402 Biographical Account of [Jfne, 



founded upon some reasons either good or bad ; but he discovered 

 nothing of the kind. He shows that the solution proposed by 

 Fontaine was incomplete and illusory in certain resptcts. Fontaine 

 had boasted that he had taught mathematicians the conditions 

 which render possible the integration of differential equations with 

 three variables. Lagrange showed him by several citations, that 

 these conditions were known to mathematicians long before 

 Fontaine was capable of teaching them. He does not deny that 

 Fontaine discovered these tiieorems himself, "at least I am per- 

 suaded," says he, " that he was as capable of finding them as any 

 person whatever." 



It was with this delicacy and moderation that he answered the 

 aggressor. Condorcet, in his elo^e of Fontaine, is o!)liged to 

 avow that, on this occasion, his friend deviated from that politeness 

 ivhieh ought never to be dispensed with, but which perhaps he 

 thought less necessary with illustrious adversaries, whose glory did 

 not stand in need of these little delicacies. Every one can esti- 

 mate the value of that apology, especially when applied to a man 

 who, by his own acknowledgment, studied the vanity of others 

 that he might wound it upon occasion. We must at least acknow- 

 ledge that he, w ho saw himself attacked in that manner when he 

 was in the right, and who knew how to maintain politeness whh an 

 adversary who had himself dispensed with it, acquired a double 

 advantage over him, besides victoriously repelling his imprudent 

 attack. 



It w ill not be expected that we should follow M. Lagrange in 

 the important researches with which he filled the Berlin Memoires; 

 and even some volumes of the Memoirs of the Turia Academy, 

 which was indebted to him for its existence. All the space that 

 can be devoted to this biographical account would not be sufficient 

 even to give an imperfect idea of the immense series of his labours, 

 which have given so much value to the Memoirs of the Berlin 

 Academy, while it had the inestimable advantage of being directed 

 by M. Lagrange. Some of these Memoirs are of such extent and 

 importance that they might pass for a great separate work, yet 

 they constitute a part only of what these twenty years enabled him 

 to produce. He had composed his Mecanique Analytique, but he 

 wanted to have it printed at Paris, where he expected that his 

 formulas would be given with more care and fidelity. On the other 

 hand, it was running too great a risk to intrust the manuscript into 

 the hands of a traveller, wl.o might not be aware of the whole of 

 its value. M. Lagrange made a copy of it, which M. Duchatelet 

 undertook to deliver to the Abbe Marie, 'vith whom he was inti- 

 mately connected. Marie fulfilled with honour the confidence 

 placed in him. His first care was to find a bookseller who would 

 undertake to publish it ; and, what it will be difficult to believe at 

 this time, he could not find one. The newer the methods in it 

 were, and the more sublime the thcor)', the fewer readers would be 

 found capable of appreciating it ; hence, without eritcrtaiuing any 



