Lagrange' s Memoirs. 75 



A^Frencb geometer, who united to much sagacity, a still greater 

 self-esteem and scarcely gave himself the trouble of studying the 

 works of others, accused Lagrange of having wandered in a new 

 path, that he had marked out, without having well understood the 

 theory ; he reproached him with committing mistakes in his asser- 

 tions and his calculations. Lagrange, in his answer showed some 

 astonishment at these uncourteous expressions, to which he was so 

 little used ; he expected at least to see them explained on some good 

 or bad reasons. But he found none of any kind. He shows that 

 the solution proposed by Fontaine was defective and illusory in cer- 

 tain respects. Fontaine had boasted of having taught geometers, the 

 conditions which render possible the hitegration of differential equa- 

 tions with three variables. Lagrange shewed him, by many cita- 

 tions, that these conditions were known by geometers long before 

 Fontaine was ever able so Jo inform them. He does not deny, in 

 other respects, that Fontaine could have found these theorems him- 

 self, " at least I am persuaded" added he, " that he was as able as 

 any one to find them." 



With these regards and this moderation he answered to the aggres- 

 sor. Condorcet, in the eulogy of Fontaine, in relation to this dispute, 

 is obliged to confess that his brother had strayed from that politesse, 

 with which he never before dispensed : but that he thought it per- 

 haps unimportant with opponents of eminence, and those whose glory 

 had no need of these trifling courtesies. We feel the worth of this 

 excuse, especially when we present it in favor of a man, who, accor- 

 ding to his own confession, applied himself, to study the vanity of 

 others, in order to wound it at a fit opportunity. It must be agreed 

 at least that he, who was seen attacked in this manner when he was 

 in the right, and who knew how to preserve this politesse towards 

 an adversary, who had dispensed with it, had gained a double ad- 

 vantage over him whose imprudent attacks he had otherwise suc- 

 cessfully repelled. 



We must not be expected to follow Lagrange step by step, in the 

 learned researches with which he has filled the Memoirs of Berlin, 

 and even some volumes of the Academy of Turin, that owed to him 

 in all respects its existence. But we cannot omit pointing out, at 

 least in a few words, the most remarkable which they contain. We 

 will cite : — 



A great memoir wherein are found the demonstration of a curious 

 proposition that Euler could not demonstrate, a new extension given 



