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. 



