Beschreibung:

LOBACHEVSKII, Nicolai Ivanovitch (1793-1856). "O nachalakh geometrii" [in Russian], in: Kazanskii vestnik , Part XXVI (Feb. & Mar. 1829), Part XXV (April 1829), Part XXVII (Nov. & Dec. 1829); Part XXVIII (Mar. & Apr. 1830); Part XXVIII (July & Aug. 1830). Kazan: University Press, 1829-30. 5 parts bound in one volume, 8 o (202 x 117 mm). 3 engraved folding plates containing geometric diagrams, 9 folding letterpress tables. (Fore-margin on pp. 291-292 in Part 4 repaired affecting a few letters of marginal note, some very minor pale dampstaining.) Modern half black straight-grained morocco gilt, t.e.g., original blue printed wrappers bound in (wrappers for part XXVII trimmed and mounted, with blue coloring added). Provenance : St. Petersburg(?), Library of the Imperial Academy of Sciences (library stamp inside front wrappers of first two parts, accession number[?] on lower margin of first page in each part; front wrappers of first and fourth part with early owners' signatures trimmed). EXCEEDINGLY RARE FIRST EDITION OF THE FIRST PUBLISHED WORK ON NON-EUCLIDEAN GEOMETRY. Born in Nizhni Novgorod (now Gorki), Russia, Nicolai Ivanovitch Lobatchevskii ("the Copernicus of Geometry"--PMM) studied at the University of Kazan from 1807 under Martin Bartels, a friend of Gauss. He received his master's degree in physics and mathematics in 1812, and was appointed professor ordinarius in 1822. During the same year he began an administrative career at the University: serving first as a member (later as chairman) of a committee formed to supervise the construction of the new university buildings, he was twice appointed dean of the department of physics and mathematics, served a ten-year term as librarian of the university, was also a rector there for nearly twenty years, and during the latter years of his career served as assistant trustee for the entire Kazan education districts from 1846-1855. The basis of what became his first published work on the subject of non-Euclidean geometry, "O nachalakh geometrii" ("On the Principles of Geometry") was first read to his colleagues at the Kazan department of physics and mathematics at a meeting held on 23 February 1826, but was not published until 1829-30 when it appeared as a series of five papers in the Kazan University Journal. "Lobachevskii's geometry represents the culmination of two thousand years of criticism of Euclid's Elements , most particularly Euclid's fifth, or parallel, postulate, which states that given a line and a point not on the line, there can be drawn through the point one and only one coplanar line not intersecting the given line. As this postulate had stubbornly resisted all attempts (including Lobachevskii's) to prove it as a theorem, Lobachevskii came to the realization that it was possible to construct a logically consistent geometry in which the Euclidean postulate represented a special case of a more general system that allowed for the possibility of hyperbolically curved space" (Norman). "O nachalakh geometrii" was misunderstood by most of Lobachevskii's contemporaries, and uncomplimentary reviews of it by mathematicians of his day began to appear, most notably from M.V. Ostrogradsky, the most famous mathematician of the St. Petersburg Academy. It was not until the latter part of the 19th century, through the further investigations of Georg Friedrich Riemann, who had studied under Gauss in Gttingen and later Berlin, that his ideas were eventually extended to break the bounds of pure mathematics. "At the same time as Lobachevsky, other geometers were making similar discoveries. Gauss had arrrived at an idea on non-Euclidean geometry in the last years of the eighteenth century and had for several decades continued to study the problems that such an idea presented. He never published his results, however, and these became known only after his death and the publication of his correspondence. Jnos Bolyai, the son of Gauss's university comrade Farkas Bolyai, hit upon Lobach