110 Lagrange's Memoirs. 



far from being suspected. This sublime composition, moreover, 

 unites all those of his preceding works that he could therein embody. 

 It is also distinguished by the philosophical spirit that reigns in it from 

 end to end. It is also the finest history of this part of the science ; 

 a history, such as could be written only by a man on a level with 

 his subject, and superior to all his predecessors, whose works he 

 analyzes. It forms a lecture of the highest interest, even for him 

 who would be far from being able to appreciate all the calculations 

 of its details. Such a reader will there perceive at least, the inti- 

 mate connection of all the principles on which the greatest geome- 

 ters have supported their researches in mechanics. He will there 

 see the geometric law of the celestial motions, deduced from simple 

 mechanical and analytical considerations. From these problems, 

 that serve to calculate the true system of the world, the author 

 passes to questions more difficult, complicated, and belonging to an- 

 other order of things. These researches are only out of pure curi- 

 osity. The author informs us so. But they prove the whole extent 

 of his resources. Therein is seen at last his new theory of the 

 variation of the arbitrary constants, of the motion of the planets, 

 that had appeared with so much eclat in the Memoires de 1' Institut, 

 where it had proved that the author, at the age of seventy five years, 

 had not descended from the high rank which he occupied so long 

 since, with the consent of all geometers. 



Throughout his writings, when he quotes an important theorem, 

 he gives credit for it to the first author. 



When hq corrects the opinions of his predecessors, or of his co- 

 temporaries, he does so with all the respect due to genius ; when 

 he demonstrates the errors of those who have attacked him, he does 

 so with the impassability of a true geometer, and the calmness of a 

 demonstrator. None of his celebrated rivals had ideas more delicate, 

 just, general, and deep. In fine, thanks to his happy labors, mathe- 

 matical science is now like one vast and beautiful palace, whose 

 foundations he renewed, whose pinnacle he crowned, and in which a 

 step cannot be taken without finding monuments of his genius. 



* The author arrived at it by very remarkable artifices of calculation. But the 

 solution is very inconvenient, notwithstanding the elegance of its fornaula. 



