A treatise of artificial fire-vvorks both for vvarres and recreation with divers pleasant geometricall obseruations, fortifications, and arithmeticall examples. In fauour of mathematicall students. Newly written in French, and Englished by the authour Tho: [sic] Malthus. Traité des feux artificiels pour la guerre, et pour la recreation. English Malthus, Francis. 1629 Approx. 157 KB of XML-encoded text transcribed from 146 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2003-11 (EEBO-TCP Phase 1). A06780 STC 17217 ESTC S109781 99845426 99845426 10323 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A06780) Transcribed from: (Early English Books Online ; image set 10323) Images scanned from microfilm: (Early English books, 1475-1640 ; 851:11) A treatise of artificial fire-vvorks both for vvarres and recreation with divers pleasant geometricall obseruations, fortifications, and arithmeticall examples. In fauour of mathematicall students. Newly written in French, and Englished by the authour Tho: [sic] Malthus. Traité des feux artificiels pour la guerre, et pour la recreation. English Malthus, Francis. Cecil, Thomas, fl. 1630, engraver. [18], 172, 171-261, [11] p. : ill. (metal cuts, woodcuts) Printed [by W. Jones] for Richard Havvkins, and are to be sold at his shop in Chancerie lane neere to Serieants Inne, [London] : 1629. A translation of: Traité des feux artificiels pour la guerre, et pour la recreation. Printer's name from STC. With an additional title page, engraved, "A treatise: of artificiall fireworkes by F. Malthus", signed: T. Cecill sc: [?fe:]. The first leaf and the last leaf are blank. With four final contents leaves. Variant: engraving on C7v also printed on C5v; mistake rectified by a cancel pasted onto C5v. Reproduction of the original in the British Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. EEBO-TCP is a partnership between the Universities of Michigan and Oxford and the publisher ProQuest to create accurately transcribed and encoded texts based on the image sets published by ProQuest via their Early English Books Online (EEBO) database (http://eebo.chadwyck.com). 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Keying and markup guidelines are available at the Text Creation Partnership web site . eng Fireworks -- Early works to 1800. 2003-05 TCP Assigned for keying and markup 2003-06 SPi Global Keyed and coded from ProQuest page images 2003-08 Jonathan Blaney Sampled and proofread 2003-08 Jonathan Blaney Text and markup reviewed and edited 2003-10 pfs Batch review (QC) and XML conversion A TREATISE OF ARTIFICIAL FIRE-VVORKS Both for VVarres and Recreation : with divers pleasant Geometricall obseruations , Fortifications , and Arithmeticall Examples . In fauour of Mathematicall Students . Newly written in FRENCH , and Englished by the Authour THO : MALTHVS . Printed for RICHARD HAVVKINS , and are to be sold at his Shop in Chancerie lane neere to Serieants Inne . 1629. A TREATISE OF ARTIFICIALL FIREWORKES by F Malthus LONDON for Richard Hawkins in Chancery Lane. 1629 THE PREFACE Apologetique to the Reader . ALthough that Warres haue beene authorized by the diuine powers , as witnesseth the new and old Testament , yet me thinkes I heare many nice , peeuish , and ignorant braines blaming me for setting downe to the view of the world ( at a few leisurely houres ) so many wayes and inuentions how to corrupt and destroy what nature and art striue to make , edifie and conserue , to whom I answer they haue the same reason to exclaim against iustice which hath found and ordained many meanes to abolish and exterminate wicked offenders : for my intention is here but onely to finde inventions to confound and ruinate Rebells and their habitations ; that afterward Empires , Kingdomes , and Common-wealths may the better liue in peace and tranquilitie : and what more is I haue set downe perspicuously this Treatise of Fire-workes , which many heretofore haue written with confusion and great danger , having pend large Volumes with most ample and idle discourses touching this subiect , whose names for modesties sake I will not here set downe with an infamous character to posteritie ( as Master Robert Norton hath done some few slight offenders names in the Preface to his translation of Vianos works , which he calleth his owne , hauing onely added seuen figures taken out of Thybourels booke , and transposing the Authours workes to disguise it ) that I bee not accounted amongst the calumniators of this age , who write with serpents tongues spitting their venome vpon the silent and sleepi●g innocents gone before vs. But I will onely shew their errors in generall , that the learners may the better auoyde them : For in some you shall see prescribed all sorts of Apothecaries drugges for the compounding of Fire-workes , which are no more capable of fire then stones , earth , or mettle , as Adamant-stone , Verdigrease , Cristall , Vitrioll , Salarmoniacke , Sublime , Mercurie , with a number of the like , which in the iudgement of ignorants may produce in Fire-workes wonderfull effects . In others you shall finde the coniunctions of combustible materials in such a sort or manner disposed and ordered to such strange ends , that you would say they were set downe to make the Reader laugh , rather then for seruice of Fire-workes eyther for Warres or Recreation , as the meanes how to poyson an Armie in the wide Field by the smoake of an artificiall Ball , is it not to be thought a very prettie imagination , or else that the Ball ought to bee somewhat bigge ; and afterward which is more ridiculous , you shall finde in the same Authours the same ingredients and mixtures prescribed for Fireworks for Pleasure and Recreation : which to mee seemes strange , that the Fire-workes whose smoakes are so venemous even as to poyson Armies in the open Fields , shall bee also fit to burne in the middle of a Cittie or Towne amongst thousands of people for Recreations : now all these idle conceites with a number of the like are printed in many new and recent bookes , the Authours whereof doubtlesse haue set downe all these ridiculous inventions by ignorance , ( thinking them good ) and not of purpose for spight ; and therefore they doe deserue pittie rather then blame ; as well as Master ROBERT NORTON , ( who hath erred onely in attributing another mans workes , and faults to bee his owne ) and what is it that giues mee cause to thinke that all these haue erred by ignorance , is because that all their workes are alike where that they doe speake of Fire-workes . But reading these absurdities with a great quantitie of others , which made mee take resolution to set my penne to paper , and shew to posteritie how and what way to auoyde their errours , having heere set downe the true rules and mixtures required for Fire-workes , both for VVarres and Recreation , with some few Geometricall obseruations necessarie for the practise of Fireworkes in warres ; and also I haue added vnto it certaine rules and maximes of Fortifications , very requisite for Enginiers to haue in their memorie , with a compendious Arithmetike , hauing written the whole first in French at some broken houres whilest I followed the warres ; and bringing certaine coppies from the Presse to my speciall and very good friends ; at whose requests I haue translated the same into English , that others might not translating it , mistake my meaning ; and the worke being already but of small commendations , they to make it of lesser . Adiew . London the 22. of May. 1629. To the Authour . THy Archimedean hand hath learnt to frame Celestiall Meteors out of Nitrous flame : And represents strange fires of differēt sorts Suted to Martiall vse , & Courtly sports : So pleasing that great Kings haue spar'd some houres To be spectators of thy golden showres . The Thames and Seyne haue seen thy Balons fly , From their affrighted bosomes to the skye : Swift beyond all beliefe ; as if thy ayme Were , to restore Prometheus theft againe . Were , when their force seems spent , breaking asunder They rain down stars , or els outroar the thunder . The Roman Apotheosis I deeme , Would still haue had a reuerent esteeme , If they had vs'd these miracles of fire , To mount their Caesars soules , & beare thē higher Then Eagles flight , but now they serue to raise , The Pyramis and Trophe of thy praise . And sure thou hast attain'd sufficient glory , In perfecting the Pyrotecnique story : Which some tooke vpon trust , & by concealing Their creditors ; made borowing to seem stealing . But their fire 's out , now thine hath pass'd the Presse . For greater fires do extinguish lesse . WILLIAM BASTIAN studious in Mathematicks . A TREATISE OF FIRE-WORKES . for Warre . CHAP. I. TO imitate nature , our first and chiefest teacher , who far from error seemes to haue produced and brought forth all things ●y a curious and speciall order ; without whose beautifull disposi●●on on the whole world had still con●●nued in the most prodigious con●●sion of Caos , which displeased the ●●●ure aspect of the highest , eternall and divine powers , being but a cloud or mixture of darknesse . My intention is here to institute and obserue an order , treating of euery thing one after another in his proper and conuenient place : beginning with artificiall Fire-workes , as the chiefest and principall cause which hath vrged me to take my penne in hand , the description of those which belong to warres , shall obtaine the first place , and next the Fire-workes for recreation or pleasure , passing from these to many pleasing Geometricall obseruations , aswell of Mecanical obseruation , as by the sines , tangents , & succents , ioyning to them a most easie & succent method to fortifie all places regularly and irregularly . And to conclude I will adde many briefe and instructiue Arithmeticall examples . Now to begin with the Fire-workes for warres , I will first describe the Morter-peece , and the vse thereof : that being an instrument , the most noble , the most vniuersal , the best of greatest effect , and of most wonderfull operation of all the instruments , the practise wherof may be vsed amongst Fire-workes for warres , for this instrument may serue for a Petard to split , breake and hurle down dores , gates or walles , likewise to massacre , teare in pieces , ouerthrow and confound assailants of any place or breach : and for diuers other most worthy offices , and accidentall occasions , which happen in the troubles of warres : whereof I will not here make a long , weary , and tedious discourse , but in few words cleerely set downe the vse of this instrument for the shooting of diuers sorts of granads , stones , or other weighty burthens to ruine rebels , their habitations and dwelling places . Then first of all I will treat of the mettle , whereof this instrument ought to be made , and measures appertaining thereunto . CHAP. II. The manner how to make the Morter-Peece . THis Instrument may bee made of diuers sorts of mettle or stuffe , according to the means , times and occasions which shall offer themselues to those who would make them , or cause them to bee made . The first and chiefest matter of all , is red copper , brasse and tinne , but very little of the two last , such as Canons are made of , without any other brickle or harsh met●●● mingled with it , and beeing made of this stuffe , let the measures following be observed . If the diameter of the calliber or bore be one foot , let the morter be two foot of length , & let the sack or hole for the powder be the third part of a foot broad , and halfe a foot deep , and let the mortar beare in thicknes an inch and a halfe , about one foote high , and the rest onely one inch thicke , the foot shall bee one inch and a halfe thicke , and made square whether the instrument be for the seruice of warres , or recreation , as doth plainely demonstrate the Figure A following . The second mettle is yron , such as commonly Ordnance for ships are made of : and being cast of this stuffe , the rules prescribed shall be found fit , onely let the mettle be somewhat ●hicker in euery place . The third ●nd fourth , and most common materialls are past-boards and can●as , or pastboords and chord , and either or these materialls must bee ioyned together with glue , and being to bee made of either of these materialls there must be had a woden foot , with the powder sacke or hole made hollow below in the wood , as is represented by the Figure B. the precedent measures being obserued which is the third part of the diametre , &c. But if the instrument be to bee made of either of the two first mettalls , that belongs to the Founders office , but of the two last materials euery man at his owne pleasure may compose it of what size he please , and to begin he must haue a wodden rowler of such bignesse as he shall desire to make the diametre of his Morter-peece , and vpon that rowler let the pastbords and canuas with good store of glue be rowled : which being done , let them dry a while vpon the rowler , and another while off from the ●owler , and when this kinde of truncke is very dry , let the woden foot be ioyned to the one end with glue and nailes very fast ; and then couer the whole with chord and glue againe ; which being well dryed , the instrument may bee of long service , provided that it bee not over-charged , and as for the length , the longest carry furthest , and the thickest dure longest , by the figure C. precedent the instrument is represented perfect , with the touch-hole in the right place required . CHAP. III. The manner how to make granades or mettle for the morter , or hand . ALl granads being made to breake , ought to be composed of the most brickle mettle that may be found , as of brasse , adding the third part of Tin to it . ( as the Founders know right well ) they may be also made of yron , or of glasse to cast out of mens hands , so that the glasse bee made very thicke , and these will worke wondrous effects , especially in any throng of horsemen or footmen . And as for the thicknesse of those which are made of brasse , if the diameter be one foot , let the mettle be one inch thicke , and let them be somewhat longer then they are round as doth demonstrate the figure A. leauing at the one end , as it were a handle , and on the other , a screwed hole ; by which meanes the granad may be charged , also , let there be made a hollow vice fitting for the former screw , which vice shall be filled with a slow composition made with gunpowder well ●ruised and culled , and then made ●nto past with oile of petrole : but if the powder be excellent good and strong , then mingle with a pound of powder , one ounce of Charcoale dust , to make it vveaker , then let ●he composition bee vvell beaten ●nto the hollovv vice , vvhich is represented by the figure B. And the granad shal be filled with fine gun-powder , which being full , let the vice be screwed into the hollow hole of the granade , onely it is to be noted that the vice must not be open at the lower end , but haue a bottom sodered strongly , wherein shall bee made three or ●●ure little holes about the bignes of a tag of a point to giue fire to ●●e powder when the granad hath f●owne the space required . For the performance wherof it is needfull that you know the quicknesse o● slownesse of the mixture wherwith the hollow screw is to be fill●d . And for the better experience , it shall bee conuenient to make of all of one with a granade made 〈◊〉 wood , cloath , pastboord , or a●y other stuffe filled with earth , ●ut let it be neere to the weight of ●●ose which you desire to make vse of , afterward , and by that meanes you may know how long ●ou ought to make your hollow vices , which are called by their ●roper tearmes Port-fires , and ●hus much of your granade being performed , novv let it bee all covered over , vvith either Chord , Canuas , or Pastboord , and dipped in glue or in pitch ; this covering may be neere halfe an inch thicke : to the end that the granade going out of the Morter vvith violence it breake not , and vvorke his execution vpon your selfe or your company instead of your enemies ; of vvhat mettall soever the granad is made , these rules are to be observed , and by the figure C , is represented a granade quite finished ; and dipped into pitch , by vvhich meanes it may bee conserved many yeares : these sorts of granads vvorke great effects falling vpon houses ; they cast downe the vvalles and coverings , likewise they vvorke vvonderous operations amongst either horsemen or footmen , tearing both man and beast in pieces , sparing nothing . CHAP. IV. The manner how to make Granads of Canuas for the Morter . THe operation or execution of these sorts of granads made of Canuas is quite contrary to those prescribed : these are onely fit to set a Towne on fire , the houses whereof are most couered with reede , straw , or broome , they are not of so violent execution as the precedent , yet notwithstanding of as great cost , and for the making of them , you must haue a wooden ●owler , which is represented by the ●igure A , of the bignesse you desire ●o make the granad ( which alwaies ought to be lesse then the Calliber or bore of your morter , to the end ●hey may bee covered afterward ) ●nd vpon the rowler make a sacke of ●uch cloth as you please , as doth re●resent the figure B , cutting a piece to ●ouer the vpper end , when the sacke ●hall be full of the composition fol●owing . Take foure pound of salt●eter , two pound of gunpowder-●ust , two pound of brimstone , all ●hese being well pulverised , let them ●e moystened with oyle of petrole , ●nd then fill your sackes with the ●ame , and cover them with chord , which done , pierce the sacke full of holes with a great bodkin , as representeth the figure E , and in euery hole , place a little yron barrell charged like a pistoll barrell , these little barrells are represented by D , which must be driuen into the sacke vp to the head , and the granad being thus disposed , let there be made at the one end a hole about one inch deepe , which shall serue to prime it with powder-dust , moystened with oyle of petrole , onely it is to be noted that the touch-holes of the little barrells be made somewhat large , to the end ●hat the rust stop them not , being ●ong time kept amongst the salt-pe●er , and so they may be conserved many yeeres , and ready for service ●n all occasions , the figure C. doth ●emonstrate the granad perfect and ●urning . CHAP. V. How to make fiery arrowes . TO avoyde all confusion , I will treat first of all the fires which are cast with violence , and afterward of those which may be cast out of mens hands . And first it is to be observed , that fiery arrowes are of great effects and noysome at sea , specially if the ships approach any thing neere , so that they may bee 〈◊〉 or cast into the sayles chording 〈◊〉 of the ships , either by cros-bowes , long bowes , or any other meanes , for so much as a ship being once a fire , hardly can it be extinguished . And thus the arrowes ought to be made : first a long shaft of wood , ●nd ioyned to it an yron head made after the manner of the figure A , and about the middle of that head , make fast a linnen bag in the forme of an oliue , leauing open a hole at ●he end before , as may be seene by the figure B , that it may bee filled with the composition following . ●ake one pound of Saltpeter , halfe a ●ound of gunpowder-dust , and ●alfe a pound of brimstone in ●ovvder : all these ingredients ●eeing well mingled , and min●ed with oyle of petrole , then fill ●e bagge round about the arrow ●ead , noted by B , and then let all be well bound about with wyre . And ●r the priming of these arrowes , dip cotten weeke into gunpowder , wet with water , but let the cotton be wel dried again before it be applied to the arrow head . Now for the ioyning of your arrow head , to the wodden shaft it ought to be so slightly fastned to it , that being shooke into any sayle , cordage , or wood , so that if any one would plucke it backe , the shaft should slip out of the head , and so continue burning in the place pretended , and to hinder that one may not pluck out the head with their hands , there may be made ● small hole quite through backeward , and so the fire will hinder a man from touching any part thereof , al●hough it should sticke in other of his fellowes clothes . There may ●e made little arrows of the same fa●hion , to be cast out of mens hands in ●ny meetings , assaults , breaches , or ●ther occasions ; and if there shall be ●reat hast for the making of them , ●esse fashion may serue , hauing onely ●●ttle stickes of wood , about a foote ●nd a halfe long , and in stead of the ●ead prescribed , a pyke ( like a ●reat nayle ) and in lieu of feathers , pieces of past-boord , stucke into the ends of the wood being slit , but the former composition shall be required . CHAP. VI. How the granads are to be charged into the morter . ALthough it seeme to be but a small difficulty to charge the granads into the morter , yet it is the greatest mastery and most curious worke which hath beene found amongst fireworks , and the most industrious Enginers that ever I yet saw , haue after beene deceived therein , and shor ●ut their granads , they not taking ●ire , which is absolutely one of the greatest faults that may be commit●ed . Then to avoyde such great er●ors it shall be needfull to note ma●y obseruations following , whereof the first is that you put not too much powder in your morter , marmarked A , but onely the powder-●ckefull ; secondly , that the priming ●f your granad be firme , not spoy●ed with dust or dyrtie moistnes , or other like thing , that it bee not also too dry , least all breake about your selfe going out of the Morter taking ●re too quicke , which all fire-works ●re very subiect to doe , then take ●eed that the granad enter not too ●ardly into the morter , which will cause it to breake in the discharging , also it is not needful that it enter too loosely . All these things being well obserued , you must haue alwaies ready port-fires for your morter , which may be made about the bignesse of your litle finger , and hollowed within about the bignes of a quill , even to the bottome , noted B , this portfire is to enter with a vice into the touch-hole of the morter , about half ●n inch , and to turne the vice without any key : there may be made 4 , buttons at the out-side of the vpper ●nd , and let this portfire be charged with a slow composition , mingling 4. ounces of charcoale with a pound of powder-dust , this being done , and your granad placed in your morter , ●o that it shake not , close vp the ●hinks round about your granade , within the morter , with grease , waxe , ●itch & grease , or any such like thing you may so cover the granad with ●ome such stuffe ; that in any weather wet or dry , you shal find no difficul●y to shoote off the granad in any place wheresoever you please . CHAP. VII . The manner how to shoot the granads . THere is no lesse difficultie well to discharge the granads then to charge them , but the contrary will easily appeare , for it is there where the hazards and dangers most great , doe meet together . And the first of all are the aduersaries Canons from whose dangers the Enginier shall easily conserue himselfe , as followeth , causing to be made a trench like vnto an halfe moone , the connexity thereof being towards the enemy , as appeareth by the figure A , this trench shall be of such bignesse ●s the Enginier may conueniently place all such things as shall be need●ull for his present vse . The second difficulty following , is how to shoot ●hem right to the places of any Fort ●or Towne desired , being not possible ●o see the places to take leuel at them without eminent danger of their Canon and musket-shot : which difficultie shall be thus auoyded , and ●et leuel right , and send the granads ●o the places required : let there bee ●e two staues set vpright , betweene ●he Towne , Fort , or Cittadell and the Trench , the one of these staues shal be somewhat long , the other may be ●hort , and that , planted vpon the ●rim of the trench ; but the longest ●omewhat distant in a right line towards the place pretended , as doth demonstrate the figures BC , these staues shall be so disposed that you may see the extremities of each , being in the trench out of the enemies sight , and by the sight of these two extremities , you may direct your granads at your pleasure inclining your ●orter-piece vpon either side , as shal 〈◊〉 needfull without danger of the e●●mie , having onelie knowne the di●●●nce betwixt the trench and the ●wne , or place of the towne which ●●u shal desire to destroy . The third ●●d last difficultie is to know the true ●●ngth or distance that your morter ●oth beare , of which to be certaine , ●●u must trie it before , shooting gra●●ds of the same weight , & with one ●●rt of powder , and with a leuel , take ●●vers sorts of elevations , & so may ●ou know such an elevation doth oa●e so far , and such carie so far with ●●ch powder such a weight , being ●●arged , the maner of taking these ●●●vations is represented by the figure 〈◊〉 , & the level in a bigger volume by ●●e figure E , this leuel being placed ●pon the mouth of the morter piece , vnder the foot thereof : wedges , yo● may giue to the morter what incli●nation shall be required : and to b● sure from all harme of your own● granads , which by chance may brea● going out of the Morter-piece , le● there be made in the trench a little corner hollow into , or behind the which you may alwayes retyre , ha●ving given fire to the Morter . It shal be also needful that some one watch where the granad doth fall whethe● too short or too farre ; that you may the better direct the next shot : thi● method is to bee observed in shooting all sorts of granads , stones , o● other like things . CHAP. VIII . A most violent method to set a Towne on fire . HItherto there hath not been found any means or inuention more certaine or violent , whereby one might convey fire for the destruction of the e●emies habitations then by the helpe of the precedent granads , which very hardly cause any disorder or combustion , vnlesse amongst houses covered with straw , whereof few are to bee found in goodly townes . And therefore I will here prescribe a ●ew way much different from the others before written ▪ against which hardly or not at all may be made any resistance or possibilitie for defence , the violence , rage , and order being of such a fearfull power and execution , prouided that the Enginier doe but meanly effect his purpose & designe , and for the practise hereof , let there be made a kind of well in the ground but sloping , as doth demonstrate the figure A , of such deepenesse as shall be thought fit , but it is to bee noted , that the neerer you are to the towne , the lesser slooping will be best , and most easie for the performance . The hollow pit or well being made , let there be placed in the bottome thereof one or two barrells of gunpowder , as shall be seen needfull , according to the proximite or ●●stance betweene the place and ●●wne , & these barrels may be places ●●●ry conueniently placed with good ●ore of straw about them to keepe ●●em from the moystures of the ●●rth . And in one , or else in both , 〈◊〉 shall place a gunlocke , making 〈◊〉 to the clicket thereof a chaine of sufficient length to reach out of the hole vpon the plaine ground , but this chaine shall be curiouslyy lodged in a small gutter , which afterward shall be covered with earth , to the end that the fire doe not ouer-heate it , then cover the barrells of powder with strong woodden planckes , or broade stones , covering them againe with earth , and then lay good store of fresh straw and bauins , and fagots , and in the midst of these let there be placed a great fagot , made of peeces of timber , of a reasonable length , be●ng well bound together with chains of yron in three or foure places , as doth appeare by the figure B , and then set fire on the straw wood , and all that shall be in the pit ▪ giving the great wood time to kindle , and this great fagot being in a great arder , let the chaines be drawn which are tyed to the latches of the gunne lockes , and doubtlesse you shall see braue sports ; and if there be many pieces of Ordnance about the towne or place thus besiedged , let them be all disposed ready to shoote where this great fagot fals , and whosoeuer would hut this inuention in practise , ought to make many of these pats about a towne , giuing fire to them all at once : but the Inginier to know iustly how far these great flaming fagots may flye , the hollow pit declining so many degrees , hee ought to make tryall before in some large place , where he may haue room for his experience : now resteth only to explicate how a man may giue fire to the stra● in the pit without danger , for so much that euery man would not least all should take fire together . Then to be free from this perill , it may be fired by a traine of powder , by a Gunlocke , a piece of match , a candles end , or other like inuention : Peradventure , you may thinke that there may be danger in drawing the chaine when all is on fire ; to which I answer these may be ioyned to it , a chord of such length as shall seeme necessarie ; The Enginier who shall put this in practise , may adde of his inuention what hee thinkes fit , Facilius est enim addere invento quam in venire . CHAP. IX . How to make Granads to cast with mens hands . HAving taught how to make Granads for the Morter , which by the violence of that most wonderfull instrument may be transported very farre over waters , walls , or bulwarks , working strange and rude executions or effects , I will now shew how it shall bee easie to make two or three sorts of Granads to bee cast out of mens hands , the effects whereof are no lesse to bee esteemed then the other , chiefly in assaults , whether it be for the offendants or defendants . The chiefest and of greatest operation is made of any kind of brickle mettle as the precedents ▪ and their fabrication is not much different from the other , onely more rounder and lesser , and the single ones hauing a long neck to seem for the Port fire , as doth appeare by the figure A , and first of all the granad is to be filled with fine gunpowder , and afterward fill the neck with a slow composition as followeth . Take 1. pound of gunpowder dust , two ounces of charcoale d●ust three ounces of saltpeter , al these well mingled together , fill the portfire required , but this mixture must be well beaten into the port-fire , and the granads being thus finished , they may be kept a yeare , ten yeares , yea twenty if need be . It is to be noted that ●hese granads must not be freed vntill a man is ready to cast them away even in the same instant , because the port-fire being consumed , the granad breaks in divers pieces , and each piece sufficient to kill eyther man or beast , and therefore the handling of them is somewhat dangerous . The second manner of Granad to bee cast out of the hand , is made also of brickle mettle , but hath no necke for a Portfire , but is onelie round , hauing in one side a hole as appears by the figure B , and at this hole it is to be filled with drie powder , and then is to bee put into this hole to stop it , cotten wieke made as followeth . Take good Gunpowder and steepe it in faire water , and being dissolved , take the cotten wieke and steep it in the Gunpowder dissolued , which done , hang it out to drie ; but let it be doubled eight or ten times , to the end that it may the better receiue the powder , and being drie , cut it in such pieces as you shal need , putting the one end into the Granad at the hole , and then put that Granad into another pot a little bigger then the Granad , as appeareth by the figure C , so that you may put a little drie powder round about the lesser Granad betweene the pots and Granad , then cover the mouth of the last earthen pot either with leather or such like stuffe ; and bind it round about with wyre , but first put the wire through pieces of match about halfe a foot of length as may appear by D , and when you desire to make vse of this sort of granad , set on fire euery end of these pieces of match , and cast the pot away , which falling either vpon the ground , or anie souldiers Armour , you shall see the earth-pot breake , the Granad split , and worke such furious effects , eyther at a breach or anie approch . The third sort of Granad is made much like to either of those precedent , except onely it may bee made double or single , of glasse or of earth onely shall be needfull to be made very thicke , and if it be to be made single , the portfire ought to be either of wood or of pastboord , and well glued in , and this last sort may work great effects . Now having somwhat largely treated of the morter , granads , and of their vse , I will speake a little of other oyly fireworkes very pernicious and noysome to all assailants . CHAP. X. How to make fiery wheeles to be cast with mens hands . FOr as much as euery souldier wil not meddle with making nor casting out of his hands granads , the handling of them being somewhat dangerous , I will here teach another manner of fireworkes , which is not much lesse offensiue , which being well compounded and compacted , and for the making thereof , these are more ingredients required , then for the precedents , and is more difficultie in making of them as followeth , Take foure pound of gunpowder in dust , one pound of charcoale dust , two pound of tarre , two pound of salt-peter , and one pound of Rosin . All these ingredients being well mingled and heat ouer the fire , steepe tow or flaxe in the same , ●n● then wrap the tow or flax about ●● whope , which is represented by A , and then cover all this againe with Gunpowder dust , & in time of need giue fire to them , and cast hem amongst your enemies ; onelie is to be obserued that the whops or circles ought not to be to large , but falling vpon a many of souldiers they may there stay and sticke , and to make them more troublesome and intangling , two may be tied a crosse on another , and then falling vpon anie man , he cannot choose but be much astonished with such a fearefull eleme●t , and put his company in great disorder . CHAP. XI . How to make a Shippe of wilde Fire . AFter a sufficient discourse of all manner of Granads , fierie arrowes and burning wheeles , I cannot thinke it extravagant or amisse to lay open to the industrious or curious , a method how to make a fiery ship at sea , which shall not begin to burne till it hit against some other vessell , rocke , or such like obstacle , or be hooked or grapled on the inside to be drawne a shore . Hee that will vndertake to build one of these must spare no reasonable cost to put his intentions or designes in execution , and first of all must be had one ship or many , according to the times and occasions wherein they shall be required ; and within the shippe shall bee disposed great store of broken Canons well charged with bullets , and from one Canon to another shall be ioyned a port-fire , so that the first , having taken fire , all the rest must neede doe the same ; these Canons shall haue their mouthes put out of the Gun-ports ready to bee discharged ; this done , let there bee good store of dry straw , small dry wood , and tow and flaxe steeped in pitch , turpentine , rosine , and tarre ; mingle and wrap the tow thus steeped , about and amongst the wood and straw , and place it betweene all the Canons ; the straw and small wood shall be so disposed , that it may take fire when the best part of the Canons are discharged , and the peece of Canon which is to giue fire to the straw , shall be set with the mouth vpward to blow part of the decke away , and at the same time giue fire to great store of granads of all sorts , to adde musket-barrells to barrells of Gunpowder ranged in order aboue the deck , to blow out these things by order , now one , then another by the helpe of slow portfires , but the beginning of this sport ought to be very violent and furious , to frighten and also teare in pieces the enemies at once , & that the rage hereof be the more furious , let the greatest part of the Canons ●●oot off thick one after another e●●n with the water , and at the same 〈◊〉 the Granads shall flye the one ●●re off , the others fall neere , now a ●●rrell of gunpowder blowes out a ●●rt of the flaming ship here , and a●n another barrell caste out a quar●●● of the vessell ardent there , casting ●●uers sorts of fire here and there as ●ls , arrowes , granads , double and ●●gle ones , made of the compositi●● prescribed in the 5. and 10. chap●●●s , but to hinder all the barrells of ●●wder from taking fire together , ●hich is no small difficultie , euery ●●rrell ought to be plastered over , ●●d then covered with glue and a ●●re-cloth , and then put into another ●●rell ; but to make them take fire e●●●y one at your pleasure , put a Port●● vnto thē , of such length , & slow composition , as you shall thinke fit●ting . Now to begin this mad spor● fasten three or foure good strong gunlockes within the ship , at one en● of the traine , which is to giue fire to the first Canon , and to every clicke or tackit of the locks , fasten an yro● rod , and let the other end of the 〈◊〉 rod passe through the ship , and ●ee made fast to peeces of strong wood , in the manner of a gyrdle on ●he outside of the ship , which is re●resented in the figure by the points ; ●o that touched vpon the outside a●y thing rudely , the locks must needs ●trike fire , and set going all the rest ; ●nd to make it give fire being hooked in the inside , to draw it ashore , 〈◊〉 out of the way , let there be made ●ast to each clicket of the locks , long wyers , and the other ends of the wyres may be fastned to pieces of wood in the inside of the ship , round about the edge , so that the first thing that shall touch it , sets all going as vpon the outside , but the pieces of wood vpon the outside ought to be very neere the water , as doth demonstrate the figure with the points , and so to conduct this ship as neere to t●● place as may bee , without dang●● there may be fast ioind to the stern piece of timber noted A , B , to the en● whereof may bee fastned two lon● ropes , and to them two little boats , i● which men shall be for the condu●cting therof . This here is but a spar● of inuention , to which the industri●ous Enginier shall adde of his wha● he please , and take this but for an entry of such workes ; for although haue here set downe gunlockes ▪ t● giue fire to the Canons , my meaning is that they bee made like gunlocks but ten times stronger , and harder i● going off , leauing to the iudgemen● of the discreet Enginier , the true disposition of his owne designes . CHAP. XII . How to make a Petard . DIego Vsan , a Spaniard , Francis Tibourele a Loreine , and Master Robert Norton an English man , hauing al written of fireworks , and neither of them all vnderstanding how to charge a simple Petard , I thought fit to end these fireworkes for wars by the description of the same , that being of great violence to make entries & breaches into towns castles , or houses , the morter prescribed , may serue to petard a place as hath beene sayd already : but whosoeuer would make exactly a Petard , ought to cast a Morter much like vnto an Apothecaries morter , as doth represent the figure A , observing the rules following , if you make it , to weigh sixe pound of mettle , let the calliber or bore be of such bignesse to containe one pound of powder ▪ or one pound and a halfe : if you adde or diminish more or lesse mettle , augment or diminish the calliber likewise , to hold the fourth part of powder which the mettle doth weigh ; and for the charging of the Petard , fill it only with the best gunpowder you can , almost to the brim ; and then couer it with a round bord made fit for the purpose , leauing aside all frivolous directions , written by others aforenamed ; and for the ●riming of the Petard , make a port-fire of slow composition , as for the precedent fireworkes of what length you please ; and to breake open the place you desire if it bee accessible , then with the heele or breach of the Petard vpon the ground or some great stone or piece of wood , and the mouth against the part of the dore , gate , or elsewhere , which you shall iudge fittest , but if the place bee vnaccessible , then make a kinde of a little Cart with two or foure wheeles , as doth appeare by the figure B with a long forke very strong to beare the Petard , and also support the requile of the Petard shooting off : This forke is represented by C , but the backer end of this forke must bee stayed either in some hole , or against a stake , or other meanes ; Now here in this treatie not intending to imitate these late Authours , who writing of artifi●iall Fire-workes ; have prescrbed natures and compositions of almost all manner of drugges , the meanes whereof may bee found in anie Apothecaryes shopppe , doubtlesse eyther to perswade the curious Readers that they had profound knowledge , many rare secrets , or else the better to hide their ignorance , by that great confusion and expence , whereunto few or none would extend and vse their purses to make proofe and experience of . I will finish this treatie of artificiall Fire-workes for Warres , and goe forward to the second treatie of Fire-workes for pleasure and recreation , and explaine in the Preface apologitike , for what vse all these vnknowne dregges are fit for , which seemes to those that are ignorant of such rare and wonderfull effects . As Salarmoniake , Antemonie , Arseneeke , Vitrioll , Stonelime , Thutie , Adamant stone , not forgetting quick siluer . THE SECOND TREATISE OF ARtificiall Fire-workes for pleasure . CHAP. I. PErspicuous & plain shall be the method to make all manner of Fire-workes for pleasure , ( which heare I will set downe for the contentment of all curious and ingenious Artists ) without such a number of vnknowne dregges for mixtures , as many heretofore haue prescribed more fittest for some prodigious actions , then to mingle for artificiall fireworkes ; and principally for those which are invented for pleasure , for these haue no need of venemous smoaks to poison the spectatours , making mirth turne to mischiefe ( which notwithstanding cannot be done in an open ayre ) neither haue they need of such a continuing , ardent and violent flame , as to consume Cities or habitations , but onely of a gentle and pleasing flame to the eyes of the spectactors ; and thus they are divided into three sorts ; The first are those which ascend and mount into the ayre ; The second are such as consume vpon the earth ; The third and last sort , are those which swim and burne in the water . Those which worke their effects in the ayre , are ●●kewise divided into three sorts , the ●hiefest and most noble of all are the ●allouns ; The second the rockets ; ●nd the third are flying saucissouns , ●hose which stand fixt vpon the ●round are also distinguished into ●hree sorts ; The first are the rockets ●or the ground , the second the fierie ●nces and the third saucissouns : The ●res for the water , may haue their ●iple diuision ; globes or balls make ●he first , double rocket ; the second , ●nd single ones the last ; and to treate ●f euery one in particular , I wil begin ●ith the rockets for the ayre ; and ●●rst of all describe their moulds , and ●he measures which must be obser●ed in making of them . CHAP. II. A method to make moulds for rocket for the Ayre . ALthough that ballou● are absolutely th● most noble sort of fir● workes , yet for so muc● as all great fireworkes are compose● rather of rockets , then of balloun● I thinke it conuenient , to begin th●● second treatise with these : first of a●● making the description of the moulds , which may bee made eith●● of brasse or wood , the one being 〈◊〉 good as the other for vse , if the mea●sures following be obserued ; whic● ●●all be conuenient for all sorts of ●●gnesses , because they depend one●● vpon the calliber or bore , and that ●eing enlarged , the other parts will ●e all enlarged also , that being dimi●●shed , all the rest will be diminished ●●kewise . Then to make a mould , the ●●lliber wherof shall be suppored an ●●ch of diamer , and is represented 〈◊〉 the figure A , then the mould ●ight to be sixe inches in length ; 〈◊〉 the breech which is represented ●y the figure C , must enter into the ●ould one inch and a halfe , and the ●och noted with O , should be three ●●ches and a halfe long , and a quar●●r of an inch in bignesse , and the ●●wler D , which is to rowle the ●artoush or coffins of paper vpon , ●●all be three quarters of an inch in ●●gnesse , & the rammer E , to charge and ram the rocket , shall be some what lesse then the rowler , to the en● that it may enter easily into the ca●●toush or coffins . Also it shall be made hollow , 〈◊〉 deepe as the broch is long , as dot● appeare at P , because the rocket mu●● be loaded , the broch being in it , 〈◊〉 ●●r the massif marked with F , shal be 〈◊〉 the same bignesse as the charger . ●he 2. other ●owlers noted G , G , or 〈◊〉 make serpents , as shall be instru●●ed hereafter , and the bodkin H , is 〈◊〉 make holes through your starres , 〈◊〉 shall follow , the Lanterne I , is pro●er to charge the composition into 〈◊〉 rockets . The figure noted K , is 〈◊〉 cartoush or coffin ready to bee ●harged , and by the figure L , is re●resented a rocket quite made . This ●ethod prescribed may be obserued 〈◊〉 all sorts of moulds , for if you ●ould make one lesser , as of halfe an ●●ch , the calliber or bore , then the ●●ngth must be 3. inches , which is 6. ●alfe inches , the breech shall enter 3. ●uarters of an inch , the broch shall be 〈◊〉 inch 3. quarters long , & the rowler ●●r the cartoush shall be half a quarter of an inch ; but if you make the calliber of two inches of diameter , 〈◊〉 the mould be 12. inches in length the breech shall be 3 inches , and th● broch 7. inches of length ; and so fo● all the other parts appertaining to th● mould . Now followes the descript●●on and manner how to make a ro●●ket . CHAP. III. How to make a flying rocket for the Ayre . FOr to make the mixture or composition of all middle-sized rockets , take a pound of gunpowder finely ●uised and boulted with two oun●●s of charcoale-dust , mingle these ●ell together , and try one rocket , ●hich if it breake , adde more char●●ale dust to the composition ; but the rocket doe not ascend , beeing ●●eak , adde more powder dust boul●●d as before said ; and so shall you make your composition stronger 〈◊〉 weaker according to your desire ; ●●stead of charcoale , you may put se●●coal● , saw-dust , or any other lik● thing , so that you keepe a Medium not putting too much nor too little which thus you shall know if th● rocket mount not , you haue adde● too much coledust ; but if it break● you haue not put coledust enough for the charcole-dust which you p●● into the powder dust , is onely to m●derate the violence of the powder and to make the rockets tayle appe●● more beautifull ; which sea-coa●● doth as well as charchoale , and 〈◊〉 charge the rocket with this comp●sition as it ought to be many rul● are required or to be obserued ; and 〈◊〉 of al that in charging the rocket , yo● put not too much cōposition at on●● in the cartoush or coffin ; 2. , that 〈◊〉 ●e beaten with a mallet 3. or 4. good ●●rokes ; and then put new composi●●on thereupon , beating it again with ●●lowes as before ; and thus putting 〈◊〉 at seuerall times the quantity of ●ne or two spoonefulls , at each time ●eating it well with a mallet , and let ●ot the cartoush bee filled higher ●hen the mould , but being iust full ●hereto , then double downe halfe of ●he paper with the bodkin beating it ●as ●he composition before ) & at last ●ierce 2. or 3. holes with the same ●odkin to the powder to giue fire , to ●ither stars , serpents , or faucessous , as ●hall be taught following ; and these ●oles are represēted by C , let the rest of the cartoush be cut even with the mould , and thus must be made all ●orts of rockets , great or little ones . ●t is to be noted , that the composition prescribed is fit ; for all sorts of rockets , great or little , but onely it must be made weaker for great one● then for little ones , adding more charcoale to it , for the whole secret is in making the composition neither to strong , nor to weake , and not as al writers hitherto haue thought , following each one the others errors , thinking that the true manner of making excellent rockets , is to put many ingredients into their compositions , wherein they haue all erred absurdly ; and last of all Master Norton , for absolutely the best composition is , that which is made of fewest ingredients ; and the rockets made thereof may be kept many yeares , and good at all times . CHAP. IV. How to make moulds for Rockets for the ground . THe mould must bee otherwise made then the precedent , because such violence is not required in these , as in those which moūt into the ayre , but onely of somewhat longer continuance ; and therefore these measures following shall serve at all times , neuer being made bigger nor lesser , but alwaies the same for all occasions . Let the calliber behalf an inch , the diameter ; and 5. or 6. inches of length ; and the rowler for the cartoush shall be foure lines in diameter which is the third part of an inch , and the rowler to charge withall somewhat lesser to enter without spoyling the cartoush : next let not the broch be longer then 3. quarters of an inch ; and the breech shall enter halfe an inch into the mould ; and the cause of this great alteration is , that the rockets which mount into the aire , haue need of great and violent strength ; and by consequence last not long , but wee desire that those vpon the ground may dure a long while , with a gentle motion , which shall be easily performed , the rules following being obserued . CHAP. V. How to make the composition for rockets vpon the ground . THis is the easiest composition of all others , for in this shall be nothing required , but onely Gunpowder well beaten and boulted , so that it be as fine as flower , and then fill your rockets by little and little , well beating it into the cartoushes or coffins with a mallet , as the rockets for the ayre , and being full within an inch of the brim of the mould , double downe one quarter of the paper , or cartoush , beating or pressing it with 3. or 4. good strokes of the mallet , and then with your bodkin , pierce a hole to the composition ; which done ; put into the cartoush about the charge of a Pistol , of good gunpowder , and then double down the one halfe of the cartoush , giuing a gentle blow or two with the mallet , & with a smal cord , or big line , choke the rest , and what shall rest aboue the choaking , cut it off , leauing a piked point , as appeareth by the figure E , in the 3. chapter of this Treatise ; and your rocket being thus finished , and primed with a little wet powder , and layd a drying , shall be ready for all occasions . CHAP. VI. The manner how to make Serpents . THe Serpents are to bee made eyther of the composition for rockets on the ground , or of that for the ayre ; for being filled with the composition fitting for the grouund ; they will spreade and sparkle liuely in the ayre , but if filled with the other composition , they will fall weaving neerer together ; notwithstanding eyther sort will shew divers pleasing actions in the ayre , being made as followeth . Let the cartoush be about foure