76 LIMITS AND FLUXIONS 



lemma, . . . however that way of reasoning may 

 do in the method of cxhaustions, where quanti ties 

 less than assignable are regarded as nothiiig ; yet, 

 for a fluxionist writing about momentums, to argue 

 that quantities must be equal because they have no 

 assignable difference, seems the most injudicious 

 step that could be taken ; . . . for, it will thence 

 foUow that ali homogeneous momentums are equal, 

 and consequently the velocities, mutations, or 

 fluxions, proportional thereto, are ali likewise 

 equal" (§ 32). 



99. As regards Newton's evanescant jam augvienta 

 illa{p\xx § 32), Berkeley argues that it means either 

 'Met the increments vanish," or else " let them 

 become infinitely small," but the latter " is not Sir 

 Isaac's sense, " since on the very same page in the 

 Introduction to the Quadrature of Curves he says 

 that there is no need of considering infinitely small 

 figures. Taking advantage of the fact that the 

 Newton of the Principia (1687) differed from the 

 Newton of the Quadratura Curvaruvi (1704), Berke- 

 ley broke out into the following philippic : " Vou 

 Sir, with the bright eyes, be pleased to teli me, 

 whether Sir Isaac's momentum be a finite quantity, 

 or an infinitesimal, or a mere limit ? If you say a 

 finite quantity ; be pleased to reconcile this with 

 what he saith in the scholium of the second lemma 

 of the first section of the first hook of his Principles 

 (our § 12): Cave intellii^as quarititatcs lìuigniliidiìic 

 deierminatas, sed cogita seìuper diniinucìidas sinc 

 limite. If you say, an infinitesimal ; reconcile this 



