A 27 29 B 13 27 2 17 26 5 16 27 Nove. B 26 28 C 14 28 3 18 27 6 17 28   C 24 * D 15 Mar. 1 4 19 28 7 18 29   D * * E 16 2 5 20 29 8 19 30   E * * F 17 3 6 21 30 9 20 1 Decem F * * G 18 4 7 22 31 10 21 2   G * * A 19 5 8 23 June 1 11 22 3   A * 27 B 20 6 9 24 2 12 23 27 Nove. B * 26 C 21 7 10 25 3 13 24 28   C 23 A Table of Fixed Feasts   January February March April May June July August Septemb October Novem. Decem. 1 Circu . a ●gnat . d d g P. & Ia. b e g Lammas c Aegyd . f Remigi . a All Sa. d f 2 b Pu. M. e e Frāde P a c Marcel . f Visi M. a d g b All son . e Bibinia g 3 c Blasius f f b Inv. cru . d g b e a c f a 4 d g Lucius g c e a c f b Francis. d Vital . g Barbara b 5 Telesph . e Agath . a a d f b d Ded. M. g c e a c 6 Epfphā . f Doroth. b b e Jo. p. latg c e Transf . a d f b d 7 g c c f a d f b e Marc. p. g c Ambro. e 8 a d d g Ap. SM . b e g c Na. M. f a d Conc. M f 9 b Apollo . e 40 Mar. e a c Primus f a d g Dionys. b e g 10 c f f b d g 7 fratr . b Laurenc e a c Tryph. f a 11 Hygin . d g g Leo Pa. c e Barnab . a c f b d Martin g b 12 e a Gregor . a d f b Nabor d g c e a c 13 f b b e g Anton. c e a d f b Lucia d 14 Hilari . g Valent. c c T. V. M. f Bonifa . a Basil. d Bonav . f b Exal . cr . e Callist . g c e 15 Paul Er. a Fa. & J. d d g b e g Ass. M. c f a d Eusebius f 16 Marcel . b e e a Ubald c f a d Cornel. g b e g 17 Anton. c f f Anicet . b d g Alexius b e a c Gregor . f a 18 Cut. S P d Simeon g g c e a c f b Lucos d g b 19 e a Ios. con . a d Prudent . f Gervasi . b d g c e Pontia . a c 20 Fab. & se f b b e g c Margar. e Bernar. a d f b d 21 Agnet . g c Benedi . c f a d f b Mat. E e Hilariō . g Ob. Ma. c Tho. a. e 22 Vincen. a d d Soter . c. g b e M Mag. g c f a d f 23 b e e George a c f a d Linus g b e g 24 Timoth. c S. Ma. f f b d S. I. B g b Bart. a. c a c f a 25 Con. P. d g An. Mag S Mar. c Urban . e a Jam. a. c f b Chrysa . d Cathar . g Na. C. b 26 Policar . e a a d f b d g Cyprian c e a Step● . c 27 f b b e Jo. pap . g c e a d f b Joh. E. d 28 g c c Vitalis f a d f August . b e Si. Iu. g c Innoce . e 29 a   d Cathar . g b Leo e Martha g Decoll . c Mich. A f a d T. Cant. f 30 b   e a Felix c Pet. ap . f a d Hieron . g b And. a. e g 31 c   f   Petrom . d g b e   c   Silvest . a A Catalogue of some famous places with their Latitude , and distance in Longitude from the Meridian of London . The Names of the Places . Difference of Meridia . H. Parts Height of the Pole D. Parts Aberden in Scotland S 0. 11667 58. 66667 Adrionaplis in Thrace A 2. 06667 43. 3333● Ag●ia in Hungarie A 1. 35000 47. 93333 Alba Julia in Transylvania A 1. 53333 47. 00000 Alepus in Syria A 2. 41667 37. 33333 Alexandria in Egypt A 2. 18333 30. 96667 Algiers in Africa A 0. 38333 35. 60000 Amsterdam in Holland A 0. 35000 52. 41667 Antwerp in Brabant A 0. 28333 51. 20000 Aracta in Chaldaea A 3. 30000 36. 00000 Arbela in Assyria A 3. 76667 37. 25000 Astracan upon Volgo in Tarta●ia A 3. 96667 50. 00000 Athens in Greece A 1. 86667 37. 00000 Bamberge in Franconie A 0. 75000 49. 61667 Bononia in Italy A 0. 71667 43. 81677 Brundusium in Calabria A 1. 28333 49. 53333 Bulgaria in Tartaria A 4. 03333 56 ▪ 00000 Burgos in Spaine S 0. 25000 42. 66667 Calecutum in India A 5. 83333 11. 50000 Cambridge in England A 0. 03333 52. 33333 Carthage in Africa A 0. 68333 34. 83333 Casan in Tartaria A 4. 00000 58. 00000 Cassels in Hessia A 0. 73333 51. 31667 Cair grand in Egypt A 2. 26667 29. 83333 Chalcedon A 2. 33333 43. 25000 Chester in England S 0. 16667 53. 26667 Cochin in India A 5 ▪ 90000 9. 90000 Cola in Lapland A 2. 30000 69. 40000 Colberg in Pomerania A 1. 03333 54. 46667 Compostella in Spaine S 0. 63333 43. 00000 Constantinople in Thrace A 2. 30000 43. 00000 Conymbre in Lusitania S 0. 58333 40. 25000 Cracow in Poland A 1. 35000 49. 96667 Crim of Precopensis in Tart●ry A 2. 70000 47. 83333 Damascus in Syria A 3. 26667 34. 00000 Dantzik of Borussia in Poland A 1. 13333 54. 38333 Doüay in Artesia A 0. 23333 50. 40000 Edenburgh in Scotland S 0. 03333 55. 95000 Epidaurus in Peloponnesis A 1. 86667 35. 50000 Famagusta in Cyprus A 2. 95000 35. 00000 Francford upon Odar A 0. 55000 50. 11667 Francford upon Maene A 0. 96667 52. 33333 Fruenburg in Borussia A 1. 36667 54. 36667 Grat●um in Stiria A 1. 06667 47. 03333 Groyning in Frizia A 0. 43333 53. 25000 Hamburg in Holsatia A 0. 66667 53. 71667 Haphnia in Denmarke A 0. 81667 55. 71667 Lipsia in Misnia A 0. 81667 51. 40000 Liverpoole in England S 0. 16667 53. 36667 LONDON in England   0. 00000 51. 53333 Lovaine in Brabant   0. 33333 50. 83333 Leyden A 0. 31667 52. 18333 Middleburg in Zeland A 0. 26667 51. 50000 Manchester in England A 0. 15000 53. 40000 Naples in Italy S 0. 96667 40. 70000 Nicomedia in Bythynia A 2. 3●333 42. 50000 Nidrosia in Norway A 0. 56667 63. 20000 Newcastle in England A 0. 01667 55. 05000 No●imberg in Germany S 0. 76667 49. 43333 Orleans in France A 0. 00000 48. 13333 Oxford in England   0. 05000 52. 06667 Paris in France S 0. 13333 48. 65000 corrected by Bullialdus A 0. 03333 48. 85000 Patavium in Liburnia A 0. 76667 45. 10000 Prague in Bohemi● A 0. 93333 50. 10000 Rhodes an Island A 3. 43333 36. 00000 Rochell in Aquitain A 0. 06667 45. 81667 Rochester in England S 0. 03333 51. 50000 Rome in Italie A 0. 83333 42. 03333 Roan in Normandi● A 0. 00000 49. 63333 Smarcanda in Tartaria A 5. 66667 45. 00000 Scutara in Dalmatia A 1. 43333 42. 38333 Sevill in Spaine S 0 ▪ 36667 37. 33333 Spahani in Persia A 4. 33333 31. 50000 Stetin in Pomerania A 0. ●6667 53. 60000 Syracusa in Sicilie A 1. ●8333 86. 83333 Tolledo in Spaine S 0. 23333 39. 90000 Tubing Wittenburg A 0. 63333 48. 56667 Valence in Spaine A 0. 10000 39 ▪ 50000 Ulme in Suevia A 0. 70000 48. 40000 Uraniburge in Denmark A 0. 83338 55 ▪ 91667 Yorke in England S 0 ▪ 05000 54. 03333 A Table to convert Sexagenary minutes , ′ ″ P 0 00 . 36 01 1. 12 02 1. 48 03 2. 24 04 3. 0 05 3. 36 06 4. 12 07 4. 48 08 5. 24 09 6. 0 10 6. 36 11 7. 12 12 7. 48 13 8. 24 14 9. 0 15 9. 36 16 10. 12 17 10. 48 18 11. 24 19 12. 0 20 12. 36 21 13. 12 22 13. 48 23 14. 24 24 15. 0 25 15. 36 26 16. 12 27 16. 48 28 17. 24 29 18. 0 30 18. 36 31 19. 12 32 19. 48 33 20. 24 34 21. 0 35 21. 36 36 22. 12 37 22. 48 38 23. 24 39 24. 0 40 24. 36 41 25. 12 42 25. 48 43 26. 24 44 27. 0 45 27. 36 46 28. 12 47 28. 48 48 29. 24 49 30. 0 50 30. 36 51 31. 12 52 31. 48 53 32. 24 54 33. 0 55 33. 36 56 34. 12 57 34. 48 58 35. 24 59 36. 0 60 36. 36 61 37. 12 62 37. 48 63 38. 24 64 39. 0 65 39. 36 66 40. 12 67 40. 48 68 41 , 24 69 42. 0 70 42. 36 71 43. 12 72 43. 48 73 44. 24 74 45. 0 75 45. ●6 76 46. 12 77 46 48 78 47 24 79 48. 0 80 48. 36 81 49. 12 82 49. 48 83 50. 24 84 51. 0 85 51. 36 86 52. 12 87 52. 48 88 53. 24 89 54. 0 90 54. 36 91 55. 12 92 55. 48 93 56. 24 94 57. 0 95 57. 36 96 58. 12 97 58. 48 98 59. 24 99 60. 0 100 and seconds into Decimals and the contrary 0 36 12 48 24 00000000 1 37 13 49 25 02777778 2 38 14 50 26 05555555 3 39 15 51 27 08333333 4 40 16 52 28 11111111 5 41 17 53 29 13888889 6 42 18 54 30 16666667 7 43 19 55 31 19444444 8 44 20 56 32 22222222 9 45 21 57 33 25000000 10 46 22 58 34 27777778 11 47 23 59 35 30555555 12 48 24 1. 00 36 33333333 13 49 25 1 37 36111111 14 50 26 2 38 38888889 15 51 27 3 39 41666667 16 52 28 4 40 44444444 17 53 29 5 41 47222222 18 54 30 6 42 50000000 19 55 31 7 43 52777778 20 56 32 8 44 55555555 21 57 33 9 45 58333333 22 58 34 10 46 61111111 23 59 35 11 47 63888889 24 1. 00 36 12 48 66666667 25 1 37 13 49 69444444 26 2 38 14 50 72222222 27 3 39 15 51 75000000 28 4 40 16 52 77777778 29 5 41 17 53 80555555 30 6 42 18 54 83333333 31 7 43 19 55 86111111 32 8 44 20 56 88888889 33 9 45 21 57 91666667 34 10 46 22 58 94444444 35 11 47 23 59 97222222   Thirds Fourths Fifths 1 0000046296 0000000772 0000000013 2 92593 1573 26 3 138889 2315 39 4 185185 3046 51 5 231481 3858 64 6 277778 4630 77 7 324074 5401 90 8 370370 6173 103 9 416667 6944 116 10 462963 7716 129 11 509259 8488 141 12 555556 9259 154 13 601852 100 1 167 14 648148 10802 180 15 694444 11574 193 16 740741 12345 206 17 78●037 13117 219 18 833333 13889 232 19 879630 14660 245 20 925926 15432 258 21 972222 16204 270 22 1018518 16975 283 23 1064814 17747 296 24 1111111 18518 309 25 1157407 19290 322 26 1203703 20062 335 27 1250000 20833 348 78 1296296 21605 360 29 1342592 22376 373 30 1388888 23148 386 31 0001435184 0000023920 0000000399 32 1481481 24691 412 33 1527777 25463 425 34 1574073 26234 438 35 1620370 27006 450 36 1666666 27778 463 37 1712963 28549 476 38 1759259 29321 489 39 1805556 30092 502 40 1851852 30864 515 41 1898148 31636 527 42 1944444 32407 540 43 1990740 33179 553 44 2037037 33950 566 45 2083333 34722 579 46 2129629 35494 592 47 2175925 36265 605 48 2222222 37037 618 49 2268518 37808 630 50 2314815 38580 643 51 2361111 39352 656 52 2407407 40123 669 53 2453703 40895 682 54 2500000 41666 694 55 2546296 42438 707 56 2592502 43210 720 57 2638889 43981 733 58 2685185 44753 746 59 2731481 45524 759 60 2777778 46296 772 H. M. P 0 0 2. 24 1 4. 48 2 7. 12 3 9. 36 4 12. 00 5 14. 24 6 16. 48 7 19. 12 8 21. 36 9 A Table to convert the houres and minutes . of a day into Decimals and the contrary . 0 24 48 12 36 000000000 1 25 49 13 37 006944444 2 26 50 14 38 013888889 3 27 51 15 39 020833333 4 28 52 16 40 027777778 5 29 53 17 41 034722222 6 30 54 18 42 041666667 7 31 55 19 43 048611111 8 32 56 20 44 055555555 9 33 57 21 45 062500000 10 34 58 22 46 069444444 11 35 59 23 47 076388889 12 36 5. 17 24 48 083333333 13 37 1 25 49 090277778 14 38 2 26 50 097222222 15 39 3 27 51 104166667 16 40 4 28 52 111111111 17 41 5 29 53 11805555● 18 42 6 30 54 125000000 19 43 7 31 55 131944444 20 44 8 32 56 138888889 21 45 9 33 57 145833333 22 46 10 34 58 152777778 23 47 11 35 59 159722222 24 48 12 36 10. 22 166666667 25 49 13 37 1 173611111 26 50 14 38 2 180555555 27 51 15 39 3 187500000 28 52 16 40 4 194444444 29 53 17 41 5 201388889 30 54 18 42 6 208333333 31 55 19 43 7 215277778 32 56 20 44 8 222222222 33 57 21 45 9 229166667 34 58 22 46 10 236111111 35 59 23 47 11 243055555 36 3. 15 24 48 12 250200000 37 1 25 49 13 256944444 38 2 26 50 14 26●888889 39 3 27 51 15 270833333 40 4 28 52 16 277777778 41 5 29 53 17 284722222 42 6 30 54 18 291666667 43 7 31 55 19 298611111 44 8 32 56 20 305555555 45 9 33 57 21 312500000 46 10 34 58 22 319444444 47 11 35 59 23 326388889 48 12 36 8. 20 24 333333333 49 13 37 1 25 340277778 50 14 38 2 26 347222222 51 15 39 3 27 354166667 52 16 40 4 28 361111111 53 17 41 5 29 368055555 54 18 42 6 30 375000000 55 19 43 7 31 381944444 56 20 44 8 32 388888889 57 21 45 9 33 395833333 58 22 46 10 34 402777778 59 23 47 11 35 409722222 1. 1 24 48 12 36 416666667 1 25 49 13 37 423611111 2 26 50 14 38 430555555 3 27 51 15 39 437500000 4 28 52 16 40 444444444 5 29 53 17 41 451388889 6 30 54 18 42 458333333 7 31 55 19 43 465277778 8 32 56 20 44 472222222 9 33 57 21 45 479166667 10 34 58 22 46 486111111 11 35 59 23 47 493055555 12 36 6. 18 24 48 500000000 13 37 1 25 49 506944444 14 38 2 26 50 513888889 15 39 3 27 51 520833333 16 40 4 28 52 527777778 17 41 5 29 53 534722222 18 42 6 30 54 541666667 19 43 7 31 55 548911111 20 44 8 32 56 555555555 21 45 9 33 57 562500000 22 46 10 34 58 569444444 23 47 11 35 59 576388889 24 48 12 36 11. 23 583333333 25 49 13 37 1 590277778 26 50 14 38 2 597222222 27 51 15 39 3 604166667 28 52 16 40 4 611111111 29 53 17 41 5 618055555 30 54 18 42 6 625000000 31 55 19 43 7 631944444 32 56 20 44 8 638888889 33 57 21 45 9 645833333 34 58 22 46 10 652777778 35 59 23 47 11 659722222 36 4. 16 24 48 12 666666667 37 1 25 49 13 673611111 38 2 26 50 14 680555555 39 3 27 51 15 687500000 40 4 28 52 16 694444444 41 5 29 53 17 701388889 42 6 30 54 18 708333333 43 7 31 55 19 715277778 44 8 32 56 20 722222222 45 9 33 57 21 729166667 46 10 34 58 22 736111111 47 11 35 59 23 743055555 48 12 36 9. 21 24 750000000 49 13 37 1 25 756944444 50 14 38 2 26 763888889 51 15 39 3 27 770833333 52 16 40 4 28 777777778 53 17 41 5 29 784722222 54 18 42 6 30 791666667 55 19 43 7 31 798611111 56 20 44 8 32 805555555 57 21 45 9 33 812500000 58 22 46 10 34 819444444 59 23 47 11 35 826388889 2. 14 24 48 12 36 833333333 1 25 49 13 37 840277778 2 26 50 14 38 847222222 3 27 51 15 39 854166667 4 28 52 16 40 861111111 5 29 53 17 41 868055555 6 30 54 18 42 875000000 7 31 55 19 43 881944444 8 32 56 20 44 888888889 9 33 57 21 45 895833333 10 34 58 22 46 902777778 11 35 59 23 47 909722222 12 36 7. 19 24 48 916666667 13 37 1 25 49 923611111 14 38 2 26 50 930555555 15 39 3 27 51 937500000 16 40 4 28 52 944444444 17 41 5 29 53 951388889 18 42 6 30 54 958333333 19 43 7 31 55 965277778 20 44 8 32 56 972222222 21 45 9 33 57 979166667 22 46 10 34 58 9861●1111 23 47 11 35 59 993055555 24 48 12 36 00 000000000   Seconds . Thirds Fourths Fifths 1 0000115741 0000001929 0000000032 0000000001 2 231481 385● 64 0000000001 3 347222 5787 96 2 4 463963 7716 0000000129 2 5 578704 9645 161 3 6 694444 0000011574 193 3 7 810185 13503 225 4 8 925926 15432 257 4 9 0001041666 17361 289 5 10 1157407 19290 321 5 11 1273148 21219 354 6 12 1388889 23148 387 7 13 1504630 25077 420 7 14 1620371 27006 453 8 15 1736112 28935 486 8 16 1851853 39864 518 9 17 1967593 32793 559 9 18 2083333 34722 582 10 19 2199074 36651 614 10 20 0002314815 0000038580 0000000643 0000000011 21 2430555 40509 675 11 22 2546296 42438 707 12 23 2662037 44367 739 12 24 2777778 46296 771 13 25 2893518 48225 803 13 26 3009259 50254 836 14 27 3125000 52183 869 14 28 3240741 54112 902 15 29 3356482 56041 934 15 30 0003472222 0000057870 0000000965 0000000016 31 0003587963 00000059799 0000000997 0000000016 32 3703704 61728 1030 17 33 3819444 63657 1062 17 34 3935185 65586 1094 18 35 4050926 67515 1126 18 36 4166667 69444 1157 19 37 4282407 71373 1189 19 38 4398148 73302 1222 20 39 4513889 75231 1254 20 40 4629630 77160 1286 21 41 4745370 79089 1318 22 42 4861111 81018 1350 22 43 4976852 82947 1382 23 44 5092592 84876 1414 23 45 5208333 86805 1446 24 46 5324074 88734 1479 24 47 5439814 90663 1511 25 48 5555555 92592 1544 25 49 5671296 94521 1676 26 50 5787037 96451 1680 27 51 5902778 98380 1641 27 52 6018518 100309 1673 28 53 6134259 102238 1705 28 54 6250000 104167 1737 29 55 6365741 106096 1770 29 56 6481481 108025 1802 30 57 6597222 109954 1834 30 58 6712963 111883 1866 31 59 6828704 113812 1898 31 60 6944444 115741 1929 32 A Table converting Hours and parts into Degrees and parts of the Aequator .     IV ‴ ″ ″ ′ 0 Ho. Deg. M D. Parts . 1 15 01 00 , 15000 2 30 02 00 , 30 3 45 03 00 , 45 4 60 04 00 , 60 5 75 05 00 , 75 6 90 06 00 , 90 7 105 07 01 , 05 8 120 08 01 , 20 9 135 09 01 , 35 10 150 10 01 , 50 11 165 11 01 , 65 12 180 12 01 , 80 13 195 13 01 , 95 14 210 14 02 , 10 15 ●25 15 02 , 25 16 240 16 02 , 40 17 255 17 02 , 55 18 270 18 02 , 70 19 285 19 02 , 85 20 300 20 03 , 00 21 315 21 03 , 15 22 330 22 03 , 30 23 345 23 03 , 45 24 360 24 03 , 60     25 03 , 75     26 03 , 90     27 04 , 05     28 04 , 20     29 04 , 35     30 04 , 50     31 04 , 65     32 04 , 80     33 04 , 95     34 05 , 10     35 05 , 25     36 05 , 40     37 05 , 55     38 05 , 70     39 05 , 85     40 06 , 00     41 06 , 15     42 06 , 30     43 06 , 45     44 06 , 60     45 06 , 75     46 06 , 90     47 07 , 05     48 07 , 20     49 07 , 35     50 07 , 50     51 07 , 65     52 07 , 80     53 07 , 95     54 08 , 10     55 08 , 25     56 08 , 40     57 08 , 55     58 08 , 70     59 08 , 85     60 09 , 00     61 09 , 15     62 09 , 30     63 09 , 45     64 09 , 60     65 09 , 75     66 09 , 90     67 10 , 05     68 10 , 30     69 10 , 35     70 10 , 50     71 10 , 65     72 10 , 80     73 10 , 95     74 11 , 10     76 11 , 25     77 11 , 40     57 11 , 55     78 11 , 70     79 11 , 85     80 12 , 00     81 12 , 15     82 12 , 30     83 12 , 45     84 12 , 60     85 12 , 75     86 12 , 90     87 13 , 05     88 13 , 20     89 13 , 35     90 13 , 50     91 13 , 65     92 13 80     93 13 , 93     94 14 , 10     95 14 , 25     96 14 , 40     97 14 , 55     98 14 , 70     99 14 , 85 A Perpetual Table for the Aequation of Time. D ♈ P. Add ♉ P. Add ♊ P. Add ♋ P. Sub. ♌ P. Sub. ♍ P. Sub. D 0 00000 14027 14639 00000 14639 14027 30 1 00555 14333 14362 00611 14917 13722 29 2 01111 14583 14055 01194 15167 13389 28 3 01638 14861 13750 0180● 15389 13055 27 4 02194 15111 13416 02416 15583 12694 26 5 02750 15333 13055 03000 15778 12333 25 6 03305 15527 12667 03583 15944 11944 24 7 03833 15722 12278 04361 16111 11555 23 8 04389 15889 11861 04750 16222 11138 22 9 04917 16027 11444 05333 16333 10722 21 10 05444 16167 11000 05917 16416 10305 20 11 05972 16278 10555 06472 16472 09861 19 12 06472 16389 10083 07000 16527 09389 18 13 07000 16444 09611 07555 16555 08944 17 14 07500 16500 09111 08083 16555 08472 16 15 07972 16555 08611 08611 16555 07972 15 16 08472 16555 08883 09111 16500 07500 14 17 08944 16555 07555 09611 16444 07000 13 18 09389 16527 07000 10083 16389 06472 12 19 09861 16472 06472 10555 16278 05972 11 20 10305 16416 05917 11000 16167 05444 10 21 10722 16333 05333 11444 16029 04917 9 22 11138 16222 04750 11862 15889 04389 8 23 11555 16111 04361 12278 15722 03833 7 24 11944 15944 03583 12667 15527 03305 6 25 12333 15778 03000 13055 15333 02750 5 26 12694 15583 02416 13426 15112 02194 4 27 13055 15389 01805 13750 1486● 01638 3 28 13389 15167 01194 14055 14583 01111 2 29 13722 14917 00611 14361 14333 00555 1 30 14027 14639 00000 14639 14027 00000 0 D ♓ Sub. ♒ Sub. ♑ Sub. ♐ Adde ♏ Add ♎ Add D The Suns mean Motions . Epochae Longit. ☉ Deg. parts Apog . ☉ Deg. parts ● ♈ & Fix . Deg. Parts . Christi . 278. 98331 70. 32264 4. 97537 1600 290. 94859 95. 59094 27. 61667 1620 291. 09815 95. 90680 27. 89968 1640 291. 24771 96. 22265 28. 18270 1660 291. 39724 96. 53851 28. 46571 1 359. 76107 0. ●1578 0. 01414 2 359. 52213 0. 03156 0. 02828 3 359. 28310 0. 04734 0. 04242 B 4 0. 02991 0. 06317 0. 05660 5 359. 79098 0. 07895 0. 07074 6 359. 55205 0. 09473 0. 0848● 7 359. 31311 0. 11051 0. 09903 B 8 0. 05982 0. 12634 0. 11321 9 359. 82089 0. 14212 0. 12735 10 359. 58196 0. 15790 0. 14149 11 359. 34303 0. 17369 0. 15563 B 12 0. 08974 0. 18951 0. 16981 13 359. 85081 0. 20529 0. 18395 14 359. 61187 0. 22107 0. 19809 15 359. 37294 0. 23686 0. 21223 B 16 0. 11965 0 25268 0. 22641 17 359. 88072 0. 26864 0. 24055 18 359. 64178 0. 28425 0. 25469 19 359. 40285 0. 30003 0. 26884 B 20 0. 14956 0. 31585 0. 28302 40 0. 29913 0. 63171 0. 56603 60 0. 44870 0. 94756 0. 84905 80 0. 59826 1. 26342 1. 13206 100 0. 74783 1. 57927 1. 41508 The Suns mean Motions . Years . Longit. ☉ Deg. parts . Apog . ☉ Deg. parts . Fixed ✴ . Deg. parts . 100 0 , 74783 1 , 57927 1 , 41508 200 1 , 49566 3 , 15854 2 , 830●6 300 2 , 24349 4 , 73781 4 , 24524 400 2 , 99132 6 , 31708 5 , 66023 500 3 , 73915 7 , 89635 7 , 07540 600 4 , 48698 9 , 47562 8 , 49048 700 5 , 23481 11 , 05489 9 , 90557 800 5 , 98264 12 , 63415 11 , 32065 900 6 , 73047 14 , 21342 12 , 73573 1000 7 , 47830 15 , 79369 14 , 15081 2000 14 , 95660 31 , 58538 28 , 30162 3000 22 , 43490 47 , 37808 42 , 45242 4000 29 , 91320 63 , 17077 56 , 60323 5000 37 , 39150 78 , 96346 70 , 75404 Ianuary 30 , 55505 0 , 00134 0 , 00120 February 58 , 15315 0 , 00255 0 , 00228 March 88 , 70820 0 , 00389 0 , 00349 April 118 , 27760 0 , 00519 0 , 00465 May 148 , 83265 0 , 00653 0 , 00586 Iune 178 , 40205 0 , 00783 0 , 00701 Iuly 208 , 95710 0 , 00917 0 , 00821 August 239 , 51215 0 , 01051 0 , 00941 September 267 , 08155 0 , 01180 0 , 01058 October 269 , 63660 0 , 01314 0 , 01178 November 329 , 20600 0 , 01444 0 , 01294 December 359 , 76107 0 , 01578 0 , 01414 The Suns mean Motions . In Dayes .   ☉ Longit. Deg. Parts . ☉ Apog . Parts . Fixed ✴ Parts 1 0. 98565 . 00004 , 00004 2 1. 97129 . 00008 , 00008 3 2. 95694 . 00013 , 00012 4 3. 94258 . 00017 , 00015 5 4. 92823 . 00022 , 00019 6 5. 91388 . 00026 , 00023 7 6. 89953 . 00030 , 00027 8 7. 88517 . 00034 , 00031 9 8. 87082 . 00039 , 00035 10 9. 85647 . 00043 , 00039 11 10. 84211 . 00048 , 00043 12 11. 82776 . 00052 , 00046 13 12. 81341 . 00056 , 00050 14 13. 79905 . 00060 , 00054 15 14. 78470 . 00065 , 00058 16 15. 77035 . 00069 , 00062 17 16. 75599 . 00073 , 00066 18 17. 74164 . 00078 , 00070 19 18. 72729 . 00082 , 00074 20 19. 71293 . 00086 , 00077 21 20. 69858 . 00091 , 00081 22 21. 68423 . 00095 , 00085 23 22. 66987 . 00099 , 00089 24 23. 65542 . 00104 , 00093 25 24. 64117 . 00108 , 00097 26 25. 62681 . 90112 , 00101 27 26. 61246 . 00117 , 00105 28 27. 59811 . 00121 , 00108 29 28. 58375 . 00125 , 00112 30 29. 56940 . 00130 , 00116 31 30. 55505 . 00134 , 00120 32 31. 54069 . 00138 , 00124 The Suns mean Motions . In Hours .   ☉ Longit. Parts . 1 , 04107 2 , 08214 3 , 12321 4 , 16427 5 , 20534 6 , 24641 7 , 28748 8 , 32855 9 , 36962 10 , 41069 11 , 45175 12 , 49282 13 , 53389 14 , 57496 15 , 61603 16 , 65710 17 , 69817 18 , 73923 19 , 78030 20 , 82137 21 , 86244 22 , 90351 23 , 94458 24 , 98565 The Suns mean Motions . In parts of an Hour .   ☉ Long. Parts . 1 , 00041 2 , 00082 3 , 00123 4 , 00164 5 , 00205 6 , 00246 7 , 00287 8 , 00328 9 , 00370 10 , 00411 11 , 00452 12 , 00493 13 , 00534 14 , 00575 15 , 00616 16 , 00657 17 , 00698 18 , 00739 19 , 00780 20 , 00821 21 , 00862 22 , 00903 23 , 00945 24 , 00986 25 , 01027 26 , 01068 27 , 01109 28 , 01150 29 , 01191 30 , 01232 31 , 01273 32 , 01314 33 , 01355 34 , 01369 35 , 01437 36 , 01478 37 , 01519 38 , 01561 39 , 01602 40 , 01643 41 , 01684 42 , 01725 43 , 01766 44 , 01807 45 , 01848 46 , 01889 47 , 01930 48 , 01971 49 , 02012 50 , 02053 51 , 02094 52 , 02135 53 , 02177 54 , 02218 55 , 02259 56 , 02300 57 , 02341 58 , 02382 59 , 02423 60 , 02464 61 , 02505 62 , 02546 63 , 02587 64 , 02628 65 , 02669 66 , 02710 67 , 02751 68 , 02793 69 , 02834 70 , 02875 71 , 02916 72 , 02957 73 , 02998 74 , 03039 75 , 03080 76 , 03121 77 , 03162 78 , 03203 79 , 03244 80 , 03285 81 , 03326 82 , 03368 83 , 03409 84 , 03450 85 , 03491 86 , 03523 87 , 03573 88 , 03614 89 , 03655 90 , 03696 91 , 03737 92 , 03778 93 , 03819 94 , 03860 95 , 03901 96 , 03942 97 , 03984 98 , 04025 99 , 04026 The Aequation of the Suns Excentrick . Degrees Aeq : Sub : ☉ Distāce Degrees   D. parts . Logarithm   1 0 , 03502 50076781 359 2 0 , 06966 50076767 358 3 0 , 10512 50076752 357 4 0 , 14012 50076724 356 5 0 , 17506 50076695 355 6 0 , 20996 50076464 354 7 0 , 24480 50076253 353 8 0 , 27580 50076041 352 9 0 , 31426 50075829 351 10 0 , 34886 50075561 350 11 0 , 38836 50075292 349 12 0 , 41776 50075023 348 13 0 , 45202 50074782 347 14 0 , 48616 50074540 346 15 0 , 52014 50074298 345 16 0 , 55400 50073888 344 17 0 , 58730 50073478 343 18 0 , 62120 50073068 342 19 0 , 65452 50072656 341 20 0 , 68766 50072245 340 21 0 , 72062 50071834 339 22 0 , 75●34 50071347 338 23 0 , 78586 50070859 337 24 0 , 81816 50070372 336 25 0 , 85020 50069833 335 26 0 , 88200 50069294 334 27 0 , 91356 50068755 333 28 0 , 94424 50068246 332 29 0 , 97586 50067736 331 30 1 , 00650 50067244 330 31 1 , 03700 5. 0066482 329 32 1 , 06714 5. 0065720 328 33 1 , 09696 5. 0064958 327 34 1 , 12648 5. 0064216 326 35 1 , 15566 5. 0063474 325 36 1 , 18448 5. 0062732 324 37 1 , 21296 5. 0061917 323 38 1 , 24112 5. 0061102 322 39 1 , 26890 5. 0060287 321 40 1 , 29630 5. 0059457 320 41 1 , 32318 5. 0058615 319 42 1 , 34996 5. 0057779 318 43 1 , 37620 5. 0056904 317 44 1 , 40214 5. 0056029 316 45 1 , 42746 5. 0055154 315 46 1 , 45248 5. 0054194 314 47 1 , 47708 5. 0053230 313 48 1 , 50122 5. 0052273 312 49 1 , 5●494 5. 0051279 311 40 1 , 54820 5. 0050285 310 51 1 , 571●0 3. 0049290 309 52 1 , 59336 5. 0048354 308 53 1 , 61522 5. 0047418 307 54 1 , 63662 5. 0046481 306 55 1 , 65754 5. 0045293 305 56 1 , 67796 5. 0044105 304 57 1 , 69790 5. 0042916 303 58 1 , 71732 5. 0041810 302 59 1 , 73784 5. 0040704 301 60 1 , 75464 5. 0039597 300 61 1 , 77254 5 , 0038450 299 62 1 , 79000 5 , 0037303 298 63 1 , 80670 5 , 0036157 297 64 1 , 82240 5 , 0035286 296 65 1 , 83876 5 , 0034415 295 66 1 , 85396 5 , 0033545 294 67 1 , 86862 ● , 0031985 293 68 1 , 88272 5 , 0030425 292 69 1 , 89624 5 , 0028866 291 70 1 , 90920 5 , 0027615 290 71 1 , 92036 5 , 0026364 289 72 1 , 93342 5 , 0025113 288 73 1 , 94466 5 , 0023831 287 74 1 , 95532 5 , 0022549 286 75 1 , 96540 5 , 0021268 285 76 1 , 97488 5 , 0019971 284 77 1 , 98378 5 , 0018674 283 78 1 , 99206 5 , 0017378 282 79 1 , 99976 5 , 0016069 281 80 2 , 00684 5 , 0014760 280 81 2 , 01332 5 , 0013451 279 82 2 , 01920 5 , 0012217 278 83 2 , 02446 5 , 0010984 277 84 2 , 02912 5 , 0009753 276 85 2 , 03317 5 , 0008067 275 86 2 , 03660 5 , 0006681 274 87 2 , 03946 5 , 0005296 273 88 2 , 04158 5 , 0003993 272 89 2 , 04316 5 , 0002690 271 90 2 , 04410 5 , 0201387 270 91 2 , 04444 5 , 0000038 269 92 2 , 04412 4 , 9998690 268 93 2 , 04320 4 , 9997342 267 94 2 , 04168 4 , 9995972 266 95 2 , 03940 4 , 9994602 265 96 2 , 03672 4 , 9993231 264 97 2 , 03328 4 , 9991886 263 98 2 , 02926 4 , 9990542 262 99 2 , 02460 4 , 9989198 261 100 2 , 01932 4 , 9987851 260 101 2 , 01342 4 , 9986506 259 102 2 , 00690 4 , 9985162 258 103 1 , 99974 4 , 9983844 257 104 1 , 99200 4 , 9982526 256 105 1 , 98362 4 , 9981208 255 106 1 , 97468 4 , 9979918 254 107 1 , 96504 4 , 9978628 253 108 1 , 95486 4 , 9977338 252 109 1 , 94406 4 , 9975992 251 110 1 , 93264 4 , 9974648 250 111 1 , 92066 4 , 9973304 249 112 1 , 98082 4 , 9972113 248 113 1 , 89606 4 , 6970824 247 114 1 , 88106 4 , 9969535 246 115 1 , 86668 4 , 9968355 245 116 1 , 85172 4 , 9967075 244 117 1 , 83622 4 , 9961795 243 118 1 , 82000 4 , 9964581 242 119 1 , 80346 4 , 9963366 241 120 1 , 78622 4 , 9962151 240 121 1 , 76844 4 , 9960958 239 122 1 , 75010 4 , 9959766 238 123 1 , 73120 4 , 9958574 237 124 1 , 71290 4 , 9957427 236 125 1 , 69180 4 , 9956279 235 126 1 , 67130 4 , 9955131 234 127 1 , 65114 4 , 9954018 237 128 1 , 62954 4 , 9952906 232 129 1 , 60668 4 , 9951794 231 130 1 , 58100 4 , 9950747 230 131 1 , 56104 4 , 9949700 229 132 1 , 53748 4 , 9948653 228 133 1 , 51356 4 , 9947664 227 134 1 , 4●892 4 , 9946676 226 135 1 , 46394 4 , 9945688 225 136 1 , 43848 4 , 9944696 224 137 1 , 41258 4 , 9943704 223 138 1 , 38622 4 , 9942712 222 139 1 , ●5944 4 , 9941772 221 140 1 , 33214 4 , 9940832 220 141 1 , ●0458 4 , 9939892 219 142 1 , ●7650 4 , 9939076 218 143 1 , 24804 4 , 9938199 217 144 ● , 21918 4 , 9937322 216 145 1 , 18994 4 , 9936519 21● 146 1 , 160●0 4 , 99●5715 214 147 1 , 13030 4 , 9934911 213 148 1 , 09994 4 , 9934180 212 149 1 , 06922 4 , 9933448 211 150 1 , 03818 4 , 9932716 210 151 1 , 00692 4 , 9932045 209 152 0 , 97610 4 , 9931375 208 153 0 , 94308 4 , 9930705 207 154 0 , 91076 4 , 9930116 206 155 0 , 87820 49929527 205 156 0 , 84526 4 , 9928938 204 157 0 , 81212 4 , 09281●8 203 158 0 , 77868 4 , 9927619 202 159 0 , 74508 4 , 9627140 201 160 0 , 71116 4 , 9926680 200 161 0 , 67698 4 , 9926239 199 162 0 , 64264 4 , 9925817 198 16● 0 , 60808 4 , 9925412 197 164 0 , 57332 4 , 9925009 196 165 0 , 53838 4 , 9924606 195 166 0 , 50356 4 , 9924274 194 167 0 , 46802 4 , 992●941 193 168 0 , 43258 4 , 9923609 192 169 0 , 39730 4 , 9923319 191 170 0 , 36134 4 , 9●23029 190 171 0 , 32554 4 , 9922739 189 172 0 , 29404 4 , 9922573 188 173 0 , 25366 4 , 9922420 187 174 0 , 21756 4 , 9922268 186 175 0 , 18140 4 , 9922193 185 176 0 , 14520 2 , 9922119 184 177 0 , 10896 4 , 9622044 183 178 0 , 07268 4 , 9921970 182 179 0 , 03636 4 , 6921896 181 180 0 , 00000 4 , 9921822 180 D Adde Logarith . D The Moons mean Motions . Epochae Longit. ☽ Anomaly . ☽ Latitude ☽   Deg. parts Deg. parts Deg. Parts . Christi . 135. 73167 215. 54194 226. 95833 1600 20. 69194 151. 57111 99. 19250 1620 154. 25389 191. 27138 259. 59252 1640 287. 81583 230. 97194 59. 99833 1660 61. 37805 270. 67222 220. 40139 1 129. 38389 88. 71889 148. 71278 2 258. 76805 177. 43750 297. 42555 3 28. 15194 266. 15639 86. 13833 B 4 170. 71250 7. 93972 248. 08028 5 300. 09639 96. 65861 36. 79305 6 69. 48028 ●85 . 37750 185. 50583 7 198. 86444 274. 09611 334. 21889 B 8 341. 42472 15. 87972 136. 16111 9 110. 80861 104. 59861 284. 87389 10 240. 19278 19● . 31750 73. 58667 11 9. 57667 282. 0●639 222. 29944 B 12 152. 13722 23. 82000 24. 24167 13 281. 52111 112. 53889 172. 97444 14 50. 90500 201. 25750 321. 66722 15 180. 28917 288. 97639 112. 38000 B 16 322. 84944 31. 76000 272. 32222 17 92. 23333 120. 47889 61. 03500 18 221. 61750 209. 19778 209. 74778 19 351. 00139 297. 91667 358. 46055 B 20 133. 56194 39. 70028 160. 40278 40 267. 12389 79. 40083 320. 80583 60 40. 68611 119. 15111 121. 20889 80 174. 24805 158. 80139 281. 61167 100 307. 81000 198. 50194 82. 01472 The Moons mean Motions . Years . Longit. ☽ Deg. parts . Anom . ☽ Deg. parts . Latitud . ☽ Deg : parts . 100 307 , 81000 198 , 50194 82 , 01472 200 255 , 62000 37 , 00361 164 , 02917 300 203 , 43000 235 , 50555 246 , 04389 400 151 , 24000 74 , 00722 328 , 05861 500 99 , 05000 272 , 50917 50 , 07333 600 46 , 86000 111 , 01083 131 , 08778 700 354 , 67000 309 , 51250 214 , 10250 800 302 , 48000 148 , 01444 296 , 11722 900 250 , 29027 346 , 51639 18 , 13194 1000 198 , 10027 185 , 01805 100 , 14639 2000 36 , 20027 10 , 03639 200 , 29305 3000 234 , 30055 195 , 05444 300 , 43944 4000 72 , 40055 20 , 07250 40 , 58611 5000 270 , 50083 205 , 09083 140 , 73250 Ianuary 48 , 46833 45 , 01444 50 , 10722 February 57 , 40722 50 , 83417 60 , 53167 March 105 , 87555 95 , 84861 110 , 64139 April 141 , 16722 127 , 79805 147 , 52194 May 189 , 63555 172 , 81250 197 , 63167 Iune 224 , 89417 204 , 76194 234 , 11222 Iuly 273 , 39555 249 , 77639 284 , 62194 August 321 , 86389 294 , 79055 334 , 73167 September 357 , 15555 326 , 74028 11 , 61222 October 45 , 62387 11 , 75472 61 , 72194 November 80 , 91583 43 , 70417 98 , 60250 December 129 , 38387 88 , 71889 148 , 71278 The Moons mean Motions . Dayes Longit. ☽ Deg. Parts . Anomaly ☽ Deg. Parts . Latitude ☽ Deg. parts . 1 13 , 17639 13 , 06500 13 , 22944 2 26 , 35278 26 , 13000 26 , 45861 3 39 , 52917 39 , 19500 39 , 68805 4 52 , 70555 52 , 26000 52 , 91722 5 65 , 88194 65 , 32500 66 , 14667 6 79 , 50833 78 , 39000 79 , 37611 7 92 , 23472 91 , 45500 92 , 60528 8 105 , 41111 104 , 52000 105 , 83472 9 118 , 58750 117 , 58472 119 , 06417 10 131 , 76389 130 , 64972 132 , 29333 11 144 , 94028 143 , 71472 145 , 52278 12 158 , 11667 156 , 77972 158 , 75222 13 171 , 29305 169 , 84472 171 , 98139 14 184 , 46944 182 , 90972 185 , 21083 15 197 , 64583 195 , 97472 198 , 44028 16 210 , 82222 209 , 03972 211 , 66944 17 223 , 99861 222 , 10472 224 , 89889 18 237 , 17500 235 , 16972 238 , 12833 19 250 , 35139 248 , 23472 251 , 35750 20 263 , 52778 261 , 29972 264 , 58694 21 276 , 70417 274 , 36472 277 , 81639 22 289 , 88055 287 , 42972 291 , 04555 23 303 , 05694 300 , 49472 304 , 27500 24 316 , 23333 313 , 55972 317 , 50444 25 329 , 40972 326 , 62444 330 , 73361 26 342 , 58611 339 , 68944 343 , 96305 27 355 , 76250 352 , 75444 357 , 19250 28 8 , 93889 5 , 81944 10 , 42167 29 22 , 11528 18 , 88444 23 , 65111 30 35 , 29167 31 , 94944 36 , 88028 31 48 , 46805 45 , 01444 50 , 10972 32 61 , 64444 58 , 07944 63 , 33889 The Moons mean Motions . In Hours .   Longit. ☽ D. Parts Anomal . ☽ D. parts Latitude ☽ D. parts 1 0 , 54889 0 , 54444 0 , 55139 2 1 , 09805 1 , 08861 1 , 10278 3 1 , 64694 1 , 63305 1 , 65389 4 2 , 19611 2 , 17750 2 , 20528 5 2 , 74500 2 , 72194 2 , 75639 6 3 , 29417 3 , 26611 3 , 30750 7 3 , 84305 3 , 81055 3 , 85889 8 4 , 39222 4 , 35500 4 , 41000 9 4 , 94111 4 , 89944 4 , 96139 10 5 , 49000 5 , 44361 5 , 51250 11 6 , 03917 5 , 98805 6 , 06361 12 6 , 58805 6 , 53250 6 , 61500 13 7 , 13722 7 , 07694 7 , 16611 14 7 , 68611 7 , 62111 7 , 71750 15 8 , 23528 8 , 16555 8 , 26861 16 8 , 79417 8 , 71000 8 , 81972 17 9 , 33305 9 , 25444 9 , 37111 18 9 , 88222 9 , 79861 9 , 92222 19 10 , 43139 10 , 34305 10 , 47361 20 10 , 98028 10 , 88750 11 , 02472 21 11 , 52944 11 , 43194 11 , 57583 22 12 , 07833 11 , 97611 12 , 12722 23 12 , 62722 12 , 5●055 12 , 67833 24 13 , 17639 13 , 06500 13 , 22944 The Moons mean Motions . In parts of an Hour .   Long. ☽ Parts . Anom . Parts . Latit . Parts . 