inches long and rowled vpon a rowler , somewhat bigger then a goose quill , as is represented by the precedent figure G , in the third chapter , the paper ought to goe about the rowler nine or ten times , and then choaked almost in the middle , yet leaving a little hole to see through , and the longest part shall be filled with the composition , but the shorter with fine grayned powder , and choaked close ; also the longest end must bee halfe choaked close ; as doth appeare by the figure F , chapter third but if you desire not to haue them wamble in the ayre , then let them not bee choaked after the composition , but as doth represent the figure G , both which figures , F , G , represent Serpents quite finished . CHAP. VII . How to make golden rayne . MAny there are ( specially in France ) who make rockets , yea and boast that they are perfect therein , who know not what golden raine is , but thinke it to be some other thing then it is ; wherefore to put them out of doubt , and to teach all others who desire the knowledge thereof , I will here set downe the description and maner how to make it . Take goose quils , and cut off the hollow ends , leaving them as long as may be , as the figure K , doth demonstrate third chap. and fill these quils with the composition of rockets for the ayre , at the last stopping euery one with a little wet powder to keepe in the dry powder , & crowning a rocket with these ( as shall be taught following , chap. 12. in its true place ) will shew a most glorious & pleasing raine , which some hauing in times past seen , haue called it golden rayne for the beauty thereof , but of later times it is more commonly called golden hear : many beautifull and strange figures may be represented in the ayre , with this maner of rayne , as shall follow in the 13 chap. treating how to represent many sorts of figures in the ayre with rockets . CHAP. VIII . The manner how to make Starres . ALthough that there bee many sorts of compositions for stars , yet I will set downe here but two of the best ; all the rest being nothing worth , but friuolous and expensiue : the fi●st and best sort , is to be made of dry powder , and the other of moystened powder as followeth . For the ●●sort take 1. pound of saltpeter , halfe a pound of brimston , and a quarter of a pound of gunpowder dust , al these being plu●ri●ed & mingled together , wrap the quantity of a nutmeg in tow in a linnen rag , or in paper , and bind it fast , as appeareth by the precedent figure H , chap 3 ▪ and to prime them , you must pierce them with the bodkin , and put stoupell or cotten wieke dipt in powder through them ( which shall be made as followeth in the 11. chap. ) and to make the second sort , take 1. pound of salt-peter , and halfe a pound of powder-dust , and halfe a pound of brimstone all these wel pulverised and mingled together , moysten them with eyther oyle of petrole , or els wi●h fair water onely , to make a past of them , wherof make little balls about the bignes of a musket bullet , and whilest they are moist , rowle them in dry powder dust , then let them dry , and then may you employ them at your pleasure , without further trouble ; for the last powder in which they are rouled , doth serue for their priming . This last sort of starres doth not make so beautifull a shew in the ayre as the others , for falling downe , the flame of them takes the forme of a lampe , hauing no force to expel it like wings as the others doe , for the flame of the others blowing out of the two sides pierced , make it stretch in length , and by that meanes shew greater in the ayre . CHAP. IX . How to make Starres giuing great Reports . TO make Starres , that each one shall giue a report like a Pistoll or bigger gunne , you must first make little saucissons ( as I taught in the chapter following , but the saucisson need not to bee couered with chord ) and being made and pierced , take as much of the former dry composition , and bind it to the end of the saucisson which is pierced , making a hole through the composition , and passe a piece of stoupell or cotten-wieke as in the other starres ; but if you take of the moyst composition , you may onely leaue the paper hollow at the end of the saucisson , fitting to contain the quantity of composition required , putting a little grained powder before , and prime these starres as the others , of the same composition ; these starres are very troublesome and little in vse , because that a great rocket can carry but few vp into the ayre , and by consequence worke but a small effect , and moreouer they are very long in making . One may make Starres in the same manner , which ending , turne to serpents and others as shall please the workeman . CHAP. X. The manner how to make Saucissons . IN this chapter , my intention is not to treate of the saucisson which flyes into the ayre , but only of that which stands firme in great workes , or else which is applyed to rockets , which thus is made as followeth ; you must haue a rowler of such bignes as you desire to haue the concauity of your saucisson , wherupon rowle as much paper as you please , and then choake it at the one end ; which done , fill it with grayned powder , & choake the ●ther end also , and cover all the sau●isson from the one end to the other , with small chord , as doth represent ●he figure I. chap. 3. and glue that ●ord with strong glue all ouer , and when you would make vse of these ●aucissons , pierce them at the end with your bodkin , and put into the ●ole a quill filled with fine powder dust , which shall serue for a portfire , and the other end of the quill shall passe through a board , whereupon you meane to fasten them , and shall enter into a portfire in the other side of the wood , which shall be fastned all along the wood , and so may you fasten what store you please neere together , or farre asunder , this quill is represented by the figure L , and by this meanes one end of the 〈◊〉 fire beginning ; all the whole ran● of saucissons will giue their repor● one after the other . But if your sa●●cisson is to be applied to a rocket , shall onely be pierced at one end , a●● primed with a little grained powde● and fasten it to the top of the rock● either with paper , parchment , or an● thing else , so that the rocket , endi● the saucissō , may take fire ; so shal yo● not faile of your intent or designe . CHAP. 11. How to make Stoupel or preparing of your Cotten wieke . TO make Stoupell , not the meanest , but the best that may be made to giue fire ( which in ●per tearme is called estoupel●●g ) to all manner of fire-workes . 〈◊〉 Cotten-wieke , and double it ●oft as shall bee needfull for your 〈◊〉 , as if it were to estoupel your fie●ances ; then double it eight or ten ●●es , and also for the stoupeling of great rockets ; but if it bee to 〈◊〉 through your starres , then 4. 〈◊〉 threds shall suffice ; so hauing do● led your cotten wieke fitting for yo● purpose , steepe it in faire water , 〈◊〉 then wring it betweene your han● and take gunpowder dust , witho●● other mixture , and steepe it in 〈◊〉 water , not putting too much wat●● nor too little , but onely till it app● like durt , and then put into it 〈◊〉 cotten wieke , and there turning a● winding it till it hath sufficiently 〈◊〉 powder in euery place and 〈◊〉 cell , then draw it out , putting a 〈◊〉 dry dust vpon it , & hang it a dry● in the sunne or els-where , and 〈◊〉 being dry , you shall haue the 〈◊〉 excellent stoppel that may bee ma● for your vse at al times , leaving 〈◊〉 all such ingredients which ignora●● ●●●●eme so highly of , as Aqua-vitae , 〈◊〉 wine , strong lee , quick-lime , ●ger , vrine , and diuers others , for ●ich I would not lose so much 〈◊〉 time as to repeat them , but 〈◊〉 goe forward , and shew how to 〈◊〉 all the parts of a rocket . CHAP. XII . The manner how to assemble and set together the parts of a rocket . WHen the rocket is finished and taken out of th● mould noted A , in the figure of the 3 chapter , an● the rocket is noted with the letter ● in the same figure , then must yo● ioyne to the end of the rocket , which is not choaked an empty cartoush 〈◊〉 coffin , much bigger then the rocke● is large , which is represented by 〈◊〉 in the same figure , in this cartous● you shall put your serpents , golde● rayne , starres , saucissons , or othe● things at your pleasure , but first of 〈◊〉 you must put in the bottome powder dust ; onelie enough to couer the bottome of the large cartoush ; and then put the serpents with the ends downeward which are to take fire ; and likewise the golden rayne in the same manner , but it is the custome to put a little powder dust amongst the stars ; this cartoush being thus filled , couer it with a single piece of paper , and afterward paste vpon that a picked cap made also of single paper , and to make perfect your rocket you must binde a rod of such length and waight , that being bound to the rocket , it must weigh down the rocket on your finger being neere to the rocket , and then stoupel your rocket , ●hat is to say , prime it with cotton-wieke , and it is thus finished either ●o fire or keepe . This method is fit for all sorts of rockets , great ones or little ones , except that little ones must haue the vpper cartoush no bigger then the rocket , onely to hold halfe a dozen of starres or serpents , or one saucisson for so much as many beeing fired together , great confusion would happen , if great rockets should bee put together , and not prepared otherwise . CHAP. XIII . How to represent diuers sorts of figures in the Ayre with Rockets . THe first and most rarest is a tree or fountaine , and is made putting many little rockets vpon one great rocket , passing all the rodes of the little ones through the large cartoush of the great rocket , and if the little rockets take fire while the great one is mounting vp , they will represent a tree : but if they take fire when the great rocket is turning downe againe towards the ground , then they will bee like to a fountaine of fire , and if there bee two or three little rockets hauing no rods amongst others they will make divers motions contrarie to the rest most pleasing . The second figure is the golden rayne ; and that is made when manie quils filled ( as aforesaid ) are put vpon a great rocket : for certainelie all those quills taking fire will seeme like a great shower of fierie rayne to those who are vnder it , but to those who are a side of , like beautifull long haire . The third figure are Starres , which are represented putting onelie manie Starres vpon a great rocket . The fourth are serpents which are alreadie described , but to make all these prescribed figures varie , you may tye manie little ones together by the ends , which take not fire , the quils , or serpents may bee tyed in like manner ; but the thread wherewithall they are tyed , must be at least two or three inches long , betwixt each one , and you shall see diuers sorts of figures in the ayre , changing themselues into much varietie . CHAP. XIV . How to make fierie boxes . THe fire-boxes are made of many rockets being put into a large cartoush the bottome whereof is couered with powder dust , and pierced in the middle to passe through a port fire or stoupell , to giue fire to the rockets within the cartoush or coffin , which flying out , leaue the cartoush most commonly whole and vncracked , those boxes are onely to be cou●red with a peece of paper , that the rockets taking fire may flie out without resistance ; and the reason why they are to bee couered , is because if manie be made one neere to another , they should not take fire all at once . CHAP. XV. How to make fierie Lances . THe vse of these lances is alwaies required in all great fireworkes , wherefore here shall be described the manner of their making . Their cartoushes are to be made as other cartoushes for rockets ; onely these may be made of pastbord , and glued as they are a rowling , if it bee to make great ones , but if for little ones , then paper shall suffice , the cartoushes being made , let them be filled with the dry composition prescribed for starres in the 8. chapter of this treatise , and prime them with wet gun powder , & the lower end of the cartoush is commonly stopped with a peece of wood , to the end that they may bee nayled or stucke when they shall bee needfull , the wood being about two inches long out of the cartoush . CHAP. XVI . The manner how to make Rockets for the water . TAke fire & water being two elements of contrary qualities , the one to the other cause the rockets which worke their effects in or vpon the water to appeare to the spectators more beautifull , and seem more rare and admirable , although that all sorts of rockets being fired , will worke their effects vpon or vnder the water , but this onelie is to be noted , that those which are made for the ayre , or for the ground , haue such strength and force , that beeing once kindled and cast into the water , they will consume themselues there , and not rise vp swimming as those which are made artificially for the water as followeth . To make good rockets for the water , the calliber of the mould ought to bee one inch of diameter , and in length eight inches , the breech to enter one inch , hauing no broach ; the rowler for the cartoush shall be three quarters of an inch of diameter , and the charger shal be somewhat lesser then the cartoush being ready to bee filled as the others . Of two sorts of composition , you shall make one as followeth ( if you desire to make a great fierie tayle appeare vpon the water , Then take one pound of salt-peter , halfe a pound of powder-dust , halfe a pound of brimstone-dust , and two ounces of charcoale-dust : but if you desire to haue it to burne cleere like a candle vpon the water , then take one pound of salt-peter , halfe a pound of brimstone-dust , and three ounces of powder-dust , all these must be well mingled together , as all other compositions ) and with either of these compositions , fill your cartoush , and ioyne to the vpper end a saucisson , and then couer it all with melted pitch , rosine , grease , or painting , to hinder the water from spoiling the paper : and to make it float and swim vpon the water , bind a rode about two foot long to it as to the others for the ayre . Now if that you desire that this Rocket charge his actions vpon the water , swimming now vpon the water , and now vnder the water , put here and there powder dust , powre to the quantity of halfe a spoonefull as you charge it ; also may you make it change colour , now red and then white fire , onely changing the composition in filling it , and so the industrious may adde many changes and diuersities as they shall thinke fit : but if you are to make a great number for a great fireworke , then the plainest are the best , onely filling therewith the first composition ; but they must be filled two or three fingers breadth with fine powder dust , to make them flye farre off , or else they must be made like rockets for the aire , and afterward charge them foure inches with composition made for water ; but to be the more certaine , it is best for those who haue great works , to make to trie one or two before they finish many , that the better they may attaine their designes , which with eie they may accomplish , if the rules prescribed be obserued ; for as I think there is not one rule neglected appertaining to the fabrication of these fireworkes prescribed ; and now I will set downe the manner how to make all sorts of ballouns and flying saucissons , which are absolutelie the beautifullest parts of fire-works for pleasure , and after them I will describe a braue fireworke for pleasure with the manner how to place , dispose and range euerie peece and part thereof , to make their play in order . CHAP. XVII . How to make Girondells or fierie Wheeles . A Girondell ( or as some call it a fierie wheele ) is often required in great or little fireworks for pleasure , and therefore I haue thought fit and necessary to set downe their description , as well as of al other parts of fire-workes : for according to the application of the Girondels in a Fireworke , one may iudge of the Enginiers industrie , for being well applied , they adorne very much a fireworke , and being ill applied they spoyle all . And to make them , you must make wheels of wood as bigge as you pretend to make Girondells , and vnto those wheeles bind fast rockets of a meane bignesse , binding the mouth of one towards the tayle of the other , and so continuing vntill you haue filled your wheele quite round , which done , couer them with paper pasted very curiously about them , that the one taking fire , they take not fire altogether , but the mouth of one shall be left vncouered and ready primed , fit to take fire , the which ending shal giue fire backward to the next , and so one to the other , euery one his turne : there may bee bound fierie Lances to these Girondells either vpright , or neere overthwart , which will shew diuersitie of fire the wheele turning : also there may bee added to these wheeles boxes of fire , prouided that they be artificially applyed in such manner , that they ballance the wheele equally , although