104 Lagrange^ s Memoirs, 



sent. Heraut de Sechelles, to whom he had applied for a passport, 

 offered to him for greater surety, a mission to Prussia. Lagrange 

 could not agree to leave his country. This repugnance, that he 

 then regarded as a misfortune, was for him a source of fortune and of 



new glory. 



The Normal School, of which he was nominated professor, but 

 which had only a short-lived existence, gave him scarcely time to lay 

 open his ideas on the foundations of arithmetic, of algebra, and of 

 their applications to geometry. 



The Polytechnic School, fruit of a more happy idea, had also 

 more lasting success ; and among the best effects that it has produced, 

 we can place that of having given up M, Lagrange to analysis. It 

 was there that he took the opportunity of developing ideas of which 

 the germ was in a memoir that he had published in 1772, and of 

 which the object was to teach the true metaphysics of the integral 

 calculus. To understand it, and to enjoy sooner these happy de- 

 velopments, we saw professors mix with young students. It was 

 there that he composed his fonctiotis analytiques, and his lessons on 

 the calculus, of which he gave many editions. Ceux qui ont ete a 

 porter de souivre ces interessantes legons, said one of these professors, 

 (M. Lacroix,) ont en le plaisir de lui voir creer sou les yeux des 

 auditeurs presque toutes les portions de sa theorie, et conserveront 

 precieusement plusieurs variantes que recueillera V histoire de la 

 science, comme des examples de la marche que suit dans V analyse 

 le genre de V invention. 



It was then also that he published his treatise on the solution of 

 numerical equations, with notes and many points of the theory of 

 algebraic equations. 



It was said that Archimedes, whose great reputation was particu- 

 larly founded, at least with historians, on machines of every kind, 

 and chiefly those that had retarded the capture of Syracuse, thought 

 little of those mechanical inventions, on which he wrote nothing. 

 It was said that he placed value only on his works of pure theory. 

 We may sometimes think that our great geometers share, in this re- 

 spect, the opinion of Archimedes. They regard a problem as solved 

 when it offers no more analytical difficulties ; as solved when nothing 

 remains but to perform differentiations, substitutions and reductions, 

 operations that in fact require scarcely any thing but patience, and a 

 certain habit. Satisfied with having dispersed the more real difficulties, 

 they are too careless about the confusion in which they leave calcu- 



