68 LIMITS AND FLUXIONS 



interpret '' Evanescant jani augìiienta illa'^ (our § 32), 

 as "let novv the increments vanish, i.c, let the 

 increments be nothing, or let there be no incre- 

 ments. " But ' ' do not the words ratio ultima stare 

 US in the face, and plainly teli us that though there 

 is a last proportion of evanescent increments, yet 

 there can be no proportion of increments which are 

 nothing, of increments which do not exist ? " You 

 grossly misinterpreted Newton. 



89. As to the third head of your objections, 

 since New^ton did not reason falsely, "he had no 

 occasion to make use of arts and fallacies to impose 

 upon his foUowers." " Having now . . . driven 

 you entirely out of your intrenchments ... I 

 should Sally out and attack you in your own. " 

 "But as they seem rather designed for shew, than 

 use, . . . to dazzle the imagination . . . [they] 

 will likewise immediately disappear like the Ghost 

 of a departed quantity,'' if you exorcise them 

 " with a few words out of the first section of the 

 Principia.''' You say that the paradox, "that 

 Mathematicians should deduce true Propositions 

 from false Principles " is accounted for by the fact 

 that one error " is compensated by another con- 

 trary and equal error." But the two are no errors 

 at ali, as is evident from the fact that true results 

 foUow when only the first operation is carried out, 

 so that no compensation is possible. Jurin argues 

 that the first supposed fallacy, without the second, 

 gives as the subtangent of y'^=^ax, the value 

 2x{2y -\- dy) -h- {2y) \ the second supposed fallacy, 