the proper vse of girondeles , is onely to garnish the angles of a great Fire-worke , without much trouble , for that confusiō is too frequent in fire-workes ; and therfore it shall be expedient to auoide the multitude of fire-workes too neere compacted together ; but placing them as much distant as conueniently may be admitted , by which meanes you shall bee the better able to attaine your designes pretended . CHAP. XVIII . The manner how to make Ballouns . THe ballouns being the perfectest part of all artificiall fire-workes for delight , I thought best to set their description heere apart from the others , to the end that the learners might the better and more easier attaine to the knowledge and perfection thereof ; and being that I haue already described the morter , which is represented by the figure A , following , I will onely referre the reader to the second chapter of the first Treatise for warres , where hee he shall find sufficient instruction for the making of the instrument . But to make a Balloune shall be required a woodden rowler , which is represented by the figure B following ▪ this rowler must be of such bignesse as you desire to make the inside of your balloune ; vpon which rowler , let there bee rowled as many pastbords as you shall think sufficient for strength being well glued together and choake this cartoush at the on● end , leauing a little hole for a portfire as shall follow , and glue it in . This portfire shall be made iust like vnto ● rocket for the ground , but only tha● the composition may be somewha● slower ; as for the ayre , and to know of what length this portfire ough● to be , it shall not bee amisse t● try a balloune filled with earth ; then your portfire being well fastned to the balloune ; place all your serpents within it , putting nothing else amongst them , but onely one or two saucissons , to breake the balloune on high , when the serpents be all on fire , these saucissons must be made of the length of your serpents , and your serpents may be of the bignes of your rockets for the ground before prescribed , but not so long , and they may bee filled with the composition either for the ground , or for the ayre : but it is to bee noted , that they must bee primed with the composition for the ayre , pressing verie stronglie the priming powder into the throat or gorge of the serpents , if it bee put in drie : but if that we●te , then onely with the end of a sticke , or else with ones finger put in a little ; as for other serpents and the two saucissons shall haue their primings somewhat longer then the serpents , to the end that all the serpents may be a fire before that the balloune breake . The serpents being not made too long , one may put two or three rankes in one balloune , as appears by the figure C , or one ranke of serpents , and over them many Starres ; all these things being thus disposed within the cartoush , let it be choaked at the other end ; and then prime the ballouns with cotten wieke steeped in gunpowder as the stoupel before spoken of ; but this cotten must be well fastned to the end of the port-fire with strong packe-thread , which done , charge the balloune in your morter , as is taught in the 6. chap. of the first Treatise ; and you may shoot it when you please . This balloun is represented perfect by the figure D , but if you will fill your ballouns with stars only , another manner of proceeding shall be required ; for as you put in your starres into the cartoush ; let there bee powder-dust mingled amongst them here and there to giue fire to the starres , and to breake the balloune being vp in the aire . There is also another sort of ballouns to be made , but the expence of making thē is so excessiue , that few or none will be at the cost , yet the description shall now follow . In stead of serpents made of paper , you may haue them Iron about the bignes of your little finger , and one inch and a halfe of length , or two inches ; and neer to the bottome there must be a double bottome in the middle whereof there shall be a little hole , that one may fill the space between the two bottoms with corned powder , and the rest is to be filled with a composition somewhat slow , the diff●rence betweene those of Iron , and the former of paper , is that many Iron ones may bee laid in a lesser space ; but in stead of a pastbord cartoush , there must bee had a woodden box , made by a Turner , and couered with canuas and glue ; the portfire must be made also of Iron , like to a little hat , hauing in the bottom two or three little holes to giue fire to the serpents ; but for the expence of one of these , there may be made halfe a dozen of the others , nay neere a dozen , wherfore I would wish no man to trouble themselues with this sort , vnlesse it be for the pleasure of some great Prince . CHAP. XIX . How to make flying Saucissons . THe method which must be obserued in making flying saucissons , is most easie , prouided that one knoweth already the manner how to make the common sort before prescribed , for the cartoushes are to bee made all alike ; onely excepted that those which are for flyers , be somewhat longer then the others , they are to be charged in like maner as the others , but the corned powder being put in , there must also be a litle powder-dust put after it , and beaten with a mallet , as the rockets for the ground yet let not more then the thicknesse of a finger be of dust-powder , and then choake it almost quite together leauing onely a hole as big as a small goose-quill , to which you shall put a little wet powder-dust for priming . They may be made otherwise , as followeth , which will make a more beautifull shew ; first of all , you must charge the cartoushesas the common saucissons , and then choake them as the common leauing onely a little hole to take fire at , or if the hole chance to stop quite vp , open it with a bodkin , but the saucissons being charged and choaked , there must be part of the cartoush left ouer and aboue that which is charged , which part shal be filled either with powder dust , or els with composition of rockets for the aire beaten wit a mallet , as before mentioned , I thinke it shall be needles to tell you that they ought to be couered with chord , being that it is sufficiently demonstrated before , it is to be noted that the saucissons which haue the powder within the choaking , doth turne wonderfully in the aire , but the other sort which haue the composition after the choaking , flye vp like to a rocket , almost carrying a great tayle after them but the tayle of the others sheweth but very little , they are both sorts represented by the figure E , in the 18. chapter . CHAP. XX. How to make short Gunnes for the Saucissons . HAving already treated sufficintly and amply of the fabrication and making of the Morter , in the imitation whereof most easily may bee made Canons to shoote flying Saucissons very high in the aire , making them of the one or the other matter or stuffe prescribed for the Morter in the second chapter of the first Treatise , but the powder sacke needs not , and the touch-hole ought to be in the middle of the bottome ; also it shall be necessary that euery Canon haue a little breech to passe through a peece of wood , wherein they may be fastned , so that a port-fire may be layed from one to another , these are represented by the figure F , in the eighteenth chapter . CHAP. XXI . The manner how to dispose and build a great or little Fire-worke . IT is a custome and vsual thing among the braue and skilfull Painters ; 1 to teach their apprentises how to draw limbs , or members , as the eye , the nose , the mouth , the eare , the hand , the foot , and afterward the whole bodie ; and in like manner , the most learned and famous Philosophers , beginning their schooles , teach their disciples what is materia , forma , & primatio ; and afterward , totum compositum ; and to imitate them in this Treatie , I haue taught the one after another , all the parties required are necessary for the composing & building of a beautifull fireworke for delight , hauing begun with the rockets for the ayre , afterward the rockets for the ground , the saucissons & rockets for the water , and following the ballouns and flying saucissons with all things belonging vnto them ; and to auoyd falling into the old prouerbe ( Ex omnibus aliquid , & in toto nihil : to know somthing of euery thing , and nothing perfectly ) I haue here set downe after all these parts the description and manner how to assemble , build and dispose any manner of artificiall fireworke great or little : and to begin , you must first cause to be built a scaffold trianguler , square , round , or of such forme and bignes as you shall desire to haue your Fire-worke , your scaffold being built , dispose thereupon your statues or figures which shall be prepared for it , let them be made of osiers , and couered with paper or canuas , and curiously painted as here is represented in this figure . Mountains , buildings and many statues , all which are to be supposed , onely osiers and paper , or canuas painted , your figures or statues thus disposed vpon your scaffold , round about the flore therof , shal be layed your saucissons , being already fastned to peeces of timber , and to the pillers of your scaffold or raile , shall be fastned your firie lances one right vpward , and the other flat along , each distant , the one from the other about halfe a foot ; and vnder the firie lances , let there be nayled a ranke of boxes of fire , which shal be ranged vpon peeces of wood as the saucissons ; all your fireworkes being thus disposed , you may place in the side which is of least esteeme , your partments of rockets made like vnto square chests , or long boxes , of such bignes and length as shal be required to hold those rockets which you meane to place in each one : bu●1 these boxes must haue a false bottom full of holes for to passe euery rod of euery rocket apart , and hauing filled let the boxe ( which by proper name is called a partment ) be couered with a leafe or two of paper pasted close ; but to giue fire to the rockets , let there be made a hole thorow the partment , through it shall passe a little peece of stoupel , or cottē wieke and giuing fire to that , all the rockets within the partment , fly out , and in the same manner shall you giue fire to all your fierie lances with a stoupel going from the one to the other ; and as for your girondells , you shall giue fire to them with a match , as you desire that they should play , and by this meanes all your fire-workes shall begin to play at once , except those parts which shall bee reserued without priming to be fiered by the hand , as best shall seeme to the artist or enginier , and so the industrious shall not faile to accomplish his designes , obseruing all the rules prescribed ; which being at large laid down I will goe forward to the next chapter , and there shew how to make a most pretious vnguent for all maner of burnings , as well of common fire , as of artificiall fire , if by hazard anie mischance arise , CHAP. XXII . A most pretious vnguent for any burning . LEt no man wonder if ( hauing ended this Treatise of fireworkes ) I take in hand to describe a little part of Chirurgerie , whch I confesse to haue taken out of a Treatise written by Thybourel , a Chirurgion of Loraine , and hauing made experience of this vnguent diuerse times as well for burnings , as that for other accidents , I may say with boldnes & truth , that there was neuer the like secret of this kind left to posteritie , specially against hurts come by fire , and which leaues lesse scarres after the healing of the places wounded , and therefore I haue set downe the very words which Thybourel hath written in the last chapter of his 4th . booke , intituled Recueil de plusieurs machines militaires . Take fresh hogges grease or lard , as much as you please , and boyle it , taking off the skim vntill there arise no more skim ; then set the lard three or foure nights in the ayre abroad , after which it must be washed in running water , to take away the saltish nature , and also to clense it white , then melt it , and keepe it for your vse . Bacon may serue in stead of lard . Otherwise . The white of an egge or fresh butter being mingled together and well beaten to an oyle are excellent . Another sort most excellent . Take a stone of vnslacked lime ( or otherwise called quicke lime ) and let it dissolue in cleere water , and when the water is setled , powre it gently out from the lime through a linnen cloth , then put as much sallet oyle as you take water together , and beating it all to an oyle , you shal haue a most excellent vnguent for all kind of burnings , neither of these vnguents haue any scarre , but are precious remedies for the afflicted We haue seene Impostures ▪ couer sores with this water alone , but obseruing superstitious ceremonies , saying vaine prayers , but we assure the posteritie , that the water onely is sufficient to heale wounds and s●res , onely washing them with it , and couering them with a linnen cloath wet in the same water , without any superstition , it doth modifie and percute , by which it doth supply nature , and doth heale sores better then our ordinary vnguents . Thus may you see how this braue Chirurgion that set forth to the face of the world the perfection of this vnguent ( which cannot be sufficient-praised ) confirming by his own confession , that the Chirurgions do not vse such good remedies in their shops and ordinarie operations ; wherfore I haue set downe his owne words , that no man may esteeme mee inuenter of Calumnies , against the practitioners of Chirurgery , nor any others , as many now adayes seemes to write with serpents tongues , stinging vertue on euery side , against whō viperous venoms patience is the only antedote , leauing them to sweat , vexe , and torment themselues in their insatiable rage , and to end my discourse touching the perfection of this vnguent , I will assure all these who shall haue neede and make vse thereof , that they shall find in operation what I haue here set downe in description . A Treatise of practicall Geometrie . TO satisfie diuers of my friends and yeeld to their desires ( whose treaties haue bin such powerfull commands to me , that I haue beene constrained to lay aside and forsake my own proper will and follow theirs , I haue set forth this little Treatise of practicall Geometrie to the view and censure of the world , which I acknowledge to be vnworthy of so many singular and industrious wits , as yearly spring vp in this Iland , and the adiacents thereunto , notwithstanding I haue giuen way to their requests for their priuat contentment , and to assure the world that I haue nothing , no not my owne will proper to my selfe , but that I will follow as neere as possible I may the precepts and documents of that ancient , wise , and diuine Philosopher Plato , who saith , Non nobis nati sumus , sed patriae & amicis ; we are not borne for our selues , but for the seruice of our countrey and friends : then for the satisfaction of my friends and seruice of those who will accept these my labours , I haue cleerely and in few words set downe the manner how anie man ( who hath neuer so little studied Geometrie ) may take any distance , or heighth , depth , or breadth with two little stickes , yea e●en strawes , being laied a crosse , also I haue set downe a method how to take any kind of heighth , distance or depth , with the Sector without anie arithmetike or rule thereof : and also by the sines tangents and secants , the whole beeing very portable , to refresh the memorie , & to strengthen and augment the knowledge of those who ( for want of practise ) haue not the perfect vse of those instruments : then first of all I will set downe the manner how to accomodate and dispose the sticks , twiggs , or strawes for the measuring of any distance . The method how to make the Crosse. HAuing two stickes , the one long , and the other somewhat short as are represented in the figure following by CF , and DE , then marke vpon the sticke CF , points the one distant from the other precisely , halfe the length of DE , and let there be a hole made through the sticke DE , so that it may slide vpon CF , from end to end , and you shall know the two parts of the crosse by these names , the longest part CF , shall be called the index , and the shortest DE , the crosse . Now if you haue any heighth to take , then fasten to one end of the crosse , as to D , a perpendicular or plummet , and for the more easie and iust operation , you should haue a foot to support the crosse ; the instrument being thus prepared , you may measure with great facility either heighth breadth , or depth , as followeth . PROPOSITION I. How to take a height accessible . LEt it be proposed to take the heighth of the Tower AB , to the base or foot whereof one may easilie approach ▪ dispose the crosse of your instrument in such sort that DCE be of equall distance there one from the other ; as thus , settle your crosse vpon the first point of the index ; then setting the instrument to your eye , goe either neerer , or retire far●her from