ii8 LIMITS AND FLUXIONS 



debate is one over words and ceases to be illumi- 

 nating. Their judgments were perverted by the 

 heat of controversy. Even theological or politicai 

 controversies could not easily surpass the verbosity 

 and haze exhibited here. 



Jurin's first objection to Robins's last analysìs is 

 the statement that the method of fluxions has no 

 relation to the method of first and last ratios ; Jurin 

 quotes from Newton in support of his contention. 

 The charge that he (Jurin) represents augmentia 

 nascentia not as finite, but as just starting out of 

 non-existence, 'Mike infinitesimals of the differential 

 calculus," Jurin denies, saying : Leibniz's differ- 

 entials **are fixed, determinate, invariable " ; he 

 himself has represented the nascent augments as 

 "quantities just starting out from non-existence, 

 and yet not arrived at any magnitude, and not as 

 finite quantities" (p. 52), and quotes Newton in 

 support of this view. According to the article in 

 the Pìiilosophical Transactions, No. 342, attributed 

 to Newton, moments are represented " by the 

 rectangles under the fluxions and the moment " ; 

 "in his calculus there is but one infinitely little 

 quantity represented by a symbol, the symbol : it 

 is also said, Prick'd letters never signify moments, 

 unless when they are multiplied by the moment 

 either exprest or understood to make them infinitely 

 little, and then the rectangles are put for moments." 

 Jurin charges that Robins has now published four 

 different interpretations of Newton's much-discussed 

 lemma. Newton's phrase, jfìunt ultimo cequales, the 



