An answer to three papers of Mr. Hobs lately published in the months of August, and this present September, 1671. Wallis, John, 1616-1703. 1671 Approx. 17 KB of XML-encoded text transcribed from 1 1-bit group-IV TIFF page image. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2004-11 (EEBO-TCP Phase 1). A67369 Wing W558 ESTC R206915 99825397 99825397 29779 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. A67369) Transcribed from: (Early English Books Online ; image set 29779) Images scanned from microfilm: (Early English books, 1641-1700 ; 2068:9) An answer to three papers of Mr. Hobs lately published in the months of August, and this present September, 1671. Wallis, John, 1616-1703. 1 sheet ([2] p.) s.n., [London : 1671] By John Wallis. Imprint from Wing. A reply to: Hobbes, Thomas. Three papers presented to the Royal Society against Dr. Wallis. Reproduction of the original in the Bodleian 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. 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Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Hobbes, Thomas, 1588-1679. -- Three papers presented to the Royal Society against Dr. Wallis. 2004-04 TCP Assigned for keying and markup 2004-06 SPi Global Keyed and coded from ProQuest page images 2004-07 Melanie Sanders Sampled and proofread 2004-07 Melanie Sanders Text and markup reviewed and edited 2004-10 pfs Batch review (QC) and XML conversion AN ANSWER TO Three Papers of Mr. Hobs , Lately Published in the Months of August , and this present September , 1671. In the former part of his first Paper ; BY reason of a Proposition of Dr. Wallis ( Prop. 1. Cap. 5. De Motu ) to this purpose ( for he doth not repeat it Verbatim : ) If there be supposed a row of Quantities infinitely many , increasing according to the natural Order of Numbers , 1 , 2 , 3 , &c. or their Squares , 1 , 4 , 9 , &c. or their Cubes , 1 , 8 , 27 , &c. whereof the last is given . It will be to a row of as many , equal to the l●st , in the first case , as 1 to 2 ; in the second case , as 1 to 3 ; in the third ▪ as 1 to 4 , &c. ( Where all that is affirmed , is but ; If we SVPPOSE That , This will Follow. Which Consequence Mr. Hobs doth not deny : and therefore all that he saith to it , is but Cavelling . ) Mr. Hobs moves these Questions , ( and proposeth them to the Royal Society , as not requiring any skil in Geometry , Logick , or Latin , to resolve them : ) 1. Whether there can be understood ( he should rather have said , supposed ) an infinite row of Quantities , whereof the last can be given . 2. Whether a Finite Quantity can be divided into an Infinite Number of lesser Quantities , or a Finite quantity consist of an Infinite number of Parts . 3. Whether there be any Quantity greater than Infinite . 4. Whether there be any Finite Magnitude of which there is no Center of Gravity . 5. Whether there be any Number Infinite . 6. Whether the Arithmetick of Infinites be of any use , for the confirming or confuting any Doctrine . In particular , therefore , to his Quaere's , I answer , 1. There may be supposed a row of Quantiti●s Infinitely many , and continually increasing , ( as the supposed parallels in the Triangle ABC , reckoning downwards from A to BC , ) whereof the last ( BC ) is given . 2. A Finite Quantity ( as AB ) may be supposed ( by such continual Bisections ) divisible into a number of parts Infinitely many ( or , more than any Finite number assignable : ) For there is no stint beyond which such division may not be supposed to be continued ; ( for still the last , how small soever , will have two halves ; ) And , all those Parts were in the Undivided whole ; ( else , where should they be had ? ) 3. Of supposed Infinites , one may be supposed greater than another . As a , supposed , infinite number of Men , may be supposed to have a Greater number of eyes . 4. A surface , or solid , may be supposed so constituted , as to be Infinitely Long , but Finitely Great , ( the Breadth continually Decreasing in greater proportion than the Length Increaseth , ) and so as to have no Center of Gravity . Such is Toricellio's Solidum Hyperbolicum acutum ; and others innumerable , discovered by Dr. Wallis , Monsieur Format , and others . But to determine this , requires more of Geometry , and Logick ( whatever it do of the Latin Tongue ) than Mr. Hobs is Master of . 5. There may be supposed a number Infinite ; that is , greater than any assignable Finite : As the supposed number of parts , arising from a supposed Section Infinitely continued . 6. There is therefore no reason , on this account , why the Doctrin of Euclide , Cavallerius , or Dr. Wallis , should be rejected as of no use . But having solved these Quaere's , I have some for Mr. Hobs to answer , which will not so easily be dispatched by him . For though Supposed Infinites will serve the Mathematicians well enough : yet , howsoever he please to prevaricate ( which , he saith , is for his Exercise , ) Mr. Hobs himself is more concerned than they , to solve such Quaere's . Let him ask himself therefore , if he be still of opinion , that there is no Argument in nature to prove , the World had a Beginning : 1. Whether , in case it had not , there must not have passed an Infinite number of years before Mr. Hobs was born . ( For , if but Finite , how many soever , it must have begun so many years before . ) 2. Whether , now , there have not passed more ; that is , more than that infinite number . 