Analyse des Équations Déterminées. Premiere Partie (Livre Premiere- Deuxieme, all published). - [FOURIER'S THEORY OF EQUATIONS]

Paris, Firmin Didot Frères, (1830) 1831. 4to. Contemp. hcalf. Richly gilt spine. A paperlabel pasted on top of spine. (4),XXIV,258 pp. and 1 folded engraved plate. A few minor brownspots. A fine, wide-margined copy.

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Scarce first edition (with the reprinted titlepage 1831 instead of 1830).Fourier's ""Analyse des equations determines"" constitutes a highly important work on the theory of equations, a work which occupied Fourier throughout his life and the last thing that he wrote. The work contains numerous theories that had not previously been published, e.g. his method of solution and applications of linear qualities, due to which he actually anticipated linear programming.The work was of great importance to Fourier himself, who had attempted to publish some of his important results on the subject as early as 1789 and who later ended up in a priority-dispute due to the much delayed publication of one of these results (the Fourier-Budan theorem). His final opus constitutes his final preparation of the Fourier-theorem as well as many other important theories and results connected to his theory of equations, and it thus presents us with his final views on this important science. ""[H]e 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 delayed 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 this 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 of 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:98). - Honeyman IV:1361.