BERKELEY' S ANALYST (1734) 83 



clares : "I absolutely and fully agree with you 

 that the incremenium in the conclusion is the 

 momentum in the Lemma," that "the momenium 

 in the Lemma" is "the momentU7n of the rectangle 

 AB." Further, Jurin says, "the incremenium in 

 the conclusion is manifesti)^ the excess of the 

 rectangle A+|<2xB4-|^, above the rectangle 

 K — \ay.^ — \b, i. e. the increment of the rectangle 

 A — J<2xB — 1^. Therefore we are agreed that the 

 moment of the rectangle AB is the increment of 

 the rectangle A — J<a:xB — |^. Consequently you 

 were mistaken in supposing that the moment of the 

 rectangle AB was the increment of the same rectangle 

 AB. . . . The moment AB is neither the increment 

 nor the decrement of AB," for if it really was the 

 increment of AB, and also its decrement, we would 

 have A<^ + B^ + ^^ = A<^ + B^ — ab, i. e. 2ab — o. Hence 

 the rectangle ab " is by his own confession equal to 

 nothing. " Jurin concludes that the fiuxion of AB 

 is not the velocity with which the increment or 

 decrement of AB is generated, but the "middle 

 arithmetical proportional between these two velo- 

 cities," this being "in like manner as I had 

 before supposed an arithmetical mean between the 

 increment and decrement of AB, which mean is the 

 moment of AB." Berkeley had considered four 

 definitions of a moment, that of a finite quantity, 

 or an infinitesimal or a mere limit, or nothing at 

 ali ; and he had found each either to contradict 

 Newton or to contradict common sense. Jurin does 

 not accept " any one of those senses." A moment, 