3. Whether , in that Infinite ( or more than infinite ) number of Years , there have not been a Greater number of Days and Hours : and , of which hitherto , the last is given . 4. Whether , if this be an Absurdity , we have not then ( contrary to what Mr. Hobs would perswade us ) an Argument in nature to prove the world had a beginning : Nor are we beholden to Mr. Hobs for this Argument ; for it was an Argument in use before Mr. Hobs was born . Nor can he serve himself ( as the Mathematicians do ) with supposed Infinites ; For his Infinites , and more than Infinites of Years , Days , and Hours , already past , must be Real Infinites , and which have actually existed , and whereof the last is given ; ( and yet there are more to follow . ) Mr. Hobs shall do well ( for his Exercise ) to solve these , before he propose more Quaere's of Infinites . In the latter part of his first Paper , HE gives us ( out of his Roset . Prop. 5. ) this Attempt of Squaring the Circle . Suppose DT be ● DC , and DR a mean proportional between DC and DT : the Semidiameter DC will be equal to the Quadrantal Arc RS , and DR to TV. That the thing is false , is already shewed in the Latin Confutation of his Rosetum , published in the Philosophical Transactions for July last past . As it is now in the English ; his Demonstration is peccant in these words , ( Col. 2. lin . 31 , 32 , 33. ) Therefore - the Arc on TV , the Arc on RS , the Arc on CA , cannot be in continual proportion ; ( with all that follows : ) There being no ground for such Consequence . But ( which is the common fault of Mr. Hobs's Demonstration ) if this Demonstration were ●ood , it would serve as well for any proportion as that for which he brings it . For if , instead of ● , he had said , 〈…〉 , or what else he pleased ; the Demonstration had been just as good as now it is , without chan●ing one syllable : That is , it will equally prove the proport●on of the Semidiameter to the Quadrantal Arc , to be , what yu please . In his second Paper . HE pretends to confute a Theorem , which hath a long time passed for truth ; ( and therefore doth no more con●ern Dr. Wallis , than other men . ) And 't is this , The four sides ●f a square being divided into any number of equal parts , for ex●mple , into 100 ; and streight lines drawn through the opposite ●oints , which will divide the Square into 100 lesser Squares : The received opinion ( saith he ) and which Dr. Wallis commonly ●seth , is , that the Root of those 100 , namely 10 , is the side of the whole Square . Which to confute , he tells us , The Root 10 is a number of Squares , whereof the whole contains 100 ; and therefore the Root of 100 Squares is 10 of those Squares , and not the s●de of any Square ; because the side of a Square is not a Super●cies , but a Line . For Answer ; I say , that 't is neither the opinion of Doctor Wallis , nor ( that I know ) of any other ( so far is it from being a Received Opinion , which Master Hobs insinuates as such ) that 10 is the Root of 100 Squares ( For surely a Bare Number cannot be the side of a Square Figure : ) Nor yet ( as Master Hobs would have it ) that 10 Squares is the Root of 100 Squares : But that 10 Lengths is the Root of 100 Squares . 'T is true that the Number 10 is the Root of the Number 100 , but not , of a 100 Squares : and , that 10 Squares is the Root ( not of 100 Squares , but ) of 100 Squared Squares : Like as 10 Dousen is the Root , not of 100 Dousen , but of 100 Dousen dousen , or Squares of a Dousen . And , as , there , you must multiply not only 10 into 10 , but Dousen into Dousen , to have the Square of 10 Dousen ; so here , 10 into 10 ( which makes 100 ) and Length into Length ( which makes a Square ) to obtain the Square of 10 Lengths , which is therefore 100 Squares , and 10 Lengths the Root or side of it . But , says he , the Root of 100 Soldiers , is 10 Soldiers . Answer . No such matter : For 100 Soldiers is not the product of 10 Soldiers into 10 Soldiers , but of 10 Soldiers into the Number 10 : And therefore neither 10 , nor 10 Soldiers , the Root of it . So 10 Lengths into the Number 10 , makes no Square , but 100 Lengths ; but 10 Lengths into 10 Lengths makes ( not 100 Lengths , but ) 100 Squares . So in all other proportions : As , if the number of Lengths in the Square side be 2 ; the number of Squares in the Plain will be twice two , ( because there will be two rows of two in a row : ) If the number of Lengths in the side , be 3 ; the number of Squares in the Plain , will be 3 times 3 , or the Square of 3 : If that be 4 , this will be 4 times 4 : And so in all other proportions . Of which , if any one doubt he may believe his own eyes . His third Paper , WHich came out just as the Answer to the two former was going to the Press , contains , for substance , the same with his Second , and the Latter part of the First : And so needs no farther Answer . Only I cannot but take notice of his usual trade of contradicting himself . His second Paper says , The side of a Square is not a Superficies , but a Line : His Third says the quite contrary , ( Prop. 1. ) A Square root ( speaking of Quantity ) is not a Line , but a Rectangle . Other faults , falsities , and contradictions , there are a great many ; which I omit , as too gross to need an Answer . And this is what I thought fit to say to Mr. Hobs's Three Papers ( rather to satisfie the importunity of others , than because I thought them worth Answering : ) And submit the whole , with all Respects , to the Royal Society , to whom Mr. Hobs makes his Appeal .