416 D'ALEMBERT. 



ditions, which other geometricians unfolded more fully 

 than the inventor of the calculus himself ; that is 

 to say, statements of the relation which must subsist 

 between the variables or rather the differentials of 

 these variables, in order that there may be a possi- 

 bility of finding the integral by the method of partial 

 differences. It appears that Fontaine,* a geometrician 



* Euler had so high an opinion of Fontaine, that in 1751 he told 

 Lalande, "If any unexpected discovery shall be made, I believe it 

 will be Fontaine that will make it." (Montucla, iv., 77, note by 

 Lalande.) His name is not even mentioned in the scientific Ency- 

 clopaedias ; nor does Professor Leslie, in his Dissertation to the 



I Encyc. Brit.,' shew that he had ever heard of it. The delay of 

 the Academy in publishing his papers is apparently suspected by 

 Montucla as having resulted from some unfair feeling towards him. 

 He was a person of the most philosophic habits, living always in 

 the country, where he cultivated a small estate j and having had the 

 misfortune to be involved in an oppressive litigation he appears to 

 have abandoned scientific pursuits during the latter years of his 

 life. (Mem., 1771.) We find him mentioned in some of the con- 

 temporary Memoirs, among the very first geometricians. Grimm 

 always treats him as such, and he gives some anecdotes of him. 

 " Fontaine vit a la campagne, et ne vient a Paris que rarement. II 

 passe aupres des connaisseurs pour le premier geometre du royaume. 



II met du genie dans ses ouvrages, et quand on le connait on n'est 

 pas difficile a persuader sur ce point. C'est un homme d'un tour 

 d'esprit tres-piquant. II reunit une finesse extreme a je ne sais 

 quoi de niais." (Corr. ii., 287.) It must, however, be confessed, that 

 Grimm writes on a subject he knew nothing of, having mixed 

 error with truth. Thus he says of D'Alembert, " Sans avoir rien 

 invente, il passe pour mettre beaucoup d'elegance et de clarte dans 

 ses ouvrages geometriques," p. 215 j thus praising him for exactly 

 that in which he is most deficient, and denying him the originality 

 which was his great merit. Of Clairaut he elsewhere says : " Un 

 tres-grand geometre, presque sur la ligne des Euler, des Fontaine, 

 des Bernouilli, et des D'Alembert. II avait moins de genie que Fon- 

 taine, plus de justesse et de surete et moins de penetration que 

 D'Alembert. Ce dernier a perdu a son mort un rival qui le tenait 

 sans cesse en haleine, et c'est une grande perte." (Corr. iv., 456.) 

 This latter passage is very just in all respects. 



