JURIN V. ROBINS AND PEMBERTON 99 



119. Robins remarks thereupon that attempts at 

 the exposition of this method, so far as it depends 

 upon his first definition, vvere made by Lucas 

 Valerius in a treatise on the centre of gravity, and 

 by Andrew Tacquet in a treatise on the cylindrical 

 and annular solids ; but the development involving 

 his second definition was first made by Newton. 

 There are a number of writers, not mentioned by 

 Robins, who might be cited as forerunners in the 

 theory of limits ; such, for instance, as Gregory 

 St. Vincent and Stevin. 



Newton's definition of momenta as the momentane- 

 ous increments or decrements of varying quantities, 

 '* may possibly be thought obscure. " Robins eluci- 

 dates thus : "In determining the ultimate ratios 

 between the contemporaneous differences of quanti- 

 ties, it is often previously required to consider each 

 of these differences apart, in order to discover, how 

 much of those differences is necessary for expressing 

 that ultimate ratio" (§ 154). For instance, Kb-\-V>a 

 only, and not the whole increment Aò-}-Ba-\-aòf is 

 called the momentum of the rectangle under A,B. 



120. Of this Discourse, a long account of twenty- 

 six pages, written by Robins himself, although his 

 name does not appear,^ was given in The Present 

 State of the Republick of Letters, London, October, 

 1735, in which it is stated that Robins wrote his 

 Discourse with the view of removing the doubts 

 which had lately arisen concerning fluxions and 



^ This account is republished in the Maihematical Tracis of the late 

 Benjamin Robins, edited by James Wilson, London, 1761, voi. ii, p. 78. 



