JURIN V. ROBIN S AND PEMBERTON 115 



magnitude " and ** ultimate ratio" as limits. This 

 exposition Robins had given in full in his Discourse. 

 The difference of interpretation of Newton's Lemma 

 I in the Principia (Book I, Section i), given by him- 

 self and by Jurin, arises from Jurin's misinterpre- 

 tation of Newton's word given. He **supposes it 

 to stand for assignable\ whereas it properly signi- 

 fies only what is actually assigned." Jurin claims 

 that by our interpretation, ''Newton is rendred 

 obnoxious to the charge of first supposing what 

 he would prove " (p. 307). Robins says in reply 

 that the statement, quantities which **are perpetu- 

 ally approaching each other in such a manner, that 

 any difference how minute soever being given, a 

 finite time may be assigned, before the end of 

 which the difference of those quantities or ratios 

 shall become less than that given difference," is an 

 obvious but not an identical proposition. Robins 

 argues, "that Sir Isaac Newton had neither 

 demonstrated the actual equality of ali quantities 

 capable of being brought under this lemma, nor 

 that he intended so to do " (p. 309) ; when quanti- 

 ties "are incapable of such equality, the phrase of 

 ultimately equal must of necessity be interpreted in 

 a somewhat laxer sense," as in Principia^ Book I, 

 Prop. 71, "prò ajqualibus habeantur, are to be 

 esteemed equal." When Newton says that the 

 number of inscribed parallelograms should be 

 augmented in infinituDi^ he does not mean that 

 the number bccomes infinitely great, but that they 

 are augmented endlessly. The nature of the motion 



