66 LIMITS AND FLUXIONS 



Sir Isaac Newton, to makc this false reasoning pass 

 upon his followers." Jurin continues : " It must 

 be owned that this doctrine . . . is not without 

 difficulties," but "bave you not altered his ex- 

 pressions in such a manner, as to mislead and con- 

 found your readers, instead of informing them," 

 thereby increasing the difficulties? " Where do 

 you find Sir Isaac Newton using such expressions 

 as the velocities of the velocities, the second, thii-d and 

 fourth velocities, the incipient celerity of an incipient 

 celerity, the nascent augnient of a nascent augvient ? " 

 As to the ''moment or increment of the rectangle 

 AB," the mathematicians take it to be ^B-f/;A ; 

 you say that the rigorous value is ^B + /;A + ^/7. 

 *'Do not they know that in estimating any finite 

 quantity how great soever . . ., a globe, suppose, 

 as big as the earth, ... or even the orb of the 

 fixed stars . . ., this omission shall not cause them 

 to deviate from the truth so much as a single pin's 

 head, nay not the millionth part of a pin's head ? " 

 The operations by fluxions are no more objection- 

 able than those by decimai fractions, where we take 

 •33333, etc, instead ofj. You say that the Marquis 

 de l'Hospital, in his Analyse des infiniment petits, 

 Prop. 2, having found the fluxion of xy to be xdy 

 ■\-ydx-\-dxdy, drops the dxdy ''without the least 

 ceremony. " But does he not especially require in 

 a postulate, "that a quantity, which is augmented 

 or diminished by another quantity infinitely less 

 than the first, may be considered as if it continued 

 the same, i.e. had received no such augmentation or 