1 , 00549 , 00544 , 00551 2 , 01098 , 01088 , 01103 3 , 01647 , 01633 , 01654 4 , 02196 , 02177 , 02205 5 , 02745 , 02722 , 02756 6 , 03294 , 03266 , 03307 7 , 03843 , 03810 , 03858 8 , 04392 , 04355 , 04410 9 , 04941 , 04899 , 04961 10 , 05490 , 05443 , 05512 11 , 06039 , 05988 , 06063 12 , 06588 , 06532 , 06615 13 , 07137 , 07077 , 07166 14 , 07686 , 07621 , 07717 15 , 08235 , 08165 , 08268 16 , 08794 , 08710 , 08819 17 , 09333 , 09254 , 09371 18 , 09882 , 09798 , 09922 19 , 10431 , 10343 , 10473 20 , 10980 , 10887 , 11024 21 , 11529 , 11432 , 11576 22 , 12078 , 11976 , 12127 23 , 12627 , 12520 , 12678 24 , 13176 , 13065 , 13229 25 , 13725 , 13609 , 13780 26 , 14274 , 14153 , 14331 27 , 14823 , 14698 , 14883 28 , 15372 , 15242 , 15434 29 , 15921 , 15787 , 15985 30 , 16470 , 16331 , 16536 31 , 17019 , 16885 , 17083 32 , 17567 , 17416 , 17633 33 , 18117 , 17966 , 18183 34 , 18665 , 18508 , 18744 35 , 19214 , 19050 , 19300 36 , 19763 , 19600 , 19850 37 , 20317 , 20133 , 20400 38 , 20867 , 20683 , 20950 39 , 21416 , 21233 , 21500 40 , 21967 , 21767 , 22050 41 , 22500 , 223●6 , 22600 42 , 23050 , 22850 , 23150 43 , 23600 , 23400 , 23700 44 , 24150 , 23950 , 24250 45 , 24700 , 24500 , 24800 46 , 25283 , 25050 , 25350 47 , 25800 , 25600 , 25900 48 , 26350 , 26133 , 26450 49 , 26900 , 26683 , 27000 50 , 27450 , 27217 , 27567 51 , 28000 , 27767 , 28117 52 , 28550 , 28300 , 28800 53 , 29100 , 28850 , 29217 54 , 29817 , 29400 , 29767 55 , 30200 , 29933 , 30317 56 , 30733 , 30483 , 30867 57 , 31283 , 31017 , 31416 58 , 31833 , 31567 , 31967 59 , 32383 , 32117 , 32517 60 , 32933 , 32666 , 33083 61 , 33491 , 33206 , 33626 62 , 34039 , 33750 , 34177 63 , 34588 , 34294 , 34728 64 , 35137 , 34838 , 35279 65 , 35685 , 35382 , 35830 66 , 36234 , 35926 , 36381 67 , 36783 , 36470 , 36932 68 , 37331 , 37014 , 37483 69 , 37880 , 37558 , 38034 70 , 38429 , 38102 , 38585 71 , 38979 , 38646 , 39139 72 , 39528 , 39190 , 39690 73 , 40077 , 39734 , 40241 74 , 40626 , 40278 , 40792 75 , 41174 , 40822 , 41343 76 , 41723 , 41366 , 41894 77 , 42272 , 41910 , 42445 78 , 42820 , 42454 , 42996 79 , 43369 , 42998 , 43547 80 , 43918 , 43542 , 44098 81 , 44466 , 44094 , 44651 82 , 45020 , 44638 , 45202 83 , 45568 , 45182 , 45753 84 , 46117 , 45726 , 46304 85 , 46666 , 46270 , 46855 86 , 47215 , 46814 , 47406 87 , 47763 , 47358 , 47957 88 , 48312 , 47902 , 48508 89 , 48861 , 48446 , 49059 90 , 49411 , 48990 , 49610 91 , 49960 , 49538 , 50165 92 , 50509 , 50082 , 50716 93 , 51058 , 50626 , 51267 94 , 51607 , 51170 , 51818 95 , 52155 , 51714 , 52369 96 , 52704 , 52258 , 52920 97 , 53253 , 52802 , 53471 98 , 53801 , 53346 , 54022 99 , 54351 , 53890 , 54573 The Aequations of the Moons Excentrick . Degrees Aeq : Sub D. parts . ☉ Distāce from Umb. 5 , 085424 Degrees 1 0 , 08356 5 , 0185341 359 2 0 , 16706 5 , 0185258 358 3 0 , 25068 5 , 0185174 357 4 0 , 33414 5 , 0184826 356 5 0 , 41750 5 , 0184479 355 6 0 , 50076 5 , 0184131 354 7 0 , 58424 5 , 0183845 353 8 0 , 66684 5 , 0183560 352 9 0 , 74962 5 , 0183274 351 10 0 , 83222 5 , 0182718 350 11 0 , 91458 5 , 0182163 349 12 0 , 99670 5 , 0181607 348 13 1 , 07854 5 , 0180979 347 14 1 , 16010 5 , 0180352 346 15 1 , ●4136 5 , 0179724 345 16 1 , 32228 5 , 0178897 344 17 1 , 40282 5 , 0178071 343 18 1 , 48302 5 , 0177244 342 19 1 , 56280 5 , 0176271 341 20 1 , 64212 5 , 0175298 340 21 1 , 72108 5 , 0174325 339 22 1 , 79908 5 , 0173200 338 23 1 , 87750 5 , 0172075 337 24 1 , 95498 5 , 0170950 336 25 2 , 03190 5 , 0169696 335 26 2 , 10830 5 , 0168443 334 27 2 , 18410 5 , 0167189 333 28 2 , 29594 5 , 0165775 332 29 2 , 33394 5 , 0164362 331 30 2 , 40792 5 , 0162948 330 31 2 , 48144 5. 0161416 329 32 2 , 55388 5. 0159884 328 33 2 , 62582 5. 0158351 327 34 2 , 69688 5. 0156656 326 35 2 , 76756 5. 0154962 325 36 2 , 83732 5. 0153267 324 37 2 , 90628 5. 0151439 323 38 2 , 97520 5. 0149611 322 39 3 , 04184 5. 0147782 321 40 3 , 12824 5. 0145848 320 41 3 , 17404 5. 0143915 319 42 3 , 22762 5. 0141961 318 43 3 , 30266 5. 0140007 317 44 3 , 36554 5. 0138052 316 45 3 , 42768 5. 0135901 315 46 3 , 48880 5. 0133649 114 47 3 , 54892 5. 0131474 313 48 3 , 60806 5. 0129254 312 49 3 , 666●0 5. 0126977 311 50 3 , 73358 5. 0124700 310 51 3 , 77940 3. 0122423 309 52 3 , 83442 5. 0120012 308 53 3 , 88836 5. 0117601 307 54 3 , 94112 5. 0115189 306 55 3 , 99296 5. 0112631 305 56 3 , 04358 5. 0110073 304 57 4 , 09306 5. 0107514 303 58 4 , 14138 5. 0104891 302 59 4 , 18854 5. 0102269 301 60 4 , 23448 5. 0099646 300 61 4 , 27924 5 , 0097259 299 62 4 , 32278 5 , 0094872 298 63 4 , 36508 5 , 0091485 297 64 4 , 40614 5 , 0088671 296 65 4 , 44708 5 , 0085856 295 66 4 , 48444 5 , 0083041 294 67 4 , 52166 5 , 0080136 293 68 4 , 54774 5 , 0077231 292 69 4 , 59222 5 , 0074326 291 70 4 , 62546 5 , 0070981 290 71 4 , 65612 5 , 0067637 289 72 4 , 68922 5 , 0064292 288 73 4 , 71674 5 , 0061720 287 74 4 , 74506 5 , 0059148 286 75 4 , 77150 5 , 0056575 285 76 4 , 79654 5 , 0053376 284 77 4 , 82020 5 , 0050177 283 78 4 , 84242 5 , 0046977 282 79 4 , 86322 5 , 0042544 281 80 4 , 89534 5 , 0038111 280 81 4 , 90048 5 , 0033678 279 82 4 , 91694 5 , 0031731 278 83 4 , 93196 5 , 0029785 277 84 4 , 94548 5 , 0027838 276 85 2 , 95750 5 , 0024588 275 86 4 , 96806 5 , 0021339 274 87 4 , 97714 5 , 0010809 273 88 4 , 98460 5 , 0014811 272 89 4 , 99078 5 , 0011534 271 90 4 , 99532 5 , 0008256 270 91 4 , 99834 5 , 0004952 269 92 4 , 99988 5 , 0001649 268 93 4 , 99988 4 , 9998345 267 94 4 , 99836 4 , 9995032 266 95 4 , 99532 4 , 9991719 265 96 4 , 99070 4 , 9988405 264 97 4 , 98460 4 , 9985193 263 98 4 , 97696 4 , 9981982 262 99 4 , 96736 4 , 9978770 261 100 4 , 95706 4 , 9972811 260 101 4 , 94476 4 , 9966852 259 102 4 , 93096 4 , 9960892 258 103 4 , 91562 4 , 9960119 257 104 4 , 89874 4 , 9959347 256 105 4 , 88034 4 , 9958574 255 106 4 , 86042 4 , 9955301 254 107 4 , 82944 4 , 9952028 253 108 4 , 81594 4 , 9948754 252 109 4 , 79146 4 , 9945474 251 110 4 , 76544 4 , 9942193 250 111 4 , 73788 4 , 9939013 249 112 4 , 70884 4 , 9935795 248 113 4 , 67888 4 , 9932577 247 114 4 , 64632 4 , 9929358 246 115 4 , 61274 4 , 9926191 245 116 4 , 57778 4 , 9923025 244 117 4 , 54128 4 , 9919859 243 118 4 , 50350 4 , 9916852 242 119 4 , 16386 4 , 9913845 241 120 4 , 42300 4 , 9910837 240 121 4 , 38086 4 , 9907779 239 122 4 , 33720 4 , 9904722 238 123 4 , 29210 4 , 9901664 237 124 4 , 24560 4 , 9899751 236 125 4 , 19772 4 , 9897838 235 126 4 , 14546 4 , 9895915 234 127 4 , 09784 4 , 9892117 237 128 4 , 04550 4 , 9888309 232 129 3 , 99248 4 , 9884500 231 130 3 , 93798 4 , 9881731 230 131 3 , 88206 4 , 9878962 229 132 3 , 87486 4 , 9876193 228 133 3 , 76638 4 , 9873574 227 134 3 , 70738 4 , 9870956 226 135 3 , 64572 4 , 9868337 225 136 3 , 58356 4 , 9865840 224 137 3 , 52020 4 , 9863343 223 138 3 , 45564 4 , 9860846 222 139 3 , 38920 4 , 9858146 221 140 ● , 32310 4 , 9855446 220 141 3 , 25514 4 , 9853746 219 142 3 , 18610 4 , 9851518 218 143 3 , 11598 4 , 9849290 217 144 3 , 04478 4 , 9847061 216 145 2 , 97260 4 , 9844966 215 146 2 , 89938 4 , 9842872 214 147 2 , 82518 4 , 9840777 213 148 2 , 75004 4 , 9838882 212 149 2 , 67392 4 , 9836987 211 150 2 , 59686 4 , 9835092 210 151 2 , 51028 4 , 9833262 209 152 2 , 44030 4 , 9831432 208 153 2 , 36074 4 , 9829601 207 154 2 , 28030 4 , 9828019 206 155 2 , 19126 4 9826437 205 156 2 , 11722 4 , 9824855 204 157 2 , 03458 4 , 9823435 203 158 1 , 95120 4 , 9822015 202 159 1 , 86718 4 , 9820595 201 160 1 , 78252 4 , 9819334 200 161 1 , 69724 4 , 9818073 199 162 1 , 61138 4 , 9816811 198 163 1 , 52494 4 , 9815083 197 164 1 , 43800 4 , 9813356 196 165 1 , 35118 4 , 9811628 195 166 1 , 26300 4 , 9811425 194 167 1 , 17430 4 , 9811223 193 168 1 , 08554 4 , 9811020 192 169 0 , 99768 4 , 9810309 191 170 0 , 90692 4 , 9809599 190 171 0 , 81714 4 , 9808889 189 172 0 , 72704 4 , 9808391 188 173 0 , 63724 4 , 9807893 187 174 0 , 546●8 4 , 9807●94 186 175 0 , 45546 4 , 9807099 185 176 0 , 36518 4 , 9806804 184 177 0 , 27352 4 , 9806509 183 178 0 , 18242 4 , 9806441 182 179 0 , 69126 4 , 9806373 181 180 0 , 00000 4 , 9806304 180 D Adde Logarith . D A Table for the finding of the second and third inaequalities of the Moon .   Subtense of the ☽ double dist . from ☉ Log●rithm . Variation Adde Parts .   0 0 , 0000000 , 00000 360 1 1 , 5805276 , 00119 359 2 1 , 8815410 , 02389 358 3 2 , 0576047 , 03555 357 4 2 , 1825049 , 04722 356 5 2 , 2793653 , 058●7 355 6 2 , 3584859 , 07055 354 7 2 , 4253610 , 08222 353 8 2 , 4832702 , 09389 352 9 2 , 5343290 , 10555 351 10 2 , 5799817 , 11722 350 11 2 , 6212586 , 12889 349 12 2 , 6589203 , 14055 348 13 2 , 6935445 , 1●194 347 14 2 , 7255502 , 16333 346 15 2 , 7553834 , 17472 345 16 2 , 7832410 , 18611 344 17 2 , 8093878 , 19750 343 18 2 , 8339081 , 20861 342 19 2 , 8572949 , 21972 341 20 2 , 8793554 , 23083 340 21 2 , 9003187 , 24194 339 22 2 , 9202845 , 25278 338 23 2 , 9393410 , 26361 337 24 2 , 9575646 , 27444 336 25 2 , 9750225 , 28528 335 26 2 , 9917737 , 29583 334 27 3 , 0078710 , 30638 333 28 3 , 0233609 , 31694 332 29 3 , 0382853 , 32722 331 30 3 , 0326819 , 33750 330 30 3 , 0526819 . 34750 330 ●1 3 , 0665●45 . 34750 329 32 3 , 0800238 . 35750 328 33 3 , 0900275 . 36750 327 34 3 , 1056210 . 37722 326 35 3 , 1178275 . 38694 325 36 3 , 1296681 . 39667 324 37 3 , 1411621 . 40655 323 38 3 , 1523276 . 41555 322 39 3 , 1630910 . 42472 321 40 3 , 1737374 . 43389 320 41 3 , 1840110 . 44278 319 42 3 , 1940149 . 45167 318 43 3 , 2037611 . 46083 317 44 3 , 2132611 . 46889 316 45 3 , 2225254 . 47722 315 46 3 , 2315637 . 48555 314 47 3 , 2403854 . 49361 313 48 3 , 2489990 . 50167 312 49 3 , 2574127 . 50944 311 50 3 , 2655340 . 51694 310 51 3 , 2706701 . 52444 309 52 3 , 2815277 . 53194 308 53 3 , 2892131 . 53916 307 54 3 , 2967325 . 54611 306 55 3 , 3040913 . 55305 305 56 3 , 3012950 . 55972 304 57 3 , 3183486 . 56611 303 58 3 , 3252569 . 57250 302 59 3 , 3320245 . 57861 301 60 3 , 3386557 . 58444 300 60 3 , 3386557 , 58444 300 61 3 , 3451546 , 59058 299 62 3 , 3515250 , 59583 298 63 3 , 3577708 , 60139 297 64 3 , 3638954 , 60667 296 65 3 , 3699022 , 61167 295 66 3 , 3757945 , 61667 294 67 3 , 815752 , 62139 293 68 3 , 3872474 , 62583 292 69 3 , 3928137 , 63000 291 70 3 , 3982770 , 63417 290 71 3 , 4036397 , 63805 289 72 3 , 4089044 , 64167 288 73 3 , 4130733 , 64500 287 74 3 , 4191487 , 64861 286 75 3 , 4241328 , 65194 285 76 3 , 4290277 , 65500 284 77 3 , 4338353 , 65778 283 78 3 , 4375575 , 66028 282 79 3 , 7431962 , 66250 281 80 3 , 4477532 , 66427 280 81 3 , 4522301 , 66667 279 82 3 , 4566282 , 66833 278 83 3 , 4609503 , 67000 277 84 3 , 4651966 , 67139 276 85 3 , 4693690 , 67250 275 86 ● , 4704690 , 67361 274 87 3 , 4465979 , 67417 273 88 3 , 4814570 , 67444 272 89 3 , 4853475 , 67472 271 90 3 , 4891707 , 67500 270 90 3 , 4891707 , 67500 270 91 3 , 4929278 , 67472 269 92 3 , 4966198 , 67444 268 93 3 , 5002479 , 67417 267 94 3 , 5038132 , 67361 266 95 3 , 5073166 , 67250 265 96 3 , 5107592 , 67139 264 97 3 , 5141418 , 67000 263 90 3 , 5174656 , 66833 262 91 3 , 5207312 , 66667 261 100 3 , 5239397 , 66472 260 101 3 , 5270918 , 66350 259 102 3 , 5301883 , 66028 258 103 3 , 5332301 , 65778 257 104 3 , 5362178 , 65500 256 105 3 , 5391524 , 65194 255 106 3 , 5420343 , 64861 254 107 3 , 5448644 , 64500 253 108 3 , 5476433 , 64167 252 109 3 , 5503717 , 63805 251 100 3 , 5530502 , 63417 250 111 3 , 5556794 , 63000 249 112 3 , 5582599 , 62583 248 113 3 , 5607923 , 62139 247 114 3 , 5632771 , 61667 246 115 3 , 5656149 , 61167 245 116 3 , 5681062 , 60667 244 117 3 , 5704515 , 60139 243 118 3 , 5727513 , 69583 242 119 3 , 5750061 , 59028 241 120 3 , 5772163 , 58444 240 120 ● , 5772163 , 58444 240 121 3 , 5793825 , 57861 239 122 3 , 5815050 , 57250 238 123 3 , 5835842 , 56611 237 124 3 , 5856206 , 55972 236 125 3 , 5876126 , 55305 235 126 3 , 5895666 , 54611 234 127 3 , 5917769 , 53916 233 128 3 , 5933457 , 53194 232 229 3 , 5951739 , 52444 231 130 3 , 5969614 , 51694 230 131 3 , 5987086 , 50944 229 132 3 , 6004159 , 50167 228 133 3 , 6029834 , 49361 227 1●4 3 , 6037118 , 48555 226 135 3 , 6053010 , 47722 225 136 3 , 6068516 , 46889 224 137 3 , 6083636 , 46083 223 138 3 , 6098374 , 45167 222 139 3 , 6106733 , 44278 221 140 3 , 6126715 , 43389 220 141 3 , 6140323 , 42472 219 142 3 , 6153558 , 41555 218 143 3 , 6166423 , 40611 217 144 3 , 6178932 , 39667 216 145 3 , 6191052 , 38694 215 146 3 , 6208820 , 37722 214 147 3 , 6314227 , 36750 213 148 3 , 6325273 , 35750 212 149 3 , 6235962 , 34750 211 150 2 , 6246295 , 33750 210 150 3 , 624629 . 33750 210 151 3 , 6256273 . 32722 209 152 3 , 6265898 . 31694 208 153 3 , 6275172 . 30638 207 154 3 , 6284096 . 29583 206 155 3 , 6292672 . 28528 205 156 3 , 6300901 . 27444 204 157 3 , 6308784 . 26361 203 158 3 , 6316323 . 25278 202 159 3 , 6333518 . 24194 201 160 3 , 6330372 . 23083 200 161 3 , 6336884 . 21972 199 162 3 , 6343056 , 20861 198 163 3 , 6348890 . 19750 197 164 3 , 6354385 . 18611 196 165 3 , 6359543 . 17472 195 166 3 , 6364364 . 16333 194 167 3 , 6368850 . 15194 193 168 3 , 6373000 . 14055 192 169 3 , 6376817 . 12889 191 170 3 , 6380299 . 11722 190 171 3 , 6387448 . 10555 189 172 3 , 6386265 . 09389 188 173 3 , 6388749 . 08222 187 174 3 , 6390901 . 07055 186 175 3 , 6392722 . 05889 185 176 3 , 6394211 . 04722 184 177 3 , 6395369 . 03555 183 178 3 , 6396295 . 02389 182 179 3 , 6396792 . 01194 181 180 3 , 6396857 . 00000 180 D Logarithm . Subst . D Bullialdus his Table of Evection .   Evectiō Subst . Scrupl . of proportiō . Variation Adde     D. Parts . Parts . Parts .   0 0 , 00000 , 00000 , 00000 ●60 1 0 , 04028 , 00873 , 01194 359 2 0 , 08055 , 01745 , 02389 358 3 0 , 12083 , 02617 , 03555 357 4 0 , 16083 , 03489 , 04722 356 5 0 , 20083 , 04362 , 05887 355 6 0 , 24111 , 05234 , 07055 354 7 0 , 28083 , 06105 , 08222 353 8 0 , 36028 , 06975 , 09389 352 9 0 , 36000 , 07845 , 10555 351 10 0 , 39944 , 08715 , 11722 350 11 0 , 43889 , 09584 , 12889 349 12 0 , 47833 , 10453 , 14055 348 13 0 , 51750 , 11320 , 15194 347 14 0 , 55667 , 12187 , 16333 346 15 0 , 59583 , 13052 , 17472 345 16 0 , 63472 , 13917 , 18611 344 17 0 , 67333 , 14780 , 19750 343 18 0 , 71222 , 15643 , 20861 342 19 0 , 75083 , 16504 , 21972 341 20 0 , 78917 , 17364 , 23083 340 21 0 , 82750 , 18223 , 24194 339 22 0 , 86528 , 19081 , 25278 338 23 0 , 9027● , 19936 , 26361 337 24 0 , 94055 , 20791 , 27444 3●6 25 0 , 97805 , 21643 , 28528 335 36 1 , 01528 , 22495 , 29583 334 27 1 , 052●2 , 23344 , 30638 333 28 1 , 08889 , 24192 , 31694 332 29 1 , 12527 , 25038 , 32722 331 30 1 , 161●8 , 25882 , 33750 330 30 1 , 16138 , 25882 , 33750 330 31 1 , 19722 , 26723 34750 329 32 1 , 23278 , 2756● , 35750 328 33 1 , 26833 , 2840 , 36750 327 34 1 , 30305 , 29237 , 37722 326 35 1 , 33750 , 30072 , 38694 325 36 1 , 37167 , 30901 , 39667 324 37 1 , 40556 , 30730 , 40655 323 38 1 , 43944 , 32553 , 41555 322 39 1 , 47222 , 33380 , 42472 321 40 1 , 50500 , 34202 , 43389 320 41 1 , 53750 , 35020 , 44378 319 42 1 , 56972 , 35836 , 45167 318 43 1 , 60139 , 3665● , 46083 317 44 1 , 63278 , 37460 , 46889 316 45 1 , 66389 , 38268 , 4772● 315 46 1 , 69444 , 39073 , 78555 314 47 1 , 72444 , 39874 , 49361 313 48 1 , 75444 , 40673 , 50167 312 49 1 , 78417 , 41469 , 50944 311 50 1 , 81●61 , 42262 , 51694 310 51 1 , 84278 , 4●051 , 52444 309 52 1 , 87139 , 43837 , 53194 308 53 1 , 89944 , 44619 , 53916 307 54 1 , 92695 , 45●99 , 54611 306 55 1 , 95333 , 46174 , 55305 305 56 1 , 97917 , 46●47 , 55972 ●04 57 2 , 00444 , 47715 , 56611 303 58 2 , 0●917 , 4848● , 57250 302 59 2 , 05333 , 4924● , 57861 301 60 2 , 07694 , 5000● , 58444 300 60 2 , 07694 , 50000 , 58444 300 61 2 , 10000 , 50753 , 59028 299 62 2 , 12250 , 51903 , 59583 298 63 2 , 14444 , 52249 , 60139 297 64 2 , 16583 , 52991 , 60667 296 65 2 , 18667 , 53729 , 61167 295 66 2 , 20694 , 54463 , 61667 294 67 2 , 22667 , 55193 , 62139 293 68 2 , 24583 , 55919 , 62583 292 69 2 , 26444 , 56640 , 63000 291 70 2 , 28222 , 57357 , 63417 290 71 2 , 29917 , 58070 , 63805 289 72 2 , 31527 , 58778 , 64167 288 73 2 , 33055 , 59482 , 64500 287 74 2 , 34527 , 60181 , 64861 286 75 2 , 35944 , 60876 , 65194 285 76 2 , 36750 , 61566 , 65500 284 77 2 , 38611 , 62251 , 65778 283 78 2 , 39889 , 62932 , 66028 282 79 2 , 41055 , 63607 , 66250 281 80 2 , 42222 , 64278 , 66472 280 81 2 , 43333 , 64944 , 66667 279 82 2 , 44361 , 65605 , 66833 278 83 2 , 45278 , 66262 , 67000 277 84 2 , 96083 , 66913 , 67139 276 85 2 , 46778 , 67559 , 67250 275 86 2 , 27417 , 68199 , 67361 274 87 2 , 48000 , 68835 , 67417 273 88 2 , 48500 , 69465 , 67444 272 89 2 , 48944 , 70091 , 67472 271 90 2 , 49333 , 70711 , 67500 70 90 2 , 49333 70711 , 67500 270 91 2 , 49667 , 71325 67472 269 92 2 , 49889 , 71933 , 67444 268 93 2 , 50000 , 72537 , 67417 267 94 2 , 49889 , 73135 , 67361 266 95 2 , 49778 , 73727 , 67250 265 96 2 , 49639 , 74314 , 67139 264 97 2 , 49444 , 74895 , 67000 263 98 2 , 49222 , 75471 , 66833 262 99 2 , 48972 , 76040 , 66667 261 100 2 , 48667 , 76604 , 66472 260 101 2 , 48333 , 77162 , 66250 259 302 2 , 47944 , 77714 , 66028 258 103 2 , 47139 , 78260 , 65778 257 104 2 , 46917 , 78801 , 65600 256 105 2 , 46278 , 79335 , 65194 255 106 2 , 45500 , 79863 , 64861 254 107 2 , 44611 , 80385 , 64500 253 108 2 , 43611 , 80901 , 64167 252 109 2 , 42556 , 81411 , 63805 251 110 2 , 41389 , 81915 , 63417 250 111 2 , 40139 , 82412 , 63000 249 112 2 , 38861 , 82903 , 62583 248 113 2 , 37583 , 83388 , 62139 247 114 2 , 36194 , 83867 , 61667 246 115 2 , 34722 , 84339 , 61167 245 116 2 , 32972 , 84805 , 60667 244 117 2 , 31222 , 85264 , 60139 243 118 2 , 29472 , 85716 , 59583 242 119 2 , 27722 , 8616● , 59028 241 120 2 , 25972 , 8660● , 58444 240 120 2 , 25972 . 86602 , 58444 240 121 ● , 24083 . 87135 , 57861 239 122 2 , 22111 . 87462 , 57250 238 123 2 , 20038 . 87882 , 56611 237 124 2 , 17833 . 88295 , 55972 236 125 2 , 15555 . 88701 , 55305 235 126 2 , 13167 . 89100 , 54611 234 127 2 , 10694 . 89493 , 53916 233 128 2 , 08138 . 89879 , 53194 232 129 2 , 05500 . 902●8 , 52444 231 130 2 , 02805 . 90631 , 51694 230 131 2 , 00055 . 90996 , 50944 229 132 1 , 97222 . 91354 , 50167 228 133 1 , 94333 . 91706 , 49●61 2●7 134 1 , 91389 . 92050 , 48555 226 135 1 , 88138 . 9●38● , 47722 225 136 1 , 85000 . 92718 , 46889 224 137 1 , 81889 . 93042 , 46083 223 138 1 , 78722 . 93358 , 45167 222 139 1 , 75500 . 93667 , 44278 221 140 1 , 72222 . 93969 , 43389 220 141 1 , 68889 . 94264 , 42472 219 142 1 , 65472 . 94552 , 41555 218 143 1 , 62000 . 94832 , 40611 217 144 1 , 58389 . 95105 , 39667 216 145 1 , 54694 . 95371 , 38694 215 146 1 , 50944 . 95630 , 37722 214 147 1 , 47167 . 95882 , 36750 213 148 1 , 43972 . 96126 , 35750 212 149 1 , 39417 . 96363 , 34750 211 150 1 , 35472 . 9659● , 33750 210 150 1 , 35472 , ●6592 , 33750 210 151 1 , 31472 , 96814 , 32722 209 152 1 , 27417 , 97029 , 31694 208 153 1 , 23305 , 97237 , 30638 207 154 1 , 19167 , 97437 , 29583 206 155 1 , 14972 , 97629 , 28528 205 156 1 , 10722 , 97815 , 27444 204 157 1 , 06417 , 97992 , 26361 203 158 1 , 02056 , 98163 , 25278 202 159 0 , 97667 , 98325 , 24194 201 160 0 , 93250 , 98481 , 23083 100 161 0 , 88778 , 98628 , 21972 199 162 0 , 84278 , ●8769 , 20861 198 163 0 , 79750 , 98901 , 19750 197 164 0 , 75167 , 99027 , 18611 196 165 0 , ●0556 , 99144 , 17472 195 166 0 , 6●944 , 99254 , 16333 194 167 0 , 61305 , 99357 , 15194 193 168 0 , 56667 , 99452 , 14055 192 169 0 , 52000 , 99535 , 12889 191 170 0 , 47333 , 99619 , 11722 190 171 0 , 42667 , 99692 , 10555 189 172 0 , 37972 , 99756 , 09389 188 173 0 , 33278 , 99813 , 08222 187 174 0 , 28556 , 99863 , 07055 186 175 0 , 23833 , 99905 , 05889 185 176 0 , 19083 , 99939 , 04722 184 177 0 , 14333 , 99966 , 03555 183 178 0 , 09556 , 99985 , 02389 182 179 0 , 04778 , 99996 , 01194 181 180 0 , 00000 , 00000 , 00000 180   Adde   Sub :   A Compounded Table of the ☽ Evection and Variation . Degrees of Equation . 3 6 9 12 15 18 21 Degrees . Sub Sub : Sub Sub Sub Sub Sub 0 0. 058 0 , 116 0 , 171 0. 224 0 , 273 0 , 299 0 , 359 360 5 0. 059 0 , 120 0 , 178 0. 235 0 , 290 0 , 321 0 , 399 355 10 0. 059 0 , 120 0 , 181 0. 242 0 , 301 0 , 338 0 , 412 350 15 0. 058 0 , 119 0 , 181 0. 245 0 , 308 0 , 349 0 , 430 345 20 0. 057 0 , 117 0 , 179 0. 243 0 , 309 0 , 354 0 , 441 340 25 0. 054 0 , 112 0 , 175 0. 239 0 , 306 0 , 353 0 , 444 335 30 0. 050 0 , 106 0 , 166 0. 232 0 , 300 0 , 349 0 , 440 330 35 0. 045 0 , 097 0 , 155 0. 219 0 , 287 0 , 339 0 , 433 325 40 0. 039 0 , 087 0 , 141 0. 202 0 , 270 0 , 321 0 , 418 320 45 0. 032 0 , 074 0 , 124 0. 184 0 , 248 0 , 298 0 , 395 315 50 0. 024 0 , 059 0 , 103 0. 158 0 , 221 0 , 271 0 , 364 310 55 0. 015 0 , 042 0 , 080 0. 129 0 , 188 0 , 237 0 , 329 305 60 0. 006 0 , 024 0 , 055 0. 097 0 , 150 0 , 196 0 , 295 300 65 0A004 0 , 005 0 , 027 0. 054 0 , 208 0 , 150 0 , 234 295 70 0. 015 0A016 0A003 0. 018 0 , 063 0 , 089 0 , 157 290 75 0. 026 0 , 038 0 , 035 0A028 0 , 013 0 , 046 0 , 116 285 80 0. 038 0 , 062 0 , 069 0. 062 0A040 0A014 0 , 048 280 85 0. 050 0 , 086 0 , 105 0. 109 0 , 096 0 , 084 0A024 275 90 0. 063 0 , 110 0 , 141 0. 157 0 , 155 0 , 143 0 , 101 270 95 0. 075 0 , 135 0 , 178 0. 205 0 , 215 0 , 184 0 , 182 265 100 0. 087 0 , 160 0 , 216 0. 265 0 , 276 0 , 282 0 , 265 160 105 0. 100 0 , 185 0 , 253 0. 304 0 , 337 0 , 353 0 , 349 255 110 0. 112 0 , 209 0 , 289 0. 353 0 , 399 0 , 4●5 0 , 434 250 115 0. 123 0 , 233 0 , 326 0. 402 0 , 460 0 , 496 0 , 520 245 120 0. 134 0 , 256 0 , 361 0. 449 0 , 520 0 , 566 0 , 604 240 125 0. 145 0 , 277 0 , 394 0. 495 0 , 579 0 , 636 0 , 688 235 130 0. 155 0 , 298 0 , 426 0. 533 0 , 635 0 , 793 0 , 768 230 135 0. 163 0 , 316 0 , 456 0. 580 0 , 688 0 , 767 0 , 848 225 140 0. 171 0 , 333 0 , 483 0. 618 0 , 738 0 , 829 0 , 923 220 145 0. 179 0 , 349 0 , 507 0. 652 0 , 883 0 , 883 0 , 992 215 150 0. 185 0 , 363 0 , 537 0. 684 0 , 824 0 , 934 1 , 057 210 155 0. 190 0 , 374 0 , 549 0. 712 0 , 862 0 , 981 1 , 114 205 160 0. 194 0 , 383 0 , 564 0. 736 0 , 895 0 , 022 1 , 168 200 165 0. 197 0 , 391 0 , 577 0. 754 0 , 922 0 , 058 1 , 215 195 180 0. 199 0 , 396 0 , 588 0. 759 0 , 945 0 , 086 1 , 254 190 175 0. 200 0 , 399 0 , 594 0 771 0 , 962 0 , 111 1 , 286 185 170 0. 201 ● , 401 0 , 597 0. 789 0 , 975 0 , 129 1 , 312 180 Degrees of Equ : Anom . Sub Sub Sub Sub Sub Sub Sub Fe●rees of Equ : Anom . 177 174 171 168 162 162 159 A Compounded Table of the ☽ Evection and Variation . Degrees of Equation . 3 6 9 12 15 18 21 Degrees of Equation . Adde Adde Adde Adde Add Adde Add 180 0. 201 0 , 401 0 , 597 0 , 789 0 , 975 1 , 129 1 , 312 180 185 0 , 200 0 , 401 0 , 599 0 , 794 0 , 981 1 , 139 1 , 331 175 190 0 , 198 0 , 398 0 , 597 0 , 794 0 , 984 1 , 145 1 , 341 170 195 0 , 195 0 , 394 0 , 593 0 , 794 0 , 983 1 , 146 1 , 346 165 200 0 , 192 0 , 387 0 , 585 0 , 782 0 , 976 1 , 143 1 , 346 160 205 0 , 187 0 , 380 0 , 575 0 , 770 0 , 964 1 , 133 1 , 338 155 210 0 , 182 0 , 371 0 , 562 0 , 755 0 , 948 1 , 117 1 , 323 150 215 0 , 176 0 , 359 0 , 547 0 , 736 0 , 928 1 , 096 1 , 300 145 220 0 , 169 0 , 347 0 , 529 0 , 715 0 , 903 1 , 071 1 , 275 140 225 0 , 162 0 , 333 0 , 509 0 , 690 0 , 875 1 , 041 1 , 242 135 230 0 , 154 0 , 317 0 , 487 0 , 663 0 , 843 1 , 006 1 , 204 130 235 0 , 145 0 , 300 0 , 463 0 , 633 0 , 707 0 , 967 1 , 161 125 240 0 , 136 0 , 283 0 , 438 0 , 600 0 , 768 0 , 924 1 , 112 120 245 0 , 127 0 , 265 0 , 412 0 , 566 0 , 727 0 , 878 1 , 059 115 250 0 , 117 0 , 246 0 , 384 0 , 530 0 , 784 0 , 829 1 , 002 110 255 0 , 107 0 , 227 0 , 355 0 , 493 0 , 638 0 , 778 0 , 943 105 260 0 , 097 0 , 206 0 , 326 0 , 454 0 , 591 0 , 724 0 , 880 100 265 0 , 087 0 , 186 0 , 295 0 , 414 0 , 542 0 , 668 0 , 815 95 270 0 , 076 0 , 165 0 , 264 0 , 374 0 , 492 0 , 611 0 , 748 90 275 0 , 066 0 , 144 0 , 237 0 , 331 0 , 441 0 , 552 0 , 679 85 280 0 , 055 0 , 121 0 , 202 0 , 291 0 , 389 0 , 493 0 , 609 80 285 0 , 045 0 , 102 0 , 170 0 , 249 0 , 337 0 , 433 0 , 538 75 290 0 , 035 0 , 082 0 , 14● 0 , 209 0 , 286 0 , 372 0 , 466 70 295 0 , 025 0 , 062 0 , 109 0 , 169 0 , 234 0 , 312 0 , 394 65 300 0 , 016 0 , 042 0 , 079 0 , 126 0 , 183 0 , 253 0 , 322 60 305 0 , 006 0 , 023 0 , 049 0 , 087 0 , 133 0 , 194 0 , 252 55 310 0S002 0 , 004 0 , 021 0 , 048 0 , 084 0 , 136 0 , 176 50 315 0 , 011 0S013 0S005 0 , 011 0 , 037 0 , 080 0 , 114 45 320 0 , 019 0 , 030 0 , 031 0S025 0S009 0 , 026 0 , 048 40 325 0 , 027 0 , 045 0 , 056 0 , 058 0 , 052 0S025 0S015 35 330 0 , 034 0 , 060 0 , 079 0 , 091 0 , 093 0 , 075 0 , 072 30 335 0 , 040 0 , 073 0 , 100 0 , 120 0 , 132 0 , 122 0 , 134 25 340 0 , 045 0 , 085 0 , 119 0 , 147 0 , 168 0 , 166 0 , 187 20 345 0 , 050 0 , 096 0 , 136 0 , 171 0 , 200 0 , 206 0 , 238 15 350 0 , 054 0 , 105 0 , 151 0 , 192 0 , 229 0 , 241 0 , 284 10 355 0 , 057 0 , 111 0 , 161 0 , 210 0 , 253 0 , 273 0 , 325 05 360 0 , 059 0 , 116 0 , 171 0 , 224 0 , 273 0 , 296 0 , 359 00 Deg : of Equated Anomaly . Add Add Add Add Add Add Add Degrees of Equated Anomaly . 177 174 171 108 165 162 159 A Compounded Table of the ☽ Evection and Variation . Deg : of Eq ▪ Anomaly . 21 24 27 80 33 36 39 Deg. of Eq ▪ Anomaly . Sub. Sub Sub Sub Sub Sub : Sub : 0 0 , 359 0 , 396 0 , 427 0 , 454 0 , 475 0 , 491 0. 499 360 5 0 , 399 0 , 433 0 , 473 0 , 509 0 , 540 0 , 565 0. 585 355 10 0 , 412 0 , 461 0 , 511 0 , 556 0 , 596 0 , 632 0. 661 350 15 0 , 430 0 , 487 0 , 542 0 , 595 0 , 644 0 , 689 0. 728 345 20 0 , 441 0 , 505 0 , 567 0 , 626 0 , 683 0 , 737 0. 786 340 25 0 , 444 0 , 513 0 , 581 0 , 649 0 , 714 0 , 775 0. 829 335 30 0 , 440 0 , 513 0 , 588 0 , 662 0 , 734 0 , 805 0. 870 330 35 0 , 433 0 , 508 0 , 585 0 , 664 0 , 744 0 , 822 0. 896 325 40 0 , 418 0 , 496 0 , 575 0 , 659 0 , 742 0 , 827 0. 910 320 45 0 , 39● 0 , 475 0 , 559 0 , 647 0 , 734 0 , 822 0. 910 315 50 0 , 364 0 , 445 0 , 532 0 , 622 0 , 715 0 , 810 0. 002 310 55 0 , 329 0 , 409 0 , 495 0 , 589 0 , 684 0 , 784 0. 884 305 60 0 , 295 0 , 365 0 , 452 0 , 545 0 , 642 0 , 747 0. 850 300 65 0 , 234 0 , 312 0 , 398 0 , 493 0 , 593 0 , 697 0. 805 295 70 0 , 157 0 , 250 0 , 336 0 , 430 0 , 531 0 , 639 0. 749 290 75 0 , 116 0 , 184 0 , 265 0 , 356 0 , 457 0 , 566 0. 681 285 80 0 , 048 0 , 112 0 , 289 0 , 277 0 , 374 0 , 483 0. 598 280 85 0A024 0 , 033 0 , 107 0 , 189 0 , 284 0 , 389 0. 503 275 90 0 , 101 0A051 0 , 013 0 , 104 0 , 184 0 , 289 0. 402 270 95 0 , 182 0 , 140 0A083 0A010 0 , 077 0 , 178 0. 289 265 100 0 , 265 0 , 233 0 , 185 0 , 118 0A037 0 , 059 0. 166 260 105 0 , 349 0 , 327 0 , 289 0 , 232 0 , 157 0A067 0. 036 255 110 0 , 43● 0 , 424 0 , 395 0 , 348 0 , 290 0 , 199 0A102 250 115 0 , 520 0 , 521 0 , 503 0 , 465 0 , 410 0 , 336 0. 246 245 120 0 , 604 0 , 618 0 , 611 0 , 584 0 , 538 0 , 431 0. 392 240 125 0 , 688 0 , 713 0 , 718 0 , 703 0 , 668 0 , 613 0. 540 235 130 0 , 768 0 , 807 0 , 824 0 , 821 0 , 798 0 , 754 0. 690 230 135 0 , 848 0 , 899 0 , 928 0 , 937 0 , 925 0 , 892 0. 839 225 140 0 , 923 0 , 986 1 , 029 1 , 051 1 , 051 0 , 829 0. 987 220 145 0 , 992 0 , 068 1 , 124 1 , 159 1 , 171 1 , 163 1. 133 215 150 1 , 057 1 , 146 1 , 214 1 , 273 1 , 288 1 , 292 1. 274 210 155 1 , 114 1 , 217 1 , 280 1 , 358 1 , 401 1 , 414 1. 410 20● 160 1 , 168 1 , 280 1 , 353 1 , 445 1 , 499 1 , 529 1. 537 200 165 1 , 215 1 , 337 1 , 441 1 , 525 1 , 590 1 , 634 1. 657 195 170 1 , 254 1 , 387 1 , 502 1 , 598 1 , 675 1 , 729 1. 764 190 175 1 , 286 1 , 427 1 , 554 1 , 662 1 , 750 1 , 817 1. 864 185 180 1 , 312 1 , 462 1 , 595 1 , 714 1 , 815 1 , 894 1. 953 180 Deg : of Equated Anomaly . Sub Sub Sub Sub Sub Sub Sub Degree of Equated Aoumaly . 159 156 153 150 147 144 141 A Compounded Table of the ☽ Evection and Variation . Deg●ees of Eq : Anom . ●2 ●4 27 3● 33 36 39 Degrees of Eq : Anom . Adde Adde Adde Adde Add Adde Add 180 1 , 321 1 , 462 1 , 595 1 , 714 1 , 815 1 , 894 1 , 953 180 185 1 , 331 1 , 488 1 , 530 1 , 758 1 , 866 1 , 959 2 , 031 175 190 1 , 341 1 , 506 1 , 656 1 , 791 1 , 911 2 , 011 2 , 093 170 195 1 , 346 1 , 513 1 , 671 1 , 816 1 , 943 2 , 053 2 , 146 165 200 1 , 346 1 , 517 1 , 678 1 , 828 1 , 963 2 , 084 2 , 186 160 205 1 , 338 1 , 514 1 , 680 1 , 833 1 , 974 2 , 101 2 , 214 155 210 1 , 323 1 , 502 1 , 672 1 , 831 1 , 978 2 , 109 2 , 227 150 215 1 , 300 1 , 482 1 , 66● 1 , 818 1 , 970 2 , 109 2 , 232 145 220 1 , 275 1 , 455 1 , 629 1 , 795 1 , 952 2 , 096 2 , 226 140 225 1 , 242 1 , 422 1 , 619 1 , 765 1 , 923 2 , 072 2 , 208 135 230 1 , 204 1 , 332 1 , 557 1 , 725 1 , 886 2 , 033 2 , 177 130 235 1 , 161 1 , 336 1 , 509 1 , 67● 1 , 840 1 , 993 2 , 136 125 240 1 , 112 1 , 285 1 , 456 1 , 623 1 , 785 1 , 939 2 , 085 120 245 1 , 055 1 , 227 1 , 396 1 , 561 1 , 722 1 , 876 2 , 023 115 250 1 , 002 1 , 165 1 , 329 1 , 491 1 , 651 1 , 805 1 , 952 110 255 0. 943 ● , 000 1 , 258 1 , 416 1 , 576 1 , 725 1 , 872 105 260 0 , 880 1 , 031 1 , 184 1 , 337 1 , 4●9 1 , 637 1 , 782 100 265 0 , 815 0 , 959 1 , 106 1 , 253 1 , 401 1 , 544 1 , 687 95 270 0 , 748 0 , 884 1 , 024 1 , 170 1 , 307 1 , 448 1 , 586 90 275 0 , 679 0 , 807 0 , 939 1 , 073 1 , 210 1 , 345 1 , 480 85 280 0 , 609 0 , 718 0 , 852 0 , 979 1 , 108 1 , 238 1 , 368 80 285 0 , 5●8 0 , 648 0 , 763 0 , 8●2 1 , 004 1 , 128 1 , 252 75 290 0 , 466 0 , 567 0 , 674 0 , 784 0 , 898 1 , 015 1 , 132 70 295 0 , 394 0 , 485 0 , 564 0 , 685 0 , 791 0 , 899 1 , 010 65 300 0 , 322 0 , 40● 0 , 485 0 , 584 0 , 682 0 , 783 0 , 887 60 305 0 , 252 0 , ●23 0 , 40● 0 , 484 0 , 573 0 , 665 0 , 774 55 310 0 , 176 0 , 243 0 , 312 0 , 384 0 , 464 0 , 547 0 , 645 50 315 0 , 114 0 , 165 0 , 223 0 , 286 0 , 397 0 , 430 0 , 508 45 320 0 , 048 0 , 089 0 , 1●7 0 , 189 0 , 250 0 , 314 0 , 384 40 325 0S015 0 , 015 0 , 052 0 , 094 0 , 145 0 , 200 0 , 260 35 330 0 , 072 0S044 0S030 0 , 000 0 , 043 0 , 089 0 , 039 30 335 0 , 134 0 , 123 0 , 107 0S084 0S053 0S019 0 , 020 . 25 340 0 , 187 0 , 188 0 , 180 0 , 168 0 , 147 0 , 124 0S093 20 345 0 , 238 0 , 248 0 , 250 0 , 247 0 , 242 0 , 223 0 , 203 15 350 0 , 284 0 , 303 0 , 316 0 , 322 0 , 323 0 , 318 0 , 305 10 355 0 , 325 0 , 353 0 , 386 0 , 392 0 , 403 0 , 407 0 , 406 05 360 0 , 359 0 , 396 0 , 427 0 , 454 0 , 475 0 , 491 0 , 4●9 00 Deg : of Equated Anomaly . Add Add Add Add Add Add Add Degrees of Equtead Anomaly . 159 156 153 15● 147 144 141 A Compounded Table of the ☽ Evection and Variation . Equated Anomaly . 39 41 45 48 51 54 57 Equated Anomaly . Sub : Sub. Sub Sub Sub Sub Sub : 0 0. 499 0 , 502 0 , 501 0 , 495 0 , 481 0 , 468 0 , 447 360 5 0. 585 0 , 599 0 , 606 0 , 610 0 , 609 0 , 600 0 , 591 355 10 0. 661 0 , 686 0 , 705 0 , 719 0 , 726 0 , 729 0 , 651 350 15 0. 728 0 , 763 0 , 793 0 , 818 0 , 837 0 , 768 0 , 854 345 20 0. 786 0 , 83● ● , 870 0 , 906 0 , 935 0 , 959 0 , 976 340 25 0. 829 0 , 887 0 , 938 0 , 983 1 , 023 1 , 057 1 , 085 335 30 0. 870 0 , 933 0 , 992 1 , 049 1 , 099 1 , 144 1 , 182 330 35 0. 896 0 , 969 ● , 037 1 , 102 1 , 162 1 , 218 1 , 266 325 40 0. 910 0 , 99● 1 , 069 1 , 144 1 , 213 1 , 274 1 , 337 320 45 0. 910 1 , 001 ● , 087 1 , 171 1 , 252 1 , 327 1 , 401 3●5 50 0. 902 0 , 996 1 , 090 1 , 085 1 , 274 1 , 360 1 , 440 310 55 0. 884 0 , 982 1 , 082 1 , 182 1 , 282 1 , 378 1 , 467 305 60 0. 850 0 , 958 1 , 066 1 , 171 1 , 275 1 , 378 1 , 480 300 65 0. 805 0 , 918 1 , 031 1 , 146 1 , 259 1 , 367 1 , 473 295 70 0. 749 0 , 863 0 , 974 1 , 103 1 , 225 1 , 344 1 , 455 290 75 0. 681 0 , 800 ● , 922 1 , 110 1 , 175 1 , 301 1 , 426 285 80 0. 598 0 , 771 0 , 84● 0 , 979 1 , 109 ● , 243 1 , 375 280 8● ● . 503 0 , 628 ● , 758 0 , 894 1 , 033 1 , 167 1 , 307 275 90 0. 402 0 , 524 0 , 655 0 , 794 0 , 937 1 , 063 1 , 228 270 9● 0. 289 0 , 412 0 , 542 0 , 680 0 , 827 0 , 977 1 , 128 265 100 0. 166 0 , 292 0 , 418 0 , 558 0 , 704 0 , 845 1 , 053 260 105 0. 036 0 , 153 0 , 282 0 , 422 0 , 568 0 , 7●5 1 , 88● 255 110 0A102 0 , 01● 0 , 137 0 , 275 0 , 423 0 , 579 0 , 742 250 115 0. 246 0A137 0A016 0 , 119 0 , 266 0 , 442 0 , 591 245 120 0. 392 0 , 292 0 , 177 0A045 0 , 091 0 , 254 0 , 417 240 125 0. 540 0 , 449 0 , 341 0 , 216 0A076 0 , 077 0 , 239 235 130 0. 690 0 , 607 0 , 537 0 , 389 0 , 256 0A108 0 , 052 230 135 0. 839 0 , 766 0 , 675 0 , 565 0 , 448 0 , 296 0A141 225 140 0. 987 0 , 925 0 , 843 0 , 342 0 , 623 0 , 487 0 , 337 220 145 1. 133 1 , 081 1 , 010 0 , 918 0 , 808 0 , 680 0 , 536 215 150 1. 274 1 , 235 ● , 174 1 , 094 0 , 992 0 , 872 0 , 737 210 155 1. 410 1 , 383 1 , 234 1 , 263 1 , 172 1 , 062 0 , 935 205 160 1. 537 1 , 541 1 , 488 1 , 429 1 , 350 1 , 249 1 , 131 200 165 1. 657 1 , 656 1 , 633 1 , 587 1 , 520 1 , 431 1 , 323 195 170 1. 