Rtviezv of the Cambridge Course of Mathematics. 307 



w 



r 



F 



sajs he, "avec beaiicoup de plaisir que vous travaillez a un 



grand ouvrage sur le calcul integral Le rapprochement 



desMethodes que vous coiuptez faire, sert a les eclairer mu- 

 tuellementj et ce qu'ellts ont decoinmun renferme le plus- 

 souvent leur vraie metapliysique; voila pourquoi cette met- 

 aphysique est presque toujours la derniere chose que I'on 

 decouvre* L'homme de genie arrive comme par instinct 

 aux resuhats; ce n'est qu'en reflechissant sur la route que 

 lui et d'autres ont suivie, qu'il parvient a generaliser les 

 Methodes, et a en decouvrir la raetaphysique." 



As a mathematical writer, Lacroix appears to have form- 



ear- 



ed himself on the model of Clairaut and Euler. In cl 

 nessand eloquence, he falls not much below the latter, and 

 in the profoundness, extent and originality of his views, he 

 13 certainly inferior to neither. He is never a servile imita- 

 tor of any of his predecessors. Ahhough he freely makes 

 ■"se of their writings when they are to his purpose, yet 

 whatever he takes from them, receives a new and original 

 character from the view which he takes of it, and from the 

 additional development which it often receives from him. 



Of Euler it is not necessary to say much, to those who 

 3re, in any degree, acquainted with mathematical science. 

 In clearness and elegance of demonstration and illustration, 

 1^ stands the prince of mathematicians, and in fertilityof in- 

 vention, he has never been surpassed. He is author of 

 '^ore than thirty separate works, and of nearly seven hundred 

 niemoirs, most of which are te be found in the volumes of 

 the Academies of Berlin and St. Petersburgh.* (Condorcet, 

 E'oge de M. Euler.) Again, says the Marquis de Condor- 

 cet, " tous les mathematiciens celebres qui existent au- 

 jourd'hui sont ses eleves. II n'en est aucun qui ne se soit 

 forme par la lecture de ses ouvrages, qui n'ait recu de lui 

 les formules, la methode qu'il emploie, qui, dans ses de- 

 couvertes ne soit guide et soutenu par le genie d' Euler.'* 

 The three volumes before us, are a part of the course of 

 onathematics, which is preparing under the direction of Pro- 

 fessor Farrar, for the use of the students of the University 

 ^n Cambridge. The two first are required to be studied 

 before admission, the last is a text book in the university 

 * course of instruction. Three other volumes have appeared, 



two oa the pure, the other on the applied mathematics ; 



t 



