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FOURIER (J.B.J.)
Analyse des équations déterminées.
P., Firmin Didot, 1831, un volume in 4 relié en demi-basane verte, dos orné de filets dorés (reliure de l'époque), (2), 24pp., 258pp., 1 planche dépliante
Reference : 8679
---- EDITION ORIGINALE de cet ouvrage de J.B.J. FOURIER dans lequel apparaît pour la premièe fois le "théorème de FOURIER" ---- BON EXEMPLAIRE ---- "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." (DSB V, p. 98) ---- Cajori, A History of Mathematics, p. 433**8679/ARM3
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3 book(s) with the same title
Analyse des équations déterminées
Paris, Firmin Didot, 1830, in-4, de (4), XXIV, 258 pages et 1 planche, demi-chagrin marron postérieur, tête dorée, Très rare premier état à la date de 1830. Edition originale de la première, et seule partie parue, de l'ultime oeuvre mathématiques de Fourier publiée posthume par son ami Navier. "In constrast with the famous work on heat diffusion, Fourier's interest in the theory of equations is remarkably little know. Yet it has a much longer personal history, for it began in his sixteenth year when he discovered a new proof of Descarte's rule of sign and was just as much in progress at the time of his death [...]. Fourier's proof was based on multiplying f(x) by (x + p), thus creating a new polynomial which contained one more sign in its sequence and one more positive (or negative) root, according as p was less (or greater) than zero, and showing that the number of preservations (or variations) in the new sequence was not inscreased relative to the old sequence. Hence the number of variations (or preservations) is increased by at least one, and the theorem follows. The details of the proof may be seen in any textbook dealing with the rule, for Fourier's youthful achievement quickly became the standard proof, even if its authorship appears to be viertually unknown[...]". "Fourier appears to have proved his own theorem while in his teens and he sent a paper to the Academy in 1789. However, it disappeared in the thrumoil of the year in Paris, and the pressure of administrative and other scientific work delayed publication of the resultats untiel the late 1810's. Then he became involved in a priority row with Ferdinand Budan de Bois-Laurent, a part-time mathematician who had previously published similar but inferior result. At the time of his death, Fourier was trying to prepare thse and many other result 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 [sic], 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." On trouve à la suite, deux extraits d'articles de Fourier tirés des Mémoires de l'Académie des Sciences portant sur le sujet de la théorie des équations : -Sur la distinction des racines imaginaires, et sur l'application des théorèmes d'analyse algébrique aux équations transcendantes qui dépendent de la théorie de la chaleur (Mémoires de l'Académie royale des sciences de l'Institut de France, tome VII, Paris, Didot, 1827, pages 605 à 624) ; -Remarques générales sur l'application des principes de l'analyse algébrique (lues à l'Académie des Sciences le 9 mars 1829 et publiées dans les Mémoires de l'Académie Royale des Sciences de l'Institut de France, tome X, Paris, Didot, 1831 ; pages 119 à 146). Bel exemplaire, à toute marge, portant l'ex-libris imprimé du bibliophile Henri Viellard et l'estampille, annulée, de l'Institut Catholique de Paris. DSB, V, p. 93-99. Couverture rigide
Bon de (4), XXIV, 258 pages et 1
"FOURIER, (JEAN BAPTISTE JOSEPH). - FOURIER'S THEORY OF EQUATIONS.
Reference : 42087
(1830)
Analyse des Équations Déterminées. Premiere Partie (Livre Premiere- Deuxieme, all published).
Paris, Firmin Didot Frères, (1830) 1831. 4to. Orig. clothbacked boards. Red titlelabel in paper with gilt lettering on spine. Spine faded and with small nicks to titlelabel and spine. Light wear to spine ends. (4),XXIV,258 pp. and 1 folded engraved plate. Htitle a bit browned. A few scattred brownspots. A wide-margined copy.
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.
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.
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.