764 1 , 778 1 , 768 1 , 741 1 , 682 1 , 605 1 , 509 190 175 1. 864 1 , 888 1 , 892 1 , 875 1 , 833 1 , 769 1 , 685 185 180 1. 953 1 , 991 2 , 005 1 , 999 1 , 973 1 , 923 1 , 851 180 Equated Anomaly . Sub Sub Sub Sub Sub Sub Sub Equated Anomaly . 141 138 135 132 129 126 123 A Compounded Table of the ☽ Evection and Variation . Equated Anomaly . 39 42 45 4● 51 54 57 Equated Anomaly . Add Add Add Add Add Add Add 180 1. 953 1 , 991 2 , 005 1. 999 1 , 973 1 , 923 1 , 851 180 185 2. 031 2 , 081 2 , 108 2. 103 2 , 098 2 , 061 2 , 004 175 190 2. 093 2 , 157 2 , 199 2. 218 2 , 215 2 , 180 2 , 142 170 195 ● . 146 2 , 218 2 , 272 2. 306 2 , 317 2 , 303 2 , 270 165 200 2. 186 2 , 269 2 , 334 2. 376 2 , 402 2 , 403 2 , 383 160 205 2. 214 2 , 307 2 , 382 2. 436 2 , 471 2 , 484 2 , 479 155 210 2. 227 2 , 330 2 , 416 2. 482 2 , 526 2 , 552 2 , 555 150 215 2. 232 2 , 340 2 , 433 2. 507 2 , 568 2 , 603 2 , 620 145 220 2. 226 2 , 34● 2 , 441 2. 523 2 , 590 2 , 639 2 , 668 140 225 2. 208 2 , 330 2 , 4●7 2. 529 2 , 600 2 , 673 2 , 696 135 230 2. 177 2 , 300 2 , 419 2. 518 2 , 600 2 , 663 2 , 708 130 235 2. 136 2 , 267 2 , 387 2. 494 2 , 583 2 , 655 2 , 712 125 240 2. 085 2 , 220 2 , 343 2. 454 2 , 551 2 , 632 2 , 696 120 245 2. 023 2 , 161 2 , 288 2. 403 2 , 500 2 , 591 2 , 666 115 250 1. 952 2 , 091 2 , 219 2. 340 2 , 446 2 , 539 2 , 572 110 255 1. 872 2 , 012 2 , 143 2. 265 2 , 375 2 , 473 2 , 558 105 260 1. 782 1 , 923 2 , 056 2. 179 2 , 292 2 , 393 2 , 484 100 265 1. 687 1 , 825 1 , 957 2. 083 2 , 198 2 , 302 2 , 387 95 270 1. 586 1 , 721 1 , 851 1. 975 2 , 094 2 , 190 2 , 297 90 275 1. 480 1 , 611 1 , 739 1. 861 1 , 975 2 , 085 2 , 186 85 280 1. 368 1 , 496 1 , 620 1. 741 1 , 853 1 , 962 2 , 063 80 285 1. 252 1 , 375 1 , 496 1. 614 1 , 726 1 , 832 1 , 933 75 290 1. 132 1 , 250 1 , 366 1. 480 1 , 490 1 , 695 1 , 795 70 295 1. 010 1 , 111 1 , 233 1. 342 1 , 449 1 , 552 1 , 650 65 300 0. 887 0 , 991 1 , 096 1. 200 1 , 303 1 , 402 1 , 499 60 305 0. 774 0 , 884 0 , 957 1. 056 1 , 153 1 , 249 1 , 342 55 310 0. 645 0 , 725 0 , 814 0. 909 1 , 001 1 , 094 1 , 181 50 315 0. 508 0 , 590 0 , 675 0. 761 0 , 872 0 , 933 1 , 018 45 320 0. 384 0 , 457 0 , 537 0. 621 0 , 691 0 , 794 0 , 852 40 325 0. 260 0 , 325 0 , 493 0. 462 0 , 516 0 , 609 0 , 684 35 330 0. 039 0 , 195 0 , 254 0. 323 0 , 380 0 , 446 0 , 515 30 335 0. 020 0 , 067 0 , 117 0. 170 0 , 227 0 , 286 0 , 348 25 340 0S093 0S057 0S016 0. 028 0 , 076 0 , 128 0 , 183 20 345 0. 203 0 , 177 0 , 146 0S110 0S071 0S028 0 , 019 15 350 0. 305 0 , 291 0 , 270 0. 245 0 , 214 0 , 179 0S141 10 355 0. 406 0 , 400 0 , 388 0. 373 0 , 452 0 , 327 0 , 296 05 360 0. 499 0 , 502 0 , 501 0. 495 0 , 481 0 , 468 0 , 447 200 Equated Anomaly . Add Add Add Add Add Add Add Equated Anomaly ▪ 141 138 135 ●32 129 126 123 A Compounded Table of the ☽ Evection and Variation . Equated Anomaly . 57 68 63 66 69 72 ●5 Equated Anomaly . Sub Sub : Sub Sub Sub Sub Sub 0 0. 447 0 , 421 0 , 391 0. 358 0 , 320 0 , 280 0 , 237 360 5 0. 591 0 , 574 0 , 552 0. 550 0 , 496 0 , 462 0 , 424 355 10 0. 651 0 , 719 0 , 606 0. 688 0 , 665 0 , 639 0 , 607 350 15 0. 854 0 , 856 0 , 752 0. 843 0 , 828 0 , 809 0 , 784 345 20 0. 976 0 , 986 0 , 990 0. 990 0 , 981 0 , 972 0 , 954 340 25 1. 085 1 , 107 1 , 121 1. 127 1 , 129 1 , 126 1 , 116 335 30 1. 182 1 , 214 1 , 240 1. 258 1 , 268 1 , 227 1 , 269 330 35 1. 266 1 , 309 1 , 345 1. 374 1 , 396 1 , 402 1 , 413 325 40 1. 337 1 , 392 1 , 348 1. 477 1 , 508 1 , 593 1 , 549 320 45 1. 401 1 , 459 1 , 517 1. 567 1 , 608 1 , 642 1 , 668 315 50 1. 440 ● , 513 1 , 580 1. 640 1 , 694 1 , 739 1 , 774 310 55 1. 467 1 , 589 1 , 631 1. 700 1 , 758 1 , 820 1 , 866 305 60 1. 480 1 , 575 1 , 663 1. 746 1 , 819 1 , 885 1 , 941 300 65 1. 473 1 , 579 1 , 680 1. 772 1 , 857 1 , 936 2 , 001 295 70 1. 455 1 , 569 1 , 676 1. 781 1 , 878 1 , 966 2 , 046 290 75 1. 426 1 , 549 1 , 663 1. 772 1 , 878 1 , 981 2 , 070 285 80 1. 375 1 , 506 1 , 63● 1. 754 1 , 966 1 , 973 2 , 074 280 85 1. 307 1 , 448 1 , 562 1. 713 1 , 839 1 , 953 2 , 074 275 90 1. 228 1 , 373 1 , 514 1. 655 1 , 749 1 , 920 2 , 035 270 95 1. 128 1 , 282 1 , 433 1. 578 1 , 622 1 , 863 1 , 993 265 100 1. 013 1 , 172 1 , 331 1. 487 1 , 639 1 , 785 1 , 929 260 105 0. 882 1 , 045 1 , 211 1. 375 1 , 538 1 , 696 1 , 845 255 110 0. 742 0 , 907 1 , 074 1. 246 1 , 424 1 , 583 1 , 744 250 115 0. 591 0 , 755 0 , 894 1. 101 1 , 275 1 , 451 1 , 621 245 120 0. 417 0 , 589 0 , 765 0. 945 1 , 124 1 , 303 1 , 479 240 125 0. 239 0 , 411 0 , 589 0. 772 0 , 957 1 , 194 1 , 325 235 130 0. 052 0 , 223 0 , 402 0. 587 0 , 775 0 , 973 1 , 156 230 135 0A141 0 , 026 0 , 204 0. 390 0 , 581 0 , 776 0 , 970 225 140 0. 337 0A175 0 , 000 0. 184 0 , 377 0 , 574 0 , 772 220 145 0. 536 0 , 378 0A208 0A026 0 , 163 0 , 361 0 , 563 215 150 0. 737 0 , 584 0 , 419 0. 240 0A063 0 , 142 0 , 344 210 155 0. 935 0 , 790 0 , 631 0. 458 0 , 273 0A080 0 , 119 205 160 1. 131 0 , 994 0 , 842 0. 675 0 , 495 0 , 306 0A107 200 165 1. 323 1 , 195 1 , 051 0. 891 0 , 717 0 , 533 0 , 337 195 170 1. 509 1 , 392 1 , 257 1. 104 0 , 937 0 , 683 0 , 568 190 175 1. 685 1 , 580 1 , 455 1. 322 1 , 153 0 , 979 0 , 784 185 180 1. 85● 1 , 758 1 , 645 1. 513 1 , 363 1 , 198 1 , ●19 180 Equated Anomaly . Sub Sub Sub Sub Sub Sub Sub Equated Anomaly . 123 120 117 ●14 111 108 105 A Compounded Table of the ☽ Evection and Variation ▪ Equated Anomaly . 57 60 63 66 69 72 75 Equated Anomaly . Adde Adde Adde Adde Add Adde Add ▪ 180 1 , 851 1 , 758 1 , 645 1 , 513 1 , 363 1 , 198 1 , 1●9 180 185 2 , 004 1 , 924 1 , 829 1 , 7●2 1 , 564 1 , 409 1 , 2●8 175 190 2 , 142 2 , 07● 1 , 990 1 , 880 1 , 753 1 , 608 1 , 448 17● 195 2 , 270 2 , 214 2 , 139 2 , 044 1 , 930 1 , 796 1 , 646 165 200 2 , 383 2 , 341 2 , 278 2 , 191 2 , 090 1 , 970 1 , 831 160 205 2 , 479 2 , 451 2 , 401 2 , 3●9 2 , 238 2 , 126 2 , 001 1●5 210 2 , 555 2 , 541 2 , 507 2 , 448 2 , 369 2 , 272 2 , 154 150 215 2 , 620 2 , 617 2 , 591 2 , 548 2 , 483 2 , 400 2 , 296 145 220 2 , 668 2 , 675 2 , 663 2 , 629 2 , 576 2 , 509 2 , 419 140 225 2 , 696 2 , 717 2 , 717 2 , 695 2 , 656 2 , 596 2 , 520 135 230 2 , 708 2 , 738 2 , 748 2 , 744 2 , 715 2 , 668 2 , 604 130 235 2 , 712 2 , 748 2 , 767 2 , 769 2 , 756 2 , 723 2 , 669 125 240 2 , 696 2 , 744 2 , 774 2 , 781 2 , 775 2 , 755 2 , 711 120 245 2 , 660 2 , 758 2 , 760 2 , 782 2 , 784 2 , 129 ● , 739 115 250 2 , 572 2 , 682 2 , 727 2 , 761 2 , 774 2 , 773 2 , 750 110 255 2 , 558 2 , 628 2 , 684 2 , 724 2 , 748 2 , 755 2 , 746 105 260 2 , 484 2 , 56● 2 , 623 ● , 687 2 , 701 2 , 7●● 2 , 721 100 265 2 , 387 2 , 478 2 , 547 2 , 601 2 , 640 2 , 666 2 , 677 95 270 2 , 297 2 , 383 2 , 457 2 , 517 2 , 56● 2 , 600 2 , 616 90 275 2 , 186 2 , 276 2 , 354 2 , 419 2 , 473 2 , 514 2 , 541 85 280 2 , 063 2 , 155 2 , 238 2 , 309 2 , 368 2 , 415 2 , 449 80 285 1 , 933 2 , 025 2 , 109 ● , 185 2 , 241 2 , 303 2 , 343 75 290 1 , 795 1 , 888 1 , 97● 2 , 048 2 , 117 2 , 176 2 , 224 70 295 1 , 650 1 , 743 1 , 829 1 , 904 1 , 975 2 , 036 2 , 088 65 300 1 , 499 1 , 590 1 , 676 1 , 754 1 , 798 1 , 889 1 , 944 60 305 1 , 342 1 , 431 1 , 516 1 , 595 1 , 663 1 , 733 1 , 791 55 310 1 , 181 1 , 268 1 , 350 1 , 416 1 , 502 1 , 569 1 , 629 50 315 1 , 018 1 , 100 1 , 181 1 , 257 1 , 329 1 , 397 1 , 459 45 320 0 , 852 0 , 930 1 , 007 1 , 081 1 , 152 1 , 219 1 , 281 40 325 0 , 684 0 , 758 0 , 831 0 , 902 0 , 971 1 , 037 1 , 099 35 330 0 , 515 0 , 584 0 , 654 0 , 717 0 , 787 0 , 841 0 , 913 30 335 0 , 348 0 , 410 0 , 474 0 , 538 0 , 602 0 , 664 0 , 723 25 340 0 , 183 0 , 238 0 , 295 0 , 333 0 , 424 0 , 473 0 , 531 20 345 0 , 019 0 , 067 0 , 119 0 , 172 0 , 226 0 , 282 0 , 337 15 350 0S141 0S099 0S054 0S006 0 , 042 0 , 092 0 , 144 10 355 0 , 296 0 , 262 0 , 224 0 , 184 0S140 0S095 0S048 05 360 0 , 447 0 , 421 0 , 391 0 , 358 0 , 320 0 , 280 0 , 237 00 Equated Anomaly . Add Add Add Add Add Add Add Equated Anomaly . 123 12● 117 114 ●11 108 105 A Compounded Table of the ☽ Evection and Variation . Equated Anomaly . 75 78 81 84 ●7 90   Equated Anomaly : Sub : Sub. Sub Sub Sub Sub   0 0. 237 0 , 193 0 , 146 0 , 099 0 , 050 0 , 000   360 5 0. 424 0 , 384 0 , 341 0 , 295 0 , 249 0 , 201   355 10 0. 607 0 , 571 0 , 532 0 , 490 0 , 446 0 , 399   350 15 0. 784 0 , 754 0 , 720 0 , 682 0 , 640 0 , 596   345 20 0. 954 0 , 931 0 , 902 0 , 869 0 , 831 0 , 789   340 25 1. 116 1 , 100 1 , 078 1 , 050 1 , 016 1 , 978   335 30 1. 269 1 , 260 ● , 245 1 , 224 1 , 198 1 , 161   330 35 1. 413 1 , 412 1 , 403 1 , 351 1 , 366 1 , 337   325 40 1. 549 1 , 555 1 , 553 1 , 544 1 , 528 1 , 505   320 45 1. 668 1 , 686 1 , 694 1 , 692 1 , 681 1 , 664   315 50 1. 774 1 , 801 1 , 819 1 , 827 1 , 826 1 , 813   310 55 1. 866 1 , 903 1 , 930 1 , 947 1 , 955 1 , 953   305 60 1. 941 1 , 990 2 , 028 2 , 054 2 , 071 2 , 077   300 65 2. 001 2 , 059 2 , 100 2 , 146 2 , 172 2 , 186   295 70 2. 046 2 , 115 2 , 171 2 , 213 2 , 257 2 , 282   290 75 2. 070 2 , 151 2 , 221 2 , 279 2 , 325 2 , 359   285 80 2. 074 2 , 170 2 , 249 2 , 319 2 , 378 2 , 422   280 85 2. 074 2 , 165 2 , 259 2 , 342 2 , 411 2 , 467   275 90 2. 035 2 , 150 2 , 250 2 , 342 2 , 426 2 , 493   270 95 1. 993 2 , 118 2 , 229 2 , 329 2 , 418 2 , 498   265 100 1. 929 2 , 060 2 , 186 2 , 300 2 , 397 2 , 487   260 105 1. 845 1 , 987 2 , 123 2 , 242 2 , 362 2 , 463   255 110 1. 744 1 , 897 2 , 040 2 , 176 2 , 302 2 , 414   250 115 1. 621 1 , 786 1 , 942 2 , 087 2 , 221 2 , 347   245 120 1. 479 1 , 654 1 , 821 1 , 979 2 , 127 2 , 259   240 125 1. 325 1 , 504 1 , 681 1 , 848 2 , 008 2 , 155   235 130 1. 156 1 , 344 1 , 524 1 , 699 1 , 870 2 , 000   230 135 0. 970 1 , 16● 1 , 355 1 , 539 1 , 714 1 , 881   225 140 0. 772 0 , 972 1 , 168 1 , 360 1 , 547 1 , 722   220 145 0. 563 0 , 766 0 , 968 1 , 166 1 , 367 1 , 547   215 150 0. 344 0 , 550 0 , 755 0 , 960 1 , 161 1 , 355   210 155 0. 119 0 , 325 0 , 533 0 , 742 0 , 949 1 , 149   20● 160 0A107 0 , 197 0 , 304 0 , 515 0 , 726 1 , 932   200 165 0. 337 0A068 0 , 073 0 , 283 0 , 495 0 , 705   195 170 0. 468 0 , 367 0A161 0 , 049 0 , 261 0 , 473   190 175 0. 784 0 , 599 0 , 397 0A188 0 , 025 0 , 238   185 180 1. 019 0 , 828 0 , 630 0 , 424 0A214 0 , 000   180 Equated Anomaly . Sub Sub Sub Sub Sub Sub   Equated Anomaly . 105 102 099 96 93 90   A Compounded Table of the ☽ Evection and Variation . Equated Anomaly . 75 7● 81 84 87 90   Equated Anomaly .   Adde Adde Adde Adde Adde Adde     180 1 , 019 0 , 828 0 , 630 0 , 424 0 , 214 0 , 000   180 185 1 , 238 1 , 054 0 , 860 0 , 658 0 , 450 0 , 238   175 190 1 , 448 1 , 271 1 , 085 0 , 888 0 , 684 0 , 473   170 195 1 , 646 1 , 480 1 , 302 1 , 112 0 , 912 0 , 705   165 200 1 , 831 1 , 682 1 , 507 1 , 326 1 , 133 0 , 932   160 205 2 , 001 1 , 858 1 , 699 1 , 527 1 , 343 1 , 146   155 210 2 , 154 2 , 022 1 , 886 1 , 716 1 , 540 1 , 355   150 215 2 , 296 2 , 175 2 , 035 1 , 886 1 , 719 1 , 547   145 220 2 , 149 2 , 310 2 , 184 2 , 044 1 , 887 1 , 722   140 225 2 , 520 2 , 426 2 , 313 2 , 184 2 , 040 1 , 881   135 230 2 , 604 2 , 518 2 , 412 2 , 307 2 , 175 2 , 000   130 235 2 , 966 2 , 598 2 , 509 2 , 405 2 , 294 2 , 155   125 240 2 , 711 2 , 657 2 , 580 2 , 489 2 , 380 2 , 259   120 245 2 , 739 2 , 661 2 , 633 2 , 553 2 , 456 2 , 347   115 250 2 , 750 2 , 712 2 , 661 2 , 596 2 , 513 2 , 414   110 255 2 , 746 2 , 719 2 , 674 2 , 616 2 , 552 2 , 463   105 260 2 , 721 2 , 705 2 , 674 2 , 626 2 , 561 2 , 487   100 265 2 , 677 2 , 673 2 , 652 2 , 616 2 , 566 2 , 498   95 270 2 , 616 2 , 621 2 , 611 2 , 588 2 , 547 2 , 493   90 275 2 , 541 2 , 554 2 , 546 2 , 538 2 , 511 2 , 467   85 280 2 , 449 2 , 471 2 , 479 2 , 473 2 , 453 2 , 422   80 285 2 , 343 2 , 371 2 , 388 2 , 392 2 , 383 2 , 359   75 290 2 , 224 2 , 259 2 , 282 2 , 294 2 , 294 2 , 282   70 295 2 , 088 2 , 132 2 , 163 2 , 182 2 , 190 2 , 186   65 300 1 , 944 1 , 990 2 , 028 2 , 057 2 , 07● 2 , 077   60 305 1 , 791 1 , 840 1 , 882 1 , 915 1 , 939 1 , 953   55 310 1 , 629 1 , 682 1 , 725 1 , 764 1 , 792 1 , 813   50 315 1 , 459 1 , 515 1 , 561 1 , 605 1 , 638 1 , 664   45 320 1 , 281 1 , 335 1 , 391 1 , 436 1 , 474 1 , 505   40 325 1 , 099 1 , 157 1 , 21● 1 , 260 1 , 302 1 , 337   35 330 0 , 913 0 , 971 1 , 026 1 , 076 1 , 124 1 , 161   30 335 0 , 723 0 , 780 0 , 835 0 , 887 0 , 934 0 , 978   25 340 0 , 531 0 , 587 0 , 638 0 , 694 0 , 743 0 , 789   20 345 0 , 337 0 , 392 0 , 447 0 , 499 0 , 548 0 , 596   15 350 0 , 144 0 , 196 0 , 248 0 , 300 0 , 351 0 , 399   10 355 0S048 0S000 0S050 0S108 0 , 149 0 , 201   05 360 0 , 273 0 , 193 0 , 146 0 , 099 0S050 0 , 000   00 Equated Anomaly . Add Add Add Add Add Add   Equated Anomaly .   105 102 99 96 93 90     A Table of the Aequations of Nodes and Moons Latitude .     Eq : Nod : Adde Scruples of prop. Latit . ☽ Eccesse Adde         D. Parts . Parts . D. parts . Parts .     0 180 0. 00000 , 00000 0 , 00000 , 00000 180 360 1 181 0 , 06389 , 00030 0 , 08694 , 00556 179 359 2 182 0 , 12750 , 00120 0 , 17361 , 01111 178 358 3 183 0 , 19083 , 00274 0 , 26000 , 01639 177 357 4 184 0 , 25389 , 00487 0 , 34639 , 02194 176 356 5 185 0 , 31667 , 00760 0 , 43278 , 02750 175 355 6 186 0 , 37944 , 01093 0 , 51917 , 03305 174 354 7 187 0 , 44139 , 01485 0 , 60528 , 03861 173 353 8 188 0 , 50250 , 01937 0 , 69139 , 04389 172 352 9 189 0 , 56305 , 02447 0 , 77722 , 04917 171 351 10 190 0 , 62305 , 03015 0 , 86278 , 05472 170 350 11 191 0 , 68222 , 03641 0 , 94806 , 06000 169 ●49 12 192 0 , 74056 , 04323 1 , 03972 , 06528 168 348 13 193 0 , 79778 , 05060 1 , 11778 , 07083 167 347 14 194 0 , 85389 , 05853 1 , 20222 , 07611 166 346 15 195 0 , 90889 , 06699 1 , 28611 , 08139 165 345 16 196 0 , 96307 , 07598 1 , ●6972 , 08694 164 344 17 197 1 , 01556 , 08548 1 , 45278 , 09222 163 343 18 198 1 , 06●67 , 09549 1 , 53556 , 09750 162 342 19 199 1 , 11639 , 10599 1 , 61778 , 10278 161 341 20 200 1 , 16472 , 11698 1 , 69944 , 10778 160 340 21 201 1 , 21167 , 12843 1 , 78083 , 11305 159 339 22 202 1 , 25694 , 14033 1 , 86139 , 11833 158 338 23 203 1 , 30056 , 15267 1 , 94167 , 12333 157 337 24 204 1 , 34250 , 1654● 2 , 02139 , 12833 156 336 25 205 1 , 38944 , 17861 2 , 10028 , 13333 155 335 26 206 1 , 42111 , 19217 2 , 17861 , 13833 154 334 27 207 1 , 45778 , 20611 2 , 25639 , 14●06 153 333 28 208 1 , 39278 , 22287 2 , 33333 , 14806 152 332 29 209 1 , 52611 , 23504 2 , 40944 , 15306 151 331 30 210 1 , 55778 , 25000 2 , 48500 , 15778 150 330 30 210 1. 55778 , 25000 2 , 48500 , 15778 150 330 31 211 1 , 58667 , 26526 2 , 56000 , 16250 149 329 32 212 1 , 61306 , 28081 2 , 63417 , 16722 148 328 33 213 1 , 63667 , 29663 2 , 70722 , 17●67 147 327 34 214 1 , 65861 , 31270 2 , 77944 , 17639 146 326 35 215 1 , 67833 , 32899 2 , 85111 , 18083 145 325 36 216 1 , 69583 , 34549 2 , 92194 , 18528 144 324 37 217 1 , 71222 , 36218 2 , 99167 , 18972 143 323 38 218 1 , 72722 , 37904 3 , 06056 , 19417 142 322 39 219 1 , 74139 , 39640 3 , 12861 , 19861 141 321 40 220 1 , 75222 , 41318 3 , 19556 , 20306 140 320 41 221 1 , 75944 , 43041 3 , 26167 , 20732 139 319 42 222 1 , 76389 , 44774 3 , 32667 , 21139 138 318 43 223 1 , 76556 , 46512 3 , 39056 , 21556 137 317 44 224 1 , 76639 , 48255 3 , 45361 , 21944 136 316 45 225 1 , 76667 , 50000 3 , 51564 , 22346 135 315 46 226 1 , 76472 , 51744 3 , 57639 , 22722 134 314 47 227 1 , 76000 , 53487 3 , 63611 , 23111 133 313 48 228 1 , 75361 , 55226 3 , 69500 , 23472 132 312 49 229 1 , 74472 , 56953 3 , 75194 , 23833 131 311 50 230 1 , 733●3 , 58682 3 , 80833 , 24194 130 310 51 231 1 , 71944 , 60395 3 , 86444 , 24556 129 309 52 232 1 , 70389 , 62096 3 , 91917 , 24917 128 308 53 233 1 , 68611 , 63781 3 , 97194 , 25250 127 307 54 234 1 , 66639 , 65451 4 , 02306 , 25583 126 306 55 235 1 , 64500 , 67101 4 , 07333 , 25917 125 305 56 236 1 , 62167 , 68730 4 , 12250 , 26194 124 304 57 237 1 , 59611 , 70336 4 , 17083 , 26500 123 303 58 238 1 , 56889 , 71918 4 , 21806 , 26806 120 302 59 239 1 , 5397● , 7347● 4 , 26306 , 27083 101 301 60 240 1 , 50889 , 75000 4 , 30722 , 27361 120 300 60 240 1 , 50889 , 75000 4 , 30722 , 27361 120 300 61 241 1 , 47611 , 76496 4 , 34972 , 27639 119 299 62 242 1 , 44167 , 77959 4 , 39111 , 27917 118 298 63 243 1 , 40583 , 79389 4 , 43139 , 28194 117 297 64 244 1 , 36833 , 80783 4 , 47028 , 28444 116 296 65 245 1 , 32917 , 82439 4 , 50778 , 28667 115 295 66 246 1 , 28833 , 83456 4 , 54389 , 28889 114 294 67 247 1 , 24667 , 84732 4 , 57861 , 29111 113 293 68 248 1 , 20250 , 85967 4 , 61194 , 29333 112 292 69 249 1 , 15750 , 87152 4 , 64389 , 29528 111 291 70 250 1 , 11139 , 88302 4 , 67417 , 29750 110 290 71 251 1 , 06361 , 89400 4 , 70306 , 29944 109 289 72 252 1 , 01417 , 90450 4 , 73056 , 30139 108 288 73 253 0 , 96389 , 91451 4 , 75639 , 30333 107 287 74 254 0 , 91306 , 92402 4 , 78111 , 30500 106 286 75 255 0 , 86167 , 93301 4 , 80500 , 30639 105 285 76 256 0 , 80889 , 94147 4 , 32639 , 30750 104 284 77 257 0 , 75500 , 94939 4 , 84694 , 30861 103 283 78 258 0 , 70000 , 95177 4 , 86611 , 30944 102 282 79 259 0 , 64444 , 96359 4 , 88333 , 31056 101 281 80 260 0 , 58833 , 96984 4 , 89917 , 31167 100 280 81 261 0 , 53139 , 97552 4 , 91●61 , 31250 99 279 82 262 0 , 47389 , 98063 4 , 92667 , 31333 98 278 83 263 0 , 41583 , 98514 4 , 9●806 , 31417 97 277 84 264 0 , 35722 , 98907 4 , 94778 , 31472 96 276 85 265 0 , 29833 , 99240 4 , 95611 , 31528 95 275 86 266 0 , 23917 , 99513 4 , 96278 , 31556 94 274 87 267 0 , 17944 , 99726 4 , 96833 , 31583 93 273 88 268 0 , 11972 , 99878 4 , 97167 , 31611 92 272 89 269 0 , 06000 , 99964 4 , 97389 , 31639 91 271 90 270 0 , 00000 , 00000 4 , 97500 , 31667 90 270     Subst .           A Table of the Moons Reductions to the Ecliptick .     Reduct . Subst .         D. parts .     0 180 , 00000 180 360 1 181 , 00417 179 359 2 182 , 00833 178 358 3 183 , 01250 177 357 4 184 , 01639 176 356 5 185 , 02028 175 355 6 186 , 02417 174 354 7 187 , 02833 173 353 8 188 , 03222 172 352 9 189 , 03611 171 351 10 190 , 04000 170 350 11 191 , 04389 169 349 12 192 , 04778 168 348 13 193 , 05●67 167 347 14 194 , 05528 166 346 15 195 , 05889 165 345 16 196 , 06194 164 344 17 197 , 06556 163 343 18 198 , 06●89 162 342 19 199 , 07194 161 341 20 200 , 07500 160 340 21 201 , 07806 159 339 22 202 , 08111 158 338 23 203 , 08389 157 337 24 204 , 08694 156 336 25 205 , 08944 155 335 26 206 , 09194 154 334 27 207 , 09444 153 333 28 208 , 09694 152 332 29 209 , 09944 151 331 ●0 210 , 10278 150 330 30 210 , 10167 150 330 31 211 , 10333 149 329 32 212 , 10500 148 328 33 213 , 10667 147 327 34 214 , 10806 146 326 35 215 , 10972 145 325 36 216 , 11111 144 324 37 217 , 11222 143 323 38 218 , 11306 142 322 39 219 , 11417 141 321 40 220 , 11500 140 320 41 221 , 11556 139 219 42 222 , 11583 138 318 43 223 , 11611 137 317 44 224 , 11639 136 316 45 225 , 11667 135 315 46 226 , 11639 134 314 47 227 , 11611 133 313 48 228 , 11583 132 212 49 229 , 11556 131 311 50 230 , 11500 130 310 51 231 , 11417 129 309 52 232 , 11306 128 308 53 233 , 11222 127 307 54 234 , 11111 126 306 55 235 , 10972 125 305 56 236 , 10778 124 304 57 237 , 10639 12● 303 58 238 , 10472 122 302 59 239 , 10306 121 391 60 240 , 10139 120 300 60 240 , 10139 120 300 61 241 , 09917 119 299 62 242 , 09667 118 298 63 243 , 09417 117 297 64 244 , 09167 116 296 65 245 , 08917 115 295 66 246 , 08667 114 294 67 247 , 08361 113 293 68 248 , 08083 112 292 69 249 , 07778 111 291 70 250 , 07472 110 290 71 251 , 07167 109 289 72 252 , 06833 108 288 73 253 , 06528 107 287 74 254 , 06167 106 286 75 255 , 05861 105 285 76 256 , 05500 104 284 77 257 , 05139 103 283 78 258 , 04750 102 282 79 259 , 04389 101 281 80 260 , 03972 100 280 81 261 , 03583 99 279 82 262 , 03194 98 278 83 263 , 02806 97 277 84 264 , 02389 96 276 85 265 , 02000 95 275 86 266 , 01611 94 274 87 267 , 01250 93 273 88 268 , 00833 92 272 89 269 , 00417 91 271 90 270 , 00000 90 270     Adde     The difference of the true ☌ or ☍ from the middle of the Obscuration . Lat. ☽ Differ . D. par Parts . 0 , 10 , 00861 0 , 20 , 01722 0 , 30 , 02611 0 , 40 , 03500 0 , 50 , 04361 0 , 60 , 05222 0 , 70 , 06083 0 , 80 , 06972 0 , 90 , 07833 1 , 00 , 08722 1 , 10 , 09583 1 , 20 , 10472 1 , 30 , 11361 1 , 40 , 12222 1 , 50 , 13083 1 , 60 , 13944 Latitude . ☽ North Desc. Adde South Asc. Adde North Asc. Subst . South Desc. Subst . A Table of the Meane Lunations . Yeers Hours : Parts Months . Common . Bissextile . Daies Hours 1 255 , 18944 complea . Hours : parts . Hours : Parts . 2 510 , 37889 January 0035 , 26556 0035 , 26556 1 24 3 056 , 83417 Februa . 0707 , 26556 0022 , 531●9 2 48 B4 336 , 02361 March. 0043 , 7972● 0057 79722 3 72 5 591 , 21306 April . 0045 , 06306 0069 , 06306 4 96 6 137 , 66833 May. 0080 , 32889 0104 , 32889 5 120 7 392 , 85778 June . 0091 , 59472 0115 , 59472 6 144 B8 673 , 04722 July . 0126 , 86028 0150 , 86028 7 168 9 218 , 50250 August 0162 , 12611 0186 , 12611 8 192 10 473 , 69194 Septem . 0173 , 39194 0197 , 39194 9 216 11 020 , 14722 October 0208 , 65778 0232 , 65778 10 240 B12 299 , 33667 Novem 0219 , 92361 0243 , 92361 11 264 13 554 , 52611 Decem. 0255 , 18944 0279 , 18944 12 288 14 100 , 98139       13 312 15 356 , 17083 Canonion Syzygiarum . 14 336 B16 635 , 36028   ☌ ☍ 15 360 17 181 , 81556       16 384 18 437 , 00500   Hours : Parts Hours : Parts . 17 408 19 692 , 19444 I 0708 , 73417 0354 , 36722 18 432 B20 262 , 64972 II 1417 , 46833 1063 , 10139 19 456 40 525 , 29944 III 2126 , 20250 1771 , 83556 20 480 60 079 , 21528 IV 2834 , 03667 2480 , 56972 21 504 80 341 , 86500 V 3543 , 67083 3189 , 30361 22 528 100 604 , 51472 VI 4252 , 40500 3898 , 03806 23 552 200 500 , 29556 VII 4961 , 13944 4606 , 77222 24 576 300 396 , 07639 VIII 5669 , 87361 5315 , 50667 25 600 400 291 , 85694       26 624 500 187 , 63778 Epochae . 27 648 600 083 , 41861 Yeares Compleat . Hours : Parts . 28 672 700 687 , 93361       29 696 800 583 , 71417   Christi . 0425 , 70667 30 720 900 479 , 49500   1600 0176 , 06694     1000 375 , 27583   1620 0439 , 31667     2000 041 , 81750   1640 0701 , 96639     3000 417 , 09333   1660 0255 , 88194     The Horizontal Parallaxes , Semidiameters , and Hourly motions of the Sun and Moon . Degrees Horiz . Paral. ☉ Semidiam . ☉ Hourly motion . ☉ Semia . Cone Shad. Horizō . Paralax . ☽ Semidiam . ☽ Hourly motion ☽ Degrees   Parts . Parts . Parts . Parts . Parts . Parts . Parts .   0 , 03855 , 26936 , 03972 , 22948 , 92692 . 25964 , 49444 360 6 , 03859 , 26968 , 03981 , 22980 , 92982 . 26043 , 49916 354 12 , 03863 , 27001 , 03990 , 23013 , 93273 . 26122 , 50388 348 18 , 03868 , 27033 , 03999 , 23046 , 93564 . 26201 , 50860 342 24 , 03872 , 27066 , 04008 , 23078 , 93854 . 26280 , 51332 336 30 , 03876 , 27099 , 04017 , 23111 , 94145 . 26359 , 51804 330 36 , 03881 , 27131 , 04026 , 2●144 , 94436 . 26438 , 52276 324 42 , 03885 , 27164 , 04035 , 23176 , 94727 . 26517 , 52748 318 48 , 03889 , 27196 , 04044 , 23209 , 95018 . 26596 , 53220 312 54 , 03894 , 27239 , 04052 , 23242 , 95308 . 26679 , 53682 306 60 , 03898 , 27271 , 04061 , 23274 , 95599 . 26754 , 54164 300 66 , 03902 , 27304 , 04070 , 23307 , 95889 . 26833 , 54636 294 72 , 03907 , 27337 , 04079 , 23340 , 96180 . 26912 , 55108 288 78 , 03911 , 27369 , 04088 , 23372 , 96471 . 26991 , 55581 282 84 , 03915 , 27401 , 04097 , 23405 , 96762 . 27069 , 55953 276 90 , 03919 , 27433 , 04106 , 23438 , 97052 . 27148 , 56425 270 96 , 03924 , 27466 , 04115 , 23470 , 97343 . 27227 , 56897 264 102 , 03928 , 27498 , 04124 , 23503 , 97634 . 27306 , 57369 258 108 , 03932 , 27531 , 04132 , 23536 , 97925 . 27385 , 57841 252 114 , 03937 , 27564 , 04141 , 23568 , 98215 . 27464 , 58313 246 120 , 03941 , ●7596 , 04150 , 23601 , 98506 . 27543 , 58785 240 126 , 03945 , 27629 , 04159 , 23634 , 98797 . 27622 , 59257 234 132 , 03950 , 27661 , 04168 , 23666 , 99087 . 27701 , 59729 228 138 , 03954 , 27694 , 04177 , 23699 , 99378 . 27780 , 60201 222 144 , 03958 , 27727 , 04186 , 23732 , 99669 . 27859 , 60673 216 150 , 03963 , 27759 , 04195 , 23764 , 99960 . 27938 , 61145 210 156 , 03967 , 27792 , 04204 , 23797 1 , 00250 . 28017 , 61617 2●4 162 , 03971 , 27824 , 04213 , 23830 1 , 00541 . 28096 , 62089 198 168 , 03976 , 27857 , 04222 , 23863 1 , 00832 . 28175 , 62461 192 174 , 03981 , 27889 , 04231 , 23896 1 , 01123 . 28254 , 6●933 186 180 , 03988 , ●7916 , 04250 , 23928 1 , 01414 . 28333 , ●3611 180 Dist ▪ 4 32 9 33 291 79 472 erēc The Declination and Meridian Angles .   ♈ ♎ ♉ ♏ ♊ ♐     Declina . Ang. Declina . Ang. Declina . Ang.     D. parts D. P. D. Parts . D. P. D. Parts . D. P.   0 0 , 00000 66. 47 11 , 51167 69 , 33 20 , 22278 77. 70 30 1 0 , 39889 66. 47 11 , 86333 69 , 52 20 , 43917 78. 07 29 2 0 , 79806 56. 48 12 , 21111 69 , 72 20 , 63583 78. 43 28 3 1 , 19694 66. 50 12 , 55583 69 , 92 20 , 83278 78. 80 27 4 1 , 59528 66. 52 12 , 89694 70 , 13 21 , 02361 79. 18 26 5 1 , 99361 66. 55 13 , 23472 70 , 35 21 , 20806 79. 57 25 6 2 , 39111 66. 58 13 , 56861 70 , 58 21 , 38528 79. 95 24 7 2 , 78778 66. 63 13 , 89917 70 , 81 21 , 55611 80. 33 23 8 3 , 18444 66. 68 14 , 22556 71 , 05 21 , 72083 80. 72 22 9 3 , 57972 66. 73 14 , 54806 71 , 30 21 , 87833 81. 12 21 10 3 , 97444 66. 78 14 , 86639 71 , 55 22 , 02917 81. 51 20 11 4 , 36778 66. 85 15 , 18056 71 , 80 22 , 17278 81. 92 19 12 4 , 76028 66. 92 15 , 49056 72 , 07 22 , 30972 82. 31 18 13 5 , 15139 67. 00 15 , 79639 72 , 33 22 , 43944 82. 73 17 14 5 , 54139 67. 08 16 , 09750 72 , 60 22 , 56222 83. 15 16 15 5 , 92972 67 , 18 16 , 39417 72 , 88 22 , 67750 83. 57 15 16 6 , 31611 67. 28 16 , 68861 73 , 17 22 , 78611 83. 98 14 17 6 , 70167 67. 40 16 , 97278 73 , 45 22 , 88694 84. 40 13 18 7 , 08500 67. 52 17 , 25500 73 , 75 22 , 98083 84. 83 12 19 7 , 46667 67. 63 17 , 53167 74 , 05 23 , 06750 85. 25 11 20 7 , 84611 67. 75 17 , 80389 74 , 35 23 , 14639 85. 68 10 21 8 , 22389 67. 88 18 , 07056 74 , 67 23 , 21806 86. 10 09 22 8 , 59944 68. 02 18 , 33250 74 , 98 23 , 28222 86. 53 08 23 8 , 97222 68. 15 18 , 58833 75 , 30 23 , 33889 86. 97 07 24 9 , 34278 68. 30 18 , 83917 75 , 63 23 , 38833 87. 40 06 25 9 , 71139 68. 47 19 , 08444 75 , 97 23 , 4300● 87. 83 05 26 10 , 07722 68. 63 19 , 32389 76 , 30 23 , 46417 88. 26 04 27 10 , 44000 68. 80 19 , 55750 76 , 65 23 , 49083 88. 70 03 28 10 , 80056 68. 97 19 , 78528 77 , 00 23 , 50972 89. 13 02 29 11 , 15750 69. 15 20 , 00722 77 , 35 23 , 52139 89. 57 01 30 11 , 51167 69. 33 20 , 22278 77 , 70 23 , 52500 90. 00 00   ♓ ♍ ♒ ♌ ♈ ♋   Tycho's Table of Refractions . Altitude ☉ ☽ ✴ ✴   Parts . Parts . Parts . 0 , 56667 , 55000 , 50000 1 , 43333 , 41667 , 35833 2 , 33333 , 33333 , 25833 3 , 28333 , 28333 , 20833 4 , 25833 , 25556 , 18333 5 , 24167 , 23889 , 16667 6 , 22500 , 23056 , 15000 7 , 21250 , 21250 , 13750 8 , 18750 , 20000 , 11250 9 , 17500 , 18889 , 10000 10 , 16667 , 17917 , 09167 11 , 15833 , 16944 , 08333 12 , 15000 , 15972 , 07500 13 , 14167 , 15000 , 06667 14 , 13333 , 14167 , 05833 15 , 12500 , 13333 , 05000 16 , 11667 , 12500 , 04167 17 , 10833 , 11667 , 03333 18 , 09583 , 10833 , 02083 19 , 08333 , 10000 , 00833 20 , 07500 , 09167 , 00000 21 , 06667 , 08333 , 00000 22 , 05833 , 07639 , 00000 23 , 05278 , 06944   24 , 04722 , 06250   25 , 04167 , 05556   26 , 03750 , 05000   27 , 03333 , 04444   28 , 02917 , 03889   29 , 02639 , 03333   30 , 02361 , 02778   31 , 02083 , 02500   32 , 01806 , 0222●   33 , 01528 , 01944   34 , 01250 , 01667   35 , 00972 , 01389   36 , 00833 , 01250   37 , 00694 , 01111   38 , 00556 , 00972   39 , 00417 , 00833   40 , 00278 , 00694   41 , 00250 , 00556   42 , 00222 , 00417   43 , 00194 , 00278   44 , 00167 , 00139   45 , 00139 , 00000   Saturns Mean Motions . Epochae Longit. ♄ Apheliō . ♄ Node ♄ Deg. parts Deg. parts Deg. Parts . Christi . 73. 13056 215. 25722 98. 98861 1600 208. 43944 265. 99722 110. 51389 1620 93. 13083 266. 63139 110. 65778 1640 337. 81722 267. 26583 110. 80194 1660 222. 50111 267. 88333 110. 94583 1 12. 22611 0. 03167 0. 00722 2 24. 45250 0. 06333 0. 01444 3 36. 67861 0. 09500 0. 02167 B 4 48. 93833 0. 12694 0. 02889 5 61. 16444 0. 15861 0. 03611 6 73. 39056 0. 19078 0. 04306 7 85. 61694 0. 22194 0. 05028 B 8 97. 87667 0. 25361 0. 05750 9 110. 10278 0. 28528 0. 06472 10 122. 32889 0. 31694 0. 07194 11 134. 55500 0. 34889 0. 07917 B 12 146. 81472 0. 38056 0. 08639 13 159. 04111 0. 41222 0. 09361 14 171. 26722 0. 44389 0. 10083 15 183. 49333 0. 47556 0. 10806 B 16 195. 75306 0. 50722 0. 11528 17 207. 97917 0. 53917 0. 12250 18 220. 20556 0. 57083 0. 12944 19 232. 43167 0. 60250 0. 13667 B 20 244. 69139 0. 63417 0. 14389 40 129. 38278 1 26861 0. 28806 60 14. 07417 1. 90278 0. 43222 80 258. 76528 2. 53694 0. 57611 100 143. 45667 3. 17111 0. 72028 Saturns mean Motions . Years . Longit. ♄ Aphel . ♄ Node ♄ Deg. parts . Deg. parts . Deg. parts . 100 143 , 45667 3 , 27111 0 , 72028 200 286 , 91361 6 , 34250 1 , 44056 300 80 , 37056 9 , 51361 2 , 16111 400 21● , 82722 12 , 68500 2 , 88139 500 357 , 28417 15 , 85611 3 , 60 67 600 140 , 74083 19 , 02750 4 , 32194 700 284 , 19778 22 , 19861 5 , 04222 800 67 , 65444 25 , 37001 5 , 76278 900 211 , 11139 28 , 5411 6 , 48306 1000 354 , 56086 31 , 71250 7 , 20333 2000 349 , 13639 63 , 42500 14 , 40667 3000 343 , 70444 95 , 13750 21 , 61000 4000 338 , 27278 126 , 85000 28 , 81333 5000 332 , 84083 158 , 56250 36 , 01667 January 1 , 03833 0 , 00278 0 , 00056 February 1 , 97639 0 , 00528 0 00139 March 3 , 01472 0 , 00778 0 , 00194 April 4 , 01944 0 , 01028 0 , 00250 May 5 , 05806 0 , 01333 0 , 00333 June 6 , 06278 0 , 01556 0 , 00389 July 7 , 10111 0 , 01833 0 , 00444 August 8 , 13972 0 , 02139 0 , 00500 September 9 , 14444 0 , 02361 0 , 00556 October 10 , 18278 0 , 02639 0 , 00611 November 11 , 18778 0 , 02917 0 , 00667 December 12 , 22611 0 , 03167 0 , 00722 Saturns Mean Motions . In Daies .   In Hours .   Long. ♄ Aphel . ♄ N●d . ♄         Long. ♄   D. parts Parts . Parts .         Parts . 1 0 , 03361 , 00000 , 00002       1 , 00139 2 0 , 06694 , 00000 , 00003       2 , 00278 3 0 , 10056 , 00028 , 00005       3 , 00417 4 0 , 13389 , 00028 , 00007       4 , 00556 5 0 , 16750 , 00056 , 00009       5 , 00694 6 0 , 20111 , 00056 , 00011       6 , 00833 7 0 , 23444 , 00056 , 00013       7 , 00972 8 0 , 26806 , 00083 , 00015       8 , 01111 9 0 , 30139 , 00083 , 00017       9 , 01250 10 0 , 33500 , 00083 , 00019       10 , 01389 11 0 , 36861 , 00111 , 00020       11 , 01528 12 0 , 40194 , 00111 , 00022       12 , 01667 13 0 , 43556 , 00111 , 00024       13 , 01806 14 0 , 46889 , 00139 , 00026       14 , 01944 15 0 , 50250 , 00139 , 00028       15 , 02083 16 0 , 53583 , 00139 , 00030       16 , 02222 17 0 , 56944 , 00167 , 00032       17 , 02361 18 0 , 60306 , 00167 , 00034       18 , 02500 19 0 , 63639 , 00167 , 00036       19 02639 20 0 , 67000 , 00194 , 00038       20 , 02778 21 0 , 70333 , 00194 , 00040       21 , 02917 22 0 , 73694 , 00194 , 00041       22 , 03083 23 0 , 77056 , 00222 , 00042       23 , 03222 24 0 , 80389 , 00222 , 00043       24 , 03361 25 0 , 83750 , 00222 , 00045           26 0 , 87083 , 00250 , 00047           27 0 , 90444 , 00250 , 00049           28 0 , 93806 , 00250 , 00051           29 0 , 97139 , 00278 , 00053           30 1 , 00500 , 00278 , 00055           31 1 , 03833 , 00278 , 00057           32 1 , 07194 , 00306 , 00059           Saturn's mean Motions in the parts of an Hour .   Long. ♄   Parts . 1 , 00001 2 , 00002 3 00004 4 , 00005 5 , 00006 6 , 00008 7 , 00009 8 , 00011 9 , 00012 10 , 00013 11 , 00015 12 , 00016 13 , 00018 14 , 00019 15 , 00020 16 , 00022 17 , 00023 18 , 00025 19 , 00026 20 , 00027 21 , 00029 22 , 00030 23 , 00032 24 , 00033 25 , 00035 26 , 00036 27 , 00037 28 , 00039 29 , 00040 30 , 00042 31 , 00043 32 , 00044 33 , 00046 34 , 00047 35 , 00048 36 , 00050 37 , 00051 38 , 00052 39 , 00054 40 , 00055 41 , 00056 42 , 00058 43 , 00059 44 , 00061 45 , 00062 46 , 00063 47 , 00065 48 , 00066 49 , 00068 50 , 00069 51 , 00070 52 , 00072 53 , 00074 54 , 00075 55 , 00076 56 , 00078 57 , 00079 58 , 00081 59 , 00082 60 , 00083 61 , 00085 62 , 00086 63 , 00087 64 , 00089 65 , 00090 66 , 00091 67 , 00093 68 , 00094 69 , 00095 70 , 00097 71 , 00098 72 , 00099 73 , 00101 74 , 00102 75 , 00103 76 , 00105 77 , 00106 78 , 00107 79 , 00109 80 , 00111 81 , 00112 82 , 00113 83 , 00115 84 , 00116 85 , 00118 86 , 00119 87 , 00120 88 , 00122 89 , 00123 90 , 00125 91 , 00126 92 , 00127 93 , 00129 94 , 00130 95 , 00131 96 , 00133 97 , 00134 98 , 00136 99 , 00137 Jupiter's mean Motions . Epochae Longit. ♃ Aphel . ♃ Node ♃   Deg. parts . Deg. Parts . Deg. Parts . Christi . 