RESEARCHES ON NUMERICAL EQUATIONS. 381 



finally, contained the elements of the work which Fourier 

 was engaged in seeing through the press when death put 

 an end to his career. 



A scientific subject does not occupy so much space in 

 the life of a man of science of the first rank without 

 being important and difficult. The subject of algebraic 

 analysis above mentioned, which Fourier had studied 

 with a perseverance so remarkable, is not an exception 

 to this rule. It offers itself in a great number of appli- 

 cat'?^ of calculation to the movements of the heavenly 

 bodies, or to the physics of terrestrial bodies, and in 

 general in the problems which lead to equations of a 

 high degree. As soon as he wishes to quit the domain 

 of abstract relations, the calculator has occasion to em- 

 ploy the roots of these equations ; thus the art of dis- 

 covering them by the aid of an uniform method, either 

 exactly or by approximation, did not fail at an early 

 period to excite the attention of geometers. 



An observant eye perceives already some traces of 

 their efforts in the writings of the mathematicians of the 

 Alexandrian School. These traces, it must be acknowl- 

 edged, are so slight and so imperfect, that we should 

 truly be justified in referring the origin of this branch 

 of analysis only to the excellent labours of our country- 

 man Vieta. Descartes, to whom we render very im- 

 perfect justice when we content ourselves with saying 

 that he taught us much when he taught us to doubt, 

 occupied his attention also for a short time with this 

 problem, and left upon it the indelible impress of his 

 powerful mind. Hudde gave for a particular but very 

 important case rules to which nothing has since been 

 added ; Rolle, of the Academy of Sciences, devoted to 

 this one subject his entire life. Among our neighbours 



