BERKELEY'S ANALYST (1734) ^7 



diminution ? " As to Newton, he takes {Principia, 

 lib. ii, lemma 2, cas. i ; our § 17) initially {A — \a) 

 {B-\b) and finally ( A + 4 «)(I^ + è ^), thereby de- 

 riving al^-\-bA, not as the increment of AB, but 

 as the increment of {l\ — \a){V> — \h). '' . . . 

 Rigorously speaking, the moment of the rectangle 

 AB is not, as you suppose, the increment of the 

 rectangle AB ; but it is the increment of the rect- 

 angle A — J <2 X B — J /^. " A moment may be either 

 an increment or a decrement ; you obtain the 

 increment aB-\-òA+aò, the decrement of AB is 

 aB + òA —ab. Which of those two will you cali the 

 moment of AB ? "I apprehend the case will stand 

 thus : àB^bA-\-ab-\-aB-\-bA — ab making twice the 

 moment of the rectangle AB ; it foUows that oB-^bA 

 will make the single moment of the same rectangle";^ 

 the velocity which the flowing rectangle has, is its 

 velocity ''neither before nor after it becomes AB, 

 but at the very instant of time that it is AB." In 

 like manner with the moment of the rectangle. 

 Let me advise you hereafter to "first examine and 

 weigh every word he [Newton] uses. " Lastly, 1 

 must observe that the moment of AB, namely 

 oB-^bA, and the increment of the same rectangle, 

 aB-\-bA-\-ab, "are perfectly and exactly equal, 

 supposing a and b to be diminished ad infiniium.'' 



88. As to your second instance of false reason- 

 ing, in Newton's hook on Quadraiurcs, apparently 

 that is "so truly Boeotian a blunder" that I know 

 not how "a Newton could be guilty of it. " You 



^ Jurin, op. cit., p. 46. 



