BUDAN, Ferdinand. Nouvelle méthode pour la résolution des équations numériques. 1807.

Paris, Courcier, 1807.

4to (267x216 mm), (10)-86 pages.  binding : Contemporary marble paper wrappers, a little worned. 19th cent. stamp of a religious institution on title page. 

references: DSB [II p.573 :"Budan is known in the theory of equations as one of the independent discoverers of the rule of Budan and Fourier, which gives necessary conditions for a polynomial equation to have n real roots between two given real numbers. He announced his discovery of the rule and described its use (...) and published the paper with explanatory notes, as 'Nouvelle méthode pour la résolution des équations numériques', in 1807. (...) The need for such a rule as his was suggested to Budan by Lagrange's 'Traite de la resolution des equations numeriques' (1767). . . . Budan's goal was to solve Lagrange's problem - between which real numbers do real roots lie? - purely by means of elementary arithmetic. Accordingly, the chief concern of Budan's 'Nouvelle méthode' was to give the reader a mechanical process for calculating the coefficients of the transformed equation in (x - p). He did not appeal to the theory of finite differences or to the calculus for these coefficients, preferring to give them 'by means of simple additions and subtractions.' (...) Budan's rule remains the most convenient for computation"].

Price : 900 €