412 Biographical Account of M. Lagrange. [June, 



This great work is entirely founded on the calculus of variations, 

 of which he was the inventor. The whole flows from a single for- 

 mula, and from a principle known before his time ; but tlie whole 

 utility of which was far from suspected. This sublime com- 

 position includes all his other preceding labours which could be 

 connected with it. It is distinguished likewise by the philosophical 

 spirit which reigns fi"Oui one end of it to the other. It is likewise 

 the best history of that part of the science, a history which could 

 only have been written by a man perfectly master of his subject, 

 and superior to all his predecessors, whose works he analyses. It 

 forms a most interesting piece of reading even to him who is not 

 capable of apprecii-.ting all the details. Such a reader will at least 

 find the intiiiiate connection of all the principles on which the 

 greatest mathematicians have founded their researches into mecha- 

 nics. He will there see the geometrical law of the celestial mo- 

 tions deduced from simple mechanical and analytical considerations. 

 From those problems, M^hich serve to calculate the true system of 

 the world, the author passes to questions more difficult, more com- 

 plicated, and which belong to another order of things. These 

 researches are only objects of pure curiosity, as the author an- 

 nounces, but they show the extent of his resources. Finally, we 

 see there his new theory of the variations of arbitrary constant 

 quantities of the motion of the planets, which had appeared with 

 so much eclat in the iMemoirs of the Institute, where it had shown 

 that tlie author, at ti»c age of /o, had not sunk from the rank 

 which he had filled for so long a lime in the opinion' of all mathe- 

 maticians. 



In every part of his writings, when he makes use of an important 

 theorem, he names the original discoverer of it. ' 



When he ojjposes the ideas of his predecessors and contempora- 

 ries, it is with all the attention due to genius : when he points out 

 the errors of those who have attacked him, it is with the apathy of 

 a true mathematician, and the calmness of a demonstiation. None 

 of his celebrated rivals had ideas more just, more fine, more gene- 

 ral, and more profound. Finally, thanks to his happy labours, the 

 ecience of mathematics is now like a vast and fine palace, the 

 foundations of which he renewed, and in which we cannot take a 

 single step without perceiving admirable monuments of his genius. 



