17 June 2008
LOBACHEVSKII, Nikolai Ivanovich. Algebra ili vychislenie konechnykh [Algebra or the Calculus of Finite Numbers]. Kazan': University Press, 1834.
8o (222 x 127mm.). (Some mostly marginal worming, catching a few letters at end, some wormholes repaired, small pale dampstain to some upper margins.) Modern quarter morocco.
FIRST EDITION of the only substantial book published in the life-time of the author, in which he demonstrates the immediate numerical determination of algebraic equations, which was also discovered independently at about the same time by the Belgian Dandelain and the Swiss K. Gräffe. Lobachevskii was the founder of non-Euclidian geometry publishing his discoveries as On the Principles of Geometry in the Kazan' Messenger in 1829-30, which included his paper read to the University Department of Physics and Mathematics in 1826 (see Printing and the Mind of Man 293).
The majority of Lobachevskii's works on non-Euclidean geometry and other mathematical and scientific fields were confined primarily to journals and small pamphlets. This is the only comprehensive book to appear in his life-time, and shows his radical approach to solving equations using a synthesis of geometrical and analytical systems. Preceding Dandelain and Graffe, he discovered how to separate the roots of equations by repeated squaring, a method suggested by Newton and in 1781 touched on by Euler. It was his unorthodox methods in this work that historians cite as essential to his solution of the parallel problem in Euclidean geometry (see Youschkevitch and Bashmakova). He originally wrote this text for a course of lectures at the University of Kazan in 1825. It was rejected by the censors for political reasons. and unfortunately Lobachevskii's efforts in mathematics outside of geometry have languished in relative obscurity. According to Gnedenko, Lobachevskii should be considered one of the major precursors to the theory of relativity. The methodology utilized in both Alegebra and his paper "The Origins of Geometry," was overlooked until Einstein demonstrated that the universe was non-Euclidean in structure and that Lobachevskii's theoretical concepts had a very practical application. A.P. Youschkevitch and I.G. Baschmakova, "Algegra ili vychisleni Konechnyhy," n Istoriko-matematicheskie issledovaniya 2, pp. 720-28; G.V. Gnedenko "O rabotah N.I. Lobachevsky po teorii veroiatnostei" ["Abouth the Works of N.I. Lobachevsky on the Theory of Relativity"= in Istoriko- matematicheskie issledovaniya 2, pp.129-136.
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