179 , 91583 148 , 42389 87 , 67722 1600 160 , 80556 188 , 02333 98 , 62306 1620 48 , 06667 188 , 51833 98 , 76000 1640 295 , 32778 189 , 01333 98 , 89667 1660 182 , 58889 189 , 50833 99 , 03333 1 30 , 34222 0 , 02472 0 , 00694 2 60 , 68444 0 , 04944 0 , 01361 3 91 , 02667 0 , 07417 0 , 02056 B 4 121 , 45222 0 , 09889 0 , 02722 5 151 , 79444 0 , 12361 0 , 03417 6 182 , 13667 0 , 14833 0 , 04111 7 212 , 47889 0 , 17333 0 , 04778 B 8 242 , 90444 0 , 19806 0 , 05472 9 273 , 24667 0 , 22278 0 , 06167 10 303 , 58889 0 , 24750 0 , 06833 11 333 , 93139 0 , 27222 0 , 07528 B 12 4 , 35667 0 , 29694 0 , 08194 13 34 , 69889 0 , 32167 0 , 08889 14 65 , 04111 0 , 34639 0 , 09583 15 95 , 38361 0 , 37111 0 , 10250 B 16 125 , 80889 0 , 39611 0 , 10944 17 156 , 15111 0 , 42083 0 , 11639 18 186 , 49361 0 , 44556 0 , 12306 19 216 , 83583 0 , 47028 0 , 13000 B 20 247 , 26111 0 , 49500 0 , 13694 40 134 , 52222 0 , 99000 0 , 27361 60 21 , 78333 1 , 48500 0 , 41056 80 269 , 04444 1 , 98000 0 , 54722 100 156 , 30556 2 , 47500 0 , 68417 Jupiters mean Motions . Years . Longit. ♃ Aphelion . ♃ Node . ♃   Deg. parts . Deg. Parts . Deg. Parts . 100 156 , 30556 2 , 47500 0 , 68417 200 312 , 61111 4 , 95000 1 , 36833 300 108 , 91694 7 , 42500 2 ▪ 05222 400 265 , 22250 9 , 89972 2 , 73639 500 61 , 52806 12 , 37472 3 , 42056 600 217 , 83361 14 , 84972 4 , 10472 700 14 , 13944 17 , 32472 4 , 78861 800 170 , 44500 19 , 79972 5 , 47278 900 326 , 75056 22 , 27472 6 , 15694 1000 123 , 05611 24 , 74972 6 , 84111 2000 246 , 11250 49 , 49972 13 , 68222 3000 9 , 16861 74 , 24889 20 , 52306 4000 132 , 22500 98 , 99833 27 , 36417 5000 255 , 28111 123 , 74806 34 , 20500 January . 2. 57694 0 , 00194 0 , 00056 February . 4. 90472 0 , 00417 0 , 00111 March. 7. 48167 0 , 00611 0 , 00167 April . 9. 97556 0 , 00806 0 , 00222 May. 12. 55250 0 , 01028 0 , 00278 June . 15. 04639 0 , 01222 0 , 00333 July . 17. 62333 0 , 01444 0 , 00389 August . 20. 20056 0 , 01667 0 , 00444 Septemb. 22. 69444 0 , 01861 0 , 00500 October . 25. 27139 0 , 02083 0 , 00556 Novemb. 27. 76528 0 , 02278 0 , 00611 Decemb. 30. 34222 0 , 02472 0 , 00694 Jupiter's mean Motions . In Dayes .   In Hours .   Long. ♃ Aphel . ♃ Nod. ♃     Long. ♃   D. parts Parts . Parts .     Parts . 1 0 , 08306 , 00006 , 00002   1 , 00333 2 0 , 16611 , 00013 , 00003   2 , 00722 3 0 , 24944 , 00020 , 00005   3 , 01028 4 0 , 33250 , 00026 , 00007   4 , 01389 5 0 , 41556 , 00033 , 00009   5 , 01722 6 0 , 49861 , 00039 , 00011   6 , 02083 7 0 , 58194 , 00046 , 00013   7 , 02417 8 0 , 66500 , 00053 , 00015   8 , 02722 9 0 , 74816 , 00059 , 00017   9 , 03111 10 0 , 83141 , 00066 , 00019   10 , 03472 11 0 , 914●4 , 00072 , 00020   11 , 03806 12 0 , 99750 , 00079 , 00022   12 , 04167 13 1 , 08056 , 00085 , 00024   13 , 04500 14 1 , 16361 , 00091 , 00026   14 , 04861 15 1 , 24694 , 00098 , 00028   15 , 05194 16 1 , 33000 , 00104 , 00030   16 , 05556 17 1 , 41306 , 00111 , 00032   17 , 05889 18 1 , 49611 , 00117 , 00034   18 , 06222 19 1 , 57944 , 00123 , 00036   19 ▪ 06583 20 1 , 66250 , 00130 , 00038   20 , 06917 21 1 , 74556 , 00136 , 00039   21 , 07278 22 1 , 82861 , 00142 , 00041   22 , 07611 23 1 , 91194 , 00149 , 00043   23 , 07972 24 1 , 99500 , 00155 , 00045   24 , 08306 25 2 , 07806 , 00162 , 00047       26 2 , 16111 , 00168 , 00049       27 2 , 24444 , 00174 , 00051       28 2 , 32750 , 00181 , 00053       29 2 , 41056 , 00197 , 00055       30 2 , 49389 , 00203 , 00057       31 2 , 57694 , 00●09 , 00059       32 ● , 66000 , 00216 , 00061       Jupiters mean Motions in the parts of an Hour . Long. ♃ Parts . 1 , 00003 2 , 00007 3 , 00010 4 , 00013 5 , 00017 6 , 00020 7 , 00024 8 , 00027 9 , 00031 10 , 00034 11 , 00038 12 , 00041 13 , 00045 14 , 00048 15 , 00052 16 , 00055 17 , 00058 18 , 00062 19 , 00065 20 , 00069 21 , 0007● 22 , 00076 23 , 00079 24 , 00083 25 , 00086 26 , 00090 27 , 00093 28 , 00097 29 , 0010● 30 , 00104 31 , 00107 32 , 00111 33 , 00114 34 , 00117 35 , 00121 36 , 00124 37 , 00128 38 , 00131 39 , 00135 40 , 00138 41 , 00142 42 , 00145 43 , 00149 44 , 00152 45 , 00156 46 , 00159 47 , 00162 48 , 00166 49 , 00169 50 , 00173 51 , 00176 52 , 00180 53 , 00183 54 , 00187 55 , 00190 56 , 00194 57 , 00197 58 , 00201 59 , 00204 60 , 00208 61 , 00211 62 , 00214 63 , 00218 64 , 00221 65 , 00225 66 , 00228 67 , 00232 68 , 00235 69 , 00238 70 , 00241 71 , 00245 72 , 00248 73 , 00251 74 , 00255 75 , 00258 76 , 00262 77 , 00265 78 , 00269 79 , 00272 80 , 00276 81 , 00279 82 , 00283 83 , 00286 84 , 00290 85 , 00293 86 , 00297 87 , 00300 88 , 00303 89 , 00307 90 , 00311 91 , 00314 92 , 00318 93 , 00321 94 , 00325 95 , 00328 56 , 00332 97 , 00335 98 , 00339 99 , 00342 The Mean Motions of Mars . Epochae Longit. ♂ Apheliō . ♂ Node ♂   Deg. parts Deg. parts Deg. Parts . Christi . 40. 71611 113. 97083 25. 30583 1600 307. 27611 148. 99833 46. 74222 1620 175. 60778 149. 43611 47. 01028 1640 43. 94000 149. 87389 47. 27806 1660 272. 27194 150. 21167 47. 54639 1 191. 28556 0. 02194 0. 01333 2 22. 57111 0. 04389 0. 02667 3 213. 85667 0. 06556 0. 04028 B 4 45. 66639 0. 08750 0. 05361 5 236. 95167 0. 10944 0. 06694 6 68. 23750 0. 13139 0. 08028 7 259. 52278 0. 15306 0. 09361 B 8 91. 33278 0. 17500 0. 10722 9 282. 61833 0. 19722 0. 12056 10 113. 90389 0. 21889 0. 13389 11 305. 18944 0. 24056 0. 14722 B 12 136. 99917 0. 26250 0. 16056 13 328. 28472 0. 28444 0. 17417 14 159. 57028 0. 30639 0. 18778 15 350. 85583 0. 32806 0. 20111 B 16 182. 66556 0. 35028 0. 21444 17 13. 95111 0. 37222 0. 22778 18 205. 23667 0. 39417 0. 24139 19 36. 52222 0. 41583 0. 25472 B 20 228. 33194 0. 43778 0. 26806 40 96. 66389 0. 47556 0. 53583 60 324. 99●11 1. 31333 0. 80389 80 193. 32778 1. 75139 1. 07194 100 61. 66000 2. 18917 1. 33972 The mean Motions of Mars . Years . Longit. ♂ Aphel . ♂ Node ♂   Deg. parts . Deg. parts . Deg : parts . 100 61 , 66000 2 , 18917 1 , 17306 200 123 , 32000 4 , 37833 2 , 67944 300 184 , 98000 6 , 56778 4 , 01944 400 246 , 64000 8 , 75694 5 , 35917 500 308 , 30000 10 , 94611 6 , 69889 600 9 , 96000 13 , 13528 8 , 03861 700 71 , 62000 15 , 32444 9 , 37833 800 133 , 28000 17 , 51361 10 , 71806 900 194 , 94000 19 , 70306 12 , 05806 1000 256 , 60000 21 , 89222 13 , 39778 2000 153 , 20028 43 , 78444 26 , 79528 3000 49 , 80028 65 , 67639 40 , 19306 4000 306 , 40056 8● , 56889 53 , 59056 5000 203 , 00056 109 , 46083 66 , 98833 January 16 , 24611 0 , 00194 0 , 00111 February 30 , 92028 0 , 00361 0 , 00222 March 47 , 16639 0 , 00556 0 , 00333 April 62 , 88833 0 , 00722 0 , 00444 May 79 , 13472 0 , 00917 0 , 00556 June 94 , 85667 0 , 01083 0 , 00667 July 111 , 10306 0 , 01250 0 , 00778 August 127 , 34917 0 , 01444 0 , 00889 September 143 , 07111 0 , 01639 0 , 01000 October 159 , 31750 0 , 01833 0 , 01111 November 175 , 03944 0 , 02028 0 , 01222 December 191 , 28556 0 , 02194 0 , 01333 The mean Motions of Mars . In Dayes .   In Hours .   Long. ♂ Apha . ♂ Node ♂     Long. ♂   D. Parts . Parts . Parts .     Parts . 1 0 , 52417 . 00006 , 00003   1 , 02194 2 1 , 04806 , 00012 , 00007   2 , 04361 3 1 , 57222 , 00018 , 00010   3 , 06556 4 2 , 09611 , 00024 , 00014   4 , 08722 5 2 , 62111 , 00030 , 00018   5 , 10917 6 3 , 14444 , 00036 , 00021   6 , 13111 7 3 , 66833 , 00042 , 00025   7 , 15278 8 4 , 19250 , 00048 , 00028   8 , 17472 9 4 , 71667 , 00054 , 00032   9 , 19667 10 5 , 24083 , 00060 , 00036   10 , 21833 11 5 , 76472 , 00066 , 00039   11 , 24028 12 6 , 28889 , 00072 , 00043   12 , 26194 13 6 , 81278 , 00078 , 00046   13 , 28389 14 7 , 33694 , 00084 , 00050   14 , 30583 15 7 , 86111 , 00090 , 00054   15 , 32750 16 8 , 38500 , 00096 , 00057   16 , 34944 17 8 , 90917 , 00102 , 00061   17 , 37111 18 9 , 43333 , 00108 , 00064   18 , 39306 19 9 , 95750 , 00114 , 00068   19 , 41500 20 10 , 48139 , 00120 , 00072   20 , 43667 21 11 , 00556 , 00126 , 00075   21 , 45861 22 11 , 52944 , 00132 , 00079   22 , 48028 23 12 , 05361 , 00138 , 00082   23 , 50222 24 12 , 57778 , 00144 , 00086   24 , 52417 25 13 , 10167 , 00150 , 00090       26 13 , 62583 , 00156 , 00093       27 14 , 15000 , 00162 , 00097       28 14 , 67417 , 00168 , 00100       29 15 , 19861 , 00174 , 00104       30 15 , 72222 , 00180 , 00108       31 16 , 24611 , 00186 , 00111       32 16 , 77028 , 00192 , 00115       The mean Motions of Mars in parts of an Hour .   Long. ♂   Parts . 1 , 00022 2 , 00043 3 , 00065 4 , 00087 5 , 00109 6 , 00131 7 , 00152 8 , 00174 9 , 00196 10 , 002●8 11 , 00240 12 , 00262 13 , 00284 14 , 00306 15 , 00327 16 , 00349 17 , 00371 18 , 00393 19 , 00415 20 , 00436 21 , 00458 22 , 00480 23 , 00502 24 , 00524 25 , 00545 26 , 00567 27 , 00589 28 , 00611 29 , 00633 30 , 00655 31 , 00676 32 , 00698 33 , 00720 34 , 00742 35 , 00764 36 , 00785 37 , 00807 38 , 00829 39 , 00851 40 , 00873 41 , 00894 42 , 00916 43 , 00938 44 , 00960 45 , 00982 46 , 01003 47 , 01025 48 , 01047 49 , 01069 50 , 01091 51 , 01112 52 , 01134 53 , 01156 54 , 01178 55 , 01200 56 , 01221 57 , 01243 58 , 01265 59 , 01287 60 , 01309 61 , 01330 62 , 01352 63 , 01374 64 , 01396 65 , 01418 66 , 01439 67 , 01461 68 , 01483 69 , 01505 70 , 01527 71 , 01548 72 , 01570 73 , 01592 74 , 01614 75 , 01636 76 , 01657 77 , 01679 78 , 01701 79 , 01723 80 , 01746 81 , 01768 82 , 01789 83 , 01811 84 , 01833 85 , 01855 86 , 01877 87 , 01898 88 , 01920 89 , 01942 90 , 01966 91 , 01988 92 , 02009 93 , 02031 94 , 02053 95 , 02075 56 , 02097 97 , 02118 98 , 02140 99 , 02162 The mean Motions of Venus . Epochae Longit. ♀ Aphel . ♀ Node ♀   Deg. parts . Deg. Parts . Deg. Parts . Christi . 42 , 77917 282 , 84556 60 , 72111 1600 352 , 47278 305 , 38500 74 , 12722 1620 176 , 34389 305 , 66667 74 , 29472 1640 0 , 21500 305 , 94833 74 , 46222 1660 184 , 08611 306 , 23000 74 , 62972 1 224 , 79306 0 , 01417 0. 00833 2 89 , 58611 0 , 02806 0 , 01667 3 324 , 37917 0 , 04222 0 , 02500 B 4 180 , 77417 0 , 05639 0 , 03361 5 45 , 56722 0 , 07028 0 , 04194 6 270 , 36028 0 , 08444 0 , 05028 7 135 , 15333 0 , 09861 0 , 05861 B 8 1 , 54833 0 , 11250 0 , 06694 9 226 , 34139 0 , 12667 0 , 07528 10 91 , 13444 0 , 14083 0 , 08361 11 315 , 92750 0 , 15472 0 , 09222 B 12 182 , 32278 0 , 16889 0 , 10056 13 47 , 11583 0 , 18306 0 ; 10889 14 271 , 90861 0 , 19722 0 , 11722 15 136 , 70167 0 , 21111 0 , 12556 B 16 3 , 09694 0 , 22528 0 13389 17 227 , 89000 0 , 23944 0 , 14222 18 92 , 68306 0 , 25333 0 , 15083 19 317 , 47611 0 , 26750 0 , 15917 B 20 183 , 87111 0 , 28167 0 , 16750 40 7 , 74222 0 , 56361 0 , 33528 60 191 , 61361 0 , 84528 8 , 50278 80 15 , 48472 1 , 12694 0 , 67028 100 199 , 35583 1 , 40861 0 , 83778 The mean Motions of Venus . Years . Longit. ♀ Aphelion . ♀ Node . ♀   Deg. parts . Deg. Parts . Deg. Parts . 100 199 , 35583 1 , 40861 0 , 83778 200 38 , 71167 2 , 81750 1 , 67583 300 238 , 06750 4 , 22611 2 , 51361 400 77 , 42333 5 , 63500 2 , 35167 500 276 , 77917 7 , 04361 4 , 18944 600 116 , 13500 8 , 45222 5 , 02750 700 315 , 49083 9 , 86111 5 , 86528 800 154 , 84639 11 , 26972 6 , 70333 900 354 , 20250 12 , 67833 7 , 54111 1000 193 , 55833 14 , 08722 8 , 37889 2000 27 , 11639 28 , 17444 16 , 75778 3000 220 , 67472 42 , 86139 28 , 13694 4000 54 , 23278 46 , 34889 33 , 51611 5000 247 , 79111 61 , 43583 41 , 89500 January . 49. 66750 0 , 00111 0 , 00083 February . 94. 52833 0 , 00222 0 , 00139 March. 144. 19556 0 , 00361 0 , 00222 April . 192. 26083 0 , 00472 0 , 00278 May. 241. 92833 0 , 00583 0 , 00361 June . 289. 99361 0 , 00694 0 , 00417 July . 339. 65833 0 , 00806 0 , 00500 August . 29. 32833 0 , 00917 0 , 00556 Septemb. 77. 39361 0 , 01056 0 , 00611 October . 127. 06083 0 , 01167 0 , 00694 Novemb. 171. 12611 0 , 01278 0 , 00750 Decemb. 224. 79306 0 , 01417 0 , 00833 The mean Motions of Venus . In Dayes .   In Hours .   Long. ♀ Aphel . ♀ Node ♀     Long. ♀   D. Parts . Parts . Parts .     Parts . 1 1 , 6022● , 00004 , 00002   1 0 , 06667 2 3 , 20444 , 00007 , 00004   2 0 , 13361 3 4 , 80639 , 00011 , 00006   3 0 , 20028 4 6 , 40861 , 00015 , 00009   4 0 , 26722 5 8 , 01083 , 00019 , 00011   5 0 , 33389 6 9 , 61306 , 00023 , 00013   6 0 , 40056 7 10 , 21528 , 00027 , 00016   7 0 , 46750 8 12 , 81750 , 00031 , 00018   8 0 , 53417 9 14 , 41944 , 00035 , 00020   9 0 , 60083 10 16 , 02167 , 00038 , 00023   10 0 , 66778 11 17 , 62389 , 00042 , 00025   11 0 , 73444 12 19 , 22611 , 00046 , 00027   12 0 , 80139 13 20 , 8●833 , 00050 , 00030   13 0 , 86806 14 22 , 43056 , 00054 , 00032   14 0 , 93472 15 24 , 03250 , 00058 , 00034   15 1 , 00167 16 25 , 63472 , 00062 , 00037   16 1 , 06833 17 27 , 23694 , 00066 , 00039   17 1 , 13500 18 28 , 83917 , 00069 , 00041   18 1 , 20194 19 30 , 44139 , 00073 , 00044   19 1 , 26861 20 32 , 04361 , 00077 , 00046   20 1 , 33556 21 33 , 64556 , 00081 , 00048   21 1 , 40222 22 35 , 24778 , 00085 , 00051   22 1 , 46889 23 36 , 85000 , 00089 , 00053   23 1 , 53583 24 38 , 45222 , 00093 , 00055   24 1 , 60250 25 40 , 05444 , 00097 , 00058       26 41 , 65639 , 00100 , 00060       27 43 , 25861 , 00104 , 00062       28 44 , 86083 , 00108 , 00065       29 46 , 4630● , 00112 , 00067       30 48 , 06528 , 00116 , 00069       31 49 , 66750 , 00120 , 00072       32 51 , 26972 , 00124 , 00074       The mean Motions of Venus in parts of an Hour .   Long. ♀   Parts . 1 , 00067 2 , 00133 3 , 00200 4 , 00267 5 , 00334 6 , 00401 7 , 00468 8 , 00534 9 , 00601 10 , 00667 11 , 00734 12 00801 13 , 00868 14 , 00935 15 , 01002 16 , 01068 17 , 01135 18 , 01202 19 , 01268 20 , 01335 21 , 01402 22 , 01469 23 , 01536 24 , 01603 25 , 01669 26 , 01736 27 , 01803 28 , 01869 29 , 01936 30 , 02003 31 , 02070 32 , 02137 33 , 02204 34 , 02270 35 , 02337 36 , 02404 37 , 02470 38 , 02537 39 , 02604 40 , 02671 41 , 02738 42 , 02805 43 , 02871 44 , 02938 45 , 03005 46 , 03071 47 , 03138 48 , 03205 49 , 03272 50 , 03339 51 , 03406 52 , 03472 53 , 03539 54 , 03606 55 , 03672 56 , 03739 57 , 03806 58 , 03873 59 , 03940 60 , 04007 61 , 04073 62 , 04140 63 , 04207 64 , 04273 65 , 04340 66 , 04407 67 , 04474 68 , 04541 69 , 04608 70 , 04674 71 , 04741 72 , 04808 73 , 04874 74 , 04941 75 , 05008 76 , 05075 77 , 05142 78 , 05209 79 , 05276 80 , 05342 81 , 05408 82 , 05475 83 , 05542 84 , 05609 85 , 05676 86 , 05743 87 , 05810 88 , 05876 89 , 05943 90 , 06009 91 , 06076 92 , 06143 93 , 06210 94 , 06277 95 , 06344 96 , 06410 97 , 06477 98 , 06544 99 , 06610 Mercuries mean Motion . Epochae Longit. ☿ Apheliō . ☿ Node ☿ Deg. parts Deg. parts Deg. Parts . Christi . 316. 26111 205. 31361 000. 0●000 1600 66. 95583 251. 63028 42. 51139 1620 81. 83944 252. 20611 43. 04250 1640 96. 72306 252. 78806 43. 57361 1660 111. 6●694 253. 35028 44. 10472 1 53. 72111 0. 02889 0. 02667 2 107. 44222 0. 05778 0. 05306 3 161. 16333 0. 08667 0. 07972 B 4 218. 97667 0. 11583 0. 10611 5 272. 69778 0. 14472 0. 13278 6 326. 41889 0. 17361 0. 15917 7 20. 14000 0. 20250 0. 18583 B 8 77. 95361 0. 23167 0. 21250 9 131. 67444 0. 26056 0. 23889 10 185. 39556 0. 28944 0. 26556 11 239. 11667 0. 31833 0. 29194 B 12 296. 92694 0. 34750 0. 31861 13 350. 65139 0. 37639 0. 34528 14 44. 37250 0. 40527 0. 37167 15 98. 09361 0. 43417 0. 39833 B 16 155. 90694 0. 46333 0. 42472 17 209. 62806 0. 49222 0. 45139 18 263. 34917 0. 52111 0. 47778 19 317. 07028 0. 55000 0. 50444 B 20 14. 88361 0. 57889 0. 53111 40 29. 76722 1. 15778 1. 06194 60 44. 65083 1. 73667 1. 59306 80 59. 53472 2. 31611 2. 12417 100 74. 41833 2. 89472 2. 65500 Mercuries mean Motions Years . Longit. ☿ Aphel . ☿ Node ☿ Deg. parts . Deg. parts . Deg : parts . 100 74 , 41833 2 , 89472 2 , 65500 200 148 , 83694 5 , 78972 5 , 31028 300 223 , 25527 8 , 68444 7 , 96528 400 297 , 67361 11 , 57917 10 , 62028 500 12 , 09222 14 , 47389 1● , 27556 600 86 , 510●6 17 , ●6889 15 , 93056 700 160 , 92889 20 , 26361 18 , 58556 800 235 , ●4750 23 , 1583● 21 , 24083 900 309 , 78250 26 , 05333 23 , 89583 1000 24 , 18417 ●8 , 94806 26 , 55083 2000 48 , 36861 5● , 89611 4● , 10194 3000 72 , 55278 86 , 84417 79 , 65278 4000 96 , 73694 115 , 79222 106 , 20333 5000 120 , 9●47● 144 , 74861 132 , 75472 January 126 , 86●89 0 , 00250 0 , 00222 February 241 , 45083 0 , 00472 0 , 00444 March 8 , 31472 0 , 00722 0 , 00667 April 131 , 08639 0 , 00972 0 , 00861 May 257 , 95028 0 , 01222 0 , 01083 June 20 , 72194 0 , 01444 0 , 01306 July 147 , 58583 0 , 01694 0 , 01528 August 274 , 44972 0 , 01917 0 , 01778 September 37 , 22139 0 , 02167 0 , 02000 October 164 , 08556 0 , 02417 0 , 02222 November 286 , 85722 0 , 02639 0 , 02417 December 53 , 72139 0 , 02889 0 , 02667 The Mean Motions of Mars . In Dayes . In Hours .   Long. ☿ Aphel . ☿ Node . ☿   Long. ☿   Deg. parts . Parts . Parts .   Parts . 1 4 , 09222 , 00008 , 00007 1 0 , 17056 2 8 , 18472 , 00015 , 00014 2 0 , 34111 3 12 , 27722 , 00023 , 00021 3 0 , 51167 4 16 , ●6944 , 00031 , 00029 4 0 , 68222 5 20 , 46194 , 00039 , 00036 5 0 , 85250 6 24 , 55444 , 00047 , 00043 6 1 , 02306 7 28 , 64667 , 00055 , 00051 7 1 , 19361 8 32 , 73917 , 00063 , 00058 8 1 , 36417 9 36 , 83193 , 00071 , 00065 9 1 , 53472 10 40 , 92389 , 00079 , 00073 10 1 , 70528 11 45 , 01611 , 00086 , 00080 11 1 , 87556 12 49 , 1086● , 00094 , 00087 12 2 , 04611 13 53 , 20111 , 00102 , 00095 13 2 , 21667 14 57 , 29333 , 00110 , 00102 14 2 , 37822 15 61 , 38583 , 00118 , 00109 15 2 , 55778 16 65 , 47806 , 00126 , 00117 16 2 , 72806 17 69 , 57056 , 00134 , 00124 17 2 , 89861 18 73 , 66306 , 00142 , 00131 18 3 06917 19 77 , 75528 , 00150 , 00139 19 3 , 23972 20 81 , 84778 , 00158 , 00146 20 3 , 41028 21 85 , 94000 , 00165 , 00153 21 3 , 58083 22 90 , 03250 , 00173 , 00161 22 3 , 75111 23 94 , 12500 , 00181 , 00168 23 3 , 92167 24 98 , 21722 , 00189 , 00175 24 4 , 09222 25 102 , 30972 , 00197 , 00182     26 106 , 40194 , 00205 , 00190     27 110 , 49444 , 00213 , 00197     28 114 , 58694 , 00221 , 00204     29 118 , 67917 , 00229 , 00212     30 122 , 77167 , 00237 , 00219     31 126 , 86389 , 00243 , 00226     32 130 , 95611 , 00251 , 00233     Mercuries mean Motions in parts of an Hour .   Long. ☿   Parts . 1 , 00170 2 , 00341 3 , 00511 4 , 00682 5 , 00852 6 , 01023 7 , 01193 8 , 01364 9 , 01534 10 , 01705 11 , 01875 12 , 02046 13 , 02217 14 , 02387 15 , 02557 16 , 02728 17 , 02898 18 , 03069 19 , 03239 20 , 03410 21 , 03580 22 , 03751 23 , 03921 24 , 04092 25 , 04262 26 , 04433 27 , 04603 28 , 04774 29 , 04944 30 , 05115 31 , 05285 32 , 05456 33 , 05626 34 , 05797 35 , 05967 36 , 06138 37 , 06●08 38 , 06479 39 , 06649 40 , 06820 41 , 06990 42 , 07161 43 , 07331 44 , 07502 45 , 07672 46 , 07843 47 , 08013 48 , 08184 49 , 08354 50 , 08525 51 , 08695 52 , 08866 53 , 09036 54 , 09207 55 , 09377 56 , 09548 57 , 09718 58 , 09889 59 , 10059 60 , 10230 61 , 10400 62 , 10571 63 , 10741 64 , 10912 65 , 11082 66 , 11253 67 , 11423 68 , 11594 69 , 11764 70 , 11935 71 , 12106 72 , 12276 73 , 12446 74 , 12617 75 , 12787 76 , 12958 77 , 13128 78 , 13299 79 , 13469 80 , 13640 81 , 13811 82 , 13981 83 , 14152 84 , 14322 85 , 14493 86 , 14663 87 , 14834 88 , 15004 89 , 15175 90 , 15345 91 , 15516 92 , 15687 93 , 15857 94 , 16028 95 , 16198 96 , 16369 97 , 16540 98 , 167●1 99 , 16882 A Table of Declinations . ♈ North Latitude . ♎ South Latitude .   0 1 2 3 4 5 6   0 0 , 00 0 , 92 1 , 83 2 , 75 3 , 67 4. 58 6. 00 30 1 0 , 40 1 , 32 2 , 23 3 , 15 4 , 07 4. 98 6. 20 29 2 0 , 80 1 , 72 2 , 63 3 , 55 4 , 47 5. 38 6. 30 28 3 1 , 20 2 , 12 3 , 03 3 , 95 4 , 87 5. 78 6. 70 27 4 1 , 60 2 , 51 3 , 43 4 , 35 5 , 27 6. 18 7. 10 26 5 2 , 00 2 , 91 3 , 83 4 , 75 5 , 83 6. 58 7. 50 25 6 2 , 40 3 , 31 4 , 23 5 , 15 6 , 06 6. 98 7. 88 24 7 2 , 78 3 , 71 4 , 63 5 , 55 6 , 46 7. 38 8. 28 23 8 3 , 18 4 , 11 5 , 03 5 , 95 6 , 86 7. 78 8. 68 22 9 3 , 58 4 , 50 5 , 42 6 , 33 7 , 25 8. 17 9. 08 21 10 3 , 97 4 , 90 5 , 80 6 , 73 7 , 65 8. 57 9. 48 20 11 4 , 37 5 , 30 6 , 20 7 , 13 8 , 05 8. 97 9. 88 19 12 4 , 77 5 , 70 6 , 60 7 , 53 8 , 45 9. 36 10. 27 18 13 5 , 15 6 , 08 7 , 00 7 , 92 8 , 83 9. 76 10. 67 17 14 5 , 55 6 , 48 7 , 40 8 , 32 9 , 23 10. 16 11. 07 16 15 5 , 93 6 , 87 7 , 78 8 , 70 9 , 62 10. 55 11. 45 15 16 6 , 32 7 , 23 8 , 15 9 , 08 10 , 00 10. 93 11. 85 14 17 6 , 70 7 , 62 8 , 53 9 , 47 10 , 38 11. 32 12. 23 13 18 7 , 08 8 , 00 8 , 93 9 , 85 10 , 68 11. 70 1● . 62 12 19 7 , 47 8 , 38 9 , 30 10 , 23 11 , 15 12. 08 13. 00 11 20 7 , 85 8 , 77 9 , 70 10 , 63 11 , 55 12. 47 13. 38 10 21 8 , 22 9 , 08 10 , 15 11 , 0● 11 , 93 12. 85 13. 80 9 22 8 , 60 9 , 53 10 , 47 11 , 38 12 , 32 13. 23 14. 15 8 23 8 , 97 9 , 92 10 , 85 11 , 77 12 , 70 13. 62 14. 53 7 24 9 , 35 10 , 28 11 , 22 12 , 13 13 , 07 14. 00 14. 90 6 25 9 , 72 10 , 65 11 , 58 12 , 50 13 , 43 14. 37 15. 28 5 26 10 , 08 11 , 02 11 , 95 12 , 87 13 , 80 14. 73 15. 65 4 27 10 , 43 11 , 38 12 , 32 13 , 23 14 , 17 15. 10 16. 02 3 28 10 , 80 11 , 75 12 , 68 13 , 60 14 , 53 15. 47 16. 38 2 29 11 , 15 12 , 08 13 , ●3 13 , 95 14 , 88 15. 82 16. 75 1 30 11 , 51 12 , 45 13 , 38 14 , 31 15 , 25 16. 18 17. 10 0 ♓ North Latitude . ♍ South Latitude . A Table of Declinations . ♈ South Latitude . ♎ North Latitude   0 1 2 3 4 5 6   0   0 , 92 1 , 83 2 , 75 3 , 67 4 , 58 5 , 50 30 1   0 , 52 1 , 45 2 , 35 3 , 27 4 , 18 5 , 10 29 2   0 , 12 1 , 05 1 , 95 2 , 87 3 , 78 4 , 70 28 3   0 ▪ 28 0 , 65 1 , 57 2 , 48 3 , 40 4 , 32 27 4   0 , 68 0 , 25 1 , 17 2 , 08 3 , 00 3 , 92 26 5   1 , 08 0 , 15 0 , 77 1 , 68 2 , 60 3 , 52 25 6   1 , 47 0 , 55 0 , 37 1 , 28 2 , 03 3 , 12 24 7   1 , 87 0 , 95 0 , 03 0 , 8● 1 , 80 2 , 72 23 8   2 , 27 1 , 35 0 , 43 0 , 48 1 , 42 2 , 33 22 9   2 , 48 1 , 73 0 , 82 0 , 10 1 , 03 1 , 95 21 10   3 , 05 2 , 13 1 , 22 0 , 30 0 , 63 1 , 55 20 11   3 , 45 2 , 53 1 , 61 0 , 68 0 , 23 1 , 15 19 12   3 , 85 2 , 93 2 , 01 1 , 07 0 , 17 0 , 77 18 13   4 , 23 3 , 32 2 , 40 1 , 47 0 , 55 0 , 38 17 14   4 , 62 3 , 68 2 , 95 1 , 87 0 , 93 0 , 00 16 15   5 , 00 4 , 08 3 , 17 2 , 25 1 , 32 0 , 38 15 16   5 , 38 4 , 47 3 , 53 2 , 63 1 , 68 0 , 77 14 17   5 , 77 4 , 85 3 , 92 3 , 00 2 , 07 1 , 15 13 18   6 , 15 5 , 23 4 , 30 3 , 38 2 , 45 1 , 53 12 19   6 , 53 5 , 62 4 , 68 3 , 77 2 , 83 1 , 92 11 20   6 , 92 5 , 98 5 , 07 4 , 13 3 , 20 2 , 28 10 21   7 , 28 6 , 35 5 , 45 4 , 50 3 , 57 2 , 65 9 22   7 , 67 6 , 73 5 , 83 4 , 88 3 , 95 3 , 02 8 23   8 , 05 7 , 12 6 , 20 5 , 25 4 , 32 3 , 38 7 24   8 , 42 7 , 50 6 , 57 5 , 63 4 , 70 3 , 75 6 25   8 , 78 7 , 87 6 , 93 6 , 00 5 , 07 4 , 12 5 26   9 , 15 8 , 23 7 , 30 6 , 37 5 , 43 4 , 48 4 27   9 , 51 8 , 58 7 , 83 6 , 72 5 , 78 4 , 83 3 28   9 , 88 8 , 95 8 , 02 7 , 07 6 , 13 5 , 18 2 29   10 , 23 9 , 30 8 , 37 7 , 42 6 , 48 5 , 53 1 30   10 , 58 9 , 65 8 , 72 7 , 77 6 , 83 5 , 88 0 ♓ North Latitude . ♍ South Latitude . A Table of Declinations . ♉ North Latitude . ♏ South Latitude .   0 1 2 3 4 5 6   0 11 , 51 12 , 45 13 , 38 14 , 31 15 , 25 16 , 18 17 , 10 30 1 11 , 87 12 , 80 13 , 73 14 , 67 15 , 60 16 , 55 17 , 47 29 2 12 , 22 13 , 15 14 , 08 15 , 02 15 , 95 16 , 19 17 , 82 28 3 12 , 55 13 , 48 14 , 42 15 , 35 16 , 30 17 , 23 18 , 17 27 4 12 , 90 13 , 83 14 , 78 15 , 70 16 , 65 17 , 58 18 , 52 26 5 13 , 23 14 , 18 15 , 12 16 , 05 17 , 00 17 , 93 18 , 87 25 6 13 , 57 14 , 52 15 , 45 16 , 40 17 , 33 18 , 28 19 , 20 24 7 13 , 90 14 , 85 15 , 78 16 , 73 17 , 67 18 , 58 19 , 53 23 8 14 , 23 15 , 18 16 , 12 17 , 07 18 , 00 18 , 95 19 , 87 22 9 14 , 55 15 , 50 16 , 43 17 , 38 18 , 33 19 , 28 20 , 20 21 10 14 , 87 15 , 82 16 , 75 17 , 70 18 , 65 19 , 60 20 , 53 20 11 15 , 18 16 , 13 17 , 07 18 , 02 18 , 97 19 , 92 20 , 85 19 12 15 , 48 16 , 43 17 , 38 18 , 33 19 , 23 20 , 23 21 , 17 18 13 15 , 80 16 , 75 17 , 70 18 , 65 19 , 60 20 , 55 21 , 48 17 14 16 , 10 17 , 05 18 , 00 18 , 95 19 , 90 20 , 87 21 , 80 16 15 16 , 40 17 , 35 18 , 30 19 , 25 20 , 20 21 , 17 22 , 10 15 16 16 , 68 17 , 63 18 , 60 19 , 55 20 , 50 21 , 63 22 , 40 14 17 16 , 97 17 , 92 18 , 88 19 , 85 20 , 80 21 , 77 22 , 70 13 18 17 , 25 18 , 20 19 , 17 20 , 13 21 , 08 22 , 05 22 , 98 12 19 17 , 53 18 , 48 19 , 45 20 , 42 21 , 37 22 , 33 23 , 27 11 20 17 , 80 18 , 77 19 , 7● 20 , 68 21 , 65 22 , 62 23 , 55 10 21 18 , 07 19 , 0● 20 , 00 20 , 95 21 , 92 22 , 88 23 , 83 9 22 18 , 3● 19 , 30 20 , 27 21 , 22 22 , 18 23 , 15 24 , 10 8 23 18 , 58 19 , 57 20 , 53 21 , 48 22 , 45 23 , 42 24 , 37 7 24 18 , 83 19 , 82 20 , 78 21 , 75 22 , 72 2● , 68 24 , 63 6 25 19 , 08 20 , 05 21 , 03 22 , 00 22 , 97 23 , 93 24 , 88 5 26 19 , 32 20 , 28 21 , 27 22 , 23 23 , 20 24 , 18 25 , 13 4 27 19 , 55 20 , 52 21 , 50 22 , 47 23 , 43 24 , 42 25 , 37 3 28 19 , 78 20 , 75 21 , 73 22 , 70 23 , 67 24 , 65 25 , 60 2 29 20 , 00 20 , 98 21 , 95 22 , 93 23 , 90 24 , 88 25 , 83 1 30 20 , 22 21 , 20 22 , 17 23 , 15 24 , 12 25 , 10 26 , 05 0 ♌ North Latitude . ♒ South Latitude . A Table of Declinations . ♉ South Latitude . ♏ North Latitude   0 1 2 3 4 5 6   0   10 , 58 09 , 65 8 , 72 7 , 77 6 , 83 5 , 88 30 1   10 , 93 10 , 00 9 , 07 8 , 12 7 , 18 6 , 23 29 2   11 , 28 10 , 33 9 , 40 8 , 47 7 , 52 6 , 57 28 3   11 , 62 10 , 67 9 , 73 8 , 80 7 , 85 6 , 90 27 4   11 , 97 11 , 02 10 , 07 9 , 13 8 , 18 7 , 23 26 5   12 , 30 11 , 35 10 , 40 9 , 47 8 , 52 7 , 57 25 6   12 , 63 11 , 68 10 , 73 9 , 80 8 , 87 7 , 83 24 7   12 , 97 12 , 01 11 , 07 10 , 12 9 , 17 8 , 20 23 8   13 , 28 12 , 33 11 , 38 10 , 47 9 , 48 8 , 52 22 9   13 , 60 12 , 65 11 , 70 10 , 75 9 , 80 8 , 83 21 10   13 , 92 12 , 97 12 , 02 11 , 07 10 , 12 9 , 15 20 11   14 , 23 13 , 28 12 , 33 11 , 38 10 , 48 9 , 45 19 12   14 , 53 13 , 58 12 , 63 11 , 68 10 , 72 9 , 75 18 13   14 , 83 13 , 88 12 , 93 11 , 98 11 , 02 10 , 05 17 14   15 , ●3 14 , 18 1● , 23 12 , 28 11 , 32 10 , 35 16 15   15 , 43 14 , 48 13 , 53 12 , 57 11 , 60 10 , 6● 15 16   15 , 72 14 , 77 13 , 80 12 , 85 11 , 88 10 , 92 14 17   16 , 00 15 , 05 14 , 08 13 , 13 12 , 17 11 , 20 13 18   16 , 28 15. 33 14 , 37 13 , 40 12 , 43 11 , 47 12 19   16 , 57 15. 60 14 , 63 13 , 67 12 , 70 11 , 73 11 20   16 , 83 15. 87 14 , 90 13 , 93 12 , 97 12 , 00 10 21   17 , 10 16. 13 15 , 17 14 , 20 13 , 23 12 , 25 9 22   17 , 37 16. 40 15 , 43 14 , 47 13 , 48 1● , 50 8 23   17 , 62 16. 65 15 , 68 14 , 72 13 , 73 12 , 75 7 24   17 , 87 16. 90 15 , 93 14 , 97 13 , 98 13 , 00 6 25   18 , 12 17. 15 16 , 17 15 , 20 14 , 22 13 , 23 5 26   18 , 35 17. 38 16 , 42 15 , 43 14 , 45 13 , 48 4 27   18 , 58 17. 60 16 , 63 15 , 65 14 , 68 13 , 68 3 28   18 , 80 17. 83 16 , 85 15 , 87 14 , 90 13 , 90 2 29   19 , 02 18. 05 17 , 07 16 , 08 15 , 12 14 , 12 1 30   19 , 23 18. 27 17 , 28 16 , 30 15 , 33 14 , 35 0 ♌ South Latitude . ♏ North Latitude . A Table of Declinations . ♊ North Latitude . ♐ South Latitude .   0 1 2 3 4 5 6   0 20 , 22 21 , 20 22 , 17 23 , 15 24 , 12 25 , 10 26 , 05 30 1 20 , 43 21 , 42 22 , 38 23 , 37 24 , 33 25 , 32 26 , 27 29 2 20 , 63 21 , 62 22 , 60 23 , 58 24 , 55 25 , 53 26 , 48 28 3 20 , 83 21 , 82 22 , 80 23 , 78 24 , 75 25 , 73 26 , 70 27 4 21 , 02 22 , 00 22 , 98 23 , 97 24 , 95 25 , 92 26 , 90 26 5 21 , 22 22 , 18 23 , 17 24 , 15 25 , 13 26 , 12 27 , 08 25 6 21 , 38 22 , 37 23 , 35 24 , 35 25 , 32 26 , 30 27 , 35 24 7 21 , 55 22 , 53 23 , 52 24 , 52 25 , 50 26 , 48 27 , 45 23 8 21 , 72 22 , 70 23 , 68 24 , 68 25 , 67 26 , 65 27 , 62 22 9 21 , 88 22 , 87 23 , 85 24 , 85 25 , 83 26 , 82 27 , 78 21 10 22 , 03 23 , 02 24 , 00 25 , 00 25 , 98 26 , 97 27 , 93 20 11 22 , 17 23 , 17 24 , 15 25 , 15 26 , 13 27 , 12 28 , 08 19 12 22 , 32 23 , 32 24 , 30 25 , ●0 26 , 28 27 , 27 28 , 23 18 13 22 , 45 23 , 45 24 , 43 25 , 43 26 , 42 27 , 40 28 , 37 17 14 22 , 57 23 , 57 24 , 55 25 , 55 26 , 53 27 , 52 28 , 50 16 15 22 , 68 23 , 68 24 , 67 25 , 65 26 , 65 27 , 63 28 , 62 15 16 23 , 78 23 , 72 24 , 77 25 , 75 26 , 75 27 , 75 28 , 72 14 17 22 , 88 23 , 88 24 , 88 25 , 87 26 , 87 27 , 87 28 , 82 13 18 22 , 98 23 , 98 14 , 98 25 , 97 26 , 97 27 , 97 28 , 92 12 19 2● , 07 24 , 07 25 , 07 26 , 05 27 , 05 28 , 05 29 , 03 11 20 23 , 15 24 , 15 25 , 15 26 , 13 27 , 13 28 , 13 29 , 12 10 21 23 , 22 24 , 22 25 , 22 26 , 22 27 , 20 28 , 20 29 , 20 9 22 23 , 28 24 , 28 25 , 28 26 , 28 27 , 27 28 , 27 29 , 25 8 23 23 , 33 24 , 33 25 , 3● 26 , 33 27 , 32 28 , 32 29 , 30 7 24 23 , 38 24 , 38 25 , 38 26 , 38 27 , 37 28 , 37 29 , 37 6 25 23 , 43 24 , 43 25 , 43 26 , 43 27 , 42 28 , 42 29 , 42 5 26 23 , 47 24 , 47 25 , 47 26 , 47 27 , 47 28 , 47 29 , 47 4 27 23 , 49 24 , 50 25 , 50 26 , 50 27 , 50 28 , 50 29 , 50 3 28 23 , 50 24 , 51 25 , 51 26 , 51 27 , 51 28 , 51 29 , 51 2 29 23 , 51 24 , 52 25 , 52 26 , 52 27 , 52 28 , 52 29 , 52 1 30 23 , 52 24 , 52 25 , 52 26 , 52 27 , 52 28 , 52 29 , 52 0 ♑ South Latitude . ♋ North Latitude . A Table of Declinations . ♊ South Latitude . ♐ North Latitude .   0 1 2 3 4 5 6   0   19 , 23 18 , 27 17 , 28 16 , 30 15 , 33 14. 35 30 1   19 , 45 18 , 47 17 , 48 16 , 50 15 , 53 14. 55 29 2   19 , 52 18 , 67 17 , 68 16 , 70 15 , 73 14. 75 28 3   19 , 85 18 , 87 17 , 88 16 , 90 15 , 92 14. 95 27 4   20 , 03 19 , 05 18 , 05 17 , 10 16 , 12 15. 1● 26 5   20 , 22 19 , 25 18 , 27 17 , ●8 16 , 30 15. 30 25 6   20 , 40 19 , 42 18 , 43 17 , 45 16 , 47 15. 47 24 7   20 , 57 19 , 58 18 , 60 17 , 62 16 , 63 15. 63 23 8   20 , 73 19 , 75 18 , 77 17 , 78 16 , 78 15. 80 22 9   20 , 90 19 , 92 18 , 93 17 , 93 16 , 93 15. 95 21 10   21 , 05 20 , 07 19 , 08 18 , 08 17 , 10 16. 08 20 11   21 , 18 20 , 18 19 , 22 18 , 22 17 , 23 16. 22 19 12   21 , 32 20 , 33 19 , 35 18 , 35 17 , 37 16. 35 18 13   21 , 45 20 , 47 19 , 47 18 , 48 17 , 48 16. 47 17 14   21 , 58 20 , 58 19 , 58 18 , 60 17 , 60 16. 58 16 15   21 , 68 20 , 68 19 , 68 18 , 70 17 , 70 16. 70 15 16   21 , 78 20 , 78 19 , 78 18 , 80 17 , 80 16. 80 14 17   21 , 88 20 , 88 19 , 88 18 , 90 17 , 90 16. 90 13 18   21 , 98 20 , 98 19 , 98 19 , 00 18 , 00 16. 98 12 19   22 , 07 21 , 07 20 , 07 19 , 08 18 , 08 17. 07 11 20   22 , 15 21 , 15 20 , 15 19 , 17 18 , 17 17. 15 10 21   22 , 22 21 , 22 20 , 22 19 , 23 18 , 23 17. 23 9 22   22 , 28 21 , 28 20 , 28 19 , 28 18 , 28 17. 2● 8 23   22 , 33 21 , 33 20 , 33 19 , 33 18 , 33 17. 33 7 24   22 , 38 21 , 38 20 , 38 19 , 38 18 , 38 17. 38 6 25   22 , 4● 21 , 43 20 , 43 19 , 43 18 , 43 17. 43 5 26   22 , 47 22 , 47 20 , 47 19 , 47 18 , 47 17. 47 4 27   22 , 50 21 , 50 20 , 50 19 , 50 18 , 50 17. 50 3 28   22 , 51 21 , 51 20 , 51 19 , 51 18 , 51 17. 51 2 29   22 , 52 21 , 52 20 , 52 19 , 52 18 , 52 17. 52 1 30   22 , 52 21 , 52 20 , 52 19 , 52 18 , 52 17. 52 0 ♑ North Latitude . ♋ South Latitude . A Table of Declinations . ♈ North Latitude . ♌ South Latitude .   0 1 2 3 4 5 6 0 0 , 00 359 , 62 359 , 22 358 , 82 358 , 42 358. 02 357. 62 1 0 , 92 0 , 53 0 , 13 359 , 73 359 , 33 358. 93 358. 53 2 1 , 83 1 , 45 1 , 05 0 , 65 0 , 25 359. 85 359. 45 3 2 , 75 2 , 37 1 , 97 1 , 57 1 , 17 0. 77 0. 37 4 3 , 67 3 , 28 2 , 88 2 , 48 2 , 08 1. 68 1. 28 5 4 , 58 4 , 20 3 , 80 4 , 40 3 , 00 2. 60 2. 20 6 5 , 50 5 , 12 4 , 72 4 , 32 3 , 9● 3. 52 3. 12 7 6 , 42 6 , 03 5 , 63 5 , 23 4 , 83 4. 43 4. 03 8 7 , 35 6 , 95 6 , 55 6 , 15 5 , 75 5. 35 4. 95 9 8 , 27 7 , 87 7 , 47 7 , 07 6 , 67 6. 27 5. 87 10 9 , 18 8 , 78 8 , 38 7 , 98 7 , 58 7. 18 6. 78 11 10 , 10 9 , 70 9 , 30 8 , 92 8 , 52 8. 12 7. 72 12 11 , 03 10 , 63 10 , 23 9 , 85 9 , 45 9. 05 8. 65 13 11 , 95 11 , 55 11 , 15 10 , 77 10 , 37 9. 97 9. 57 14 12 , 88 12 , 48 12 , 08 11 , 70 11 , 30 10. 90 10. 50 15 13 , 80 13 , 42 13 , 02 12 , 63 12 , 23 11. 67 11. 43 16 14 , 7● 14 , 3● 13 , 95 13 , 57 13 , 17 12. 77 12. 37 17 15 , 67 15 , 27 14 , 88 14 , 50 14 , 10 13. 70 13. 30 18 16 , 58 16 , 20 15 , 82 15 , 43 15 , 03 14. 65 14. 25 19 17 , 52 17 , 13 16 , 75 16 , 37 15 , 97 15. 58 15. 18 20 18 , 45 18 , 07 17 , 68 17 , 30 16 , 90 16. 52 16. 12 21 19 , 38 19 , 00 18 , 62 18 , 23 17 , 85 17. 47 17. 07 22 20 , 33 19 , 93 19 , 55 19 , 18 18 , 80 18. 42 18. 01 23 21 , 27 20 , 88 20 , 50 20 , 13 19 , 75 19. 37 19. 97 24 22 , 20 21 , 83 21 , 45 21 , 08 20 , 70 20. 32 20. 92 25 23 , 15 22 , 78 22 , 40 22 , 03 21 , 65 11. 27 21. 87 26 24 , 10 23 , 73 23 , 35 22 , 98 22 , 60 22. 22 22. 83 27 25 , 03 24 , 68 44 , 32 23 , 95 23 , 57 23. 18 23. 80 28 25 , 98 25 , 63 25 , 27 24 , 90 24 , 52 24. 15 24. 77 29 26 , 95 26 , 58 26 , 22 25 , 85 25 , 48 25. 12 25. 73 30 27 , 90 27 , 55 27 , 18 26 , 82 26 , 45 26. 08 26. 70 A Table of Right Ascensions . ♈ South Latitude ♎ North Latitude . 