CRTTICISMS BY BRITISH WRITERS 275 



As usually happens in reformations, so here, some 

 meritorious features were discarded along with what 

 was antiquated. William Hales, in 1804, referred 

 to the much neglected Discourse of Benjamin Robins 

 (i735)> with its full and complete disavowal of 

 infinitesimals and clear-cut, though narrow, con- 

 ception of a limit. By a curious turn in the 

 process of events, Robins was quite forgotten in 

 England, and D'Alembert's definition was recom- 

 mended and widely used in England. Now Robins 

 and D'Alembert had the same conception of a limit ; 

 both held to the view that variables cannot reach 

 their limits. However, there was one difìference 

 between the two men: Robins embodied this restric- 

 tion in his definition of a limit ; D'Alembert omitted 

 it from his definition, but referred to it in his 

 explanatory remarks. D'Alembert says : ^ 



** On dit qu'une grandeur est la limite d'une autre 

 grandeur, quand la seconde peut approcher de la 

 première plus près que d'une grandeur donnée, si 

 petite qu'on là puisse supposer, sans pourtant que la 

 grandeur qui approche, puisse jamais surpasser la 

 grandeur dont elle approche ; ensorte que la différ- 

 ence d'une pareille quantité à la limite est absolu- 

 ment inassignable." Further on in the same article 

 we read : "A proprement parler, la limite ne co- 

 incide jamais, ou ne devient jamais égale à la 

 quantité dont elle est la limite ; mais celle-ci s'en 



^ Art. "Limite" in the Encyclopédie, ou dictionnaìre rais sonni' des 

 Sciences des arts et des tnétiers, puh li é par M. Diderot, et M. D Alembert, 

 Paris, 1754. See also the later edition of Geneva, 1772. 



