624 PHILOSOPHICAL TRANSACTIONS. [anNO I67I. 



any finite magnitude of which there is no centre of gravity? 5. Whether there 

 be any number infinite ? 6. Whether the arithmetic of infinites be of any use 

 for the confirming or confuting any doctrine ? 



For answer, in general, I say, 1. Whether those things be or be not; yea, 

 whether they can or cannot be; the proposition is not at all concerned, which 

 affirms nothing either way; but whether they can be supposed, or made the 

 supposition, in a conditional proposition. As when I say, if Mr. Hobbes were 

 a mathematician, he would argue otherwise; I do not affirm that either he is, 

 or ever was, or will be such. I only say, upon supposition, if he were what he 

 is not, he would not do as he does. 2. Many of these quaeries have nothing to 

 do with the proposition ; for it has not one word concerning gravity or centre 

 of gravity, or greater than infinite. 3. That usually in Euclid, and all after 

 him, by infinite is meant only more than any assignable finite, though not ab- 

 solutely infinite, or the greatest possible. 4. Nor do they mean, when infinites 

 are proposed, that they should actually be, or be possible to be performed ; but 

 only, that they be supposed ; it being usual with them, upon supposition of 

 things impossible, to infer useful truths. And Euclid in his second postulate, 

 requiring the producing a straight line infinitely, either way, did not mean that 

 it should be actually performed; for it is not possible for any man to produce a 

 straight line infinitely, but only that it be supposed. And if AB, pi. 14, fio-. 4^ 

 be supposed so produced, though but one way, its length must be supposed to 

 become infinite, or more than any finite length assignable; for, if but finite, a 

 finite production would serve. But, if so produced both ways, it will be yet 

 greater, that is, greater than that infinite, or greater than was necessary to 

 make it more than any finite length assignable. And whoever does thus sup- 

 pose infinites, must consequently suppose one infinite greater than another. 

 Again, when by Euclid's 10th proposition, the same AB, fig. 5, may be bi- 

 sected in M, and each of the halves in ???, and so onwards, infinitely; it is not 

 his meaning, when such continual section is proposed, that it should be actually 

 done, (for who can do it?) but that it be supposed. And upon such supposed 

 section infinitely continued, the parts must be supposed infinitely many ; for no 

 finite number of parts would suffice for infinite sections. And if further, the 

 same AB so divided, be supposed the side of a triangle ABC, fig. 0, and from 

 each point of division supposed lines, as mc, Mc, &c. parallel to BC; these 

 parallels, reckoning downward from A to BC, must consequently be supposed 

 infinitely many; and those in arithmetical progression, as 1, 2, 3, &c. each ex- 

 ceeding its antecedent as much as that exceeds the next before it; and whereof 

 the last (B C) is given ; and their squares, as 1, 4, 9, &c. their cubes, as 1, 8, 27, 

 &c. And this I say, to show that the supposition of infinite, with these at- 

 tendants, is not so new, or so peculiar to Cavallerius or Dr. Wallis, but that 



