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Lecons sur la Théorie mathematique de la Lutte pour la Vie. (Mathematical theory of the struggle for life) - [THE MATEMATIZATION OF BIOLOGY]
Paris, Gauthier-Villars, 1931. Royal 8vo. Uncut in orig. printed wrappers. Uppe and lower part of backstrip gone. VI,214 pp. + Publisher's cat. (7) pp.
First edition of this pioneering book on mathematical treatment of the dynamics of animal populations. ""The book mustbe considered as the most important contribution to the mathematization of biology made during the first half of the century, together with Lotka (1925). The origin of Volterra's direct intervention in the field of biomathematical research emerge clearly from his correspondance, manuscripts and direct testimony. In late 1925 D'Ancona showed him the results of a statistical survey of fish populations in the Upper Adriatic sea that pointed to a curious phenomenon. As a general rule, the percentage of predatory fish in the total fish catch in several ports in the Upper Adriatic remained constant, while it displayed an appreciable increase duringh the period 1915-18, that is, the years during which Italy was at war and the naval conflict in the Adriatic had led to an interruption of fishing activities. D'Ancona suggested that the lull in fishing activities was the cause of the increase in the number of predators, and he asked Volterra to provide a mathematical proof of this. Volterra threw himself into the question and came up with a description of the interaction between prey and predators beased on a simple mathematical model, which has since become famous and is known as the 'Lotka-Volterra equations'. (G. Israel in Landmarks Writings in Western Mathematics 1640-1940). - Vito Volterra (1860-1940) may be considered one of the greatest Italian mathematicians living between the 19th and the 20th centuries who also enjoied great international prestige. (G. Israel).
Sur les Vibrations des Corpes élastiques isotropes.
(Berlin, Stockholm, Paris, Alqvist & Wiksell, 1894). 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler."", vol. 18, pp. 161-232.
First edition. ""Vito Volterra (1860-1940), who succeeded Beltrami as professor of mathematical physics at Rome, is the first of the founders of a general theory of integral equations. He wrote papers on the subject from 1884 on and principal ones in 1896 and 1897."" (Morris Kline).
Sur la stratification d'une masse fluide en équilibre.
Berlin, Stockholm, Paris, Beijer, 1903. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 27, pp. 105-124.
First printing of Volterra's paper on the distribution of pressure around spheres in a viscous fluid. ""Volterra’s scientific work covers the period from 1881, when he published his first papers, to 1940 when his last paper was published in the Acta of the Pontifical Academy of Sciences. His most important contributions were in higher analysis, mathematical physics, celestial mechanics, the mathematical theory of elasticity, and mathematical biometrics. His major works in these fields included the foundation of the theory of functionals and the solution of the type of integral equations with variable limits that now bear his name, methods of integrating hyperbolic parctical differential equations, the study of hereditary phenomena, optics of birefringent media, the motion of the earth’s poles and elastic dislocations of multiconnected bodies, and, in his last years, placing the laws of biological fluctuations on mathematical bases and establishing principles of a demographic dynamics that preset analogies to the dynamics of material systems."" (DSB).
Sur la Théorie des Variations des Latitudes.
Berlin, Stockholm, Paris, Beijer, 1899. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 22, pp. 201-357.
First edition. As the north and south poles, instead of being fixed points on the earth's surface, wander round within a circle of ab. 5o ft. in diameter, the result is a variability of terrestial latitudes generally. Volterra gives an elaborate mathematical analysis of these yearly fluxtuations.
Sur les vibrations lumineuses dans les milieux biréfringents.
[Berlin, Stockholm, Paris, Beijer, 1892]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16, pp. 153-215.
First printing of Volterra's paper on the vibrations of light in a birefringence media.
Sur les vibrations lumineuses dans les milieux biréfringents.
[Berlin, Stockholm, Paris, Beijer, 1892]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16, pp. 153-215.
First printing of Volterra's paper on the vibrations of light in a birefringence media.
Lecons sur la théorie mathématique de la lutte pour la vie. Rédigees par Marcel Brelot.
Paris, Gauthier-Villars, 1931, gr. in-8vo, VI + 214 p. + 3 ff. (cat. de l’éditeur), pages jaunies, qqs faux-plies due a la brochage du livre, brochure originale.
Première édition d’un ouvrage important. Sur le plan mathématique, Volterra est un des pères de l'analyse fonctionnelle. Il s'intéresse ainsi aux fonctionnelles (qu'il appelle des fonctions de ligne), qui sont des fonctions définies non pas sur l'ensemble des nombres réels, mais sur des ensembles de fonctions. Il est notamment le fondateur de la théorie des équations intégrales, et publie quelques articles sur les équations aux dérivées partielles.
(SLACES, NVVA)
Phone number : 41 (0)26 3223808
Poincaré,Henri. - Volterra, Vito. - Hadamard, Jacques. - Langevin, Paul.
Reference : 108710
Henri Poincaré. L’oeuvre scientifique. L’oeuvre philosophique.
Paris, Féix Alcan 1914, 180x110mm, 264pages, reliure demi-chagrin. Auteur et titre doré au dos, plats papier marbré.
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Sur les équations intégro-différentielles et leurs applications.
[Berlin, Stockholm, Paris, F. & G. Beijer, 1912]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 35. Fine and clean. Pp. 295-356.
First printing.
L'oeuvre mathématique de Weierstrass (+) Sur les Propriétes du potentiel et sur les Fonctions Abéliennes [Poincaré] (+) Sur la Théorie des Variations des Latitudes [Poincaré].
Berlin, Stockholm, Paris, Beijer, 1899. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 22, 1899. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. pp. 1-18" Pp. 89-178" Pp. 201-358.[Entire volume: (4), 388, 2 pp].
First printing of these important papers: POINCARÉ: First edition. ""As soon as he came into contact with the work of Riemann and Weierstrass on Abelian Functions and algebraic geometry, Poincaré was very much attracted by those fields. His papers on these subjects occupy in his complete works as much space as those on automorphic functions, their dates ranging from 1881 to 1911. One of his main ideas in these papers is that of ""reduction"" of Abelian functions. Generalizing particular cases studied b Jacobi, Weierstrass, and Picard, Poincaré proved the general ""complete reducibility"" theorem...""(DSB).VOLTERRA: First edition. As the north and south poles, instead of being fixed points on the earth's surface, wander round within a circle of ab. 5o ft. in diameter, the result is a variability of terrestial latitudes generally. Volterra gives an elaborate mathematical analysis of these yearly fluxtuations.