180. Adde .   0 1 2 3 4 5 6 0   0. 38 0 , 78 1 , 18 1 , 58 1 , 98 2 , 38 1   1. 30 1 , 70 2 , 10 2 , 50 2 , 90 3 , 30 2   2. 22 2 , 62 3 , 02 3 , 42 3 , 82 4 , 22 3   3. 13 3 , 53 3 , 93 4 , 33 4 , 73 5 , 13 4   4. 05 4 , 45 4 , 85 5 , 25 5 , 65 6 , 05 5   4. 97 5 , 37 5 , 77 6 , 17 6 , 57 6 , 97 6   5. 90 6 , 30 6 , 70 7 , 10 7 , 50 7 , 88 7   6. 82 7 , 22 7 , 62 8 , 02 8 , 42 8 , 80 8   7. 73 8 , 13 8 , 53 8 , 93 9 , 33 9 , 72 9   8. 66 9 , 07 9 , 47 9 , 85 10 , 25 10 , 63 10   9. 58 9 , 98 10 , 38 10 , 77 11 , 17 11 , 55 11   10. 50 10 , 90 11 , 30 11 , 68 12 , 08 12 , 47 12   11. 42 11 , 82 12 , 22 12 , 60 13 , 00 13 , 38 13   12. 33 12 , 73 13 , 13 13 , 52 13 , 92 14 , 30 14   13. 27 13 , 65 14 , 05 14 , 43 14 , 83 15 , 22 15   14. 20 14 , 58 14 , 97 15 , 35 15 , 75 16 , 13 16   15. 12 15 , 50 15 , 88 16 , 27 16 , 67 17 , 05 17   16. 03 16 , 42 16 , 80 17 , 18 17 , 58 17 , 97 18   16. 97 17 , 35 17 , 73 18 , 12 18 , 50 18 , 88 19   17. 90 18 , 28 18 , 67 19 , 03 19 , 42 19 , 80 20   18. 83 19 , 22 19 , 60 19 , 97 20 , 35 20 , 72 21   19. 76 20 , 15 20 , 53 20 , 90 21 , 28 21 , 65 22   20. 70 21 , 08 21 , 47 21 , 83 22 , 20 22 , 57 23   21. 63 22 , 01 22 , 40 22 , 77 23 , 13 23 , 50 24   22. 58 22 , 95 23 , 33 23 , 70 24 , 07 24 , 43 25   23. 52 23 , 88 24 , 27 24 , 63 25 , 00 25 , 35 26   24. 47 24 , 83 25 , 20 25 , 57 25 , 93 26 , 28 27   25. 42 25 , 78 26 , 15 26 , 50 26 , 87 27 , 22 28   26. 37 26 , 72 27 , 08 27 , 43 27 , 80 28 , 15 29   27. 32 27 , 67 28 , 02 28 , 37 28 , 73 29 , 08 30   28. 27 28 , 63 28 , 97 29 , 32 29 , 67 30 , 02 A Table of Right Ascensions . ♉ North Latitude . ♏ South Latitude . 180 Adde .   0 1 2 3 4 5 6 0 27 , 90 27 , 55 27 , 18 26 , 82 26 , 45 26 , 08 25 , 70 1 28 , 85 28 , 50 28 , 13 27 , 78 27 , 42 27 , 05 26 , 67 2 29 , 82 29 , 45 29 , 10 28 , 75 28 , 38 28 , 02 27 , 63 3 30 , 77 30 , 42 30 , 07 29 , 72 29 , 35 28 , 98 28 , 62 4 31 , 72 31 , 38 31 , 03 30 , 68 30 , 32 29 , 97 29 , 60 5 32 , 70 32 , 37 32 , 00 31 , 65 31 , 30 30 , 95 30 , 58 6 33 , 67 33 , 33 32 , 97 32 , 63 32 , 28 31 , 93 31 , 57 7 34 , 63 34 , 30 33 , 96 33 , 62 33 , 27 32 , 92 32 , 56 8 35 , 60 35 , 28 34 , 95 34 , 61 34 , 26 33 , 91 33 , 55 9 36 , 57 36 , 27 35 , 93 35 , 60 35 , 25 34 , 90 34 , 55 10 37 , 55 37 , 25 36 , 92 36 , 59 36 , 25 35 , 90 35 , 55 11 38 , 55 38 , 23 37 , 91 37 , 58 37 , 25 36 , 91 36 , 56 12 39 , 53 39 , 23 38 , 90 38 , 58 38 , 25 37 , 92 37 , 57 13 40 , 52 40 , 22 39 , 90 39 , 58 39 , 26 38 , 93 38 , 58 14 41 , 51 41 , 21 40 , 90 40 , 59 40 , 27 39 , 95 39 , 60 15 42 , 51 42 , 21 41 , 90 41 , 60 41 , 28 40 , 97 40 , 63 16 43 , 51 43 , ●1 42 , 91 42 , 61 42 , 30 41 , 98 41 , 65 17 44 , 51 44 , 22 43 , 92 43 , 62 43 , 32 43 , 00 4● , 67 18 45 , 52 45 , 23 44 , 93 44 , ●3 44 , 33 44 , 02 43 , 70 19 46 , 53 46 , 24 45 , 95 45 , 65 45 , 35 45 , 05 44 , 73 20 47 , 53 47 , 25 46 , 97 46 , 67 46 , 38 46 , 08 45 , 77 21 48 , 55 48 , 27 47 , 98 47 , 70 47 , 42 47 , 12 46 , 82 22 49 , 57 49 , 28 49 , 00 48 , 73 48 , 45 48 , 15 47 , 87 23 50 , 58 50 , 30 50 , 03 49 , 77 49 , 48 49 , 20 48 , 92 24 51 , 60 51 , 33 51 , 07 50 , 80 50 , 53 50 , 25 49 , 97 25 52 , 63 52 , 37 52 , 10 51 , 85 51 , 58 51 , 30 51 , 03 26 53 , 67 5● , 40 53 , 15 52 , 90 52 , 63 52 , 37 52 , 10 27 54 , 70 54 , 45 54 , 20 53 , 95 53 , 70 53 , 43 53 , 17 28 55 , 7● 55 , 48 55 , 25 55 , 00 54 , 75 54 , 50 54 , 23 29 56 , 77 56 , 53 56 , 30 56 , 05 55 , 82 55 , 57 55 , 30 30 57 , 80 57 , 58 57 , 35 57 , 12 56 , 88 56 , 63 56 , 38 A Table of Right Ascensions . ♉ South Latitude . ♏ North Latitude . 180. Adde .   0 1 2 3 4 5 6 0   28 , 27 28. 62 28 , 97 29 , 32 29 , 67 30 , 02 1   29 , 22 29. 57 29 , 92 30 , 27 30 , 62 30 , 95 2   30 , 17 30. 52 30 , 87 31 , 22 31 , 57 31 , 90 3   31 , 12 31. 47 31 , 82 32 , 17 32 , 52 32 , 85 4   32 , 08 32. 4● 32 , 77 33 , 12 33 , 45 33 , 78 5   33 , 05 33. 38 33 , 72 34 , 07 34 , 40 34 , 73 6   34 , 02 34. 35 34 , 68 35 , 02 35 , 35 35 , 68 7   34 , 98 35. 32 35 , 65 35 , 97 36 , 30 36 , 63 8   35 , 95 36. 28 36 , 62 56 , 93 37 , 25 37 , 5● 9   36 , 93 37. 25 37 , 58 37 , 90 38 , 22 38 , 5● 10   37 , 90 38. 22 38 , 55 38 , 87 39 , 18 39 , 48 11   38 , 88 39 , 20 39 , 52 39 , 83 40 , 15 40 , 45 12   39 , 87 40. 18 40 , 50 40 , 80 41 , 12 41 , 42 13   40 , 85 41. 17 41 , 47 41 , 77 42 , 08 42 , 38 14   41 , 83 42 , 15 42 , 45 42 , 75 43 , 05 43 , 35 15   42 , 82 43 , 13 43 , 43 43 , 73 44 , 03 44 , 32 16   43 , 81 44 , 12 44 , 42 44 , 72 45 , 00 45 , 28 17   44 , 81 45 , 11 45 , 40 45 , 70 45 , 98 46 , 25 18   45 , 81 46 , 10 46 , 39 46 , 68 46 , 97 47 , 23 19   46 , 82 47 , 10 47 , 38 47 , 67 47 , 95 48 , 22 20   47 , 82 48 , 10 48 , 38 48 , 66 48 , 93 49 , 20 21   4● , 83 49 , 10 49 , 38 49 , 65 49 , 92 50 , 18 22   49 , 84 50 , 10 50 , 38 50 , 64 50 , 90 51 , 17 23   50 , 85 51 , 11 51 , 38 51 , 63 51 , 89 52 , 15 24   51 , 87 52 , 12 52 , 39 52 , 63 52 , 88 53 , 14 25   52 , 88 53 , 13 53 , 39 53 , 63 5● , 88 54 , 13 26   53 , 92 54 , 15 54 , 40 54 , 64 54 , 88 55 , 12 27   54 , 93 55 , 18 55 , 42 55 , 65 55 , 89 56 , 12 28   55 , 97 56 , 20 56 , 43 56 , 67 56 , 90 57 , 11 29   57 , 00 57 , 22 57 , 45 57 , 68 57 , 91 58 , 12 30   58 , 03 58 , 25 58 , 48 58 , 70 58 , 92 59 , 12 A Table of Right Ascensions . ♊ North Latitude ♐ South Latitude . 180 Adde .   0 1 2 3 4 5 6 0 57 , 80 57. 58 57 , 35 57 , 12 56 , 88 56 , 63 56 , 38 1 58 , 85 58. 63 58 , 40 58 , 17 57 , 95 57 , 70 57 , 47 2 59 , 88 59. 68 59 , 45 59 , 23 59 , 02 58 , 78 58 , 55 3 60 , 93 60. 73 66 , 52 60 , 30 60 , 08 59 , 87 59 , 63 4 61 , 98 61. 78 61 , 58 61 , 37 61 , 17 60 , 95 60 , 73 5 63 , 05 62. 85 62 , 65 62 , 45 62 , 25 62 , 03 61 , 83 6 64 , 10 63. 92 63 , 72 63 , 53 63 , 33 63 , 13 62 , 93 7 65 , 15 64. 98 64 , 78 64 , 62 64 , 42 64 , 22 64 , 03 8 66 , 22 66. 05 65 , 87 65 , 70 65 , 50 65 , 32 65 , 13 9 67 , 28 67. 12 66 , 95 66 , 78 66 , 60 66 , 42 66 , 23 10 68 , 35 68. 18 68 , 03 67 , 87 67 , 70 67 , 52 67 , 35 11 69 , 42 69. 27 69 , 12 68 , 95 68 , 80 68 , 63 68 , 47 12 70 , 48 70. 35 70 , 20 70 , 05 69 , 90 69 , 75 69 , 58 13 71 , 7 71. 43 71 , 28 71 , 15 71 , 00 70 , 85 70 , 70 14 72 , 63 72. 52 72 , 37 72 , 25 72 , 10 71 , 97 71 , 82 15 73 , 70 73. 60 73 , 47 73 , 35 73 , 22 73 , 08 72 , 95 16 74 , 78 74. 68 74 , 55 74 , 45 74 , 32 74 , 20 74 , 07 17 75 , 87 75. 77 75 , 65 75 , 55 75 , 43 75 , 32 75 , 20 18 76 , 95 76. 85 76 , 75 76 , 65 76 , 55 76 , 45 76 , 33 19 78 , 03 77. 93 77 , 85 77 , 75 77 , 67 77 , 57 77 , 47 20 79 , 12 79. 03 78 , 95 78 , 87 78 , 78 78 , 68 78 , 60 21 80 , 20 80. 13 80 , 05 79 , 98 79 , 90 79 , 82 79 , 73 22 81 , 28 81. 22 81 , 15 81 , 08 81 , 02 80 , 93 80 , 87 23 82 , 37 82. 30 82 , 25 82 , 18 82 , 13 82 , 07 82 , 00 24 83 , 47 83. 40 83 , 35 83 , 30 83 , 25 83 , 20 83 , 15 25 84 , 55 84. 50 84 , 45 84 , 42 84 , 37 84 , 33 84 , 28 26 85 , 63 84. 60 85 , 55 85 , 53 85. 48 85 , 47 85 , 38 27 86 , 73 86. 70 86 , 67 86 , 65 86. 6● 86 , 60 86 , 57 28 87 , 82 87. 80 87 , 77 87 , 73 87. 78 87 , 73 87 , 70 29 88 , 92 88. 90 88 , 88 88 , 88 88 : 87 88 , 87 88 , 85 30 90 , 00 90. 00 90 , 00 90 , 00 90. 00 90 , 00 90 , 00 A Table of Right Ascensions . ♊ South Latitude . ♐ North Latitude . 180 Adde .   0 1 2 3 4 5 6 0   58 , 03 58 , 25 58 , 48 58 , 70 58 , 92 59 , 12 1   59 , 07 59 , 28 59 , 50 59 , 72 59 , 92 60 , 13 2   60 , 10 60 , 32 60 , 52 60 , 73 60 , 93 61 , 13 3   61 , 15 61 , 35 61 , 55 61 , 77 61 , 95 62 , 14 4   62 , 18 62 , 38 62 , 58 62 , 80 62 , 97 63 , 15 5   63 , 23 63 , 42 63 , 62 63 , 83 63 , 98 64 , 17 6   64 , 28 64 , 47 64 , 65 64 , 87 65 , 02 65 , 18 7   65 , 33 65 , 52 65 , 68 65 , 90 66 , 03 66 , 20 8   66 , 38 66 , 57 66 , 73 66 , 93 67 , 07 67 , 22 9   67 , 45 67 , 52 67 , 77 67 , 97 68 , 10 68 , 25 10   68 , 50 68 , 67 68 , 82 68 , 98 69 , 12 69 , 27 11   69 , 57 69 , 72 69 , 87 70 , 01 70 , 15 70 , 28 12   70 , 63 70 , 77 70 , 92 17 , 05 71 , 18 71 , 32 13   71 , 70 71 , 82 71 , 97 72 , 08 72 , 22 72 , 35 14   72 , 77 72 , 88 73 , 02 73 , 13 73 , 25 73 , 38 15   73 , 83 73 , 95 74 , 07 74 , 18 74 , 30 74 , 42 16   74 , 90 75 , 02 75 , 12 75 , 23 75 , 33 75 , 45 17   75 , 97 76 , 08 76 , 18 76 , 28 76 , 38 76 , 48 18   77 , 05 77 , 15 77 , 25 77 , 33 77 , 43 77 , 52 19   78 , 12 78 , 22 78 , 30 78 , 38 78 , 47 78 , 55 20   79 , 20 79 , 28 79 , 35 79 , 43 79 , 52 79 , 58 21   80 , 28 80 , 35 80 , 42 80 , 48 80 , 57 80 , 63 22   81 , 35 81 , 42 81 , 47 81 , 53 81 , 60 81 , 67 23   82 , 42 82 , 48 82 , 53 82 , 58 82 , 65 82 , 70 24   83 , 50 83 , 55 83 , 60 83 , 65 83 , 70 83 , 75 25   84 , 58 84 , 62 84 , 67 84 , 70 84 , 75 84 , 78 26   85 , 67 85 , 68 85 , 73 85 , 75 85 , 80 85 , 82 27   86 , 75 86 , 77 86 , 80 86 , 82 86 , 85 86 , 87 28   87 , 83 87 , 83 87 , 87 87 , 87 87 , 90 87 , 90 29   88 , 92 88 , 92 88 , 93 88 , 93 88 , 95 88 , 95 30   90 , 00 90 , 00 90 , 00 90 , 00 90 , 00 90 , 00 A Table of Right Ascensions . ♋ North Latitude ♑ South Latitude . 180 Adde .   0 1 2 3 4 5 6 0 90 , 00 90 , 00 90 , 00 90. 00 90 , 00 90 , 00 90 , 00 1 91 , 08 91 , 10 91 , 12 91. 12 91 , 13 91 , 13 91 , 15 2 92 , 18 92 , 20 92 , 23 92. 23 92 , 27 92 , 27 92 , 30 3 93 , 27 93 , 30 93 , 33 93. 35 93 , 38 93 , 40 93 , 43 4 94 , ●7 94 , 40 94 , 45 94. 47 94 , 52 94 , 53 94 , 62 5 95 , 45 95 , 50 95 , 55 95. 58 95 , 63 95 , 67 95 , 72 6 96 , 53 96 , 60 96 , 65 96. 70 96 , 75 96 , 80 96 , 85 7 97 , 63 97 , 70 97 , 75 97. 82 97 , 87 97 , 93 98 , 00 8 98 , 72 98 , 78 98 , 85 98. 92 99 , 98 99 , 07 99 , 13 9 99 , ●0 99 , 87 99 , 95 100. 02 100 , 10 100 , 18 100 , 27 10 100 , ●8 100 , 97 101 , 05 101. 13 101 , 22 101 , 32 101 , 40 11 101 , 97 102 , 07 102 , 15 102. 25 102 , 33 102 , 43 102 , 53 12 103 , 05 103 , 15 103 , 25 103. 35 103 , 45 103 , 55 103 , 67 13 104 , 13 104 , 2● 104 , 35 104. 45 104 , 57 104 , 68 104 , 80 14 105 , 22 105 , 32 105 , 45 105. 55 105 , 68 105 , 80 105 , 93 15 106 , 30 106 , 40 106 , 53 106. 65 106 , 78 106 , 92 107 , 05 16 107 , 37 107 , 48 107 , 63 107. 75 107 , 90 108 , 0● 108 , 18 17 108 , 43 108 , 57 108 , 72 108. 85 108 , 00 109 , 15 109 , 30 18 109 , 52 109 , 65 109 , 80 109. 95 110 , 10 110 , 25 110 , 42 19 110 , 58 110 , 73 110 , 88 111. 05 111 , 20 111 , 37 111 , 53 20 111 , 65 111 , 82 111 97 112. 13 112 , 30 112 , 48 112 , 65 21 112 , 72 112 , 88 113 , 05 113. 22 113 , 40 113 , 58 113 , 77 22 113 , 78 113 , 95 114 , 13 114. 30 114 , 50 114 , 68 114 , 87 23 114 , 85 115 , 02 115 , 22 115. 38 115 , 58 115 , 78 115 , 97 24 115 , 90 116 , 08 116 , 28 116 47 116 , 67 116 , 87 117 , 07 25 116 , 95 117 , 15 117 , 35 117. 55 117 , 75 117 , 97 118. 17 26 118 , 02 118 , 22 118 , 42 118. 63 118 , 83 119 , 05 119. 27 27 119 , 07 119 , 27 119 , 48 119. 70 119 , 92 120 , 13 120. 37 28 120 , 12 120 , 32 120 , 55 120. 77 120 , 98 122 , 22 121. 45 29 121 , 15 121 , 37 121 , 60 121. 83 122 , 05 122 , 30 122. 53 30 122 , 20 122 , 42 122 , 65 122. 88 123 , 12 123 , 37 123. 62 A Table of Right Ascensions . ♋ South Latitude . ♑ North Latitude . 180 Adde .   0 1 2 3 4 5 6 0   90 , 00 90 , 00 90 , 00 90 , 00 90 , 00 90 , 00 1   91 , 08 91 , 08 91 , 07 91 , 07 91 , 05 91 , 05 2   92 , 17 92 , 17 92 , 13 92 , 13 92 , 10 92 , 10 3   93 , 25 93 , 23 93 , 20 93 , 18 93 , 15 93 , 13 4   94 , 3● 94 , 32 94 , 27 94 , 25 94 , 20 94 , 18 5   95 , 42 95 , 38 95 , 33 95 , 30 95 , 25 95 , 22 6   96 , 50 96 , 45 96 , 40 96 , 35 96 , 30 96 , 25 7   97 , 58 97 , 52 97 , 47 97 , 42 97 , 35 97 , 30 8   98 , 65 98 , 58 98 , 53 98 , 47 98 , 40 98 , 33 9   99 , 72 99 , 65 99 , 58 99 , 52 99 , 43 99 , 37 10   100 , 80 100 , 72 100 , 65 100 , 57 100 , 48 100 , 42 11   101 , 88 101 , 78 101 , 70 101 , 62 101 , 53 101 , 45 12   102 , 95 102 , 85 102 , 75 102 , 67 102 , 57 102 , 48 13   104 , 03 103 , 92 103 , 82 103 , 72 103 , 62 103 , 52 14   105 , 10 104 , 98 104 , 88 104 , 77 104 , 67 104 , 55 15   106 , 17 106 , 05 105 , 93 105 , 82 105 , 70 105 , 58 16   107 ▪ 23 107 , 12 106 , 98 106 , 87 106 , 75 106 , 62 17   108 , ●0 108 , 18 108 , 0● 107 , 92 107 , 78 107 , 65 18   109 , 37 109 , 23 109 , 08 108 , 95 108 , 82 108 , 68 19   110 , 43 110 , 28 110 , 13 110 , 99 110 , 85 109 , 72 20   111 , 50 111 , 33 111 , 18 111 , 02 111 , 88 110 , 73 21   112 , 55 112 , 38 112 , 2● 112 , 03 112 , 90 111 , 75 22   113 , 62 113 , 4● 113 , 27 113 , 07 113 , 93 112 , 78 23   114 , 67 114 , 48 114 , 32 114 , 10 114 , 97 113 , 80 24   115 , 72 115 , 53 115 , 35 115 , 13 115 , 98 114 , 82 25   116 , 77 116 , 58 116 , 38 116 , 17 116 , 02 115 , 83 26   117 , 82 117 , 62 117 , 42 117 , 20 117 , 03 116 , 85 27   118 , 85 118 , 65 118 , 45 118 , 23 118 , 05 117 , 86 28   119 , 90 119 , 68 119 , 48 119 , 27 119 , 07 118 , 87 29   120 , 93 120 , 72 120 , 50 120 , ●8 120 , 08 119 , 88 30   121 , 97 121 , 75 121 , 52 121 , 30 121 , 08 120 , 88 A Table of Right Ascensions . ♌ North Latitude ♒ South Latitude . 180 Adde .   0 1 2 3 4 5 6 0 122 , ●0 122 , 42 122 , 65 122 , 88 123 , ●2 123. 37 123. 62 1 123 , ●3 123 , 47 123 , 70 123 , 95 124 , ●8 124. 43 124. 70 2 124 , 27 124 , 52 124 , 75 125 , 00 125 , 25 125. 50 125. 77 3 125 , 30 125 , 55 125 , 80 126 , ●5 126 , 30 126. 57 126. 83 4 126 , 33 126 , 60 126 , 85 127 , 10 127 , 37 127. 63 127. 90 5 127 , 37 127 , 63 127 , 90 128 , 15 128 , 42 128. 70 128. 97 6 128 , 40 128 , 67 128 , 93 129 , 20 129 , 47 129. 75 130. 03 7 129 , 42 129 , 70 129 , 97 130 , 23 130 , 52 130. 80 131. 08 8 130 , 43 130 , 72 131 , 00 131 , 27 131 , 55 131. 85 232. 13 9 131 , 45 131 , 73 132 , 02 132 , 30 132 , 58 132. 88 133. 18 10 132 , 46 132 , 75 133 , 03 133 , 33 133 , 62 133. 92 134. 23 11 133 , 47 133 , 77 134 , 05 134 , 35 134 , 65 134. 95 135. 27 12 134 , 48 134 , 78 135 , 07 135 , 37 135 , 67 135. 98 136. 30 13 135 , 48 135 , 78 136 , 08 136 , 38 136 , 68 137. 00 137. 33 14 136 , 49 136 , 79 137 , 09 137 , 39 137 , 70 138. 02 138. 35 15 137 , 4● 237 , 79 138 , 09 138 , 40 138 , 72 139. 03 139. 37 16 138 , 48 138 , 78 139 , 10 139 , 41 139 , 73 140. 05 140. 40 17 139 , 47 139 , 78 140 , 10 040 , 41 140 , 74 141. 07 141. 42 18 140 , 46 140 , 77 141 , 09 141 , 42 141 , 74 142. 08 142. 43 19 141 , 45 141 , 76 142 , 09 142 , 41 142 , 75 143. 09 143. 44 20 142 , 43 142 , 75 143 , 08 143 , 41 143 , 75 144. 10 144. 44 21 143 , 41 143 , 73 144 , 07 144 , 40 144 , 74 145. 10 145. 45 22 144 , 38 144 , 72 145 , 05 145 , 39 145 , 74 146. 09 146. 45 23 145 , 36 145 , 70 146 , 03 146 , 38 146 , 73 147. 08 147. 44 24 146 , 33 146 , 67 147 , 02 147 , 37 147 , 72 148. 07 148. 43 25 147 , 30 147 , 65 148 , 00 148 , 35 148 , 70 149. 05 149. 42 26 148 , 27 148 , 62 148 , 97 149 , 32 149 , 68 150. 03 150. 40 27 149 , 23 149 , 58 149 , 93 150 , 28 150 , 65 151. 01 151. 38 28 150 , 18 150 , 55 150 , 90 151 , 25 151 , 62 151. 98 152. 37 29 151 , 15 551 , 50 151 , 87 152 , 22 152 , 52 152. 95 153. 33 30 152 , 10 152 , 45 152 , 82 153 , 18 153 , 55 153. 92 154. 30 A Table of Right Ascensions . ♌ South Latitude ♒ North Latitude . 180. Adde .   0 1 2 3 4 5 6 0   121 , 97 121 , 75 121 , 52 121 , 30 121 , 08 120. 88 1   123 , 00 122 , 78 122 , 55 122 , 32 122 , 09 121. 88 2   124 , 03 123 , 80 123 , 57 123 , 33 123 , 10 122. 89 3   125 , 07 124 , 82 124 , 58 124 , 35 124 , 11 123. 88 4   126 , 08 125 , 85 125 , 60 125 , 36 125 , 12 123. 88 5   127 , 12 126 , 87 126 , 61 126 , 37 126 , 12 125. 87 6   128 , 13 127 , 88 127 , 61 127 , 37 127 , 12 126. 86 7   129 , 15 128 , 89 128 , 62 128 , 37 128 , 11 127. 85 8   130 , 16 129 , 90 129 , 62 129 , 36 129 , 10 128. 83 9   131 , 17 130 , 90 130 , 62 130 , 35 130 , 08 129. 82 10   132 , 18 131 , 90 131 , 62 131 , 34 131 , 07 130. 80 11   133 , 18 132 , 90 132 , 62 132 , 33 132 , 05 131. 78 12   134 , 19 133 , 90 133 , 61 133 , 32 133 , 03 132. 77 13   135 , 19 134 , 89 134 , 60 134 , 30 134 , 02 133. 75 14   136 , 19 135 , 88 135 , 58 135 , 28 135 , 00 134. 72 15   137 , 18 136 , 87 136 , 57 136 , 27 135 , 97 135. 68 16   138 , 17 237 , 85 137 , 55 137 , 25 136 , 95 136. 65 17   139 , 15 138 , 83 138 , 53 138 , 23 137 , 92 137. 6● 18   140 , 13 139 , 82 139 , 50 139 , 20 138 , 88 138. 5● 19   141 , 12 140 , 80 140 , 48 140 , 17 139 , 85 139. 55 20   142 , 10 141 , 78 141 , 45 141 , 13 140 , 82 140. 52 21   143 , 07 142 , 75 142 , 42 142 , 10 141 , 78 141. 47 22   144 , 05 143 , 72 143 , 38 143 , 07 142 , 75 142. 4● 23   145 , 02 144 , 68 144 , 35 144 , 03 143 , 50 143. 37 24   145 , 98 145 , 65 145 , 32 144 , 98 144 , 65 144. 3● 25   146 , 95 146 , 62 146 , 28 145 , 93 145 , 60 145. ●7 26   147 , 92 147 , 58 147 , 23 146 , 88 146 , 55 146. 22 27   148 , 88 148 , 53 148 , 18 147 , 83 147 , 48 147. 15 28   149 , 83 149 , 48 149 , 13 148 , 78 148 , 43 148. 1● 29   150 , 77 150 , 43 150 , 08 149 , 73 149 , 38 149. ●● 30   151 , 73 551 , 38 151 , 03 150 , 68 150 , 33 149. 9● A Table of Right Ascensions . ♈ North Latitude . ♓ South Latitude . 180 Adde .   0 1 2 3 4 5 6 0 152 , 10 152 , 45 152 , 82 153. 18 153 , 55 153 , 92 154 , 30 1 153 , 05 153 , 42 153 , 78 154. 15 154 , 52 154 , 88 155 , 27 2 154 , 02 154 , 37 154 , 73 155. 10 155 , 48 155 , 85 156 , 23 3 154 , 97 155 , 32 155 , 68 156 , 0● 156 , 43 156 , 82 157 , 20 4 155 , 90 156 , 27 156 , 65 157. 02 157 , 40 157 , 78 158 , 17 5 156 , 85 157 , 22 157 , 60 157. 97 158 , 35 158 , 73 159 , 13 6 157 , 80 258 , 17 158 , 55 158. 92 159 , 30 159 , 68 160 , 08 7 158 , 73 159 , 12 159 , 50 159. 87 160 , 25 160 , 63 161 , 03 8 159 , 67 160 , 07 160 , 45 160. 82 161 , 20 161 , 58 161 , 99 9 160 , 62 161 , 00 161 , 38 161. 77 162 , 15 162 , 53 162 , 93 10 161 , 55 161 , 93 162 , 32 162. 70 163 , 10 163 , 48 163 , 88 11 162 , 48 162 , 87 163 , 25 163. 63 164 , 03 164 , 42 164 , 82 12 163 , 42 163 , 80 164 , 18 164. 57 164 , 97 165 , 35 165 , 75 13 164 , 33 164 , 73 165 , 21 165. 50 165 , 90 166 , 30 166 , 70 14 165 , 27 165 , 67 166 , 05 166. 43 166 , 83 167 , 23 167 , 63 15 166 , 20 166 , 58 166 , 98 167. 37 167 , 77 168 , 33 168 , 57 16 167 , 12 167 , 52 167 , 92 168. 30 168 , 70 169 , 10 169 , 50 17 168 , 05 168 , 45 168 , 85 569. 23 169 , 62 170 , 03 170 , 43 18 168 , 97 169 , 37 169 , 77 170. 15 170 , 55 170 , 95 171 , 35 19 169 , 90 170 , 30 170 , 70 171. 08 171 , 48 171 , 88 172 , 28 20 170 , 82 171 , 22 171 , 62 172. 02 172 , 42 172 , 82 173 , 22 21 171 , 73 172 , 13 172 , 53 172. 93 173 , 33 173 , 73 174 , 13 22 172 , 65 173 , 05 173 , 45 173. 85 174 , 25 174 , 65 175 , 05 23 173 , 58 173 , 97 174 , 37 174. 77 175 , 17 175 , 57 175 , 97 24 174 , 50 174 , 88 175 , 28 175. 68 176 , 08 176 , 48 176 , 88 25 175 , 42 175 , 80 176 , 20 176. 60 177 , 00 177 , 40 177. 80 26 176 , 33 176 , 72 177 , 12 177. 52 177 , 92 178 , 32 178. 72 27 177 , 25 177 , 63 178 , 03 178. 43 178 , 83 179 , 23 179. 63 28 178 , 17 178 , 55 178 , 95 179. 35 579 , 75 180 , 15 180. 55 29 179 , 08 179 , 47 179 , 87 180 27 180 , 67 181 , 07 181. 47 30 180 , 00 180 , 38 180 , 78 181. 18 181 , 58 181 , 98 182. 38 A Table of Right Ascensions . ♍ South Latitude ♓ North Latitude . 180 Adde .   0 1 2 3 4 5 6 0 152 151 , 73 151 , 37 151 , 03 150 , 68 150 , 33 149 , 98 1 153 152 , 68 152 , 33 151 , 98 551 , 63 151 , 27 150 , 92 2 154 153 , 62 153 , 28 152 , 92 152 , 57 152 , 20 151 , 85 3 154 154 , 58 154 , 22 153 , 85 153 , 50 153 , 13 152 , 78 4 155 155 , 52 155 , 17 154 , 80 154 , 43 154 , 07 153 , 72 5 156 156 , 48 156 , 12 155 , 73 155 , 37 155 , 00 154 , 65 6 157 157 , 42 157 , 05 156 , 67 156 , 30 155 , 93 155 , 57 7 158 158 , 37 157 , 99 157 , 60 157 , 23 156 , 87 156 , 50 8 159 159 , 30 158 , 92 158 , 53 158 , 17 157 , 80 157 , 43 9 160 160 , 23 159 , 85 159 , 47 159 , 10 158 , 72 158 , 35 10 161 161 , 17 160 , 78 160 , 40 160 , 03 159 , 65 159 , 28 11 162 162 , 10 161 , 72 161 , 33 160 , 97 160 , 58 160 , 20 12 163 163 , 03 162 , 65 162 , 27 161 , 88 161 , 50 161 , 12 13 164 163 , 97 163 , 58 163 , 20 162 , 82 162 , 42 162 , 03 14 165 164 , 88 164 , 50 164 , 12 163 , 73 163 , 33 163 , 95 15 166 165 , 80 165 , 42 165 , 03 164 , 65 164 , 25 163 , 87 16 167 166 , 73 166 , 35 165 , 95 165 , 57 165 , 17 164 , 78 17 168 167 , 67 167 , 27 166 , 87 166 , 48 166 , 08 165 , 70 18 168 168 , 58 168 , 18 167 , 78 167 , 40 167 , 00 166 , 62 19 169 169 , 50 169 , 10 168 , 70 168 , 32 167 , 92 167 , 53 20 170 170 , 42 170 , 02 169 , 62 169 , 23 168 , 83 168 , 45 21 171 171 , 34 170 , 93 170 , 53 170 , 15 169 , 75 169 , 37 22 172 172 , 27 171 , 87 171 , 47 171 , 07 170 , 67 170 , 28 23 173 173 , 18 172 , 78 172 , 38 171 , 98 171 , 58 171 , 20 24 174 174 , 10 173 , 70 173 , 30 172 , 90 172 , 50 172 , 12 25 175 175 , 03 174 , 63 174 , 23 173 , 83 173 , 43 173 , 03 26 176 175 , 95 175 , 55 175 , 15 174 , 75 174 , 35 173 , 95 27 177 176 , 87 176 , 47 176 , 07 175 , 67 175 , 27 174 , 87 28 178 177 , 78 177 , 38 176 , 98 176 , 58 176 , 18 175 , 78 29 179 178 , 70 178 , 30 177 , 90 177 , 50 177 , 10 176 , 70 30 179 179 , 62 179 , 32 178 , 82 178 , 42 178 , 02 177 , 62 A Table of Ascensional Differences . Poles . 1 2 3 4 5 6 7 Degrees of Declination . 1 00. 01 00. 0● 00 , 05 00 , 07 00 , 08 00 , 10 00 , 12 2 0. 03 0. 06 0 , 10 0 , 13 0 , 17 00 , 22 0 , 25 3 0. 05 0. 10 0 , 15 0 , 22 0 , 27 0 , 32 0 , 37 4 0. 06 0. 13 0 , 22 0 , 28 0 , 35 0 , 42 0 , 50 5 0. 08 0. 16 0 , 27 0 , 35 0 , 43 0 , 53 0 , 62 6 0. 10 0. 21 0 , 32 0 , 42 0 , 53 0 , 63 0 , 73 7 0. 11 0. 25 0 , 37 0 , 50 0 , 62 0 , 73 0 , 87 8 0. 13 0. 28 0 , 42 0 , 57 0 , 70 0 , 85 0 , 98 9 0. 15 0. 32 0 , 48 0 , 63 0 , 80 0 , 95 1 , 12 10 0. 18 0. 35 0 , 53 0 , 70 0 , 88 1 , 07 1 , 23 11 0. 20 0. 38 0 , 58 0 , 78 0 , 97 1 , 17 1 , 37 12 0. 21 0. 42 0 , 63 0 , 85 1 , 07 1 , 28 1 , 50 13 0. 23 0. 47 0 , 70 0 , 93 1 , 15 1 , 38 1 , 62 14 0. 25 0. 50 0 , 75 1 , 00 1 , 25 1 , 50 1 , 75 15 0. 26 0. 53 0 , 80 1 , 07 1 , 35 1 , 62 1 , 88 16 0. 28 0. 57 0 , 87 1 , 15 1 , 43 1 , 73 2 , 01 17 0. 30 0. 62 0 , 92 1 , 23 1 , 53 1 , 83 2 , 15 18 0. 32 0. 65 0 , 98 1 , 30 1 , 63 1 , 95 2 , 28 19 0. 35 0. 68 1 , 03 1 , 38 1 , 73 2 , 07 2 , 42 20 0. 36 0. 73 1 , 10 1 , 45 1 , 82 2 , 20 2 , 57 21 0. 38 0. 77 1 , 15 1 , 53 1 , 92 2 , 32 2 , 70 22 0. 40 0. 82 1 , 22 1 , 62 2 , 03 2 , 43 2 , 85 23 0. 42 0. 85 1 , 28 1 , 70 2 , 13 2 , 55 2 , 98 24 0. 44 0. 88 1 , 33 1 , 78 2 , 23 2 , 68 3 , 03 25 0. 46 0. 93 1 , 40 1 , 87 2 , 33 2 , 82 3 , 28 26 0. 48 0. 98 1 , 47 1 , 95 2 , 45 2 , 93 3 , 43 27 0. 51 1. 02 1 , 53 2 , 05 2 , 55 3 , 07 3 , 58 28 0. 53 1. 07 1 , 60 2 , 13 2 , 67 3 , 20 3 , 75 29 0. 55 1. 13 1 , 67 2 , 22 2 , 78 3 , 33 3 , 90 30 0. 58 1. 15 1 , 73 2 , 32 2 , 90 3 , 48 4 , 07 31 0. 60 1. 20 1 , 80 2 , 40 3 , 01 3 , 62 4 , 23 32 0. 62 1. 25 1 , 88 2 , 50 3. 13 3 , 77 4 , 40 A Table of Ascensional Differences . Height . 8 9 10 11 12 13 14 Degrees of Declination . 1 00 , 13 00. 15 00 , 18 00 , 20 00 , 22 00 , 23 00 , 25 2 0 , 28 0. 32 0 , 35 0 , 38 0 , 42 0 , 47 0 , 50 3 0 , 42 0. 48 0 , 53 0 , 58 0 , 63 0 , 70 0 , 75 4 0 , 57 0. 63 0 , 70 0 , 78 0 , 85 0 , 93 1 , 00 5 0 , 70 0. 80 0 , 88 0 , 97 1 , 07 1 , 15 1 , 25 6 0 , 85 0. 95 1 , 07 1 , 17 1 , 28 1 , 38 1 , 50 7 0 , 98 1. 12 1 , 23 1 , 37 1 , 50 1 , 62 1 , 73 8 1 , 13 1. 27 1 , 42 1 , 57 1 , 72 1 , 87 2 , 00 9 1 , 27 1. 43 1 , 60 1 , 77 1 , 93 2 , 10 2 , 27 10 1 , 42 1. 60 1 , 78 1 , 97 2 , 15 2 , 33 2 , 52 11 1 , 57 1. 77 1 , 97 2 , 17 2 , 37 2 , 57 2 , 78 12 1 , 72 1. 93 2 , 15 2 , 37 2 , 58 2 , 82 3 , 03 13 1 , 87 2. 10 2 , 33 2 , 57 2 , 82 3 , 05 3 , 30 14 2 , 00 2. 27 2 , 5● 2 , 78 3 , 03 3 , 30 3 , 57 15 2 , 17 2. 43 2 , 70 2 , 98 3 , 27 3 , 55 3 , 83 16 2 , 32 2. 60 2 , 90 3 , 20 3 , 50 3 , 80 4 , 10 17 2 , 47 2. 78 3 , 08 3 , 40 3 , 73 4 , 05 4 , 37 18 2 , 62 2. 95 3 , 28 3 , 62 3 , 97 4 , 30 4 , 65 19 2 , 77 3. 13 ● , 48 3 , 83 4 , 28 4 , 57 4 , 92 20 2 , 93 3. 30 3 , 68 4 , 05 4 , 43 4 , 82 5 , 20 21 3 , 10 3. 48 3 , 88 4 , 28 4 , 68 5 , 08 5 , 50 22 3 , 25 3. 67 4 , 08 4 , 50 4 , 93 5 , 35 5 , 78 23 3 , 42 3. 85 4 , 30 4 , 7● 5 , 18 5 , 62 6 , 12 24 3 , 58 4. 05 4 , 50 4 , 63 5 , 43 5 , 90 6 , 37 25 3 , 75 4. 23 4 , 72 5 , 20 5 , 68 6 , 18 6 , 68 26 3 , 93 4. 43 4 , 93 5 , 43 5 , 95 6 , 47 6 , 98 27 4 , 10 4. 63 5 , 15 5 , 68 6. 22 6 , 75 7 , 30 28 4 , 28 4. 83 5 , 38 5 , 93 6. 48 7 , 05 7 , 62 29 4 , 47 5. 03 5 , 62 6 , 18 6. 77 7 , 35 7 , 95 30 4 , 65 5. 25 5 , 85 6 , 45 7 : 05 7 , 67 8 , 28 31 4 , 85 5. 47 6 , 08 6 , 70 7. 33 7 , 97 8 , 62 32 5 , 03 5. 68 6 , 33 6 , 98 7. 63 8 , 30 8 , 97 A Table of Ascensional Differences . Poles . 15 16 17 18 19 20 21 Degrees of Declination . 1 00 , 27 00 , 28 00 ; 30 00 , 32 00 , 35 00 , 37 00 , 38 2 0 , 53 0 , 57 0 , 62 0 , 65 0 , 68 0 , 73 0 , 77 3 0 , 80 0 , 87 0 , 92 0 , 98 1 , 03 1 , 10 1 , 15 4 1 , 07 1 , 15 1 , 23 1 , 30 1 , 38 1 , 45 1 , 53 5 1 , 35 1 , 27 1 , 53 1 , 63 1 , 73 1 , 82 1 , 92 6 1 , 62 1 , 73 1 , 83 1 , 95 2 , 07 2 , 20 2 , 32 7 1 , 95 2 , 01 2 , 15 2 , 28 2 , 42 2 , 57 2 , 70 8 2 , 15 2 , 32 2 , 47 2 , 62 2 , 77 2 , 93 3 , 10 9 2 , 43 2 , 60 2 , 78 2 , 95 3 , 13 3 , 30 3 , 48 10 2 , 70 2 , 90 3 , 08 3 , 28 3 , 48 3 , 68 3 , 88 11 2 , 98 3 , 20 3 , 40 3 , 62 3 , 83 4 , 05 4 , 28 12 3 , 27 3 , 50 3 , 73 3 , 97 4 , 20 4 , 43 4 , 68 13 3 , 55 3 , 80 4 , 05 4 , 30 4 , 57 4 , 82 5 , 08 14 3 , 83 4 , 10 4 , 37 4 , 65 4 , 92 5 , 20 5 , 50 15 4 , 12 4 , 40 4 , 70 5 , 00 5 , 30 5 , 60 5 , 90 16 4 , 40 4 , 72 5 , 03 5 , 35 5 , 67 5 , 98 6 , 32 17 4 , 70 5 , 03 5 , 37 5 , 70 6 , 03 6 , 38 6 , 73 18 5 , 00 5 , 35 5 , 70 6 , 07 6 , 42 6 , 78 7 , 17 19 5 , 30 5. 67 6 , 05 6 , 42 6 , 82 7 , 20 7 , 60 20 5 , 60 5. 98 6 , 38 6 , 78 7 , 20 7 , 62 8 , 03 21 5 , 90 6. 32 6 , 73 7 , 17 7 , 60 8 , 03 8 , 47 22 6 , 22 6. 65 7 , 10 7 , 55 8 , 00 8 , 45 8 , 92 23 6 , 5● 6. 98 7 , 45 7 , 93 8 , 40 8 , 88 9 , 37 24 6 , 85 7. 33 7 , 82 8 , 32 8 , 82 9 , 32 9 , 83 25 7 , 18 7. 68 8 , 20 8 , 72 9 , 23 9 , 77 10 , 32 26 7 , 52 8. 03 8 , 58 9 , 12 9 , 67 10 , 23 10 , 78 27 7 , 85 8. 40 8 , 97 9 , 53 10 , 10 10 , 68 11 , 28 28 8 , 18 8. 77 9 , 35 9 , 95 10 , 55 11 , 15 11 , 78 29 8 , 53 9. 15 9 , 75 10 , 38 11 , 17 11 , 63 12 , 28 30 8 , 90 9. 53 10 , 17 10 , 82 11 , 47 12 , 13 12 , 80 31 9 , 27 9. 92 10 , 58 11 , 27 11 , 93 12 , 63 13 , 33 32 9 , 63 10. 32 11 , 01 11 , 72 12 , 42 13 , 15 13 , 88 A Table of Ascensional Differences . Height . 22 23 24 25 26 27 28 Degrees of Declination . 1 00 , 40 00. 42 00 , 45 00 , 47 00 , 48 00 , 51 00 , 53 2 0 , 82 0. 85 0 , 88 0 , 93 0 , 98 1 , 02 1 , 07 3 1 , 22 1. 28 1 , 33 1 , 40 1 , 47 1 , 53 1 , 60 4 1 , 62 1. 70 1 , 78 1 , 87 1 , 95 2 , 05 2 , 13 5 2 , 03 2. 13 2 , 23 2 , 33 2 , 45 2 , 55 2 , 67 6 2 , 43 2. 55 2 , 68 2 , 82 2 , 93 3 , 07 3 , 20 7 2 , 85 2. 98 3 , 13 3 , 28 3 , 43 3 , 58 3 , 75 8 3 , 25 3. 42 3 , 58 3 , 75 3 , 93 4 , 10 4 , 28 9 3 , 67 3. 85 4 , 05 4 , 23 4 , 43 4 , 63 4 , 83 10 4 , 08 4. 30 4 , 50 4 , 72 4 , 93 5 , 15 5 , 38 11 4 , 50 4. 73 4 , 97 5 , 20 5 , 45 5 , 68 5 , 93 12 4 , 93 5. 18 5 , 43 5 , 68 5 , 95 6 , 22 6 , 48 13 5 , 35 5. 63 5 , 90 6 , 18 6 , 47 6 , 75 7 , 05 14 5 , 78 6. 08 6 , 37 6 , 68 6 , 98 7 , 30 7 , 62 15 6 , 22 6. 53 6 , 85 7 , 18 7 , 53 7 , 85 8 , 18 16 6 , 65 6. 98 7 , 33 7 , 68 8 , 05 8 , 40 8 , 77 17 7 , 10 7. 45 7 , 82 8 , 20 8 , 58 8 , 97 9 , 35 18 7 , 55 7. 93 8 , 32 8 , 72 9 , 12 9 , 53 9 , 85 19 8 , 00 8. 40 8 , 82 9 , 23 9 , 67 10 , 10 10 , 55 20 8 , 45 8. 88 9 , 32 9 , 77 10 , 23 10 , 68 11 , 15 21 8 , 92 9. 38 9 , 83 10 , 32 10 , 78 11 , 28 11 , 77 22 9 , 40 9. 88 10 , 37 10 , 87 11 , 37 11 , 88 12 , 40 23 9 , 88 10. 38 10 , 90 11 , 42 11 , 95 12 , 48 13 , 05 24 10 , 37 10. 90 11 , 43 11 , 98 12 , 55 13 , 12 13 , 70 25 10 , 87 11. 42 11 , 98 12 , 57 13 , 15 13 , 80 14 , 35 26 11 , 37 11. 95 12 , 55 13 , 15 14 , 77 14 , 38 15 , 03 27 11 , 88 12. 48 13 , 12 13 , 73 14 , 38 15 , 05 15 , 72 28 12 , 40 13. 05 13 , 70 14 , 35 15 , 03 15 , 72 16 , 42 29 12 , 93 13. 62 14 , 28 14 , 48 15. 68 16 , 40 17 , 13 30 13 , 48 14. 18 14 , 90 15 , 62 16. 35 17 , 12 17 , 88 31 14 , 05 14. 78 15 , 52 16 , 27 17 , 03 17 , 83 18 , 63 32 14 , 62 15. 38 16 , 15 16 , 93 17 , 75 18 , 57 19 , 40 A Table of Ascensional Differences . Poles . 29 30 31 32 33 34 35 Degrees of Declination . 1 00 , 5● 00 , 58 00 , 60 00 , 62 00 , 65 00 , 67 00 , 70 2 1 , 12 1 , 15 1 , 20 1 , 25 1 , 30 1 , 35 1 , 40 3 1 , 67 1 , 73 1 , 80 1 , 88 1 , 95 2 , 03 2 , 10 4 2 , 22 2 , 32 2 , 40 2 , 50 2 , 60 2 , 70 2 , 80 5 2 , 78 2 , 90 3 , 01 3 , ●3 3 , 25 3 , 38 3 , 52 6 3 , 33 3 , 48 3 , 62 3 , 77 3 , 92 4 , 07 4 , 22 7 3 , 90 4 , 07 4 , 23 4 , 40 4 , 57 4 , 75 4 , 93 8 4 , 47 4 , 65 4 , 85 5 , 03 5 , 23 5 , 43 5 , 65 9 5 , 03 5 , 25 5 , 47 5 , 68 5 , 90 6 , 13 6 , 37 10 5 , 62 5 , 85 6 , 0● 6 , 33 6 , 58 6 , 83 7 , 10 11 6 , 18 6 , 45 6 , 70 6 , 98 7 , 25 7 , 53 7 , 82 12 6 , 77 7 , 05 7 , 33 7 , 63 7 , 93 8 , 25 8 , 57 13 7 , 35 7 , 67 7 , 97 8 , 30 8 , 62 8 , 97 9 , 30 14 7 , 93 8 , 28 8 , 62 8 , 97 9 , 32 9 , 68 10 , 05 15 8 , 53 8 , 90 9 , 27 9 , 63 10 , 02 10 , 42 10 , 82 16 9 , 13 9 , 53 9 , 92 10 , 32 10 , 7● 11 , 15 11 , 58 17 9 , 75 10 , 17 10 , 58 11 , 02 11 , 45 11 , 90 12 , 37 18 10 , 38 10 , 8● 11 , 27 11 , 72 12 , 18 12 , 67 13 , 15 19 11 , 00 11 , 47 11 , 93 12 , 42 12 , 92 13 , 43 13 , 85 20 11 , 63 12 , 13 12 , 63 13 , 15 13 , 67 14 , 22 14 , 77 21 12 , 28 12 , 80 13 , 33 13 , 88 14 , 43 15 , 00 15 , 65 22 12 , 93 13 , 48 14 , 05 14 , 62 15 , 22 15 , 82 16 , 45 23 13 , 62 14 , 18 14 , 78 15 , 38 16 , 00 16 , 63 17 , 28 24 14 , 28 14 , 90 15 , 52 16 , 15 16 , 80 17 , 48 18 , 17 25 14 , 98 15 , 62 16 , 27 16 , 93 17 , 63 18 , 33 19 , 05 26 15 , 68 16 , 35 17 , 03 17 , 75 18 , 47 19 , 20 19 , 97 27 16 , 40 17 , 10 17 , 83 18 , 57 19 , 32 20 , 10 20 , 90 28 17 , 13 17 , 88 18 , 63 19 , 40 20 , 20 21 , 01 21 , 85 29 17 , 90 18 , 67 19 , 45 20 , 27 21 , 10 21 , 95 22 , 83 30 18 , 67 19 , 47 20 , 30 21 , 15 22 , 02 22 , 92 23 , 85 31 19 , 45 20 , 30 21 , 17 22 , 05 22 , 97 23 , 92 24 , 88 32 20 , 27 21 , 15 22 , 05 23 , 98 23 , 93 24 , 93 25 , 95 A Table of Ascensional Differences . Height . 36 37 38 39 40 41 42 Degrees of Declination . 1 00 , 73 00 , 75 00 , 78 00 , 82 00 , 83 00 , 87 00 , 90 2 1 , 45 1 , 53 1 , 57 1 , 62 1 , ●8 1 , 73 1 , 80 3 2 , 18 2 , 27 2 , 35 2 , 43 2 , 52 2 , 62 2 , 70 4 2 , 92 3 , 01 3 , 13 3 , 25 3 , 37 3 , 48 3 , 62 5 3 , 65 3 , 78 3 , 92 4 , 07 4 , 22 4 , 37 4 , 52 6 4 , 38 4 , 55 4 , 72 4 , 87 5 , 07 5 , 25 5 , 43 7 5 , 12 5 , 32 5 , 50 5 , 70 5 , 92 6 , 13 6 , 35 8 5 , 87 6 , 08 6 , 30 6 , 53 6 , 77 7 , 02 7 , 27 9 6 , 60 6 , 85 7 , 10 7 , 47 7 , 63 7 , 88 8 , 20 10 7 , 37 7 , 63 7 , 92 8 , 22 8 , 50 8 , 82 9 , 1● 11 8 , 12 8 , 42 8 , 73 9 , 05 9 , 38 9 , 73 10 , 08 12 8 , 88 9 , 22 9 , 57 9 , 92 10 , 27 10 , 65 11 , 0● 13 9 , 65 10 , 02 10 , 40 10 , 77 11 , 17 11 , 58 12 , 00 14 10 , 43 10 , 83 11 , 23 11 , 65 12 , 08 12 , 53 12 , 97 15 11 , 23 11 , 65 12 , 08 12 , 53 13 , 00 13 , 47 13 , 97 16 12 , 03 12 , 48 12 , 95 13 , 43 13 , 92 14 , 43 14 , 97 17 12 , 83 13 , 32 13 , 82 14 , 33 14 , 87 15 , 42 15 , 98 18 13 , 65 14 , 17 14 , 70 15. 25 15 , 82 16 , 40 17 , 01 19 14 , 48 15 , 03 15 , 60 16. 18 16 , 80 17 , 42 18 , 07 20 15 , 33 15 , 92 16 , 32 17. 13 17 , 78 18 , 45 19 , 13 21 16 , 18 16 , 82 17 , 45 18. 12 18 , 78 19 , 50 20 , 22 22 17 , 08 17 , 73 18 , 40 19. 10 19 , 82 20 , 57 21 , 33 23 17 , 97 18 , 65 19 , 37 20. 10 20 , 87 21 , 65 22 , 47 24 18 , 87 19 , 60 20 , 35 21. 13 21 , 93 22 , 77 23 , 63 25 19 , 80 20 , 57 21 , 35 22. 18 23 , 03 23 , 92 24 , 83 26 20 , 75 21 , 57 22 , 40 23. 27 24 , 17 25 , 08 26 , 05 27 21 , 73 22 , 58 23 , 47 24. 37 25 , 32 26 , 28 27 , 30 28 22 , 72 23 , 61 24 , 55 25. 50 26 , 50 27 , 52 28 , 60 29 23 , 75 24 , 68 25 , 67 26. 67 27 , 72 28 , 80 29 , 95 30 24 , 80 25 , 78 26 , 82 27. 87 28 , 98 30 , 12 31 , 32 31 25 , 80 26 , 92 28 , 00 29. 12 30 , 28 31 , 48 3● , 75 32 27 , 00 28 , 08 29 , 22 30. 90 31 , 52 32 , 90 34 , 23 A Table of Ascensional Differences . Poles . 43 44 45 46 47 48 49 Degrees of Declination . 