74 LIMTTS AND FLUXIONS 



95. " I bave said (and I venture stili to say) that 

 a fluxion is incomprehensible : that second, third, 

 and fourth fluxions are yet more incomprehensible : 

 that it is not possible to conceive a simple infini- 

 tesimal : that it is yet less possible to conceive an 

 infinitesimal of an infinitesimal, and so onward. 

 What bave you to say in answer to this ? Do you 

 attempt to clear up the notion of a fluxion or a 

 difference ? Nothing like it " (§ 17). 



96. Berkeley quotes from Newton's Principia 

 and QuadratUì^e of Curves, and then asks, " Is it 

 not plain that if a fluxion be a velocity, then the 

 fluxion of a fluxion may, agreeably thereunto, be 

 called the velocity of a velocity? In like manner, 

 if by a fluxion is meant a nascent augment, will it 

 not then foUow that the fluxion of a fluxion or 

 second fluxion is the nascent augment of a nascent 

 augment?" (§ 23). 



97. "I had observed that the great author had 

 proceeded illegitimately, in obtaining the fluxion 

 or moment of the rectangle of tvvo flowing quan- 

 tities. ... In answer to this you allege that the 

 error arising from the omission . . . is so small 

 that it is insignificant (§ 24). . . . If you mean 

 to defend the reasonableness and use of approxi- 

 mations ... I bave nothing to say. . . . That 

 the method of fluxions is supposed accurate in 

 geometrica! rigour is manifest to whoever considers 

 what the great author writes about it . . . In 

 rebus mathernaticis errores guam minimi 7ion sunt 

 contemnendi'' (§ 25 ; our § 30). 



