124 LIMITS AND FLUXIONS 



hook reviews. On the last page of the August 

 number, the editor apologises to the readers and 

 assures them * * they shall hereafter have no occa- 

 sion to complain upon this head." In Robins's 

 reply, ^ both ''Robins" and '* Fhilalethes " appear 

 in the third person, as if the writer were some out- 

 sider. Robins says : ' * Newton does not intermix 

 his simple and plain description of fluxions with the 

 terms used in the doctrine of prime and ultimate 

 ratios ; for his description of fluxions is contained 

 in the two first paragraphs of his Introduction to 

 the Quadratures, in which no terms of the other 

 doctrine occur " (p. 89). The Lemma is, of course, 

 taken up again, Robins claiming his interpretation 

 legitimate, " for two quantities may constantly tend 

 to equality during some finite space of time, and 

 before the end of that time come nearer together 

 than to have any difference, which shall be given ; 

 and yet at the end of that time have stili a real 

 difference," while Jurin's interpretation was not 

 "any difference that shall be given," but '*any 

 assignable difference," which would mean that the 

 limit must be reached. Mr. Robins says (p. 97) : 

 '* It is not difificult to assign a very probable reason, 

 which led Sir Isaac Newton to the use of this 

 expression [fiunt ultimo aequales], for before him it 

 had not been unusual for geometers to speak of the 

 last sums of infinite progressions, which is an ex- 



^ " Remarks on the Considerations relating to Fluxiojis, eie, that 

 were published by Philalethes Cantabrigiensis in the Republick of 

 Letters for the last month," Republick of Letters, August, 1736, 

 pp. 87-110. 



