i6o LIMITS AND FLUXIONS 



the increment o continually to decrease, the ratio 

 of these synchronal increments may be made to 

 approach to it nearer than by any assignable 

 difìference, and can never come up with. it before 

 the time when the increments themselves vanish. 

 . . . For tho', strictly speaking, it should be 

 allowed that there is no last proportion of vanishing 

 quantities, yet on this account no fair and candid 

 reader would find fault with Sir Isaac Newton, for 

 he has so plainly described the proportion he calls 

 by this name, as sufficiently to distinguish it from 

 any other whatsoever : So that the amount of ali 

 objections against the justice of this method in 

 finding out the last proportion of vanishing 

 quantities can arise to little more than this, that 

 he has no right to cali the proportions he finds out 

 according to this method by that name, which sure 

 must be egregious trifling. However, as on this 

 head our author seems to talk with more than usuai 

 confidence of the advantage he has over his oppo- 

 nents, and gives us what he says is the amount of 

 Sir Isaac's reasoning, in a truly ridiculous light, it 

 will be proper to see on whom the laugh ought to 

 fall, for I am sure somebody must bere appear 

 strangely ridiculous, ... I readily allow whatever 

 consequence he is pleased to draw from it, if it 

 appears that Sir Isaac, in order to find the last 

 ratios proposed was obliged to make two incon- 

 sistent suppositions. To confute which nothing 

 more need be said than barely to relate the sup- 

 positions he did make. 



