152 LIMITS AND FLUXIONS 



so far diminish'd, as to become infinitely less than 

 A and B ; at the same time ab will become infinitely 

 less than either a^ or ^A (for ^ aV) . ab -. -.Vi .b^ and 

 ^A . ab \ : A . a)^ and therefore it will vanish in 

 respect of them. In which case the Moment of the 

 Product or Rectangle will be a^-{-bA, as before " 

 (p. xv). Newton, however, prefers the more direct 

 way previously explained. 



Proceeding to Newton himself, we find (on p, 24) 

 the following definition : " The Moments of flowing 

 Quantities (that is, their indefinitely small Parts, 

 by the accession of which, in infinitely small por- 

 tions of Time, they are continually increased) are 

 as the Velocities of their Flowing or Increasing. 

 Wherefore if the Moment of any one, as ;r, be repre- 

 sented by the Product of its Celerity x into an 

 indefinitely small Quantity (that is, by x 0), the 

 Moments of the others v, j/, z, will be represented 

 by vo, fo, éo ; because vo, xo, yo, and èo^ are to each 

 other as v^ x, y, and i." On p. 25 terms contain- 

 ing (? as a factor " will be nothing in respect of the 

 rest. Therefore I reject them." 



1 50. Colson appended extensive annotations to 

 Newton's treatise. In these annotations, p. 250, 

 Colson speaks of '' smallest particles," but the term 

 '' smallest " does not occur in Newton's definition. 

 However, Colson says that he does not mean 

 **atoms" nor "definite and determinate magni- 

 tude, as in the Method of Indivisibles," but things 

 "indefinitely small; or continually decreasing, till 



^ Here a^ . ab : : V> . h means a^ : ab : -. ^ : b. 



