ii6 LIMITS AND FLUXIONS 



assumed by Jurin to explain how the limit may be 

 reached is excessively complex. Moreover, ''to 

 assert that any collection of these inscribed and 

 circumscribed parallelograms can ever become 

 actually equal to the curve, is certainly an impro- 

 priety of speech, . . . the essence of indivisibles 

 consists in endeavouring to represent to the mind 

 such inscribed or circumscribed figure, as actually 

 subsisting, equal to the curve" (p. 312). Our 

 interpretation " thus removes this doctrine quite 

 beyond the reach of every objection " (p. 315). 

 Robins argues that Newton's ultimce rationes^ 

 quibuscuni quantitates evanescunt are not rationes 

 quantitatum ultìmaruin ; but only limits, to which 

 the ratios of these quantities, which themselves 

 decrease without limit, continually approach ; and 

 to which these ratios can come within any differ- 

 ence, that may be given, but never pass, nor even 

 reach those limits" (p. 316). ''Newton has 

 expressly told us, that the quantities, he calls 

 nascentes and evanescentes, are by him always con- 

 sidered as finite quantities" (p. 321). 



131. The 7nome?ita of quantities occur in Newton's 

 De analysi per cBquationes numero terminoìmm infinitas, 

 drawn up in 1666. Newton says "that he there 

 called the moment of a line a point in the sense of 

 Cavalerius, and the moment of an area a line in the 

 same sense " (see our § 47), that " from the moments 

 of time he gave the name of moments to the momen- 

 taneous increases, or infinitely small parts of the 

 abscissa and area generated in moments of time . . . 



