Biography of M. Le Comte Lagrange, 245 



la matter^ ma excite a en tracer a V aide de vos lumieres, une 

 solution analytique a laquelle je ne donnerai aucune publicite 

 jusqu a ce que vous-mtme ayez public la suitede vos recherches 

 pour ne vous enlever aucune partie de la gloire qui vous est due. 



If these delicate proceedings, and the testimonies of the 

 highest esteem should flatter a young man who was not 

 twenty four years old, they do no less honour to a great 

 man, who, holding then the sceptre of mathematics, knew 

 how to receive in this manner the work which pointed out 

 to him his successor. 



But these eulogies are contained in a letter : hence we 

 might think that the great and good Euler may have suf- 

 fered himself to go on in some of the exaggeration permitted 

 in the epistolary style ; let us see then how he afterwards 

 expressed himself in the dissertation which his letter an- 

 nounced. Here is the beginning : 



'•After I had long and vainly fatigued myself in seeking 



for this integral, (postquam diu et multum desudassem 



nequicquam inquisivissem) what was my astonishment 

 (penitus obstupui) when I learned that in the Memoirs of 

 Turin, this problem is found resolved with as much ease as 

 excellence. This fine discovery caused me the more admi- 

 ration as it is the more different from the methods which I 

 have given, and as it surpasses them considerably in sim- 

 plicity." It is thus that Euler begins the memoirs, in 

 which he explains with his usual clearness, the reasons of 

 the method of his young rival, and the theory of this new 

 calculus, which he has called the calculus of variations. 



To render more sensible all the different motives which 

 gave birth to the admiration that Euler showed with 

 such noble candour, it will not be useless to recur to the 

 origin of the different researches of Lagrange^ such as he 

 gave it himself two days before his death. 



The first attempt to determine the maximum and mini- 

 mum in all indefinite integral formulas, had been made on 

 account of the curve of the swiftest descent, and the isope- 

 rimeters of Bernouilli. Euler had reduced them to a general 

 method, in an original work, which exhibits throughout 

 ►a deep knowledge of the calculus ; but, however ingenious 

 his method was, it had not all the simplicity which we can 

 desire in a work of pure analysis. The author himself 