1 00 , 93 00 , 97 01 , 00 01 , 03 01 , 07 01 , 12 01 , 15 2 1 , 87 1 , 93 2 , 00 2 , 07 2 , 15 2 , 22 2 , 30 3 2 , 80 2 , 90 3 , 00 3 , 12 3 , 22 3 , 33 3 , 45 4 3 , 7● 3 , 87 4 , 01 4 , 15 4 , 30 4 , 45 4 , 62 5 4 , 68 4 , 85 5 , 02 5 , 20 5 , 38 5 , 58 5 , 78 6 5 , 62 5 , 83 6 , 03 6 , 25 6 , 47 6 , 70 6 , 95 7 6 , 57 6 , 82 7 , 05 7 , 30 7 , 57 7 , 83 8 , 12 8 7 , 53 7 , 80 8 , 08 8 , 37 8 , 67 8 , 98 9 , 30 9 8 , 50 8 , 80 9 , 12 9 , 43 9 , 78 10 , 13 10 , 50 10 9 , 47 9 , 80 10 , 15 10 , 53 10 , 90 11 , 30 11 , 70 11 10 , 45 10 , 82 11 , 22 11 , 62 12 , 03 12 , 47 12 , 92 12 11 , 43 11 , 85 12 , 27 12 , 72 13 , 18 13 , 65 14 , 15 13 12 , 43 12 , 88 13 , 35 13 , 83 14 , 33 14 , 85 15 , 40 14 13 , 45 13 , 93 14 , 43 14 , 97 15 , 50 16 , 08 16 , 67 15 14 , 47 15 , 00 15 , 53 16 , 12 16 , 70 17 , 32 17 , 95 16 15 , 51 16 , 08 16 , 67 17 , 27 17 , 90 18 , 57 19 , 27 17 16 , 57 17 , 17 17 , 80 18 , 45 19 , 13 19 , 85 20 , 60 18 17 , 63 18 , 28 18 , 97 19 , 67 20 , 38 21 , 15 21 , 95 19 18 , 73 19 , 42 20 , 15 20 , 88 21 , 67 22 , 48 23 , 33 20 19 , 83 20 , 58 21 , 35 22 , 13 22 , 97 23 , 85 24 , 75 21 20 , 98 21 , 77 22 , 57 23 , 42 24 , 30 25 , 23 26 , 20 22 22 , 13 22 , 97 23 , ●3 24 , 73 25 , 67 26 , 67 27 , 70 23 23 , 32 24 , 20 24 , 12 26 , 08 27 , 08 28 , 13 29 , 23 24 24 , 53 25 , 47 26 , 43 27 , 45 28 , 52 29 , 63 30 , 80 25 25 , 78 26 , 77 27 , 80 28 , 87 30 , 00 31 , 20 32 , 43 26 27 , 03 28 , 10 29 , 18 30 , 33 31 , 53 32 , 80 34 , 13 27 28 , 37 29 , 48 30 , 63 31 , 85 33 12 34 , 47 35 , 88 28 29 , 73 30 , 90 32 , 12 33 , 42 34 , 77 36 , 20 37 , 70 29 31 , 13 32 , 37 33 , 67 35 , 03 36 , 47 38 , 00 39 , 62 30 32 , 58 33 , 88 35 , 27 36 , 72 38 , 25 39 , 88 41 , 62 31 33 , 97 35 , 47 36 , 93 38 , 48 40 , 12 41 , 87 43 , 73 32 35 , 63 37 , 12 38 , 67 40 , 32 42 , 07 43 , 95 45 , 9● A Table of Ascensional Differences . Height . 50 51 52 53 54 55 56 Degrees of Declination . 1 01. 20 01. 23 01 , 28 01 , 33 01 , 38 01 , 43 01 , 48 2 2. 38 2. 47 2 , 57 2 , 65 2 , 75 2 , 87 2 , 97 3 3. 58 3. 72 3 , 85 3 , 98 4 , 13 4 , 28 4 , 45 4 4. 78 4. 95 5 , 13 5 , 32 5 , 52 5 , 73 5 , 95 5 5. 98 6. 20 6 , 43 6 , 67 6 , 92 7 , 18 7 , 45 6 7. 20 7. 45 7 , 73 8 , 01 8 , 32 8 , 63 8 , 97 7 8. 42 8. 72 9 , 03 9 , 38 9 , 73 10 , 27 10 , 48 8 9. 63 10. 00 10 , 37 10 , 75 11 , 15 11 , 58 12 , 02 9 10. 88 11. 28 11 , 70 12 , 13 12 , 58 13 , 07 13 , 58 10 12. 13 12. 58 13 , 05 13 , 53 14 , 05 14 , 58 15 , 15 11 13. 40 13. 88 14 , 40 14 , 95 15 , 52 16 , 12 16 , 75 12 14. 67 15. 22 15 , 78 16 , 38 17 , 02 17 , 67 18 , 37 13 15. 63 16. 57 17 , 18 17 , 08 18 , 53 19 , 25 20 , 01 14 17. 28 17. 93 18 , 62 19 , 32 20 , 07 20 , 87 21 , 70 15 18. 62 19. 32 20 , 07 20 , 83 21 , 63 22 , 50 23 , 40 16 19. 98 20. 73 21 , 53 22 , 37 23 , 25 24 , 17 25 , 15 17 21. 37 22. 18 23 , 03 23 , 93 24 , 88 25 , 88 26 , 95 18 22. 78 23. 65 24 , 57 25 , 55 26 , 57 27 , 65 28 , 80 19 24. 23 25. 17 26 , 15 27 , 18 28 , 28 29 , 45 30 , 68 20 25. 72 26. 72 27 , 77 28 , ●8 30 , 07 31 , 32 32 , 65 21 27. 23 28. 30 29 , 43 30 , 62 31 , 90 33 , 25 34 , 68 22 28. 80 29. 93 31 , 13 32 , 42 33 , 78 35 , 23 36 , 80 23 30. 40 31. 62 32 , 90 34 , 28 35 , 75 37 , 32 39 , 00 24 32. 05 33. 35 34 , 73 36 , 22 37 , 80 39 , 48 41 , ●0 25 33. 77 35. 17 36 , 65 38 , 23 39 , 93 41 , 75 43 , 73 26 35. 53 37. 05 38 , 63 40 , 33 40 , 17 44 , 15 4● , 30 27 37. 38 39. 00 40 , 70 42 , 55 44 , 70 46 , 68 49 , 07 28 39. 32 41. 03 42 , 88 44 , 88 47 , 03 49 , 40 52 , 02 29 41. 35 43. 20 45 , 20 47 , 35 49 , 73 52 , 33 55 , 27 30 43. 48 45. 48 47 , 65 50 , 02 52 , 62 55 , 53 58 , 87 31 45. 73 47. 90 50 , 27 52 , 88 55 , 80 59 , 10 62 , 97 32 48. 13 50. 50 53 , 12 56 , 02 59 , 32 63 , 17 67 , ●8 A Table of oblique Ascensions . S. D. 1 2 3 4 5 6 ♈ 0 000 , 00 000 , 00 000 , 00 000 , 00 000 , 00 000 , 00   4 3 , 63 3 , 60 3 , 58 3 , 55 3 , 53 3. 48   8 7 , 28 7 , 23 7 , 17 7 , 12 7 , 07 7 , 00   12 10 , 95 10 , 87 10 , 77 10 , 68 10 , 60 10 , 53   16 14 , 62 14 , 50 14 , 38 14 , 28 14 , 17 14 , 07   20 18 , 32 18 , 17 18 , 03 17 , 90 17 , 77 17 , 62   24 22 , 05 21 , 87 21 , 70 21 , 55 21 , 38 21 , 22   28 25 , 80 25 , 62 25 , 42 25 , 23 25 , 05 24 , 83 ♉ 2 29 , 60 29 , 38 29 , 17 28 , 95 28 , 73 28 , 50   6 33 , 43 33 , 18 32 , 95 32 , 72 32 , 45 32 , 22   10 37 , 32 37 , 05 36 , 78 36 , 52 36 , ●5 35 , 98   14 41 , 23 40 , 95 40 , 65 40 , 37 40 , 08 39 , 78   18 45 , 22 44 , 90 44 , 60 44 , 28 43 , 98 43 , 67   22 49 , 25 48 , 90 48 , 58 48 , 25 47 , 92 47 , 58   26 53 , 30 52 , 95 52 , 62 52 , 27 51 , 90 51 , 55 ♊ 0 57 , 43 57 , 07 56 , 70 56 , 33 55 , 95 55 , 58   4 61 , 62 61 , 22 60 , 83 60 , 47 60 , 07 59 , 68   8 65 , 83 65 , 42 65 , 03 64 , 63 64 , 22 63 , 83   12 70 , 08 69 , 67 69 , 27 68 , 85 68 , 43 68 , 03   16 74 , 37 73 , 95 73 , 53 73 , 12 72 , 68 72 , 27   20 78 , 68 78 , 27 77 , 83 77 , 40 76 , 98 76 , 55   24 83 , 02 82 , 60 82 , 17 81 , 73 81 , ●0 80 , 87   28 87 , 38 86 , 95 86 , 52 86 , 07 85 , 63 85 , 20 ♋ 2 91 , 75 91 , 32 90 , 88 90 , 45 90 , 03 89 , 58   6 96 , 12 95 , 68 95 , 25 94 , 80 94 , 38 93 , 95   10 100 , 45 100 , 03 99 , 60 99 , 17 98 , 75 98 , 32   14 104 , 78 104 , 37 103 , 95 103 , 53 103 , 10 102 , 68   18 109 , 10 108 , 68 108 , 28 107 , 87 107 , 45 107 , 05   22 113 , 38 112 , 97 112 , 58 112 , 18 111 , 78 111 , 38   26 117 , 63 117 , 2● 116 , 85 116 , 47 116 , 08 115 , 70   30 121 , 83 121 , 47 121 , 10 120 , 73 120 , 35 119 , 98 A Table of oblique Ascensions . S. D 1 2 3 4 5 6 ♌ 0 121 , 83 121 , 47 121. 10 120 , 73 120 , 35 119 , 98   4 125 , 98 125 , 63 125. 30 124 , 93 124 , 58 124 , 23   8 130 , 10 129 , 75 129. 4● 129 , 10 128 , 77 128 , 43   12 134 , 17 133 , 85 133. 53 133 , 23 132 , 92 132 , 60   16 138 , 18 137 , 90 137. 62 137 , 32 137 , 0● 136 , 75   20 142 , 15 141 , 88 141. 62 141 , 35 141 , 08 140 , 82   24 146 , 08 145 , 85 145. 62 145 , 37 145 , 12 144 , 85   28 149 , 97 149 , 77 149. 53 149 , 32 149 , 10 148 , 87 ♍ 2 153 , 82 153 , 63 153. 43 153 , 25 153 , 05 152 , 85   6 157 , 63 157 , 47 157. 30 157 , ●3 156 , 93 156 , 80   10 161 , 42 161 , 27 161. 13 161 , 00 160 , 87 160 , 72   14 165 , 17 165 , 07 164. 93 164 , 83 164 , 73 164 , 62   18 168 , 90 168 , 82 168. 72 168 , 63 168 , 57 168 , 48   22 172 , 62 172 , 55 172. 50 172 , 43 172 , 38 172 , 33   26 176 , 32 176 , 28 176. 27 176 , 23 176 , 20 176 , 17 ♎ 0 180 , 00 180 , 00 180. 00 180 , 00 180 , 00 180 , 00   4 183 , 68 183 , 72 183. 73 183 , 77 183 , 80 183 , 83   8 187 , 38 187 , 45 187. 50 187 , 57 187 , 62 187 , 67   12 191 , 10 191 , 18 191. 28 191 , 37 191 , 43 191 , 52   16 194 , 83 194 , 93 195. 07 195 , 17 195 , 27 195 , 38   20 198 , 58 198 , 73 198. 87 199 , 00 199 , 13 199 , 28   24 202 , 37 202 , 53 202. 70 202 , 87 20● , 02 203 , 20   28 206 , 18 206. 37 206. 57 206 , 75 206 , 95 207 , 15 ♏ 2 210 , 03 210. 23 210. 47 210 , 68 210 , 90 211 , 13   6 213 , 92 214. 15 214. 38 214 , 63 214 , 88 215 , 15   10 217 , 85 218. 12 218. 38 218 , 58 218 , 92 219 , 18   14 221 , 82 222. 10 222. 38 222 , 53 222 , 97 223 , 25   18 225 , 83 226. 15 226. 47 226 , 38 227 , 08 227 , 40   22 229 , 90 230. 25 230. 57 230 , 90 231 , 23 231 , 57   26 234 , 02 234. 37 234. 70 235 , 07 235 , 42 235 , 77   30 238 , 17 238. 53 238. 90 239 , 27 239 , 65 240 , 02 A Table of oblique Ascensions . S. D. 1 2 3 4 5 6 ♐ 0 238 , 17 238 , 53 238 , 90 239 , 27 239 , 65 240. 02   4 242 , 37 242 , 77 243 , 15 243 , 53 243 , 92 244. 30   8 246 , 62 247 , 03 247 , 42 247 , 82 248 , 22 248. 62   12 250 , 90 251 , 32 251 , 72 252 , 13 252 , 55 252. 95   16 255 , 22 255 , 63 256 , 05 256 , 47 256 , 90 257. 32   20 259 , 55 259 , 97 260 , 40 260 , 83 261 , 25 261. 68   24 263 , 88 264 , 32 264 , 75 265 , 20 265 , 62 266. 05   28 26● , 25 268 , 68 269 , 12 269 , 55 269 , 97 270. 42 ♑ 2 272 , 62 273 , 05 273 , 48 273 , 93 274 , 37 274. 80   6 276 , 98 277 , 40 277 , 83 278 , 27 278 , 70 279. 13   10 281 , 32 281 , 73 282 , 17 282 , 60 283 , 02 283. 45   14 285 , 63 286 , 05 286 , 47 286 , 88 287 , 32 287. 73   18 289 , 92 290 , 33 290 , 73 291 , 15 291 , 57 291. 97   22 294 , 17 294 , 58 294 , 97 295 , 37 295 , 78 296. 17   26 298 , 38 298 , 78 299 , 17 299 , 53 299 , 93 300. 32 ♒ 0 302 , 57 302 , 93 303 , 30 303 , 67 304 , 05 304. 42   4 306 , 70 307 , 05 307 , 38 307 , 73 308 , 10 308. 45   8 310 , 75 311 , 10 311 , 42 311 , 75 312 , 08 312. 42   12 314 , 78 315 , 10 315 , 40 315 , 72 316 , 02 316. 33   16 318 , 77 319 , 05 319 , 35 319 , 63 319 , 92 320. 22   20 322 , 68 322 , 95 323 , 22 323 , 48 323 , 75 324. 02   24 326 , 57 326 , 82 327 , 05 327 , 28 327 , 55 327. 78   28 330 , 40 330 , 62 330 , 83 331 , 05 331 , 27 331. 50 ♓ 2 334 , 20 334 , 38 334 , 58 334 , 77 334 , 95 335. 17   6 337 , 95 338 , 13 338 , 30 338 , 45 338 , 62 338. 78   10 341 , 68 341 , 83 341 , 97 342 , 10 342 , 23 342. 38   14 345 , 38 345 , 50 345 , 62 345 , 72 345 , 83 345. 93   18 349 , 05 349 , 13 349 , 23 349 , 32 349 , 40 349. 47   22 352 , 72 352 , 77 352 , 83 352 , 88 352 , 93 353. 00   26 356 , 37 356 , 40 356 , 42 356 , 45 356 , 47 356. 52   30 360 , 00 360 , 00 360 , 00 360 , 00 360 , 00 360. 00 A Table of oblique Ascensions . S. D. 7 8 9 10 11 12 ♈ 0 000 , 00 000. 00 000 , 00 000 , 00 000 , 00 000 , 00   4 03 , 47 03. 43 03 , 40 03 , 38 03 , 35 03 , 33   8 06 , 95 06. 88 06 , 83 06 , 78 06 , 72 06 , 67   1● 10 , 4● 10. 35 10 , 27 10 , 18 10 , 10 10 , 00   16 13 , 95 13. 83 13 , 72 13 , 60 13 , 50 13 , 37   20 17 , 48 17. 33 17 , 20 17 , 05 16 , 92 16 , 77   24 21 , 05 20. 87 20 , 72 20 , 53 20 , ●8 20 , 20   28 24 , 65 24. 47 24 , 27 24 , 07 23 , 87 23 , 67 ♉ 2 28 , 30 28. 07 27 , 85 27 , 63 27 , 40 27 , 18   6 31 , 98 31. 72 31 , 48 31 , 23 30 , 82 30 , 73   10 35 , 72 35. 45 35 , 18 34 , 90 34 , 63 34 , 35   14 39 , 50 39. 20 38 , 92 38 , 62 38 , 32 38 , 02   18 43 , 35 43. 03 42 , 72 42 , 40 42 , 08 41 , 75   22 47 , ●5 46. 92 46 , 57 46 , 23 45 , ●0 45 , 53   26 51 , 20 50. 83 50 , 48 50 , 12 49 , 77 49 , 38 ♊ 0 55 , 20 54. 83 54 , 47 54 , 08 53 , 70 53 , 32   4 59 , 28 58. 90 58 , 52 58 , 12 57 , 72 57 , 32   8 63 , 42 63. 03 62 , 62 62 , ●0 61 , 80 61 , 37   12 67 , 60 67. 20 66 , 78 66 , 35 65 , 93 65 , 50   16 71 , 85 71. 42 70 , 98 70 , 53 70 , 12 69 , 68   20 76 , 12 75. 68 75 , 22 74 , 80 74 , 35 73 , 92   24 80 , 42 79. 98 79 , 53 79 , 08 78 , 63 78 , 18   28 84 , 75 84. 32 83 , 87 83 , 42 82 , 97 82 , 52 ♋ 2 89 , 12 88. 68 88 , 23 87 , 78 87 , 33 86 , 88   6 93 , 48 93. 05 92 , 60 92 , 17 91 , 72 91 , 27   10 97 , 88 97. 45 97 , 00 96 , 57 96 , 12 95 , 68   14 102 , 27 101. 83 101 , 40 100 , 95 100 , 52 100 , 10   18 106 , 63 106. 22 105 , 80 105 , 37 104 , 95 104 , 52   22 110 , 97 110. 58 110 , 17 109 , 77 109 , 35 108 , 92   26 115 , 30 114. 92 114 , 53 114 , 13 113 , 73 113 , 32   30 119 , 60 119 , 23 118 , 87 118 , 48 118 , 10 117 , 72 A Table of oblique Ascensions . S. D 7 8 9 10 11 12 ♌ 0 119 , 60 119 , 23 118 , 87 118 , 48 118 , 10 117 , 72   4 123 , 87 123 , 52 123 , 17 122 , 80 122 , 43 122 , 07   8 128 , 10 127 , 77 127 , 42 127 , 07 126 , 75 126 , 38   12 132 , 30 131 , 97 131 , 65 131 , 33 131 , 02 130 , 68   16 136 , 45 136 , 15 135 , 87 135 , 57 135 , 27 134 , 97   20 140 , 55 140 , 28 140 , 02 139 , 75 139 , 47 139 , 18   24 144 , 63 144 , 38 144 , 15 143 , 90 143 , 65 143 , 38   28 148 , 67 148 , 45 148 , 22 148 , 02 147 , 78 147 , 55 ♍ 2 152 , 67 152 , 47 152 , 28 142 , 08 151 , 88 151 , 68   6 156 , 65 156 , 47 156 , 30 156 , 13 155 , 97 155 , 80   10 160 , 58 160 , 43 160 , 30 160 , 15 160 , 02 159 , 87   14 164 , 50 164 , 38 164 , 27 164 , 15 164 , 05 163 , 93   18 168 , 40 168 , 30 168 , 22 168 , 13 168 , 05 167 , 97   22 172 , 27 172 , 22 172 , 15 172 , 10 172 , 05 171 , 98   26 176 , 13 176 , 12 176 , 08 176 , 07 176 , 03 176 , 00 ♎ 0 180 , 00 180 , 00 180 , 00 180 , 00 180 , 00 180 , 00   4 183 , 87 183 , 88 183 , 92 183 , 93 183 , 97 184 , 00   8 187 , 73 187 , 78 187 , 85 187 , 90 187 , 95 188 , 02   12 191 , 60 191 , 70 191 , 78 191 , 87 191 , 95 192 , 03   16 195 , 50 195 , 62 195 , 73 195 , 85 195 , 95 196 , 07   20 199 , 42 199 , 57 199 , 70 199 , 85 199 , 98 200 , 13   24 200 , 35 203 , 53 203 , 70 203 , 87 204 , 03 204 , 20   28 207 , 33 207 , 53 207 , 72 207 , 92 208 , 12 208 , 32 ♏ 2 211 , 33 211 , 55 211 , 78 211 , 98 212 , 22 212 , 45   6 215 , 37 215 , 62 215 , 85 216 , 10 216 , 35 216 , 62   10 219 , 45 219 , 72 219 , 98 220 , 25 220 , 53 220 , 82   14 223 , 55 223 , 85 224 , 13 224 , 43 224 , 73 225 , 03   18 227 , 70 228 , 03 228 , 35 228 , 67 228 , 98 229 , 32   22 231 , 90 232 , 23 232 , 58 232 , 93 233 , 25 233 , 62   26 236 , 13 236 , 48 236 , 83 237 , 20 237 , 57 237 , 93   30 240 , 40 240 , 77 241 , 13 241 , 52 242 , 90 242 , 28 A Table of oblique Ascensions . S. D. 7 8 9 10 11 12 ♐ 0 240 , 40 240 , 77 241 , 13 241. 52 241. 90 242. 28   4 244 , 70 245 , 08 245 , 47 245. 87 246. 27 246. 68   8 249 , 03 249 , 42 249 , 83 250. 23 250. 65 251. 08   12 253 , 37 253 , 78 254 , 20 254. 63 255. 05 255. 48   16 257 , 73 258 , 17 258 , 60 259. 05 259. 48 259. 90   20 262 , 12 262 , 55 263 , 00 263. 43 263. 88 264. 32   24 266 , 52 266 , 95 267 , 40 267. 83 268. 28 268. 73   28 270 , 88 271 , 32 271 , 77 272. 22 272. 67 273. 12 ♑ 2 275 , 25 275 , 68 276 , 13 276. 58 277. 03 277. 48   6 279 , 58 280 , 02 280 , 47 280. 92 281. 37 281. 82   10 283 , 88 284 , 32 284 , 78 285. 20 285. 65 286. 08   14 288 , 15 288 , 58 289 , 02 289. 47 289. 88 290. 32   18 292 , 40 292 , 80 293 , 22 293. 65 294. 07 294. 50   22 296 , 58 296 , 97 297 , 38 297. 80 298. 20 298. 63   26 300 , 72 301 , 10 301 , 48 301. 88 302. 28 302. 68 ♒ 0 304 , 80 305 , 17 305 , 53 305. 92 306. 30 306. 68   4 308 , 80 309 , 17 309 , 52 309. 88 310. 23 313. 62   8 312 , 75 313 , 08 313 , 43 313. 77 314. 10 314. 47   12 316 , 65 316 , 97 317 , 28 317. 60 317. 92 318. 25   16 320 , 50 320 , 80 321 , 08 321. 38 321. 68 321. 98   20 324 , 28 324 , 55 324 ▪ 82 325. 10 325. 37 325. 65   24 328 , 02 328 , 28 328 , 52 328. 77 329. 18 329. 27   28 331 , 70 331 , 93 332 , 15 332. 37 332. 60 332. 82 ♓ 2 335 , 35 335 , 53 335 , 73 335. 93 336. 13 336. 33   6 338 , 95 339 , 13 339 , 28 339. 47 339. 62 339. 80   10 342 , 52 342 , 67 342 , 80 342. 95 343. 08 343. 23   14 346 , 05 346 , 17 346 , 28 346. 40 346. 50 346. 63   18 349 , 57 349 , 65 349 , 73 349. 82 349. 90 350. 00   22 353 , 05 353 , 12 353 , 13 353. 22 353. 28 353. 33   26 356 , 53 356 , 57 356 , 60 356. 62 356. 65 356. 67   30 360 , 00 360 , 00 360 , 00 360. 00 360. 00 360. 00 A Table of oblique Ascensions . S. D. 13 14 15 16 17 18 ♈ 0 000 , 00 000 , 00 000 , 00 000 , 00 000 , 00 000 , 00   4 03 , 28 03 , 27 03 , 23 03 , 20 03 , 17 03 , 13   8 06 , 60 06 , 55 06 , 48 06 , 43 06 , 37 06 , 30   12 09 , 93 09 , 83 09 , 75 09 , 67 09 , 57 09 , 47   16 13 , 27 13 , 15 13 , 02 12 , 92 12 ▪ 78 12 , 67   20 16 , 63 16 , 48 16 , 33 16 , 18 16 , 03 15 , 88   24 20 , 03 19 , 85 19 , 67 19 , 50 19 , 32 19 , 15   28 23 , 47 23 , 27 23 , 07 22 , 85 22 , 65 22 , 45 ♉ 2 26 , 95 26 , 72 26 , 48 26 , 25 26 , 03 25 , 78   6 30 , 47 30 , 22 29 , 97 29 , 70 29 , 45 29 , 17   10 34 , 07 33 , 80 33 , 52 33 , 22 32 , 98 32 , 63   14 37 , 72 37 , 40 37 , 10 36 , 78 36 , 47 36 , 15   18 41 , 43 41 , 10 40 , 77 40 , 43 40 , 08 39 , 73   22 45 , 20 44 , 83 44 , 48 44 , 13 43 , 77 43 , 40   26 49 , 02 48 , 65 48 , 28 47 , 90 47 , 52 47 , 12 ♊ 0 52 , 92 52 , 53 52 , 15 51 , 75 51 , 33 50 , 93   4 56 , 92 56 , 50 56 , 08 55 , 68 59 , 25 54 , 83   8 60 , 97 60 , 53 60 , 10 59 , 67 99 , 25 58 , 80   12 65 , 07 64 , 63 64 , 20 63 , 75 63 , 28 62 , 83   16 69 , 23 68 , 80 68 , 35 67 , 88 67 , 92 66 , 95   20 73 , 47 73 , 00 72 , 55 72 , 08 71 , 62 71 , 15   24 77 , 73 77 , 27 76 , 82 76 , 35 75 , 88 75 , 40   28 82 , 07 81 , 60 81 , 13 80 , 67 80 , 20 79 , 72 ♋ 2 86 , 42 85 , 95 85 , 50 85 , 02 84 , 55 84 , 07   6 90 , 82 90 , 35 89 , 90 89 , 42 88 , 95 88 , 47   10 95 , 23 94 , 77 94 , 32 93 , 85 9● , 38 92 , 92   14 99 , 65 99 , 20 98 , 77 98 , 30 97 , 83 97 , 37   18 104 , 08 103 , 65 103 , 22 102 , 77 102 , 30 101 , 87   22 108 , 52 108 , 08 107 , 67 107 , 23 106 , 80 106 , 35   26 112 , 92 112 , 52 112 , 10 111 , 68 111 , 27 110 , 85   30 117 , 32 116 , 93 116 , 55 116 , 15 115 , 73 115 , 33 A Table of oblique Ascensions . S. D. 13 14 15 16 17 18 ♌ 0 117 , 32 116 , 93 116 , 55 116 , 15 115 , 73 115 , 33   4 121 , 70 121 , 33 120 , 95 120 , 58 120 , 20 119 , 80   8 126 , 03 125 , 70 125 , 33 124 , 98 124 , 62 124 , 25   12 130 , 37 130 , 03 129 , 70 129 , 37 129 , 03 128 , 68   16 134 , 67 134 , 37 134 , 05 133 , 73 133 , 43 133 , 10   20 138 , 90 138 , 63 138 , 35 138 , 05 137 , 77 137 , 47   24 143 , 13 142 , 88 142 , 62 142 , 37 142 , 10 141 , 83   28 147 , 32 147 , 08 146 , 87 146 , 63 146 , 40 146 , 17 ♍ 2 151 , 48 151 , 28 151 , 07 150 , 87 150 , 67 150 , 47   6 155 , 62 155 , 45 155 , 27 155 , 10 154 , 92 154 , 73   10 159 , 73 159 , 58 159 , 43 159 , 28 159 , 13 158 , 98   14 163 , 82 163 , 70 163 , 57 163 , 47 163 , 33 163 , 22   18 167 , 88 167 , 80 167 , 70 167 , 62 167 , 52 167 , 42   22 171 , 93 171 , 87 171 , 82 171 , 75 171 , 68 171 , 62   26 175 , 97 175 , 93 175 , 92 175 , 88 175 , 85 175 , 82 ♎ 0 180 , 00 180 , 00 180 , 00 180 , 00 180 , 00 180 , 00   4 184 , 03 184 , 07 184 , 08 184 , 12 184 , 15 184 , 18   8 188 , 07 188 , 13 188 , 18 188 , 25 188 , 32 188 , 38   12 192 , 12 192 , 20 192 , 30 192 , 38 192 , 48 192 , 58   16 196 , 18 196 , 30 196 , 43 196 , 53 196 , 67 196 , 78   20 200 , 27 200 , 42 200 , 57 200 , 72 200 , 87 201 , 02   24 204 , 38 204 , 55 204 , 73 204 , 90 205 , 08 205 , 27   28 208 , 52 208 , 72 208 , 93 209 , 13 209 , 33 209 , 53 ♏ 2 212 , 68 212 , 92 213 , 13 213 , 37 213 , 60 213 , 83   6 216 , 87 217 , 12 217 , 38 217 , 63 217 , 90 218 , 17   10 221 , 10 221 , 37 221 , 65 221 , 95 222 , 23 222 , 53   14 225 , 33 225 , 63 225 , 95 226 , 27 226 , 57 226 , 90   18 229 , 63 229 , 97 230 , 30 230 , 63 230 , 97 2●1 , 32   22 233 , 97 234 , 30 234 , 67 235 , 02 235 , 38 235 , 75   26 238 , 30 238 , 67 239 , 05 239 , 42 239 , 80 240 , ●0   30 242 , 68 243 , 07 243 , 45 243 , 85 244 , 27 244 , 67 A Table of oblique Ascensions . S. D. 13 14 15 16 17 18 ♐ 0 242 , 68 243 , 07 243 , 45 243 , 85 244 , 27 244 , 67   4 247 , 08 247 , 48 247 , 90 248 , 32 248 , 73 249 , 19   8 251 , 48 251 , 92 252 , 33 252 , 77 253 , 20 253 , 65   12 255 , 92 256 , 35 256 , 78 257 , 27 257 , 70 258 , 13   16 260 , 35 260 , 80 261 , 23 261 , 70 262 , 17 262 , 63   20 264 , 77 265 , 23 265 , 68 266 , 15 266 , 62 267 , 08   24 269 , 18 269 , 65 270 , 10 270 , 58 271 , 05 271 , 53   28 273 , 58 274 , 05 274 , 50 274 , 98 275 , 45 275 , 93 ♑ 2 277 , 93 278 , 40 278 , 87 279 , 33 279 , 80 280 , 28   6 282 , 27 282 , 73 283 , 18 283 , 65 284 , 12 284 , 60   10 286 , 53 287 , 00 287 , 45 287 , 92 288 , 38 288 , 85   14 290 , 77 291 , 20 291 , 65 29● , 12 292 , 08 293 , 05   18 ●94 , 9● 295 , 37 295 , 80 296 , 25 296 , 72 297 , 17   22 299 , 03 299 , 47 299 , 90 300 , 33 300 , 75 301 , 20   26 303 , 08 303 , 50 303 , 92 304 , 32 304 , 75 305 , 17 ♒ 0 307 , 08 307 , 47 307 , 85 308 , 25 308 , 67 309 , 07   4 310 , 98 311 , 35 311 , 72 312 , 10 312 , 48 312 , 88   8 314 , 80 315 , 17 315 , 52 315 , 87 316 , 23 316 , 60   12 318 , 57 318 , 90 319 , 23 319 , 57 319 , 92 320 , 27   16 322 , 38 322 , 60 322 , 90 323 , 22 323 , 53 323 , 15   20 325 , 93 326 , 20 326 , 48 326 , 78 327 , 07 327 , 37   24 329 , 53 329 , 78 330 , 03 330 , 30 330 , 55 330 , 83   28 333 , 05 333 , 28 333 , 52 33● , 75 333 , 97 334 , 22 ♓ 2 336 , 53 336 , 73 336 , 93 337 , 15 3●7 , 35 337 , 55   6 339 , 07 340 , 15 340 , 33 340 , 50 340 , 68 340 , 85   10 343 , 37 343 , 52 343 , 67 343 , 82 343 , 97 344 , 12   14 346 , 73 346 , 85 346 , 98 347 , 08 34● , 22 347 , 33   18 350 , 07 350 , 17 350 , 25 350 , 33 350 , 43 350 , 53   22 353 , 40 353 , 45 353 , 52 353 , 57 353 , 63 353 , 70   26 356 , 72 356 , 73 356 , 77 356 , 80 356 , 83 356 , 87   30 360 , 00 360 , 00 360 , 00 360 , 00 360 , 00 360 , 00 A Table of oblique Ascensions . S. D. 19 20 21 22 23 24 ♈ 0 000 , 00 000 , 00 000. 00 000 , 00 000 , 00 000 , 00   4 03 , 12 03 , 08 03. 05 03 , 02 02 , 98 02 , 95   8 06 , 25 0● , 18 06. 12 06 , 05 05 , 98 05 , 92   12 09 , 38 09 , 28 09. 18 09 , 10 09 , 00 08 , 90   16 12 , 53 12 , 42 12. 28 12 , 17 12 , 03 11 , 90   20 15 , 73 15 , 58 15. 42 15 , 27 15 , 10 14 , 93   24 18 , 97 18 , 78 18. 58 18 , 40 18 , 20 18 , 00   28 22 , 23 22 , 02 21. 80 21 , 58 21 , 35 21 , 13 ♉ 2 25 , 38 25 , 30 25. 05 24 , 80 24 , 55 24 , 30   6 28 , 92 28 , 65 28. 35 28 , 08 27 , 80 27 , 52   10 32 , 35 32 , 05 31. 73 31 , 43 31 , 12 30 , 80   14 35 , 83 35 , 52 35. 17 34 , 83 34 , 50 34 , 15   18 39 , 40 39 , 05 38. 68 38 , 33 37 , 95 37 , 60   22 43 , 03 42 , 67 42. 28 41 , 90 41 , 50 41 , 10   26 46 , 73 46 , 33 45. 93 45 , 53 45 , 12 44 , 68 ♊ 0 50 , 52 50 , 10 49. 68 49 , 25 48 , 82 48 , 37   4 54 , 40 53 , 97 53. 53 53 , 07 52 , 63 52 , 15   8 58 , 35 57 , 90 57. 45 56 , 97 56 , 50 56 , 02   12 62 , 38 61 , 92 61. 45 60 , 97 60 , 47 59 , 98   16 66 , 48 66 , 03 65. 53 65 , 05 64 , 53 64 , 02   20 70 , 67 70 , 18 69. 68 69 , 18 68 , 67 68 , 15   24 74 , 92 74 , 42 73. 92 73 , 42 72 , 90 72 , 38   28 79 , 22 78 , 73 78. 22 77 , 70 77 , 20 76 , 67 ♋ 2 83 , 58 83 , 08 82. 58 82 , 07 81 , 57 81 , 03   6 87 , 98 87 , 48 86. 98 86 , 48 85 , 97 85 , 45   10 92 , 43 91 , 95 91. 45 90 , 95 90 , 33 89 , 92   14 96 , 90 96 , 42 95. 93 95 , 48 94 , 95 94 , 47   18 101 , 40 100 , 92 100. 47 99 , 98 99 , 48 98 , 98   22 105 , 92 105 , 43 105. 00 104 , 52 104 , 05 103 , 57   26 110 , 42 109 , 97 109. 53 109 , 08 108 , 63 108 , 17   30 114 , 92 114 , 50 114. 08 113 , 65 113 , 50 112 , 77 A Table of oblique Ascensions . S. D ▪ 19 20 21 22 23 24 ♌ 0 114 , 92 114 , 50 114. 08 113 , 65 113 , 50 112 , 77   4 119 , 42 119 , 02 118. 62 118 , 20 117 , 80 117 , 37   8 123 , 88 123 , 51 123. 13 122 , 73 122 , ●5 121. 95   12 128 , 33 128 , 00 127. 63 127 , 27 126 , 90 126 , 53   16 132 , 78 132 , 47 132. 12 131 , 80 131 , 45 131. 10   20 137 , 18 136 , 88 136. 57 136 , 27 135 , 95 135 , 63   24 141 , 58 141 , 30 141. 01 140 , 73 140 , 47 140 , 17   28 145 , 92 145 , 85 145. 42 145 , 18 144 , 9● 144 , 67 ♍ 2 150 , 25 150 , 03 149. 82 149 , 58 149 , 37 149 , 13   6 154 , 57 154 , 37 154. 18 153 , 98 153 , 80 153 , 60   10 158 , 83 158 , 68 158. 52 158 , 53 158 , 20 158 , 03   14 163 , 10 162 , 97 162. 85 162 , 72 162 , 60 162 , 45   18 167 , 33 167 , 23 167. 15 167 , 05 166 , 97 166 , 85   22 171 , 57 171 , 50 171. 43 171 , 38 171 , 32 171 , 25   26 175 , 80 175 , 77 175. 73 175 , 70 175 , 67 175 , 63 ♎ 0 180 , 00 180 , 00 180. 00 180 , 00 180 , 00 180 , 00   4 184 , 20 184 , 23 184. 27 184 , 30 184 , 33 184 , 37   8 188 , 43 188 , 50 188. 57 188 , 62 188 , 68 188 , 75   12 192 , 67 192 , 77 192. 85 192 , 95 193 , 03 193 , 15   16 196 , 90 197 , 03 197. 15 197 , 28 197 , 40 197 , 55   20 201 , 17 201 , 32 201. 48 201 , 47 201 , 80 201 , 97   24 205 , 43 205 , 63 205. 82 206 , 02 206 , 20 206 , 40   28 209 , 75 209 , 97 210. 18 210 , 42 210 , 63 210 , 87 ♏ 2 214 , 08 214 , 15 214. 58 214 , 82 215 , 07 215 , 33   6 218 , 42 218. 70 218. 99 219 , 27 219 , 53 219 , 83   10 222 , 82 223. 12 223. 43 223 , 73 224 , 05 224 , 37   14 227 , 22 227. 53 227. 88 228 , 20 228 , 55 228 , 90   18 231 , 67 232 , 00 232. 37 232 , 73 233 , 10 233 , 47   22 236 , 12 236 , 49 236. 87 237 , 27 237 , 65 238 , 05   26 240 , 58 240 , 98 241. 38 241 , 80 242 , 20 242 , 63   30 245 , 08 245 , 50 245. 92 246 , 35 246 , 50 247 , 23 A Table of Oblique Ascensions . S. D. 19 20 21 22 23 24 ♐ 0 245 , 08 245 , 50 245 , 92 246. 35 246 , 50 247 , 23   4 249 , 58 250 , 03 250 , 47 250. 92 251 , 37 251 , 83   8 254 , 08 254 , 57 255 , ●0 255. 48 255 , 95 256 , 43   12 258 , 60 259 , 08 259 , 53 260. 02 260 , 52 261 , 02   16 263 , 10 263 , 58 264 , 07 264. 52 265 , 05 265 , 53   20 267 , 57 268 , 05 268 , 55 269. 05 269 , 67 270 , 08   24 272 , 02 272 , 52 273 , 02 273. 52 274 , 03 274 , 55   28 276 , 42 276 , 92 277 , 42 277. 93 278 , 43 278 , 97 ♑ 2 280 , 78 281 , 27 281 , 78 282. ●0 282 , 80 283 , 33   6 285 , 08 285 , 58 286 , 08 286. 58 287 , 10 287 , 62   10 289 , 33 289 , 82 290 , 32 290. 82 291 , 33 291 , 85   14 293 , 52 293 , 97 294 , 47 294. 95 295 , 47 295 , 98   18 297 , 62 298 ▪ 0● 298 , 55 299. 03 299 , 53 300 , 02   22 301 , 65 302 , 10 302 , 55 30● . 03 303 , 50 303 , 98   26 305 , 60 306 , 03 306 , 47 306. 93 307 , 33 307 , 85 ♒ 0 309 , 48 309 , 90 310 , 32 310. ●5 311 , 18 311 , 63   4 313 , 27 313 , 67 314 , 07 314. 47 314 , 88 315 , 32   8 316 , 97 317 , 33 317 , 72 318. 10 318 , 50 318 , 90   12 320 , 60 320 , 95 321 , 32 321. 67 322 , 05 322 , 40   16 324 , 17 324 , 48 324 , 83 325. 17 325 , 50 325 , 85   20 327 , 65 327 , 95 328 , 27 328. 57 328 , 88 329 , 20   24 331 , 08 331 , 35 331 , 65 331. 92 332 , 20 332 , 48   28 334 , 62 334 , 70 334 , 95 335. 20 335 , 45 335 , 70 ♓ 2 337 , 77 337 , 98 338 , 20 338. 42 338 , 65 338 , 87   6 341 , 03 341 , 22 341 , 42 341. 60 341 , 80 342 , 00   10 344 , 27 344 , 42 344 , 58 344. 73 344 , 90 345 , 07   14 347 , 47 347 , 58 347 , 72 347. 83 347 , 97 348 , 10   18 350 , 62 350 , 72 350 , 82 350 ▪ 90 3●1 , 00 351 , 10   22 353 , 75 353 , 82 353. 88 353. 95 354 , 02 354 , 08   26 356 , 88 356 , 92 356. 95 356. 98 357 , 02 357 , 05   30 360 , 00 360 , 00 360. 00 360. 00 360 , 00 360 , 00 A Table of oblique Ascensions . S. D. 25 26 27 28 29 30 ♈ 0 000 , 00 000 , 00 000 , 00 010 , 00 000 , 00 000 , 00   4 02 , 88 02 , 95 02 , 85 02 , 80 22 , 78 02 , 73   8 05 , 85 05 , 78 05 , 70 05 , 63 05 , 58 05 , 50   12 08 , 80 08 , 70 08 , 58 08 , 48 08 , 38 08 , 27   16 11 , 77 11 , 63 11 , 50 11 , 35 11 , 20 11 , 07   20 14 , 77 14 , 60 14 , 43 14 , 25 14 , 07 13 , 90   24 17 , 82 17 , 60 17 , 40 17 , 18 16 , 98 16 , 77   28 20 , 90 20 , 67 20 , 42 20 , 18 19 , 92 19 , 68 ♉ 2 24 , 01 23 , 77 23 , 48 23 , 22 22 , 92 22 , 65   6 27 , 22 26 , 92 26 , 62 26 , 30 26 , 00 25 , 67   10 30 , 48 30 , 15 29 , 82 29 , 48 29 , 13 28 , 78   14 33 , 82 33 , 45 33 , 07 32 , 72 32 , 32 31 , 95   18 37 , 22 36 , 83 36 , 43 36 , 03 35 , 62 35 , 22   22 40 , 70 40 , 28 39 , 88 39 , 45 39 , 00 38 , 57   26 44 , 25 43 , 83 43 , 37 42 , 93 42 , 47 42 , 00 ♊ 0 47 , 90 47 , 47 47 , 00 46 , 32 46 , 03 45 , 53   4 51 , 68 51 , 20 50 , 72 50 , 22 49 , 72 49 , 20   8 55 , 53 55 , 03 54 , 53 54 , 00 53 , 48 52 , 95   12 59 , 48 58 , 97 58 , 43 57 , 90 57 , 35 56 , 82   16 63 , 52 62 , 98 62 , 45 61 , 92 61 , 33 60 , 78   20 67 , 63 67 , 10 66 , 55 66 , 00 65 , 43 64 , 85   24 71 , 83 71 , 30 70 , 75 70 , 18 69 , 62 69 , 03   28 76 , 13 75 , 58 75 , 03 74 , 47 73 , 88 73 , 30 ♋ 2 80 , 50 79 , 75 79 , 40 78 , 83 78 , 25 77 , 67   6 84 , 92 84 , 38 83 , 83 83 , 27 82 , 68 82 , 10   10 89 , 40 88 , 87 88 , 32 87 , 77 87 , 20 86 , 62   14 93 , 93 93 , 40 92 , 85 92 , 32 91 , 75 91 , 18   18 98 , 48 97 , 98 97 , 45 96 , 92 96 , 35 95 , 82   22 103 , 08 102 , 58 102 , 08 101 , 55 101 , 03 100 , 48   26 107 , 68 107 , 20 106 , 73 106 , 22 105 , 72 105 , 20   30 112 , 30 111 , 87 111 , 40 110 , 92 110 , 43 109 , 93 A Table of oblique Ascensions . S. D 25 26 27 28 29 30 ♌ 0 112 , 30 111 , 87 111. 40 110 , 92 110 , 43 109 , 93   4 116 , 93 116 , 53 116. 07 115 , 62 115 , 15 114 , 67   8 121 , 55 121 , 15 120. 71 120 , 30 119 , 85 119. 40   12 126 , 17 125 , 78 125. 38 124 , 98 124 , 57 124 , 15   16 130 , 77 130 , 40 130. 03 129 , 67 129 , 28 128 , 90   20 135 , 32 134 , 98 134. 65 134 , 32 133 , 97 133. 62   24 139 , 87 139 , 75 139 , 28 138 , 97 138 , 65 138 , 33   28 144 , 40 144 , 13 143. 87 143 , 65 14● , 30 143 , 03 ♍ 2 148 , 92 148 , 67 148. 43 148 , 18 147 , 95 147 , 68   6 153 , ●0 153 , 20 153. 00 152 , 78 152 , 57 152 , 35   10 157 , 87 157 , 70 157. 53 157 , 35 157 , 17 157 , 03   14 162 , 33 162 , 18 162. 05 161 , 90 161 , 77 161 , 62   18 166 , 77 166 , 65 166. 55 166 , 43 166 , 33 166 , 22   22 171 , 18 171 , 12 170. 03 170 , 97 170 , 90 170 , 82   26 175 , 60 175 , 57 175. 53 175 , 40 175 , 47 175 , 42 ♎ 0 180 , 00 180 , 00 180. 00 180 , 00 180 , 00 180 , 00   4 184 , 40 184 , 43 184. 47 184 , 52 184 , 53 184 , 58   8 188 , 82 188 , 88 188. 97 189 , 03 189 , 10 189 , 18   12 193 , 23 193 , 35 193. 45 193 , 57 193 , 67 193 , 78   16 197 , 67 197 , 82 197. 95 198 , 10 198 , 23 198 , 38   20 202 , 13 202 , 30 202. 47 202 , 65 202 , 83 202 , 97   24 206 , 60 206 , 80 207. 00 207 , 22 207 , 43 207 , 65   28 211 , 08 211 , 33 211. 57 211 , 82 212 , 05 212 , 32 ♏ 2 215 , 60 215 , 87 216. 13 216 , 35 216 , 70 216 , 97   6 220 , 13 220. 25 220. 73 221 , 03 221 , 35 221 , 67   10 224 , 68 225. 02 225. 35 225 , 68 226 , 03 226 , 38   14 229 , 23 229. 60 229. 97 230 , 33 230 , 72 231 , 10   18 233 , 83 234 , 22 234. 62 235 , 02 235 , 42 235 , 85   22 238 , 45 238 , 85 239. 28 239 , 70 240 , 15 240 , 60   26 243 , 07 243 , 47 243. 93 244 , 38 244 , 85 245 , 33   30 247 , 70 248 , 13 248. 60 249 , 08 249 , 57 250 , 07 A Table of oblique Ascensions . S. D. 25 26 27 28 29 30 ♐ 0 247 , 70 248 , 13 248 , 60 249 , 08 249 , 57 250 , 07   4 252 , 32 252 , 80 253 , 27 253 , 78 254 , 28 254 , 80   8 256 , 92 257 , 42 257 , 92 258 , 45 258 , 97 259 , 52   12 261 , 52 262 , 02 262 , 55 263 , 08 263 , 65 264 , 18   16 266 , 07 266 , 60 267 , 15 267 , 68 268 , ●5 268 , 82   20 270 , 60 271 , 13 271 , 68 272 , 2● 27● , 80 273 , 38   24 275 , 08 275 , 62 276 , 17 27● , 73 277 , 32 277 , 90   28 279 , 50 280 , 05 280 , 60 281 , ●7 281 , 75 282 , 33 ♑ 2 283 , 87 284 ▪ 42 284 , 97 28● , 53 286 , 12 2●6 , 70   6 288 , 17 288 , 70 289 , 25 289 , 82 290 , 35 290 , 97   10 292 , 37 292 , 90 293 , 45 294 , 00 294 , 57 295 , 15   14 296 , 48 297 , 02 297 ▪ 55 298 , 08 298 , 67 299 , 22   18 300 , 52 301 , 03 301 , 57 302 , 10 302 , 65 303 , 18   22 304 , 47 304 , 97 305 , 47 306 , 00 306 , 52 307 , 05   26 308 , 32 308 , 80 309 , 28 309 , 78 310 , ●8 310 , 80 ♒ 0 312 , 10 312 , 53 313 , 00 313 , 68 31● , 97 313 , 47   4 314 , 75 315 , 17 316 , 63 316 , 07 317 , 53 317 , 00   8 319 , 30 319 , 72 320 , 12 320 , 55 321 , 00 321 , 43   12 322 , 78 323 , 17 323 , 57 323 , 97 324 , 38 324 , 78   16 326 , 18 326 , 55 326 , 93 327 , 28 327 , 68 328 , 05   20 329 , 52 329 , 85 330 , 18 330 , 52 330 , 87 331 , 22   24 332 , 78 333 , 08 333 , 35 33● , 70 334 , 00 334 , 33   28 335 , 99 336 , 23 336 , 52 336 , 78 337 , 08 337 , 35 ♓ 2 339 , 10 339 , 33 339 , 58 339 , 82 340 , 08 340 , 32   6 342 , 18 342 , 40 342 , 60 342 , 82 343 , 02 343 , 23   10 345 , 23 345 , 40 345 , 57 345 , 75 345 , 93 346 , 10   14 348 , 23 348 , 37 34● , 50 348 , 65 348 , 80 348 , 93   18 351 , 20 351 , 30 351 , 42 351 , 52 351 , 62 351 , 73   22 354 , 15 354 , 22 354 , 28 354 , 37 354 , 42 354 , 50   26 357 , 12 357 , 05 357 , 15 357 , 20 357 , 22 357 , 27   30 360 , 00 360 , 00 360 , 00 360 , 00 360 , 00 360 , 00 A Table of oblique Ascensions . S. D. 31 32 32. 18 33 34 35 ♈ 0 000 , 00 000 , 00 000. 00 000 , 00 000 , 00 000 , 00   4 02 , 70 02 , 67 02. 66 02 , 62 02 , 58 02 , 53   8 05 , 43 05 , 35 05. 34 05 , 27 05 , 18 05 , 10   12 08 , 17 08 , 05 08. 03 07 , 93 07 , 80 07 , 68   16 10 , 92 10 , 78 10. 75 10 , 60 10 , 45 10 , 28   20 13 , 70 13 , 52 13. 49 13 , 32 13 , 02 12 , 92   24 16 , 53 16 , 32 16. 28 16 , 07 15 , 85 15 , 58   28 19 , 42 19 , 17 19. 12 18 , 87 18 , 62 18 , 32 ♉ 2 22 , 35 22 , 07 21. 01 21 , 73 21 , 43 21 , 12   6 25 , 33 25 , 02 24. 96 24 , 67 24 , 32 23 , 95   10 28 , 42 28 , 05 27. 98 27 , 67 27 , 28 26 , 88   14 31 , 55 31 , 15 31. 08 30 , 73 30 , 32 29 , 88   18 34 , 78 34 , 35 34. 27 33 , 90 33 , 45 32 , 98   22 38 , 10 37 , 65 37. 57 37 , 17 36 , 68 36 , 17   26 41 , 52 41 , 03 40. 94 40 , 52 40 , 00 39 , 87 ♊ 0 45 , 03 44 , 52 44. 42 43 , 98 43 , 43 42 , 87   4 48 , 67 48 , 12 47. 02 47 , 55 47 , 00 46 , 40   8 52 ▪ 40 51 , 83 51. 73 51 , 25 50 , 67 50 , 05   12 56 , 23 55 , 63 55. 53 55 , 05 54 , 43 53 , 82   16 60 , 20 59 , 60 59 , 49 58 , 98 58 , 35 57 , 70   20 64 , 25 63 , 65 63. 54 63 , 02 62 , 38 61 , 72   24 68 , 4● 67 , 80 67. 69 67 , 17 66 , 52 65 , 85   28 72 , 68 72 , 07 71. 96 71 , 43 70 , 78 70 , 08 ♋ 2 77 , 03 76 , 4● 76. 31 75 , 80 75 , 15 74 , 47   6 81 , 48 80 , 88 80. 77 80 , 25 79 , 60 78 , 93   10 86 , 02 85 , 42 85. 31 84 , 78 84 ▪ 15 83 , 48   14 90 , 62 90 , 01 89. 90 89 , 38 88 , 77 88 , 12   18 9● , ●7 94 , 67 94. 57 94 , ●7 93 , 47 92 , 83   22 99 , 95 99 , 38 99. 28 98 , 80 98 , 22 97 , 60   26 104 , ●7 104 , 12 104. 02 103 , 57 103 , 00 102 , 40   30 109 , 43 108 , 92 108. 