RESEARCHES ON NUMERICAL EQUATIONS. 383 
certain calculations become necessary, but they are very 
simple, and whatever be the precision desired, they lead 
without any trouble to the solutions sought for. 
I doubt whether it were possible to cite a single scien- 
tific discovery of any importance which has not excited 
discussions of priority. The new method of Fourier for 
solving numerical equations is in this respect amply 
comprised within the common law. We ought, however, 
to acknowledge that the theorem which serves as the 
basis of this method, was first published by M. Budan; 
that according to a rule which the principal Academies 
of Europe have solemnly sanctioned, and from which the 
historian of the sciences dares not deviate without falling 
into arbitrary assumptions and confusion, M. Budan 
ought to be considered as the inventor. I will assert 
with equal assurance that it would be impossible to re- 
fuse to Fourier the merit of having attained the same 
object by his own efforts. I even regret that, in order 
to establish rights which nobody has contested, he deemed 
it necessary to have recourse to the certificates of early 
pupils of the Polytechnic School, or Professors of the 
University. Since our colleague had the modesty to 
suppose that his simple declaration would not be suffi- 
cient, why (and the argument would have had much 
weight) did he not remark in what respect his demon- 
stration differed from that of his competitor ?—an admir- 
able demonstration, in effect, and one so impregnated 
with the elements of the question, that a young geometer, 
M. Sturm, has just employed it to establish the truth of the 
beautiful theorem by the aid of which he determines not 
the simple limits, but the exact number of roots of any 
equation whatever which are comprised between two 
given quantities. 
