io6 LIMITS AND FLUXIONS 



flowing quantity, proportional to the velocity of the 

 flowing quantities." According to Jurin, Newton 

 puts a, b, e to signify either the moments, or the 

 velocities, of the flowing quantities A, B, C. 

 Leibniz looks upon them as differences. Newton, 

 says Jurin, never used indivisibles, and his method 

 to find the differences of variable quantities is not 

 *'rigorously geometrical," but is more rigorous 

 than the treatment given by Leibniz. 



Robins's Rejoinder 

 126. Robins replied in the Republick of Letters 

 for December, 1735, in a Rcview of some of the 

 Principal Objections that have been made to the 

 Doctrine of Fluxions and Ultimate Propoj'tions ; with 

 some Remarks on the different Methods that have been 

 taken to obviate them. Robins does not here men- 

 tion Philalethes any more than the latter referred 

 directly to Robins. The objections to fluxions, 

 says Robins, are levelled at Newton's expression, 

 fluxiones sunt in ultima ratione decrementoi-um evan- 

 escentium vel prima nascentium. " Which being 

 usually thus translated, that fluxions are in the 

 ultimate ratio of the evanescent decrements, or in 

 the first ratio of the nascent augments, it has from 

 hence been ask'd, what these nascent or evanescent 

 augments are ? " There are difficulties of interpre- 

 tation, whether the augments have quantity or 

 have not. One way out of this difiiculty which 

 has been pointed out, is to say : "the limit of the 

 proportion that the decrements bear to each other 



