TEXT-BOOKS, 17 36-1 741 159 



not the sense of words . . . if . . . you make it 

 synonymous to the word Fluxion, then the velocity 

 of velocity . . . is nothing but plain common 

 sense" (p. 19). Moments are not used by the 

 author. The author says that, were he to write 

 a treatise on fluxions, **in order to understand 

 equations where Fluxions of different orders are 

 jumbled together ; it would be convenient to re- 

 present ali Fluxions not as before, but as quantities 

 of the same kind with their Fluents. . . . The 

 Fluxion of a quantity anyhow flowing at any given 

 instant is a quantity found out by taking it to the 

 Fluxion of an uniformly flowing quantity in the 

 ultimate proportion of those synchronal changes 

 which then vanish " (pp. 34, 35). The variables 

 X and x"^ have the synchronal augments and 



nox''~^-\-^ — —^o^x"~^-\-, etc. , which are to one 



2 



another as i : nx''~'^ -\-- ^-ox""'^-]-, etc. *'Let 



2 



now these arguments vanish, and their last ratio 



will be I : nx^'K" *'This our author says is no 



fair and conclusive reasoning, because when we 



suppose the * increments to vanish, we must suppose 



their proportions, their expressions, and everything 



else derived from the supposition of their existence 



to vanish with them. ' To this I answer, that our 



author himself must needs know thus much, viz. 



That the lesser the increment is taken, the nearer 



the proportion of the increments of x and x"" will 



arrive to that of i to nx"'"^, and that by supposing 



