86 LIMITS AND FLUXIONS 



motion " a translation from absolute place to absolute 

 place, "1 and relative motion, "from one relative 

 place to another. Mr. Walton's is plainly neither 

 of these sorts of motion " ; hence, he argues against 

 Newton. " VVhen ab is nothing, that is, when a 

 and b are nothing, he denies that A^+ B^ is nothing. 

 This is one of the inconsistencies which I leave the 

 reader to reconcile." In his Vindication he holds 

 that, " to obtain the last ratio of synchronal incre- 

 ments, the magnitude of those increments must be 

 infinitely diminished " ; in his Catechism . . . fully 

 Answered "he chargeth me as greatly mistaken in 

 supposing that he explained the doctrine of fluxions 

 by the ratio of magnitudes infinitely diminished. " ^ 

 In his Catechism . . . fully Answered "he tells us 

 that ' fluxions are measured by the first and last 

 proportion of isochronal increments generated or 

 destroyed by motion.' A little later he says, these 

 ratios subsist when the isochronal increments have 

 no magnitude." Can "isochronal increments sub- 

 sist when they have no magnitude " ? Berkeley 



translation and velocity, as when he says, "... isochronal increments 

 must be macie to vanish by a Retroversion of the Motion before we can 

 obtain the Moiions with which they vanish, or begin to be generated ; 

 that is, before we can obtain the Flujdons of the Quantilies, the Name 

 given by Sir Isaac Newton to those Motions." J. Walton, Catechism 

 . . . fully Answered, pp. i8, 19. 



^ I. Newton, Principia, Definitions, Scholium, def. viii. 



2 What Walton actually wrote was, that Berkeley had been mistaken 

 in supposing that he explained fluxions '' by the Ratios of Magnittides 

 infinitely diininish'd, or by Proportions betiveen nothingsT Three 

 pages earlier Wallon had denied ihat Newton and he measured fluxions 

 " by the Prop ortions of Magnitudes infinitely small." Evidently Walton 

 meant to exclude the *' infinitely small," but used ' ' magnitudes infinitely 

 diminished" at one time as magnitudes "infinitely small," and at 

 anoiher time as signifying something else, namely, "increments" that 

 " vanish." 



