2 Biographical Account of [July, 



engaged in a correspondence with the great Euler, though it 

 must be acknowledged that the letters of Euler were those of a 

 master to his scholar ; but all inequality between them speedily 

 disappeared. At the age of twenty-four Lagrange published his 

 Calculus of Variations, which had been some time in his possession. 

 It was the greatest degree of generalization and extension that 

 could be given to the important discovery of Descartes on the 

 analysis of indeterminate quantities. It was received with admi- 

 ration. Euler especially, who had written on the same subject 

 one of his best works, and who had reason to regret that an idea 

 so simple and so fruitful had escaped him, was the first person to 

 point out and celebrate the method of his young rival. He wrote 

 several papers by way of commenting on it; and it was he that 

 gave it the name of the Calculus of Variations. Lagrange him- 

 self was satisfied with giving it the name of an essay. 



Lagrange did justice to this great honour, by acquiring new 

 titles to glory. In 1764 he gained the prize proposed by the 

 Academy of Sciences on the libration of the rnoon. Not only did 

 his analysis embrace the whole of the question proposed, but he 

 likewise pointed out to mathematicians the extent and fecundity 

 of the principle of virtual velocities in the solution of mecha- 

 nical problems. This idea contains the germ of one of his 

 finest works, which he called Mecanique Analyticjue, because 

 he reduced under a single analytical formula all imaginable 

 mechanical questions, supposing the direction and the mode of 

 action of the forces known. M. de Lagrange gained four other 

 great prizes proposed by the Academy of Sciences. We would 

 not properly appreciate the importance of this circumstance 

 unless we attend to the nature of the questions proposed in such 

 cases. They consisted of the most important points of science, 

 Of the most difficult and profound theories towards which the 

 efforts of mathematicians were drawn. We may almost reckon 

 the steps made by science by the number of such questions pro- 

 posed and resolve 3 



M. de Lagrange quitted his country in 1766. Euler, who had 

 been director of the Berlin Academy, went at that time to 

 Petersburg!'. Frederick the Great proposed to d'Alembert to 

 succeed him. D'Alembert returned his thanks to the King, and 

 pointed out Lagrange as a proper person to fill the place. La- 

 grange, accordingly, was chosen. His arrival in Berlin was 

 marked by a fine work on numerical equations, which constitutes 

 the foundation of the treatise that he afterwards published on 

 that subject. Soon afterwards he communicated his researches 

 on algebraic equations ; and during the 22 years that he conti- 

 nued Director of the Berlin Academy he published about 60 

 dissertations on all parts of mathematics, on partial differences, 

 finite differences, probabilities, the theory of numbers, and the 



