276 LIMITS AND FLUXIONS 



approche toujours de plus en plus, & peut en différer 

 aussi peu qu'on voudra. . . . On dit que la somme 

 d'une progression géométrique décroissante dont le 

 premier terme est <^ & le second b, est (a — ò) / (aa) ; 

 cette valeur n'est poit proprement la somme de la 

 progression, c'est la limite de cette somme, c'est-à- 

 dire la quantité dont elle peut approcher si près 

 qu'on voudra, sans jamais y arriver exactement." 



233. That even the best expositions of limits and 

 the calculus that the Continent had to offer at that 

 time were recognised in England to be imperfect, is 

 shown by a passage in a letter which William Rowan 

 Hamilton wrote in 1828 to his friend John T. 

 Graves : ^ 



**I have always been greatly dissatisfied with 

 the phrases, if not the reasonings, of even very 

 eminent analysts, on a variety of subjects. . . . An 

 algebraist who should thus clear away the meta- 

 physical stumbling-blocks that beset the entrance 

 of analysis, without sacrificing those concise and 

 powerful methods which constitute its essence and 

 its value, would perform a useful work and deserve 

 well of Science." 



^ Life of Siy William Rowan Hamilton, by Robert P. Graves, voi. i, 

 1882, p. 304. 



