fURIN V. ROBINS AND PEMBERTON 105 



VVith unusual lucidity, for that period, Jurin says 

 Oli the subject of limits : * ' Now whether a quantity, 

 or ratio, shall arrive at its limit, or shall not arrive 

 at it, depends entirely upon the supposition we 

 make of the time, during which the quantity, or 

 ratio, is conceived constantly to tend or approach 

 towards its limit." If we assume the approach to 

 be made in a finite time, the limit is reached, other- 

 wise it is not reached. Of a variable which "can 

 never attingere limitem " Newton gìves one illustra- 

 tion at the end of the Scholium : that of two 

 quantities having at first a common difference and 

 increasing together by equal additions, ad infinitum. 

 Since they can never be really and in fact increased 

 ad infinitum, says Jurin, their ratio cannot arrive at 

 its limit. What Newton wanted to meet was the 

 objection, "that if the last ratio's of evanescent 

 quantities could be assigned, the last magnitudes 

 of those quantities might likewise be assigned." 

 Newton says No, "for those last ratio's, wìth which 

 the quantities vanish, strictly speaking, are not the 

 ratio's of the last quantities ... but they are the 

 limits" which those ratios can never "arrive at," 

 "before the quantities are dÀvcì\m^\i^à. ad infinitum.'' 

 As to the sense in which Newton uses the word 

 evanescent or vanishing, in the Scholium under 

 consideration, Jurin inclines to the view that '*both 

 imply one single instant, or point of time." 



125. In the Principia, Book II, Section 2, 

 Lemma 2 (our §§ 16-19), Newton defines moment 

 as " a momentaneous increment, or decrement, of a 