83 108 , 38 107 , 83 107 , 27 A Table of oblique Ascensions . S. D 31 32 52 18 33 34 35 ♌ 0 1●9 , 4● 108 , 9● 108 , 83 10● , 38 107 , 83 107 , 27   4 114 , 18 113 , 70 113 , 61 11● , 18 112 , 67 112 , 13   8 118 , 95 118 , 48 118 , 40 118 , 01 117 , 52 117 , 03   12 123 , 72 123 , 28 123 , 20 122 , 85 122 , 38 121 , 92   16 128 , 52 128 , 10 128 , 03 127 , 70 127 , 27 126 , 85   20 133 , 25 132 , 88 132 , 81 132 , 50 13● , 12 131 , 72   24 138 , 00 137 , 68 137 , 62 137 , 32 136 , 98 136 , 62   28 142 , 73 142 , 43 142 , 38 142 , 12 141 , 82 141 , 48 ♍ 2 147 , 43 147 , 17 147 , 12 146 , 90 146 , 63 146 , 35   6 152 , 13 151 , 90 151 , 86 151 , 67 151 , 43 151 , 18   10 156 , 80 156 , 62 156 , 58 156 , 42 156 , 22 156 , 03   14 161 , 47 161 , 32 161 , 29 161 , 15 161 , 00 160 , 83   18 166 , 12 166 , 00 165 , 98 165 , 88 165 , 77 165 , 63   22 170 , 80 170 , 67 170 , 66 170 , 60 170 , 52 170 , 43   26 175 , 38 175 , 33 175 , 32 175 , 30 175 , 27 175 , 22 ♎ 0 180 , 00 180 , 00 180 , 00 180 , 00 180 , 00 180 , 00   4 184 , 62 184 , 67 184 , 68 184 , 70 184 , 73 184 , 78   8 189 , 20 189 , 33 189 , 34 189 , 40 189 , 48 189 , 57   12 193 , 88 194 , 00 194 , 02 194 , 12 194 , 23 194 , 37   16 198 , 53 198 , 68 198 , 71 198 , 85 199 , 00 199 , 17   20 203 , 20 203 , 38 203 , 42 203 , 58 203 , 78 203 , 97   24 207 , 87 208 , 10 208 , 14 208 , 33 208 , 57 208 , 82   28 212 , 57 212 , 83 212 , 88 213 , 10 213 , 37 203 , 65 ♏ 2 217 , 27 217 , 57 217 , 62 217 , 88 218 , 18 218 , 52   6 222 , 00 222 , 32 222 , 38 222 , 68 223 , 02 223 , 38   10 226 , 75 227 , 12 227 , 19 227 , 50 227 , 88 228 , 28   14 231 , 48 231 , 90 231 , 97 232 , 30 232 , 73 23● , 15   18 236 , 28 236 , 72 236 , 80 237 , 15 237 , 62 238 , 08   22 241 , 05 241 , 52 241 , 60 241 , 99 242 , 48 242 , 97   26 245 , 82 246 , 30 246 , 39 246 , 82 247 , 33 247 , 87   30 250 , 57 251 , 08 251 , 17 251 , 62 252 , 17 252 , 73 A Table of oblique A scensions . S. D. 31 32 52. 18 33 34 35 ♐ 0 250 , 57 251 , 08 251 , 17 251. 62 252 , 17 252 , 73   4 255 , 33 255 , 88 255 , 98 256. 4● 257 , 00 257 , 60   8 260 , 05 260 , 6● 260 , 71 261. 20 261 , 78 262 , 40   12 264 , 73 265 , ●3 265 , 43 265. 93 26● , 53 267 , 17   16 269 , 38 269 , 99 270 , 10 270. 62 271 , 23 271 , 88   20 273 , 90 274 , 58 274 , 69 275. 22 275 , 85 276 , 52   24 278 , 52 279 , 12 279 , 23 279. 75 280 , 40 281 , 07   28 282 , 97 283 , 58 283 , 69 284. 20 284 , 85 285 , 53 ♑ 2 287 , 32 287 , 93 288 , 04 2●8 . 57 289 , 22 289 , 92   6 291 , 58 292 , 20 292 , 31 292. 83 293. 48 294 , 15   10 295 , 75 296 , 15 296 , 46 296. 98 297 , 62 298 , 28   14 299 , 80 300 , 40 300 , 51 301. 02 301 , 65 302 , 30   18 303 , 77 304 , 37 304 , 47 304. 95 305 , 57 306 , 18   22 307 , 60 308 , 17 308 , 27 308. 75 309 , ●3 309 , 95   26 311 , 33 311 , 88 312 , 98 312. 45 313 , 00 313 , 60 ♒ 0 314 , 97 315 , 48 315 , 58 316. 02 316 , 57 317 , 13   4 318 , 48 318 , 97 319 , 06 319. 48 320 , 00 320 , 13   8 321 , 90 322 , 35 322 , 4● 322. 8● 323 , 32 323 , 83   12 325 , 22 325 , 65 325 , 73 326. 10 326 , 55 327 , 02   16 328 , 45 328 , 85 328 , 92 329. 27 329 , 68 330 , 12   20 331 , 58 331 , 95 332 , 02 332. 33 332 , 82 333 , 12   24 334 , 67 334 , 98 335 , 04 335. 33 335 , 68 336 , 05   28 337 , 65 337 , 93 338 , 99 338. 27 338 , 57 338 , 88 ♓ 2 340 , 58 340 , 83 340 , 88 341. 13 341 , 38 341 , 68   6 343 , 47 343 , 68 34● , 72 343. 93 344 , 15 344 , 42   10 346 , ●0 346 , 48 346 , 51 346. 68 346 , ●8 347 , 08   14 349 , 08 349 , 22 349 , 25 349. 40 349 , ●5 349 , 72   18 351 , 83 351 , 95 351 , 97 352. 07 352 , 20 352 , 32   22 354 , 57 354 , 65 354. 66 354. 73 354 , 82 354 , 90   26 357 , 30 357 , 33 357. 34 357. 38 357 , 42 357 , 47   30 360 , 00 360 , 00 360. 00 360. 00 360 , 00 360 , 00 A Table of oblique Ascensions . S. D. 36 37 38 39 40 41 ♈ 0 000 , 00 000 , 00 000 , 00 000 , 00 000 , 00 000 , 00   4 02 , 50 02 , 13 02 , 42 02 , 37 02 , 33 02 , 27   8 05 , 03 04 , 93 04 , 85 04 , 77 04 , 67 04 , 57   12 07 , 57 07 , 43 07 , 30 07 , 17 07 , 02 06 , 88   16 10 , 12 09 , 95 09 , 77 09 , 58 09 , 40 09 , 22   20 12 , 72 12 , 50 12 , 28 12 , 05 11 , 80 11 , 58   24 15 , 35 15 , 10 14 , 82 14 , 57 14 , 27 13 , 98   28 18 , 03 17 , 75 17 , 42 17 , 12 16 , 80 16 , 47 ♉ 2 20 , 77 20 , 45 20 , 08 19 , 73 19 , 37 18 , 98   6 23 , 58 23 , 20 22 , 82 22 , 42 22 , 00 21 , 57   10 26 , 48 26 , 05 25 , 63 25 , 18 24 , 73 24 , 25   14 29 , 43 28 , 97 28 , 52 28 , 03 27 , 53 27 , 02   18 32 , 50 32 , 0● 31 , 50 ●0 , 97 30 , 43 29 , ●8   22 35 , 67 35 , 13 34 , 58 34 , 03 33 , 45 32 , 87   26 38 , 93 38 , 35 37 , ●8 37 , 18 ●6 , 57 35 , 93 ♊ 0 42 , 30 41 , 70 41 , 10 40 , 47 39 , 82 ●9 , 15   4 45 , 80 45 , 18 44 , 53 4● , 9● 4● , 20 42 , 50   8 49 , 42 48 , 78 48 , 10 47 , 43 46 , 72 46 , 00   12 53 , 15 52 , 50 51 , 82 51 , 10 50 , 38 49 , 63   16 57 , 05 56 , 37 55 , 65 54 , 93 54 , 18 53 , 42   20 61 , 05 60 , 35 5● , 6● 58 , 88 58 , 12 57 , 33   24 65 , 17 64 , 47 63 , 73 62 , 99 62 , 20 61 , 40   28 69 , 40 68 , 70 67 , 97 67 , 22 66 , 43 65 , 63 ♋ 2 73 , 78 73 , 07 72 , 33 71 , 08 70 , 78 69 , 99   6 78 , ●5 77 , 55 76 , 82 76 , 07 75 , 28 74 , 48   10 82 , 82 82 , 12 81 , 40 80 , 65 79 , 88 79 , 10   14 87 , 47 86 , 77 86 , 07 85 , 35 84 , ●8 83 , 82   18 92 , 18 91 , 52 90 , 83 90 , 13 89 , 40 88 , 65   22 96 , 97 96 , 32 95 , 67 94 , 98 94 , 28 93 , 55   26 101 , 82 101 , 18 100 , 57 99 , 90 99 , 22 98 , 52   30 106 , 70 106 , 10 105 , 50 104 , 87 104 , 22 103 , 55 A Table of Oblique Ascensions . S. D. 36 37 38 39 40 41 ♌ 0 106 , 70 106 , 10 105 , 50 104. 87 104 ▪ 22 103. 55   4 111 , 60 111 , 03 110 , 45 109. 87 109. 25 108. 62   8 116 , 50 115 , 9● 115 , 43 114. 88 114. 30 113. 70   12 121 , 43 120 , 95 120 , 45 119. 92 119. 37 118. 82   16 126 , ●8 125 , 93 125 , 46 124. 98 124. 47 123. 95   20 131 , 32 130 , 88 130 , 47 130. 02 129. 57 129. 08   24 136 , 25 135 , 86 135. 47 135. 08 134. 67 134. 23   28 141 , 15 140 , 82 140 , 46 140. 12 139. 73 139. 37 ♍ 2 146 , 05 145 , 75 145 , 45 145. 13 144. 80 144. 48   6 150 , 95 150 , 68 150 , 42 150. 14 149. 87 14● . 58   10 155 , 82 155 , 60 155 , 38 155. 15 154. 90 154. 68   14 160 ▪ 68 160 , 50 160 , 32 160. 14 159. 95 159. 77   18 165 , 52 165 , 38 165 , 25 165. 12 164. 98 164. 83   22 170 , 35 170 , 27 170 , 17 170. 08 170. 00 169. 88   26 175 , 18 175 , 13 175 , 10 175. 05 175. 00 174. 95 ♎ 0 180 , 00 180 , 00 180 , 00 180. 00 180. 00 180. 00   4 184 , 82 184 , 87 184 , 90 184. 95 185. 00 185. 05   8 189 , 65 189 , 73 189 , 83 189. 92 190. 00 190. 12   12 194 , 48 194 , 62 194 , 75 194. 88 194. 02 195. 17   16 199 , 32 199 , 50 199 , 68 199. 86 200. 05 200. 23   20 204 , 18 204 , 40 204 , 62 204. 85 205. 10 205. 32   24 209 , 05 209 , ●2 209 , 58 209. 86 210. 13 210. 42   28 213 , 95 214 , 25 214 , 55 214. 87 215 ▪ 20 215. 52 ♏ 2 218 , ●5 219 , 18 219 , 54 219. 88 220. 27 220. 63   6 223 , 75 224 , 14 224 , 5● 224. 92 225. 33 225. 77   10 228 , 68 229 , 12 229 , 53 229. 98 230. 43 230. 92   14 233 , 62 234 , 07 234 , 54 235. 02 235. 53 236. 05   18 238 , 57 239 , 05 239 , 55 240. 08 240. 63 241. 18   22 243 , 50 244 , 02 244 , 57 245. 12 245. 70 246. 30   26 248 , 40 248 , 97 249 , 55 250. 13 250. 75 251. 38   30 253 , 30 253 , 90 254 , 50 255. 13 255. 78 256. 45 A Table of oblique Ascensions . S. D. 36 37 38 39 40 41 ♐ 0 253 , 30 25● , 90 254 , 50 255 , 13 255 , 78 256 , 45   4 258 , 13 258 , 82 259 , 4● 260 , 10 260 , 78 261 , 48   8 263 , 03 263 , 68 264 , 33 265 , 02 265 , 72 266 , 45   12 267 , 82 268 , 48 269 , 17 269 , 87 270 , 60 271 , 35   16 272 , 53 273 , 23 273 , 93 274 , 65 275 , 42 276 , 18   20 277 , 18 277 , 88 27● , 60 279 , 35 280 , 12 280 , 90   24 281 , 75 282 , 45 283 , 18 283 , 93 284 , 72 285 , 52   28 286 , 22 286 , 93 287 , 67 288 , 92 289 , 22 290 , 01 ♑ 2 290 , 60 291 , ●0 291 , 03 292 , 78 293 , 57 294 , ●7   6 294 , 83 295 , 53 296 , ●7 297 , 01 279 , 80 298 , 60   10 298 , 95 299 , 65 300 , 37 301 , 12 301 , 88 302 , 67   14 302 , 95 303 , 63 304 , 35 30● , 07 305 , 82 306 , 58   18 306 , 85 307 , 50 308 , 18 308 , 90 309 , 62 310 , 37   22 310 , 58 311 , 22 311 , 90 312 , 57 313 , 28 314 , 00   26 314 , 20 314 , 82 315 , 47 316 , 10 316 , 80 317 , 50 ♒ 0 317 , 70 318 , 30 318 , 90 319 , 53 320 , 18 320 , 85   4 321 , 07 321 , 65 322 , 22 322 , 82 323 , 43 324 , 07   8 324 , 33 324 , 87 325 , 42 325 , 97 326 , 55 327 , 13   12 327 , 50 328 , 00 328 , 50 329 , 03 329 , 57 330 , 12   16 330 , 57 331 , 03 331 , 48 331 , 97 332 , 47 332 , 98   20 333 , 52 333 , 95 334 , 37 334 , 82 335 , 27 335 , 75   24 336 , 42 336 , 80 337 , 18 337 , 58 338 , 00 338 , 43   28 339 , 23 339 , 55 339 , 92 340 , 27 340 , 63 341 , 02 ♓ 2 341 , 97 342 , 25 342 , 58 342 , 88 343 , 20 343 , 53   6 344 , 65 344 , 90 345 , 18 345 , 43 345 ▪ 73 346 , 02   10 347 , 28 347 , 50 347 , 72 347 , 95 348 , 20 348 , 42   14 349 , 88 350 , 05 350 , 23 350 , 42 350 , 60 350 , 78   18 352 , 43 352 , 57 352 , 70 352 , 83 352 , 98 353 , 12   22 354 , 97 355 , 07 355 , 15 355 , 23 355 , 33 355 , 43   26 357 , 50 357 , 87 357 , 58 357 , 63 357 , 67 357 , 73   30 360 , 00 360 , 00 360 , 00 360 , 00 360 , 00 360 , 00 A Table of oblique Ascensions . S. D. 42 43 44 45 46 47 ♈ 0 000 , 00 00 , 00 000 , 00 000 , 00 000 , 00 000 , 00   4 02 , 22 02 , 18 02 , 13 02 , 07 02 , 00 01 , 92   8 04 , 47 04 , 37 04 , 27 04 , 15 04 , 03 03 , 92   12 06 , 73 06 , 57 06 , 42 06 , 25 06 , 08 05 , 92   16 09 , 00 08 , 80 08 , 60 08 , 38 08 , 15 07 , 92   20 11 , 33 11 , 07 10 , 82 10 , 53 10 , 25 09 , 97   24 13 , 70 13 , 40 13 , 08 12 , 73 12 , 40 12 , 05   28 16 , 12 15 , 77 15 , 40 15 , 02 14 , 62 24 , 20 ♉ 2 18 , 60 18 , 20 17 , 77 17 , 33 16 , 88 16 , 42   6 21 , 13 20 , 68 20 , 20 19 , 72 19 , 22 18 , 68   10 23 , 77 23 , 27 22 , 75 22 , 20 21 , 65 21 , 07   14 26 , 48 25 , 93 25 , 37 24 , 78 24 , 17 23 , 52   18 29 , 30 28 , 73 28 , 10 27 , 47 26 , 78 26 , 08   22 32 , 25 31 , 62 30 , 95 30 , 25 29 , 55 28 , 80   26 35 , 27 34 , 58 33 , 88 33 , 17 32 , 38 31 , 77 ♊ 0 38 , 45 ●7 , 73 36 , 98 36 , 23 35 , 40 34 , 57   4 41 , 77 41 , 03 40 , 23 39 , 42 38 , 57 37 , 68   8 45 , 22 44 , 45 43 , 63 42 , 78 41 , 87 40 , 97   12 48 , 85 48 , 03 47 , 18 46 , 30 45 , 40 44 , 42   16 52 , 60 51 , 77 50 , 88 49 , 98 49 , 05 48 , 05   20 56 , 50 55 , 65 54 , 78 53 , 83 52 , 88 51 , 87   24 60 , 57 59 , 72 58 , 80 57 , 87 56 , 88 55 ▪ 87   28 64 , 70 63 , 92 63 , 01 62 , 07 61 , 07 60 , 05 ♋ 2 69 , 03 68 , 28 67 , 35 66 , 43 65 , 45 64 , 42   6 73 , 65 72 , 78 71 , 88 70 , 93 69 , 97 68 , 95   10 78 , 27 77 , 42 76 , 53 75 , 60 74 , 65 73 , 63   14 83 , 02 82 , 18 81 , 30 80 , 40 79 , 47 78 , 47   18 87 , 87 87 , 07 86 , 20 85 , 33 84 , 4● 83 , 43   22 92 , 78 92 , 01 91 , 18 90 , 33 89 , 45 88 , 52   26 97 , 78 97 , 03 96 , 25 95 , 43 94 , 58 93 , 70   30 102 , 85 102 , 13 101 , 38 100 , 62 99 , 80 98 , 97 A Table of oblique Ascensions . S. D. 42 43 44 45 46 47 ♌ 0 102 , ●5 102 , 13 10● , 38 100. 62 99 , 80 98 ▪ 97   4 107 , 95 107 , 27 10● , 57 105. 83 105 ▪ 07 104. 28   8 11● , 0● 112 , 45 111 , 78 111. 10 110. 38 109. 63   12 1●8 , 25 117 , 65 117 , 0● 116. ●8 115. 73 115. 03   16 123 , 4● 122 , 88 122 , 32 121. 70 121. 27 120. 47   20 128 , 60 128 , 10 127 , 58 127. ●● 126. 48 125. 90   24 133 , 90 133 , 35 132 , 87 132. 42 131. ●7 131. 33   28 138 , 97 138 , 57 138 , 1● 137. 72 137. 25 136. 78 ♍ 2 144 , 13 143 , 78 143 , 40 143. 03 142. 63 142. 50   6 149 , 30 148 , 98 14● , 67 148. 33 148. 00 147. 65   10 154 , 43 154 , 17 153 , 92 153. 63 153. 35 153. 07   14 159 , 57 159 , 37 159 , 15 158 ▪ 93 158. 70 158. 47   18 164 ▪ 68 164 , 52 164 , 37 164. 20 164. 03 163. 87   22 169 ▪ 80 169 , 68 169 , 58 169. 47 169. ●7 169. 25   26 174 , 90 174 , 85 174 , 80 174. 73 174. 67 174. 63 ♎ 0 180 , 00 180 , 00 180 , 00 180. 00 180. 00 180. 00   4 185 , 10 185 , 15 185 , 20 185. 27 185. 33 185. 37   8 190 , 20 190 , 32 190 , 42 190. 53 190. 63 190. 75   12 195 , 32 195 , 48 195 , 63 195. 80 195. 97 196. 13   16 200 , 43 200 , 63 200 , 85 201. 07 201. 30 201. 53   20 205 , 57 2●5 , 83 206 , 08 206. 37 206. 65 206. 93   24 210 , 70 211 , 02 211 , 33 211. 67 212. 00 212. 35   28 215 , 87 216 , 22 216 , 60 216. 97 217. 37 217. 50 ♏ 2 221 , 03 221 , 43 221 , 87 222. 28 222. 75 223. 22   6 226 , 20 226 , 65 2●7 , 13 227. 58 228. 13 228. 67   10 231 , 40 231 , 90 232 , 42 232. 97 233. 52 234. 10   14 236 , 58 ●37 , 12 237 , 68 238. ●0 238. 73 239. 53   18 241 , 75 242 , 35 24● , 97 243. 62 244. 27 244. 97   22 246 , 92 247 , 55 248 , 22 248. 90 249. 62 250. 37   26 252 , 05 252 , 73 253 , 43 254. 17 254. 93 255. 72   30 257 , 15 257 , 87 258 , 62 259 , 38 260. 20 261. 03 A Table of Oblique Ascensions . S. D. 42 43 44 45 46 47 ♐ 0 257 , 15 257 , 87 258 , 62 259 , 38 260 , 20 261 , 03   4 262 , ●2 262 , 97 263 , 75 264 , 57 265 , 42 266 , 20   8 267 , 22 267 , 99 268 , 82 209 , 67 ●70 , 55 271 , 48   12 272 , 13 272 , 93 273 , 80 274 , 67 275 , 58 276 , 57   16 276 , 98 277 , 8● 278 , ●0 279 , 60 280 , 53 281 , 53   20 281 , 73 282 , 58 283 , 47 284 , 40 285 , 35 286 , 37   24 286 , ●5 287 , 22 288 , 12 289 , 07 290 , 03 291 , 05   28 290 , 97 291 , 72 292 , 65 293 , 57 294 , ●5 295 , 58 ♑ 2 295 , 30 296 , 08 296 , 99 297 , 93 298 , 93 299 , 95   6 299 ▪ 43 300 , 28 301 , 20 302 , 13 303 , 12 304 , 13   10 30● , 50 304 , 35 305 , 32 306 , ●7 307 , 1● 308 , 13   14 307 , 40 308 , 23 309 , 12 310 , 02 310 , 95 311 , 95   18 311 , 15 311 , 97 312 , 82 313 , 60 314 , 60 315 , 58   22 314 , 78 315 , 55 316 , 37 317 , 22 318 , 13 319 , 03   26 318 , 23 318 , 97 319 , 77 320 , 58 321 , 43 322 , 32 ♒ 0 321 , 55 322 , 27 323 , 02 323 , 77 324 , 60 325 , 43   4 324 , 73 325 , 42 326 , 12 326 , 83 327 , 62 328 , ●3   8 327 , 75 328 , 38 329 , 05 329 , 75 330 , 45 331 , 20   12 330 , 70 331 , 27 331 , 90 332 , 53 333 , 22 333 , 92   16 333 , 52 334 , 07 334 , 63 335 , 22 335 , 83 336 , 4●   20 336 , 23 336 , 73 337 , ●5 337 , 80 338 , 35 338 , 93   24 338 , 87 339 , 32 339 , 80 340 , 28 340 , 78 341 , 32   28 341 , 40 341 , 80 34● , 23 342 , 67 343 , 12 34● , 58 ♓ 2 343 , ●8 344 , 23 344 , 60 344 , 98 345 , 38 345 , ●0   6 346 , 30 346 , 60 346 , 9● 347 , 27 347 , 60 347 ▪ 95   10 348 , 63 34● , 9● 349 ▪ 18 349 , 47 349 , 75 350 , 0●   14 351 , 00 351 , 20 351 , 40 351 , 62 351 , ●5 352 , ●8   18 353 , 27 353 , 4● 353 , 58 35● , 75 35● , 92 354 , ●8   22 355 , 53 355 , 63 355 , 73 355 , 8● 255 , 97 ●56 , ●8   26 357 , 78 357 , 82 357 , 87 357 , 93 358 , 00 35● , 08   30 360 , 00 360 ▪ 00 360 , 00 360 , 00 360 , 00 3●0 , 00 A Table of oblique Ascensions . S. D. 47. 47 48 49 50 51 51. 53 ♈ 0 00 , 00 00 , 00 00 , 00 00 , 00 00. 00 00 , 00   4 01 , 90 01 , 88 01 , 83 01 , 77 01. 68 01 , 65   8 03 , 87 03 , 80 03 , 6● 03 , 53 03. 40 03 , 32   12 03 , 83 05 , 73 05 , 53 05 , 37 05. 13 05 , 02   16 07 , 81 07 , 67 07 , 42 07 , 15 06. 87 06 , 72   20 09 , 82 09 , 65 09 , 3● 09 , 00 08. 67 08 , 48   24 11 , 88 11 , 68 11 , 30 10 , 92 10. 50 10 , 27   28 14 , 00 13 , 77 13 , 33 12 , 87 12. 38 12 , 12 ♉ 2 16 , 19 15 , 93 15 , 42 14 , 88 14. 33 14 , 01   6 18 , 43 18 , 15 17 , 57 16 , 97 16. 35 16 , 00   10 20 , 73 20 , 35 19 , 82 19 , 15 18. 47 18 , 08   14 23 , 18 22 , 85 22 , 17 21 , 43 20. 67 20 , 23   18 25 , 73 25 , 38 24 , 47 23 , 82 23. 01 22 , 55   22 28 , 40 28 , 03 27 , 22 26 , 35 25. 47 24 , 97   26 31 , 22 30 , 77 29 , 88 28 , 98 28. 02 27 , 50 ♊ 0 34 , 13 33 , 68 32 , 75 31 , 78 30. 77 30 , 20   4 37 , 23 36 , 75 35 , 78 34 , 77 33. 70 33 , 10   8 40 , 48 40 , 01 38 , 98 37 , 92 36. 80 36 , 13   12 43 , 90 43 , 40 42 , 37 41 , 23 40. 08 39 , 43   16 47 , 53 47 , 02 45 , 93 44. 78 4● . 58 42 , 92   20 51 , 38 50 , 40 49 , 70 4● , 53 47. 32 46 , 60   24 55 , 35 54 , 80 53 , 67 52 , 48 51. 22 50 , 50   28 59 , 50 58 , 97 57 , 83 5● , 63 55. 37 54 , 65 ♋ 2 63 , 87 63 , 3● 6● , 18 61 , 00 59. 73 59 , 01   6 68 , 42 67 , 87 66 , 73 65 , 55 64. 30 63 , 58   10 73 , 12 72 , 57 71 , 47 70 , 30 69. 07 68 , 37   14 77 , 97 77 , 43 76 , 33 75 , 20 73. 98 73 , 32   18 82 , 93 82 , 43 81 , 40 80 , 27 79. 13 7● , 47   22 88 , 05 87 , 57 86 , 53 85 , 35 84. 35 83 , 72   26 93 , 27 92 , 77 91 , 80 90 , 78 89. 70 89 , 10   30 98 , 53 98 , 08 97 , 15 96 , 18 95. 17 94 , 60 A Table of oblique Ascensions . S. D 47. 47 48 49 50 51 51. 53 ♌ 0 098 , 53 098 , 08 097 , 15 096 , 18 095 , 17 094 , 60   4 103 , 88 103 , 45 10● , 57 101 , 67 100 , 70 100 , 17   8 109 , 27 108 , 87 103 , 05 107 , 20 106 , 30 105 , 80   12 114 , 70 114 , 32 113. 77 112 , 77 111 , 95 111 , ●8   16 120 , 15 119 , 80 119. 12 118 , 38 117 , 62 117 , 18   20 125 , 62 125 , 28 124. 65 123 , 98 123 , 30 122 , 92   24 131 , 08 130 , 82 130. 2● 129 , 62 129 , 02 128 , 67   28 136 , 53 136 , 30 135. 80 135 , 27 134 , 72 134 , 40 ♍ 2 142 , 02 141 , 78 141. 35 140 , 88 140 , 40 140 , 13   6 147 , 43 147 , 28 146. 90 146 , 50 146 , 10 145 , 87   10 152 , 92 152 , 75 152. 43 152 , 10 151 , 77 151 , 57   14 158 , 33 158 , 22 157. 97 157 , 70 157 , 43 157 , 27   18 163 , 75 163 , 68 163. 48 163 , 28 163 , 08 162 , ●7   22 169 , 18 169 , 13 169. 00 168 , 87 168 , 73 168 , 65   26 17● , 60 174 , 57 174. 51 174 , 45 174 , 37 174 , 33 ♎ 0 180 , 00 180 , 00 180. 00 180 , 00 180 , 00 180 , 00   4 185 , 40 185 , 43 185. 49 185 , 55 185 , 63 185 , 67   8 190 , 82 190 , 87 191. 00 191 , 13 191 , 27 191 , 35   12 196 , 25 196 , 32 196. 52 196 , 72 196 , 92 197 , 03   16 201 , 67 201 , 78 202. 03 202 , 30 202 , 57 202 , 73   20 207 , 08 207 , 25 207. 57 207 , 90 208 , 23 208 , 43   24 212 , 57 212 , 72 213. 10 213 , 50 213 , 90 214 , 13   28 217 , ●8 218 , 22 218. 65 219 , 12 219 , 60 219 , 87 ♏ 2 223 , 47 223. 70 224. 20 224 , 73 225 , 28 225 , 60   6 228 , 92 229. 18 229. 78 230 , 38 230 , 98 231 , ●3   10 234 , 38 234 , 72 235. 35 236 , 02 236 , 70 237 , 08   14 239 , 85 240. 20 240. 20 241 , 6● 242 , 38 242 , 82   18 245 , 30 245 , 68 246 , 62 247 , 23 248 , 05 248 , 52   22 250 , 73 251 , 13 251. 9● 252 , 70 253 , 70 254 , 20   26 256 , 12 256 , 55 257. 43 258 , 33 259 , 30 259 , ●3   30 261 , 47 261 , 92 262. 85 26● , 82 264 , 83 265 , 40 A Table of oblique Ascensions . S. D. 47 48 49 50 51 51. 53 ♐ 0 261 , 47 261 , 92 262 , 85 263 , 12 264 , 83 265 , 40   4 266 , 23 267 , 23 268 , 20 269 , 20 270 , 30 270 , 90   8 272 , 95 272 , 43 273 , 47 274 , 65 275 , 65 276 , 28   12 277 , 07 277 , 57 278 , 60 279 , 72 280 , 87 281 , 53   16 282 , 03 282 , 57 283 , 67 284 , 80 286 , 02 286 , 68   20 286 , 88 287 , 43 288 , 53 289 , 70 290 , 93 291 , 63   24 291 , 58 292 , 13 293 , 27 294 , 45 295 , 70 296 , 42   28 296 , 13 296 , 67 297 , 82 299 , 00 300 , 27 300 , 99 ♑ 2 300 , 50 301 , 03 30● , 17 303 , 37 304 , 63 305 , 35   6 304 , 65 305 , 20 306 , 33 307 , 52 308 , 78 309 , 50   10 308 , 62 309 , 60 310 , 30 311 , 47 312 , 68 313 , 40   14 312 , 47 312 , 98 314 , 07 315 , 22 316 , 42 317 , 08   18 316 , 10 316 , 60 317 , 63 318 , 77 319 , 92 320 , 57   22 319 , 52 319 , 99 321 , 02 322 , 08 313 , 20 343 , 17   26 322 , 77 323 , 25 324 , 22 325 , 23 326 , 30 326 , 90 ♒ 0 325 , 87 326 , 32 327 , 25 328 , 22 329 , 23 329 , 80   4 328 , 78 329 , 23 330 , 12 331 , 02 331 , 98 332 , 50   8 331 , 60 331 , 97 3●2 , 78 333 , 65 334 , 53 335 , 03   12 334 , 27 334 , 62 335 , 53 336 , 18 336 , 99 337 , 45   16 336 , 82 337 , 15 337 , 83 338 , 57 339 , 33 339 , 77   20 339 , 27 339 , 65 340 , 18 340 , 85 341 , 53 341 , 92   24 341 , 57 341 , 85 342 , 43 343 , 03 343 , 65 344 , 00   28 343 , 81 344 , 07 344 , 58 345 , 12 345 , 67 345 , 99 ♓ 2 346 , 00 346 , 23 346 , 67 347 , 13 347 , 62 347 , 88   6 34● , 12 348 , 32 348 , 70 349 , 08 349 , 50 349 , 7●   10 350 , 18 350 , 35 350 , 67 351 , 00 351 , 33 351 , 52   14 352 , 19 352 , 33 352 , 58 352 , 85 353 , 13 353 , 28   18 354 , 17 354 , 27 354 , 47 354 , 63 354 , 87 354 , 98   22 356 , 13 356 , 20 356 , 33 356 , 47 356 , 60 356 , 68   26 358 , 10 358 , 12 358 , 17 358 , 32 358 , 32 358 , 35   30 360 , 00 360 , 00 360 , 00 360 , 00 360 , 00 360 , 00 A Table of oblique Ascensions . S. D. 52 53 54 55 56 57 ♈ 0 00 , 00 00 , 00 00. 00 00 , 00 00 , 00 00 , 00   4 01 , 62 01 , 53 01. 47 01 , 38 01 , 30 01 , 20   8 0● , 25 03 , 10 02. 95 02 , 78 02 , 62 02 , 43   1● 04 , 92 04 , 68 04. 45 04 , 20 03 , 95 03 , 67   16 06 , 58 06 , 28 05. 97 05 , 65 05 , 28 04 , 93   20 08 , 30 07 , 92 07. 53 07 , 12 06 , 68 06 , 22   24 10 , 07 09 , 60 09. ●3 08 , 63 08 , 10 07 , 55   28 11 , 88 11 , 33 10. 78 10 , 22 09 , 58 08 , 93 ♉ 2 13 , 75 13 , 13 12. 33 11 , 83 11 , 12 10 , 37   6 15 , 70 15 , 02 14. 30 13 , 53 12 , 73 11 , 87   10 17 , 75 16 , 98 16. 18 15 , 33 14 , 43 13 , 48   14 19 , 87 19 , 03 18. 13 17 , 50 16 , 22 15 , 18   18 22 , 13 21 , 22 20. 25 19 , 23 18 , 15 17 , 00   22 24 , 52 23 , 52 22. 47 21 , 37 20 , 20 18 , 93   26 27 , 03 25 , 97 24. 83 23 , 65 22 , 37 21 , 01 ♊ 0 29 , 70 28 , 37 27. 37 26 , 10 24 , 73 23 , 28   4 32 , 57 31 , 37 30. 10 28 , 73 27 , 32 25 , 75   8 35 , 60 34 , 37 33. 01 31 , 58 30 , 08 28 , 45   12 38 , 85 37 , 53 36. 13 34 , 68 33 , 05 31 , 35   16 42 , 32 40 , 95 39. 52 37 , 98 36 , 33 34 , 55   20 45 , 98 44 , 60 43. 12 41 , 55 39 , 85 38 , 00   24 49 , 88 48 , 48 46. 97 45 , 38 43 , 63 41 , 77   28 54 , 03 52 , 58 51. 08 49 , 47 47 , 73 45 , 85 ♋ 2 58 , 40 56 , 98 55. 47 53 , 82 52 , 08 50 , 20   6 6● , 97 61 , 55 60. 05 58 , 45 56 , 72 54 , 83   10 67 , 75 66 , 37 64. 88 63 , 32 61 , 62 59 , 77   14 72 , 73 71 , 37 69. 93 68 , 40 66 , 73 64 , 95   18 77 , 87 76 , 57 75. 17 73 , 68 72 , 08 70 , 38   22 83 , 17 81 , 92 80. 58 79 , 13 77 , 62 75 , 98   26 88 , 57 87 , 37 86. 10 84 , 75 83 , 32 81 , 77   30 94 , 10 92 , 97 91. 77 90 , 63 89 , 13 87 , 68 A Table of oblique Ascensions . S. D. 52 53 54 55 56 57 ♌ 0 094 , 10 092 , 97 091 , 77 090 , 63 089 , 13 087 , 68   4 099 , 70 098 , 63 097 , 52 096 , 33 095 , 07 09● , 70   8 105. 37 104 , 37 103 , 32 102 , 23 101 , 05 099 , 78   12 111 , 07 110 , 15 109 , 18 108 , 17 107 , 08 105 , 93   16 116 , 82 115 , 98 115 , 08 114 , 18 113 , 17 112 , 12   20 122 , 58 121 , 82 121 , 01 120 , 19 119 , 27 118 , 32   24 128 , 37 127 , 68 126 , 95 126 , 20 125 , 40 124 , 52   28 134 , 13 133 , 53 132 , 88 132 , 21 131 , 50 130 , 75 ♍ 2 139 , 90 139 , 37 138 , 80 138 , 22 137 , 60 136 , 95   6 145 , 67 145 , 20 144 , 72 144 , 22 143 , 70 143 , 13   10 151 , 40 151 , 01 150 , 63 150 , 21 149 , 78 149 , 32   14 157 , 13 156 , 83 156 , 52 156 , 18 155 , 85 155 , 48   18 162 , 87 162 , 63 162 , 40 162 , 17 161 , 90 161 , 62   22 168 , 58 168 , 43 168 , 27 168 , 12 167 , 95 167 , 75   26 174 , 30 174 , 22 174 , 13 174 , 07 173 , 98 173 , 88 ♎ 0 180 , 00 180 , 00 180 , 00 180 , 00 180 , 00 180 , 00   4 185 , 70 185 , 78 185 , 87 185 , 93 186 , 02 186 , 12   8 191 , 42 191 , 57 191 , 73 191 , 88 192 , 05 192 , 25   12 197 , 13 197 , 37 197 , 60 197 , 83 198 , 10 198 , 38   16 202 , 87 203 , 17 203 , 48 203 , 82 204 , 15 204 , 52   20 208 , 60 208 , 99 209 , 37 209 , 79 210 , 22 210 , 68   24 214 , 32 214 , 80 215 , 28 215 , 78 216 , 30 216 , 87   28 220 , 10 220 , 63 221 , 20 221 , 78 222 , 40 223 , 05 ♏ 2 225 , 87 226 , 47 227 , 12 227 , 79 228 , 50 229 , 25   6 231 , 63 232 , 32 233 , 05 233 , 80 234 , 60 235 , 48   10 237 , 42 238 , 18 238 , 99 239 , 81 240 , 73 241 , 68   14 243 , 18 244 , 02 244 , 92 245 , 82 246 , 83 247 , 88   18 248 , 93 249 , 85 250 , 82 251 , 83 252 , 92 254 , 07   22 254 , 62 295 , 63 256 , 68 257 , 77 258 , 95 260 , 22   26 260 , 30 261 , 37 262 , 48 263 , 67 264 , 93 266 , 30   30 265 , 90 267 , 03 268 , 23 269 , 37 270 , 87 272 , 32 A Table of oblique Ascensions . S. D. 52 53 54 55 56 57 ♐ 0 265 , 90 267 , 03 268 , 23 269 , 37 270 , 87 272 , 32   4 271 , 43 272 , 63 273 , 90 275 , 25 276 , 68 278 , 23   8 276 , 83 278 , 08 279 , 42 280 , 87 282 , 38 284 , 02   12 282 , 13 283 , 43 284 , 83 286 , 3● 287 , 92 289 , 62   16 287 , ●7 288 , 63 290 , 07 291 , 60 293 , 27 295 , 05   20 292 , 25 293 , 63 295 , 12 296 , 68 298 , 38 300 , 23   24 297 , 03 298 , 45 299 , 95 301 , 55 303 , 28 305 , 17   28 301 , 60 303 , 02 304 , 53 306 , 18 307 , 92 309 , 80 ♑ 2 305 , 97 307 , 42 308 , 92 310 , 53 312 , 27 314 , 15   6 310 , 12 311 , 52 313 , 03 314 , 62 316 , 37 318 , 23   10 314 , 02 315 , 40 316 , 88 318 , 45 320 , 15 322 , 00   14 317 , 68 319 , 05 320 , 48 322 , 02 323 , 67 325 , 45   18 321 , 15 322 , 47 323 , 87 325 , 32 326 , 95 328 , 65   22 324 , 40 325 , 63 326 , 99 328 , 42 329 , 92 331 , 55   26 327 , 43 328 , 63 329 , 90 331 , 27 332 , 68 334 , 25 ♒ 0 330 , 30 331 , 43 332 , 63 333 , 90 335 , 27 336 , 72   4 332 , 97 334 , 03 335 , 17 336 , 35 337 , 63 338 , 99   8 335 , 48 336 , 48 337 , 53 338 , 63 339 , 80 341 , 07   12 337 , 87 338 , 78 339 , 75 340 , 77 341 , ●5 343 , 00   16 340 , 13 340 , 97 341 , 87 342 , 50 343 , 78 344 , 82   20 342 , 25 343 , 02 343 , 82 344 , 67 345 , 57 346 , 52   24 344 , 30 344 , 98 345 , 70 346 , 47 347 , 27 348 , 13   28 346 , 25 346 , 87 347 , 67 348 , 17 348 , 88 349 , 63 ♓ 2 348 , 15 348 , 67 349 , 22 349 , 78 350 , 42 351 , 07   6 349 , 12 350 , 40 350 , 87 351 , 37 351 , 90 352 , 45   10 351 , 93 352 , 08 352 , 47 352 , 88 353 , 32 353 , 78   14 353 , 70 353 , 72 354 , 03 354 , 35 354 , 72 355 , 07   18 355 , 42 355 , 32 355 , 55 355 , 80 356 , 05 356 , 33   22 356 , 08 356 , 90 357 , 05 357 , 22 357 , 38 357 , 57   26 358 , 75 358 , 43 358 , 53 358 , 62 358 , 70 358 , 80   30 360 , 00 360 , 00 360 , 00 360 , 00 360 , 00 360 , 00 A Table of Positions for the Pole of 1 2 3 4 5 6 7 North Declination under the Earth , and South above it . 0 0 , 79 1 , 58 2 , 38 3 , 17 3 , 98 4 , 80 5 , 62 1 0 , 78 1 , 55 2 , 33 3 , 10 3 , 90 4 , 70 5 , 50 2 0 , 75 1 , 52 2 , 27 3 , 03 3 , 82 4 , 58 5 , 37 3 0 , 73 1 , 48 2 , 22 2 , 95 3 , 73 4 , 48 5 , 25 4 0 , 72 1 , 45 2 , 17 2 , 88 3 , 63 4 , 38 5 , 12 5 0 , 70 1 , 42 2 , 12 2 , 82 3 , 55 4 , 27 5 , 00 6 0 , 68 1 , 38 2 , 07 2 , 75 3 , 45 4 , 17 4 , 88 7 0 , 67 1 , 35 2 , 01 2 , 67 3 , 37 4 , 07 4 , 75 8 0 , 65 1 , 30 1 , 97 2 , 60 3 , 28 3 , 95 4 , 63 9 0 , 63 1 , 27 1 , 90 2 , 53 3 , 18 3 , 85 4 , 50 10 0 , 60 1 , 23 1 , 85 2 , 47 3 , 10 3 , 73 4 , 38 11 0 , 58 1 , 20 1 , 80 2 , 38 3 , 02 3 , 63 4 , 25 12 0 , 57 1 , 17 1 , 75 2 , 32 2 , 92 3 , 52 4 , 12 13 0 , 55 1 , 12 1 , 68 2 , 23 2 , 83 3 , 42 4 , 00 14 0 , 53 1 , 08 1 , 63 2 , 17 2 , 73 3 , 30 3 , 87 15 0 , 52 1 , 05 1 , 58 2 , 10 2 , 63 3 , 18 3 , 73 16 0 , 50 1 , 01 1 , 52 2 , 01 2 , 55 3 , 07 3 , 60 17 0 , 48 0 , 97 1 , 47 1 , 93 2 , 45 2 , 97 3 , 47 18 0 , 47 0 , 93 1 , 40 1 , 87 2 , 35 2 , 85 3 , 33 19 0 , 43 0 , 90 1 , 35 1 , 78 2 , 25 2 , 73 3 , 20 20 0 , 42 0 , 85 1 , 28 1 , 72 2 , 17 2 , 60 3 , 05 21 0 , 40 0 , 82 1 , 23 1 , 63 2 , 07 2 , 48 2 , 92 22 0 , 38 0 , 77 1 , 17 1 , 55 1 , 95 2 , 37 2 , 77 23 0 , 37 0 , 73 1 , 10 1 , 47 1 , 85 2 , 25 2 , 63 24 0 , 33 0 , 70 1 , 05 1 , 38 1 , 75 2 , 12 2 , 48 25 0 , 32 0 , 65 0 , 98 1 , 30 1 , 65 1 , 98 2 , 33 26 0 , 30 0 , 60 0 , 92 1 , 22 1 , 53 1 , 87 2 , 18 27 0 , 27 0 , 57 0 , 85 1 , 12 1 , 43 1 , 73 2 , 03 28 0 , 25 0 , 52 0 , 78 1 , 03 1 , 32 1 , 60 1 , 87 29 0 , 23 0 , 47 0 , 72 0 , 95 1 , 20 1 , 47 1 , 72 30 0 , 20 0 , 43 0 , 65 0 , 85 1 , 08 1 , 32 1 , 55 31 0 , 18 0 , 38 0 , 58 0 , 77 0 , 97 1 , 18 1 , 38 32 0 , 17 0 , 33 0 , 50 0 , 76 0 , 85 1 , 03 1 , 22 Latitude of 51 deg . 53 parts . Positiō . 1 2 3 4 5 6 7 South Declination under the Earth , and North above it . 32 1. 40 2 , 83 4 , 27 5 , 67 7 , 12 8 , 57 10 , 02 31 1. 38 2 , 78 4 , 18 5 , 57 7 , 00 8 , 42 9 , 85 30 1. 37 2 , 73 4 , 12 5 , 48 6 , 88 8 , 28 9 , 68 29 1. 33 2 , 70 4 , 05 5 , 38 6 , 77 8 , 13 9 , 52 28 1. 31 2 , 65 3 , 98 5 , 30 6 , 65 8 , 00 9 , 37 27 1. 30 2 , 60 3 , 91 5 , 22 6 , 53 7 , 87 9 , 20 26 1. 27 2 , 57 3 , 85 5 , 12 6 , 43 7 , 73 9 , 05 25 1. 25 2 , 51 3 , 78 5 , 03 6 , 32 7 , 62 8 , 90 24 1. 23 2 , 47 3 , 72 4 , 95 6 , 22 7 , 48 8 , 75 23 1. 20 2 , 43 3 , 67 4 , 87 6 , 12 7 , 35 8 , 60 22 1. 18 2 , 40 3 , 60 4 , 78 6 , 02 7 , 23 8 , 47 21 1. 17 2 , 35 3 , 5● 4 , 70 5 , 90 7 , 12 8 , 32 20 1. 15 2 , 31 3 , 48 4 , 62 5 , 80 7 , 00 8 , 18 19 1. 13 2 , 27 3 , 41 4 , 55 5 , 72 6 , 87 8 , 03 18 1. 10 2 , 23 3 , ●7 4 , 47 5 , 62 6 , 75 7 , 90 17 1. 08 2 , 20 3 , 30 4 , 40 5 , 52 6 , 63 7 , 73 16 1. 07 2 , 15 3 , 25 4 , 31 5 , 42 6 , 53 7 , 63 15 1. 05 2 , 12 3 , 18 4 , 23 5 , 33 6 , 42 7 , 50 14 1. 03 2 , 08 3 , 13 4 , 17 5 , 23 6 , 30 7 , 37 13 1. 02 2 , 05 3 , 08 4 , 10 5 , 13 6 , 18 7 , 23 12 1. 00 2 , 01 3 , 02 4 , 02 5 , 05 6 , 08 7 , 12 11 0. 98 1 , 97 2 , 97 3 , 95 4 , 95 5 , 97 6 , 98 10 0. 97 1 , 93 2 , 91 3 , 87 4 , 87 5 , 87 6 , 85 9 0. 93 1 , 90 2 , 85 3 , 80 4 , 78 5 , 75 6 , 73 8 0. 91 1 , 87 2 , 80 3 , 73 4 , 68 5 , 65 6 , 60 7 0. 90 1 , 83 2 , 75 3 , 67 4 , 60 5 , 53 6 , 48 6 0. 88 1 , 80 2 , 70 3 , 58 4 , 52 5 , 43 6 , 35 5 0. 87 1 , 75 2 , 65 3 , 52 4 , 42 5 , 33 6 , 23 4 0. 85 1 , 71 2 , 58 3 , 45 4 , 3● 5 , 22 6 , 12 3 0. 83 1 , 68 2 , 53 3 , 38 4 , 35 5 , 12 5 , 98 2 0. 81 1 , 65 2 , 48 3 , 30 4 , 15 5 , 02 5 , 87 1 0. 80 1 , 62 2 , 4● 3 , 23 4 , 07 4 , 90 5 , 73 0 0. 97 1 , 58 2 , 38 3 , 17 3 , 98 4 , 80 5 , 62 A Table of Positions for the Pole of 8 9 10 11 12 13 14 North Declination under the Earth , and South above it . 0 6 , 45 7 , 22 8 , 05 8 , 88 9 , 73 10 , 57 11 , 60 1 6 , 32 7 , 07 7 , 87 8 , 68 9 , 52 10 , 33 11 , 18 2 6 , 17 6 , 90 7 , 70 8 , 50 9 , 32 10 , 10 10 , 9● 3 6 , 03 6 , 73 7 , 52 8 , 30 9 , 10 9 , 87 10 , 68 4 5 , ●8 6 , 58 7 , 35 8 , 10 8 , 88 9 , 63 10 , 43 5 5 , 75 6 , 42 7 , 17 7 , 92 8 , 67 9 , 42 10 , 18 6 5 , 60 6 , 17 6 , 98 7 , 72 8 , 45 9 , 18 9 , 93 7 5 , 47 6 , 10 6 , 82 7 , 51 8 , 23 8 , 95 9 , 68 8 5 , 32 5 , 95 6 , 63 7 , 31 8 , 02 8 , 70 9 , 43 9 5 , 18 5 , 78 6 , 45 7 , 11 7 , 80 8 , 47 9 , 17 10 5 , 03 5 , 62 6 , 27 6 , 91 7 , 58 8 , 23 8 , 92 11 4 , 88 5 , 45 6 , 08 6 , 71 7 , 37 8 , 00 8 , 65 12 4 , 73 5 , 28 5 , 90 6 , 51 7 , 15 7 , 75 8 , 40 13 4 , 58 5 , 12 5 , 72 6 , 31 6 , 92 7 , 52 8 , 13 14 4 , 45 4 , 95 5 , 53 6 , 10 6 , 70 7 , 27 7 , 87 15 4 , 28 4 , 78 5 , 35 5 , 90 6 , 47 7 , 02 7 , 60 16 4 , 13 4 , 62 5 , 15 5 , 69 6 , 23 6 , 77 7 , 33 17 3 , 98 4 , 43 4 , 97 5 , 48 6 , 00 6 , 52 7 , 07 18 ● , 83 4 , 27 4 , 73 5 , 27 5 , 77 6 , 27 6 , 78 19 3 , 68 4 , 08 4 , 57 5 , 05 5 , 45 6 , 00 6 , 52 20 3 , 52 3 , 92 4 , 37 4 , 83 5 , 23 5 , 75 6 , 23 21 3 , 35 3 , 73 4 , 17 4 , 60 5 , 05 5 , 48 5 , 93 22 3 , 20 3 , 55 3 , 97 4 , 38 4 , 80 5 , 22 5 , 65 23 ● , 03 3 , 37 3 , 75 4 , 15 4 , 55 4 , 95 5 , 32 24 2 , 87 3 , 17 3 , 55 3 , 92 4 , 30 4 , 67 5 , 07 25 2 , 70 2 , 98 3 , 33 3 , 68 4 , 05 4 , 38 4 , 75 26 2 , 52 2 , 78 3 , 12 3 , 45 3 , 78 4 , 10 4 , 45 27 2 , 35 2 , 58 2 , 90 3 , 20 3 , 52 3 , 82 4 , 13 28 2 , 17 2 , 38 2 , 67 2 , 95 3 , 25 3 , 52 3 , 82 29 1 , 98 2 , 18 2 , 43 2 , 70 2 , 97 3 , 22 3 , 48 30 1 , 80 1 , 98 2 , 20 2 , 43 2 , 68 2 , 90 3 , 15 31 1 , 60 1 , 75 1 , 97 2 , 18 2 , 40 2 , 60 2 , 82 32 1 , 42 1 , 53 1 , 72 1 , 90 2 , 10 2 , 27 2 , 47 Latitude of 51 deg . 53 parts . Position 8 9 10 11 12 13 14 South Declination under the Earth , And North above it . 32 11 , 48 12 , 90 14. 38 15 , 87 17 , 37 18 , 87 20 , 40 31 11 , 30 12 , 68 14. 13 15 , 58 17 , 07 18 , 53 20 , 05 30 11 , 10 12 , 47 13. 90 15 , 33 16 , 78 18 , 23 19 , 72 29 10 , 92 12 , 25 13. 67 15 , 07 16 , 50 17 , 92 19 , 38 28 10 , 73 12 , 05 13. 43 14 , 82 16 , 22 17 , 61 19 , 05 27 10 , 55 11 , 85 13. 20 14 , 57 15 , 95 17 , 31 18 , 73 26 10 , 38 11 , 65 12. 98 14 , 32 15 , 68 17 , 03 18 , 42 25 10 , 20 11 , 45 12. 77 14 , 08 15 , 42 16 , 75 18 , 12 24 10 , 03 11 , 27 12. 55 13 , 85 15 , 17 16 , 47 17 , 80 23 9 , 87 11 , 07 12. 35 13 , 62 14 , 9● 16 , 18 17 , 55 22 9 , 70 10 , 88 12. 13 13 , 38 14 , 67 15 , 92 17 , 22 21 9 , 55 10 , 70 11. 93 13 , 17 14 , 42 15 , 65 16 , 93 20 9 , 38 10 , 52 11. 73 12 , 93 14 , 17 15 , 38 16 , 63 19 9 , 22 10 , 35 11. 53 12 , 72 14 , 02 15 , 13 16 , 35 18 9 , 07 10 , 17 11. 33 12 , 50 13 , 70 14 , 87 16 , 08 17 8 , 92 10 , 00 11. 13 12 , 28 13 , 47 14 , 62 15 , 80 16 8 , 77 9 , 82 10. 95 12 , 08 13 , 23 14 , 37 15 , 53 15 8 , 62 9 , 65 10. 75 11 , 87 13 , 00 14 , 12 15 , 27 14 8 , 45 9 , 48 10. 57 11 , 67 12 , 77 13 , 87 15 , 00 13 8 , 32 9 , 32 10. 38 11 , 45 12 , 57 13 , 62 14 , 73 12 8 , 17 9 , 15 10. 20 11 , 25 12 , 32 13 , 38 14 , 47 11 8 , 01 8 , 98 10. 01 11 , 05 12 , 10 13 , 13 14 , 22 10 7 , 87 8 , 82 9. 