A oe ee en 
e rf 
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- 
cations 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 
