LOBACHEVSKY, Nikolai Ivanovich . Algebra ili vychislenie konechnykh [Algebra or the Calculus of Finite Numbers]. Kazan: University Press, 1834.

First edition of the only monograph published in the life-time of the author, in which he demonstrates the immediate numerical determination of algebraic equations.

The majority of Lobachevsky's works on non-Euclidean geometry and other mathematical and scientific fields were confined primarily to journals and small pamphlets (see following lots). 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 his contemporaries, 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 Lobachevsky's efforts in mathematics outside of geometry have languished in relative obscurity. According to Gnedenko, Lobachevsky should be considered one of the major precursors to the theory of relativity. The methodology utilized in both Algebra and his paper "The Origins of Geometry," was overlooked until Einstein demonstrated that the universe was non-Euclidean in structure and that Lobachevsky'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" ["About the Works of N.I. Lobachevsky on the Theory of Relativity"= in Istoriko- matematicheskie issledovaniya 2, pp.129-136.

Octavo (222 x 127 mm). Title-page is the variant without typographic border, priority unknown. (Some very pale dampstain at start and a scattered few spots, repairs to lower margins of π3 and 1.6.) 20th-century Russian leatherette gilt, uniform slipcase. Provenance: cancelled ownership inscription on title – V.M. Loseva (private library bookplate).