the obiect you desire to measure vntill you see A the highest part thereof by the two extremities of the crosse CD , ( the inden being paralled to the earth ) which will happen in the point C , and not else-where : that being measured , will be alwayes the iust height of the Tower required , onelie obserue that you must alwayes adde to the distance betweene you and the Tower the length of the foot , which supporteth your instrument , and so you shall haue preciselie the heighth required : for scarce euer will it happen , that the instrument may be placed leuell with the base or foote o● the height required , but if that should chance to be , then the extremitie of the index C would ariue in the point G , and so nothing to be added , but onelie measure the distance betweene G and B , and that would be the iust height required ; but if it chance that you may not plant the instrument in the point C , by reason of some inconueniences which may happen retire further backe , and put forward the crosse to the second point of the index , and then accord your visuele lines to see the point A , ( the index alwaies being paralel to the ground ) which then will happen twice the height required , distant from the foot thereof : but if it happen that going backe you ascend anie little mountaine , or descend into any little valley , you are then to obserue some point in the wall of the Tower , which the index shall direct you to by the line visuel , & adde onlie the height thereof vnto halfe the distance twixt you and the Tower , and that shall be the height required most exactlie : and thus you shall neuer faile in your operations . PROPOSITION . II. How to take a height inaccessible , or one height vpon another height . SVppose the altitude BC , to be required , to the foot whereof one may come may come no neerer then to the point D , then at the point D , accord your visuell lines in B and C , the index being alwaies leuell with the ground and the crosse fixed vpon the first marks or point of the index , then set a marke there in D , and going backe towards F , as farre as E , and put forward the crosse to the second point of the index , and then direct your lines visuel againe in B and in C which will arriue in E , and not elsewhere , then measure the distance betweene DE , which will be the altitude precisely required , but if you desire the heighth of the Tower B , and mountaine leuell with the foote of your instrument , then you must adde the length of the staffe , which supporteth it as in former obseruations . And to haue the altitude A B vpon the top of BC , you must take two other obseruations in FG as before , setting your instrument in F , the crosse being fixed vpon the second point of the index , and direct your visuell lines in A and in C , and then set vp a mark in F , and goe backe , putting forward the crosse to the third point of the index , and direct your visuell lines againe in A and in C , which will happen in G , and not elsewhere , then measure the distance betweene FG , which shall bee equall to the altitude of the Tower AC , and ha●●ing taken already the altitude BC , you may verie easilie substract the little altitude BC from the greater Altitude AC , and then will rest the altitude AB , which is required . PROP. III. How to take any distance vpon a place accessible or inaccessible . IF it were proposed to take the distance AB , and that the place were accessible onelie in the middle vpon the ●●ne CF , then dispose your instrument as before the crosse placed vpon the first point of the index , and going forward or backward vpon ●he line CF , direct your visuel lines 〈◊〉 A and in B by the two extreami●es of the crosse , the end of the index resting against your eie , then measure the distance betweene you and the point F , and that shall be iust half the distance required betweene AB , but if the place be inaccessible , so that you may not approch neerer then the point D , put forward the crosse to the second point of the index , & then direct your visuel lines to AB , and leaue a marke at D , and put forward the crosse one point more , and going backe vpon the line DE , vntill you may direct your visuel lines by the extreamities of the crosse againe in A and B , then measure the distance between DE , and that will be halfe the distance betweene AB , and so may you operate going backe , and putting forward the crosse . PROPOSITION IV. Another manner how to take a distance inaccessible . SVppose the distance AB to bee taken , and that B is the neerest place that may be required , then there must be set a marke , and withdrawing backward in a straight line towards C , and there againe plant another marke at C , then going right towards one side , as towards F , counting your places equall to the number which you haue alreadie found B and C , and there direct your visuel lines in BGC , as in this figure at D , leauing there a mark , goe straight along towards F , not moouing the crosse of your instrument , and going along make trial where your visuel lines may be directed again in A and in C , which will be in the point E , and not else-where , then leaue there a marke , and measure the distance betweene DE , and that shall bee the distance which you require , which is AB , the demonstration of this proposition is grounded vpon the second and fourth propositions of 6 of Euclide . PROP. V. How to take a distance onely vpon a line parallell to it . LEt the distance AB bee required , the which may neither bee seene , nor come neere vnto , but onelie vpon the line or banke CK , then vpon that banke draw out a straight line with markes , as the line CK , paralell to the wall AB , and set a marke in K , then goe backe towards D , and direct your visuel lines in B and in K , by the extreamities of the crosse GH , then leauing the crosse in the same state and a marke at D , withdraw your selfe further back towards C , vntill you may direct your visuel lines to A and K , which will happen in C , and not elsewhere , and leaue there another marke , then measure the distance betweene CD , and the same shall bee the breach AB , equall to CD , and the demonstration of this proposition is grounded in the 29. and 33. propositions of the 1. of Euclide . PROP. VIII . How to take the depth of a valley . TO take the depth of a Valley , there is somewhat more difficult then in the former operations , because there are more obseruations to bee made , and to begin you must from the point B obserue in some place opposite a ●a●ke leuell with the horison as A , the leuell whereof you may easilie take at this instrument , as is taught in the second proposition by the helpe of the plumbet : then from the point B , take the distance BC , as in the fift proposition , or else mecanikelie , which being done , direct your visuel lines from B to A , and to C , and leauing the instrument in same state , turning your selfe about , frame the same angle vpon the plaine , which will be FBH , then plan● markes vpon the lines BF and BH , and vpo● the line BH , count as many paces or fathoms as you shall haue found betweene B and C , and at the end of your paces ▪ 〈…〉 marke , which will bee at E , thi● being done , dispose your instrument to make a right angle , placing the crosse vpon the ●irst point of the index , for the crosse maketh alwaies a right angle when the crosse is vpon the fift point . The instrument being thus disposed , walke vpon the line BF , vntill you may direct your visuell lines ( by the extreamities of the crosse ) to B and E , or els to FE , which will happen in D , and no where else , then measure the line DE , and it will be equall to the depth required G C , the demonstration of this proposition is grounded in the 26 , of the 1. of Euclide , or vpon the equalite of the two triangles BG C , and BDE , which are both equall and equall angles . Although this operation be somewhat more obscure then the others , yet I thinke that it is sufficiently explained , and therfore I will goe forward to the vse of the sector . PROP. IX . The manner how to take either distance or altitude with the Sector . SVppose the altitude AD were to be taken to the foot whereof you may approch open the Sector 45 adding to it the sights then going forward or backward vpon the line DI , vntill you may see the highest part of the altitude A , through the two vpper sights , the inferior branch of the Sector , being paralell to the earth or horison , then measure the distance betweene the center of the Sector and the Tower , adding to that distance the length of the leg , which supporteth your Sector , and that shal be the altitude required , as appeares in the figure following AB , and BC , are of equall distance , and adding the length of the foot of the sector , you will find , that it will be height of BD , which doth accomplish the altitude of the Tower. But to take a distance in any plaine , as in the figure precedent , the same operation may be vsed , except onely the two branches of the sector shall be turned paralell to the horison or ground , hauing first made a right angle at the point G , or you may operate otherwise , first of all prolong a straight line as EGH of what length you please , then open your sector to a right angle , and set it the point G , so that you may see through two sights the point E , and where the line visuel of the other two sights strikes along , set vp a merke as in I , then goe towards it , and at your pleasure in the same line , set your sector opening it , so that you may see the point E and G , and keeping your instrument at the same width , & in the same place place , only turne it to the other side , so that you may see the point G thorow the sights which before saw E , and where the other visuell line shall cut the first line EGH , set a marke which will be in H precisely , and that shall be the distance required GE , the demonstration of this proposition is grounded vpon the 4. and 26. of the 1. of Euclide . PROP. X. How to take any distance or altitude inaccessible with the Sector . TO obtaine the altitude AB , you must first take the distance BC. as is taught by the 9. Proposition precedent , and knowing the distance BC , which I suppose to be 100 fathom , set in the point C your Sector , and direct your visuell line through the two vpper sights to the top of the altitude A , and let the branch of the Sector be paralel with the ground , then leaving your instrument at the same width , let fall a perpendicular line vpon the line of the Sector divided into equall parts , passing by the 100 number of the inferior branch noted D , and note what nūber the perpendicular doth cut vpon the vpper branch of the Sector noted H , which I suppose here to be● the 150 part or number , and then set the two points of a paire of compasses vpon the two numbers , to wit , the one point vpon 100 , and the other point vpon 150. of the equall parties , then transport the points of the compasse all along one branch of the Sector vpon the line of equall parties , and the two points shall denote as many parties vpon the line of the Sector as the Towre doth containe fathoms in altitude , adding the length of the foote which supporteth the Sector , the demonstration of this Proposition is grounded vpon the 4. Proposition of the 6. of Euclide . PROP. XI . Of Sines , Secants ▪ and Tangents . BEcause the most noble , most artificiall , and most certaine way of taking of Altitudes , Distances , or other Dimentions , is by Sines , Secants , or Tangents , I haue set downe their operations in such Propositions as are vsuall in this subiect at the end of this Treatise of Practicall Geometrie , and before I enter on the method of operation , it is necessary to define what the said Sines , Secants , & Tangents are . 1. A righ● Sine is halfe the Subtence of of the double Arke . A Subtence , sometimes called a Cord , is a right line drawne from any part of the Circumference of a Circle , vnto any other part of the same Circumference , so the right line DE is the Subtence or Cord of the Ark DGH halfe of which is DF , the Sine of the Arke DG ; and so is MN the Subtence of the Circumference or Arke MGN , halfe of it is MI , which is the Sine of the Arke MG ; now the Arke MG is halfe of the Arke MGN , and MI is halfe of the Subtence of that double Arke , viz. MGN ; hence it is according to the definition aforesaid , that the Sine of any Arke is halfe the Subtence of the double Arke ; by the same reason OT is the Sine of the Arke BO and MS is the Sine of the Arke BOM and so of others . Note further that the totall Sine , the Sine of 90 , or the Radius , is nothing else but the Semidiameter of any Circle , viz. CB , or CG . If a line be drawne tou●h a Cir●l● , it is called a Tangent , ( a tango ) as ●he line AB toucheth the Circumference of the Circle in B , and so AB is called a Tangent line , and is s●●●uated on the Terme of the Radius CB , and perpendicular thereto , by the 18 Proposition of the 3. of Euclid . 2. The Secant of an Arke is a line contained betweene the Center and the line Tangent , so that it passe by the given Arke , so if BO be a given Arke , CQ is the Secant thereof , and if BM be a given Arke , then is CR the Secant thereof . 3. The Tangent of an Arke is a line contained betweene the tearme of the Secant , and the touch point , so BQ is the Tangent of the Arke BO , and BR is the Tangent of the Arke BM , &c. PROPOSITION . XII . Hovv to take any altitude or distance by the Sines , Tangents and Secants . A of 51 , degrees will haue for his sines , 77715 , parts . B of 90. degrees will haue for his sines , 100,000 . parts . C of 39. degrees will haue for his sines , 62932. parts . Then working by the rule of three , you say if the sines of A 77715. giue the side BC of 100 fathoms , how many fathoms will the sines of C , 6.932 for the side AB , and dispose your rule of three as followeth . If 77715 — 100 — 62932. And hauing multiplied the second number by the third or the third by the second , and diuided the product by the first number , and the quotient of the diuision will be for the side AB 80. fathoms , 70. inches , 4. lines and 11 / 12 parts of a line And ●o find out the side AC , you must operate in the same manner by the rule of three , & say if the sine A of 79715 giues the side BC of 100. fathoms , how many fathoms will the sine B giue , which is 100,000 . for the side AC , and hauing multipli●d the second number by the third , and diuided the product by the first , the quotient will be 128. fathoms , 48. inches , 7. lines , & ●4875 / 77715. part of a line , which is almost one line for the side AC , and thus may you know any kind of distance with great facilitie , onely knowing the angles and one side . PROP. XIII . How to take any altitude or distance inaccessible by the sines . LEt the altitude AC bee proposed to be taken , and the neerest comming to it is B , then in that point B , take the angle ABC , as in the chapter before , which is of 61. degrees , then assemble 61. with 90. the right angle opposite and the whole is 151 , which you must substract from 180 , and then will rest 29 for the angle A , and so the three angles of the ●●iangle are known , but neither side ; ●nd therefore to know one of the ●●des , that wee may operate by the ●●es , tangents and secants , retir● ●●rther backe or aside to D , and mea●●re your paces or fathoms from B to ● , which I suppose here to bee 300. ●aces , and in the point D , take the angle ADB , which is 37. degrees , and then may know that the angle exterior ABD , is of a hundred and nineteene degrees , for it is equall to the two interior angles ABC and BAC by the 32. proposition of the 1. of Euclide , or otherwise it is the complement of the halfe circle , of which the angle interior ABC of 61 degrees is taken out , now you haue the knowledge of two angles ADB , and DAB , the which being ioyned , substract them from 180. and then the third angle will remaine DA B , then shal you know the three angles of the triangle A BD , and one of the sides by which you may come to the knowlege of the side A B of the first ●riangle A BC by the sine , and by the knowledge of the side A B , you may also know the side AC , by the sines , tangents and secants , as in the precedent chapter : and so in all manner of altitudes or distances , accessibles or inaccessibles , and it is to bee noted , that one is not boūd to wright backward , taking the second obseruation in D , but at the pleasure of the workeman to make choise of the fairest place in the field , so I thinke no difficulty shal be found in these works The manner how to take the plane of a towne , or any place out of musket-shot . SVppose you were to take the plane ABCDE ; first , hauing considered that the scituation of the plane hath a crooked arke BA● ; those two lines must be supposed straight as EQ and BP , making an obtuse angle at the point A , and being farre off from this plane in the point P , consider that the lines PB and QE , make but one angle in the point A , thē leauing a marke at P , withdraw from thence into some other place of field where your eye may rightly meete with the line AE , which will happen in Q where you must set another