1814.] M. Lagrange. 40? 



appointed to examine and reward useful inventions. He had been 

 appointed one of the administrators of the Mint. This commission 

 ottered him few objects to lix his attention, and could in no degree 

 remove his apprehensions. It was again proposed to draw him to 

 Berlin, and to restore him to his former situation. He had agreed 

 to the proposal. Herault de Seclielles, to whom he had applied for 

 a passpoilj otfered him, for the greater security, a mission to 

 Prussia. Madame Lagrange would not consent to quit her country. 

 This rejuignance, whicli at tliat time he considered as a misfortune, 

 was to liim a source of fortune and of new glory. 



Tlie Normal School, of which he was named Professor, but 

 which had only an ephemeral existence, scarcely gave iiim time to 

 explain his ideas respecting the foundation of arithiiietic axid algebra, 

 and their application to geometry. 



Tiic Polytcrhnie School, the result of a happier idea, had likewise 

 a more duraljle success : and among tlie best cfl'ects which it pro- 

 duced, we may place that of having restored Lsigrange to Analysis. 

 It was there that he had an oi)porti!nity of developing those ideas, 

 the germ of wiiich was to be found in two memoirs that he had 

 published in 177-j and the object of which was to explain the true 

 metaphysics of the differential and integral calculus. To render 

 these happy dcvelopcments more easily understood, the professor 

 associated himself with his pupils. It was then that he com- 

 posed his Analytical Tunctions, and his Lectures on that Calculus, 

 of which he published several editions. " Those who have it in 

 their power to attend these interesting lectures," said publicly one 

 of the Professors (M. Lacroix), " have the pleasure to see him 

 create before the eyes of his audience almo'rt the wliole of his 

 theory, and will carefully preserve several variations which the his- 

 torian of the science will collect as examples of the path followed 

 in analysis by the genius of invention. 



It was then likewise that he published his treatise on the nume- 

 rical solution of equations, with notes on several points of the 

 tiieory of algebraic equations. 



It is said that Archimedes, wliose great reputation, at least with 

 tlie historians, is founded upon the machines of all kinds, by means 

 of which he retarded the taking of Syracuse, despised these mecha- 

 nical inventions, on wliich he wrote nothing, and placed import- 

 ance only in his works of pure theory. We may sometimes con- 

 ceive thai the great mathematicians of our age entertained the same 

 sentiments with Arcirnnedes. They consider a problem as solved 

 when it prcscnis no analytical dilhculty, wlicn notliing remains to 

 be done but differentiations, substitutions, and reductions, opera- 

 tions whicli require merely patience, atid a certain dexterity derived 

 from practice. SatisHed with having removed all the real diihcul- 

 ties, they concern themselves perhaps too little with the embarrass- 

 ments vviiich they leave to the calculator, and with the long labour 

 neccisarv in order to make use of their formula, even after it ba» 



