BERKELEY'S ANALYST (1734) 91 



II I. One is not so easily convinced of the ability 

 and sincerity of Jurin. That at first he should 

 argue that quantities may be dropped because small, 

 and afterwards admit that this argument was in- 

 tended for popular consumption, is not reassuring. ^ 

 That he should fail to see the soundness of Berke- 

 ley's criticism of Newton's proof {A-\-\a){^-[-\b) 

 -{A-\a){B-\ b) for the increment of AB is 

 somewhat surprising, even if it must be admitted 

 that neither Walton nor any other eighteenth- 

 century mathematician appears to bave seen and 

 admitted the defect. In this connection we quote 

 from a letter which Hamilton wrote De Morgan 

 in 1862 vvhen Hamilton was seeing his Elenients of 

 Quaternions through the press : ^ 



**When your letter arrived this morning, I was 

 deep in Berkeley's ' Defence of Freethinking in 

 Mathematics ' ; ... I think there is more than 

 mere plausibility in the Bishop's criticisms on the 

 remarks attached to the Second Lemma of the 

 Second Book of the Principia ; and that it is very 

 difficult to understand the logie by which Newton 

 proposes to prove, that the motnentum (as he calls 

 it) of the rectangle (or product) AB is equal to 

 ^B + ^A, if the momenta of the sides (or factors) 

 A and B be denoted by a and b. His mode of 

 getting rid of ab appeared to me long ago (I must 

 confess it) to involve so much of artifice^ as to 



^ See our §§ 97, 102, 103. 



* Life of Stì- Williaftì Rowan Hamilton^ by R. P. Graves, voi. iii, 

 P. 569. 