mark now consider that if a line be drawne from Q to P , it will forme a triangle APQ , whereof you may know two angles , P QA and AP Q which being done with your instrument , and you find the angle AP Q to bee of 45. degrees , and PA Q of 34. degrees , then adde 45. to 34. and commeth in the whole 79. which you must substract from 180 degrees , and there will rest 101 for the third angle PAQ by the 32. proposition , lib. 1. of Euclide , and the angle EAB is equall to the angle PAQ by the 15. proposition 1. then let vs conclude that we haue the angle BAE of 101. degrees , which was vnknowne , then shall it be necessary in the place noted H , to know how the side CD is scituated in respect of the parts of the world , and with a declinatorie we shall find it to be seated North , West & Southeast , which shall serue vs for the knowledge of all the rest : and in the former manner may be taken all the other angles of the plane proposed , and to haue the distance of each side of the plane , you must measure one onely as before taught , which I suppose it shall be B C , which shall bee found to bee 100 fathoms , and hauing found aside homologe to it or like to it , and diuided into an hundred parts equally , it shall serue for a scale to measure all the rest by . CHAP. I. A treaty of fortifications as well regularly as irregularly . IT is not my intention to treate here of all manner of fortifications , but onely of those which by the generall and common opinions are held and approoued to bee the best for the defence and conseruation of deseruing places ; and to begin this Treatise , I will set downe certaine rules which are now held for maximes of the best fortifications . Let the flanked angle be open 90. degrees , or the neerest to 90. that may be it is the angle A in the next trianguler figure . Let the flanking angle be not aboue 150. degrees open , but the lesser , shall alwayes be the best , this angle is BLC in the same figure . Let not the line of defence be longer then musket-shot , which is 100 , or 110 fathom , it is CK or BI in the same figure . The largest necke or gorge of a bastion or bulwarke is alwayes the best and the longest flanke lines , specially if eares be to be built vpon them , CN or MI are nose lines Now shal follow al the denominations of fortifications for the better intelligence of the better treating of them . CHAP. II. Denominations of the parties of Fortifications . A Flanked angle is the point of a bulwarke in the figure following , it is the angle SBN. A flanking angle is BLC , which is made by two lines of defence meeting in the point L. A line of defence is the distance from the flanke to the angle flanked , as here BI , or CK . The flanke is K or L. The line of the flanke is KN or IM . The curtine is the strait line drawne from one flanke to the other , as here KI . The shoulder of a bulwarke is N or M. The pane of a bulwarke is BN . The eare is alwayes built vpon the line of the flanke , as in the second figure following . The capital or chief line is BI or FC Bastion or bulwarke is a piece contained within two lines , two panes , and two flankes . The necke or gorge of a bastion is the distance betweene the two flanks for the entrie into the bastion . A rampard is the earth raised against the wall in the inside to strengthen it against Canon shot . The parapet is the elevation aboue the string of the wall . The counter escarp is the exteriour brim of the towne ditch . A halfe moone is a peece loose from the towne raised of earth , and inuironed with a ditch to hinder the assault of the enemies , it is sometimes made in forme trianguler , but sometimes oblong as occasion is , now shall follow the Treatise of the regular forts , and first of all the trianguler . CHAP. III. How to build a trianguler Fort. SVppose A BC to be the Triangle , where in a Fort three square is to be built . From the point C , as the center , and from the distance CB , let the arke BTA for 60. degrees be described , which shall be diuided into two equall parts at the point T. And againe , the arke BT into foure other equall parts , and O B shall bee an arke of 7½ degrees , by which draw the line CO , and it shall forme the diminished angle OCB of 7½ degrees . And to find the point for the flanke diuide the angle QCE in two equall parts by the straight lines CH , which teacheth vs the point I , for the flanke and then take the distance FI , and carry it to EK , and the point K shall be another flanke , then draw the lines of the flankes KN and IM perpendicularly to the courtine KI , which is drawn from the flanke K to the flank I , and the same vpon the two other sides , and you shall haue the trianguler sort perfect . The flanked angle is of 45. degrees , and the flanking angle is 165. degrees open , which is somewhat farre from the best maximes of fortifications . CHAP. IV. How to build a square Fort. LEt the square ABCD bee in which you desire to build the Fort , draw the two diagonales AD. CB , which cut E the center of the Fort from the point D as center , and from the distance DC , let the arke CGF bee drawne , which shall bee diuided in three equall parts , and from the point G draw the straight line GD , which formeth the diminished angle GDC of 15. degrees , and the intersection of the line GD in H doth shew the line capitoll CH , which shall be transported into IKL , and then draw the straight lines CI. DH and their fellowes , and to find the point for the Flanke , diuide the angle FDG in two equall parts by the line DM , which cutting the line CI doth shew vs the point N for the Flanke , then take the distance IN , and beare it to HO , and the point O shall be another Flanke , then draw the courtine ON , and from the points O and N draw the two straight lines OP and N Q perpendicularly to the courtine ON . Doe the same vpon each other side , and you will haue perfected the square fortres The Flanked angle is of 60. and the Flanking angle is open 150. degrees . CHAP. V. How to build the Pantagone Fort. THe five sides and five lines being drawne from the point A as center , and from the distance AB . ●et the ●rke BD of 60. degrees be described , which shall bee diuided into ●oure equal parts , of which BE is one ●nd from the point E ▪ draw the right ●ine AE , which cutting the line BC●t ●t the point F , doth giue the part BF●or ●or the capitall line ; which distance must be transported to the other lines AG , &c. then from the point B , draw the straight line BG , and so the others which shall bee lines of defence . And to find the Flanke , diuide th● angle EAC in two equal parts by the right line HA and the intersection which it maketh vpon the line BG at the point I shall be the Flanke , then take the distance GI , and transport it into FK , and so to IG , and the point K shall be a Flanke and the point I , then draw the line KI , which shall be a courtine , and draw the lines KL . and IM , which shal be the Flank lines being drawne perpendicularly to the courtine , and doing the same to euery other side , you shall haue the desired Fort. CHAP. VI. How to build the Fort Hexagone . HAuing diuided your circle into sixe equall parts , and drawne the sixe straight diagonall lines and the sixe sides . From the point B as center , & from the distance AB , let the arke ADC of 60. degrees be described , and it shall be diuided into foure equall parts , whereof AD is one . From the point D , draw the straight line DB , which cutting the line AC at the pont E , doth giue the distance AE for the capitall line , then transport that distance to BF . And to find the point for the Flank diuide the angle D BC in two equall parts by the straight line G B , which cutting the line AF at the point H doth shew that point for the Flanke , then take that distance HF , and transport it to EI , and to all the rest . From the point I , draw the straight lines IK perpendicularly to the curtin IH , and draw the other line HL perpendicularly also , and doe the same vpon each other side , and you shall haue the Hexagone perfect , but if you will make eares , they must bee built vpon the two third parts of the lines of the Flanke IK HL as appeares at . CHAP. VII . How to build the Heptagone . LEt BKLMNO be the Heptagone giuen , and the center therof A from whence shall be drawn the seuen lines AN. AK . AP , &c. Then from the point K as center , and from the space KB , let the arke BCA of 60. degrees be described , which shall be diuided into foure equall parts , whereof BC shall be one of 15 degrees , from the point C draw the right line CK , the which cutting the line AN , at the point D , giueth that part for the capitall line . Then take the distance ND , and carrie it to KI , and to al the rest likewise , then from the point N draw the right line NI , which shall be the line of defence , and all the others like vnto it . And to find the point for the flank , diuide the angle AKC in two equall parts by the right line GK , which cutting the right line NI at the point F sheweth that intersection F , for the point of the flanke take the distance and cary it to D and E , and the point E shall be another Flanke , then draw from E to F the line ( which makes the courtine ) then the two perpendicular lines for the Flanke lines : whereupon shall be built the eares , and doing the same vpon each side your fort shal be perfect , as required . CHAP. VIII . How to build the Octogone . FIrst let the square AB CD be made , & then the square EFGH . And to finde the place for the Flanke , diuide the angle ADC by the strait line DI , and the intersection K sheweth the point for the Flanke , as in the Forts precedent , and so transport to euery side as in the other , and you shall haue the Fort finished . CHAP. IX . The description of the heigth , depth , and thicknes of euery part of a compleat Fortification . AB The largiour or breadth of the rampard 66. foot . AC Height of the rampard , 14. foot . GA the interiour heele of the rampard 14. foot . EF The breadth of the parapet 20. foot . EH Height of the parapet 6. foot . BI . The exterior heele of the parapet 7. foot . IK . The couered walke vnder the false bray 20 foot . KL The parapet of the false bray 20 foot . MN The breadth of the ditch 120 foot , & the depth therof ought to be 10 foot . NO The heele of the ditch 10 foot . OP The couered walk of the counterescarpe . PQ The counter escarpe 6. foot of height . CHAP. X. The manner how to fortifie places irregularly . VPon a line of 100. fathoms is to be made a tenayle ; vpon a line of 150. fathoms two half bastions . Vpon a line of 200. fathoms a double tenayle . Vpon a line of 250. fathoms or therabout is to be made one bastion , and two halfe bastions . CHAP. XI . A Fortification irregular . SVppose the place QRSTV to bee fortified without diminishing the place , and having taken it vpon a faire sheet of paper and well considered , all the measures thereof then without this plane conduct the line AB of 250. fathom , and vpon that line ( according to the rules precedent ) build one bastion , and two halfe bastions taken from the Octogon , and then shall you bee at the point A , and from the point A , draw the line AP of 150. fathom , or thereabout , vpon which you may build two halfe bastions ; then draw the line PO , vpon which you shall as before build one bastion and two halfe bastions , and so vpon the line OX , and vpon all the others according to the length that they shall be found . But if it should be required , that the Towne-walls should serue for the courtines , the figure following shall be an example either for a part or for all about a towne . CHAP. XII . Another manner of fortifying irregularly . SVppose that one would fortifie the plane BAPLMNO , but in such hast , and with so little cost that the towne walls should serue round for the courtines , the plane then being taken vpon a faire sheet of paper , and hauing drawne the line CDEF of 400. fathom , it shall be found necessary to build vpon the same one bastion two half bastions and a tenaile , viz. the bastion E , the two halfe bastions D and F , and the tenaile DC , & hauing drawn the lines round about the town , leauing sufficient space be●wene them and the walls to build bulwarkes or bastions , you may take for the length of euery line of defence , that is to say from the flanke of one bastion to the point of another , 100. or 110 fa●hom and so euery bastion shall bee scowred with musket-shot , as the forts built regularly . This may serue for an example to those who by chance , may haue occasiō to repair or strengthen any part of a towne , wall , or the whole , and for the fortifying of the wall , the earth must be raised in the inside as a rampard . A TREATISE OF Arithmetike . CHAP. I. Addition SInce that Arithmetike is absolutely necessary , and required in diuers and many Geometricall operations , I haue added the examples following onely to renew and refresh the memorie of those who haue alreadie studied it ; and not those who are quite ignorant therin , ( commending them to large and ample Treatises together with masters of the scien●e ) but for such as by a weake memory haue let slip the habitude which by practise they had in times past obtaind , who may easily recouer by this short Treatie sufficient knowledge to performe any ordinary operation beginning with Addition , which is a collection of many numbers in one , as hee who would adde together the numbers ABC , following to haue the summe D , must begin with the first colon : And say 2 and 5 , or 7 and 1 is 8 , and set 8 vnder the line , as appeares by the example aboue , then in the second colon , say 3 and 4 or 7 , and pose them as before ; afterward say for the 3. colon 6. are sixe , & posing or setting the numbers collected directly vnder the figures not collected as 8 vnder 2 , and 7 vnder 3 , and sixe vnder sixe , but if any should bee aboue the number of 9 , then to set 0 in the place , and set forward all the tens . The Proofe . MAy be made in casting all the 9 away , though many times fals but by substraction is the way most certaine , as thus , begin with the last collon and say 6 , cut of 6 , rest nothing , and giue the 6 vnder the line a flash , then 4 and 3 , or 7 and 7 , out of 7 rest nothing , and as before giue it a flash , then 1 , 5 and 2 , or 8 , which as before shall be made nothing , the 8 vnderneath . CHAP. II. Substraction . SVbstraction is to take away a little number from , or out of a greater , as if one would from 8 6 4 2 take away 4 3 2 1 , then must the numbers bee disposed as followeth , the greater number vppermost , and the lesser vndermost , then draw a line : Great number   8642. A Lesser number   4321. B   rest 4321. C And say he that of 2 in the rank paieth one , rests 1 , the which set vnder the line , then of 4 pay 2 , rests 2 , which must also bee set vnder the line , and who payes 3 out of 6. rests 3. setting them as before , then 4. out of 8 rests 4. which shall bee also set as the others in the example aboue . The Proofe . IS made in adding the lesser number B with the rest C as followeth . Little nummer .   4321   rest 4321 Great number .   