JURIN V. ROBIN S AND PEMBERTON ni 



very point of time that they arrive at this equality. 

 For a demonstrated truth must be owned, though 

 we do not perfectly see every step by which the 

 thing is brought about." 



*'We have therefore no occasion for the delinea- 

 tion of a line less than any line that can be assigned. 

 We acknowledge such delineation to be utterly 

 impossible ; as likewise the conception of such a 

 line, as an actually existing, fixed, invariable, 

 determinate quantity," Jurin here begins to dis- 

 avow infinitesimals. 'M am very free to own that 

 Sir Isaac Newton does not always consider this 

 coincidence, or rather equality, of the variable 

 quantity, or ratio and its ultimate, as necessary in 

 his method." 



128. The debate between Jurin and Robins had 

 reduced itself by this time, not so much to the 

 discussion of the logicai foundations of fluxions, as 

 to the discussion of what Newton's own views on 

 the subject had been. Robins prepared a long 

 paper on the subject for the Aprii, 1736, issue of 

 the Republick of Letters^ under the title : A Dis- 

 sertation shewing, that the Account of the doctrine of 

 Fluxions, and of prime and ultimate ratios, delivered 

 in a treatise entitledy ' A discourse concerning the 

 nature and certainty of Sir Isaac Newton's methods 

 of fluxions, and of prime and ultimate ratios, ' is 

 agreeable to the real sense and meaning of their great 

 inventor. The paper covers 45 pages. Robins 

 repeats the fundamental definitions and historical 

 statements given in his earlier papers, and directs 



