keviero of the Cambridge Course of Mathematics. 30l 



says he, "avec beaucoup de plaisir que vous travaillez a un 



grand ouvrage sur le calcul integral Le rapprochement 



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

 tuellement, et ce qu'elles ont de coinmun renferme le olus- 

 souvent leurvraie metaphysique; voila pourquoi cette met- 

 aphysique est presque toujours la derniere chose que Ton 

 decouvre. L'homme de genie arrive comme par instinct 

 aux resultats ; ce n'est qu'en reflechissani sur la route que 

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

 Methodes, et a en decouvrir la metaphysique." 



As a mathematical writer, Lacroix appears to have form- 

 ed himself on the model of Clairaut and Euler. In clear- 

 ness and eloquence, he falls not much below the latter, and* 

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

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

 tor of any of his predecessors. Although he freely makes 

 use 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 

 are, in any degree, acquainted with mathematical science. 

 In clearness and elegance of demonstration and illustration, 

 he stands the prince of mathematicians, and in fertility of in- 

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

 more than thirty separate works, and of nearly seven hundred 

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

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

 Eloge de M. Euler.) Again, says the Marquis de Condor- 

 cet, " tous les mathematiciens celebres qui existent au~ 

 jourd'hui sont ses eleves. II n'tn 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 

 mathematics, which is preparing under the direction of Pro- 

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

 in 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 on the pure, the other on the applied mathematics ; 



