Analyse des Équations déterminées...Première Partie by FOURIER, Jean Baptiste Joseph, Baron

[all published]. 2 p.l., xxiv, 258 pp. Large 4to, cont. half-calf & marbled boards (very carefully rebacked with orig. spine laid-down), spine gilt, pale blue lettering piece on spine. Paris: Firmin Didot Frères, 1831. First edition of the work which first contains "Fourier's theorem" on the number of real roots between two chosen limits. "At the time of his death, Fourier was trying to prepare these and many other results for a book to be called Analyse des équations déterminées; he had almost finished only the first two of its seven livres. His friend Navier edited it for publication in 1831 inserting an introduction to establish from attested documents (including the 1789 paper) Fourier's priority on results which had by then become famous. Perhaps Fourier was aware that he would not live to finish the work, for he wrote a synopsis of the complete book which also appeared in the edition. The synopsis indicated his wide interests in the subject, of which the most important not yet mentioned were various means of distinguishing between real and imaginary roots, refinements to the Newton-Raphson method of approximating to the root of an equation, extensions to Daniel Bernoulli's rule for the limiting value of the ratio of successive terms of a recurrent series, and the method of solution and applications of linear inequalities. Fourier's remarkable understanding of the last subject makes him the great anticipator of linear programming."-D.S.B., V, p. 98. Very nice copy. Old library stamp on title. ❧ Cajori, A History of Mathematics, p. 433-This book "contains much original matter, in particular there is a demonstration of Fourier's theorem on the position of the roots of an algebraical equation.".