83 10 , 85 11 , 88 12 , 90 13 , 95 9 7 , 72 8 , 65 9. 65 10 , 65 11 , 67 12 , 67 13 , 70 8 7 , 58 8 , 48 9. 47 10 , 45 11 , 45 12 , 43 13 , 43 7 7 , 43 8 , 33 9. 28 10 , 25 11 , 23 12 , 18 13 , 18 6 7 , 30 8 , 17 9. 12 10 , 05 11 , 02 11 , 95 12 , 93 5 7 , 15 8 , 02 8. 93 9 , 85 10 , 80 11 , 72 12 , 68 4 7 , 02 7 , 85 8. 75 9 , 67 10 , 58 11 , 50 12 , 43 3 6 , 87 7 , 70 8. 58 9 , 47 10 , 37 11 , 27 12 , 18 2 6 , 73 7 , 5● 8. 40 9 , 27 10 , 15 11 , 03 11 , 93 1 6 , 58 7 , 37 8. 23 9 , 08 9 , 95 10 , 80 11 , 68 0 6 , 45 7 , 22 8. 05 8 , 88 9 , 73 10 , 57 11 , 43 A Table of Positions for the Pole of 15 16 17 18 19 20 21 North Declination under the Earth , and South above it . 0 12 , 30 13. 18 14 , 07 14 , 95 15. 87 16 , 80 17 , 77 1 12 , 03 12. 90 13 , 77 14 , 63 15. 52 16 , 43 17 , 38 2 11 , 77 12. 62 13 , 45 14 , 30 15. 18 16 , 07 17 , 00 3 11 , 50 12. 32 13 , 15 13 , 97 14. 83 15 , 70 16 , 62 4 11 , 23 12. 07 12 , 83 13 , 65 14. 48 15 , 35 16 , 23 5 10 , 97 11. 75 12 , 53 13 , 32 14. 13 14 , 98 15 , 85 6 10 , 68 11. 45 12 , 23 13 , 00 13. 80 14 , 60 15 , 45 7 10 , 35 11. 17 11 , 92 12 , 67 13. 45 14 , 23 15 , 07 8 10 , 01 10. 87 11 , 60 12 , 3 13 , 10 13 , 87 14 , 67 9 9 , 97 10. 58 11 , 28 12 , 00 12 , 73 13 , 50 14 , 28 10 9 , 60 10. 28 10 , 98 11 , 67 12 , 38 13 , 12 13 , 88 11 9 , 32 9. 98 10 , 67 11 , 33 12 , 03 12 , 75 13 , 48 12 9 , 03 9. 6● 10 , 33 10 , 98 11 , 67 12 , 37 13 , 08 13 8 , 75 9. 38 10 , 02 10 , 65 11 , 30 11 , 98 12 , 68 14 8 , 47 9. 08 9 , 70 10 , 30 10 , 95 11 , 60 12 , 27 15 8 , 18 8 , 78 9 , 37 9 , 95 10 , 57 11 , 20 11 , 87 16 7 , 90 8. 47 9 , 03 9 , 60 10 , 20 10 , 82 11 , 45 17 7 , 60 8. 15 8 , 70 9 , 25 9 , 83 10 , 42 11 , 03 18 7 , 30 7. 83 8 , 37 8 , 88 9 , 45 10 , 01 10 , 60 19 7 , 00 7. 52 8 , 01 8 , 53 9 , 05 9 , 60 10 , 17 20 6 , 70 7. 20 7 , 68 8 , 17 8 , 67 9 , 18 9 , 73 21 6 , 40 6. 87 7 , 33 7 , 78 8 , 27 8 , 77 9 , 30 22 6 , 08 6. 58 6 , 97 7 , 40 7 , 87 8 , 35 8 , 85 23 5 , 77 6. 20 6 , 62 7 , 02 7 , 47 7 , 92 8 , 40 24 5 , 45 5. 85 6 , 28 6 , 63 7 , 05 7 , 48 7 , 93 25 5 , 12 5. 50 5 , 87 6 , 23 6 , 63 7 , 03 7 , 45 26 4 , 78 5. 15 5 , 48 5 , 83 6 , 20 6 , 57 6 , 98 27 4 , 45 4. 78 5 , 10 5 , 42 5 , 77 6 , 12 6 , 48 28 4 , 12 4. 42 4 , 72 5 , 00 5 , 32 5 , 65 5 , 98 29 3 , 77 4. 0● 4 , 32 4 , 57 4 , 70 5 , 17 5 , 4● 30 3 , 40 3. 65 3 , 90 4 , 13 4 , 40 4 , 67 4 , 97 31 3 , 03 3. 27 3 , 48 3 , 68 3 , 9● 4 , 17 4 , 43 32 2 , 67 2. 87 3 , 05 3 , 23 3 , 45 3 , 65 3 , 88 Latitude of 51 deg . 53 parts . Positiō . 15 16 17 18 19 20 21 South Declination under the Earth , and North above it . 32 21 , 9● 23 , 50 25 , ●8 26 , 67 28 , 28 29 , 95 31 , 65 31 21 , 57 2● , 10 24 , 65 26 , 22 27 , 80 29 , 43 31 , 10 30 21 , 20 22 , 72 24 , 23 25 , 77 27 , 33 28 , 93 30 , 57 29 20 , 83 22 , 33 23 , 82 25 , 33 27 , 03 28 , 4● 30 , 05 28 20 , 48 21 , 95 23 , 42 24 , 90 26 , 4● 27 , 92 29 , 55 27 20 , 15 21 , 58 23 , 03 24 , 4● 25 , 97 27 , 48 29 , 05 26 19 , 8● 21 , 22 22 , 65 24 , 07 25 , 53 27 , 03 28 , 55 25 19 , 48 20 , 87 22 , 27 23 , 67 25 , 10 26 , 57 28 , 08 24 19 , 15 20 , 52 21 , 88 23 , 27 24 , 68 26 , 12 27 , 77 23 18 , 83 2● , 17 21 , 52 22 , 80 24 , 27 25 , 68 27 , 13 22 18 , 52 19 , 78 21 , 17 22 , 50 23 , 87 25 , 25 26 , 68 21 18 , 20 19 , 50 20 , 80 22 , 12 23 , 47 24 , 83 26 , 23 20 17 , 90 19 , 17 20 , 45 21 , 7 23 , 07 24 , 42 25 , 80 19 17 , 60 18 , 85 20 , 12 21 , 37 22 , 68 24 , 00 25 , 37 18 17 , 30 18 , 53 19 , 77 21 , 02 22 , 28 23 , 58 24 , 93 17 17 , 00 18 , 22 19 , 43 20 , 65 21 , 90 23 , 18 24 , 50 16 16 , 70 17 , 90 19 , 10 20 , 30 21 , 53 22 , 78 24 , 08 15 16 , 42 17 , 5● 18 , 77 19 , 95 21 , 17 22 , 40 23 , 67 14 16 , 13 17 , 28 18 , 43 19 , 60 20 , 78 22 , 00 23 , 27 13 15 , 85 16 , 98 18 , 12 19 , 25 20 , 43 21 , 62 22 , 85 12 15 , 57 16 , 68 17 , 80 18 , 9● 20 , 07 21 , 23 22 , 45 11 15 , 28 16 , 38 17 , 47 1● , 57 19 , 70 20 , 85 22 , 05 10 15 , 00 16 , 08 17 , 15 18 , 23 19 , 35 20 , 48 21 , 65 9 14 , 73 15 , 78 16 , 85 17 , 90 19 , 00 20 , 10 21 , 25 8 14 , 45 15 , 50 16 , 53 17 , 57 18 , 63 19 , 73 20 , 87 7 14 , 25 15 , 20 16 , 22 17 , 23 18 , 28 19 , 37 20 , 47 6 13 , 92 14 , 92 15 , 90 16 , 90 17 , 9● 19 , 00 20 , 08 5 13 , 65 14 , 62 15 , 60 16 , 58 17 , 60 18 , 62 19 , 68 4 1● , 37 14 , 33 15 , 30 16 , 25 17 , 25 18 , 25 19 , 30 3 13 , 18 14 , 05 14 , 98 15 , 9● 16 , 90 17 , 90 18 , 92 2 12 , 83 13 , 75 14 , 68 15 , 60 16 , 55 17 , 53 18 , 53 1 12 , 57 13 , 47 14 , 37 15 , 27 16 , 22 17 , 17 18 , 15 0 12 , 30 13 , 18 14 , 07 14 , 95 15 , 87 16 , 80 17 , 77 A Table of Positions for the Pole of 22 23 24 25 26 27 28 North Declination under the Earth , and South above it . 0 18 , 73 19 , 73 20. 72 21. 75 22. 93 23 , 72 25 , 00 1 18 , 33 19 , 32 20. 27 21. 28 22. 45 23 , 20 24 , 47 2 17 , 92 18 , 88 19. 83 20. 82 21. 95 22 , 70 23 , 93 3 17 , 52 18 , 45 19. 38 20. 35 21. 47 22 , 18 23 , 40 4 17 , 12 18 , 03 18. 93 19. 88 20. 98 21 , 67 22 , 87 5 16 , 70 17 , 60 18. 48 19. 42 20. 48 21 , 17 22 , 33 6 16 , 30 17 , 18 18. 03 18. 93 20. 00 20 , 65 21 , 80 7 15 , 88 16 , 75 17. 58 18. 47 19. 50 20 , 13 21 , 25 8 15 , 48 16 , 32 17. 13 18. 00 19. 00 19 , 62 20 , 72 9 15 , 07 15 , 88 16. 67 17. 52 18. 50 19 , 08 20 , 17 10 14 , 65 15 , 43 16. 22 17. 03 18. 00 18 , 57 19 , 62 11 14 , 23 15 , 00 15. 75 16. 55 17. 50 18 , 03 19 , 07 12 13 , 80 14 , 55 15. 28 16. 07 16. 98 17 , 50 18 , 52 13 13 , 38 14 , 10 14. 82 15. 57 16. 47 16 , 97 17 , 95 14 12 , 95 13 , 65 14. 35 15. 07 15. 95 16 , 42 17 , 38 15 12 , 52 13 , 20 13. 87 14. 57 15. 42 15 , 87 16 , 82 16 12 , 08 12 , 75 13. 38 14. 07 14. 88 15 , 32 16 , 23 17 11 , 63 12 , 28 12. 90 13. 55 14. 35 14 , 75 15 , 65 18 11 , 18 11 , 80 12. 40 13. 03 13. 82 14 , 18 15 , 05 19 10 , 73 11 , 33 11. 90 12. 52 13. 27 13 , 62 14 , 45 20 10 , 28 10 , 85 11. 40 11. 98 12. 70 13 , 03 13 , 85 21 9 , 82 10 , 35 10. 88 11. 43 12. 15 12 , 60 13 , 23 22 9 , 33 9 , 85 10. 35 10. 88 11. 55 11 , 83 12 , 60 23 8 , 85 9 , 35 9. 82 10. 33 10. 98 11 , 23 11 , 95 24 8 , 37 8 , 83 9. 28 9. 77 10. 38 10 , 60 11 , 30 25 7 , 87 8 , 32 8. 73 9. 18 9. 78 9 , 97 10 , 65 26 7 , 37 7 , 78 8. 17 8. 60 9. 17 9 , 33 9 , 97 27 6 , 85 7 , 25 7. 60 8. 00 8. 55 8 , 67 9 , 28 28 6 , 33 6 , 68 7. 02 7. 40 7. 90 8 , 00 8 , 58 29 5 , 80 6 , 12 6. 43 6. 82 7. 25 7 , 32 7 , 90 30 5 , 25 5 , 55 5. 82 6. 13 6. 58 6 , 62 7 , 12 31 4 , 68 4 , 95 5. 20 5. 48 5. 90 5 , 88 6 , 37 32 4 , 12 4 , 35 4. 57 4. 82 5. 18 5 , 15 5 , 60 Latitude of 51 deg . 53 parts . Positiō . 22 23 24 25 26 27 28 South Declination under the Earth , and North above it . 32 33. 35 34 , 95 36 , 87 38 , 68 40 , 68 42 , 28 44 , 40 31 32. 78 34 , 52 36 , 23 38 , 02 39 , 97 41 , 55 4● , 63 30 32. 22 33 , 92 35 , 62 37 , 37 39 , 28 40 , 82 42 , 88 29 31. 67 33 , 35 35 , 00 36 , 73 38 , 62 40 , 12 42 , 13 28 31. 13 32 , 78 34 , 42 36 , 10 37 , 97 39 , 43 41 , 42 27 30. 62 32 , 22 33 , 83 35 , 50 37 , 32 38 , 77 40 , 72 26 30. 10 31 , 68 33 , 27 34 , 90 36 , 70 38 , 10 40 , 03 25 29. 60 31 , 15 32 , 70 34 , 32 36 , 08 37 , 47 39 , 35 24 29. 10 30 , 63 32 , 15 33 , 73 35 , 48 36 , 83 38 , 70 23 28. 62 30 , 12 31 , 62 33 , 17 34 , 88 36 , 20 ●8 , 05 22 28. 13 29 , 62 31 , 08 32 , 62 34 , 30 35 , 60 37 , 40 21 27. 65 29 , 12 30 , 55 32 , 07 33 , 72 35 , 00 36 , 77 20 27. 18 28 , 62 30 , 03 31 , 52 33 , 17 34 , 40 36 , 15 19 26. 73 28 , 13 29 , 53 30 , 98 32 , 60 33 , 82 35 , 55 18 26. 28 ●7 , 67 ●9 , 03 30 , 27 32 , 05 33 , 25 34 , 95 17 25. 80 27 , 18 28 , 53 29 , 95 31 , 52 32 , 68 34 , 35 ●6 25. 38 26 , 7● 28 , 05 29 , 43 30 , 98 32 , 12 33 , 77 15 24. 95 ●6 , 27 27 , 57 28 , 93 30 , 45 31 , 57 33 , 18 14 24. 52 25 , 82 27 , 08 28 , 43 29 , 92 31 , 02 32 , 62 13 24. 08 25 , 37 26 , 62 27 , 93 29 , 40 30 , 47 32 , 05 12 2● . 67 24 , 92 26 , 15 27 , 43 28 , 88 29 , 93 31 , 48 11 23. 23 24 , 47 25 , 68 26 , 95 28 , 37 29 , 40 30 , 93 10 22. 82 24 , 0● 25 , 23 26 , 47 27 , 87 28 , 87 30 , 38 9 22. 40 2● , 58 24 , 77 25 , 98 27 , 37 28 , 35 29 , 83 8 21. 98 23 , 15 24 , 30 25 , 50 26 , 87 27 , 82 29 , 28 7 21. 58 22 , 72 13 , 85 25 , 03 26 , 37 27 , 30 28 , 75 6 20. 17 22 , 28 23 , 40 24 , 57 25 , 87 26 , 78 28 , 20 5 20. 77 21 , 87 ●2 , 95 24 , 08 25 , 38 26 , 27 27 , 67 4 20. 35 21 , 43 22 , 50 23 , 62 24 , 88 25 , 77 27 , 13 3 19. 95 21 , 02 22 , ●5 23 , 15 24 , 40 25 , 25 26 , 60 2 19. 55 20 , 58 21 , 77 22 , 68 23 , 92 24 , 73 26 , 07 1 19. 13 20 , 15 21 , 17 22 , 22 23 , 42 24 , 23 25 , 53 0 18. 73 19 , 73 20 , 72 21 , 75 22 , 93 2● , 72 25 , 00 A Table of Positions for the Pole of 29 30 31 32 33 34 35 North Declination under the Earth , and South above it . 0 26 , 13 27 , ●0 28. 52 29. 77 31. 07 32 , 40 33 , 82 1 ●5 , 58 26 , 72 27. 92 29. 15 30. 42 31 , 73 33 , 12 2 25 , 02 26 , 15 27. 32 28. 52 29. 77 31 , 05 32 , 42 3 24 , 47 25 , 57 26. 72 27. 88 29. 12 30 , 37 31 , 72 4 23 , 92 24 , 98 26. 11 27. 27 28. 47 29 , 70 31 , 01 5 23 , 35 24 , 23 25. 50 26. 63 27. 82 29 , 02 30 , 30 6 22 , 80 23 , 82 24. 90 26. 00 27. 15 28 , 33 29 , 60 7 22 , ●3 23 , 23 24. 28 25. 37 26. 50 27 , 65 28 , 88 8 21 , 67 22 , 65 23. 67 24. 73 25. 83 26 , 97 28 , 17 9 21 , 10 22 , 05 23. 05 24. 08 25. 17 26 , 27 27 , 45 10 20 , 52 21 , 48 22. 43 23. 43 24. 48 25 , 57 26 , 72 11 19 , 95 20 , 85 21. 82 22. 78 23. 82 24 , 87 26 , 00 12 19 , 37 20 , 25 21. 18 22. 13 23. 13 24 , 15 25 , 25 13 18 , 78 19 , 63 20. 55 21. 47 22. 45 23 , 43 24 , 52 14 18 , 20 19 , 02 19. 90 20. 80 21. 75 22 , 72 23 , 77 15 17 , 60 18 , 40 19. 25 20. 13 21. 13 21 , 98 23 , 00 16 17 , 00 17 , 77 18. 60 19. 45 20. 33 21 , 25 22 , 23 17 16 , 38 17 , 13 17. 93 18. 75 19. 60 20 , 50 21 , 45 18 15 , 75 16 , 48 17. 25 18. 05 18. 88 19 , 73 20 , 67 19 15 , 13 15 , 83 16. 58 17. 35 18. 15 18 , 97 19 , 87 20 14 , 50 15 , 17 15. 88 16. 62 17. 40 18 , 18 19 , 05 21 13 , 85 14 , 50 15. 18 15. 88 16. 63 17 , 40 18 , 17 22 13 , 20 13 , 82 14. 47 15. 15 15. 85 16 , 25 17 , 37 23 12 , 52 13 , 12 13. 73 14. 38 15. 07 15 , 77 16 , 53 24 11 , 85 12 , 40 13. 00 13. 62 14. 27 14 , 92 15 , 65 25 11 , 15 11 , 68 12. 25 12. 83 13. 43 14 , 07 14 , 77 26 10 , 45 10 , 95 11. 48 12. 02 12. 60 13 , 20 13 , 85 27 9 , 57 10 , 20 10. 68 11. 20 11. 75 12 , 30 12 , 92 28 9 , 00 9 , 25 9. 88 10. 37 10. 87 11 , 38 11 , 97 29 8 , 23 8 , 63 9. 07 9. 50 9. 97 10 , 45 10 , 98 30 7 , 47 7 , 83 8. 22 8. 62 8. 05 9 , 48 9 , 97 31 6 , 68 7 , 00 7. 35 7. 55 7. 10 8 , 48 8 , 93 32 5 , 87 6 , 15 6. 47 6. 78 6. 13 7 , 63 7 , 87 Latitude of 51 deg . 53 parts . Position 29 30 31 32 33 34 35 South Declination under the Earth , And North above it . 32 46 , 40 48 , 45 50. 57 52 , 75 55 , 00 57 , 17 59 , 77 31 45 , 58 47 , 60 49. 68 51 , 82 54 , 03 56 , 32 58 , 70 30 44 , 80 46 , 77 48. 82 50 , 92 53 , 08 55 , 32 57 , 67 29 44 , 03 45 , 97 47. 97 50 , 03 52 , 17 54 , ●8 56 , 65 28 43 , 27 45 , 18 47. 15 49 , 17 51 , 27 53 , 42 55 , 67 27 42 , 53 44 , 40 46. 35 48 , 3● 50 , 38 52 , 50 54 , 72 26 41 , 82 43 , 65 45. 55 47 , 52 49 , 53 51 , 60 53 , 78 25 41 , 12 42 , 92 44. 78 46 , 70 48 , 70 50 , 73 52 , 87 24 40 , 42 42 , 20 44. 03 45 , 87 47 , 87 49 , 88 51 , 98 23 39 , 75 41 , 48 43. 30 45 , 07 47 , 07 49 , 03 51 , 10 22 39 , 07 40 , 78 42. 57 44 , 27 46 , 27 48 , 22 50 , 27 21 38 , 42 40 , 10 41. 85 4● , 50 45 , 50 47 , 40 49 , 47 20 37 , 77 39 , 43 41. 15 42 , 79 44 , 73 46 , 62 48 , 58 19 37 , 13 38 , 77 40. 45 42 , 98 43 , 98 45 , 83 47 , 77 18 36 , 52 38 , 12 39. 78 41 , 25 43 , 25 45 , 07 46 , 97 17 35 , 88 37 , 47 39. 10 40 , 52 42 , 52 44 , 30 46 , 18 16 35 , 27 36 , 83 38. 43 40 , 80 41 , 80 43 , 55 45 , 40 15 34 , 67 36 , 20 37. 78 39 , 08 41 , 08 42 , 82 44 , 63 14 34 , 07 35 , 58 37. 13 38 , 38 40 , 38 42 , 08 43 , 87 13 33 , 48 34 , 97 36. 48 38 , 68 39 , 68 41 , 37 43 , 12 12 32 , 90 34 , 35 35. 85 37 , 00 39 , 00 40 , 65 42 , 38 11 32 , 32 33 , 75 35. 22 36 , 31 38 , 32 39 , 93 41 , 63 10 31 , 75 33 , 15 34. 60 ●6 , 65 37 , 65 39 , 23 40 , 92 9 31 , 17 32 , 55 33. 98 35 , 97 36 , 97 38 , 53 40 , 18 8 30 , 60 31 , 95 33. 37 34 , 30 36 , 30 37 , 67 39 , 47 7 30 , 03 31 , 37 32. 92 34 , 63 35 , 63 37 , 15 38 , 75 6 29 , 47 30 , 78 32. 13 33 , 98 34 , 98 36 , 47 38 , 03 5 28 , 92 30 , 20 31. 53 32 , 32 34 , 32 35 , 78 37 , 33 4 28 , 35 29 , 62 30. 92 32 , 67 33 , 67 35 , 10 36 , 62 3 27 , 80 29 , 03 30. 32 31 , 01 33 , 02 34 , 43 35 , 92 2 27 , 25 28 , 45 29. 72 30 , 37 32 , 37 33 , 75 35 , 22 1 26 , 68 27 , 88 29. 12 30 , 72 31 , 71 33 , 07 34 , 51 0 26 , 13 27 , 30 28. 52 29 , 07 31 , 07 32 , 40 33 , 81 A Table of Positions for the Pole of 36 37 38 39 40 41 42 North Declination under the Earth , and South above it . 0 35 , 27 36 , 78 38 , 38 40 , 07 41 , 82 43 , 70 45 , 68 1 34 , 53 36 , 02 37 , 60 39 , 25 40 , 98 42 , 83 44 , 78 2 33 , 82 35 , 10 36 , 82 38 , 45 40 , 13 41 , 97 43 , 88 3 33 , 08 34 , 52 36 , 03 37 , 63 39 , 30 41 , 08 42 , 98 4 32 , 35 33 , 77 35 , 25 36 , 82 38 , 45 40 , 22 42 , 05 5 31 , 62 33 , 00 34 , 47 36 , 00 37 , 60 39 , 33 41 , 17 6 30 , 88 32 , 23 33 , 67 35 , 20 36 , 75 38 , 45 40 , 25 7 30 , 15 31 , 47 32 , 88 34 , 37 35 , 90 37 , 57 39 , 33 8 29 , 40 30 , 70 32 , 08 33 , 53 35 , 05 36 , 68 38 , 42 9 28 , 67 29 , 93 31 , 28 32 , 78 34 , 18 35 , 78 37 , 48 10 27 , 90 29 , 15 30 , 47 31 , 85 33 , 32 34 , 88 36 , 55 11 27 , 15 28 , 37 29 , 65 31 , 02 32 , 43 33 , 97 35 , 60 12 26 , 38 27 , 57 28 , 82 30 , 15 31 , 55 33 , 05 34 , 65 13 25 , 67 26 , 77 27 , 98 29 , 30 30 , 65 32 , 12 33 , 68 14 24 , 83 25 , 95 27 , 15 28 , 42 29 , 78 31 , 18 32 , 72 15 24 , 03 25 , 13 26 , 30 27 , 37 28 , 82 30 , 23 31 , 72 16 23 , 07 24 , 30 25 , 43 26 , 63 27 , 90 29 , 27 30 , 71 17 22 , 43 23 , 47 24 , 57 25 , 73 26 , 95 28 , 28 29 , 70 18 21 , 62 22 , 62 23 , 68 24 , 82 26 , 00 27 , 30 28 , 67 19 20 , 78 21 , 75 22 , 78 2● , 88 25 , 01 26 , 28 27 , 62 20 19 , 93 20 , 87 21 , 87 22 , 93 24 , 03 25 , 25 26 , 55 21 19 , 07 19 , 97 20 , 93 21 , 95 23 , 03 24 , 20 25 , 47 22 18 , 18 19 , 05 19 , 98 20 , 97 22 , 00 23 , 13 24 , 35 23 17 , 30 18 , 13 19 , 01 19 , 97 20 , 78 22 , 05 23 , 22 24 16 , 40 17 , 18 18 , 03 18 , 93 19 , 72 20 , 93 22 , 05 25 15 , 47 16 , 22 17 , 01 17 , 88 18 , 78 19 , 78 20 , 85 26 14 , 51 15 , 22 15 , 98 16 , 80 17 , 65 18 , 62 19 , 63 27 13 , 58 14 , 03 14 , 92 15 , 70 16 , 50 17 , 42 18 , 38 28 12 , 38 13 , 10 13 , 83 14 , 57 15 , 32 16 , 18 17 , 08 29 11 , 52 12 , 10 12 , 72 13 , 40 14 , 10 14 , 95 15 , 75 30 10 , 47 11 , 00 12 , 57 11 , 20 12 , 83 13 , 58 14 , 37 31 9 , 38 9 , 87 10 , 38 10 , 95 11 , 53 12 , 22 12 , 93 32 8 , 27 8 , 70 9 , 17 9 , 17 10 , 30 10 , 80 11 , 45 Latitude of 51 deg . 53 parts . Position 36 37 38 39 40 41 42 South Declination under the Earth , And North above it . 32 62 , 27 64 , 87 67 , 60 70. 97 73 , 33 76 , 60 79 , 92 31 61 , 15 63 , 70 66 , 38 69. 18 72 , 10 75 , 18 78 , 43 30 60 , 07 62 , 57 65 , 20 67. 93 70 , 80 73 , 42 77 , 00 39 59 , 01 61 , 47 64 , 05 66. 7● 69 , 53 72 , 50 75 , 63 28 57 , 98 60 , 40 62 , 93 65. 57 68 , 32 71 , 22 74 , 28 27 57 , 00 59 , 37 61 , 85 64. 43 67 , 30 69 , 98 72 , 98 26 56 , 02 58 , 35 60 , 78 63. 3● 65 , 98 68 , 78 71 , 73 25 55 , 07 57 , 35 59 , 73 62. 25 64 , 85 67 , 62 70 , 52 24 54 , 13 56 , 38 58 , 73 61. 20 63 , 75 66 , 47 69 , 32 23 53 , 23 55 , 43 57 , 75 60. 17 62 , 68 65 , 35 68 , 15 22 52 , ●5 54 , 52 56 , 78 59. 17 61 , 63 64 , 27 67 , 01 21 51 , 47 53 , 6● 55 , 83 58. 18 60 , 60 63 , 20 65 , 90 20 50 , 60 52 , 70 54 , 90 57. 20 59 , 60 62 , 15 64 , 82 19 49 , 75 51 , 82 5● , 98 56. 25 58 , 62 61 , 12 63 , 75 18 48 , 92 50 , 95 53 , 08 55. 32 57 , 63 60 , 10 62 , 70 17 48 , 10 50 , 10 5● , 20 54. 40 56 , 68 59 , 12 61 , 67 16 47 , 30 49 , 27 51 , 33 53. 50 55 , 90 58 , 13 60 , 65 15 46 , 50 48 , 43 50 , 47 52. 60 54 , 82 57 , 17 59 , 65 14 45 , 70 4● , 62 49 , 62 51. 71 53 , 90 56 , 22 58 , 66 13 44 , 87 46 , 80 48 , 78 50. 83 52 , 98 55 , 28 57 , 68 12 44 , 15 46 , 00 47 , 95 49. 98 52 , 08 54 , 35 56 , 72 11 43 , 38 45 , 20 47 , 12 49. 12 51 , 20 53 , 43 55 , 77 10 43 , 63 44 , 42 46 , 30 48. 28 50 , 32 52 , 52 54 , 82 9 41 , 87 43 , 63 45 , 48 47. 43 49 , 45 51 , 62 53 , 88 8 41 , 1● 42 , 87 44 , 68 46. 60 48 , 58 50 , 72 52 , 95 7 40 , 38 42 , 10 43 , 88 45. 77 47 , 90 49 , 83 52 , 03 6 39 , 65 41 , 33 43 , 10 44. 93 46 , 88 48 , 95 51 , 12 5 38 , 92 40 , 57 42 , 30 44. 13 46 , 03 48 , 07 50 , 20 4 38 , 18 39 , 80 41 , 52 43. 32 45 , 18 47 , 18 49 , 30 3 37 , 45 39 , 05 40 , 73 42. 50 44 , 33 46 , 32 48 , 38 2 36 , 72 38 , 30 39 , 95 41. 68 43 , 50 45 , 43 47 , 48 1 36 , 00 37 , 53 39 , 17 41. 88 42 , 65 44 , 57 46 , 58 0 35 , 27 36 , 78 38 , 38 40. 07 41 , 82 43 , 70 45 , 68 A Table of Positions for the Pole of 43 44 45 46 47 48 49 North Declination under the Earth , and South above it . 0 47 , 80 50 , 12 52 , 60 55 , 32 58 , 40 61 , 93 66 , 05 1 46 , 87 49 , 15 51 , 60 54 , 28 57 , 33 60 , 82 64 , 90 2 45 , 93 48 , 18 50 , 59 53 , 25 56 , 25 59 , 72 63 , 75 3 45 , 00 47 , 22 49 , 59 52 , 20 55 , 18 58 , 60 62 , 60 4 44 , 07 46 , 25 48 , 58 51 , 17 54 , 10 57 , 48 61 , 43 5 43 , 12 45 , 27 47 , 58 50 , 12 53 , 02 56 , 35 60 , 27 6 42 , 18 44 , 28 46 , 57 49 , 07 51 , 93 55 , 23 59 , 10 7 41 , 23 43 , 30 45 , 55 48 , 02 50 , 83 54 , 10 57 , 93 8 40 , 27 42 , 31 44 , 52 46 , 95 49 , 73 52 , 95 56 , 42 9 39 , 30 41 , 32 43 , 48 45 , 88 48 , 62 51 , 68 55 , 55 10 38 , 33 40 , 31 42 , 45 44 , 80 47 , 33 50 , 6 54 , 35 11 37 , 35 39 , 30 41 , 38 43 , 70 46 , 3● 49 , 47 53 , 13 12 36 , 37 38 , 27 40 , 33 42 , 60 45 , 22 48 , 28 51 , 90 13 35 , 37 37 , 23 39 , 25 41 , 48 44 , 07 47 , 08 50 , 65 14 34 , 35 36 , 18 38 , 17 40 , 35 42 , 90 45 , 25 49 , 38 15 33 , 33 35 , 12 37 , ●7 39 , 20 41 , 70 44 , 62 48 , 10 16 32 , 28 34 , 03 35 , 77 38 , 05 40 , 50 43 , 37 46 , 78 17 31 , 23 32 , 95 34 , 80 36 , 87 39 , 27 42 , 08 45 , 45 18 30 , 17 31 , 83 33 , 63 35 , 65 38 , 02 40 , 78 44 , 10 19 29 , 07 30 , 70 32 , 45 34 , 43 36 , 73 39 , 45 42 , 72 20 27 , 97 29 , 53 31 , 25 3● , 18 35 , 43 38 , 08 41 , 30 21 26 , 80 28 , 18 30 , 03 31 , 90 34 , 18 36 , 70 39 , 85 22 25 , 67 27 , 15 28 , 77 30 , 58 33 , 73 35 , 27 38 , 35 23 24 , 48 25 , 92 27 , 48 29 , 23 31 , 32 33 , 80 36 , 82 24 23 , 27 24 , 65 26 , 17 27 , 87 29 , 88 32 , 30 35 , 98 25 22 , 02 23 , 35 24 , 80 26 , 45 28 , 40 30 , 73 33 , 62 26 20 , 75 22 , 02 23 , 42 24 , 98 26 , 87 29 , 13 31 , 92 27 19 , 47 20 , 63 21 , 97 23 , 47 25 , 28 27 , 47 30 , 17 28 18 , 07 19 , 22 20 , 48 21 , 90 23 , 30 25 , 73 28 , 33 29 16 , 67 17 , 75 18 , 93 20 , 28 21 , 93 23 , 93 26 , 43 30 15 , 05 16 , 23 17 , 33 18 , 60 20 , 15 22 , 05 24 , 43 31 13 , 83 14 , 65 15 , 67 16 , 83 18 , 28 20 , 07 22 , 32 32 12 , 17 13 , 00 13 , 93 15 , 00 16 , 33 27 , 98 20 , 43 Latitude of 51 deg . 53 parts . Positi● 43 44 45 46 47 48 49 South Declination under the Earth , and North above it . 32 83 , 43 87 , 23 91 , 27 95 , 63 100 , 47 106 , 88 112 , 00 31 82 , 77 85 , 58 89 , 53 93 , 80 98 , 52 103 , 80 109 , 78 30 80 , 38 84 , 00 87 , 87 92 , 03 96 , 65 101 , 82 107 , 67 29 78 , 93 82 , 48 86 , 27 90 , 35 94 , 87 99 , 93 105 , 67 28 77 , 53 81 , 02 84 , 72 88 , 73 93 , 17 98 , 13 103 , 77 27 76 , 17 80 , 60 83 , 23 87 , 17 91 , 52 96 , 40 101 , 93 26 74 , 85 78 , 22 81 , 78 85 , 65 89 , 63 94 , 73 100 , 18 25 73 , 58 76 , 88 80 , 40 84 , 18 88 , 40 9● , 13 98 , 48 24 72 , 33 75 , 58 79 , 03 82 , 77 86 , 92 91 , 57 96 , 12 23 71 , 12 74 , 22 77 , 72 81 , 40 85 , 48 90 , 07 95 , 28 22 69 , 9● 73 , 08 76 , 43 80 , 05 84 , 07 88 , 60 93 , 75 21 68 , 78 71 , 8● 75 , 17 78 , 73 82 , 70 87 , 17 92 , 25 20 67 , 63 70 , 70 73 , 95 77 , 45 81 , 37 85 , 78 90 , 80 19 66 , 53 69 , 53 72 , 75 76 , 20 80 , 07 84 , 42 89 , 37 18 65 , 43 68 , 40 71 , 57 74 , 98 78 , 78 83 , 08 88 , 00 17 64 , 37 67 , 28 70 , 40 73 , 77 77 , 53 81 , 78 86 , 65 16 63 , 32 66 , 20 69 , 27 72 , 58 76 , 30 80 , 50 85 , 32 15 62 , 27 65 , 12 68 , 13 71 , 43 75 , 10 79 , 25 84 , 00 14 61 , 25 64 , 05 67 , 03 70 , 28 73 , 90 78 , 02 82 , 72 13 60 , 23 63 , 00 65 , 95 69 , 15 72 , 73 76 , 78 81 , 45 12 59 , 23 61 , 97 64 , 87 68 , 03 71 , 58 75 , 58 80 , 20 11 58 , 25 60 , 93 63 , 87 66 , 93 70 , 43 74 , 40 78 , 97 10 57 , 27 59 , 92 62 , 75 65 , 83 69 , 30 73 , 23 77 , 75 9 56 , 30 58 , 91 61 , 72 64 , 75 68 , 18 72 , 07 76 , 55 8 55 , 33 57 , 92 60 , 68 63 , 68 67 , 07 70 , 92 75 , 35 7 54 , 37 56 , 93 59 , 65 62 , 62 65 , 97 69 , 73 74 , 17 6 53 , 42 55 , 95 58 , 63 61 , 57 64 , 87 68 , 63 73 , 00 5 52 , 48 54 , 85 57 , 62 60 , 52 63 , 78 67 , 50 71 , 83 4 51 , 53 53 , 98 56 , 61 59 , 47 62 , 70 66 , 38 70 , 67 3 50 , 60 53 , 01 55 , 60 58 , 43 61 , 62 65 , 27 69 , 50 2 49 , 67 52 , 05 54 , 60 57 , 41 60 , 53 64 , 15 68 , 35 1 48 , 73 51 , 08 53 , 60 56 , 35 59 , 47 63 , 05 67 , 20 0 47 , 80 50 , 12 52 , 60 55 , 32 58 , 40 61 , 93 66 , 05 A Table of Positions for the Pole of 50 51 51. 53 Positiō 50 51 51. 53 North Declination under the Earth , and South above it . 0 71 , 23 78. 83 90 , 00 South Declination under Earth , and North above it . 32 119 , 33 129 , 33 141 , 87 1 70 , 03 77. 60 88 , 08 31 116 , 97 126 , 73 139 , 13 2 68 , 85 76. 37 87 , 48 ●0 114 , 72 124 , 32 136 , 62 3 67 , 65 75. 12 86 , 22 2● 112 , 58 122 , 00 134 , 23 4 66 , 45 73. 88 84 , 97 28 110 , 55 119 , 87 132 , 00 5 65 , 40 72. 63 83 , 68 27 108 , 62 117 , 83 129 , 88 6 64 , 03 71. 38 82 , 40 26 106 , 73 115 , 87 127 , 87 7 6● , 82 70. 12 81 , 12 25 105 , 00 114 , 00 125 , 93 8 61 , 60 68. 83 79 , 82 24 103 , 28 112 , 18 124 , 08 9 60 , 35 67. 55 78 , 50 23 101 , 62 110 , 45 122 , 28 10 59 , 10 66. 25 77 , 18 22 100 , 02 108 , 77 12● , 57 11 57 , 83 64. 95 75 , 85 21 98 , 47 107 , 13 118 , 88 12 56 , 57 63. 53 74 , 48 20 96 , 93 105 , 55 117 , 27 13 55 , 27 62. 27 73 , 12 19 95 , 47 104 , 00 11● , 68 14 53 , 95 60. 90 71 , 72 18 94 , 02 102 , 48 114 , 13 15 52 , 58 59 , 52 70 , 30 17 92 , 60 101 , 02 11● , 63 16 51 , 25 58. 10 68 , 85 16 91 , 22 99 , 57 111 , 15 17 49 , 87 56. 65 67 , 37 15 89 , 88 98 , 15 109 , 70 18 48 , 45 54. 18 65 , 87 14 88 , 52 96 , 77 108 , 28 19 47 , 00 53. 67 64 , 32 13 87 , 20 95 , 40 106 , 88 20 45 , 53 52. 12 62 , 73 12 85 , 90 94 , 05 105 , 52 21 44 , 00 50. 53 61 , 1● 11 84 , 63 92 , 72 104 , 15 22 4● , 45 48. 90 59 , 4● 10 83 , ●2 91 , 42 102 , 82 23 40 , 85 47. 22 57 , 72 9 82 , 12 90 , 12 101 , 50 24 39 , 18 4● . 48 55 , 92 8 80 , 92 88 , 83 100 , 18 25 ●7 , 47 4● . 67 54 , 07 7 79 , 65 87 , 55 98 , 88 26 35 , 70 41. 80 52 , 13 6 78 , 43 86 , 28 97 , 60 27 ●3 , 85 39. 83 50 , 12 5 77 , 07 85 , 03 96 , 32 28 31 , 92 37. 80 48 , 0● 4 76 , 02 83 , 78 95 , 03 29 29 , 88 35. 63 45 , 77 3 74 , 82 82 , ●5 93 , 78 30 27 , 75 33. 35 43 , 38 2 7● , 6● 81 , 30 92 , 52 31 25 , 30 30. 93 40 , 87 1 72 , 43 80 , 00 91 , 92 32 23 , 10 28. 33 38 , 1● 0 71 , 23 78 , 83 90 , 00 A Table shewing the Elevation of the Pole upon the several circles of Position of the 11 , 12. 2 , and 3. Houses for 6● degrees of Latitude . Latitude 11 & 3 12 & 2 Poles Elevat . Poles Elevat . 1 0 , 48 0 , 85 2 0 , 98 1 , 72 3 1 , 48 2 , 58 4 1 , 98 3 , 45 5 2 , 48 4 , 32 6 3 , 00 5 , 18 7 3 , 52 6 , 07 8 4 , 03 6 , 95 9 4 , 53 7 , 82 10 5 , 05 8 , 68 11 5 , 57 9 , 55 12 6 , 08 10 , 43 13 6 , 60 11 , 30 14 7 , 12 12 , 18 15 7 , 63 13 , 07 16 8 , 15 13 , 95 17 8 , 68 14 , 83 18 9 , 22 15 , 72 19 9 , 75 16 , 60 20 10 , 30 17 , 50 21 10 , 85 18 , 38 22 11 , 42 19 , 28 23 11 , 63 20 , 18 24 12 , 53 21 , 08 25 13 , 12 21 , 99 26 13 , 70 22 , 89 27 14 , 30 23 , 80 28 14 , 90 24 , 71 29 15 , 50 25 , 63 30 16 , 12 26 , 55 31 16 , 73 27 , 48 31 16 , 73 27. 48 32 17 , 35 28. 42 33 17 , 98 29. 35 34 18 , 63 30. 28 35 19 , 30 31. 23 36 19 , 97 32. 18 37 20 , 65 33. 13 38 21 , 33 34. 08 39 22 , 03 35. 03 40 22 , 75 36. 00 41 23 , 48 36. 97 42 24 , 23 37. 95 43 25 , 00 38. 93 44 25 , 78 39. 92 45 26 , 57 40. 90 46 27 , 37 41. 89 47 28 , 18 42. 88 48 29 , 03 43. 89 49 29 , 90 44. 90 50 30 , 78 45. 92 51 31 , 68 46. 93 51. 53 32 , 18 47. 47 52 32 , 62 47. 95 53 33 , 57 48. 98 54 34 , 53 50. 01 55 35 , 53 51. 05 56 36 , 55 52. 08 57 37 , 58 53. 13 58 38 , ●5 54. 18 59 39 , 75 55. 23 60 40 , 88 56. 30 A general Table of Positions .     55 54 53 52 51. 53 5● 50 The Poles Elevation upon every circle of Position . 1 0 , 70 0 , 73 0 , 75 0 , 78 0 , 79 0 , 02 0 , 83 2 1 , 40 1 , 45 1 , 50 1 , 57 1 , 58 1 , 62 1 , 68 3 2 , 00 2 , 18 2 , 27 2 , 35 2 , 38 2 , 43 2 , 52 4 2 , 80 2 , 92 3 , 03 3 , 13 3 , 17 3 , 25 3 , 37 5 3 , 51 3 , 65 3 , 78 3 , 92 3 , 98 4 , 07 4 , 22 6 4 , 22 4 , 38 4 , 55 4 , 71 4 , 80 4 , 88 5 , 07 7 4 , 83 5 , 12 5 , 32 5 , 50 5 , 62 5 , 70 5 , 92 8 5 , 65 5 , 87 6 , 08 6 , 30 6 , 45 6 , 53 6 , 77 9 6 , 37 6 , 60 6 , 85 7 , 10 7 , 22 7 , 37 7 , 63 10 7 , 10 7 , 37 7 , 63 7 , 9● 8 , 05 8 , 22 8 , 50 11 7 , 82 8 , 12 8 , 42 8 , 73 8 , 88 9 , 05 9 , 38 12 8 , 57 8 , 88 9 , 22 9 , 57 9 , 73 9 , 92 10 , 27 13 9 , 30 9 , 65 10 , 02 10 , 40 10 , 57 10 , 77 11 , 17 14 10 , 05 10 , 43 10 , 83 11 , 23 11 , 43 11 , 65 12 , 08 15 10 , 82 11 , 23 11 , 65 12 , 08 12 , 30 12 , 53 13 , 00 16 11 , 58 12 , 02 12 , 48 12 , 95 13 , 18 13 , 43 13 , 92 17 12 , 37 12 , 83 13 , 32 13 , 82 14 , 07 14 , 30 14 , 87 18 13 , 15 13 , 65 14 , 17 14 , 70 14 , 95 15 , 25 15 , 82 19 13 , 95 14 , 48 15 , 03 15 , 60 15 , 87 16 , 18 16 , 80 20 14 , 77 15 , 33 15 , 92 16 , 52 16 , 80 17 , 13 17 , 78 21 15 , 60 16 , 20 16 , 82 17 , 45 17 , 77 18 , 12 18 , 78 22 16 , 43 17 , 07 17 , 73 18 , 40 18 , 73 19 , 10 19 , 82 23 17 , 28 17 , 97 18 , 65 19 , 37 19 , 73 20 , 10 20 , 87 24 18 , 32 18 , 87 19 , 60 20 , 35 20 , 72 21 , 13 21 , 93 25 19 , 05 19 , 80 20 , 57 21 , 37 21 , 75 22 , 18 23 , 03 26 19 , 97 20 , 75 21 , 57 22 , 40 21 , 93 23 , 27 24 , 15 27 20 , 90 21 , 72 22 , 58 23 , 47 23 , 72 24 , 37 25 , 32 28 21 , 85 22 , 72 23 , 62 24 , 55 25 , 00 25 , 50 26 , 50 29 22 , 65 23 , 75 24 , 68 25 , 67 26 , 13 26 , 67 27 , 72 30 23 , 85 24 , 80 25 , 78 26 , 82 27 , 30 27 , 87 28 , 98 31 24 , 88 25 , 88 26 , 92 28 , 00 28 , 52 29 , 12 30 , 28 32 25 , 95 27 , 00 28 , 08 29 , 22 29 , 77 30 , 40 31 , 62 33 27. 05 28 , 15 29 , 30 30 , 48 31 , 08 31 , 73 33 , 02 34 28. 18 29 , 35 30 , 55 31 , 80 32 , 40 33 , 10 34 , 47 35 29. 37 30 , 58 31 , 85 33 , 17 33 , 48 34 , 55 35 , 98 36 30. 58 31 , 87 33 , 20 34 , 58 35 , 27 36 , 03 37 , 57 37 31. 85 33 , 20 34 , 60 36 , 07 36 , 78 37 , 60 39 , 22 38 33. 17 34 , 58 36 , 07 37 , 62 38 , 38 39 , 25 40 , 97 39 34. 55 36 , 03 37 , 60 39 , 25 40 , 07 40 , 98 42 , 80 40 35. 98 37 , 57 39 , 22 40 , 97 41 , 48 42 , 80 44 , 75 41 37. 50 39 , 17 40 , 75 42 , 78 43 , 70 44 , 75 46 , 83 42 39. 08 40 , 85 42 , 73 44 , 70 45 , 68 46 , 82 49 , 07 43 40. 77 42 , 65 44 , 65 46 , 77 47 , 80 49 , 03 51 , 48 44 42. 55 44 , 55 46 , 70 48 , 98 50 , 12 51 , 45 54 , 13 45 44. 45 46 , 60 48 , 90 51 , 38 52 , 60 54 , 07 57 , 05 46 46. 48 48 , 80 51 , 28 54 , 00 55 , 32 56 , 98 60 , 33 47 48. 67 51 , 18 53 , 92 56 , 92 58 , 40 59 , 27 64 ▪ 13 48 51. 05 53 , 80 56 , 82 60 , 20 61 , 60 64 , 07 68 , 73 49 53. 67 56 , 70 60 , 10 64 , 00 66 , 05 68 , 68 74 , 85 50 56. 57 59 , 98 63 , 90 68 , 62 71 , 23 74 , 82 90 , 00 51 59. 85 63 , 80 68 , 53 74 , 75 78 , 83 90 , 00   51. 53 61. 88 65 , 20 71 , 53 79 , 53 90 , 0     52 63. 67 68 , 42 74 , 70 90 , 00       53 68. 32 74 , 62 90 , 00         54 74. 53 90 , 00           55 90 〈…〉             A Catalogue of the more notable Fixed Stars , with their Longitude , Latitude , and Magnitude , for the yeare 1650 Compleat . About the North Pole. Names of the Sta●res . Longit. D. Parts Latit . D. Parts .   Mag. The Polar Star ♊ 23 , 74916 66 , 04167 N 2 The higher of the 2 in □ of them that precede of the lesser Bear ♌ 7 , 98250 72 , 85000 N 2 The lower of the same ♌ 15 , 39183 75 , 38333 N 3 That neerest the Pole ♊ 27 , 20750 63 , 91667 N 6 The higher preceding in □ of the greater Bear ♌ 10 , 27417 49 , 66667 N 2 The lower of the same ♌ 14 , 43250 45 , ●5000 N 2 The higher of those following of the Quadrat ♌ 26 , 13250 51 , 61667 N 2 The lower of the same ♌ 25 , 45750 47 , 10000 N 2 The last but two in the taile ♍ 3 , 87417 54 , 30000 N 2 The last but one in the taile ♍ 10 , 64917 56 , 36667 N 2 The last in the taile ♍ 21 , 90750 54 , 41667 N 2 The tongue of the Dragon ♏ 18 , 64917 76 , 28333 N 4 The bright Star in the head ♑ 17 , 77417 81 , 88333 N 5 The Girdle of Ceph●us ♉ 0 , 9241● 71 , 11667 N 3 Arcturus ♎ 19 , 35●●● ●1 , 04167 N 1 The bright Star of the Crown ♍ 7 , 34917 44 , 38333 N 2 The head of Hercules ♐ 11 , 22417 37 , 38333 N 3 The bright Star of the Harp ♑ 10 , 41417 61 , 78333 N 1 The bright Star of the Swan , in the breast of ♓ 0 , 59917 59 , 93333 N 2 Cassiopeia ♉ 2 , 99917 46 , 58333 N 3 The head of Medusa ♉ 21 , 32417 22 , 37500 N 3 In the the right side of Perse●s ♉ 26 , 99083 30 , 08333 N 2 The little Goat Capella ♊ 16 , 96417 22 , 84167 N 1 In the head of Ophiuchus ♐ 17 , 54083 35 , 95000 N 3 Names of the Starres . Longit. D. Parts Latit . D. Parts .   Mag. In the middle of the Serpents neck ♍ 17 , 20750 25 , 58333 N 2 The bright Starre in the shoulder of the Eagle ♑ 26 , 85750 29 , 35833 N 2 The bright Starre of the taile of the Dolphin ♒ 9 , 24083 29 , 13333 N 3 The Mouth of Pegasus ♒ 27 , 07417 22 , 12500 N 3 The first Star of the wing Pegasus ♓ 18 , 64917 19 , 43333 N 2 In the putting forth of the thigh of Pegasus ♓ 24 , 52417 ●1 , 11667 N 2 The head of Anromeda ♈ 9 , 49083 25 , 70000 N 2 The more Southern in the Girdle ♈ 25 , 52417 25 , 98333 N 2 In the South foot Androm●da ♉ 9 , 35750 27 , 77500 N 2 In the top of the Triangle ♉ 2 , 02417 16 , 82500 N 4 About the Zodiack . Names of the Starres . Longit. D. Parts Latit . D. Parts .   Mag. The first Star of Aries ♈ 28 , 32417 7. 13333 N 4 The bright Starre in the top of the head of Aries ♉ 2 , 80750 9. 95000 N 3 The south Eye of Taurus ♊ 4 , 91583 5. 51667 S 1 The north Eye of Taurus ♊ 3 , 69083 2. 60833 S 3 The bright Star of the Pleiades ♉ 25 , 10750 4. 00000 N 5 The higher head of Gemini ♋ 15 , 39083 10. 03333 N 2 In the lower head of Gemini ♋ 18. 42417 6. 63333 N 2 Bright foot of Gemini ♋ 18 , 55750 6. 80●33 S 2 In the South arm of Cancer ♌ 8 , 76583 5. 13333 S 2 The bright Star in the neck of Leo ♌ 24 , 19083 8. 78333 N 3 The Heart of Leo ♌ 24 , 99083 0. 43333 N 2 In the extream of the taile of Leo ♍ 16 , 75750 12. ●0000 N 1 In Virgo's wing . Vindemia●rix ♎ 5 , 08083 16. 25833 N 1 Virgins Spike ♎ 18 , 97417 1. 98333 N 3 South Ballance ♏ 10 , 22417 0. 43333 N 1 North Ballance ♏ 14 , 50750 8. 58333 N 2 The highest in the fore-head of Scorpio ♏ 28 , 30750 1. 08333 N 2 Scorpions heart ♐ 4 , 92417 4. 45000 N 1 Names of the Starres . Longit. D. Parts Latit . D. Parts .   Mag. Former of the 3. in the head of Sagit . ♑ 8 , 64917 1 , 40833 N 4 Northern in the former horn ♑ ♑ 29 , 00750 7 , 04167 N 3 The succeeding bright Starre in the taile of Capricorn ♒ 18 , 70750 2 , 48333 S 3 The left shoulder of Aquarius ♒ 17 , 52417 8 , 70000 N 3 The shank of Aquarius ♓ 4 , 07417 8 , 16667 S 3 In the effusion ♒ Fomahant ♒ 28 , 89917 21 , 00000 S 1 In the mouth of the south Fish ♓ 13 , 74083 9 , 06667 N 5 The bright ✴ in the joyning of both nets of Pisces ♈ 24 , 49083 9 , 06667 S 3 Towards the South Pole. Names of the Starres . Longit. D. Parts Latit . D. Parts .   Mag. In the snout of the Whale ♉ 10 , 22417 7. 83333 S 4 Bright ✴ of the taile of the Whale ♓ 27 , 64083 20. 78333 S 2 Bright shoulder of Orion ♊ 13 , 90750 16. 10000 S 2 Middlemost of the Belt of Orion ♊ 18 , 60750 24. 55833 S 2 Bright ✴ in the left Foot Orion ♊ 11 , 99083 31. 18333 S 1 Orions foot in the River ♊ 10 , 40750 27. 90833 S 3 The last in the taile of the Hare ♊ 27 , 07417 38. 43333 S 4 Great Dogs mouth . Sirius ♋ 9. 29917 39. 50000 S 1 Lesser Dog. Procyon ♋ 21 , 01583 15. 95000 S 2 In the top of the Ships stern ♌ 6 , 59917 43. 30000 S 3 Brightest in Hydra ♍ 22 , 46583 22. 40000 S 1 In the Southern Hemisphere . Names of the Starres . Longit. D. Parts Latit . D. Parts .   Mag. Bright ✴ of the Cranes head ♒ 12 , 56667 12. 83333 S 2 Going out of the Cranes taile ♒ ●7 , 5833● ●4 . 60000 S 2 Bright ✴ of the Phaenix's neck ♓ 9 , 8833● 40. 16667 S 2 Head of Indus ♑ 28 , 30000 ●2 . 50000 S 4 The Peacocks head ♑ 17 , 45000 ●6 . 00000 ● 2 The Sparrows head ♎ 19 , 01667 72. 43333 S 5 In the bill of the Goose ♒ 4. 60000 45. 91667 S 3 The head of Hydrus ♓ 4 , 68333 64. 08333 S 3 FINIS .