6 M. Arago's Historical Eloge of Joseph Fourier. 



the Faculty of Sciences : this memoir, in fine, contained the 

 basis of the work which Fourier was engaged in printing at the 

 time of his death. 



A scientific subject does not occupy so much space, in the 

 life of a learned man of the highest order, without possessing 

 importance and difficulty. The question of Algebraic analy- 

 sis, of which we have just made mention, and which Fourier 

 studied with such remarkable perseverance, is not an exception 

 to this rule. It presents itself in a great number of applications 

 of the calculus to the movement of the stars, or to the physics 

 of terrestrial bodies, and generally in the problems which lead 

 to equations of a high order. Whenever he wishes to leave the 

 region of abstractions, the calculator has need of the roots of 

 these equations ; thus, the art of discovering them by means of 

 an uniform method, whether exactly or approximately, naturally 

 early excited the attention of geometricians. 



An attentive examination begins to discover some traces of 

 their efforts in the writings of the mathematicians of the school 

 of Alexandria. Those traces, it must be admitted, are so slight 

 and so imperfect, that it might almost be allowable for us not 

 to date the origin of this branch of analysis farther back than 

 the excellent works of our countryman Viete. Descartes, to 

 whom we render very incomplete justice when we content our- 

 selves with saying that he taught us much in teaching us to 

 doubt, also occupied himself for a short time with this problem, 

 on which he left the indelible mark of his powerful hand. 



Hudde gave for a particular, but very important case, rules 

 to which nothing has been since added ; Rolle, of the Academy 

 of Sciences, devoted his whole life to this one question. Among 

 our neighbours, on the other side of the channel, Harriot, New- 

 ton, M'Laurin, Stirling, Waring, in fact all the illustrious geo- 

 metiicians whom England produced during the last century, 

 also made it the object of their researches. Some years after- 

 wards, the names of Daniel Bernoulli, Euler, Fontaine, were 

 added to this host of great names ; and at length Lagrange 

 entered on the career in his turn, and, at his very commence- 

 ment, substituted for the imperfect, although most ingenious 

 efforts of his predecessors, a complete and perfectly unobjec- 



