JURIN V. ROBINS AND PEMBERTON 109 



The Debate Continued 



1 27. Robins's article was foUowed in the January, 

 1736, number of the Republick of Letters by 

 Philalethes's Considerations occasioned by a Paper in 

 the last Republick of Letters^ concerning some late 

 Objections against the Do et r ine of Fluxioìis^ and the 

 different Methods that have beeii taken to obviate 

 them, Jurin denies having said that there was 

 an ** intermediate state" between augments being 

 **any real quantity" and being "actually vanished"; 

 he says he gave Newton's declaration that " their 

 magnitude cannot be assigned or determined. " Such 

 intermediate magnitudes, in Jurin's opinion, cannot 

 be " represented to the mind," but their ratio can 

 be represented to the mind, by contemplating the 

 ratio, *'not in the vanishing quantities themselves, 

 but in other quantities permanent and stable, 

 which are always proportional to them " (p. 'jG). 

 As to Newton's Lemma i in Section i, Book I of 

 the Principia^ if the great author meant to conclude^ 

 that the quantities '*approach nearer than any 

 given difference," then he first supposed what he 

 would prove, and proved only what he had before 

 supposed. Of this he could not be guilty. Besides, 

 Newton's words,^ " fiunt eequales," do absolutely 

 subvert such an interpretation. Jurin says that 

 he does not claim that coincidence is necessary for 

 rigorous proof; he admits that in Robins's treat- 

 ment of prime and ultimate ratios, coincidence is 



1 Newton's words are " fiunt ultimo aequales." See our § 4. 



