Budan, Ferdinand

Nouvelle methode pour la resolution des equations numeriques

      Paris: Courcier, 1807. pBudan de Boislaurent, Ferdinand F. D. (fl. 1800-1853). Nouvelle methode pour la resolution des Equations numeriques d'un degre quelconque. . . . 4to. [8] 86 [2, incl. errata]pp. Paris: Courcier, 1807. 268 x 206 mm. Modern quarter morocco, marbled boards in period style. Light soiling, a few edges frayed, but very good. 19th cent. stamp of Stonyhurst College on half-title. /p#11;p First Edition. Announces Budan's independent discovery of what is now known as the rule of Budan and Fourier, which gives necessary conditions for a polynomial equation to have n real roots between two given real numbers. "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 mEthode 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" (DSB). /p