i84 LIMITS AND FLUXTONS 



so many discoveries, so many new theorìes and 

 problems occurred to him, that, instead of a vindi- 

 catory pamphlet, his work carne out a complete 

 system of fluxions, with their application to the 

 most considerable problems in geometry and naturai 

 philosophy. This work was published at Edinburgh 

 in 1742. . . . Piis demonstrations had been, several 

 years before, communicated to Dr. Berkeley, and 

 Mr. Maclaurin had treated him with the greatest 

 personal respect and civility : notwithstanding 

 which, in his pamphlet on tar- water, ^ he renews 

 the charge, as if nothing had beeh done ; for this ex- 

 cellent reason, that difìerent persons had conceived 

 and expressed the same thing in different ways. . . . 

 Mr. Maclaurin found it necessary, in demonstrating 

 the principles of fluxions, to reject altogether those 

 exceptionable terms {infinite and infinitesimal\ and 

 to suppose no other than finite determinale quan- 

 tities, such as Euclid treats of in his geometry." 



167. In Chapter 1, p. 57, Maclaurin defines a 

 fluxion : " The velocity with which a quantity flows, 

 at any term of the time while it is supposed to be 

 generated, is called its Fluxion which is therefore 

 always measured by the increment or decrement 

 that would be generated in a given time by this 

 motion, if it was continued uniformly from that 

 term without any acceleration or retardation : or 

 it may be measured by the quantity that is gener- 

 ated in a given time by an uniform motion which 

 is equal to the generating motion at that term." 



1 In the second cdition Berkeley gave the article the name oi Siiis, 