8642 And the sum shall be the first number A , if the substraction haue beene well made . CHAP. III. Multiplication . MVltiplication is the assumption of one number , as many times as the other , containeth in it selfe vnities . As if one would multiply 6. by 3 , that is , to take as oft 6 as 3 containes vnities , as in the example aboue , where 2 taken 4 times makes 8 , and 5 taken 4 times makes 20. so that the number A multiplied by the nūber B multiplicator 4 times comprehended , make the product 2608. The Proofe . IS made onely diuiding the product 2608 by the multiplication 4 and the quotient will be 652. if the multiplication were well made , as appeares in the example following . CHAP. IV. Diuision . DIvision is the separation of a number into aliquot partes thereof , as to diuide 5689 by 25. the figures must be disposed , as followeth , viz. the diuisor vnder the first figures of the number , which is to be diuided , as for example . And after the last figure of the number , shall bee drawne a halfe circle to separate the quotient . The numbers being thus disposed , then say 2 in 5 how many times , and it shall be found twice ; then set 2 behind the halfe circle as in the first example following ; and then say twice 2. are 4 of 5 rests 1 , dashing out the 2 and the 5. and set the 1 ouer 5 , and say againe twice 5 are 10. and strike out the 5 diuisor vnder the 6. and also the 1. ouer the 5 , then set forward your divisor one figure more as in the second example , and say 2 in 6. how how many times , and it shal be found 2 , and say twice 2 are 4 , and 4 out of 6. rests 2. which shall be set ouer the 6 , then say twi●e 5 are 10. and 10. out of 18. rests 8 and 1 out of 2. rests 1. then dash out the 2. and set 1. ouer it ; and also dash out the 5 and 2. diuisors , and set more forward the divisors , as in the third example , and say 2 how many times 18. and it shall be found 7. times , and having set the 7 , say 7 times 2 is 14. and 14 out of 18 rests 4 , and set the 4 ouer the 8 ; and to conclude , say 7 times 5 are 35 , and 35 out of 39 rests 4 , and 3 out of 4 rests 1 , and so your diuision is ended , as appeares here following by three examples one of each operation . The Proofe . Multiplie the quotient 227. by the diuisor 25 , and to the product partiall , adde the numbers which rest , viz. 14. if any rest , and then adde the whole together , and the product shall be the first number if the diuision hath beene well made as in the example following . CHAP. V. Rules of Fractions . A Fraction is a number noting the partes aliquot of an entire or whole number , whereof it is said to be a fraction as a penny , the twelfth part of a shilling , one inch the foure and fortieth part of an Ell , &c. CHAP. VI. How to reduce intiers and Fractions all into Fractions . TO reduce 8¾ and 5⅔ all infractions you must multiplie 8 by 4 , saying 4. times 8 is 32 , and the 3 being added , makes 35 , which shall be set aboue a line iust vnder the first figures , and vnder that line set 4 , as in the example following , to shew that the 45 are al fourth parts , and doe in the like manner by the 5⅔ , and say 3 times 5 are 15 , and 2 makes 17. and so you shall haue 17. thirds , as in the example following . To reduce 8¾ and 5⅔ all into fractions . CHAP. VI. To reduce all fractions into one denomination . TO bring these two fractions to one deno . the 35 quarters numerators must bee multiplied by the other numerators 17. thirds , and set the product ouer a line as here following , then multiply the 4 denominator by the other 3. denominator , and set the product of those vnder the line , and then will there be , Addition of Fractions . TO adde ⅔ to ¼ the figures , dispose the figures as followeth , and say 3 times 1 is 3 , and set the 3. ouer a line aboue the head of the others , and then say 4 times 2 are 8. and set them ouer a line aboue the head of the others also , then say 3 and 8 are 11 , and set them ouer a line betweene the first numbers and the 11 , shall be numerators , and say 4 times 3 are 12 , & set them vnder the middle line , and those shall bee denominators , and so you shall haue eleuen twelfth parts as followeth . But if the numerator bee greater then the denominator , then it shall bee diuided by the denominator , and the product shall be an entire or entires , and what resteth ( if any rest ) shall bee fraction , which ought to be abridged , as appeareth here following . Where the numerator 38 is greater then the denominator 24. then being diuided by the denominator 24. doth yeeld 1 intire , and 14 / 14 the which being abridged come to 7 / 12 , which is almost two thirds , and so of all others . CHAP. VII . Additions of intiers and fractions . BEing proposed to 243⅔ vnto 462¼ , the intiers must be added as in the first chapter of Addition and the fractions must be added as in the precedent chapter , and set product as appeares following . CHAP. VIII . Substraction of Fractions . WHosoeuer would substract ⅔ from ¾ must dispose the figures , as in the example following ; and first multiply the numerators by the denominators a crosse , as 3-times 3 are 9. and 4 times 2 are 8 , and set 9 and 8 ouer the lines aboue the heads of the others , and then say take 8 out of 9 , and there rests 1 , which must bee set ouer a line betweene both , and afterward say 3-times 4 is 12 , multiplying denominators by denominators , and set them vnder the middle line , which shall bee the denominators for the rest , as appeares cleerely in the example following . Out of 9 pay 8 rest 1 CHAP. IX . Substractions of intiers and fractions . TO substract 1831 from 267 2 / ● the fractions must first be multiplyed as in the example following ; and say twice 2 are 4 , and set the 4 ouer a line , then 3 times 1 are 3 , and set them ouer a line , and then who payes 3 out of 4. rests 1 , which must be set ouer the middle line , which done , multiply the one denominator by the other , and set the product vnder that which doth rest , as followeth . But if the fraction of the receiued should be lesse then the fraction of the summe paid , then must there be one borrowed from the whole or intire number , and count it according to the denomination of the fraction ; for if the denominator bee 4 , then shall the intier be 4 / 4 , if 5 , then 5 / 5 , if 6 then 6 / 6 , &c. CHAP. X. Multiplication of Fractions . LEt there bee proposed a superficies in the forme of a paralellogram , vulgarly cald square , the sides whereof the one is in length 7 / 8 of a fathom , and the other in breadth ¾ , and these two fractions are to bee multiplied together to find out how much the whole superficies doth containe the figures must be disposed as followeth . And multiplie one numerator by the other numerator , and then one denominator by the other denominator , saying 3 times seuen is 21 , and set them ouer head , then foure times 8 is 32 , and set them vnderneath , and the whole will bee 21 / 32 parts of a fathom , which certainely containeth the required superficies . CHAP. XI . Multiplication of entiers and Fractions . TO multiply ¼ by 2½ , you must first of al reduce the whole into fractions , and then as here aboue multiply numerator by numerator , and denominator by denominator , and the product will bee 45 / ●8 , as plainely appeares by the example following . But if it were proposed to multiply greater numbers , as 20 by 15 26 / 29 , then multiply the 15. intiers by the deno . 29. of the fraction , & then adde the numerator 26 of the same fraction ; which done will mount to 461 / 29 , then set the 461 ouer a line , and the 29. vnder it , and afterward multiply the 20 intiers by the 461. which done , diuide the product of the whole by the denominator 29. and the numqer required shall bee 317 27 / 19 , as appeares : CHAP. XII . The diuision of Fractions . TO diuide ¾ by ⅓ , each numerator is to bee multiplied by each denominator opposite , and set the product ouer a line aboue them , and then diuide the greatest product by the least as followeth . CHAP. XIII . To diuide intiers and fractions by intiers and fractions . TO diuide 12⅔ by 3⅙ , they must first be reduced all into fractions as before , and then you must multiply the numerators by the denominators acrosse as followeth , and then diuide the greatest product by the least , as this example doth cleerely demonstrate . CHAP. XIV . Evaluation of fractions which may not be abridged . SVppose you were to abridge 7 / 9 parts of a fathom , first you must consider what are the parts of the intier or whole , as 6. foot , or 72. inches : then you must multiply the numerator 7 , by the denominator 72 parts , and let the product bee diuided by the denominator 9 , and then you will finde 56 inches for the eualuation of 7 / 9 parts of a fathom . By this meanes any fraction may be abridged as well in Geometrie as as commerce , although they seeme not to be abridged . CHAP. XV. For the eualuation of measuring lands . YOu must consider that the fathom of 6 foot in length , doth containe in superficies 36. and that the 72 inches in length doth contain in superficies 5184 inches , and of other measures then to valuate a fraction of 19 / 4● parts of a fathom , square in superficies you must multiply 5184 by 19. and diuide the product by 47 , and there will be 2095 inches for the square of 29 / 47 of a fathom square and so of other like measures . CHAP. XVI . Of the rule of three without fractions . MVltiply the second number 400 by the third 12. and product 4800 by the first number 4 , and the quotient shall be the number required , and dispose your rule as followeth . months — pounds — months . If in 4 — 400 — 12 The probation of this Rule . IS to multtplie the first number 4 by the fourth number 1200 , and to multiplie the second by the third , and the two products will bee equall if the rule bee well made . CHAP. XVII . Of the rule of three with intiers and fractions . FIrst all the intiers must bee reduced into fractions as followeth . yards pounds yards . If 2¼ 12½ 7½ 9 / 4 25 / 2 15 / 2 Which done , you must multiply the second number of fractions as by the third number of fractions 15 , & then againe multiply the product by 4 the denominator of the first number , and then say 2 times 2 , or 4 , and 4 times 9 is 36 , which must bee set vnder the line , by which you shal diuide the first product 1500 , and the quotient shall be the number required , as appeares , Heere followeth two examples , differing the one from the other ; whereof the manner of multiplying the one , is more easier then the other the first is multiplyed as the precedent , but the last is multiplied first by all the intirres , viz. by 3 , by 8 and by three , leauing the fraction ● by it selfe , and after all take the thir● of the intier , viz. of 50000 , saying th● third part of 5 is one rest 2 , for the 10 which is valuated at 20 , then say the third part of 20 is 6 , and so rests 2 for the second 0 , and so to the end , and what shall rest at last , shall be set ouer a line , and your 3 4th or 5 vnder the line , then all being added together , you shal diuide the product cutting off the figures to the quantitie of the first number , saying , by ten , by a hundred , by a thousand , by ten thousand , by a hundred thousand , & the remainder is the number required , as appeareth , 191⅔ . The first example . The second number being mul●●plied by the third , doth mount to 57500000 , and being diuided by the first multiplyed by 3 , as before is taught , the quotient will be 191 2 / ●0 . The second example . CHAP. XVIII . Extraction of the square roote . FIrst dispose your numbers as followeth out of which you meane to draw the roote separating your figures by two and two beginning at the latter end ; but first strike the halfe circle 73 / 21 / 01 ( and then say the root of 73 is 8 , and set 8 before the half circle , & rests 9 , then double the quotient 8 , and say 2 times 8 are 16 , and set the 6 vnder the last figure of the second part of figures , and 1 vnder the first figure of the first part a● in this first example . Then say how many times is 1 in 9 , and it shall be 5. which you shall also set vnder the 1 of the second separation , as apppeares in this second example . And then say 5 times 1 are 5 , which taken out of 9 rests 4 , and 5 times 6 are 30 , and 30 out of 32 rests 2 , and 3 out of 4 rest 1 , and then againe say 5 times 5 are 25 , which out of 3● rest 6. and 3. out of 12. rest 9. and then double the quotient , and say twice 5 are 10 set 0 vnder 0 of the last separation , and keepe ● in memorie , and say twice 8 are 16 , and 1 that I keepe in mind makes 17 , then set downe 7 vnder the 5 , and the 1 vnder the 6 of the middle separation , as appeares in this example following . And then say how many times is 1 in 9 and it shall be 5 times , which shall be set downe for quo●ient , and also vnder the last figure 1 , and then say 5 times 1 are 5 , out of 9 re●ts 4 , and 5. times 7 are 35 , which out of 36 rests 1 , and 3 out of 4 rests 1 , and 5 times 0 is 0 , and 5. times 5 are 25. out of 31 rests 6 , & 3 out of 10 rests 7 , and 1 out of 1 rests 0 , and so the rule is ended as appeares following . CHAP. XIX . Another example of the square root . After you haue separated your figures by two and two , and drawne 251 the square roote , there doth yet rest 268 , which must bee reduced into fractions , and to begin set that rest 268 ouer a line at the end of your root , and that rest shall be numerator of the fraction ; and to finde the denominator only , double the root 251 if it be bigger then the rest , but if less as here , adde one to the doubling of the first figure , saying twice 1 is 2 , and 1 that I adde makes 3 , adde only double the rest , and set it vnder the line , and that shall be the denominator of the fraction ; and to haue the root of this fraction here aboue , first take the root of the numerator , and set that root ouer a line , and it shall be numerator as appeares following . Then draw roote of the denominator , and set it vnder the line , and that shall be a denominator , and so you shall finde 16 / 22 , and what rests is vnsensible . But because that this fraction 16 / 22 is not precisely perfect , and that there is a rest in each extraction , you may operate as followeth to haue it mooue exactly , adde as well to the numerator as to the denominator two 00 , or foure , or sixe , &c. and from each product or quotiēt out of one figure for euery two 00 which you shall haue added , and the more that you adde 00 , the more precisely you shall haue the roote as appeares following . But if it were proposed to extract the square roote of 16 / 25 , there would nothing rest , nor would it bee needfull to adde any 00 , for the root of 16 is 4 and the root of 25 is 5 , and so wee should haue 4 / 5 , and the like in all such other accidents ; and thus much for Arithmetike . Vale. FINIS . THE CONTENTS . A Treatise of Fire-works for Warre , page 1. The manner how to make the Morter-peece . pag. 5. The manner how to make Granades or mettle for the morter or hand , pag. 10. The manner how to make Granades of Canuas for the Morter . page 16 How to make fierie arrowes . pag. 20 How the Granads are to be charged into the Morter . page 24 Thn manner how to shoote the Granads , page 28 A most violent method to set a towne on fire . page 33 How to make Granads to cast with mens hands . pag. 39 How to make fierie wheeles to bee cast vvith mens hands . pag 45 How to make a ship of wild fire . pag. 48 How to make a Petard . pag 55 A Treatise of artificiall fireworkes for pleasure . page 61 A method to make moulds for rockets for the ayre . page 64 How to make flying rockets for the ayre . page 69 How to make moulds for rockets for the ground . pa. 74 How to make the composition for rockets vpon the ground page 76 The manner how to make Serpents . pa 78 How to make golden rayne . pag. 81 How to make starres , pag. 83 How to make Starres giuing great reports . page 86 The manner how to make Saucissons , page 88 How to make Stoupell or preparing of your cotton-wieke . pag. 91 Thu manner hovv to assemble and set together the parts of a rocket . pag ▪ 94 Hovv to represent diuers sorts of figures in the ayre with rockets . page 97 Hovv to make fierie boxes . pa. 101 How to make fierie lances . pag. 103 The manner hovv to make rockets for the vvater . page 105 Hovv to make Girondels or fiery wheeles pag. 110 The manner hovv to make Ballons . pag. 113 Hovv to make flying Saucissons . pa. 120 Hovv to make short Guns for the Saucissons . page 123 The manner hovv to dispose and build a great or little fireworke . pag. 125 A most pretious vnguent for any burning . pag. 131 A Treatise of practicall Geometrie . page 136 The method hovv to make the Crosse. pag. 139 Hovv to take a height accessible . pag. 141 How to take a height inaccessible , or one height vpon another height . pag. 145 Hovv to take any distance vpon a place accessible or inaccessible . page 149 Another manner how to take a distance inaccessible . pa. 151 How to take a distance onely vpon a line paralell to it . pag. 165 Hovv to take the depth of a Vally . p. 157 The manner how to take either distance or altitude vvith the Sector . pag. 161 How to take any distance or altitude inaccessible with the Sector . pag. 165 Definitions of Sines , Tangents , and Secants . pag. 168 Hovv to take any altitude or distance by the Sines , Tangents , & Secants . pag. 171 Hovv to take any altitude or distance inaccessible by the Sines . pag. 176 The manner hovv to take the Plane of a towne or any place out of musket-shot . page 180 A Treatise of Fortification , as vvell regularly as irregularly . pag. 184 Denominations of the parties of Fortification . pag. 186 Hovv to build a trianguler Fort. p. 189 Hovv to build a square Fort. pa 192 Hovv to build the Pan●agone Fort ▪ p. 195 Hovv to build the Fort Hexagone . p. 198 Hovv to build the Heptagone . pa. 201 Hovv to build the Octogone . p. 204 The description of the height , de●th , and thicknes of euery part of a compleat Fortication . p. 206 The manner how to fortifie places irregularly . p. 209 A Fortification irregular . p. 210 Another manner of fortifying irregularly . p. 213 A Treatise of Arithmetike . Addition . p. 216 Of Substraction . pag. 219 Of multiplication . p. 222 Of diuision . p. 224 Hovv to reduce intiers and Fractions into Fractions . p. 229 To reduce all fractions into one denomination . pag. 230 Ad●itions of intiers and fractions . p. 234 Substraction of Fractions . p. 235 Addition of Fractions . p. 231 Substractions of intiers and fractions . p. 237 Multiplication of Fractions . p. 239 Multiplication of entiers , and Fractions . p 241 The diuision of Fractions . p. 243 To diuide intiers and fractions by in●iers and fractions . p. 44 Eualuation of fractions which may not be ●bridged . p 245 For the eualuation of measuring lands . p 246 Of the Rule of three without fractions . p ●48 The probation of this Rule . p. 249 Of the Rule of three with intiers and fractions . p. 250 The first Example . p. 253 The second example . p. 25● Extraction of the square roote . p. 255 Another example of the square roote . p. 258 MILITARY BOOKS PRINTED FOR T. and I. 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