VOL. VI.] PHILOSOPHICAL TRANSACTIONS. Oil 



Euclid admits it, and all mathematicians with him, as at least supposable, wlie- 

 ther possible or not. 



In particular, therefore, to his queries I ans\\'er, 1 . There may be supposed a 

 row of quantities infinitely many, and contirlually increasing, (as the supposed 

 parallels in the triangle ABC, reckoning downwards from A to BC,) wljereof 

 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 so- 

 ever, 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 increases, and so as to have no 

 centre of gravity. Such is Toricellio's Solidum Hyperbolicum acutum ; and 

 Others innumerable, discovered by Dr. Wallis, M. Fermat, and others. But 

 to determine this, requires more of geometry and logic than Mr. Hobbes 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 sup- 

 posed section infinitely continued. — 6. There is therefore no reason on this ac- 

 count, why the doctrine of Euclid, Cavallerius, or Dr. Wallis, should be re- 

 jected as of no use. 



But having solved these^ quaeries, I have some for Mr. Hobbes 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 prevari- 

 cate, which he says is for his exercise, Mr. Hobbes himself is more concerned 

 than they, to solve such quasries. 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 in- 

 finite number of years before Mr. Hobbes 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. Hobbes would persuade us, an argument in nature to prove the world had 

 a beginning. Nor are we beholden to Mr. Hobbes for this argument; for it 

 was an argument in use before Mr. Hobbes was born. Nor can he serve him- 



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