2 Remarks on M. Delamlre's [July, 



induce Newton to gire that synthetic form to the Principia which 

 they possess ; and because, if we except a small number of points 

 respecting algebraic calculus, and the theory of equations, he has 

 treated in his writings of none of the points which constitute 

 modern analysis. 



It is stated likewise that Lagrange was Professor of the Artillery 

 Academy at the age of sixteen.* But if rigid accuracy be required, 

 this statement seems to me doubtful ; for Lagrange has often told 

 me that he did not begin the study of mathematics till 1753, when 

 he was seventeen years of age ; and he told me (only once indeed) 

 that he was named Professor at the age of nineteen. 



As it may be an object of curiosity to know his first labours, I 

 shall state them according to his own information. He studied first 

 arithmetic, the elements of Euclid, and the algebra of Glairaut : 

 then in less than two years he read the following books, in the order 

 in which I name them: the Analytical Institutions of Mademoiselle 

 Agnesi, the Introduction of Euler, the Lectures of John Bernoulli, 

 the Mechanics of Euler, the two first books of the Principia of 

 Newton, the Dynamics of D'Alembert, the Integral Calculus of 

 Bougainville, and the Differential Calculus and Methodus Inve- 

 niendi of Euler. It is well known that it was this last work which 

 led him to the discovery of the calculus of variations. 



While speaking of the origin of this brilliant discovery, such as 

 Lagrange himself related it two days before his death, the author 

 has inadvertently allowed an error of some importance to escape 

 him, which renders the details of this subject very obscure, f The 

 discovery of the method of variations is confounded with one of its 

 finest applications, the general theorem of mechanics, to which the 

 name of the principle of the least action has been given. To- 

 render this evident it will be necessary to quote the following 

 passage from the biographical account of Lagrange. 



The first attempts to determine the maximum and minimum in all 

 indefinite integral formulas were made upon the occasion of the curve 

 of swiftest descent, and the isoperimetres of Bernoulli. Euler had 

 brought them to a general method, in an original work in which the 

 profoundest knowledge of the calculus is conspicuous. But however 

 ingenious Ms method was, it had not all the simplicity which one 



• The statement, sixteen years, was made in consequence of the last conversa- 

 tion of Lagrange with M. Chapt.il. The Journal tie l' Empire, of the 28th April, 

 1813, gave the same age. M. Virev in his notice, printed about the same time, 

 said fifteen years; but M. Cossali, in bis Eloge printed in Italy, sa_\s nineteen 

 years ; that is to say, in 1755. By that time Lagrange had communicated impor- 

 tant discoveries to Euler; and to be Professor of the Elements of Mathematics at 

 sixteen, he had no occasion for any of those analytical works which he began to 

 read at the age of seventeen. — Note by the Editor of the Moniteur. 



t What rendered these details obscure was the necessity of abridging them for 

 the public reading of the article, in consequence of which at least a third of the 

 whole was omitted. At first the method of variations, and the principle of least 

 action, were named separately ; and in a note the two Latin passages given in the 

 text were cited, one relative to P d f, the other to the metaphysical principle. — 

 Note by tfyt Editor of the Moniteur. 



