Page:The Journal of Classical and Sacred Philology, Volume 1, 1854.djvu/268

 258 Journal of Philology. confusion of thought which, with all his gigantic force as a verbal critic, he too often displays when the sense, and not the language, of his author is in question. If the passage when thus deprived of all meaning could prove anything, it would tend to prove the very contrary. Lucretius really does allude to i. 615 622, Prce- terea nisi erit minimum, parvissima quceque Corpora constabunt ex partibus infinitis. . . Ergo rerum inter summam minimamque quid escit? Nil erit ut distet, &c. And this passage will indirectly prove his point, granting the false assumption, an assumption common apparently to all ancient reason ers, that if any two things consist of an infinite number of parts these two things will be equal* ; a paralogism which misled Bentley f, and which Newton in the second of his memorable letters to him thus clearly exposes : " I conceive the paralogism lies in the position that all infinites are equal. The generality of mankind consider infinites no other ways than indefinitely ; and in this sense they say all infinites are equal ; though they would speak more truly if they should say, they are neither equal nor unequal nor have any certain difference or proportion one to another. In this sense therefore no conclusions can be drawn from them about the equality, proportions or differences of things ; and they that attempt to do it usually fall into paralogisms. So when men argue against the infinite divisibility of magnitude by saying that if an inch may be divided into an infinite number of parts, the sum of those parts will be an inch ; and if a foot may be divided into an infinite number of parts, the sum of those parts must be a foot ; and therefore since all infinites are equal, those sums must be equal, that is, an inch equal to a foot ; the falseness of the conclusion shows an error in the premisses : and the error lies in the position that all infinites are equal. ... A mathema- tician would tell you that though there be an infinite number of infinite little parts in an inch, yet there is twelve times that number of such parts in a foot ; that is, the infinite number of those parts in a foot is not equal to, but twelve times bigger than the infinite number of them in an inch." H. M. dian atomist, (see Daubeny's Atomic t Compare the elaborate but incon- Theory, p. 8) there would in the case elusive argument which he grounds on supposed be no difference of magnitude this assumption in the 3rd and 6th of between a mustard seed and a mountain, his Boyle Lectures, a gnat and an elephant, each alike con-
 * Thug, according to Kanadi, the In- taining an infinity of particles,