324: Biographical Account of [May, 



has sometliing sensible. He recalls names and facts which are well 

 known to most people. Wliat is surprising is that such a first essay 

 should be the production of a young man, who took possession of a 

 subject treated liy ISewton, Taylor, Bernoulli, D'Alembert, and 

 Euier. He appears all at once in the midst of these great mathe- 

 tnaticians as their equal, as a judge, who in order to put an end to 

 a difficult dispute, points out how far each of them is in the right, 

 and how far they have deceived themselves; determines the dispute 

 between them, corrects their errors, and gives them the true solu- 

 tion, which they had perceived without knowing it to be so. 



Euler saw the merit of the new method, and took it for the ob- 

 ject of his profoundest meditations. D'Alembert did not yield the 

 point in dispute. In his private letters, as well as in his printed 

 memoirs, he proposed numerous objections, to which Lagrange 

 afterwards answered. But these ol^jcctions may give rise to this 

 question : How comes it that, in a science in which every one 

 admits the merit of exactness, geniuses of the first order take dif- 

 ferent bides, and continue to dispijte for a long time ? The reasoii 

 is that in problems of this kind, the solutions of which cannot be 

 subjected to the proof of experiment, besides the part of the cal- 

 culation which is subjected to rigorous laws, and respecting which 

 it is not possible to entertain two opinions, there is always a meta- 

 physical part which leaves doui/t and obscurity. It is because in 

 the calculations themselves mathematicians are often content witli 

 pointing out the way in which the demoi.stration may Be made; 

 thev suppress the developements which are not always so super- 

 fluous as they think. The care of filling up these blanks would 

 require a labour which the author alone would have the courage to 

 accomplish. Even he himself, drawn on by his subject and by the 

 habits which he has acquired, allows hiraseM' to L'ap over the inter- 

 mediate ideas. He divines his definhive equation, instead of arriv- 

 ing at it step by step with an attention that would prevent every 

 mistake. Hence it happens that more timid calculators sometimes 

 point out mistakes in the calculations of an Euler, a D'Alembert, a 

 Lagrange. Hence it happens that men of very great genius do not 

 at first agree, from not having studied each other with sufficient 

 attention to understand each other's meaning. 



The first answer of Euler was to make Lagrange an associate of 

 the Berlin Academy. When he announced to him this nomination 

 on the 20th of October, 1759, he said, *' Your solution of the 

 problem of isoperlmetres leaves nothing to desire; and I am happy 

 that this subject, with which I was almost alone occupied since the 

 first attempts, has been carried by you to the highest degree of per- 

 fection. The importance of the matter has induced nie to draw 

 up, with your assistance, an analytical solution of it. But I shall 

 not publibh it till you yourself have published the sequel of your 

 researches, that I may not deprive you of any part of the glory 

 wlilch is your due." ; 



If these delicate proceedings and the testimonies of the highest 



