

1814.] Biographical Account of M. Lagrange. 



resolving the problems which you will meet with in him ; for when 

 you merely read the solutions of another, you will neither perceive 

 the reasons which induced him to turn to tins side or that, nor the 

 difficulties which he met with in his passage." 



One day, while speaking to me of his dislike to give directions 

 about one mode of study rather than another, he ascribed it to his 

 never having had a master nor^companion in bis labours ; in conse- 

 quence of which he never had an opportuniiy of investigating ihat 

 subject: " Not," said he, " that i could not speak of it as well as 

 another; for I reflected at an early age upon the best method of. 

 proceeding in the study of analysis, and I laid down a certain 

 number of principles, which 1 have always faithfully followed, and 

 which I will mention to you. 



" I never studied more than one book at a time ; but if it was a 

 good book I read it to the end. 



" 1 did not perplex myself with the difficulties, but left them to 

 return to twenty times in succession if necessary. If after all these 

 efforts 1 could not make them out, I examined how another mathe- 

 matician treated the same point. 



" 1 never quitted the book 1 had chosen without understanding 

 it thoroughly, and 1 passed by every thing with which 1 was well 

 acquainted when I met with it again. 



" I considered reading large treatises of pure analysis as quite 

 useless. Too great a variety of methods pass at once before the eyes. 

 It is in the works in which they are applied to use that we ought to 

 study these methods. We can estimate their utility, and we learn 

 the method of using them. In my opinion we ought to devote our 

 time and our labour chiefly to the applications. In general we 

 should satisfy ourselves with consulting the great works on the 

 calculus, unless we find in them methods either new or curious on 

 account of their analytical uses. 



" During my reading 1 reflected chiefly on what could have led 

 rny author to such or such a transformation or substitution, and on 

 the advantage which resulted from it. Alter this 1 examined 

 whether some other would not have answered better, that 1 might 

 become expert in this great means of analysis. 



" I always read with the pen in my hand, developing all the 

 calculations, and exercising myself on all the questions that I 

 found; and 1 considered it as an excellent practice to make an 

 analysis of the methods, and even an extract of the results, when 

 the work was important, or highly esteemed. 



" Prom the very beginning of my career I endeavoured to make 

 myself master of certain subjects, that I might have an opportunity 

 of inventing improvements ; and I always, as far as possible, made 

 theories to myself of the essential points, in order to fix them more 

 completely in my mind, to lender them my own, and to accustom 

 my »ell to composition ? 



'• 1 took care to recur Frequently to mathematical considerations, 

 which 1 considered as very proper to give force and correctness to 

 the judgment. 



