JURIN V. ROBINS AND PEMBERTON 117 



because we have no ideas of infinitely little quantities, 

 he introduced fluxions into his method, that it might 

 proceed by finite quantities as much as possible." 

 Prime and ultimate ratios he introduced later. 

 Newton says in that place that in his proofs he 

 uses for a finite moment of time, though some- 

 times, for brevity, he supposes infinitely little. 

 Thus Newton used in two senses ; in the fluxions 

 published in 1693 in Wallis's algebra, is used in 

 the sense of indivisibles ; in 1704 he gave it a 

 second signi fication in the Quadratura Curvarum. 

 Robins sums up his dissertation thus: ** Hence it 

 is very manifest, that as Sir Isaac Newton used at 

 first indivisibles, so he soon corrected those faulty 

 notions by his doctrine of fluxions, and afterwards 

 by that of prime and ultimate ratios. And ali the 

 absurdity of expression, and ali the inconsistency 

 with himself charged on him by the author of the 

 Analyst, arises whoUy from mis-representation." 

 This paper was badly arranged and below the level 

 of Robins's earlier contributions. 



132. Robins's long paper in the Republick of 

 Letters was followed in the July and August 

 (voi. xxviii, 1736) numbers by Considerations 

 upon some passages of a Dissertation conce rning the 

 Doctrine of Fluxions^ published by Mr. Robins in the 

 Republick of Letters for Aprii last, by Philalethes 

 Cantabrigiensis. The paper extends over 136 pages, 

 and could not be easily accommodated in a single 

 number. From now on the disputants, particularly 

 Jurin, are no longer in a calm frame of mind. . The 



